\^. 3 ^N ^ ^^ ^ Zf N Digitized by the Internet Archive in 2009 with funding from NCSU Libraries http://www.archive.org/details/cyclopediaofarch02amer Cyclopedia of Architecture, Carpentry and Building A General Reference Work ON ARCHITECTURE, CARPENTRY, BUILDING, SUPERINTENDENCE, CONTRACTS, SPECIFICATIONS, BUILDING LAW, STAIR-BUILDING, ESTIMATING, MASONRY, REINFORCED CONCRETE, STEEL CONSTRUCTION, ARCHITECTURAL DRAWING, SHEET METAL WORK, HEATING, VENTILATING, ETC. Prepared by a Staff of ARCHITECTS, BUILDERS, AND EXPERTS OF THE HIGHEST PROFESSIONAL STANDING Illustrated with over Three Thousand Engravings TEN VOLUMES CHICAGO AMERICAN TECHNICAL SOCIETY 1908 Copyright, 1907 BY AMEklCAN SCHOOL OF CORRESPONDENCE Copyright, 1907 BY AMERICAN TECHNICAL SOCIETY Entered at Stationers' Hall, London All Rights Reserved Authors and Collaborators JAMES C. PLANT Superintendent of Computing Division, Office of Supervising Architect. Treasury Washington, D. C. WALTER LORING WEBB, C. E. Consulting Civil Engineer. Author of "Railroad Construction," "Economics of Railroad Construction," etc. J. R. COOLIDGE, Jr., A. M. Architect, Boston. President, Boston Society of Architects. Acting Director, Museum of Fine Arts, Boston. V» H. V. VON HOLST, A. B., S. B. Architect, Chicago. President, Chicago Architectural Club. ^• FRED T. HODGSON Architect and Editor. Member of Ontario Association of Architects. Author of "Modern Carpentry," "Architectural Drawing, Self-Taught," "The Steel Square," " Modern Estimator," etc. ALFRED E. ZAPF, S. B. Secretary, American School of Correspondence. AUSTIN T. BYRNE Civil Engineer. Author of " Highway Coiistruction," " Materials and Workmanship." HARRIS C. TROW, S. B. Editor of Textbook Department, American School of Correspondence. American Institute of Electrical Engineers. V WM. H. LAWRENCE, S. B." Associate Professor of Architecture, Massachusetts Institute of Technology. Authors and Collaborators— Continued EDWARD NICHOLS Architect, Boston. H. W. GARDNER, S. B. Assistant Professor of Architecture, Massachusetts Institute of Technology. ALFRED E. PHILLIPS, C. E., Ph. D. Professor of Civil Engineering, Armour Institute of Technology. GEORGE C. SHAAD, E. E. Assistant Professor of Electrical Engineering, Massachusetts Institute of Technology. MORRIS WILLIAMS Writer and Expert on Carpentry and Building. HERBERT E. EVERETT Department of Architecture, University of Pennsylvania. E. L. WALLACE, B. S. Instructor, American School of Correspondence. American Institute of Electrical Engineers. OTIS W. RICHARDSON, LL. B. Of the Boston Bar. WM. G. SNOW, S. B. Steam Heating Specialist. Author of " Furnace Heating," Joint Author of " Ventilation of Buildings." American Society of Mechanical Engineers. W. HERBERT GIBSON, C. E. Expert on Reinforced Concrete. ELIOT N. JONES, LL. B. Of the Boston Bar. Authors and Collaboratoi^s— Continued R. T. MILLER, Jr., A. M., LL. B. President. American School of Correspondence. WM. NEUBECKER Instructor, Sheet Metal Department of New York Trade School. WM. BEALL GRAY Sanitary Engineer. Member of National Association of Master Plumbers. EDWARD MAURER, B. C. E. Professor of Mechanics, University of Wisconsin. V» EDWARD A. TUCKER, S. B. Architectural Engineer. Member of the American Society of Civil Engineers. V» EDWARD B. WAITE Head of Instruction Department, American School of Correspondence. American Society of Mechanical Engineers. Western Society of Engrineers. ALVAH HORTON SABIN, M. S. Lecturer in New York University. Author of " Technology of Paint and Varnish," etc. American Society of Mechanical Engineers. W GEORGE R. METCALFE, M. E. Head of Technical Publication Department, Westinghouse Elec. & Mfg. Co. Formerly Technical Editor, Street Railway Review. Formerly Editor of Textbook Department, American School of Correspondence. HENRY M. HYDE Author, and Editor "The Technical World Magazine." CHAS. L. HUBBARD, S. B., M. E. Consulting Engineer. With S. Homer Wood bridge Co., Heating, Ventilating, and Sanitary Engineers. Authors and Collaborators— Continued FRANK CHOUTEAU BROWN Architect, Boston. Author of " Letters and Lettering." DAVID A. GREGG Teacher and Lecturer in Pen and Ink Rendering, Massachusetts Instituteof Technology. CHAS. B. BALL Civil and Sanitary Engineer. American Society of Civil Engineers. ERVIN KENISON, S. B. Instructor in Mechanical Drawing, Massachusetts Institute of Technology. CHAS. E. KNOX, E. E. Consulting Electrical Engineer. American Institute of Electrical Engineers. JOHN H. JALLINGS Mechanical Engineer FRANK A. BOURNE, S. M., A. A. L A. Architect, Boston. Special Librarian, Department of Fine Arts, Public Library, Boston. ALFRED S. JOHNSON, Ph. D. Formerly Editor " The Technical World Magazine." GILBERT TOWNSEND, S. B. With Post & McCord, New York City. HENRY C. BUCK, A. B., A. M. Instructor, American School of Correspondence. American Institute of Electrical Engineers. Authorities Consulted THE editors have freely consulted the standard technical literature of America and Europe in the preparation of these volumes. They desire to express their indebtedness particularly to the following eminent authorities whose well-known works should be in the library of everyone connected with building. Grateful acknowledgment is here made ?lso for the invaluable co- opei'ation of the foremost architects, engineers, and builders in making these volumes thoroughly representative of the very best and latest prac- tice in the design and construction of buildings; also for the valuable drawings and data, suggestions, criticisms, and other courtesies. J. B. JOHNSON, C. E. Formerly Dean, College of Mechanics and Engineering, University of Wisconsin. Author of "Engineering Contracts and Specifications," "Materials of Construction," Joint Author of "Theory and Practice in the Designing of Modern Framed Struc- tures." ^• JOHN CASSAN WAIT, M. C. E., LL. B. Counselor-at-Law and Consulting Engineer ; Formerly Assistant Professor of Engineer- ing at Harvard University. Author of " Engineering and Architectural Jurisprudence." T. M. CLARK Fellow of the American Institute of Architects. Author of "Building Superintendence," "Architect, Builder, and Owner before the Law." FRANK E. KIDDER, C. E., Ph. D. Consulting Architect and Structural Engineer; Fellow of the American Institute of Architects. Author of "Architect's and Builder's Pocket-Book," "Building Construction and Superintendence ; Part I, Masons' Work ; Part II, Carpenters' Work ; Part III, Trussed Roofs and Roof Trusses ; " "Churches and Chapels." AUSTIN T. BYRNE, C. E. Civil Engineer. Author of "Inspection of Materials and Workmanship Employed in Construction," "Highway Construction." W. R. WARE Formerly Professor of Architecture, Columbia University. Author of " Modern Perspective." Authorities Consulted — Continued CLARENCE A. MARTIN Professor of Architecture at Cornell University. Author of " Details of Building Construction." FRANK N. SNYDER Architect. Author of " Building- Details." CHARLES H. SNOW Author of " The Principal Species of Wood, Their Characteristic Properties." V» OWEN B. MAGINNIS Author of " How to Frame a House, or House and Roof Framing." HALBERT P. GILLETTE, C. E. Author of "Handbook of Cost Data for Contractors and Engineers." OLIVER COLEMAN Author of "Successful Houses." CHAS. E. GREENE, A. M., C. E. Formerly Professor of Civil Engineering, University of Michigan. Author of " Structural Mechanics." LOUIS de C. BERG Author of "Safe Building." GAETANO LANZA, S. B., C. & M. E. Professor of Theoretical and Applied Mechanics, Massachusetts Institute of Technology. Author of "Applied Mechanics." V IRA 0. BAKER Professor of Civil Engineering, University of Illinois. Author of " A Treatise on Masonry Construction." GEORGE P. MERRILL Author of " Stones for Building and Decoration." , FREDERICK W.TAYLOR, M.E.,and SANFORD E.THOMPSON, S.B., C.E. Joint Authors of "A Treatise on Concrete, Plain and Reinforced." AuthoHties Cbnsulted— Continued A. W. BUEL and C. S. HILL Joint Authors of " Reinforced Concrete." NEWTON HARRISON, E. E. Author of " Electric Wiring, Diagrams and Switchboards." FRANCIS B. CROCKER, E. M., Ph. D. Head of Department of Electrical Engineering, Columbia University ; Past President, American Institute of Electrical Engineers. Author of " Electric Lighting." J. R. CRAVATH and V. R. LANSINGH Joint Authors of " Practical Illumination." JOSEPH KENDALL FREITAG, B. S., C. E. Author of "Architectural Engineering," "Fireproofing of Steel Buildings." WILLIAM H. BIRKMIRE, C. E. Author of "Planning and Construction of High Office Buildings," "Architectural Iron and Steel, and Its Application in the Construction of Buildings," "Compound Riveted Girders," " Skeleton Structures," etc. V* EVERETT U. CROSBY and HENRY A. FISKE Joint Authors of " Handbook of Fire Protection for Improved Risk." CARNEGIE STEEL COMPANY Authors of "Pocket Companion, Containing Useful Information and Tables Appertain- ing to the Use of Steel." J. C. TRAUTWINE, C. E. Author of " Civil Engineer's Pocket-Book." ALPHA PIERCE JAMISON, M. E. Assistant Professor of Mechanical Drawing, Purdue University. Author of "Advanced Mechanical Drawing. " FRANK CHOUTEAU BROWN Architect, Boston. Author of " Letters and Lettering." Authorities Consulted— Continued HENRY McGOODWIN Author of " Architectural Shades and Shadows." VIGNOLA Author of "The Five Orders of Architecture." American Edition by Prsf. Ware. CHAS. D. MAGINNIS Author of " Pen Drawing, An Illustrated Treatise." FRANZ S. MEYER Professor in the School of Industrial Art, Karlsruhe. Author of "Handbook of Ornament," American Edition. RUSSELL STURGIS Author of "A Dictionary of Architecture and Building-," and "How to Judge Archi- tecture." A. D. F. HAMLIN, A. M. Professor of Architecture at Columbia University. Author of " A Textbook of the History of Architecture." RALPH ADAMS CRAM Architect. Author of "Church Building." C. H. MOORE Author of " Development and Character of Gothic Architecture.'' ROLLA C. CARPENTER, C. E,, M. M. E. Professor of Experimental Enprineering. Cornell University. Author of " Heating and Venlilating Buildings." WILLIAM PAUL GERHARD Author of "A Guide to Sanitary House Inspection." I. J. COSGROVE Author of " Principles and Practice of Plumbing." ■c S 1^ ^ <-? y <; iQ o Q uj !._ in t/3 u O •fH u 01 «J M w u o *\«t 7tgsA*J!^ SUMMER COTTAGE FOR THE MISSES DUMMER, AT HARBOR POINT, MICH. Poiul & Pond, Arohitfcls, I'hicafio. Built iu liiua. Cost, $7,300. Plans and Tnicrior are Shown on Pages K6 and ito. For ev/ord r I IHE rapid evolution of constructive methods in recent ^^'. years, as illustrated in the use of steel and concrete, ^' and the increased size and complexity of buildino-s, has created the necessity for an authority which shall embody accumulated experience and approved practice aloncr a variety of correlated lines. The Cyclopedia of Architecture, Carpentry, and Building is designed to till this acknowledo-ed need. C There is no industry that compares with Euildino- 'm the close interdependence of its subsidiary trades. The Architect, for example, who knows nothing of Steel or Concrete con- struction is to-day as much out of place on important work as the Contractor who cannot make intelligent estimates, or who understands nothing of his legal rights and responsibilities. A carpenter must now know something of Masonry, Electric Wiring, and, in fact, all other trades employed in the erection of a build- ing; and the same is true of all the craftsmen whose handiwork will enter into the completed structure. C Neither pains nor expense have been spared to make the present work the most comprehensive and authoritative on the subject of Building and its allied industries. The aim has been, not merely to create a work which will appeal to the trained expert, l)iit one that will coiiiiiu'nd itself also to tlii' becrinner and the self-taught, practical man hy giving liiiii a workincr knowledge of the principles and luctiiods, not only of his own particular trade, hut of all other branches of the ]juilding Indus- try as well. The various sections have 1)een ])repared especially for home study, each written by an acknowledwd authority on the subject. The arrangement of matter is such as to carry the student forward by easy stages. Series of review questions are inserted in each volume, enabling the reader to test his knowl- edge and make it a j)ermanent j)OSsession. The illustrations have been selected with unusual care to elucidate the text. ^ The work will l)e found to cover many important topics on which little information has heretofore been available. This is especially apparent in such sections as those on Steel, Concrete, and Reinforced Concrete Construction; Building Superintendence; Estimating; Contracts and Specifications, including the princi- ples and methods of awarding and executing Government con- tracts; and Building Law. ^ The Cyclopedia is a compilation of many of the most valu- able Instruction Papers of the American School of Correspond- ence, and the method adopted in its preparation is that which this School has developed and employed so successfully for many years. This method is not an experiment, but has stood the severest of all tests — that of practical use — which has demonstrated it to be the best yet devised for the education of the busy working man. ^ In conclusion, grateful acknowledgment is due the staff of authors and collaborators, without whose hearty co-operation this work would have been im[)Ossiblc. Table of Contents VOLUME II Carpentry Bu Gilbert Townsendi Page *11 Natural Timber — Timber in Commercial Form — Varieties of Timber — General Characteristics of Timber — The Steel Square — Laying Out — Light Framing — Joints and Splices- The Wall — The Sill — The Corner Posts — The Ledger Board — The Plate — Braces — Studding — Nailing Surfaces — Partitions — Masonry Walh — Cap and Sole — Bridging ^Shrinkage and Settlement — Floors — Girders — Joists — Headers and Trimmers — The Roof — Varieties of Roofs — The Rafters — The Ridge — Interior Supports — Dormer Windows — Rafter Bevels — Common Rafters — Valley Rafters — Hip Rafters — Jack Rafters — Backing of Rafters — Attic Partitions ^Battered Frames — Trussed Partitions — Inclined and Bowled Floors — Balconies and Galleries — Timber Trusses — Towers and Steeples — Pendentives — Niches — Vaults and Groins Stair-Building . By Fred T. Hodgson and Morris Williams Page 153 Definition of Terms — Setting Out Stairs — Use of Pitch-Board — Well-Hole — Trimming — Straight Flights — Dog-Legged Stairs — Platform Stairs — Winding Stairs — Circular Stairs — Elliptical Stairs — Bullnose Steps — Open-Newel Stairs — • Stairs with Curved Turns — Geometrical Stairs —Cylinder — Kerfing — Methods of Strengthening Stairs — Common Types of Stairs — Handrailing — Wreaths — Projection — Tangents — Tangent System of Squaring Wreath Joints — Face- Mould — Bevels to Square the Wreaths — How to Put Curves on the Face-Mould — Arrangement of Risers in and around a Well-Hole Estimating By Edward Nichols Page 229 Prices — Catalogues — Profit — Percentage — Duplicate Parts —Transportation — Approximate Estimates — Estimating by the Square — Estimating by Quant- ities — Preparation — Definitions — Units — Rules and Tables — Excavation — Stonework — Brickwork — Chimneys — Flue Lining — Mason's Supplies — Cellar Columns — Drain Pipe — Carpentry — Board Measure — Prices of Lumber — Cost of Frame, Windows, Doors, Stairs, Inside and Outside Finish — Hardware — Roofing — Plastering — Painting — Heating — Plumbing — Gasfitting — Electrical Work — Labor — Typical Specimen of Estimate — Schedules The Steel Square .... Bi/ Morris Williams Page 341 Face — Tongue — Blade — Back — Octagon Scale — Brace Rule — Board Measure — Finding Miters and Lengths of Sides of Polygons — Steel Square Applied to Roof Framing — Heel Cut of Common, Hip, and Valley Rafters — Jack Rafters — Roofs of Equal and Unequal Pitch Review Questions , Page 371 *For page numbers, see foot of pages. ■tFor professional standing of authors, see list of Authors and Collaborators at front of volume. u u o < u X o a a < a CARPENTRY. PART I. The art of Carpentry has been practiced by men in all ages and in all lauds, and is likely to continue as long as there is any timber out of which dwellings and utensils can be made. Under different conditions and in widely separated parts of the world there have been developed various methods of doing the same work, and men have attained to various degrees of proficiency in the handling of tools, and in the making of the tools themselves. From the time when the primitive man built himself a hut out of brush-wood and mud, to the present day, when we live in comfortable dwelhngs built of seasoned timber-, there has been constant progress and development, so that there has accumulated a vast amount of experi- ence to which we are the fortunate heirs. The carpenter has always found his material at hand, provided by nature, and needing only to be cut down and shaped to suit his purposes. In those places where wood did not grow near by, there were no carpenters ; but instead, workers in stone or clay. A knowledge of the characteristics of wood, which plays so important a part in all our lives and which is so plentiful in our own land, is likely to prove of advantage to anyone, and is an abso- lute necessity to a carpenter. Let us therefore, first of all, devote some space to a consideration of timber, both in its natural state, and in its commercial form as prepared for the market. NATURAL TIMBER. Wood is one of the most common of building materials, and may be seen everywhere in its natural state as well as in various forms prepared for use. It is all taken originally from some kind of tree or shrub, and a consideration of the manner of growth of the tree itself will explain many peculiarities and defects of timber in its commercial form. 11 CARPENTRY Classes of Trees. The trees from which most of our timber is taken are of two kinds : the " broad-leaved," such as the oak, poplar, and maple, and the " conifer " or " needle-leaved," such as the pines, the fir, and the cedar. In the South some timber is used which comes from another class of trees, of which the palms are the most common representatives ; the use of this timber, however, is very limited. In general, it may be said that the wood from the broad- leaved trees is " hardwood " while that from the conifers is " soft- wood," but this rule does not hold true in all cases. rianner of Growth. There is a marked difference between the three classes of trees mentioned above in regard to tlieir manner of growth. While the members of the third class, the palms and others, grow only at the top, and have the same diameter of trunk after years of development, the members of the other two classes in- crease in size of trunk as well as in height. Each year a new layer of wood is formed on the outside of the trunk and branches, underneath the bark, and the age of the tree may usually be determined by counting the number of layers. In the center of the tree there is always a small whitish part, called the " pith," about which the wood itself is ^. , ^ ,. ._ arranged in concentric rings, as shown in Fig. 1. Section of Log. *= " ' Fig. 1, in which A is the pith, B the woody part of the tree, and C the bark. The arrangement of the wood in concentric rings is due to the fact tliat it was formed gradually, one layer being added each year, and for this reason the rings or layers are called " annual rings." The wood nearest the center, or pith, is considerably harder and darker in color than that which is on the outside nearer the bark ; it is called the " heartwood " to distinguish it from the other which is called the " sap wood." Only the heartwood should be used for building work. The reason why it is harder than the sapwood is that it is older and has been compressed more and more each year as the tree has increased in size, and the pores have gradually become filled up. The sapwood is soft and of lighter color and shows that it has been recently formed. The time required to transform the wood from sapwood into heartwood varies from nine to thirty-fiva IS CAIlPE:STilY years, according to the nature of the tree, and those trees which per- form this hardening in the shortest time are usually the most durable. The sap rises in the spring from the roots of the tree to the branches and twigs, forming the leaves, and in the autumn it Hows back acrain between the wood and the bark. Thus a new annual ring is formed. The width of the annual rings varies from ^^ inch to ^ inch according to the character of the tree and the position of the ring. In general it may be said that the widest rings are found nearest the center, or pith, and that they grow regularly narrower as they approach the bark. . Also they are wider at the bottom of the trunk than at the top. The rings are very seldom circular or regular in form, but follow the contour of the tree trunk. In addition to the annual rings there may be seen on the cross-section of any log other lines which run from the center toward the bark at right angles to the annual rings. These are called the " medullary " rays. Usually they do not extend to the bark, but alternate, with others which start at the bark and run inward toward the center but are lost before they reach the pith. This is shown at E and F in Fig. 1. Details of Structure. The two above-mentioned classes of wood differ considerably in their structure, that of the conifers being very simple and regular in arrangement, while that of the broad- leaved trees is complex and irregular. The wood is made up of bundles of fibers or long tubes, parallel to the stem jf the tree, which are crossed by other fibers that form the medullary rays, passing from the pith to the bark and binding the whole together. Besides these there are resin ducts and other fibers scattered through the trunk of the tree. The arrangement is shown in Fig. 2. A A are the long fibers, and B B the pith or medullary fibers. Of course these are so small that the individual fibers cannot be distinguished without the aid of a powerful microscope. In pine more than fifteen thousand pith rays occur on a square inch of section. Fijr. 2. Arrangement of Fibers. 13 CAKPENTIiY Grain of Wood. Woods are commonly spoken of as " fine- grained," " coarse-grained," " cross-grained," or " straight-grained." The wood is said to be fine-grained when the annual rings are relatively narrow, and coarse-grained when these rings are wide. Fine-grained wood can be made to take a high polish while with coarse-grained wood, in general, this is not possible. "When the fibers are straight, and parallel to the direction of the trunk of the tree, the wood is said to be straight-grained, but if they are distorted or if they are twisted so as to be spiral in form, not growing straight up but following around the trunk of the tree, the wood is said to be cross-grained. Fig. 3. B C Grain of Wood. In Fig. 3 are shown three pieces of timber of which A is absolutely cross-grained, B is partially cross-grained and, C is straight-grained. Defects. Most of the defects which render timber unsuitable for building are due to irregularities in the growth of the tree from which the timber was taken. These defects are known by various names, such as " Heart- shakes," " Windshakes," " Starshakes," and " Knots." Other defects are due to deterior- ation of the timber after it has been in place for some time or even before the tree has been felled, among which are " Dry Hot " and "Wet Rot." The defects of the first class are defects of structure — those of the second class are defects of the material itself. Hcnrtshahe. Fig. 4 shows what is known as a heartsliake. There is first a small cavity at the heart of the tree caused l»y decay, and flaws or cracks extend from it out toward the bark. The heartshake is most often found in those trees which are old, rather than in young, vigorous saplings ; it is especially to be feared in hemlock timber. Wimhhake. Fig. 5 shows what is known as a wiuvlshake or cupshake. This is caused by a separation of the annual rings one from another so that a crack is formed in the body of the tree , this Fig. 4. Heartshake. 14 CATJPEXTRV Fig. 5. Windsliake. crack may extend for a considerable distance up the trunk. This defect is said to be caused by the expansion of the sapwood, and it is also claimed that it is caused by the wrenching to which the tree is subjected by high winds. Wiudshakes are very often found in pine timber. A starshake is very much like a heartshake, the chief difference being that the starshake cracks extend right across the center of the trunk without any appearance of decay at that point. Dry rot in timber is caused by a fungus growth, and takes place most readily when the timber is in such a position that it is alternately wet and dry. If wood is kept perfectly dry, or, on the other hand, is kept constantly under water, it will last indefinitely without any sign of rot. For this reason piles should always be cut off below the water level. Decay takes place very rapidly when the wood is in a confined position, as when buried in a brick wall, so that the gases cannot escape. Tt is also hastened by warmth, and is much more common in the South than in the northern states. Decay may be prevented by-introducing into the timber certain salts, such as the salts of mercury. It may also be prevented by heating the wood to a temperature above 150 degrees Fahrenheit and maintaining that temperature. All wood should be perfectly seasoned before being painted, and good ventilation should always be provided for. Wood should be especially protected when- ever in contact with masonry from which it may absorb moisture. Wet rot is a form of decay which takes place in the growing tree. It is caused by the tree becoming saturated with water, as in a swamp or bog, and it may be communicated from one piece of timber to another by contact. Warping in timber is the result of the evaporation or drying out of the water which is held in the cell walls of the wood in its natural state, and the consequent shrinkage of the piece. If timber were perfectly regular in structure, so that the shrinkage would be the same in every part, there would be no warping ; but wood is made up of a large number of fibers, the walls of which are of differ- 15 8 CARPENTRY ent thickness in different parts of the tree or log, so that in drying one part shrinks much more than another. Since the wood is rigid, one part cannot shrink or swell without changing the shape of the whole piece, because the block as a whole must adjust itself to the new conditions ; consequently the timber warps. In Fig. 6, if the fibers in the top portion of tl>e piece near the face ah e happen to have, on the average, thicker walls than those Fig. 6. in the bottom portion, near the face c d g, the top part will shrink more than the bottom ; the distance a h, originally equal to the dis- tance c d, becomes smaller^nd the shape of the whole piece changes, as show^n in Fig. 7. The only way in which warping can be prevented is to have the timber thoroughly dried out before it is used. After it is once thor- oughly seasoned it will not warp unless it is allowed to absorb more moisture. . All wood that is to be used for fine work, where any warp- ing after it is in place will spoil the appearance of the whole job, must be so seasoned, eitlier in the open air or in a specially prepared kiln. The wood of the " conifers," whicli is very regular in its struc- ture, shrinks more evenly and warps less than the wood of the broad- leaved trees with its more complex and irregular structure. Sapwood, also, as a rule shrinks more than does heartwood. Checks also are due to the uneven shrinkage of timber. In any log there is a chance for the wood to shrink in two directions — alone: the radial lines following the direction of the medullary rays, and around the circumference of the log, following the direction of the annual rings. If the wood shrinks in both directions at the same rate, the only result will be a decrease in the volume of the log, but if it shrinks more rapidly in one of these directions than it does in 16 CARPENTRY Fig. 8. Cracks Caused by Shrinkage. the ether, the log must crack around the outside as shown in Fig. 8. This cracking is called " checking," and is likely to take jjlace. In timber which has been pre- pared for the market it shows itself in the form of cracks which extend along the faces of solid square timbers and boards, and seriously impairs the strength. Tig. 9 shows checks in a square post or column. Knots are very common in all timber. They are formed at the junction of the main tree trunk and a branch or limb. At such points the fibers in the main trunk, near the place where the branch comes in, do not follow straight along up the trunk, but are turned aside and follow alon£r the branch as shown in Fig. 10. Frequently a branch may be broken off near the trunk while the tree is still young, and the tree continue to grow. The trunk will increase in size until the end of the branch, which was left behind buried in the main trunk, is entirely covered up. Meanwhile the end of the branch dies and a knot is formed. This bit of dead wood has no connection with the living wood about it. In time it works loose, and when the tree is sawed up into boards the knot may drop out. A Fig. 9. Checks in Square Post. knot does not seriously impair a piece subjected to a compressive stress, so long as it remains in place, but it greatly weakens a piece subjected to tension. A knot always spoils the appearance of any wood which is to be polished. TIMBER IN ITS COMMERCIAL FORM. Conversion of Timber. Timber may be found in lumber yards in certain shapes ready for use, having been cut from the logs and relieved of the outside covering, or bark. There are various methods of cut- ting up the logs to form boards, planks and heavy Fig. 10. Knots. timbers. If the log is to be squared off to form but 17 10 CARPENTRY in Fig. 11 one heavy beam, a good rule to follow is to divide the diameter into three equal parts, and draw perpendiculars to the diameter at these points, one on each side of the diameter, as shown at A and B The points c and d in which these perpendiculars cut the circumference of the tree trunk^ together with the points & and / in which the chosen diameter cuts the circum- ference of the tree trunk, will be the four corners of the timber. The lines joining these points will give an outline of the timber. This will be found to be the largest and best timber which can be cut from the log. Fig. 11. Squaring off a Log. Another good rule is to divide the diameter of the log into four equal parts and proceed in the same way as described above, using the outside quarter points on the diameter as shown in Fig. 12. This method will give a stiffer beam but it will not be so strong. In Fig. 13 are shown several different methods of cutting planks from a log. First it is divided into quarters, and the planks are cut out as shown. The method shown at A, called " quarter sawing," is the best. All the planks are cut radiating from the center and there will be no splitting and warping. A fairly good method is that shown at B, where the planks are pretty nearly in radial lines and may be much more easily cut out than can those shown at A. The method shown at C is a common one and leads to fairly good results, although only the plank in the center is on a radial line. It is practically as good a method as that I shown at B and is much more simple. The method shown at D is not so good as the others ; planks cut in this way being very liable to warp and twist. If the silver grain, caused by the cutting of the medullary rays, is desired, the planks should be cut as at A or B. Planks may sometimes be simply sliced from tlie log as shown in Fig. 14, without first dividing it into quarters. This is the worst possible way to cut them, as the natural tendency of the timber to Fig. 12. Squaring off a Log. 18 CARPEXTRY 11 shrink causes the planks to curl up as shown in Fi". 15. It is almost impossible to flatten them out again and they cannot be used as they are. VARIETIES OF TIMBER. There are a great many different kinds of timber growinf^ in the United States, and a considerable quantity is imported from other countries. Each variety possesses certain characteristics which render it especially suitable for use in one part of the build- Fig. 13. Quarter Sawiug. Fig. 14. Straight Sawing. ing, while the same peculiarities of growth or of texture may unfit it for use in another place. For timbers which are to be partly buried in the ground a wood is required which is able to withstand the deteriorating effects of contact with the earth ; and for this purpose chestnut, white cedar, cypress, redwood or locust may be used. For light framing we need a cheap, light wood free from struc- tural defects such as knots and shakes, and which can be obtained in fairly long, straight pieces. Spruce, yellow pine, white pine and hemlock all satisfy these requirements fairly well, spruce being per- haps a little better than the others, and at any rate more popular. For heavy framing, such as wooden trusses, girders and posts, we require a strong timber and one which can be obtained in lar'^e, long pieces. Georgia pine, Oregon pine and white oak may all be used for such work, and also Xorway pine and Canadian red pine. A wood which is easily worked and which will also withstand the effects of the weather Fig. 15. is needed for the outside finish ; for this we select white pine and 19 12 CARPENTRY also cypress and redwood. The same woods are used for shingles, clapboards and siding, with the addition of cedar for sliingles, and sometimes Oregon pine and spruce for siding. For the interior finish is cliosen a wood which will make a pleasing appearance, and which will take a polish ; while for floors, hardness and resistance to wear are the further requirements. For floors, oak, hard pine, and maple are good ; and for the rest of the interior finish, white pine, cypress and redwood, or any of the hard woods such as ash, butternut, cherry and mahogany, may be selected. Some of the more important varieties of timber usad in car- pentry will now be mentioned, and a brief description of each kind given to convey an idea of its characteristics and the part of the country from which it comes. EVERGREENS OR CONIFERS. Cedar. There are five different kinds of white cedar in the United States, of which four are different species of the white cedar, and the fifth is what is known as " canoe " cedar. The wood is not very strong, but is light and soft, possessing considerable stiffness and a fine texture. In color it is grayish brown, the sapwood being, however, of a lighter shade than the heartwood. It seasons quickly, is very durable and does not shrink or check to any great extent. Its principal use in carpentry is for shingles, for w^iich its durability makes it especially valuable, and for posts and ties. The trees are usually scattered among others of different kinds, forming occasion- ally, however, quite considerable forests. They are found all through the northern part of the country and on the Pacific coast in Cali- fornia, Oregon and Washington. Some of the trees are of medium size while others are very large, especially the canoe cedar in the Northwest. In addition to the white cedars, there are the red cedars, which are similar to the others, but have a somewhat finer texture. There are two varieties, the red cedar and redwood, the former found prin- cipally in the southern states and the latter only in California. Eed cedar is used but little in building construction except for cabinet work and veneers, but redwood has been used extensively in the West for outside finish, shingles and clapboards. Its resistance to 80 CARPENTRY 13 fire is remarkable, which makes it valuable for the exterior of dwell- ings, but it is too soft for interior finish. Cypress. This wood is found in the southern states only, where it grows in the swamp land along the banks of the rivers. Although there are a great many varieties, they are similar in their general characteristics and differ only in quality. " Gulf cypress," growing near the Gulf of Mexico, is the best. The timber is light, straight-grained and soft, and is used for shingles and siding, water tables, sills and gutters. It does not warp and shows great resist- ance to dampness. Hemlock. There are two varieties of hemlock, one found in the northern states, from Maine to Minnesota, and also along the Alleghanies, southward to Georgia and Alabama; and the other found in the West, from Washington to California, and eastward to Montana. The eastern tree is smaller than the western, and its wood is lighter and softer and generally inferior. The timber is of a light reddish-gray color, fairly durable, but shrinks and checks badly, and is rough, brittle, and usually cross-grained. It is sometimes used in the East for cheap framing, but it is so liable to imperfections such as windshakes and starshakes that it is not suitable for this purpose. It is often used for rough boarding or sheathing. Spruce. There are three kinds of spruce — white, black, and red, of which the white spruce is the variety commonly found on the market. The wood is light and soft, but fairly strong, and is of a whitish color. It is much used in the northeastern* states for light framincT, but can be obtained only in small sizes. It is considered by many to be the best framing timber, excepting the pines. The white spruce is found scattered throughout all of the north- ern states, along the streams and lakes, the larger varieties being in Montana. The black spruce is found in Canada and in some of the north- em states. It is distinguished from the other varieties only by its leaves and bark. The red spruce is sametimes known as Newfoundland red pine and is found in the northeastern part of North America. Its wood is similar to the black spruce. Pines. There are two distinct classes of pines used in building work, the soft and the hard pines, both of which are found in great 21 14 CARPENTRY abundance scattered over the whole of the United States. Tlie great variety of uses to which pine timber may be apphed in building con- struction and the ease with wliich it can be cut and shipped to mar- ket, make it the most popular wood in use at the present time. The softer varieties are used for outside finishing of all sorts, and the harder kinds for heavy framing and for flooring. The tree itself is very tall, with a straight trunk and few branches, so that timbers can be obtained in large sizes and great lengths. There are many different kinds of pines, which are recognized in various parts of the country under various names, but there are five general classes into which the species is commonly divided, though the same timber may be called by dift'erent names in two different localities, as will be seen. 1. The term "hard pine" is used to designate any pine which is not white pine, and is a very general classification, thougli it is often met with in specifications and in works on Carpentry. 2. "White pine," "soft pine " and "pumpkin pine" are terms which are used in the eastern states for the timber from the white pine tree, while on the I'acific coast the same terms refer to the wood of the sugar pine. 3. The name " yellow pine " when used in the northeastern part of the country applies almost always to the pitch pine or to one of the southern pines, but in the West it refers to the bull pine. 4. " Georgia pine " or " longleaf yellow pine " is a term used to distinguish the southern hard pine which grows in tlie coast region from North Carolina to Texas, and which furnishes the strongest pine lumber on the market. 5. " Pitch pine " may refer to any of the southern pines, or to pitch pine proper, which is found along tbe coast from New York to Georgia and among the mountains of Kentucky. Of the soft pines there are two Kinds, the white pine and the sugar pine, the latter being a western tree found in Oregon and Cali- fornia, while the former is found in all the northern states from Maine to Minnesota. There is also a smaller species of white pine found along the Rocky Mountain slopes from Montana to New Mexico. There are ten different varieties of hard pine, of which, however, only five are of practical importance in the building industry. These are the " longleaf southern pine," the " shortleaf southern pine," the " yellow pine," the " loblolly pine " and the " Norway pine." 22 CARPENTRY 15 The longleaf pine, also known as the " Georgia pine," the " yel- low pine ■' and the " long straw pine," is a large tree, which forms ex- tensive for^ists in the coast region from North Carolina to Texas. It yields very hard, strong timber which can be obtained in long, straight pieces of very large size. The loblolly pine is also a large tree, but has more sapwood than the longleaf pine, and is coarser, lighter and softer. It is the com- mon lumber pine from Virginia to South Carolina, and is also found in Texas and Arkansas. It is known as well by the name of " slash pine," " old field pine, '' " rosemary pine," " sap pine," and " short straw pine," and in the West as the Texas pine. The shortleaf pine is much like the loblolly pine and is the chief lumber tree of Missouri and Arkansas. It is also found in North Carolina and Texas. The Norway pine is a northern tree found in Canada and the northern states. It never forms forests, but is scattered among other trees, and sometimes forms small groves. The wood is fine-grained and of a white color, but is largely sapwood and is not durable. BROAD-LEAVED TREES. Ash is a wood that is frequently employed for interior finishing in public buildings, such as schoolhouses, and in the cheaper classes of dwelling houses. It is one of the cheapest of the hard woods ; it is strong, straight-grained and tough, but is coarse in texture. It shrinks moderately, seasons with little injury, and will take a good polish. The trees do not grow together in forests, but are scattered. They grow rapidly, and attain only medium height. Of the six different species found in the United States, only two, the " white ash " and the " black ash," are used extensively in building work. The first is more common in the basin of the Ohio liiver, but is also found in the North from Maine to Minnesota, and in the South, in Texas. The black ash is found from Maine to Minnesota, and southward to Virginia and Arkansas. There is very little difference between the two species. The black ash is also known as the " hoop ash " and the " ground ash." Beech. Another wood used to some extent for inside finish is the beech. It is heavy, hard and strong, but of coarse texture like the ash. In color it is light brown, or white. It shrinks and checks 23 16 CARPENTRY during the process of drying and is not dura^^le tvlien placed in con- tact with the ground. It works easily, stands well, and ta'ces a good polish. Birch is a very handsome wood of a brown color and with a satiny luster. It takes a good polish, works easily, and does not warp after it is in place, but it is not durable if exposed. It is used quite extensively for inside finish, and to imitate cherry and mahog- any, as it has a grain which is very similar to the grain of these woods. The trees are of medium size and form large forests. They are found throughout the eastern payt of the United States. Butternut is also used as afiuish'mg wood, and is cheaper than many of the other harder woods. It is light, but not strong, and is fairly soft. In color it is light brown. The trees, of medium size, are found in the eastern states from Maine to Georgia. Cherry is a wood which is frequently used as a finishing wood for the interior of dwellings and of cars and steamers ; but owing to the fact that it can be obtained only in narrow boards, it is most suit- able for moulded work, and work which is mufeh cut up. The wood is heavy, hard, strong and of fine texture. The heartwood is of a reddis'h brown color, while the sapwood is yellowish white. It is very handsome and takes a good polish, works easily and stands well. It shrinks considerably in drying. The timber is cut from the wild black cherry tree, which is of medium size and found scat- tered among the other broad-leaved trees along the western slope of the Alleglianies and as far west as Texas. Chestnut timber is used in cabinet work, for interior finishing, and sometimes for heavy construction. It is light, fairly soft, but not strong. It has a rather coarse texture, works easily and stands well, but shrinks and checks in drying. The timber is very durable. The tree grows in the region of the Alleglianies, from Maine to Michigan, and southward to Alabama. Elm. There are five species of elm trees in the United States, scattered throughout the eastern and central states. I'lie trees are usually large and of rapid growth, and do not form forests. The timber is hard and tough, frequently cross-grained, hard to work, and shrinks and checks in drying. The wood has not been used very extensively in building, but has a beautiful figured grain, can take a high polish, and is well adapted to staining. The texture is coarse to fine, and the color is brown with shades of gray and red. 24 CARPENTRY 17 Gum. The wood of the gum tree is used extensively for cabinet work, furniture, and interior finish. It is of fine texture and handsome appearance, heavy, quite soft, yet strong, and reddish brown in color. It warps and checks badly, is not durable if exposed, and is hard to work. The species of gum tree used in carpentry is the sweet gum, which is of medium size, with straight trunk; it does not form forests, though it is quite abundant east of the Mississippi Eiver. riaple. Almost all of the maple usedin building work comes from the sugar maple tree, which is most abundant in the region of the Great Lakes, but which is also found from Alaine to Minnesota, and south- ward to Florida. The trees are of medium to large size, and form quite considerable forests. The wood is heavy and strong, of fine texture, and often has a fine wavy grain which gives the effect known as " curly." It is of a creamy white color, shrinks moderately, works easily and takes a good polish. It is often used for flooring, and sometimes for other inside finish. Oak. There are about twenty different kinds of oak to be found in various parts, of the United States, but there are three dis- tinctly different species, which are sold separately. These are the " white oak," the " red oak " and the " live oak." The red oak is usually more porous, less durable and of coarser texture than the white oak or the live oak. The trees are of medium size and form a large proportion of all the broad-leaved forests. Live oak was once extensively used, but has become scarce and is now expensive. Both the red oak and the white oak are used for inside finishing, but they are liable to shrink and crack and must therefore be thoroughly seasoned. They are of slightly different color, the white oak having a straw color while the red oak has a reddish tinge, so that they can- not be used together where the work is to be finished by polishing. Oak is always better if quarter-sawed, when it shows what is known as the " silver grain." Poplar. This wood is also known as " whitewood " and " tulip wood." • There are a number of different varieties growing in various parts of the country. The tree is large, and is most common in the Ohio Basin, but does not form forests. The wood is light, soft, free from knots, and of fine texture. In color it is white, or yellowish- white, and frequently it has a satiny luster. It can be so finished as to retain its natural appearance, but it is often stained to imitate 25 18 CAIirENTKY some of the more costly woods, such as cherry. It is used exten- sively for cheap inside finish and fittings, such as shelving, and some- times for doors, but it warps badly if it is not thoroughly seasoned. Sycamore is frequently used for finishing, and is a very hand- some wood. It is heavy, hard, strong, of coarse texture, and is usually cross-grained. It is hard to work, and shrinks, warps, and checks considerably. The tree is of large size and rapid growth, found in all parts of the eastern United States, but is most common along the Ohio and Mississippi Rivers. Black Walnut is a wood which has been and is still used very extensively for interior finishing and in the manufacture of furniture. It is a heavy, hard timber, of coarse texture, and of a dark-brown color. Very handsome pieces having a beautiful figure, may be selected for veneers for furniture and cabinet work. Although the wood shrinks somewhat in drying, it works easily, stands well, and will take a very good polish. The tree is large and of rapid growth. It was formerly very abundant in the Alleghany region, and was found from New England to Texas and from Michigan to Florida, but it is now becoming scarcer and the timber is expensive. Imported Timber. Besides the woods which grow in the United States, a number of others are brought in from foreign lands for use in the best grade of public buildings and private residences. The most popular of these are the mahogany, rosewood, satinwood, French burl, and Circassian walnut. Mahogany comes from Cuba and Mexico, and formerly was obtained also from Santo Domingo and Honduras. It is generally imported in the rough log and cut up by the purchasers as it is required. The wood is easy to work, will take an excellent polish, and stays in place very well if it is well seasoned. It varies in color from very light to deep red and becomes darker witli age. It is usually employed in the form of veneers on account of its cost. Satinwood comes from the West Indies, French burl from Per- sia, and Circassian walnut from near the Black Sea. They are all very expensive and are used only as veneers, and in only the finest work. GENERAL CHARACTERISTICS OF TIMBER. In speaking of wood we are accustomed to use certain words to express our idea of its mechanical properties, or of its probable 26 CARPENTRl 1;) behavior under certain conditions. Thus we say that a wood is hard, or tough, or brittle, or flexible, and frequently we use tliese terras without having a clear understanding of just what they mean. A very brief discussion of some of these properties or characteristics of timber will now be given in order that we may see what peculiarities of structure or of growth cause them. Hardness. If a block of wood is struck with a hammer when lying on a bench, the hammer-head will make an impression or dent in the wood, which will be deeper or shallower according as the wood is soft or hard. A wood is said to be very hard when it requires a pressure of about 3,000 pounds per square inch to make an impression one-twentieth of an inch deep. A hard wood requires only about 2,500 pounds to produce the same effect. Fairly hard wood will be indented by a pressure of 1,500 pounds, and soft woods require even less. Maple, oak, elm and hickory are very hard; ash, cherry, birch and walnut are hard ; the best qualities of pine and spruce are fairly hard ; and hemlock, poplar, redwood and butternut are soft. Toughness. " Toughness " is a word which is often used in relation to timber, and implies both strength and pliability, such as is found in the wood of the elm and hickory. Such timber will withstand the effect of jars and shocks which would cause other woods, like pine, to be shattered. Flexibility. Timber is said to be flexible when it bends before breaking instead of breaking off short, or, in other words, a flexi- ble wood is the opposite of one which is brittle. The harder woods, taken from the broad-leaved trees, are usually more flexible than the softer woods, taken from the cone-bearing trees. The wood of the main tree trunk is more flexible than that of the limbs and branches, and moist timber is more flexible than dry wood. Hickory is one of the most flexible woods. Cleavage. Most woods split very easily along the grain, espe- cially when the arrangement of the fibers is simple, as in the conifers. In splitting with an axe, the axe-head acts as a wedge and forces the fibers apart, and usually the split runs along some distance ahead of the axe. Hard woods do not split so easily as soft woods, and seasoned wood not so easily as green wood, while all timber splits most easily along radial lines. 87 20 CARPENTRY THE STEEL SQUARE. If it is important that a workman should know his material thoroughly, it is even more essential that he should understand his tools and be able to apply them in the most useful way to any par- ticular piece of work. This is especially true of the tool known as the " Carpenter's. Steel Square " which is without doubt the most useful of all the tools to be found in a carpenter's chest, but which is not always thoroughly understood even by experienced workmen. As the square will be referred to frequently in these pages a brief description of it will be given. |mTT|TT|TWTJTTpTJ^ , 60 18 B( 84 a§ 30 ,60 ,24 Wl , I ,3 , I ,2 5 W wyv A m F|TF 3 2I 1 o CVJ CM CM CO CM B M ro OJ ;^-^ tn^ ll|lllll|1l|ll|li|ll|lt: r\) 03 01 ICCDU m MO) WCJ ^0> 0)CTI 001 ^M- u^ en: 0)z Fig. 17. Fig. 16. Carpenter's Steel Square. It is shown in Figs. 16 and 17, each view showing one side of the square. It is essentially a measuring and calculating tool, and all of the various markings and scales found on either side have their own special uses. All squares are not alike, there being several kinds on the market and in daily use among mechanics, but the 28 CARPENTRY 2 I variations in the markings on the different squares are so slight that if one is explained the others can be readily understood. There are three parts to the tool which are distinguished by special names, the tongue, the blade and the heel. The longer, wider arm is called the blade ; the shorter, narrower arm is called the tongue ; and the point in which the tongue and the blade meet, on the outside edge of the square, is called the heel. In the figures, A is the blade, B the tongue, and C the heel. In carefully made tools, the blade is two feet long and two inches wide, while the tongue is from fourteen to eighteen inches long and one and one-half inches wide. Starting at the heel and reading away from it, the outside edges of the blade and the tongue on both sides of the square, are divided into inches and fractions of an inch, one side of the square showincr sixteenths and the other side showing twelfths. Starting at the interior angle opposite the heel, the inside edges are divided in a similar way except that the inches on both sides of the square are divided into eighths only. In some squares one of these scales is shown divided into thirty-seconds of an inch. On one side of the blade the inch marks are numbered in both directions, from the heel outward, and also from the end of the blade inward, toward the heel, so that each inch mark has two numbers, one showing its distance m mches, from the heel, and the other showing its distance from the end of the blade. Tliese extra numbers are very useful in measuring the depth of mortises and in all similar work. The arrangement is shown in Fiw 16. On the other side of the blade, which is shown in Fig. 17, in addition to the scales on the two edges, we find a column of figures directly under each of the inch marks on the outer edge. The fig- ures are arranged in eight rows, parallel to the edges of the square. and the rows are marked off by lines running the full length of the blade. These figures enable a man to tell at a glance the number of board-feet in a piece of timber whose dimensions he knows. Under the twelve-inch mark there are figures showing the different lengths which can ISe -measured in this way, so that each row of figures cor- responds to a certain length, found under the twelve-inch mark. Under each of the other inch marks there are figures, each of whirh gives the number of board-feet in a plank one inch thick, whose 29 22 CAUPKNTIJY •width in inches is indicated by the number of the inch marks under which the figure is found, and whose length, in feet, is indicated by the number found in the same row with the figure itself under the twelve-inch mark. There are seven or eight different lengths given, and twenty-three different widths for each length, the widths varying from two inches up to twenty-four inches. The figures expressing the board measure are given as feet and inches, the number of feet being separated from the number of inches by a vertical line, with tlie feet on the left and the inches on the right. Tor instance, 118 is read as eleven feet and eight inches. On the same side of the square which shows the board measure on tlie blade, we find on the tongue what is known as the " brace rule," placed in tlie middle of the tongue between the two scales which are marked off along the edges. The brace rule consists of two similar numbers representing length in feet, placed one above the other, with a third number placed just to the right of them, as || 33.94. The two similar numbers represent the length, in feet, of the side of a perfect square, and the third number represents the length of the diagonal of this square, expressed in feet and decimals of a foot. In other words the nundier to the right is equal to the square root of the sum of the squares of the other two numbers, or is equal to one of these numbers multiplied by tlie square root of 2, which is 1.414, in accordance with the principle that tlie lengtli of tlie diag- onal of a square is equal to the length of the side nnlltiplied by the square root of two. There are a number of diil'erent sets of figures like this on the tongue of the square ; they are very useful in find- ing the length of braces which make an angle of forty-five degrees with the post into which they frame, or which have a total rise equal to their total run. On the same side of the tongue which shows the brace rule, placed near the heel of the square, is found another scale which may be called the " Scale of Hundredths." It consists of a number of lines drawn along the tongue parallel to the edges, which are just one- tenth of an inch apart. They are drawn diagonally, so that the end of one line is directly under the starting point of the next line. By means of this scale any number of hundredths of an inch can be readily measured off. The scale mav be seen in Vv' 17. 30 CARPENTRY 23 The opposite side of the square shows two lines, drawn near together in the center of the tongue. Parallel to the edges and between these lines a single line of dots is placed. They are a little more than one-fifth of an inch apart and numbered by tens. The dots constitute what is called the " octagon scale," and are used in the process of cutting a stick of octagonal section out of a stick of square section. Suppose for example we take a stick ten inches square and wish to cut from it a stick of octagonal section. We will first draw a line lengthwise in the center of each of the four faces of the square stick. Then applying the square, we measure off on both sides of this center line, in each face, perpendicular to the edges of the piece, as many of the spaces shown by the line of dots as there are inches in the side of the square stick. Thus in this case, we measure off ten. spaces on each side of each center line, and then draw through the points thus located two lines in each face, parallel to the center line and equidistant from it. These eight lines represent the eight edges of the octagonal stick, and by cutting away the four corners, the desired shape is obtained. This completes the description of the markings upon the square, and although there are undoubtedly some squares in use which may not be exactly like the model described, they all have nearly the same markings, arranged in the same way or with but slight variations. Some of the numerous applications of the square in the solution of practical problems in Carpentry are explained in connection with the work on " framing," and others will suggest themselves to the thoughtful student. The uses to which the instrument may be put are so many and so various that it would require a large book to explain them all, but those who use the tool constantly will readily discover them and perhaps many new ones besides. LAYING OUT. Having now considered the material and the most important of the tools with which the carpenter performs his work, we shall pass to a consideration of the work itself, and see how a building of wooden construction is put together. In undertaking the construction of any building, the first thing to do is to make a very thoughtful examination of the piece of ground upon which the structure is to be placed This is very important, 31 21 CARPENTRY since tlie character of the soil up(ja which a dwelling is located will very largely determine its sanitary condition, and will inlluence to a great extent the health of the occupants. Very often a difference of a few yards in the position of a building will be enough to cause the difference between a perfectly dry cellar and one which is constantly flooded with water. Water is, indeed, the one thing above all others which must be guarded against, since it is almost impossible to keep it out of a cellar which is sunk in damp ground. At a certain distance below the surface of the earth there is always to be found what is known as " ground water." This stands always nearly at a level, so that it is not met with so near the surface of a slight knoll or other elevation as in the case of a depression. If possible, the house should be so located that the bottom of the cellar need not come below the ground-water level, and consequently it should be placed on comparatively high land. Below the surface of a hill, however, there may be a stratum of rock which will hold the rain water and prevent it from sinking at once to the ground-water level. Such a ledge of rock causes the water to collect, and then flow off in small subterranean streams, which will almost surely penetrate the walls of a cellar if it happens to be in their path. A good way to discover the depth of the ground-water level, or the existence of rock ledges beneath the surface of tlie ground, is to dig a number of small, deep holes at various points of the site. These should be carried below the projwsed level of the cellar bottom. A suitable location for the building may thus be chosen. When the approximate position of the structure has been decided upon, the next step is to " stake it out." That is, the position of the corners of the building must be located and marked in some way on the ground, so that when the excavation is begun the workmen may know what are the exact boundaries of the cellar. This " stakinsr out" should always be carefully attended to, no matter how small the building may be. In works of importance it is always best to have the work done by an engineer, but on small work it is customary for the contractor or the architect to attend to it. It is well to have at hand some instrument with which angles can be accurately measured, such as a transit ; but the work can be done v6ry satisfactorily with a tape measure and a " mason's square." This simple instrument is composed of three sticks of timber nailed together as shown in Fig. 32 CARPENTRY '>5 18, to form a right-angled triangle. It is important that the tape used should be accurate, a steel tape being always preferable, and that the square should give an exact right angle. A mistake in the staking out may cause endless trouble when the erection of the building itself is begun, and it is then too late to remedy it. There are several different lines which must be located at some time during the construction, and they may as well be settled at the start. These are : the line of excavation, which is outside of all ; the face of the basement wall, inside cf the excavation line ; and, in the case of a masonry building, the ashlar line, which indicates the out- side of the brick, or stone walls. In the case of a wooden structure only the two outside lines need be located, and often only the line of the excavation is determined at the outset. The first thing to do is to lay out upon the ground the main rectangle of the build- ing, after which the secondary rectangles which indicate the position of ells, bay windows, etc., may be located. Starting at any point on the lot where it is desired to place one corner of the building, a stake should be driven into the ground and a li. - laid out either parallel or perpendiculai .o the street upon which the structure is to face. At the end of this line, which forms one side of our rectangle, and the length of which is determmed by the dimensions of the buildincT, another stake should be driven, and these two stakes will determine the direction and the length of the line. The exact location of the ends of the line may be indicated by a nail driven into the top of each stake. After one line has been thus laid out, others may be laid out perpendicular to it at its ends, with the aid of the mason's square and the tape measure. The accuracy of the right angle may be checked by the use of the " three-four-five " rule. This rule is based upon the fact that a triangle, whose three sides are respectively three, four, and five feet long, is an exact right-angled triangle, the right angle being always the angle between the three-foot and th« four-foot sides. This fact may be proven by applying the well- known theorem which states that the length of the hypothenuse of Mason's Square. 33 26 CAIIPENTKY a right-angled triangle is equal to the square root of the sum of the squares of the other two sides. The rule may he used as follows : Lay off on one of the side lines already laid out on the ground, ^. any multi])le of three feet, as nine feet, or twelve feet. On the other line, presumably at right angles to the first one, lay off the same multiple of four feet, as twelve feet, or sixteen feet. Now a straight line, measured between the points so obtained, should have a length equal to the same multiple of five feet, as fifteen feet or twenty feet. If this is not found to be the case, the angle laid out is not an exact right angle, and instead of a rectangle we have a parallel- ogram as ^hown in Pig. 19. This will not do at all, and the inaccuracy must be cor- rected. It is possible to lay out the right angle in the first place by this same method, using two flexible cords, respect- ively four feet and five feet long. The end of the four-foot cord should be fastened at the end of the side line of the build- ing, and the end of the five-foot cord should be fastened on this same side line, three feet away from the corner. When the loose ends of both cords are held together, and the cords are both Fig. 20. Position of Corner. drawn taut, the point where the ends meet will be a point on the side line of the building perpendicular to tlie first side line. It is evident that tliis point must be just four feet from the corner, and that the distance between it and the point on the other side line three feet from the corner, must be five feet. 34 CARPENTRY 27 After all the corners of the building have been located, their position should be indicated by the use of " batter boards." One of these is shown in Fig. 20. It will be seen that it consists of a post A, which is set up at the corner, together with two horizontal pieces B, B, which extend outward for a short distance along the sides of the rectangle that has been laid out. The horizontal pieces may be braced securely as shown, and, the whole will be a permanent indication of the position of the corner. Notches may be cut in the top of the horizontal pieces to indicate the position of the various lines, and cords may then be stretched between the notches from batter board to batter board. These cords will give the exact location of the lines. Another way to indicate the position of the lines is by driving small nails into the tops of the, batter boards instead of , , '. .1 1 , -1 Fig. 21. Batter Boards, cutting notches in them ; but nails may * be withdrawn, while the notches, when they are once cut, cannot easily be obliterated. -Batter boards should always be set up very securely, so that they will not be displaced during the building operations. If there is danger that the form of batter board shown in Fig. 20 may be displaced, because of the large size of the structure and the length of time during which they must be used, the form shown in Fig. 21 may be substituted. Two of these, at right angles to each other, must be placed at each corner. LIGHT FRAHINQ. After the building has been laid out, and the batter boards are in place, the next work which a carpenter is -called upon to do is the framing. This consists in preparing a skeleton, as we may say, upon which a more or less ornamental covering is to be placed. Just as the skeleton is the most essential part of the human body, so is the frame the most essential part of a wooden building; and upon the strength of this frame depends the .strength and durability of the structure. When the carpenter comes to the work, lie finds everything prepared for him; the cellar has been dug and the 35 28 CARPENTRY Fig. 22. Splice. foundation walls and the underpinning have been built. It is his business to raise the framework on top of them. First is the wall, then the floors and the roof. Tiierefore the subject may be subdivided, and considered un- der these three main headings. In connection with the walls we may consider the partitions as well as the outside walls, and in connection with the floors we may consider the stairs, while the roof may be taken as comprising the main roof and also subordinate roofs over piazzas, balconies and ells. This covers all the framing that will be found in a wooden building, except special framing, which will be treated later. Whatever fram- ing there is in a brick or stone building is similar to that in a wooden building, with the slight differences which may be noted as we come to them. JOINTS AND SPLICES. Joints. Before beginning a description of the framing of the wall, it will be well to consider the methods employed in joining pieces of timber together. Tlie number of different kinds of con- nections is really very small, and the principles upon which they are based may be mastered very quickly. All connections between pieces of timber may be classified as joints or as splices. By a " splice " we mean a connection between two pieces which extend in the same direction, as shown in Fig. 22, and each one of which is merely a continuation of the other. The only reason for the existence of such a connection is the fact that sticks of timber can be obtained only in limited lengths, and must therefore very often ba pieced out. By a " joint" we mean any con- nection between two pieces which come together at an angle, as Fig. 23. Joint. 36 CARPENTRY 29 shown in Fig. 23, and which are therefore not continuous. Sucli a connection may be required in a great many places, and especially at the corners of a building. Joints. The principal kinds of joints to be met with in car- pentry are the "bi tt joint," the "mortise-and-tenon joint," the "gained joint," the " halve I joint," the "tenon-and-tusk joint," and the "double tenon joint." The Butt Joint. This is the most simple of all the joints, and is made by merely placing the two pieces together and nailing them firmly to each other, after both have been trimmed square and true. Such a joint is shown in Fig. 24. The two pieces are perpendicular to each other and neither piece is cut. The nails are driven diag- onally through both pieces, an operation which is known as " toe- nailing," and are driven home, if necessary, with a nail set. This is called a " square " butt joint. Fig. Fig. 24. Butt Joint. Fig. 25. Oblique Butt Joint. 25 shows two pieces which are not perpendicular to each other. They are trimmed to fit closely together, and are then nailed in place. Such a joint is called an "oblique" butt joint. The butt joint does not make a strong connection between" the pieces, and should not be used if much strength is required. It depends entirely upon the nails for its strength, and these are very likely to pull out. This form of joint is sometimes modified by cutting away a part of one of the pieces, so that the other may set down into it as shown in Fig. 26, the square joint at A, and the oblique joint at B. This gives much additional strength to the joint, especially in the case shown at B, where there may be a tendency for one piece to slide along the other. 37 30 CARPEXTIil The nortise=and-Tenon Joint. From the modified butt joint it is only a step to the " mortise-and-tenoii " joint, which is formed by cutting a liole called a " mortise " in one of the pieces of timber, to receive a projection called a " tenon " which is cut on the end of the other piece. This is shown in Fig. 27. Tlie mortise is at <( and the tenon at /'. It will be noticed that there is a hole bored Ficr. 26 A. Modified Butt Joints. Fig. 26 B. through the tenon at c, and another hole in the mortised piece at d. These holes are so placed that when the pieces are joined together, a wooden pin may be driven through both holes, thus preventing the tenon from being withdrawn from the mortise. This pin should always be inserted in a mortise-and-tenon joint. Ordinarily it is of hard wood even when the pieces to be joined are themselves of soft wood, and it may be of any desired size. Hound pins from three-quarters to seven-eigiiths of an inch in diameter are ordinarily employed, although it may sometimes be found better to use a square pin. The Bridge Joint. Tlie form of mortise-and-tenon joint described above may be used wherever the pieces are perpendicu- lar to each other. When, however, the pieces are inclined to each other, a modification of the above joint known iis the " bridge " or "straddle" joint is employed. This joint is shown in Figs. 28 and 29. It is similar to tlie square mortise-and-tenon joint, hav- ing a similar mortise and tenon, but these are cut in a slightly different way. In Fig. 28 the tenon a is cut in the end of the inclined uiece and fits into the mortise h cut in the other piece. 38 CARPENTRY 31 In Fig. 29 the mortise a is cut in the end of the inclined piece and the tenon h is cut in the other piece. The Gained Joint. The joints whicli have so far been described are applicable only where the members are subjected to Fig. 27. Mortise-aud-Tenon Joint. Fig. 28. Bridge Joiut. direct compression, as in the case of posts or braces, or in certain cases where direct tension is the only force acting on the x^ieces. When bending and shearing are to be expected, as in the case of Fig. 29. Bridge Joint. Fig. oO. Gained Joiut. floor beams connecting to sills or girders, a. slightly different sort of joint must be employed. . One of the most common joints for such places is a modifica- tion of the mortise-and-tenon joint which is known as the " gained joint." An example of this form of connection is shown in Fig. 30, and it may be seen that the end of one piece is tenoned in a peculiar way. The tenon proper is the part a-h-c and this tenon 39 32 CARPENTIIY sets into a corresponding mortise cut in the other piece as shown. It is evident that the tenon cannot be held in place by a pin, hut it may be secured by nailing. The reason for this peculiar form of tenon may be explained as follows: A floor beam, or any other timber which is loaded transversely, has a tendency to fall to the ground, and must be supported at its ends either by resting directly on a wall or sill, or by being mortised into the latter member. Moreover, in order that the end of the piece resting on the support may not be crushed or broken, a certain amount of bearing surface must be Fig. 31. Tenon-and-Tusk Joints. Fig. 32. available. This same bearing surface must be provided in every case no matter whether the timber rests directly on the top of the sill or is mortised into it. Of course the simplest connection is obtained by resting the transverse piece directly on top of the sill without cutting either piece ; but such a joint is not stiff and strong, and it is often necessary to bring the timbers flush with each other at the top or at the bottom. For this reason a mortised joint is used; and in order to obtain the required amount of bear- ing surface without cutting the pieces too much, the form of tenon shown is employed. The available bearing area here is furnished by the surfaces d-n and h-c and it may easily be seen that this area is the same as would be available if the piece rested directly on top of the sill. The operation of cutting such a tenon and mortise is known a« "gaining," and one piece is said to be "gained" into the other. The Tenon-and-Tusk Joint. A joint in very common use 40 CARPENTRY 83 in such situations as have just been mentioned is a development of the gained joint which is called the " tenon-and-tusk " oi- tiie "tusk-tcnon" joint. This joint is shown in Fig. 31. The charac- teristic feature is to be found in the peculiar shape of the tenon which is cut in the end of one of the pieces to be joined, as shown in the lio-ure. It may be seen that there is a small square tenon b cut in the extreme end of the piece, and that in addition to this there are other cuts c which constitute the " tusk." The bearing area is furnished partly by the under side of the tenon and partly by the under side of the tusk. Fig. 33. Methods of Securing Tenons. Fig. 34. This joint makes a very good connection, and the cutting of the mortise does, not weaken the piece of timber so much as does the mortise for a gained joint. It is especially applicable when it is desired to have the pieces flash on top, though it may also be used in other positions. ' When the top of the tenoned piece must project above the top of the mortised piece, the tenon may be cut as shown in Fig. 32. There are several ways of securing the tenon in place. The simplest is that shown in Fig. o3, where the pin h is passed through the tenon and the mortised piece 80 as to hold the tenon securely in place. Another scheme is to cut the square tenon a little longer, as shown in Fig. 34, so as to pass clear through the mortised piece, and to fasten it with a peg b on the other side. The peg may be cut slightly tapering, as shewn, so that when it is driven in place it will draw the pieces together. Still another plan is shown m Fig. 35. Here a small square hole a is cut in the header seme Fig. 3:. Method of Securing Tenon. 41 84 CARPENTRY distance back from tlie tenon unci a nut c is placed in it, while a bolt l is passed through a hole bored lengthwise in tlie header to receive it. The bolt passes through the nut, which may be screwed up tight, thus drawing the pieces closely together and making the joint tiglit. In screwing this uji, it is the bolt which must be turned, while the nut is held stationary by the side of the square hole in which it is inserted and which is iust larsre enoucrh to receive it. Fig. 36. Double Teuuu Joint. Fig. 37. Halved Joint. The Double Tenon Joint. Fig. 36 shows a form of tenon joint called the " double tenon " joint, which is not very extensively used at the present time but which has some advantages. As may be readily seen, there are two small tenons a and h through which a pin may be passed if desired. The Halved Joint, A form of joint which may be used to connect two pieces that meet at a corner of a building, is shown in Fig. 37. This is known as the " halved" joint from the fact that both pieces are ciit half way through and then placed together. The pieces are held in place by nails or spikes. If one piece meets the other near the center instead of at the end of the piece, and if there is danger that the two pieces may pull away from each other, a form of joint called the "dovetail" halved joint is used. This is shown in Fig. 38. Both the tenon and the mortise are cut in the shape of a fan, or dovetail, which prevents them from being pulled apart. This joint may also be 42 d o z a u X -s S ^. o i> fc. ;-j ° < H Z £ o >, cci '^ fa g z 5 Q > < .9 is V. to o *• O :S ci ■■ 4> 4-1 §K ? o o S U;2 «o rt I, o s u 0? < rt M Dh Q (0 Z o ■-1 K < 3 I! cc - o S K i; ^ O ^ c b. ir ^ i; o bi: '2> ee o ^ '^ >< ^ fc. ^ u z .a o t> OT •< r S Ol, >, :i o " ^' Q c jE |r2 ^3 H c < 2 U c r/1 *^ S O 3 s CARPENTRY 35 cut as shown in Fig. 39, with the flare on only om-) side of the tenon, the other side being straight. Splices. As ah-eady exphiined, a splice is merely a joint between two pieces of timber which extend in the same direction, and is sometimes necessary because one long piece cannot be con- veniently or cheaply obtained. The only object in view, then, is Fig. 38. Dovetail Halved Joint. Fig. 39. Dovetail Joint. to fasten the piece will be rt#1 ¥^ k two timbers together, in such a way that the finished in all respects equivalent to a single unbroken piece, and will satisfy all the requirements of the un- broken piece. This is really the only measure of the efficiency of a splice. There are three kinds of forces to which a piece may be subjected, namely : compression, ten- sion, and bending. A splice which would be very effective in a timber acted upon by one of these forces might be absolutely worthless in a piece "which must resist one of the other forces. We have, therefore, three classes of splices, each designed to resist one of these three forces. Splices for Compression. The simplest splices are those to resist compression alone, and of these the most simple is that shown in Fig. 40. This piece is said to be " fished ; " the two parts are merely sawed off square and the ends placed together. A couple of short pieces A A, called " fish plates " are H»v^ Fig. 40. Fished Splice. 43 36 CARPENTRY nailed on opposite sides to keep the parts in line. In the splice shown in Fig. 40, these are of wood, and ordinary nails are used to fasten them in place, but in more important work thin iron plates are used, the thickness being varied to suit the conditions. They are held in place by means of bolts with washers and nuts. If for any reason, it is desired not to use plates of this kind, four small pieces called dowels may be used, as indicated in Fig. 41. These dowels may be set into the sides of the tim- bers to be spliced, so that they do not project at all beyond the faces of these pieces and a very neat job may thus be obtained. It is but a step to pass from this simple splice to the " halved " splice shown in Fig. 42. It will be noticed that it is much like the halved joint described above, the only difference being that the pieces are continuous, instead of perpendicular to each other. The nature of the splice will be easily understood from the figure Fig. 41. Splice Using Dowels. Fig. 42. Halved Splice. Fig. 43. Beveled Splice. without further explanation. A modification of this which is somewhat more effective, is shown in Fig. 43. The cuts are here made on a bevel in such a way that the parts fit accurately when placed together, and the splice is called a "beveled" splice. The halved splice is perhaps the best that can be used to 44 CARPENTRY 37 resist direct compression, and when it is combined with fish pLates and bolts as s^iown in Fig. 44 it may be used in cases wliere some tension is to be expected. It will be noticed that in Fig. 44 the ends of the timbers are cut witli a small additional tongue a but this does not materially strengthen the splice and it adds consider- ably to the labor of forming it. In general it may be said that the simplest splice is the most effective. Whenever the pieces are cut to fit into one another, as they do in the halved and beveled splices, the splice is known as a " scarf " splice, and the operation of cutting and joining the parts is called "scarfing." Scarf splices are used, as we. have already seen, both alone and in combination with fish plates. The fished splice is always the stronger, but the splice where scarfing alone is resorted to has the neatest appearance. Fig. 44. Halved Splice with Fish Plates. Fig. 45. Splice for Tension. Splices for Tension. There are several common forms of splices for resisting direct tension. These differ from each other mainly in the amount of labor mvolved in making them. The simplest of them is shown in Fig. 45, and it will be seen that it is only a slight modification of the halved splice used for resisting compression. It is evident that the pieces cannot pull apart in the direction of their length until the timber crushes along the face marked a-h, or shears along the dotted line a-c. By varying the dimensions of the splice it may be made suitable for any situation. The parts are held closely together by the light fishplates shown in the figure, which also incidentally add something to the strength of the splice. Instead of cutting the ends of the beams square, as shown in Fig. 45, they frequently are cut on a bevel as shown in Fig. 46, 45 38 CARPENTRY and a further modification may be introducetl by inserting a small "key" of hard wood between the pieces for them to pull against. This key is usually made of oak and may be in two parts, as shown in Fig. 47, each part in the shape of a wedge, so that when they are driven into place a tight joint may be obtained. The two wedge-shaped pieces may be driven in from opposite sides, the hole being made a little smaller than the key. If the key is made Fig. 46. Splice for Tension. Fig. 47. Splice with Two Keys. much too large for the hole, however, a so-called " initial '' stress is brought into the timbers, which uses up some of their strength even l)efore any load is applied. This should be avoided. If it is desired, two or more keys may be employed in a splice, the only limiting condition being that they must be placed far enough apart so that the wood will not shear out along the dotted line shown in Fig. 47. Another feature of the splice here shown Fig. 48. Keys. Fig. 49. Tension Splice with Fish Plates. is the way in which the pieces are cu.t with two bevels on the end instead of one. One bevel starts at the edge oi the key and is very gradual, the other starts at the extreme end of the piece and 46 CARPENTRY 39 IS rather steep and sharp. . Tliese bevels can be used only in joints which resist tension alone. If such a splice were subjected to compression, the beveled ends would slide on each other and push by eacli other very easily, except as they are prevented from so doing by the fish plates, if these are used. Tension Splice with Fish Plates. The splices for tension which have so far been described have all been scarf joints, but there is a fished splice which is very commonly used for tension. This splice is shown in Fig. 49. The fish plates, in this case of wood, are cut into the two pieces to be spliced, so as to hold them firmly together. The pieces cannot be pulled apart until one of the plates shears off along the dotted line a-h. The distance c-d must also be made large enough so that the piece will not shear. This splice is very often used for the lower chords of wooden trusses, and it is really one of the best that can be used for resisting direct tension. Splices for Bending. It sometimes happens that a piece which is subjected to a bending stress must be spliced, and in this case the splice must be formed to suit the existing conditions. It is well known that in a tim- ber which is resisting a bend- ing stress the upper part of the piece is in compression, and the tendency is for the fibers to crush, while the lower part of the piece is in tension, and the ten- dency is for the fibers • to pull apart. To provide for this, a form of splice must be selected which combines the features of the tension and compression splices. Fig. 50 shows such a splice. The parts are scarfed together as in the case of the other splices described, but in this case the end of the top piece is cut off. square to offer the greatest possible resistance to crush- ing, while the underneath piece is beveled on the end, as there is no tendency for the timbers to crush. These cuts are shown in the figure. We have already seen that in the lower part of the splice Fig. 50. Splice for Beuding. 47 40 CARPENTRY there is a tendency for the parts to be pulled away from each other. In order to prevent this, a fish plate a is used, which must be heavy enough to take care of .all the tension, since it is evident tha't tlic wood cannot take -any of this. The plate must be securely bolted to both parts of the splice. Tliere is no need of a fish plate on the top of the pieces because there is no tendency for tlie pieces to pull apart on top, and the bolts shown in the figure are sufficient to prevent them from being displaced. In any case where it is not desirable to scarf the pieces in a splice subjected to bending, the form of butt joint shown in Fig. 51 may be used. The phites (either of wood or iron) are m this case bolted to the sides of the pieces. If wood is used, of course the plates must be made very much heavier than if iron is used. Fig. 51. Butt Joint. In either case they must be large enough to take care of all the bending stress, and a sufficient number of bolts must be used to fasten them securely to both parts of the splice. THE WALL. Let us next consider the framing of the walls of the build- ing. In this work there are two distinct methods known respect- ively as " braced framing " and " balloon framing," of which the first is the older and stronger method, wliile the second is a modern development and claims to be more philosophical, as well as more economical, than the other. Balloon framing has come into use only since 1850, and is still regarded with disfavor by many architects, especially in the eastern states. Figs. 52 and 53 show the framing of one end of a small building by each of these methods, the braced framing in Fig. 52, and the balloon framing in Fig. 53. Braced Frame. In a full-braced frame all the pieces sliould 6e fastened together with mortise-and-tenon joints, but this is much modified in common practice, a so-called " combination '" frame being used, in which some pieces are mortised together and 48 CARPENTRY 41 others are fastened by means of spikes only. A framework is constructed consisting in each wall of the two "corner posts" A A (Fig. -52), the " sill " B, and the " plate " C, together with a horizontal " girt " D at each story, to support the floors, and a diagonal " brace " E at each corner, which, by keeping the corner square, prevents the frame from being distorted. Balloon Frame. In a balloon frame there are no braces or girts , and the intermediate studs F F F (Fig. 53) are carried straight up from the sill H to the plate K, with a light horizontal piece J, called a " ribbon " or " ledger board," set into them at each floor level to support the floors. This frame depends mainly Pig. 52. Braced Frame. Fig. 53. Balloon Frame. upon the boarding for its stifPness, but sometimes light diagonal braces are set mto the studs at each corner to prevent distortion. The methods by which all these pieces are framed together will be explained in detail under the proper headings. The Sill. The sill is the first part of the frame to be set in place. It rests directly on the underpinning and extends all around the building, being jointed at the corners and spliced where necessary ; and since it is subject to much cutting and may be called upon to span quite considerable openings (for cellar windows, etc.) in the underpinning, it must be of good size. Usually it is made of six by six square timber, but in good work 49 42 CARPENTRY Fig. 54. Sill Placed on Wall. it should be six by eight, and nothing lighter than six by six should be used except for piazza sills. For piazza sills a four by six timber is used. The material is generally spruce, although sometimes it is Norway pine or native pine (depending upon the locality). The sill should be placed on the wall far enough back from the outside face to allow for the water table, which is a part of the outside finish ; and one inch should be regarded as the mini- mum distance between the out- side face of the sill and the outside face of the underpinning (see Fig. 54). A bed of mortar A, preferably of cement mortar, should be prepared on the top of the underpinning, in which the sill C should rest ; and the under side of the sill should be painted with one or two coats of linseed oil to prevent it from absorbing moisture from the masonry. In many cases, at intervals of eight or ten feet, long bolts B are set into the masonr3^ These bolts extend up through holes bored in the sill to receive them, and are fastened at the top by a washer and a nut screwed down tight. Tliey fasten the sill, and consequently the whole frame, securely to the underpinning, and should always be provided in the case of light frames in exposed positions. The beams or "joists " D, which form ' the framework of the first floor, are supported at one or both ends by the sill and may be fastened to it in any one of several different ways. The ideal method is to hang the joist in a patent hanger fastened to the sill as shown in Fig. 55, wliere A is the sill, B the joist, and C the hanger. In this case neither the sill nor the joist need be Fig. 55. Patent ITauger. 50 CARPENTRY 43 weakened by cutting, but this is too expensive a method for ordi- nary work, although the saving in laljor largely offsets the cost of the hanger. Tlie usual method is to cut a mortise in the sill to receive a tenon cut in the end of the joist (as shown at A in Fig. 56). These mortises are cut in the inside upper corner-of the sill, are about four inches deep and cut two inches into the width of the sill, and are fixed in position by the spacing of the joists. Mortises are also cut in the sill to receive tenons cut in the lower ends of the studs (as shown at B in Fig. 57). They are cut the full thickness of the studding, about one and one-half inches in the width of the sill and about two inches deep. The position of these is fixed by the spac- ing of the studding, and by the con- dition that the outer face of the studding must be flush with the outer face of the sill in order to leave a plain surface for the boarding. The sills are usually halved and pinned together at the cor- ners, as shown in Fig. 58 ; but sometimes they are fastened together by means of a tenon A cut in one sill, which fits into a mortise cut Fig. 56. Mortise in Sill. Fig. 57. Mortise iu Sill for Studding. in the other, as shown in Fig. 59, This may be stronger than the other method, but the advantasre trained is not sufiicient to com- pensate for the extra labor involved. Sills under twenty feet in 51 44 CARPENTRY length should be in one piece, but in some cases splicing may be necessary. A scarf joint should always be used, the splice should be made strong, and the pieces should be well fitted together. In some parts of the country it is customary to " build up " the sill from a number of planks two or three inches thick, which are spiked securely together. A six- by-six-inch sill may be made in this way from three planks, two inches thick and six inches wide, as shown in Fig. 60. Planks of any length may be used, and may be so arranged as to break joints with each other so that the sill may be made continuous, without splicing. It is often easier and cheaper to build up a sill in this way than it is to use a large, solid timber, and if the parts are well spiked together, such a sill is fully as good as the other. When a sill of this kind is used, however, it should always be placed on the wall in such a way that the planks of which it is made up will set up on edge and not lie flat. Fig. 58. Joint of Sills at Corner. Fig. 59. Joint of Sills at Corner. Fig. 60, ••Built-up" Sill. The Corner Posts. After the sill is in place, the first floor is usually framed and roughly covered at once, to furnish a sur- face on which to work, and a sheltered place in the cellar for the storage of tools and materials, after which the framing of the wall is continued. The corner posts are first sot up, tlien the girts and the plate are framed in between them, witli the braces at the cor- ners to keep everything in place ; and lastly the whole is filled in with studding. The corner posts are pieces four by eight, or 52 CARPENTRY 46 sometimes two pieces four by four placed close together. Corner posts must be long enough to reach from the sill to the plate* The post is really a part of only one of the two walls which meet at the corner, and in the other wall a " furring stud " of two-by- four stuif is placed close up against the post so as to form a solid Fig. 61. Corner Post with One Furring Stud. Fig. 62. Corner Post with Two Furring Studs. corner, and give a firm nailing for the lathing in both walls. This arrangement is shown in plan in Fig. 61. A is the corner post, B the furring stud, C the plastering, and D the boarding and shingling on the outside. Sometimes a four-by-four piece is used for the corner post and a two-by-four furring stud is set close against it in each wall to form the solid corner, as shown in plan in Fig. 62; but a four-by- four-stick is hardly large enough for the long corner post, and the best practice is to use a four-by- eight, although in very light framing a four-by-six might be used. A tenon is cut in the foot of the corner post to fit a mortise cut in the sill, and mor- tises c c, Fig. 63, are cut in the post at the proper level to re- ceive the tenons cut in the girts. Holes must also be bored to receive the pins d d which fasten these members to the post. The braces are often only nailed in place, but it is much better to cut mortises in the posts for these also, as shown at A in Fig. 64. The plate is usually fastened to the posts by means of spikes only, but it may be mortised to receive a tenon cut in the top of the post. Fig. 63. Mortises in Corner Post. 53 46 CAKPENTRY In the case of a billojii fniiiie no mortises need be cut in the posts for the girts or braces, as they are omitted in this frame; but the post must be notched instead, as shown in Fig. 65, to receive the ledger board or ribbon and the light braces which are some- times used. The Qirts. The girts are always made of the same width as the posts, being flush with the face of the post botli outside and inside, and the depth is usnally eight inches, although sometimes a six-inch timber may be used. The si/e is, tlierefore, usually four by eight. A tenon at each end fits into the mortise cut in the Fig. 64. Brace for Post and Sill. post, and the whole is secured by means of a pin il d as shown in Fig. 03. The pin should always be of hard wood and about seven- eighths inch in diameter. It is evident that if the gifts in two adjacent walls were framed into the corner post at the same level, the tenons on the two girts would conflict with each other. (See Fig. 63.) For this reason the girts A which run parallel with the floor joists are raised above the girts B on which these joints rest, and are called "raised girts" to distinguish them from the others which are called "dropped girts." The floor joists are carried by the dropped girts, and the raised girts are so placed that they are just flush on top with the joists which are parallel to them. The Ledger Board. The heavy girts are used only in the 54 CARPENTRY 47 braced frame. In the balloon frame, light [)ieces called "ledger boards " or " ribbons " are substituted for them. These are usu- ally made about one inch thick and six or seven inches deep, and are notched into the posts and intermediate studs instead of being Fig. 65. Fig. 66. . Fig. 67. Notched Studs for Ledger Boards. framed into them as in the braced frame. This notchinsr is shown in Fig. 66 in which A is the ledger board and B the stud. The ledger boards themselves are not cut at all, but the floor joists which they carry are notched over them, as sliown in Fig. 67, and spiked to them and to the stndding. In Fig. 67 A is the joist, B the ledger board, and C the studo Even in the braced frame a ledger botird is usually employed to support the joists of the attic floor, which carry little or no weight. Tlie disadvantage of the ledger board is that as a tie between the corner posts it is less effective than the girt, and consequently a wall in which it has been substituted for the girt is not as stiff as one in which the girt is used. The PlatCo The plate serves two purposes: first, to tie the studding together at the top and form a finish for the wall ; and second, to furnish a support for the lower ends of the rafters. (See Fig. 68). It is thus a connecting link between the wall and the roof, just as the sill and the girts are connecting links between Fig. 68. Fig. 69. Construction at Plate. 55 4b CAKPENTR£ the floors and the wall. Sometimes the plate is also made to support the attic floor joists, as shown in fig. 68, in which A is a rafter, B tlie joist spiked to the rafter, C the plate built up from two two-by-four pieces, and D the wall stud. It acts in this case like a girt, but this arrangement is not very common, the attic floor joists usually being supported on a ledger board as shown in Fig. 67o The plate is merely spiked to the corner posts and to the top of the studding; but at the corner where the phites in two adjacent walls come together, they should be connected by a framed joint, usually halved together in the same way as the sill. In the braced frame, a fairly heavy piece, usually a four by six, is used, although a four by four is probably sufficiently strong. In a balloon frame the usual prac- tice is to use two two-by-four pieces placed one on top of the other and breaking joints, as shown at A in Fig. 70, in order to form a continuous piece. The corner joint is then formed, as shown at B in Fig. 70. No cutting is done on the plate except at the corners, the rafters and the attic floor joists being cut over it, as shown in Figs. 68 and 69. Braces. Braces are used as permanent parts of the structure only in braced frames, and serve to stiffen the wall, to keep the corners square and true, and to prevent the frame from being dis- torted by lateral forces, such as wind. In a full-braced frame, a brace is placed wherever a sill, girt, or plate makes an angle with a corner post, as shown at E in Fig. 52. Braces are placed so as to make an angle of fortj'-five degrees with the post, and should be long enough to frame into the corner post at a height of from one- third to one-half the height of the story. This construction is often modified in practice, and the braces, are placed as showni at A in Fig. 71. Such a frame is not quite so stiff and strong as the regular braced frame, but it is sufficiently strong in most cases. Fig. 70. Construction at Corner, " Breaking Joints." 56 CARPENTRY 49 The braces are made the same width as the posts and girts, usually four iuches, to be flush with these pieces botii outside and iuside, and are made of three-by-four or foiu"- by-four stuff. They are framed into the posts and girders or sills, by means of a tenon cut in the end of the brace, and a mortise cut in the post or girt, and are secured by a hard- wood pin. The pin should be three-quarters or seven-eighths inch in diameter. The con-' nection is shown in Fig. 64. In a balloon frame, there are no perma- nent braces, but light strips are nailed across the corners while the framework is beino- erected, and before the boarding has been put on, to keep the frame in place. As soon as the outside boarding is in place these are removed. This practice is also modified, and sometimes light braces are used as perma- ^'^' '^^' ^'"'"^ ^'^'^^' nent parts of even a balloon frame. They are not framed into the other membere, however, but are merely notched into them and spiked as sho\\Ti in Fig. 72. A is the brace, B the sill, C the corner post, and D D are studs. In such a case every stud must be notched to receive the brace, which is really the same as the temporary brace mentioned above, except that it is notched into the studs instead of being merely nailed to them, and is not removed when the boarding is put on. These braces are usually made of one-by-three-inch stuff. Studding. When the sill, posts, girts, plates, and braces are in place, the only step that remains to complete the rough framing of the wall is the filling in of this framework with studding. The studding is of two kinds, the heavy pieces which form the frames Fiff. Temporary Brace. 57 50 CARPENTRY -A for tlie door and window openings, and llie stops for the partitions ; and the lighter pieces which are merely " filling-in " studs, and which are kno^vn by that name, or as " intermediate " studding. , The frames for the door and window openings are usually made in a braced frame, from four-by -four-inch pieces. A ver- tical stud A A, Fig. 73, is placed on each side of the opening, the proper distance being left between them, and horizontal pieces B B are framed into them at the proper level to form the top and the bottom of the opening. In all good work a small truss is formed above each opening by setting up two pieces of studding C C over the opening, in the form of a triangle. This is to receive any weight whicli comes from the studding directly above the opening, and cjjrry it to eithgr side* of the opening where it is received by the studding and in tliis way 'carried down to the sill. Such a truss is shown in Fig. 73. The pieces used are three by four or four by four, and may be" either framed into the other members or merely spiked. There should be a space D of at least one inch between the piece B forming the top of the window frame and the piece E form- ing the bottom of the truss, so that if the truss sags at all it will not affect the window frame. This is a point that is not generally recognized. The piece B is usually made to serve both as the top of the window and the bottom of the truss. Fig. 74 shows the fi-aming for the top of a window opening in a balloon-framed building, Avhere the ledger-board is partly sup- ported by the studs directly over the opening. Since the floor joists rest on the ledger-board, there may be considerable weiglit carried onto these studs ; and to prevent the bottom of the truss from sacrinnjr under this weight, a rod should be inserted as shown. Fiff. 73. Truss over Window. 58 k •-1 o o < o 3C u » H O M H S o < u N (/} >- CQ CC < O <; a X u s o s u S 3 PQ c/: O ■rH *^ •a 3 o fa o n o a a 03 g «© U) c: a s MH .^ i3 IS t£i •J w •J ce •-r ^ . w o ^ O 3 < o o 2 K ■$ . o ^-5 H d w o o --- w -E H MS « K K ^C O M C cs go Z Mj^ < i:» S 2^ w -"5 S ^>> E £:: « o :j N ^ = c« t- - >- Ss n ceo: sa ^:!i < ^^ " 2o ^ lis t*" feO ° ^^ Z ^^ < ^ J, o oj: - cbO as » »■ u ii- z < 5 11 _J n 2t w S-^ 0)- s S" >^ u cd a alt J < u »- o w t, h- ": U) E "^ a)-- E :: ■ S cS K "5 ^- (D s a: SI L- *s 3 n CQ c3 ^ « OS 3 O n CARPENTRY 51 In the balloon fnune, the door and window studs are almost always made of two two-by-foilr pieces i)laced close together, and in this case the connection of the pieces forming tlie top and Fig. 74. Truss over Window. Balloon Frame. bottom of the frame with those forming the sides is made as shown at A in Fig. 75. It should be noticed that in a balloon frame all studding is carried clear up from the sill to the plate, so that if there is an opening in the wall of the first story, and no corresponding open- ings in those of the second or third story, the door and window studding must still be carried double, clear up to the plate, and material is thus wasted. In designing for balloon frames, therefoi-e, it is well to take care that the window openings in the second story come directly above those in t!ie first story wherever this is possible. The same difficulty does not occur in the case of a braced frame, because in such a frame the studding in each story is independent of that in the story above or below it, and the openings may be arranged independently in the different stories. Fiff. 75. 59 52 CARPENTRY Nailing Surfaces. Wlieievur a partition meets an outside wall, a stud wide enough to extend beyond the partition on both sides and afford a solid nailing for the latliing must be inserted. A nailing surface must be provided for the lathing on both the outside wall and the partition, and the first stud in the partition wall is therefore set close up against the wall stud, forming a solid corner. This arrangement is shown in plan in Fig. 76. The large wall stud A is usually made of a four-by-eiglit piece set flat- wise in the wall so that if the partition is, say, four inches wide, there is a clear nailing surface of two inches on each side of the partition. A four-l)y-six piece could also be used here, leaving a clear nailing surface of one inch on each side of the partition. 3 F==, Fig. 76. Fig. 77. Fig. 78. Arrangement of Studding for Nailing Surfaces. Sometimes the same thing is accomplished by using two four- by-four pieces placed close together as shown in phin in Fig. 77, instead of one four-by-eight piece. Sometimes two pieces, two-by- four or three-by-four, are used, placed far enough a[)art so that they afford a space for nailing on each side of the partition, as shown in plan in Fig. 78. Whenever this is done, small blocks A, Fig. 79, should be cut in between the two studs at intervals of two to three feet throughout their height, to give them added stiff- ness and make them act together. The end in view in every case is to obtain a solid corner on each side of the partition where it joins the wall, and any con- struction winch accomplishes this is good. In the best work, however, the four-by-eight solid piece is used, and this construc- tion can always be depended upon. It makes no difference what the angle between the wall and the partition may be, but usually this angle is a right angle. Intermediate Studding. The pieces which make up the largest part of the wall frame are tlie " filling-in," or " intermedi- ate " studs. These, as the name implies, are used merely to fill up the frame made by the other heavier pieces, and afford a nail- 60 CARPEXTIIY ing surface for the boarding, which covers the frame on the out- side, and the hithing, which covers it on the inside. The filUng-in studs are usually placed sixteen inches apart, measured from the cenl;er of one stud to the center of the next. In especially good work they are sometimes placed only twelve inches apart on cen- ters, but this is unusual. In no case should they be placed more than sixteen inches apart, even in the lightest work. The studs are made the full width of the wall, usually four inches, but some- times in large buildings (such as churches) five or even six inches. They are almost always two inches thick, two by four being the ordinary dimensions for studding, and the lengths are cut to fit the rest of the frame. In the braced frame, 'there must necessarily be a great deal of cuttincT of the intermediate stud- ding, because all the large pieces are made the full width of the wall, and the intermediate stud- ding mast be cut to fit between them. In the balloon frame, how- ever, the intermediate studding in all cases extends clear up from the sill to the plate, and no cutting is necessary except the notching to receive the other parts of the frame. • (See Fig. 53.) In a balloon frame it often happens that the studs are not long enough to reach from the sill to the plate and they must be pieced out with short pieces which are spliced onto the long stud. This splicing is called "fishing," and it is accomplished by nailing a short, thin strip of wood A A on each side of the stud as shown in Fig. 40 in order to join the two pieces firml}' together. The strips should be well nailed to each piece. All door and window studs should have a tenon cut at the foot of the piece to fit a mortise cut in the sill. Intermediate studs are merely spiked to the sill without being framed into it. The tenons are cut in two different ways, as shown in Figs. 80 and 81. They are always made the full thickness of the piece, an^ by the first method they are placed in the middle of the Fig. 79. Wall Studdincr. 61 54 CARPENTliY piece, as shown. The width of the tenon is about one and one- lialf inches, leaving an inch and a-half on the outside and one incli on the inside of the stud. Another way is to make the tenon on the inside of the stud, as shown in Fig. 81, tlie tenon being an inch and a-half wide as before. There is no choice between these two methods, both being good. Partitions. The studding used in partition walls is usually of two- by-four stuff, although two-by-three studding may sometimes be used to advantage if the partition does not support any floor joists. The partition walls are made four inches wide, the same as in the outer walls, except in the case of so-called " furring " par- titions. These are built around chimney breasts and serve to conceal the brickwork and furnish a surface for plastering. They are formed by placing the studding flatwise, iii order to make a thin wall; and as it is usually specified that no woodwork shall _^ = T, come within (tne inch of any mA ,. .ri ,,,,, , ,,,, « i ^ chimney, a one-inch s})ace is letx between the brickwork iwid the Fig. 80. TeuousforStuds. Fig.81. Fig. 82. Plastering around Chimney. furring wall. It is possible to apply the plaster directly to the brickwork, and this is sometimes done, but there is alwitTy-s danger that cracks will appear in the plastering at the corner A, Fig. 82, between the chimney breast and the outside wall. This cracking is due to the unequal settle- ment of the brickwork aiul the woodwork, since the plastering goes with the wall to which it is applied. The method of con- structing the furring wall is shown in plan in Fig. 83. A A are the furring studs, B is the plastering, and C C the studding in the outside wall. The arrangement without the furring wall is shown in plan in Fig. 82. If there are any openings in the furring wall such as fireplaces, or "thimbles" for stove pipes, it is necessary to frame around them in tlie same way as was explained for door and window o[)enings in the outside walls. 62 CARPENTRY 55 See Fig. 84. A A are furring stuus, B B ure pieces forming the top and bottom of the opening. Fig. 83. Furring Wall around Chimney. Masonry Walls. If the outside walls of the building are of brick or stone, a wooden " furring " wall is usually built just inside of the outer wall ; this furnishes a surface for plastering and for nailing the inside finish. The studding for these walls is two-by-four or two-by-thvee set close up against the masonry wall A- Fig. 84. Opening for Thimble. Fig. 85. Furring for Brick Wall. and preferably spiked to it (see Fig. 85). Spikes are usually driven directly into the mortar between the bricks or stones of the wall, but sometimes wooden blocks or wedges are inserted in the masonry wall to afford a nailing. "Wherever a wooden partition wall meets a masonry exterior wall at an angle, the last stud of the partition wall should be 63 56 CARPENTRY securely spiked to the inasoiiiy wall, to prevent cracks iu tlio plastering. Cap and Sole. All partition walls are finished at the top and hottom by horizontal pieces, called respectively the cap and the sole. The sole rests directly on the rough flooring whenever there is no partition under the one which is being built ; but if there is a partition in the story below, the cap of the lower par- tition is used as the sole for the one above. The sole is made wider than the studding forming the partition wall, so that it pro- jects somewhat on each side and gives a nailing for the plasterer's Fig. 86. Sole Piece. Fig. 87. Partitioa Cap. grounds and for the inside finish. It is usually made about two inches tliick and five and a-half inches wide, when the partition is composed of four-inch studding, and this leaves a nailing surface of three-quarters of an inch on each side. The sole is shown at B in Fig. 86. The cap is usually made the same width as the stud- ding, and two inches thick, so that a two-by-four piece may be used in most cases ; but if the partition is called upon to support the floor beams of the floor above, the cap may liave to be made three or even four inches thick, and some architects favor the use of hardwood such as Georgia pine for tlie partition caps. The cap is shown at A, Fig. 87. Bridging, in order to stiffen the partitions, short pieces of studding are cut in between the regular studding in such a way as to connect each piece with the pieces on each side of it. Thus, if one piece of studding is for any reason excessively loaded, it will 64 CARPENTRY 57 not have to carry the whole load alone but will be assisted by the other pieces. This operation is called " bridging," and there are two kinds, which may be called "horizontal bridging" and "diag- onal bridging." The horizontal bridging consists of pieces set in horizontally between the vertical studding to form a contmuous horizontal line across the wall, every other piece, however, being a little above or below the next piece as shown in Fig. 88. The pieces are two inches thick and the full width of the studding ; and in addi- tion to strengthening the wall, they prevent fire or vermin from passing through, and also may be utilized as a naihng surface for any inside finish such as wainscoting or chair rails. The second method, which we have called diagonal bridging, is more effective in preventing the partition from sagging than is the straight bridging, but both methods may be used with equal propriety. In the diagonal bridging the short pieces are set in diagonally as is shown in Fig. 89, instead of horizontally, between the vertical studding. Tliis method is cer- tainly more scientific than the other, since a continuous truss is formed across the w^all. All partitions should be bridged by one of these methods, at least once in the height of each story, and the bridging pieces should be securely nailed to the vertical studding at both ends. It is customary to specify two tenpenny nails in each end of each piece. Bridging should be placed in the exterior walls as well as in the partition walls ; and as a furtlier precaution against fire, it is good practice to lay three or four courses of brickwork, in mortal-, on top of the bridging in all walls, t^revent the fire from gaining headway in the wall before burning waugli and being discovered. This construction is shown in Fig. 90. Special Partitions. A partition in which there is a sliding door must be made double to provide a space into which the door Fig. 88. Horizontal Bridging. 65 58 CAPiPEXTRY may slide when it is open. This is done by buihling two walls far enough apart to allow the door to slide between them, the studding being of two-by-four or two-by-three stuff, and placed either flatwise or edgewise in the wall. If the studdii)g is placed flatAvise in the wall, a thinner wall is possible, but the construction is not so good as in the case where the studs are placed edgewise. if the partition is to support a floor, one wall must be made at least four inches thick to support it, and the sttids in ,he other wall Fig. 89. Diagonal Bridging. Fig. 90. Brick Work on Bridging. may then be placed flatwise if desired, and the floor supported entirely on the thick wall. The general arrangement is shown in plan in Fig. 91. It is better to use two-by-three studding set edgewise in each wall so as to make two three-inch walls with space enough between to allow the door to slide freely after the pocket has been lined with sheathing. A piece of studding A, Fig. 92, should be cut in horizontally between each pair of studs B, eight or ten irches above the top of the door, in order to keep the pocket true and square. The pocket should be lined on the inside with matched sheathing C. It is well known thjit ordinary partitions are very good con- dirctors of sound ; and in certain cases, as in te-nement houses, this is objectionable, so that special construction is required. If tw© 66 CARPENTRY 59 walls are bui-t entirely separate from each other, and not touching at any place, the transmission of sound is much retarded; and if heavy felt paper or other material is put in between the walls, the partition is made still more nearly sound-proof« In order to decrease tlie thickness of guch a wall as much as possible, the "staggered" partition is used, in which there are two sets of stud- ding, one for each side of the wall, but arranged alternately instead of in pairs as in the double partition. The arrangement is shown in plan in Fig. 93. The two walls are entirely separate from each other and the felt paper may be worked in between the studs as shown, or the whole space may be packed full of some sound-proof and fireproof material such as min- eral wool. There is a so-called "quilting paper" or "sheathing quilt " manufactured from seaweed, which is much used for this pur- pose The inside edges of the two :^s -^ -^ ■- •- h ^ -TiS. m^ 'm ■- -~ ■- ^ Fig. 91. Double Partition for Sliding Door. Fig. 92. Double Partition. Fig. 93. Sound-proof Partition. sets of studs are usually placed on a line, making the whole wall eight inches thick where four-inch studding is used, and the studs may be placed about sixteen inches on centers in each wall. Each set of studding should be bridged separately. Another case where a double wall may be necessary, is where pipes from heaters or from plumbing fixtures are to be carried ui the wall In case of hot pipes, care must be taken to have the space large enough so tliat the woodwork will not come danger- ously near the pipes. 67 00 CARPENTRY An important matter in connection with the framing of the partitions is the way in which they are supported ; but this involves knowledge of the framing oi the floor, and therefore it will be left for the present. It will 'jn taten up after we have considered the floor framing. Shrinkage and Settlement. An important point which must be considered in connection with the framing of the walls and partitions, is the settlement due to the shrinkage of timber as it seasons after being put in place. Timber always shrinks con- siderably across the grain, but very little in the direction of the grain ; so it is the horizontal members such as the sills, girts, and joists which cause trouble, and not the vertical members such as the posts and studding. Every inch of horizontal timber between the foundation wall or interior pier and the plate is sure to con- tract a certain amount, and as the walls and partitions are sup- ported on these horizontal members, they too must settle somewhat. If the exterior and interior walls settle by exactly the same amount, no harm will be done, since the floors and ceilings will remain level and true as at first ; but if they settle unequally, all the levels in the building will be disturbed, and the result will be cracking of the plastering, binding of doors and windows, and a general distortion of the whole frame. This must be avoided if possible. It is evident that one way to prevent unequal settlement, sc far at least as it is due to the shrinkage of the timber, is to make the amount of horizontal timber in the exterior and interior walls, equal. Thus, starting at the bottom, we have from the masonry of the foundation wall to the top of the first-floor joists in the out- side walls, ten inches, or the depth of the joists themselves, since these rest directly on the top of the wall. In the interior we have, if the joints are framed flush into a girder of equal depth, the sqjne amount, so that here the settlement will be equal. But the studding in the exterior wall rests, not on the top of the joists, but on the top of the six-inch sill, while the interior studding rests on top of the ten-inch girder. Here is an inequality of four inches which must be equalized before the second floor level is readied. If the outer ends of the second-floor joists rest on the top of an eight-inch girt, and the inner ends on a four-inch par- 68 CARPENTRY 61 titioii cap, this equalizes tlie horizontal timber inside ami outside, and the second tloor is safe against settlement. The same process of equalization may be continued to the top of the building, and if this is done it will go far- toward preventing the evils resulting from settlement and shrinkage. With a balloon frame this cannot be done, because there are no girts in the outside walls, but only ledger-boards which are so fastened that they cannot shrink, while in the interior walls we have still the partition caps. All that can be done iu this case is to make the depths of the sills and interior girders as nearly equal as possible, and to make the partition caps as shallow as will be consistent with safety. THE FLOORS. After the wall, the next important part of the house frame to be considered is tlie floors, which are usually framed while the wall is being put up and before it is finished. They must be made not only strong enough to carry any load which may come upon them, but also stiff enough so that they will not vibrate when a person walks across the floor, as is the case in some cheaply-built houses. The floors are formed of girders and beams, or "joists," the girders being large, heavy timbers which support the lighter joists when it is impossible to allow these to span the whole distance between the outside walls. Girders are generally needed only in the first floor, since in all the other floors the inner ends of the joists may be supported by the partitions in the floor below. The}- are usually of wood, though it may sometimes be found economical to use steel beams in large buildings. Wrought iron was once used, but steel is now xjheaper and has taken the place of Avrought iron. It is rarely, however, that this will be found expedient, and hard pine girdei-s will answer very well in most cases. The conn^tions used in the case of steel girders will be explained later. The girders may be of spruce or even of hemlock, but it is hard to get the hemlock in such large sizes as would be required for such girders, and spruce, too, is hardly strong enough for the purpose. Southern pine, therefore, is usually employed for girders in the best work. 69 G2 CARPENTRY The size of the girdei- depends on the span, or the distance between the supporting walls, and upon the loads which the floor is expected to carry. In general, the size of a beam or girder varies directly as the length of the span, so that if we have two spans, one of which is twice as great as the other, the girder for tlie longer span should be twice as strong as the girder for the smaller span. In ordinary houses, however, all the girders are made about eight by twelve inches in section, although sometimes an eight-by-eight timl)er would suffice, and sometimes perliaps a twelve-inch piece would be required. It should be remembered in deciding upon the size of this piece, that any girder is increased in strength in direct proportion to the width of the timber (that is, a girder 12 inches wide is twice as strong as one 6 inches wide), but in direct proportion also to the square of the depth (that is, a girder 12 inches p. Q^ deep is four times as strong as one 6 inches deep). Hence the most eco- nomical girder is one which is deeper than it is wide, such as an eight-by-twelve stick; and the widtii may be decreased by any amount so long as it is wide enough to provide sufficient stiff- ness, and the depth is sufficient to enable the piece to carry the load placed upon it. If the piece is made too narrOAV in proportion to its depth, however, it is likely to fail by '* buckling," that is, it would bend as shown in Fig. 94. The width should be at least equal to one-sixth of the depth. There are at least three ways in which the joists may be sup- ported by the girder. The best but most expensive method is to support the ends of the joists in patent hangers or stirrup irons which connect with the girder. This method is the same as was described for the sill, except that with the girder a double stirrup iron, such as that shown in Fig. 95, may be used. These stirrup- iron hangers are made of wrought iron, two and one-half or three inches wide, and about three-eighths of an inch thick, bent into the required shape. They usually fail by the crushing' of the wood of the girders, especially when a single hanger, like thut 70 CAflPENTIir 63 shown ill Fig. 96, is used. Fig. 97 shows a double stirrui>iron hanger in use. Patent liangers as shown in Fig. 98 are by far the best. If hangers of any kind are used, there will be no cutting of the girdtir except at the ends whei-e It frames into the sill, and even there a hanger may I>e used. The girder may be placed so that the joists will be flusli with it on top, or so that it is flush Fig. 95. Fig. 90. with the sill on top. If the joists are flush with the girder on top, and are framed into the sill in the ordinary way, as shown in Fig. 99, the girder cannot be flush on top with the sill ; wliile, on the other hand, if the girder is flush Avith the sill on top, it cannot at the same time be flush with the joists on top. If joist hangers are used on the girder to support the joists, they will probably be Iron v3t>r; I o-o mST rLODD PLAN aoum ELUEMOTOM STABLE FOR MR. J. S. HANNAH, LAKE FOREST, ILL. Shepley, Rutan & Coolidge, Architects, Chicago, 111. For Location, See Vol. I, Page 74; for Exterior and Plans of House, See Vol. I, Pages 74 and 90. / CAKPENTKY G7 the floor joists, unless it lias auotlier partition under it. Such partitions may be supported in several different ways : A very heavy joist, or two joists spiked together, may be placed under the partition, as shown at A in Fig. 105. In this figure, C is the sole, B the under or rough flooring, and D, D, D the studding. 'JMiis metliod is objectionable for two reasons : It is often found convenient to run pipes up in the partition, and if the single joist is placed directly under the partition this cannot be done" except rtfr Fig. 105. Joists Supi)orting Partition. Fig. 106. by cutting the joist and thus weakening it. Moreover, if the single joist is used, there is no solid nailing for the finished upper flooring, unless the joist is large enough to project bej-ond the partition studding on each side. Tlie joist is seldom, if ever, large enough for this, and the finished floormg must therefore be nailed only to the under flooring at the end where it butts against the partition, so that a weak, insecure piece of work is the result. This may be seen by referring to the figure. A much better way is to use two joists far enough apart to project a little on each side of the partition, as shown at A, A in Fig. lOG, and thus afford a nailing for the finished flooring. These joists must be large enough to support the weight of the partition without sagging any more than do the other joists of the floor, and therefore joists three or even four inches thick should be used. Tiiey should be placed about six or seven inches apart on centers, and plank bridging should be cut in between them at intervals of from fourteen to twenty inches (as shown at E in Fig. 106), in order to stiffen them and make them act together. This plank bridging should be made of pieces of joist two inches 75 68 CARPENTRY Fig. 107. Partition Supported by Strips. thick and of the same depth as the floor joists, and shoukl be so placed that the grain will in every case be horizontal. A partition supported as described above is bound to settle somewhat as the ten or more inches of joist beneath it shrinks in seasoning, and the settlement may cause cracks in the plaster- ing at the corner between the partition and an outside wall. In order to prevent this settle- ment, partitions running parallel with the floor joists are often supported on strips which are nailed to the under side of the floor joists, as shown at A in Fig. 107. These strips cannot be allowed to project into the room below, and so they must be made as thin as possible consistent with safety. Strips of iron plate about one-half inch thick, and wide enough to support the partition studs, are therefore used for this purpose, and are fastened to the joists by means of bolts or lag ^^^.^ screws. Partitions which run - at rioht ano^les to the floor joists can also be supported in this way. If a partition runs at right angles to the joists near the center of their span, the tendency for the joists to sag under it will be very great, and they must be strengthened either by using larger joists, or by placing them closer together. If the span of the floor joists is large and the partition is a heavy one, it may be necessary to put in a girder running at right angles to the joists to carry the partition. In this case the partition studs will set directly on the girder, which may be a large timber, or in some cases, a steel I-beam. Fi". 108. Headers and Trimmers. 76 CARPENTRY 69 FijT. 109. Connection of Joist to Sill. Headers and Trimmers. Another case where a girder may be necessary in a floor above the first, is where an opening is to be left in the floor for a chimney or for a stair well. Tlie timbers on each side of such an opening are called "trimmers," and must be made heavier than the ordinary joists; while a piece called a "header" must be framed in between them to receive the ends of the joists, as shown in Fig. 108. The trimmers may be made by simply doubling up the floor joists on each side of the open- ing, or, if necessary, I-beams or heavy wooden girders may be used. In most cases these trim- mers may be built up by spiking together two or three joists, and the header may be made in the same way. Joist Connections. Joists are also " gained " into the sill as shown in Fig. 56, in which case a mortise is cut in the sill and a corresponding tenon is cut in the end of the joist. The mortise was illustrated and described in connection with the sill, while the end of the joist is cut as shown in Fig. 56, the tenon being about four inches deep and gained into the sill about two inches. This brings the bottom of the joist flush with the bottom of the sill, and the top of the joist somewhat above the top of the sfll, according to the depth of the joist. The top of a ten-inch joist would come four inches above the top of a six-inch sill, and the joist would rest partly on the masonry wall as shown in Fig. 100, thus relieving the connection of a part of the stress due to the weight of the loaded joist. A common but very bad method of framing the joist to the sill is simply to " cut it over " the sill without mortising the latter, as shown in Fig. 109. This does not make a strong connection even when the joist rests partly on the masonry wall; and if it is not so supported it is almost sure to fad. by splitting, as shown in Fig. 110, under a very small loading. In fact, it would be much stronger if the joist were turned upside Fiff. 110. T7 70 CARPENTRY down. Frequently the joist is cut as shown in Fig. Ill, where the tenon is sunk into a mortise cut in the sill, thus bringing the top of the joist flush with the top of the sill ; but iu this case the bottom of the joist will almost invariably drop below the bottom of the sill, and the wall must be cut away to make room for it, as shown in Fig. 102. It is also weak in the same way as is the connection shown in Fig. 110. The frammg of the joists into the girders may be accom- plished in several different ways, according to the posi- tion of the girder. This plac- ing of the girder is quite an important point. The top of the floor, on which rest the sole-pieces of the cross-par- titions, must remain always true and level, that is, the outside ends of the joists must be at the same level as the inside ends. Otherwise the doors in the cross-partitions will not fit their frames, and cannot be opened or shut, and the plastering is almost sure to crack. Both ends of the joists will sink somewhat, on account of the shrinkage of the timber in seasoning, and the only way to make sure that the shrinkage at the two ends will be the same is to see that there is the same amount of horizontal timber at each end betw^een the top of the floor and the solid masonry. This is because timber shrinks very much across the grain, but almost not at all along the grain. If the joist Fig. 111. Joist Mortised into Sill. Fig. 112. Joist Framed into Girder. is framed properly into the sill, so that it is flush on the bottom with the sill, we have at the outer end of the joist a depth of horizontal timber equal to the depth of the joist itself, as shown in Fig. 100; and in order to have the same depth of timber at the inside, the bottom of the joist must be flush with the bottom of the girder, which usually rests on brick piers. Of course the top of the gii'der must not in any case come above the tops of the floor joists; therefoie, in general, the 78 CARPENTIJY 71 girder must be equal in depth to the floor joists and flush with tliese joists on top and bottom, as shown in Fig-. 112. This method is not always followed, however, in spite of its evident superiority ; and the girder is often sunk several inches below the tops of the floor joists, as shown in Fig. 100, or even in some cases very much below, as shown in Fig. 113. Both of these methods cause an unsightly projection- below the ceiling of the cellar. Where the joists are brought flush with the girder top and bottom, they may be framed into it with a tenon- and-tusk joint, the joists being cut as shown in Fig. 101, with a tenon as there shown, and a hole bored through the tenon to receive a pin to hold the joist in place. Other methods of fram- ing tenon-and-tusk joints are shown in Figs. 33, 34, and 35, and also a double-tenon joint in Fig. 36, which might be used in this case, although it is much inferior to the tenon-and-tusk joint. Two joists framing into a girder from opposite sides should be fastened strongly together, either by an iron strip passing over the top of the girder and secured to each joist, as shown in Fig. 114, or by means of a "dog" of romid bar iron, which is bent at Fig. 113. Joist Sized Down on Girder. Fig. 114. Use of Straps and Dogs. Fig. 115. the ends and sharpened so that it may be driven down into the abutting ends of the joists, as shown in Fig. 115. These bars should be used at every fifth or sixth joist, to form a series of continuous lines across the building from sill to sill. If the girder is sunk a little below the tops of the joists, these may be gained into it in the same way as they are gainctl 79 72 CARPENTRY into the sill. In this case joists should be arranged as shown in Fig. 116, so that they will not conflict with one another; and the two adjacent joists may be spiked together, thus giving additional stiffness to the floor. If the tenon-and-tusk connection is used, the joists may be arranged exactly opposite each other, provided that the girder is sufficiently wide, but it is alwa3'^s much better to arrange them as shown in Fig. ^\. \^^ ^^ 117, even in this case. The tenon may then be carried clear through the girder and fastened by a dowel, as shown. Very rarely a simple double- tenon joint, such as that shown in Fig. 36, might be used, but it is much inferior to either the gaining or the tenon-and-tusk joint. If the girder is sunk very much below the tops of the joists, as in Fig. 113, these will usually rest on top of it and be fastened by spikes only, or will be " sized down " upon it about one inch, as shown. There is no mortising of- the girder in either case. Joists are also thus sized down upon the girts and partition caps, and are uDtched over the ledger-boards as shown in Fig. 67. In cutting the joists for sizing and notching, the measurements should be taken in every case from the toji of the joists, since they may not all be of exactly the same depth, and the tops must all be on a level after they are in place. This is really the only reason why the joists should be sized down at all, because otherwise they might simply rest upon the top of the girder, or girt, and be fastened by nailing. Connection to Brick Wall. When a joist or girder is sup- ported at either end on a brick wall, there will either be a hole Fig. 116. Joists Framing over Girder. Fig. 117. 80 CARPENTRY 73 left ill the wall to receive it, or the wall will be corbeled out to form a seat for the beam. If the beam enters the wall the end should be cut as shown in Fig. 118, so that in case of the failure of the beam from overloading or from fire, it may fall out without injuring the wall. Every fifth or sixth joist is held in place by an "^C ^m ^m Fig. 118. Joist Supported by Brick Wall. Fig. 119. Use of Anchor. anchor (as shown in Fig. 119), of which there are several kinds on the market. Fio-. 120 shows the result when a beam which is cut off square on the end, falls out of the wall. There must always be left around the end of a beam which is in the wall a sufficient space to allow for proper ventilation to prevent dry rot, and the end should always be well painted to keep out the moisture. Patent wall-hangers and box anchors are often used to support the ends of joists in brick buildings, but only in case of heavy floors. The floor framing in a brick building is the same as that in a building of wood except that there is no girt to receive the ends of the floor boards, so that Fig. 120. a joist must be placed close against the inside of the wall all around the building to give a firm nailing for the flooring. Crowning. In any floor, whether in a wood or a brick building, if the span of the floor joists is very considerable so that 81 74 CARPENTRY there is any chance for detiectiou they must be "crowned" in order to offset the effect of such deflection. The operation called "crowning" consists in shaping the top of each joist to a slight curve, as shown in Fig. 121 B, so that it is an inch or so higher in the middle than it is at the ends. As the joist sags or deflects, the top becomes level while the convexity will show itself in the bot- tom as shown in Fig. 121 A. Joists need not be crowned unless the span is quite large and the loads heavy enough to cause a deflection of an inch or more at the center of the joist. Fig. 121A. Crowning. Fig. 121B. Bridging. Floor frames are "bridged" in much the same way as was descril)ed fr)r the walls, and for much the same i)ur- pose, namely, to stiffen the floor frame, to prevent unequal deflec- tion of the joists, and to enable an overloaded joist to get some assistance from the pieces on either side of it. Bridging is of two kinds, "plank bridging" and "cross bridging," of which the first has alreadv been shown in connec- ticn with the partition supports. Plank bridging is not very effective for stiffening the floor, and cross bridging is always preferred. This bridsrinof is somewhat like the diajronal bridmng: used in the walls, and consists of pieces of scantling, usually one-by-three or two-by-three in size, cut in diagonally between the floor joists. Each jnece is nailed to the top of one joist and to the ■ bottom of the next; and two pieces which cross each other are set close tosxether between the s:vme two joists, forming a sort of St. Andrew's cross, whence we get the name "cross bridging," or "herring-bone bridging " as it is sometimes called. The arrangement is shown in Fig. 122, and the bridging should be placed in straight lines at intervals of eight or Fig. 122. Diagonal Bridging. 89 CARPENTRY 10 ten feet across the whole length of the floor. Each piece should be well nailed with two eightpeniiy or tenpenny nails in each end. If this is well done there will be formed a kind of con- tinuous truss across the whole length of the floor which will pre- vent any overloaded joist from sagging below the others, and which will greatly stiffen the whole floor so as to prevent any vibration. The bridging, however, adds nothing to the strength of the floor. Porch Floors. A word might appropriately be inserted at this point in regard to the floors of piazzas and porches. These luay be supported either on brick -piers or on wooden posts, but preferably on piers, as these are much more durable than posts. If piers are used, a sill, usually four by six in size, should be laid on the piers all around, and light girders should be inserted between the piers and the wall of the house in order to divide the floor area into two or three panels. The joists may then be framed parallel to the walls of the house, and the floor boards laid at right angles to these walls. The whole frame should be so constructed that it will pitch outward, away from the house at the rate of one inch in five or six feet, thus bringing the outside edge low^er than the inside edge and giving an opportunity for the water to drain off. 5tairs. The stairs are built on fi'ames called " stringers "or "carriages," which may be considered as a part of the floor fram- ing. They consist of pieces of plank two or three inches thick and twelve or more inches wide, which are -cut to form the steps of the stairs and which are then set up in place. There are usually three of these stringers under each flight of stairs, one at each side and a third in the center, and they, are fastened at the bottom to the floor and at the top to the joists which form the stair well. This subject will be taken up more fully under "Stair Hnilding." Fig. 123. Support of Corner. 76 CAKPENTKY Unsupported Corners. An interesting place in a floor fram- ing plan is where we have a corner without any support beneath it, as at the corner a in Fig. 123. This corner must be supported from the three points ?>, c, and d, and the figure shows how this is accomplished. A piece of timber e is placed across from h to c, and another piece starts from d and rests on the piece h 1> a.re Jtrcl- rafters which are shorter than the common rafters and which do not extend from the plate to the ridge, but a aa Fig. 134. Framing Plan of Roof. are connected at one end to a hip or vallci) rafter, e c are the valley rafters, ^vhicll are needed at every corner between the main building and an ell or other projection, while the hip rafters are found at every outside corner. At the points where the val- ley rafters are situated there are troughs or valleys formed by the roof surfaces — as these pitch downwards on l)oth sides toward the valley rafter — while at the outside corners, M'here the hip rafters are found, the roof surfaces pitch upward on each side to the hip rafter. This may be seen by looking at any hip and valley roof as actuallv constructed. 90 > CO •a o o g I o O O 4> o o o 73 CAKPENTRY 81 111 pitcli or gable roofs there are no hip rafters, hut there may be valley rafters and jack rafters, while common rafters are to be found in all roofs. The Ridge. In the lean-to roof the rafters rest at the top against the wall of the building of which the ell, or porch, is a part; and the framing of the roof consists simply in setting them up and securing them in place with spikes or nails. The pitch roof, however, is formed on the principle that two pieces which are inclined against each other will hold each other up, and so the rafters must rest against each other at the top in pairs, as shown in Fig. 135. It is customary to insert between the rafters, at the top, a piece of board about one inch in thickness and deep enough Fig. 135. Top of Rafters. Fig. 136. Ridge Pole Between Tops of Rafters. to receive the whole depth of the rafter, as shown at a in Fig. 136. This piece of board is called the Tidge or the ridge pole and extends the whole length of the roof. It serves to keep the rafters from falling sideways, and keeps the roof frame in place until the roof boardino- is on. It is sometimes e.xtended above the rafters, and forms a center for some form of metal finish for the ridge, as shown in Fio-. 137. Interior Supports. In small roofs which have to cover only narrow buildings and in which the length of the rafters is small, there is no necessity for any interior support. When the rafters have been cut to the correct length, set up against the ridge, and secured in place, the framing is complete. In roofs of large span, however, the rafters would sag in the middle if they were not streno-thened in some way, so it is customary to put a vertical sup- port under them. This support may be formed by placing a piece 81 82 CARPENTRY of Btudding under each rafter, somewhere between the j)late and the ridge, and if this is done very much lighter rafters can be used than would otherwise be considered safe. It is claimed by some that it is cheaper to do this than to use the heavy rafters. A more common way of supporting the long rafters is to use fewer upright pieces and to place a horizontal piece a on top of them, running the whole length of the building and supporting each rafter. This is shown in Fig. 138. An upright piece h should be placed under every sixth or seventh rafter in order to give the necessary stiffness to the whole construction. For the uprights, pieces of ordinary studding, two by four inches or two by three inches in size, may be used, "When there is to be a finished attic in the Fig. 137. Cross Section at Ridge Pole. Fig. 138. Support for Long Rafters. building these upright studs may be made to form the side walls of the attic rooms, and must then be spaced sixteen inches, or thereabouts, on centers. In this case a piece of studding could be placed under each rafter. Such walls are called choarf walls. Another form of interior support is the collar heam or tie heam. This is a piece of timber which extends between the rafters on opposite sides of the roof and ties them together, as shown at a in Fig. 139. It may be a piece of board about one inch thick and eight or ten inches wide, which is nailed onto the side of the rafter at each end. It is placed as near the center of the rafter as may be practicable, and in the case where a finished attic is required it forms the support for the ceiling. For this reason it must be at a considerable height from the attic floor, and 98 CARPENTRY 83 cannot always be placed very near the center of the rafter. The important point is to see .that it is well nailed at each end. A very interesting form of gable roof is that in which there is a double gable with a valley between, which forms the roof of Fig. 139. Tie Beam Support for Rafters. Fig. 140. Pitch Roof with Double Gable. the ell, the main roof being a simple pitch roof. This is shown in Fig. 140. Fig. 141 shows how such a roof may be framed. The piece a is placed in the wall and supported by the stiiddino- and serves as a plate to receive the ends of the pieces ^, which are val- Fig. HI. Framing for Double Gable. ley rafters. These, together with the piece c, form the framing for the shallow valley between the two gables. The valley rafters on the outside, marked d in the figure, are similar to those used 93 84 CARPENTRY in tlie case of a single gable. The pieces e e are jack rafters and are very short. This form of roof is not common, but in some places it gives a good effect. Framing of Qambrel Roof, A gambrel roof is framed in very much the same way as is a pitch or a hi|) roof. The slope of the roof, however, is broken at a point about midway between the plate and the ridge. The part of the roof above this break makes an angle with the horizontal plane of less than forty-five degrees, usually, while the portion below the break make an angle with the horizontal plane greater than forty-five degrees. This is shown in Fig. 126. The lower slope may almost be considered a part of the wall, and at the point where the slope changes there is a secondary plate from which the tipper slope starts, as shown at a in P^ig. 1-1:2. The second- ary plate may be utilized as a support for the ends of the ceiling joists 1>^ which should also be securely spiked to the rafters, as shown in the figure. The rafters r, forming the upper slope, must be cut over the plate a^ and firm- ly spiked to it, while at the top they rest against a ridge board d. The rafters between them and bisect this line at r. "With o as a center and c a as a radius describe the semicircle a d e fh. At any distance g above a h draw a line d f parallel to a 1>, cutting the semicircle at the points d and f. Also bisect the arc at e. Then by joining the points a d e y and h by straight lines as shown, we will have the out- line of a gambrel roof. The proportions of the roof may be varied by varying the distance g. Gambrel roofs are not very strong unless they are stiffened by cross partitions in the attic stories, and these should be provided whenever it is possible. Ko gambrel roof, unless it is well braced, should be used on a building which is exposed to high winds, or which is likely to receive a heavy weight of snow. Framing of Mansard Roof. A mansard roof is framed in very much the same way as is a gambrel roof, as may be seen in Fig. 144, Kesting on the main wall plate a we have a piece h which is inclined sliohtly inward, and which supports at its upper end a secondary plate e. On the plate c rests the outer end of the deck rafter d which is nearly horizontal. The piece h is a piece of studding, t^vo by four inches to four by six inches in size, depending upon the size of the roof. It supports the whole weight from the rafters, carrying it to the main wall plate and thence into the walls of the building. This member should always be straight, and the curved shape which is usual on mansard roofs is obtained by the use of the furring piece <\ This piece is nailed to the upright member b at the top, and at the bottom it is secured to the lool'oiit f Vih.\ch. also forms a support for the pro- jecting cornice. The floor joist g is supported on a ledger-board Fig. 144. Framing of Man- sard Roof. 95 S6 CARPENTRY //, or it may rest directly on the plate a. The piece of studding i is merely a furring stud to form the wall of the attic room. It may be omitted entirely if desired, or if the attics are to be unfin- ished. The ceiling joist h may be supported on a ledger-board as shown, or may be simply spiked to the studding i or to the upright J. The studding i may rest directly on the floor joists (j with a sole piece ^ at the bottom, as shown. The plate c should be of a good size, at least four by six inches, and should not be placed more than two or three feet above the ceiling joists h. The ceiling joists act as ties across the building and prevent the plates e from spreading apart, as they receive the thrust from the rafters d. For this reason it is better to have the ceiling joist h fastened to the upright h rather than to the furrincr stud %. o Dormer Windows. In Fisfs. 145 and 146 are shown what are known as dormer windows, this name being applied to all windows in the roofs of buildings, w^hatever may be their size or Fig. 145. Dormer Window. Fig. UG. Donuor Window. shape. The figures show two different kinds of dormers which are in general use, the one shown in Fig. 145 resting entirely on the roof, while the one shown in Fig. 14(3 is merely' a continuation of the wall of the building above the line of the eaves. The second type is often seen on low buildings, only one story in height, while the other kind is employed on larger structures. In order to construct a dormer M'indow an opening must be made in the roof surface, and the window must be built up over the opening. Headers are framed in between two of the rafteus as shown at a and h in Fig. 147, and thus a rectangular openmg is formed in the roof frame. The rafters c and d^ which form the sides of the opening, are called trimmers and should be much stronger than the common rafters. Usually the trijnmers are U6 CAKPEXTRY 87 made by doubling the ordinary rafters. The headers receive the ends of the rafters which are cut by the opening, and must be large enough to carrj- the weight which comes from them beside sup- porting the walls of the dormer. Timbers four by eight inches to six by ten. inches, according to the size of the dormer, are usually large enough for the headers and often smaller timbers may be safely used. The headers are shown in section at a and h in Fig. 148, and it will be noticed that they are not put in in exactly the same way. The piece at the top a is so placed that its longer dimension is at right angles to the plane of the roof, while the piece at the bottom h has its longer dimension vertical. In the case shown in Fio-. 146, where the front wall of the dormer is merely an extension of the main wall of the Fig. U7. Headers for Dormer Windows. Fig. 148. Longitudinal Sections Through Dormer Windows. building, there is no need of the lower header J, the main wall plate taking its place and supporting the studding for the front wall of the dormer, as shown at the ritfht hand side of Fio-. 14S. Fio;. 148 shows sections taken throuo-h two dormers of tho types mentioned above, parallel to the direction of the main rafters 07 88 CARPENTKY and at right angles to the main wall plate of the building. At the left is a section taken through the type of dormer shown in Fig. 145, while at the right a section of the other type is shown. The studs c c, which form the side walls of the dormer, are notched over the trimmer rafters and roof boarding about one inch, and allowed to continue downward to the attic floor. This is shown at J). At i measured aloncr the line of inter- section of the two roof surfaces. The point b corresponds to the point /" in Fig. 152, and a portion of the plate is shown at c. Referring to the plan in Fig. 153, we see that the line / vi is parallel to the ridge i ]i. so that the angle / in h determines the ])evel at the top of the rafter 1 in' is a right angle, so that the square of h III is equal to the square of h 1 plus the square of I 'in', and that the square of / ///' is equal to the square of / in ])lus the square of m m' . Kemembering that l> 1 represents just one foot of the span of the roof A, that 'in in' is the rise of the roof surface A per Fig. 155. ralc\il;ttinp: Length of V;illcy " Kafters. 106 « >. •a < CS . ^2 Ho £? S:i . ^ to j< 09 .-^ <: <- E ? " ^ ^ ^ i OS 3 *i rf - CO c •■;: ? - < 5 " - - =^ -> ■: o t X . o S = i Ml . ^ ' « 5 O r3 O W C5 a a o a = 5 Cf. -. X ■c- :&.^ ^8 .1- *» 00 » — 13 l« K O Wo (3 .. C ^ U 0) ^ a fl t> o a > « TtBBACB ^ L FIRST AND SECOND STORY PLANS OF HOUSE FOR MR. C. M. THOMPSON, CAMBRIDGE, MASS. Cram, Goodhue & Ferguson, Architects, Boston and New York. \ CARPENTRY 97 foot of ran, and that I rti is the run of the roof surface B which will give this same rise, it will be seen that the lenath h m' may- be easily obtained. By using the steel square we may avoid squar- ing all of these quantities. In Fig. 156, let us suppose that we have a piece of timber from which we wish to cut the valley rafter. Suppose that we have selected the point mJ as the starting point, corresponding to the pointy' in Fig. 152, and that we have made the foot cut as shown, and as explained above for the common rafters. We now wish to get theJength of the rafter so that we can make the plumb cut or down b&vel at the top of the piece. If we place the square along the edge of the piece as shown by the light full lines M^ith the dis- tance Hi 111 on the tongue and the distance I //i on the blade, we ? gives the cut. w'i: Fig. 158. Cutting Valley Rafters. . Fig. 159. Cutting Double Bevel. The double bevel at the point o in Fig, 153 is obtained, as shown in Fig. 159, by applying the square on both sides of the center line of the top edge of the rafter, using different values for 111 'III and VI I, according to the pitch of the roof surfaces. This gives the two cuts along the blade of the s(|iiare, in its two linal positions, shown by the full lines. It will be noticed that in making all of these cuts for valley rafters, there are two distances, vi vt and in /, which are used as starting points, and by which the position of the S(|uare on the piece is determined, vi vi, as has already been explained, is the 108 CARPENTRY 99 ("I'^e of one of the two inteiv ^etiiik roof surfaces, corresponding to a run of one foot, -while ni I is' tiie run of the other roof surface which corresponds to a rise of m in in this roof. These distances are easily determined from the pitch of the two intersecting roof surfaces, which is always known, and from them any bevel on any Valley rafter can be found, as well as the run, or Riuit^ of the valley rafter, its rise, its length, etc. Hip Rafters. Fig. 160 shows the plan of a roof in which there are some hip rafters. Ki one end we have a square hip A, and at the opposite end we have a skew hip B. The hip rafters are shown at a h^ a e, d . , and d f. They rest on the plate at the foot, and bear agains*: tlio ridge board a d at the top. At , which is twelve inches. Now supj)ose that tlie liney a e be drawn through the point (I ])erpendicular to the liij» line r/ y, and let it represent 4, is eight inches, as explained above, and we need only to find the distances // e and // /" in order to detern)ine the two bevels. The distances a e and a f in the plan, Fig. 1G8, are the same as // c and ///'in Fig. 1()4:. Kow let us find a e. The length of a h was assumed at the start to be twelve inches, and d h was found to be eight inches. On account of the similarity of triangles, — i is equal to :=— , so that }> e\^ -^ of a h. or eighteen inches. Then (( e must be about tweJity-one and one-half inches, and // e in Fig. 1()4:, is the same. We now know both Ji e and a h in Fig. 104, and these two distances determine the bevel of the line a e. In the same way, the distance A fmny be foiuid and the bevel of the line a f uiay be determined. It may somotiines be found more convenient to draw the roof plan accuiately to scale and then to scale the distances, instead of calculating th.3iii, but this amounts to the same noting in the ^^,,jj_ 'pjjy bevels of the liueiS df \ and a e may also be found gra[)h- \ ically as shown in Fig. 165. Sup- \ pose this plan to be drawn accu- \ rately to a fairly large scale, / Starting with the point a on the 'y^^ >4 hip line d y, we draw the line ~/r'Z'^\ ■ ^ ^ /■> perpendicular to the hip _ I /'I'jvv iine^ and the lines a l> and a c per- '^ ^ ^ peadicular to the wall lines d e ^'^' "^ViudhS^Beve^^'^'"'^ °' '"^^ ^^ /• 1^^»'"'» ^ ^^'^^ can draw the line h a" making the same angle with a h that the roof surface A makes with the horizontal plane. Then if if a" be drawn from a perpendicular to a h the dis- tance a a" will be equal to the actual elevation of the point (( above the point b. Thus distance can be laid off along the hip line, d (j perpendicular to the line/' a e, by swinging the point a" around Hi CARPENTRY 105 tO(^'. Then the distance a a is equal to the elevation of the point a above the point ^, and above the points e and / also. The lines a' e and a f make the same ancrle with the line fa e that the lines a e and a f\ in Fig. 104, make with the horizontal, and we can get the bevels from these lines. At PI is shown a small sec- tion taken vertically through the hip rafter, similar to the section of the rafter shown in Fio-. 164. Valley Rafters. In Fig. 106 we have a plan in outline of a part of a roof with a valley a Ij between the roof surfaces C and D and with ridges A c and b d. Let us assume the pitches of the roof surfaces to be, as before, eight inches to the foot for C and twelve inches to the foot for D. Assume a e to be twelve inches, and e /'will be eight inches and the point /'must be eight inches F'ig. 166. Roof with Valley and Ridges. / \ \ • Fig. \6'i. Method of Finding Bevels. above tlie points/, as explained in the case of the hip rafter. Since we know a e and e f in Fig. 166 Ave can find e i from the simi- larity of the triangles, as in the case of the hip rafter, and then we can find both a i and f L Ivnowincr a /, and knoM-ino; the pitch of the roof surface C", we can find the elevation of the point / above the point a. Since we know that the point/* is eight inches above the point a we can find the elevation of the point / above the point f, and this with the distance/' / Mill give the bevel of the line/ i iu Fig. 167. In the same way the bevel of the line/ / may be found. These bevels can be laid off on the vertical sec- tion of the valley rafter which is cut out when the foot cut is made, and the distances at which the tops of the jacks, E and F in Fig. 167, must be set above the top of the valley rafter g may be determined. In order that the lines/" / and // iu Fig. 167 inay come on the surface of the valley rafter section, they may be drawn 115 106 CARPENTKY •'4- Fig. 168. Grapbloal Method of Finding Bevels. sloping downward instead of upward, as shown at/"?'' andy/'. The j)oiiit/'is always in the center of the top edge of the valley rafter. Fig. 1()S shows how the bevels for the valley rafter may be found graphically. Starting with the point/' we can draw lines ofjh ^ ^ h ^nd a is shown another partition ninuing parallel to the ridge, and at 2> '2 still another, running 116 CARPENTRY 107 parallel to the rafters. Kow since all the rafters slope upwards from the plate to the ridcre, it is evident that the tops of all the studs must be cut on a bevel if they are to fit closely against the undersides of the rafters. This is illustrated in Fig. 170, where the stud A must fit ao-ainst the rafter B. dhJl ?n A i i k V / / / ^ , 9 i k / / /; '/ '/ n o ■ r B chJ I r Fig. 169. Framing Plan of Small Roof. Fig. 170. Connection of Studs and Rafters. To take the simplest case first, let us consider the stud marked r. Since all the rafters have the same pitch or slope, all the studs in the partition n 6> will have the same bevel at the top, and if we find the bevel for one we can cut the bevel for all. Fig. 170 shows this stud drawn to a larger scale and separated from the rest; a h c d is a plan of the stud, and the rafter is shown at efgh. We will take the distance /' Jl, or the run of the part of the rafter shown, as one foot exactly. Kow if A and B represent a side elevation of the rafter and stud looking in the direction shown by the arrow, the run, of the part of the rafter shown is the distance j q. and the distance q o should be equal to the rise of the rafter in one foot. Let the rise in this case be nine inches. Then Jv n shows the bevel of the top of the stud. If the stud is a two by four stick, the distance /.' /' is just four inches, or one-third of the run of the rafter, and consequently the distance r n is just three inches, or one-third of the rise of the rafter. In the case of the studs forming the partition q^ q i'l Fig- 161), the bevel is found in the same way, the only difference being that the rafter now crosses the stud, as shown in Fig. 171, where Fit 171 Rafter Stud and 117 108 CARPENTRY a h c ' h' c and d\ tjivincr the bevel shown in the figure. This bevel luay be cut by drawing any line all the way around the stud, S(iuare with tlie edcjes, as shown at m v. and laviiitJ" off front tliis line on tlie edges of the stud the distances a a'\ u' />'', c' <■", and d' d". Lines drawn across the faces of the stud con- necting the points so obtained M'ill give the exact bevel. Fig. 173. Stnrt and Diagonal R;iftLT. SPECIAL FRAMING. AVe have, in the preceding pages, considered the flaming M"hich enters intoa l>uildini£ of lio-ht construction, such as an ordi- nary dwelling house, but there are certain classes of structures which call for heavier framing, or framing of special character. Among these may be mentioned hattered frames, or frames Avith inclined walls; trussed partitions; in<-lined and bowled floors; special forms of reinforced beams and girders; the framing for balconies and galleries; tiiiil)er trusses; towers and spires; domes, pendentives and niches; and vaults and groins. T])ese subjects will be now taken up and discussed, and the methods employed in framing such structures will be explained. Battered Frames, ^onietinies it is necessary to build a structure with the walls inclined inward, so that they approach 118 CARPENTRY 109 each otlier at the top, and so that the top is smaller than the bot- tom. This is the case with the frames which support water tanks or windmills. An elevation of one side of a frame of this kind is shown in Fig. 173 with a plan in outline at A. It will be seen that the corner posts a a are inclined and approach each other at the top, so that they are not perpendicular to the sill at the bot- tom. This means that the foot of the post, where it is tenoned into the sill, must be cut on a bevel, and the bevel must be cut diagonally across the post, from corner to corner, since the post pitches diagonally toward the center, and is set so that its outside faces coincide approximately with the planes of the sides of the structure as indicated in the plan shown in Fig. 17-1:. The girts h. Fig. 17;), will also have to have special bevels cut at their ends, where they are framed into the posts. Pig. 173. Battered Frame. Fig. 174. Bevel of Corner Post After a corner post has been cut to the proper bevel to fit against the sill the section cut out at the foot will be diamond- shaped, as shown at a h c d in Fig. 171, which shows a plan of one corner of the sill. It will be noticed that the faces a h and a d of the post do not coincide with the edges of the sill « /"and a g. If the structure is merely a frame and is not to be covered over with the boarding on the outside, it is not necessary that the out- side faces of the post should coincide exactly with the planes of the sides of the structure, and in this case posts of square or rect- angular section may be used, with no framing except the bevels and the mort': ? for the girts. If, however, the frame is to be covered in, the poct must be J«c'Aw? so as to be able to receive the boarding. The backing consists in cutting the post to such a shape that when the bevel is cut at the foot, the section cut out will be similar to that shown ?it e h c d in Fig. 171. The hacked post must then 119 110 CARPENTRY be set on the sills so tliat the jxjint e will come at the corner a. The face of the post e h will then coincide with the face of the sill af. The post slioiild be backed before the bevels are cut because setting it back the distance a e may make a difference in the re- quired length between bevels. If the post was of square section before backing it will have, after backing, a ])eculiar rhoi!il)us- shaped section, as is shown at A in Fig. 174-. Here A i j k shows the original square section, and I i j I' shows the section after backing. These sections are taken square across the post perpen- dicular to the edores, o Fig. 175 shows how the amount of backing necessary in any particular case may be determined. Suppose that wo have a case where the frame is not square in plan, as shown in Fig. 173, but Fig. 175. Determining Amoimt of Bacldng. is rectancrular, one side beincr-inuch longer than the other. In this case the diagonal of the frame formed by the sills will not coincide with the diagonal of the section of the post. Fig. 175 shows at A a plan of the post as it would appear if it were set up perpendicular to the sills. The sills are shown by the dotted lines. At B is shown an elevation of the post looking in the direction shown by the arrow //. The section shown at A is taken on the line V /'. In the frame, however, the post is indini'd toward the center, so that the section cut out at the foot of the ])ost by the plane of the top of the sill will not be square M'ith the edges of the post as is the section ij^ but will be at an angle Mith them. Such a section is taken on the line I- 1 and is shown at 0. 120 CARPENTRY 111 The section of the post is shown by m n o j> and the sill is indicated by the dotted lines. The post must now be backed so that this section will take the form shown by q n o j>, the sides J) q and n q being parallel to the sides of the sill w^ r and 'nh s. This point q determines the position of the outside corner of the post after it has been backed and corresponds to the point t on the line k I. Then the line t u is the elevation of the outside corner of the post after backing, and the section i j cuts this line at h. The corner shown by the line t ii must be diagonally opposite the inside corner of the post, so it must bo indicated on the section shown at A by the point e. Then e h o d is the shape to which the post must be trimmed. This can be laid out on the square end of the rough post and it can then be trimmed to the correct shape. The backing will then be complete. Fig. 17G shows how the foot cut for the inclined post may be obtained by using the steel square. In Fig. 173 it will be seen that the post a slopes toward the center in the elevation there shown, and it likewise slopes toward the cen- ter in the other elevations, either with the same pitch or with ^ different pitch. The result of the two slopes is to cause the post to slope diagonally. It is an easy matter to find the pitch in each elevation since it depends upon the size of the base and top, and the height between them. We then have the two '^^' '' cut!^^"^ pitches, the combination of which gives the true pitch, diagonally. They caiiy however, be treated separately. The square may be applied to the post, as shown in Fig. 170, with the rise on the blade and the run on the tongue, and a line may be drawn along the tongue. The post can then be turned over and the 'pitch shown in the other elevation may be laid off on the adjacent side in the same way with the rise on the blade and the run on the tongue of the square. Thus a continuous line ah cd may be drawn around the post and it can be cut to this line. Trussed Partitions. It is very often necessary to construct- a partition in some story of a building above the first, and in such a position that there can be no support — as, for instance, a parti- tion in the story below — beneath it. In this case the partition 121 112 CARPENTRY must l)e made self supporting in some way. The usual method is to huikl what is known as a trussed partition. This consists of a timber truss,' lijrlit or heavy, according as the distance to be spanned is small or great, which is built into the partition and covered over with lathing and plastering or with sheathing. Fig. 177 and 178 show two forms of trussed partitions which are in common use. The one shown in Fig. 177 may be employed for a solid partition, or a partition with a door opening in tlie mid- dle, while the one shown in Fig. 178 is applicable where the Avail must be ])ierced by door openings in the sides. The truss must be so designed that it will occupy as little space as possible in a lateral direction, so that the partition need not l)e abnormally Fit;:. 177. Trussed Partition. Fig. 178. Trussed Partition. thick. If possible it is best to make the truss so that it will go into a four-inch partition, but if necessary five or si.\-inch stud- ding may be used and the truss members may be inci'eased in size accordingly. The faces of the truss members should be Hush with the faces ol" the partition studdincj, so as to receive lathiiif or sheath inn-. The size of the truss meml)ers depends entirely upon the weight which the ])artition is called u|)on to carrv. Besides its own weight a partition is often called upon to carry one end of a set of lloor joists, and sometimes it supports columns which re- ceive the whole weiglit of a story above. In any case the pieces must be very strongly framed or spiked together, and sound mate- rial, free from shakes and knot holes, must be used. Inclined and Bowled Floors. In any large room which is to be used as a lecture hall, the floor should not be perfectly level 122 •\ to ■< E Q o 5 > s K O b U CO O U) tS Oh OJ a o o « n 5 m '-' «^ ^ 9 o ■a id el o S 3 E o o OS u o z > I - o w tn a) 3 o o O w T3 a CO tf] < fi , M M M O >* ^ eg ^5 is. ■3 < ;3 (4 d ?: ♦J o Ol, pa S o t> s •4.^ H ja u s u fl b: 7) 3 S U) P o ID Eh b •a H 1 M Xi a Tl o s 2: . cl Sh (H < tG OQ CARPENTRY 113 throughout, but should be so constructed as to be higher at the back of the room than it is at the front. The fall of such a floor from back to front should be not more than three quarters of an inch in one foot, and a fall of one-half an inch in one foot is much better. If the floor has a greater slope than this it becomes very noticeable when anyone attempts to walk over it. The simplest way to arrange for the slope is to construct what is known as an inclined floor, which rises steadily from front to back so that a line drawn across it from side to side, parallel to the front or rear wall of the room, will be level from end to end. There are two methods of build- ing an inclined floor, the differ- Fig. 179. Inclined Floor. ence between them beino- iu the arrangement of the girders and floor joists. The two methods are shown in Figs. 179 and 180. lig. 179 shows the sirrangement when it is necessary to have the girders run from the back to the front of the room, parallel to the slope of the floor. In this case the girders a are set up on an incline, and the joists b resting on top of them, are level from end to end. Each line of joists is at a different elevation from the lines' of joists on each side of it. The floor laid on top of the joists will then have the required inclination. The slope of the girders must be the same as the slope required for the finished floor. Fig. ISO shows the arrano-ement when it is desired that the girders shall run from side to side of the room, at right ancrles to the direction of the slope of the floor. The joists a will then be parallel to the direction of the slope, and are inclined to the hori- zontal, while the girders h are level from end to end. Each line of girders is at a different elevation from every other line of girders, and these elevations must be so adjusted that the joists Sana Fig. 180. Inclined Floor. 123 114 CARPENTRY resting on top of the girders will slope steadily from end to end. When a simple inclined floor is employed, the seats must be arranged in straight rows, extending across the room from side to side, so that each line of seats may be level from end to end. This arrangement is not always desirable, however, and it is often much better to have the seats arranged in concentric rings all fac- ing the speaker's platform. In this case a howled floor must be built. A bowled floor is so constructed that a segment of a circle, drawn on the floor fi-om a center in the front of the room, on, or near, the speaker's platform, will be perfectly level throughout its ■'^^^^^<^^:f^^i^^:^;^i^::^i^^i^ Fig. 181. rraming Plan of Bowled Floor. length. This means that the floor must pitch upward in all direc- tions from the speaker's platform or, in other words, it must be hoveled. There are two methods of constructing a floor of this kind. The simplest way is to build first an ordinary inclined floor, M'hich slopes from the front to the back of the rooi^i, and then to build up the bowled floor with furring pieces. This method should always be followed when it is necessary to keep the space beneath the lecture ball free from posts or columns. 124 CARPENTRY 115 The second method is to arrange girders, as shown in the framing plan of a bo^Yled floor in Fig. ISl. These girders A A are tangent to concentric circles which have their center at the speaker's platform, and each line of girders is at a different eleva- tion. The elevations of the different lines of girders are so ad- justed that the floor joists B B which rest on them will slope steadily upward as they recede from the ]>]atf()rm. The girders maybe supported on posts beneath the floor of the hall, and if the space under the floor is not to be used for another room, this is a very good method to employ. Immediately around the j^latform there will be a space D, the floor of which will be level, and the slope will start several feet away from the platform. Heavy Beams and Girders. For ordinarv frame buildino-s, there will be uo difliculty in obtainincr timbers larcre enouo-h for every purpose, but in large structures, or in any buildincr where heavy loads must be carried, it is often impossible to get a single stick which is strong enough to do the work. In this case it becomes necessary to use either a steel beam or a trussed o-irder of wood, or to build up a compouud wooden girder out of a number of single sticks, fastened together in such a way that they will act like a single piece. Steel beams are very often employed for girders when a sino-Ie timber will not sufiice, and .although they are expensive, the sav- ing in labor helps to offset the extra cost of the material. Wherever wooden joists or girders come in contact with a steel beam they must be cut to fit against it. The steel shape most commonly employed is the I-beam, and the wooden members must be cut at the ends so as to fit between its flancres. This is shown in Fig. 182. The joist h is supported on the lower flange of the I-beam c and the strap a prevents it from falling away from the steel member. The strap is bolted or spiked to the wooden beam and is bent over the top flange of the steel beam as shown. If two wooden beams frame into the sleel beam opposite each other, a straight strap may be used, passing over the top of the steel beam and fastened to both the wooden beams, thus hold! no- them together. If a better support is desired for the end of the wooden beam, an angle may be riveted to the web of the steel I-beam, as 125 nr, CARPENTRY shown in V\cr. 183, and the end of the wooden joist may be sup- ported on tlie angle. This is an expensive detail, however, and it is seldom necessary. If a timher is not strontr enough to carry its load, and if it is not desirable to re])lace it Mith a steel beam, it may be strengthened by trussing. Thei'e are two methods of trussing lieams; by the ^ L's riveted ■-IbolC: FiR. 182. I- Beam and Wooden Joist. Fig. 183. I-Heani Construction. addition of compression members above the beam, and by the addi- tion of tension members below it. The first method should be em])loyed whenever, for any reason, it is required that there be no projection below the bottom of the beam itself. The second method is the one most commonly nsed, especially in warehouses, stables, and other buildings where the appearance is not an impor- -tant consideration. In Fiij;. 1 h which may l)e of wrought iron or steel. The beam itself is best made in two parts e e placed Fig. 184. Trussed Beam. side by side, as shown in the section at A, witii the ])arts ff a fit- tincj in between tlieni. The section shown at A is taken on the line <■ (1. The depth of tlie girder may be varied to suit the con- ditions of each case. In oeneral the deeper it is made the stronger it becomes, provided that the joists are made sufficiently strong. 126 CARPENTRY 117 Usually girders of this kind are made shallow enough so that they will be contained in the thickness of the floor and will not project above it. A slight i)rojection below the ceiling is not a serious disadvantage. The floor joists // may be supported on the pieces e e, as shown at A. In Figs. 185 and 186 are shown examples of girders which are trussed by the second method, with tension rods (/ d below the Cast //-on Sear^rj^s ^ •S/ee/ rod Fig. 185. King Post Trussed Beam. beam. These rods are of wrought iron or steel, and the struts a a are of cast iron. The struts may be made of wood if they are short, or if the loads to be carried are not heavy. Sometimes the girders are made very shallow, and the struts a a are then merely wooden blocks placed between the beam e and the rod d to keep them apart. The girder shown in Fig. 185 is known as a Ung. post trussed beam, while the one shown in Fig. 18(3, with two struts instead of one, is known as a queen-jwst trussed beam. The beam itself Pig. 186. Queen Post Trussed Beam. stick, and the rods may be made in pairs, passing one on each side of the beam. In the latter case the struts would simply bear against the bottom of the beam, as shown in the illustrations, being fastened to it by bolts or spikes, so that they will not slip sideways^ It sometimes happens that a heavy girder is required in a situation where trussing cannot ])e resorted to, and where steel beams cannot readily be obtained. In this case the only resource is to build up a compound beam from two or more single pieces. A girder of this kind can be constructed without much difliculty, and can be so put together as to be able to carry from eighty to 127 118 CARPENTRY ninety ])er cent of the load which a solid j)iece of the same dimen- sions Mill hear. There are many ways of combining the single timbers to form com])onnd beams, some of the most common of M'hieh Mill be described. The most simple combination is that shown in Fig. 1S7. The two sincrle timbers are bolted tot^ether side by side, with some- times a small space betAveeu them. The bolts should be spaced about two feet apart and staggered,, as shown, so that two Mill not come side by side. Usually bolts three-quarters of an inch in diameter are used. In Fig. 188 is shown a modification of this girder knoM-n as a fitch-plate girder. It lias a plate of wrought iron or steel, inserted betM'een the tM'o timbers, and the M'hole is held firmly together by bolts. The size of the plate should be in j)roportion to the size of the timbers, so as to make the most economical combination. If Me have two pieces of timber out of which Me M'ish to make a compound girder, it is almost always possible to get a stronger combination by placing them one on top of the other, than by placiiig them side by side. This is because the strength of a l)eam varies as the square of its depth ^ but only directly as its width. For this reason most compound girders are composed of single sticks placed one abov'e the other. The tendency is for each piece to bend independently, and for the two parts to slide by each other, as shoM'u in Fig. 180. This tendency must be overcome and the parts so fastened together that they M'ill act like a single piece. There are several methods in common use by M'hich this object is accomplished. Fig. 190 shoM'S the most common method of building up a compound girder. The timbers are placed together, as shown, and narrow strips of M'ood are nailed firmly to both parts. The strips are placed close against each other and have a slope of about forty-five degrees, sloping in opposite directions, however, on opposite sides of the girder. It has been claimed that a built up girder of this kind Las a strength ninety-five per cent as great as the strength of a solid piece of the same size, but it is very doubt- ful Mhether this is true in most cases. Actual tests seem to indi- cate that such girders have an efficiency of only about seventy-five 128 CARPENTRY 119 per cent. They usually fail by the splitting of the side strips, or the pulling out and bending of the nails, but seldom by the break- ing of the main pieces. It is, therefore, essential that the strips should be very securely nailed to each of the parts which make up the girder, and that they should also be carefully selected so that only those pieces which are free from all defects may be used. bolts jpaced 2 o" i J. <^ o © © •t^ Bolts jpaced 2 o" Jo © © Fig. 187. Compound Beams. Fig. 188. Flitch-Plate Girders. These girders are liable to considerable deflection, and should not be used in situations where such deflections would be harmful. In Fig. 191 is shown another form of girder with the parts notched, as shown, so as to lock together. This prevents them from slipping by each other. Bolts are employed to hold the parts Woo/ sfrip% a t-t-s ' sfops ^P^;^: Fig. 189. Flexure of Compound Beams. Fig. 190. Compound Girder. together, so that the surfaces will always be in close contact. While this form of girder is very easily constructed, it has many disadvantages. A great deal of timber is wasted in cutting out the notches, as these must be deep enough to prevent crushing of the wood at the bearino- surfaces, and thus the full streno-th of the sticks is not utilized. Moreover, it is apt to deflect a good deal. Oaf r l.Aews - g?l h— ^ Fig. 191. Notched Beam. Fig. 192. Keyed Beam, and its eSiciency is not so great as that of other forms. On the whole it is considered to be greatly inferior to the form of girder previously described. The form of compound beam which is almost universally con- sidered the best is. that shown in Fig. 192. This is known as the 129 120 CAKPEXTKY 'kexjed leam,, its characteristic feature being the use of It'i/a to keep the parts from sliding on each other. The strength of a keyed beam has been found by actual experiment to be nearly ninety-five per -cent of the strength of the solid timber, while the deflection when oak keys were used was only about one-quarter more than the deflection of the solid beam. By using keys of cast iron in- stead of wood this excess of deflection in the built-up girder can be reduced to a very small percentage. The keys should be made in two parts, each shaped like a wedge, as explained in connection with the keys for tension splices, and should be driven from op- posite sides into the holes made to receive them, so as to fit tightly. They should be spaced from eight to sixteen inches apart, center to center, according to the size of the timbers, and should be spaced more closely near the ends of the beam than near the mid- dle. In the center of the span there should be left a space of four or five feet without any keys. Balconies and Galleries. In churches and lecture halls it is almost always customary to have one or more balconies or galleries, extending sometimes around three sides of the main auditorium, but more often in the rear of the room only. These galleries are supported by the wall at the back and by posts or columns in front, and the framing for them is usually a simple matter. Ficf. 198 shows a sectional view of a gallery frame, as they are commonly constructed. There is a girder a in front, which rests on top of the columns #, and supports the lower ends of the joists J, forming the gallery floor. The size of these pieces will depend upon the dimensions of the gallery, the spacing of the columns which support the girders in front, and various other considerations. Usually joists two by ten or three by twelve, and girders eight by ten or ten by twelve will be found to be suf- ficiently strong. The joists should be spaced from fourteen to twenty inches, center to center. Very of ten cast iron columns are employed to support the girders. At the top, where the joists rest on the wall, they should be cut, as shown in the figure, so that they may have a horizontal bearing on the masonry, and at least every second joist must be securely anchored to the wall, as is the one shown. Usually galleries are made with straight fronts, but if it is desired that the seats should be arranged in concentric 130 CARPENTRY 121 rings, all facing the speaker, the joists may be placed so as to radiate from the center from which the seats are to be laid out. The seats are arranged in steps, one above the other, and the framing for the steps must be built up on top of the joists, as shown in the figure. Horizontal pieces, c c c usually two by four or three by four in size, are nailed to the joists at one end, and at the other end are supported by upright pieces d d d. The up- rights are either two by four pieces resting on top of the joists or strips of board, one inch to one and one-half inches thick, Mhich are nailed to the sides of the joists and to the sides of the hori- zontal pieces. Both methods are shown in the figure. If boards are used, they should be placed on both sides of the joists. Great Fig. 193. Section of Gallery Frame. care should be taken to see that the horizontal pieces are truly horizontal. Balconies and galleries almost always project a considerable distance beyond the line of columns which support the lower ends of the joists. This projection varies from three feet to ten or twelve feet. If the overhang is not more than five feet, it can be supported by extending the joists beyond the girder, as is shown in Fig. 193. A strip of board, tf, about one and one-half inches thick, is nailed to the side of the joist, and a furring piece / is nailed on top of the joist at its lower end to make it horizontal. The railing at the front of the gallery should be about two feet high, and may be framed with two by fonr posts, g having a cap h of the same size on top. If the overhang of a gallery is more than about five feet it must usuaiiy be supported by a brace, as shown in Fig. 194. 131 122 CAKPENTKY The brace a is nailed to the post h and to the overhanging joist r, or may be framed into these pieces. If the construction is very light, the brace may consist of strips of board nailed to the sides of the joists, but in heavy work it must be a timber of a good size, well framed into both the post and the joists. These braces can Fig. 194. Support for Extension Beyond Girder. only be placed at points where there are posts, and to support the ends of the joists M'hich come between the posts there must be a girder d running along the front of the gallery and supported by the braced cantilevers at the points where posts are placed. Timber Trusses. In the discussion of roofs and roof fram- ing, only those were considered which could be framed with ordi- nary rafters, spaced from one foot Q /Q =M -a c^a -b -b b b Wb to two feet apart, between cen- ters, but it is very often necessary to build roofs of larger span, for which ordinary rafters, even if supported by dwarf walls and collar beams, are not suUiciently stroncr. In this case a different method of framing is employed. Instead of a number of rafters spaced fairly close together, and all of equal strength, we have a few heavy trusses, placed at intervals of ten feet or more, and span- ning tlie entire distance between the side walls. On top of the trusses are laid J;;<7'Z^/^, which it has a ten- dency to do. The block is set into the chord of the truss to a depth sufficient to keep the purlin from sliding downward as it receives the weight from the rafters e taken not to Aveaken the chord too much in cutting these mortises. Tn Ficr. 202 are shown the two most common methods of formino- tlie joint between the top chord and the tie beam of a truss. The connection shown at A depends upon the bolts for its strength, while that shown at B depends upon the wrought iron straps (f, which are bent so as to engage notches cut in tlje tie beam h. The piece c is very often added beneath the tie beam, at the bearing, to strengthen it at this point, where it is subject to considerable bending stress. Tlie block d is merely for filling and to protect the bolts when they pass be- tween the chord and the tie beam. It may be omitted in many cases. The plate /" is placed between the nuts or bolt heads and the wood to prevent the crushing of the latter. Washers should be used with all bolts for this purpose. Fig. 203 shows how the joint at the center of the tie beam of a king post truss, or any joint between two struts, may be formed. The tie beam l-j, shown at a, and b h are the struts. The blocks c, Fig. 201. Support for ' Purlins. Fig. 202. Joints at Top Chord and Tie Beams. set between tlie struts, receive the thrust from them. They should be notched into the tie beam re, deep enough to take care of any inequality between the thrusts from the two struts, wliich have a tendency to balance each other. This block is often made of cast 136 CARPENTRY 127 iron. It may be omitted altogether, in M'Lich case the struts will come close together and bear against each other. The rod d is the king post which supports the tie beam a at this point. It is often made of wood, and sometimes the struts 1) h are framed into it instead of being framed into the tie beam a. Fig. 204 shows a form of connection for the peak of a truss, where the two top chords or j!/r?*;?r-?'^?«? rafters come too-ether. The plate a acts as a tie to keep these members in place, as does the bent plate 5, also. The plate b, moreover, prevents the crush- ing of the timber by the nut of the king post tie rod. The purlin c supports the rafters and is hollowed out at the bottom to admit the nut d. The two principal rafters bear against each other and must Fig. 303. Joint at Center of Tie Beam. Fig. 204. Peak of Truss. be cut so that the bearing area between them will be sufficient to prevent the crushing of the timber. In light trusses the king post e is often made of wood and is carried up between the principal rafters so that these members bear against it on each side. If this construc- tion is adopted it must be remembered that the post is a tension member, and is held up by the principal rafters, and these pieces must be mortised into it in such a way as to accomplish this result. There are a great many different ways of arranging the details for wooden trusses, each case usually requiring details peculiar to itself and unlike those for any other case. There are, therefore, no hard and fast rules which can be laid down to ofovern the de- sign of these connections. A perfect understanding of the action of each piece and its relation to all the other pieces is the only thing which will insure an economical and appropriate desicrn. The aim should always be to arrange the details so that there will be as little cutting of the pieces as possible, and so that the stresses may pass from one to the other without over- straining any part of the work. 137 128 CARPEXTKY Towers and Steeples. Towers are ;i very common feature in building construction, ranging in size from the small cupola seen almost invariably on barns and stables, to the high tapering spire which is the distinguishing mark of the country church. They have roofs of various shapes, some in the form of pyra- mids, with four, eight, or twelve sides, some of conical form, and others bell -shaped or having a slightly concave surface. The construction of all these forms of towers is much the same, consisting of an arrangement of posts and braces which becomes more elaborate as the tower or steeple becomes larger. The bracing is the most impor- tant consideration, because the towers will be exposed to the full force of the wind and must be able to stand the great strain to which they are subjected. Fig. 205 shows a section through the frame of a simple cupola. It has posts a a at each corner, which rest at the bottom on the sills h h. Tiie sills are supported on extra heavy collar beams r, which are very securely S])iked to the rafters of the main roof III ill. The corner posts ex- tend clear up to the uuiin plate (7 <:/, which supports tlie rafters c e of the cu])ola. There are hij) raft- ers at the corner of the roof, which bear at the top against a j)iece of scantling /* placed in the center of the roof. This scantling extends a])Ove the roof surface far enouu;h to receive some kind of metal finial which forms the finish at the extreme top of the cupola; and at the bottom it is firmly fastened to the tie (j which is cut ill between the ])lates. The braces // Ji h // stilf'en the frames against the wind, (lirts ,* 7 are cut in l)etween the corner posts and form the top and bottom of the slat frame opening R, besides tieing the posts together. The sides of the opening for the slat frame are formed by the vertical studs I' k. The rafters of the Fig 205. Frame for Cupola. 138 < CI •^ IS bO c4 Oh £ ID O E IZ « < -a ' U 13 o in Ou E o X H o o « bo a o o V HI E 3 o 2 is * a ^ o 9 0) W &< O » 3 J3 -a o o O o 3 O X E o o a: •a d e4 01 C3 c« h O FIREPLACE IN DINING ROOM OF HOUSE FOR MR. C. M. THOMPSON, CAMBRIDGE, MASS. Cram, Goodhue & Ferguson, Architects, Boston and New York. CARPENTRY 129 main roof in in are placed close up against tlie corner posts on the outside, and the posts may be spiked to them. The pieces o o are of plank two inches thick, and are simply furring pieces placed at intervals of a foot and a half to two feet all around the cupola to give. the desired shai:)e to the bottom part. The size of the pieces will de^oend upon the size of the cupola. The posts may be four by four inches or six by six inches, and the braces, girts and intermediate studding may be three by four inches or four by six inches. Other towers are framed in a manner SMuilar to that described for cupolas. There is always a base or drum, Mith posts at the corners and with the walls filled in with studding, which supports a plate at the top. The rafters forming the tower roof rest at the foot on this plate, and at the top they bear against a piece of scantling which is carried down into the body of the tower for a considerable distance and is there fastened to a tie passing betvreen rafters on opposite sides. This is shown in Fig, 206. The tie a is securely nailed to the rafters at each end, and to the scantlincr in the middle. The scantling is cut so as to have as' many faces as the roof has sides, four for a square hip roof, eight for an octagon roof, and so on. Each face receives one of the hip rafters and the intermediate rafters are framed in between them. If the roof is conical or bell-shaped, as shown in the figure, the scantling at the top may be cylindrical in form. Although the roof shown is bell-shaped, the rafters are not cut to fit the curve. They are made straight and are filled out by furring pieces l 1>. Pieces of plank c c are cut in between the furring pieces, as shown, so as to give a nailing for the board- ing, and they are cut to the shape of segments of circles, so as to form complete circles around the tower when they have been put in place. If a tower of this shape is to be built, leaving a number of Fig. 306. Frame for Tower. 139 130 CARPENTRY faces and hips, the curve of the hip rafters will not be the same as the curve shown by a section through one of the faces of the tower. In order to find the true curve for the hip rafters the same method is followed as was explained for the hip rafter in an ogee roof over a bay window, using the principle that any line drawn in the roof surface parallel to the plate is horizontal throughout its length. J>V this means any number of points in the curve of the hip I'after may be obtained and the curve for the hip may be drawn through them. Thus a pattern for the hip rafter may be obtained. Fig. 207 shows the method of framing a cluiivli spire, or other high tapering tower. The drum A is square and is sup- ported by the posts a a^ one at each corner, which rest on the sills J> 1). The sills are supported by the roof trusses of the main roof. The corner posts extend the full height of the drum and are strongly braced in all four faces, with intermediate vertical studding c e between them to form the framework for these faces. The spire itself may rest on top of this square drum or there may be another eight- or twelve-sided drum constructed on top of the first on which the spire may rest. This depends upon the design of the spire. The ]iip rafters d d d d do not rest directly on top of the drum, how- ever, as this arrangement would not give sutticient anchorage for the spire. They are made so as to pass close inside the plate e at the top of the drum and are securely bolted to this plate with strong bolts. This is shown at II which is a ])lan of the top of the drum, showing the hip rafters in place. The plate is shown at ./^"and the hi J) rafters at Y/^7//;? at right angles to its Tormer direction and parallel to the wall line we may obtain the point /' which is a plan of one point in the surface of the elliptical vault. The elevation of this point also above the springing lines must be the same as for the point s and may be laid off, as shown at Z' 7^/. By finding other points in a similar way the curve n 111 r of the elliptical vault may be readily determined. 150 < < H > O *J < < ? ° U H 0. •< X o < >-l U Q < X STAIR-BUILDING Introducton-. In the following instructions in the art of Stair^ building, it is the intention to adhere closely to the practical phases of the subject, and to present only such matter as will directly aid the student in acquiring a practical masten- of the art. Stair-building, though one of the most important subjects con- nected with the art of building, is probably the subject least under- stood by designers and by workmen generally. In but few of the plans that leave the offices of Architects, are the stairs properly laid down; and many of the books that have been sent out for the purpose of giving instruction in the art of building, have this common defect- that the body of the stairs is laid down imperfectly, and therefore presents great difficulties in the construction of the rail. The stairs are an important feature of a building. On entering a house they are usually the first object to meet the eye and claim the attention. If one sees an ugly staircase, it will, in a measure, condemn the whole house, for the first impression produced will hardly afterwards be totally eradicated by commendable features that may be noted elsewhere in the building. It is extremely important, therefore, that both designer and workman shall see that staircases are properly laid out. Stairways should be commodious to ascend — inviting people, as it were, to go up. When winders are used, they should extend past the spring line of the cylinder, so as to give proper \ndth at the narrow end -(see Fig. 72) and bring the rail there as nearly as possible to the same pitch or slant as the rail over the square steps. When the hall is of sufficient width, the stairway should not be less tlian four feet wide, so that two people can conveniently pass each other thereon. The height of riser and width of tread are governed by the staircase, which is the space allowed for the stairway; but, as a general rule, the tread should not be less than nine inches wade, and the riser should not be over eight inches high. Seven-inch riser 153 STAIR-BUILDING Fig. 1. Illustrating Rise. Kun, and Pitch. and eleven-inch tread will make an easy stepping stairway. If you increase the width of the tread, you must reduce the height of the riser. The tread and riser together should not be over eighteen inches, and not less than seventeen inches. These dimensions, however, cannot always be adhered to, as conditions will often compel a devia- tion from the rule; for instance, in large buildings, such as hotels, railway depots, or other public buildings, treads are often made 18 inches wide, having risers of from 2h inches to 5 inches depth. Definitions. Before pro- ceeding further with the subject, it is essential that the student make himself familiar with a few of the terms used in stair-building. The term rise and run is often used, and indicates certain dimensions of the stairway. Fig. 1 will illustrate exactly what is meant; the line ^ 5 shows the nm, or the length over the floor the stairs will occupy. From 5 to C is the rise, or the total height from iop of lower floor to top of upper floor.* The line D is the pitch or line of nosings, showing the angle of inclination of the stairs. On the three lines shown — the rim, the rise, and the pitch — depends the whole system of stair-building. The bochj or staircase is the room or space in which the stairway is contained. This may be a space including the width and length of the stairway only, in which case it is called a close stairway, no rail or baluster being necessary. Or the stairway may be in a large apartment, such as a passage or hall, or even in a large room, openings being left in the upper floors so as to allow road room for persons on the stairway, and to furnish communication between the stairways and the different stories of the building. In such cases we have what are known as open stairivays, from the fact that they are not closed on both sides, the steps showing their ends at one side, while on the other side they are generally placed against the wall. Sometimes stairways are left open on both sides, a practice not ♦Note.— The measure for the rise of a stairway must always be taken from the top of one floor to the top of the next. 154 STAIR-BUILDING uncommon in hotels, public halls, and steamships. When such stairs are employed, the openings in the upper floor should be well trimmed with joists or beams somewhat stronger than the ordinary joists used in the same floor, as will be explained further on. Tread. This is the horizontal, upper surface of the step, upon which the foot is placed. In other words, it is the piece of material that forms the step, and is generally from Ij to 3 inches thick, and made of a width and length to suit the position for which it is intended. In small houses, the treads are usually made of |-inch stuff. Riser. This is the vertical height of the step. The riser is gen- erally made of thinner stuff than the tread, and, as a rule, is not so heavy. Its duty is to connect the treads together, and to give the stairs strength and soliditv. Rise and Run. This term, as already explained, is used to indi- cate the horizontal and vertical dimensions of the stairway, the rise meaning the height from the top of the lower floor to the top of the second floor; and the run meaning the horizontal distance from the face of the first riser to the face of the last or top riser, or, in other words, the distance between the face of the first riser and the point where a plumb line from the face of the top riser would strike the floor. It is, in fact, simply the distance that the treads would make if put side by side and measured together — without, of course, taking in the nosings. Suppose there are fifteen treads, each being 11 inches wide; this would make a run of 15 X 11 = 165 inches = 13 feet 9 inches. Sometimes this distance is called the going of the stair ; this, however, is an English term, seldom used in America, and when used, refers as frec^uently to the length of the single tread as it does to the run of the stairway. String-Board. This is the board forming the side of the stairway, connecting with, and supporting the ends of the steps. AMiere the steps are housed, or grooved into the board, it is known by the term housed string; and when it is cut through for the tread to rest upon, and is mitered to the riser, it is known by the term cut and mitered string. The dimensions of the lumber generally used for the purpose in practical work, are 9h inches width and | inch thickness. In the first-class stair^'ays the thickness is usually 1|^ inches, for both front and wall strings. 155 STAIR-BUILDING risers and treads together Fig. 2 shows the manner in which most stair-builders put their T and T show the treads; R and R, the risers; S and S, the string; and 0, the cove mouldings under the nosings A" and A . B and B show the blocks that hold the treads and risers together; these l)locks should be from 4 to (5 inches long, and made of very dry wood ; their section may be from 1 to 2 inches square. On a tread 3 feet long, three of these blocks should be used at about equal distances apart, putting the two outside ones about 6 inches from the strings. They are glued up tight into the angle. First warm the blocks; next coat two adjoining sides with good, strong glue; then put them in position, and nail them firmly to both tread and riser. It will be noticed that the riser has a lip on the upper Fig. 3. Common Method of Join- ing Risers and Treads. edge, which enters into a groove in the tread. This lip is generally Vertical Section )f Stair Steps. Fig. A. End Section of Riser. Fig. .5. End Section of Tread. about s mch long, and may be § inch or h inch in thickness. Care nfiust be taken in getting out the risers, that they shall not be made too narrow, as allowance must be made for the lip. If the riser is a little too wide, this will do no harm, as the ovd- wndth may hang down below the tread ; but it must be cut the exact width where it rests on the string. The treads must be made the exact width required, before they are grooved or have the nosing 156 STAIR-BUILDING 5 Fig. G. Side Elevation of Fiuish- ed Steps ^vith Return Nosings and Cove Moulding. worked on the outer edge. The Hp or tongue on the riser should fit snugly in the groove, and should bottom. By following these last instructions and seeing that the blocks are well glued in, a good solid job will be the result. Fig. 3 is a vertical section of stair sieps in which the risers are shown tongued into the under side of the tread, as in Fig. 2, and also the tread tongued into the face of the riser. This last method is in general use throughout the country. The stair-builder, when he has steps of this kind to construct, needs to be very careful to secure the exact width for tread and riser, including the tongue on each. The usual method, in getting the parts prepared, is to make a pattern show- ing the end section of each. The millman, with these patterns to guide him, will be able to run the material through the machine without any danger of leaving it either too wide or too narrow; while, if he is left to himself without patterns, he is liable to make mistakes. These patterns are illustrated in Figs. 4 and 5 respectively, and, as shown, are merely end sections of riser and tread. Fig. 6 is a side elevation of the steps as finished, with return nosings and cove moulding complete. A front elevation of the finished step is shown in Fig. 7, the nosing and riser returning against the base of the newel post. Often the newel post projects past the riser, in front; and when such is the case, the riser and nosing are cut square against the base of the newel. Fig. 8 shows a portion of a cut and mitered string, w^hich will give an excellent idea of the method of construction. The letter O shows the nosing, F the return nosing with a bracket termi- nating against it. These brackets are about j\ inch tliick, and are planted (nailed) on the string; the brackets miter with the ends of the risers; the ends of the brackets which miter with the risers, are Fig. 7. Front Elevation of Finished Steps. 157 6 STAIR-BUILDING Fig. 8. Portion of a Cut and Mitered Siring, Showing Method of Constructing Stairs. to be the same height as the riser. The lower ends of two baUis- ters are shown at G G; and the dovetails or mortises to receive these are shown at E E. Generally two balusters are placed on. each tread, as shown ;-l)ut there are some- times instances in which three are used, while in others only one baluster is made u.se of. An end portion of a cut and mitered string is shown in Fig. 9, with part of the string taken away, show- ing the carriage — a rough piece of lumber to which the finished string is nailed or otherwise fastened. At C is shown the return nosing, and the man- ner in which the work is finished. A rough bracket is sometimes nailed on the carriage, as shown at 7), to support the tread. The balusters are shown dovetailed into the ends of the treads, and are eidicr glued or nailed in place, or both. On the lower edge of string, at B, is a return bead or moulding. It will be noticed that the rough carriage is cut in snugly against the floor joist. Fig. 10 is a plan of the portion of a stairway shown in Fig. 9. Here the position of the string, bracket, riser, and tre.atl can be seen. At the lower step is shown how to miter the riser to the string; and at the second step is shown how to miter it to the bracket. Fig. 11 shows a (|uick method of marking the ends of the treads for the dovetails for balusters. The templet A is made of some thin material, preferably zinc or hardwood. The dovetails are outlined as shown, and the intervening portions of the material are cut away, leaving the dovetail portions solid. The templet is then nailed or screwed to a gauge-block E, Kit 9. Knd Portion of Cut and Miiered String, with Part Itenioved to Show Carriage. 158 STAIR-BUILDING Fig. 10. Plau of Portion of Stair. when the whole is ready for use. The metliod of using is clearly indicated in the illustration. Strings. There are two main kinds of stair strings — wall strings and cut strings. These are divid- ed, again, under other names, as Jioused strings, notched strings, staved strings, and rough strings. Wall strings are the supporters of the ends of the treads and risers that are against the wall; these strings may be at both ends of the treads and risers, or they may be at one end only. They may be housed (grooved) or left solid. When housed, the treads and risers are keyed into them, and glued and blocked. When left solid, they have a rough string or carriage .spiked or screwed to them, to lend additional support to the ends of risers and treads. Stairs made after this fashion are generally of a rough, strong kind, and are especially adapted for use in factories, shops, and warehouses, where strength and rigidity are of more importance than mere external appearance. Open strings are outside strings or supports, and are cut to the proper angles for receiving the ends of the treads and risers. It is over a strino- of this sort that the rail and balusters range; it is also on such a string that al nosings return; hence, in some localities, an open string is known as a return string. Housed strings are those that have grooves cut in them to receive the ends of treads and risers. As a general thing, wall strings are housed. The housings are made from | to f inch deep, and the lines at top of tread and face of riser are made to correspond with the lines of riser and tread when in position. The back lines of the housings are so located that a taper wedge may be driven in so as to force the tread and riser close to the face shoulders, thus making a tight joint. Rough strings are cut from undressed plank, and are used for strengthening the stairs. Sometimes a combination of rough-cut strings is used for circular or geometrical stairs, and, when framed together, forms the support or carriage of the stairs. Fig. 11. Templet Used to Mark Dovetail Cuts for Balusters. 159 8 STAIR-BUILDING Staved strings are V)uilt-up strings, and are composed of narrow pieces glued, nailed, or bolted together so as to form a portion of a cylinder. These arc sometimes used for circular stairs, though in ordinary practice the circular part of a string is a part of the main string bent around a cylinder to give it the right curve. Notched stmigs are strings that carry only treads. They are generally somewhat narrower than the treads, and are housed across their entire width. A sample of this kind of string is the side of a common step-ladder. Strings of this sort are used chiefly in cellars, or for steps intended for similar purposes. Setting Out Stairs. In setting out stairs, the first thing to do is to ascertain the locations of the first and last risers, with the height of the story wherein the stair is to be placed. These points should be marked out, and the distance between them divided off equally, giving the number of steps or treads required. Suppose we have between these two points 15 feet, or 1:iriL than any of the other risers, because, as above explained, tlie thick- ness of the first tread is always taken off it; thus, if the tread is 1} inches thick, the riser in this case would only require to be G|^ inches wide, as 7f —11 = G|. The string must be cut so that 'the line at IF will be onlv 6\: inches from the line at SJ, and these two lines must be parallel. The first riser and tread having been satisfactorily dealt with, the rest can easily be marked off by simply sliding the pitch-board along the line .1 until the outer end of the line S| on the pitch-board strikes the outer end of the line 7| on the string, when another tread and another riser are to be marked off. The remaining risers and treads are marked off in the same manner. Sometimes there may be a little difficulty at the top of the stairs, in fitting the string to the ^ „ _^ trimmer or loists: but, as it c / \ p X \ / \ 7x /\j is necessary first to become expert with the pitch-board, the method of trimming the well oi- attaching the cylinder to the string will be left until other matters have been discussed. Fig. 18 shows a portion of the stairs in position. 8 and S show the strings, which in this case are cut square; that is, the part of the string to which the riser is joined is cut square across, and the butt or end wood of the riser is seen. In this case, also, the end of the tread is cut square off, and flush with the string and riser. Both strings in this instance are open strings. L^sually, in stairs of this kind, the ends of the treads are rounded off similarly to the front of the tread, and the ends project over the strings the same distance that the front edge projects over the riser. If a moulding or cove is used under the nosing in front, it should be carried round on the string to the back edge of the tread and cut off scjuare, for in this case the back edge of the tread will be square. A riser is shown at R, and it will be noticed that it runs down behind the tread on the back edge, and is either nailed or screwed to the tread. This is the American practice, though in England the riser usually rests on the tread, which extends clear back to string as shown at the toj) tread in the diagram. It is much better, however, for general purposes, that the riser go behind the tread, as this tends to make the whole stairwav much stronger. 164 STAIR-BUILDING 13 Fig. 18. Portion of Stair in Position. Housed strings arc those which carry the treads and risers without their ends being seen. In an open stair, the wall string only is housed, the other ends of the treads and risers resting on a cut string, and the nosings and mouldings being returned as be- fore described. The manner of housing is shown in Fig. 19, in which the treads T T and the risers R R are shown in position, secured in place respectively by means of wedges X X and F F, which should be well covered with good glue before insertion in the groove. The housings are generally made from h to f inch deep, space for the wedge being cut to suit. In some closed stairs in which there is a housed string betw een the newels, the string is double-tenoned into the shanks of both newels, as shown in Fig. 20. The string in this example is made 12f inches wide, which is a very good width for a string of this kind; but the thickness should never be less than H inches. The upper new^l is made about 5 feet 4 inches long from drop to top of cap. These strings are generally capped wdth a subrail of some kind, on which the baluster, if any, is cut-mitered in. Generally a groove, the width of the square of the balusters, is worked on the top of the subrail, and the balusters are worked out to fit into this groove; then pieces of this material, made Hie width of the groove and a little thicker than the groove is deep, are cut so as to fit in snugly between the ends of the balusters resting in the groove. This' makes a solid job; and the pieces between the balusters may be made Showing Method of Housing Treads and Risers. 165 14 STAIR-BUILDING of any shape on top, cither beveled, rounded, or moulded, in which case much is added to the appearance of the stairs. Fig. 21 exhibits the method of attaching the rail and string to the bottom newel. The dotted lines indicate the form of the tenons cut to fit the mortises made in the newel to receive them. Fig. 22 shows how the string fits against the newel at the top; also the trimmer E, to which the newel post is fastened. The string in this case is tenoned into the upper newel post the same way as into the lower one. "1 Fig. 20. Showing Metbod of Con- necting Hmisi'd Siring to Newels. Fig. 21. MctliiKl of Cnnnei't- iug liiiil and String lu Bottom Newel. The open string shown in Fig. 23 is a portion of a finished string, showing nosings and cove returned and finishing against the face of the string. Along the lower edge of the string is shown a bead or moulding, where the plaster is finished . A portion of a stair of the better class is shown in Fig. 24. This is an open, bracketed string, with returned nosings and coves and scroll brackets. These brackets are made about ^ inch thick, and may be in any desirable pat- tern. The end next the riser should be mite red to suit; this will require the ri.ser to be f inch longer than the face of the string. The upper part of the bracket should run under the cove moulding; and the tread should project over the string the full | inch, so as to cover the 166 STAIR-BUILDING 15 bracket and make the face even for the nosing and the cove moukling to fit snugly against the end of the tread and the face of the bracket. Great care must be taken about this point, or endless trouble will follow. In a bracketed stair of this kind, care must be taken in plac- ing the newel posts, and provision must be made for the extra f inch due to the brack- et. The newel post must be set out from the string f inch, and it will then align with the baluster. We have now de- scribed several methods of dealing with strings; but there are still a few other points connected with these members, both housed and open, that it will be necessary to explain, before the young work- man can proceed to build a fair flight of stairs. The connection of the wall string to the lower and upper floors, and the manner of affixing the outer or cut string to the upper joist and to the newel, Fig. 23. Connections of String and Trimmer at Upper Newel Post. Fig. 23. Portion of Finished String, Showing Returned Nosings and Coves, also Bead Moulding. Fig. 21. Portion of Open, Bracketed String Stair, with Returned Nos- ings and Coves, Scroll Brack- ets, and Bead Moulding. are matters that must not be overlooked. It is the intention to show how these things are accomplished, and how the stairs are made strong by the addition of rough strings or bearing carriages. 167 16 STAIR-BUILDING Fig. 25. 5=.ide Elevatiop of Part of Stall' with Open. Cut aud Mitered String. FiL^ 25 irives a side view of part of a s(air of tlic better class, with one open, cut and mitered string. In Fig. 26, a plan of this same stair- way, W S shows the wall string; R S, the rough string, placed there to give the structure strength; and S, the outer or cut and mitered string. At A A the ends of the risers are shown, and it will be noticed that they are mitered against a vertical or riser line of the string, thus preventing the end of the riser from being seen. The other end of the riser is in the housing in the wall string. The outer end of the tread is also mitered at the nosing, and a piece of material made or worked like t)ie nosing is mitered against or returned at the end of the tread. The end of this returned piece is again returned on itself back to the string, as shown at N in Fig. 25. The moulding, which is f-inch cove in this case, is also returned on itself back to the string. The mortises shown at B B B B (Fig. 26), are for the balusters. It is always the proper thing to saw the ends of the treads ready for the balusters before the treads are attached to the string; then, when the time arrives to put up the rail, the back ends of the mortises can be cut out, when the treads will be ready to receive the balusters. The mortises are dovetailed, and, of course, the tenons on the balus- ters must be made to suit. The treads are finished on the bench ; and the return nosings are fitted to them and tacked on, so that they may be taken off to insert the balusters when the rail is being put in position. Fig. 27 shows the manner in which a wall string is finished at the foot of the stairs. S shows the string, with moulding wrought on the upper edge. This moulding may be a simple ogee, or may consist of a number of members; or it may be only a bead; or, again, the edge of the string maybe r B B B it B ;^ws 7RS 30S Fig. 26. Plan of Part of Stair Shown in Fig. 25. 168 STAIR-BUILDING 17 Fig. 27. Showing How Wall String is Fin- ished at Foot of Stair. left quite plain; this will be regulated in great measure by the style of finish in the hall or other part of the house in which the stairs are placed. B shows a portion of a baseboard, the top edge of which has the same finish as the top edge of the string. B and A together show the junction of the string and base. F F show blocks glued in the angles of the steps to make them firm and solid. Fig. 28 shows the manner in which the wall string S is finished at the top of the stairs. It will be noticed that the moulding is worked round the ease-off at A to suit ' the width of the base at B. The string is cut to fit the floor and to butt against the joist. The plaster line under the stairs and on the ceiling, is also shown. Fig. 29 shows a cut or open string at the foot of a stairway, and the manner of dealing with it at its junction with the newel post K. The point of the string should be mortised into the newel 2 inches, 3 inches, or 4 inches, as shown by the dotted lines; and the mortise in the newel should be cut near the center, so that the center of the balus- ter will be directly opposite the central line of the newel post. The proper way to manage this, is to mark the central line of the baluster on the tread, and then make this line correspond with the central line of the newel post. By careful attention to this point, much trouble will be avoided where a turned cap is used to receive the lower part of the rail. The lower riser in a stair of this kind will be somewhat shorter than the ones above it, as it must be cut to fit between the newel and Fig. 28. Showing How Wall String is Fin- ished at Top of Stair. 169 18 STAIR-BUILDING the wall string. A portion of the tread, as well as of the riser, will also butt against the newel, as shown at W. If there is no spandrel or wall under the open string, it may run down to the floor as shown by the dotted line at 0. The piece is glued to the string, and the moulding is worked on the curve. If there is a wall under the string S, then the base B, shown by the dotted lines, will finish against the string, and it should have a mould- ing on its upper edge, the same as that on the lower edge of the string, if any, this moulding being mitered into the one on the string. When there is a base, the piece is of course dispensed with. The square of the newel should run down by the side of a joist as shown, and should be firmly secured to the joist either by spiking or by some other suitable device. If the joist runs the other way, try to get the newel post against it, if possible, either by furring out the joist or by cutting a por- tion off the thickness of the newel. Tlie solidity of a stair and the firmness of the rail, depend very much upon the rigidity of the newel post. The above sugges- Sc[uare :^ ^ Joist 3xio Fig. 29. shmvintr How a Cut or Open String tions are applicable where great IS Finished at Foot of Stair. rr ^ o strength is required, as in public buildings. In ordinary work, the usual method is to let the newel rest on the floor. Fig. 30 shows how the cut string is finished at the top of the stairs. This illustration requires no explanation after the instructions already given. Thus far, stairs having a newel only at the bottom have been dealt with. There are, however, many modifications of straight and return stairs which have from two to four or six newels. In such- cases, the methods of treating strings at their finishing points must necessarily be somewhat different from those described; but the general principles, as shown and explained, will still hold good. Well-Hole. Before proceeding to describe and illustrate neweled stairs, it will be proper to say something about the ivcll-hole, or the 170 < X o u 9 ^'S .J < H (A STAIR-BUILDING 19 opening tlirougli the floors, through which the traveler on the stairs ascends or descends from one floor to another. Fig. 31 shows a well-hole, and the manner of trimming it. In this instance the stairs are placed against the wall; but this is not necessary in all cases, as the well-hole may be placed in any part of the building. The arrangement of the trimming varies according as the joists are at right angles to, or are parallel to, the wall against which the stairs are built. In the former case (Fig. 31, A) the joists are cut short and tusk-tenoned into the heavy trimmer T T , as shown in the cut. This trimmer is again tusk-tenoned into two heavy joists T J and T J, which form the ends of the well-hole. These heavy joists are called trimming joists; and, as they have to carry a much heavier load than other joists on the ^ame floor, they are made much heavier. Sometimes two or three joists are placed together, side by side, being bolted or spiked together to give them the desired unity and strength. In constructions requiring great strength, the tail and header joists of a well-hole are sus- pended on iron brackets. If the opening runs paral- lel with the joists (Fig. 31, B), well-hole should be left a little 30. Showing How a Cut or Open String is Finished at Top of Stair. the timber forming the side of the heavier than the other joists, as it will have to carry short trimmers (T J and T J) and the joists run- ning into them. The method here shown is more particularly adapted to brick buildings, but there is no reason v.'hy the same system may not be applied to frame buildings. Usually in cheap, frame buildings, the trimmers T T are spiked against the ends of the joists, and the ends of the trimmers are sup- ported by being spiked to the trimming joists T J, T J. This fs not very workmanlike or very secure, ami should not be tlone, as it is not nearly so strong or durable as the old method of framing the joists and trimmers together. Fig. 32 shows a stair with three newels and a j^latform. In ihis 171 20 STAIR-BUILDING example, the first tread (No. 1) stands forward -of the newel post two-thirds of its width. This is not necessary in every case, but it is sometimes done to suit conditions in the hallway. The second newel is placed at the twelfth riser, and supports the upper end of the first P h T.J. "ET Fig. 31. Showing Ways of Trimming Well-Hole when Joists Rim in Different Dii'eclioiis. cut string and the lower end of the second cut string. The platform (12) is supported l^y joists which are framed into the wall and are fastened against a trimmer running from the wall to the newel along the line 12. This is the case only when the second newel runs down to the floor. If the second newel does not run to the floor, the framework supporting the platform will need to be built on studding. The third newel stands at the top of the stairs, and is fastened to the joists of the second floor, or to the trimmer, somewhat after the manner of fastening shown in Fig. 29. In this example, the stairs have IC risers 172 STAIR-BUILDING 21 and 15 treads, the platform or lamling (12) making one tread. The figure IG shows the floor in the second storv. This style of stair will require a well-hole in shape about as shown in the plan; and where strength is required, the newel at the top should run from floor to floor, and act as a support to the joists and trimmers on which the second floor is laid. Perhaps the best way for a beginner to go about building a stair- way of this type, will be to lay out the work on the lower floor in the exact place where the stairs are to be erectetl, making everything orm 1^ 11 10 9 8 7 6 5 A 3 ? 1 t- ■Hi ID Ql ^ _^ -1 ro 1 |_j^y -^5"x5" 6"x6" ^ ID ■^ J5"x5" ID Pig. 32. Staii- with Three Newels and a Platform. full size. There will be no difficulty in doing this; and if the positions of the first riser and the three newel posts are accurately defined, the building of the stairs will be an easy matter. Plumb lines can be raised from the lines on the floor, and the positions of the platform and each riser thus easily determined. Not only is it best to line out on the floor all stairs havino^ more than one newel ; but in constructino; any kind of stair it will perhaps be safest for a beginner to lay out in exact position on the floor the points over which the treads and risers v.ill stand. By adopting this rule, and seeing that the strings, risers, and treads correspond exactly with the lines on the floor, many cases of annoyance will be avoided. Many expert stair-builders, in fact, adopt this method in their practice, laying out all stairs on the floor, including even the carriage strings, and they cut out all the material from the lines obtained on the floor. By following this method, one can see exactly the requirements in each particular case, and can rectify any error without destroying valuable material. 173 22 STAIR-BUILDIXG Laying Out. In order to afford the student a clear idea of what is meant by hujing out on the floor, an example of a simple close- string stair is given. In Fig. 33, the letter F shows the floor line; L is the landing or platform; and W is the wall line. The stair is to be 4 feet wide over strings; the landing, 4 feet wide ; the height from floor to landing, 7 feet; and the run from start to finish of the stair, 8 feet 8! inches. The first thing to determine is tlie dimensions of the treads and risers. The wider the tread, the lower must be the riser, as stated before. No definite dimensions for treads and risers can be given, as the steps have to be arranged to meet the various difficulties that may occur in the working out of the construction; but a common rule is this: ]\Iake the width of the tread, plus twice the rise, equal to 24 inches. This will give, for an 8-inch tread, an 8-inch rise; for a 9-inch tread, a T^-inch rise; for a 10-inch tread, a 7-inch rise, and so on. Having the height (7 feet) and the run of the flight (8 feet 8-2 inches), take a rod about one inch square, and mark on it the height from floor to landing (7 feet), and the length of the going or run of the flight (S feet S^ inches). Consider now what are the dimensions which can be given to the treads and risers, remembering that there will be one more riser than the number of treads. Mark oft' on the rod the landing, forming die last tread. If twelve risers are desired, divide the height (namely, 7 feet) by 12, which gives 7 inches as the rise of each step. Then divide the run (namely, 8 feet 8;^ inches) by 11, and the width of the tread is found to be 9^ inches. Great care must be taken in making the pitch-board for marking off the treads and risers on the string. The pitch-board may be mafle from dry hardwood about « inch thick. One end and one side must be perfectly sfjuare to each other; on the one, the width of the tread is set oft', and or^ the other the height of the riser. Connect the two points thus obtained, and saw the wood on this line. The addition of a gauge-piece along the longest side of the triangular piece, com- pletes die pitch-board, as was illustrated in Fig. 15. The length of the wall and outer string can be ascertained by means of the pitch-board. One side and one edge of the wall string must be squared; but the outer string must be trued all round. On the strings, mark the positions of the treads and risers by using the pitch-board as already explained (Fig. 17). Strings are usually 174 STAIR-BUILDIXG 23 made II inches wide, but may be made 12^ inches wide if necessary for strensrth. After the widths of risers and treads have been determined, and the string is ready to lay out, apply the pitch-board, marking the N J — ' Fig. 33. Method of Laying Out a Simple, Close-String Stair. first riser about 9 inches from the end ; and number each step in succes- sion. The thickness of the treads and risers can be drawn bv using thin strips of hardwood made the width of the housing required. Now allow for the wedges under the treads and behind the risers, and thus find the exact width of the housing, which should be about f inch 175 24 STAIK-BUILDING deep; the treads and risers will reciuire to be made U inches longer than shown in the plan, to allow for the housings at both ends. Before putiing the stair together, be sure that it can be taken into the house and put in position without trouble. If for any reason it cannot be put in after being put together, then the parts must be assembled, wedged, and ghied up at the spot. It is essential in laying out a plan on the floor, that the exact positions of the first and last risers be ascertained, and the height of the story wherein the stair is to be placed. Then draw a plan of the hall or other room in which the stairs will be located, including sur- rounding or adjoining parts of the room to the extent of ten or twelve feet from the place assigned for the foot of the stair. All the door- ways, branching passages, or windows which can possibly come in contact with the stair from its commencement to its expected ter- mination or landing, must be noted. The sketch must necessarily in- clude a portion of the entrance hall in one part, and of the lobby or landing in another, and on it must be laid out all the lines of the stair from the first to the last riser. The height of the story must next be exactly determined and taken on the rod ; then, assuming a height of risers suitable to the place, a trial is made by division in the manner previously explained, to ascertain how often this height is contained in the height of the story. The quotient, if there is no remainder, will be the number of risers required. Should there be a remainder on the first division, the opera- ■ tion is reversed, the number of inches in the height being made the dividend and the before-found quotient the divisor; and the operation of reduction by division is carried on till the height of the riser is obtained to the thirty-second part of an inch. These heights are then set off as exactly as possible on the story rod, as shown in Fig. 33. The next operation is to show the risers on the sketch. This the workman will find no trouble in arranging, and no arbitrary rule can be given. A i)art of the foregoing may appear to be repetition; but it is not, for it must be rememl)ered tliat scarcely any two flights of stairs are alike in run, rise, or pitch, and any departure in any one dimension from these conditions leads to a new series of dimensions that must be dealt with independently. The principle laid down, however, applies to all straight flights of stairs; and the student who has followed 176 STAIR-BUILDING 25 closely and retained the pith of what has been said, will, if he has a fair knowledge of the use of tools, be fairly equipped for laying out and constructing a plain, straight stair with a straight rail. Plain stairs may have one platform, or several; and they may turn to the right or to the left, or, rising from a platform or landing, may run in an opposite direction from their starting point. When two flights are necessary for a story, it is desirable that each flight should consist of the same number of step.s; but this, of course, will depend on the form of the staircase, the situation and height of doors, and other obstacles to be passed under or over, as the case may be. In Fig. 32, a stair is shown with a single platform or landing and three newels. The first part of this stair corresponds, in number of risers, with the stair shown in Fig. 33; the second newel runs down to the floor, and helps to sustain the landing. This newel may simply by a 4 by 4-inch post, or the whole space may be inclosed with the spandrel of the stair. The second flight starts from the platform just as the first flight starts from the lower floor, and both flights may be attached to the newels in the manner shown in Fig. 29. The bottom tread in Fig. 32 is rounded off against the square of the newel post; but this cannot well be if the stairs start from the landing, as the tread v/ould project too far onto the platform. Sometimes, in high-class stairs, provision is made for the first tread to project well onto the landing. If there are more platforms than one, the principles of construc- tion will be the same; so that whenever the student grasps the full conditions governing the construction of a single-platform stair, he will be prepared to lay out and construct the body of any stair having one or more landings. The method of laying out, making, and setting up a hand-rail will be described later. Stairs formed with treads each of equal width at both ends, are named straight flights; but stairs having treads wider at one end than the other are known by various names, as winding stairs, dog-legged stairs, circular stairs,, or elliptical stairs. A tread with parallel sides, having the same width at each end, is called a flyer; while one having one wide end and one narrow, is called a winder. These terms will often be made use of in what follows. 177 26 STAIR-BUILDING The elevation and plan of the stair shown in Fig. 34 may be called a dog-krjgcd stair with three winders and six fl}'ers. The flyers, however, may be extended to any number. The housed strings to receive the winders are shown. These strings show exactly the manner of construction. The shorter string, in the corner from 1 to 4, which is shown in the plan to contain the housing of the first winder and half of the second, is put up first, the treads being leveled by aid of a spirit level; and the longer upper string is put in place after- wards, butting snugly against the lower string in the corner. It is then fastened firmly to the wall. The winders are cut snugly around the newel post, and well nailed. Their risers will stand one above another on the post; and the straight string above the wiiiders will enter the post on a line with the top edge of the uppermost winder. Platform stairs are often constructed so that one flight will run in a direc- tion opposite to that of the other flight, as shown in Fig. 35. In cases of this kind, the landing or })latform requires to have a length more than double that of the treads, in order that both flights may have the same width. Sometimes, however, and for various reasons, the upper flight is made a little narrower than the lower; but tliis expedient should be avoided when- ever possible, as its adoption unbalances the stairs. In the example before us, eleven treads, not including the landing, run in one direction; while four treads, including the landing, run in the opposite direction; or, as workmen put it, the stair "returns on itself." The elevation Fig. 31. Elovafidii and Pl.an of Dog-Tjep:ged Stair with Three Winders and Six Klyers. 178 STAIR-BUILDIXC 27 \£ Lar>dinq m 10 a 13 14 !5 Newel 16 Wall Fig. 35. Plan of Platform Stair Returning on Itself. sho^^^l in Fio;. 36 illustrates the manner in which the work is executed. The various parts are shown as follows: Fig. 37 is a section of the top landing, with baluster and rail. Fig. 3S is part of the long newel, showing mortises for the strings. Landinq I2 2z=:zz2zrrzzzzz2Z2zzzzzs Lan ding Base Fig. 36. Elevation Showing Construction of Platform Stair of whicli Plan is Given in Fig. o5. 179 28 STAm-BUIT>DIXG >/M/^^M t Fig. 39 rcprescMits part of the bottom newel, showing the string, moulding on the outside, and cap. Fig. 40 is a section of the top string enlarged. Fig. 41 is the newel at the 'bottom, as cut out to receive bottom step. It must be remembered that there is a cove under each tread . This may be nailed in after the stairs are put together, and it adds greatly to the appearance. We may state that stairs should have carriage 'pieces FiK. H7. scition fixed from floor to floor, under the stairs, to support of Top Landiiip, ' i i Baiuster.amiKaii. ^hcm. Tliesc may be notched under the steps; or roucjh hrachcts may be nailed to the side of the car- riaire, and carried under each riser and tread. There is also a framed spandrel which helps materially to carry the weight, makes a sound job, and adds greatly to the appearance. This spandrel may be made of ] {-incli material, with panels and mouldijigs on the front side, as shown in Fig. 30. The joint between the top and bottom rails of the spandrel at the angle, should be made as shown in Fig. 42 with a cross-tongue, and glued and fastened with long screws. Fig. 43 is simply one of the panels showing the ^ Fig. 38. String Fig. 39. Mortises in Liower Newfl for String, Out- .sideMoulding.and Cap. miters on the moulding and the shape Mortises in Long n 1 • » ji • Newel. of the sections. As there is a conven- ient space under the landing, it is commonly used for a closet. In setting out stairs, not only the proportions of treads and risers must be considered, but also the material available. As this material runs, as a rule, in certain si^cs, it is best to work so as to conform to it as nearly as possible. In ordinary stairs, 11 by 1 -inch common stock is used for strings and treads, and 7-inch by f-inch stock for risers; in stairs of a better class, Fig. 40. Euiarg- widcr and thicker material may be used. The rails ed^sectioiiot Top ^^,^ ^^^ ^^ various heights; 2 feet 8 inches mav be 180 STAIR-BUILDIXG 29 taken as an average heiglit on the stairs, and 3 feet 1 inch on hincHno-s, with two balusters to each step. In Fig. 3G, all the newels and balusters are shown square; but it is much better, and' is the more common practice, to have them Newel Fig. 41. Xe-n-el Cut to Receive Bottom Step. Fig. i2. Showiug Method of Joining Spandrel Rails, witti Cross-Touyue Glued and Screwed. turned, as this gives the stairs a much more artistic appearance. The spandrel under the string of the stairs\-ay shows a style in which many stairs are finished in hallways and other similar places. Plaster is sometimes used instead of the panel work, but is not nearly so good as woodwork. The door under the landing may open into a closet, cr may lead to a cellarway, or through to some other room. In stairs with winders, the width of a winder should, if possible, be nearly the width of the regular tread, at a distance of 14 inches from the narrow end, so that the length of the step in walking up or down the stairs may not be interrupted; and for this reason and several others, it is always best to have three winders only in each quarter-turn. Above all, avoifl a four-winder turn, as this makes a breakneck stair, which is more difficult to construct and incon- venient to use. Bidlnose Tread. No other stair, perhaps, looks so well at the starting point as one having a hidinosc step. In Fig. 44 are shown a plan and elevation of a flight of stairs having a bullnose tread. The method of obtaining the lines and setting out the body of the stairs, Mouldin Fig. AX Panel in Spandrel. Sho'w iug Miiei-.s ou Moulding, and Shape of Section." 181 30 STAIR- BUILDING is the same as has ahvady been explained for other stairs, with the exception of the first two steps, which are made with circular ends, as shown in tlie plan. These circular ends are worked out as here- after described, and are attached to the newel and string as shown. Scale of& ^Feet y^ Fig. 44. Elevation and Plan of Stair with Bullnose Tread. The example shows an open, cut string with brackets. The spandrel under the string contains short panels, and makes a very handsome finish. The newels and balusters in this case are turned, and the latter have cutwork panels between them. 18^ STAIR-BUILDING 31 Fig. 45. Section through Bullnose Step. Bullnose steps are usually built up with a three- piece block, as shown in Fig. 45, which is a sec- tion through the step indicating the blocks, tread, and riser. Fig. 46 is a plan showing how the veneer of the riser is prepared before being bent into position. The block /I indi- cates a wedge which is glued and driven home after the veneer is put in place. This tightens up the work and makes it sound and clear. Figs. 47 and 48 show other methods of forming bullnose steps. Fig. 49 is the side elevation of an open-string stair with bullnose steps at the bottom; .showing the lower end of the string, and the manner in which it is prepared for fixing to the blocks of the step. Fig. i%. Plan showing Preparation of Veneer before , Bending into Position. Fig. 51 is a section through the string, showing the bracket, cove, and projection of tread over same. Figs. 52 and 53 show respectively a plan and vertical section of the bottom part of the stair. The blocks are shown at the ends of the steps (Fig. 53), with the veneered parts of the risers going round them; also the position where the string is fixed to the blocks (Fig. 52) ; and Ne^A/e1 '^/M//MM//A Fig. 47 Methods of Forming Bullnose Steps. Fig. 48. the tenon of the newel is marked on the upper step. The section (Fig. 53) shows the manner in which the blocks are built up and the newel tenoned into them. 1R9 32 STAIR-BUILDING Fig. 49. Side Klevation of Open-Strin Stair with BuUnose Steps. The newel, Fig. 49, is rather an elaborate affair, being carved at the base and Oii the body, and having a carved rosette planted in a small, sunken panel on tliree sides, the rail butting against the fourth side. Open-Newel Stairs. Before leav- ing the subject of straight and dog- logired stairs, the student should be made familiar with at least one example of an open-newel stair. As the same principles of construction govern all styles of open-newel stairs, a single example will be sufficient. The student must, of course, understand that he himself is the greatest factor in planning stairs of this type; that the setting out and design- ing will generally devolve on him. By exercising a litde thought and foresight, he can so arrange his plan that a minimum of both labor and material will be recjuired. Fig. 54 shows a plan of an open-newel stair having two landings and closed strings, shown in elevation in Fig. 55. The dotted lines show the carriage timbers and trimmers, also the lines of risers; while the treads are shown by full lines. It will be noticed that the strings and trimmers at the first landing are framed into the shank of the second newel post, which runs down to the floor; while the top newel drops below the fascia, and has a turned and carved drop. This drop hangs below both the fascia and the string. The lines of treads and risers are shown by dotted lines and crosshatchcd sections. The position of the carriage timbers is shown both in the landings and in the runs Ki-. r.i. Sf.iiou of the stairs, the projecting ends of these timbers being luiit'i. ti ug. j.^,ppQ^^,(] t(j i^g resting on the wall. A scale of the plan and elevation is attached to the ])lan. In Fig. 55, a story rod is .shown at the right, with the numl)er oi ri.sers spaced oft' thereon. The design of the newels, spandrel, framing, and paneling is shown. Fig. .50. Lower End of Siring to Connect with BuUuose Step. 184 STAIR-BUILDING 33 Fig. 53. Plan of Bottom Part of BuUuose Stall" Fig. .53. Vertical Section through Bottom Part of Bullnose Stair. Only the central carriage timbers are shown in Fig. 54; but in a stair of this width, there ought to be two other timbers, not so heavy, perhaps, as the central one, yet strong enough to be of service in lend- ing additional strength to the stairway, and also to help carry the laths and plaster or the paneling which may be necessary in completing the under side or soffit. The strings being closed, the butts of their balusters must rest on a subrail which caps the upper edge of the outer string. ^ ^■ V ^ '.\ ^---Tf--^ JJ 4f a -w Well -Hole I!! 5ll ^:-jJ:i:i:.g Qjll Hi!i .3!i; tr —J Carnage _, -i.\ Vr it- — i I S' n 7 Feet -B Fig. 54. Plan of Open-Newel Stair, with Two Landings and Closed Strings. 185 34 STAIR-BUILDING The first newel should pass through the lower floor, and, to insure solidity, should be secured by bolts to a joist, as shown in the elevation. The rail is attached to the newels in the usual manner, with handrail bolts or other suitable device. The upper newel should be made fast to the joists as shown, either by b-olts or in some other Fig. 55. Elfvatioii of Open-Newel Stair Shown in Pliui in Fig. 51. eflicient manner. The intermediate newels are left .square on the .•^liank below tlie .stairs, and may be fastened in the floor below either by morti.H*' and tenon or by making u.se of joint bolts. Everything about a stair .should be made solid and .sound; and every joint should .set firmly and elo.sely; or a .shaky, rickety, .sijueaky .stair will be the result, which is an abomination. Stairs with Curved Turns. Sufficient e.\am})les of .stairs having angles of greater or less degree at t^j; tin-n or change of direction, to 18B HALL AND PARTIALLY ENCLOSED STAIRCASE IN LONG HALL, GREYROCKS, ROCKPORT. MASS. Frank Chouteau Brown, Architect, Boston, Mass. For Plans and Exteriors, See Vol. I, Pages 272, 282, and 299. HALL AND STAIRCASE IN HOUSE AT WOLLASTON, MASS, Frank Chouteau BijQYfn, Architect STAIR.BUILDIXG 35 enable the student to build any stair of this class, have now been given. There are, however, other types of stairs in common use, whose turns are curved, and in which newels are employed only at the foot, and sometimes at the finish of the flight. These curved turns may be any part of a circle, according to the requirements of the case, but turns of a quarter-circle or half-circle are the more common. The string forming the curve is called a cylinder, or part of a cylinder, as the case may be. The radius of this circle or cylinder may be any length, according to the space assigned for the stair. The opening around which the stair winds is called the icell-hole. Fig. 56 shows a portion of a stairway having a well-hole with a 7-inch radius. This stair is rather peculiar, as it shows a quarter- space landing, and a quarter-space having three winders. The reason for this is the fact that the landing is on a level with the floor of another room, into which a door opens from the landing. This is a problem very often met with in practical work, w'here the main stair is often made to do the work of two flights because of one floor being so much lower than another. A curved stair, sometimes called a geometrical stair, is shown in Fig. 57, containing seven winders in the cylinder or well -hole, the first and last aligning with the diameter. In Fig. 58 is shown another example of this kind of stair, con- taining nine winders in the well-hole, with a circular wall-string. It is not often that stairs are built in this fashion, as most stairs having a circular well-hole finish against the wall in a manner similar to that shown in Fig. 57. Sometimes, however, the workman will be confronted with a plan such as shown in Fig. 58; and he should know how to lay out the wall-string. In the elevation. Fig. 58, the string is shown to be straight, similar to the string of a common straight flight. This results from having an equal width in the winders along the wall-string, and, as we have of necessity an equal width in the risers, the development of the string is merely a straight piece of board, as in an ordinary straight flight. In laying out the string, all we have to do is to make 4- f 7- 6 ^ > i >■ 8 -IB [T 0) 1 w 1 Landing r < // (-lA^ Fie. 56. Stair Serving for Two Flights, with Mid-Floor Landing. 187 36 STAIR-BUILDING a coininon pitch-hoard, and, with it as a templet, mark the hues of the treads and risers on a straiglit piece of board, as shown at 1, 2, 3, 4, etc. If you can manage to bend the string without kerfing (grooving), it will be all the better; if not, the kerfs (grooves) must be parallel to the rise. You can set oiit with a straight edge, full size, on a rough platform, just as shown in the diagram; and W'hen the string is bent and set in place, the risers and winders will have their correct positions. To bend these strings or otherwise prepare them for fastening against the wall, perhaps the easiest way is to saw the string with a fine saw, across the face, making parallel grooves. This method of bending is called kerpig, above referred to. The kerfs or grooves must be cut parallel to the lines of the risers, so as to be vertical when the string is in place. This method, however — handy though it may be — is not a good one, inasmuch as the saw groove will show more or less in the finished work. Another method is to build up or stave the string. There are Fig. 57. Geometrical Stair with Seven Winders. Baee a 9 Line Plan Fig. 58. Plan of Circular Stair and Layout of Wall String for Same. several ways of doing this. In one, comparatively narrow pieces are cut to the required curve or to portions of it, and are fastened together, edge to edge, w'ith glue and screws, until the necessary width is obtained (see Fig. 59). The heading joints may be either butted or beveled, the latter being stronger, and should be cross-tongued. Fig. GO shows a method that may be followed when a wide string is required, or a piece curbed in the direction of its width is needed 188 STAIR-BUILDING 37 for any purpose. The pieces arc stepped over each otlier to suit the desired curve; and though shown square-edged in the figure, they are usually cut beveled, as then, by reversing them, two may be cut out of a batten. Panels and quick sweeps for similar purposes are obtained in the manner shown in Fig. 61, by joining up narrow boards edge to edge Fiff. 59. Methods Of Building Up Strings. Fig. 60. at a suitable bevel to give the desired curve. The internal curve is frequently worked approximately, before gluing up. The numerous joints incidental to these methods limit their uses to painted or unim- portant work. In Fig. 62 is shown a WTeath-piece or curved portion of the outside string rising around the cylinder at the half-space. This is formed by reducing a short piece of string to a veneer between the springings; bending it upon a cylinder made to fit the plan; then, when it is secured in position, filling up the back of the veneer with staves glued across it; and, finally, gluing a piece of canvas over the whole. The appearance of the wreath-pi ce after it has been built up and removed i.-om the cylinder is indicated in Fio;. 63. The canvas back has been omitted to show the staving; and the counter- wedge key used for connecting the wreath-piece with the string is shown. The wreath- piece is, at this stage, ready for marking the outlines of the steps. Fig. 62 also shows the drum or shape around which strings may be bent, whether the strings are formed of veneers, staved, or kerfed. Another drum or shape is shown in Fig. 64. In this, a portion of a cylinder is formed in the manner clearly indicated; and the string, being set out on a veneer board sufficiently thin to bend easily, is laid Fig. 61. Buikling Up a Curved Panel or Quick Sweep. 189 38 STAIR-BUILDING down round the cun'c, such a number of pieces of hke thickness being then ackled as will make the required thickness of the string. In working this methotl, glue is introduced between the veneers, which Fig. 63. Wroath- Piece Bent around Cylinder. Fig. a"?. CompletedWrealh- Piece Removed from Cylinder. Fig. 64. Another Drum or Shape for JUiilding Curved Strings. are then (juiekly strained down to the curved piece with hand screws. A string of almost any length can be formed in this way, by gluing a few feet at a time, and when that dries, removing the cylindrical curve and gluing down more, until the whole is completed. Several other methods will suggest them.selves to the workman, of building up good, solid, circular strings. One method of laying out the treads and risers around a cylinder or drum, is shown in Fig. 65. The line D shows the curve of the rail. The lines showing treads and risers may be marked off on the cylinder, or they may be marked off after the veneer is bent around the drum or cylinder. There are various methods of making inside cylinders or wells, and of fastening same to strings. One method is shown in Fig. G6. This gives a strong joint when properly made. It will be noticed that the cylinder is notched out on the back; the two blocks shown at the back of the offsets are wedges driven in to secure the cylinder in place, and to drive it up tight to the strings. Fig. 67 shows an 8-inch well- hole with cylinder complete; also the method of trimming and finish- ing same. The cylinder, too, is shown in such a manner that its con- struction will be readily understood. Stairs having a cylindrical or circular opening always require a weight support underneath them. This support, which is generally made of rough lumber, is called the carriage, because it is supposed 190 STAIR-BUILDIXG 39 to carry any reasonable load that may be placed upon the stairway. Fig. 6S shows the under side of a half-space stair having a carriage beneath it. The timbers marked S are of rough stuff, and may be 2-inch by 6-incli or of greater dimensions. If they are cut to fit the risers and treads, they will require to be at least 2-inch by S-inch. In preparing the rough carriage for the winder^, it will be best to let the back edge of the tread project beyond the back of the riser so that it forms a ledge as shown under C in Fig. 69. Then fix the cross-carriage pieces under the winders, with the back edge about flush with the backs of risers, securing one end to the well with screws, and the other to the wall string or the wall. Now cut short pieces, marked (Fig. 68), and fix them tightly in between the cross-carriage and the back of the riser as at 5 6 in the section. Fig. 69. These carriages should be of 3-inch by 2-inch material. Now get a piece of wood, 1-inch by 3-inch, and cut pieces C C to fit tightly between the top back edge of the winders (or the ledge) and the pieces marked B B in section. This method makes a \exy sound and strong job of the winders; and if the stuff is roughly planed, and blocks are glued on each side of the short cross-pieces 0, it is next to impossible for the winders ever to spring or squeak. When the weight is carried in this manner, the plasterer will Fig. 65. Laying Out Treads and Risers around a Drum. i::-'^. Fig. OC. One :Metbod of Making an Inside Well. Fig. 6" Construction and Trimming of 8-Inch. Well-Hole. .have very little trouble in lathing so that a graceful soffit will be made under the stairs. The manner of placing the main stringers of the carriage S S, is shown at .1, Fig. 69. Fig. 68 .shows a complete half-space stair; 191 40 STAIR-Bnr.DIXG one-half of this, finished as shown, will answer well for a quarter-spaee stair. Another method of forming a carriage for a stair is shown in Fig. 70. Tins is a pecnliar but very handsome stair, inasmuch as the first and the last four steps are parallel, but the remainder balance or datice. The treads are numbered in this illustration ; antl the plan of the handrail is shown ex- tending from the scroll at the bottom of the stairs to the landing on the second story.* The trimmer T at the top of the stairs is also shown ; and the rough strings or carriages, R S,R S, R S, are represented by dotted lini's. This plan represents a stair with a curtail step, and a scroll handrail rest- iiii"- over the curve of the curtail step. This type of stair is not now much in vogue in this c o u n t r y, though it is adopted occa- sionally in some of the larger cities. The use of heavy newel posts instead of curtail steps, is the prevailing style at present. In laying out geometrical stairs, the steps are arranged on prin- ciples already described. The well-hole in the center is first laid down and the steps arranged around it. In circular stairs with an open well- hole, the handrail being on the inner side, the width of tread for the steps should be set ort" at about 18 inches from the handrail, this giving an approximately uniform rate of progress for anyone ascending or descending the stairway. In stairs with the rail on the outside, as sometimes occurs, it will be sufficient if the treads have the proper width at the middle point of their length. Where a flight of stairs will likely be subject to great stress and wear, the carriages should be made much heavier than indicated in ^ B 1 \ 5 S S Fig. OS. Umler Side of Il:Uf-Sp:xc-e Stair, with Carriages aud Cross;Carriage.s. 192 STAIR-BUILDING 41 m^ Fig. 63. Method of Reinforcing Stair. the foregoing figure.s; uikI there may be cases when it will be necessary to use iron bolts in the sides of the rough strings in order to give them greater strength. This necessity, however, will arise only in the case of stairs built in public buildings, churches, halls, factories, ware- houses, or other buildings of a simi- lar kind. Sometimes, even in house stairs, it may be wise to strengthen the treads and risers by spiking pieces of board to the rough string, ends up, fitting them snugly against the under side of the tread and the back of the riser. The method of doing this is shown in Fig. 71, in which the letter shows the pieces nailed to the string. Types of Stairs in Common Use. In order to make the student familiar with types of stairs in general use at the present day, plans of a few of those most likelv to be met with will now be given. Fig. 72 is a plan of a straight stair, with an ordi- nary cylinder at the top provided for a return rail on the landing. It also shows a stretch-out stringer at the starting. Fig. 73 is a plan of a stair with a lantling and return steps. Fig. 74 is a plan of a stair with an acute angular landing and cylinder. Fig. 75 illustrates the same kind of stair as Fig. 74, the angle, however, being obtuse. Fig. 7G exhibits a stair having a half-turn with two risers on land- Fig. 70. Plan Showing One Method of Constructing Carriage and Triimuiug Winding Stair. ings. Fig. 77 is a plan of a quarter-space stair with four winders. Fig. 78 shows a stair similar to Fig. 77, but with six winders. 193 42 STAIH-BUILDIXG I \ Fig. 72. Plan of Straicht Stair with Cylinder at Top for Return Kail. Fig. 79 shows a stair having five Fig. 71. Reinforcing: Treatls anrt Ri-sers by Blocks Nailed to String. dancing winders. Fig. 80 is a plan of a half-space stair having five dancing winders and a quarter-space landing. Fig. SI .shows a half-space stair with dancing winders all around the cylinder. Fig. 82 shows a geometrical stair having ^^■iIlders all around the cylinder. Fig. 83 shows the plan and elevation of stairs which turn around a central post. This kind of stair is frequently used in large stores and in clubhouses and other similar places, and has a very graceful appearance. It is not ^•cI•y difficult to build if properly planned. Tlie only form of stair not shown which the student may be called upon to build, would very likely be one having an elliptical plan; l)ut, as this form is so seldom u.scd — being Fig. 7x Plan of Stair viih foniul, ill fact, ouly ill public buildiiigs or I.iandiug and Return steps. ^ • i c great mansions — it rarely falls to the lot of the ordinary workman to be called upon to design or construct a stairway of this type. ^ J Fig. 74. I'lan of Stair with Acute- Angle Landing and Cylinder. Fig. 75. Plan of Stair with Obtuse- Angle Lauding and Cylinder. 194 STAIR-BUILDING 43 Fig. 77. Quarter-Space Stair with Four Winders. Fig. 76. Halt-Turn Stair with Two Risers on Landings. Fig. 79. Stair with Five Dancing Winders. ) Fig. 78. Quarter- Space Stair with Six Winders. Fig. 81. Half-Space Stair with Dancing Winders all around Cylinder. GEOMETRICAL STAIRWAYS AND HANDRAILINQ Fig. 80. Half-space Stair with ^he term geometrical is applied to stair- "^SiS^SlclLandtnT ^"^^^ ^^'^^'"^g ^^")' ^''''^ ^^ ^^^^'^ ^«^ '^ P^'^"" The rails over the steps are made con- tinuous from one story to another. The resulting winding or twisting pieces are called wreaths. Wreaths. The construction of wreaths is based on a few geometrical problems — namely, the projection of straight and curved lines into an oblique plane; and the finding of the aigle of inclination of the plane into which the lines and curves are projected. This angle 195 44 STAIR-BUILDIXG Fitr. 82. Geometrical Stair with VViutlers all Arouud fvliiKler. Fig. 83. Plan and Eleva- tion of Stair.s Turning around a Central Post. is calk'tl the bevel, and by its use the wreath is made to twist. In Fig. 84 is shown an obtuse- ill^ angle plan; in Fig. 85, an acute-angle ])lan; and in Fig. 86, a semicircle en- closed within .straight lines. Projection. A knowledge of how to project the lines and curves in each of these plans into an oblique plane, and to find the angle of inclination of the plane, will enable the student to construct any and all kinds of wreaths. The straight lines a, h, c, d in the plan. Fig. 8G, are known as tangents; and the curve, the central line of the plan wreath. The straight line across from n to n is the diameter; and the perpendicular line from it to the lines c and h is the radius. A tangent line may be defined as a line touching a curve without cutting it, and is made use of in handrailing to square the joints of the wreaths. Tangent System. The tangent system of bandrailing takes its name from the use made of the tangents for this purpose. In Fig. 86, it is shown that the joints connecting the central line of rail with the plan rails \o of the straight flights, are placed right at the springing; that is, they are in line with the diameter of the semi- circle, and .square to the side tangents a and d. The center joint of the crown tangents is shown to be square to tangent.s h and c. When these lines are projected into an oblique plane, the joints of the wreaths can be made to butt square by applying the bevel to them. 106 STAIR-BUILDING 45 Fig. 84. Obtuse- Angle Plan. plane Jbmt All handrail wrcath.s are assumed to rest on an oblique plane while ascending around a well-hole, either in connecting two flights or in connecting one flight to a landing, as the case may be. /Tanqem In the simplest cases of construction, the wreath rests on an inclined plane that in- clines in one direction only, to either side of the well-hole ; while in other cases it rests on a that inclines to two sides. Fig. 87 illustrates what is meant by a plane inclining in one direction. It will be noticed that the lower part of the figure is a reproduction of the cjuad- rant enclosed by the tangents a and b in Fig. 86. The quadrant. Fig. 87, represents a central line of a wreath that is to ascend from the joint on the plan tangent a the height of h above the tangent b. In Fig. 88, a view of Fig. 87 is given in which the tangents a and b are shown in plan, and also the quadrant representing the plan central line of a wreath. The curved line extending: from a to h in this figure represents the development of the central line of the plan wreath, and, as shown, it rests on an oblique plane inclining to one side onlv — namelv, to the side of the plan tangent a. The joints are made square to the devel- oped tangents a and 7?i of the in- clined plane; it is for this purpose only that tangents are made use of in wreath construc- tion. They are shown in the figure to consist of two lines, a and m, which are two adjoining sides of a developed section (in Fig. 86. semicircular pian. Fig. 85. Acute- Angle Plan. Joint b / c a ^ .2 IS \ d n ^ Joint Joint ^ n ] Diameter 1 vy w 1 1 p LJ X97 46 STAIR-BUILDIXG Joint FiR. R7. Illustrating: Plane Inclined in One Direction Only. this case, of a sc|uare prism), the section being the assumed inchned plane whereon the wreath rests in its ascent from a to h. The joint at h, if made square to the tangent ni, will be a true, square butt-joint; so also will be the joint at a, if made square to the tangent a. In practical work it will be required to find the correct goemetrical angle between the two developed tangents a and m; and here-, again, it may be observed that the finding of the Joint correct angle between the two developed tangents is the essential purpose of every tangent system of handrailing. In Fig. 89 is shown the geometrical solu- tion — the one necessary to find the angle between the tangents as required on the face- mould to square the joints of the wreath. The figure is shown to be similar to Fig. 87, except that it has an additional portion marked "Section." This section is the true shape of the oblique plane whereon the wreath ascends, a view of which is given in Fig. 8S. It will be observed that one side of it is the developed tangent m; another side, the developed tangent a" (= a). The angle between the two as here presented is the one required on tlu> face- mould to square the joints. In this example, Fig. 89, owing to the plane being obli(jue in one direction only, the shape of the .section is found by merely drawing the tangent a" at riglit angles to the tangent m, making it equal in length to the level tangent a in the plan. By drawing lines parallel to a" and m re.spectively, the form of the section will be found, its outlines being the por- jections of the plan lines; and the angle between the two tangents, as already saiil, is the angle required on the face-moukl to scjuare the joints of the wreath. The solution here presented will enable the student to find the Tanqent a Fig. 88. Plan Line of Rail Pro- jected intfX^iiliqufPlant'Incliued to One Side Only. 198 STAIR-BUILDING 47 Joint <> > -Tanqe-nt-y \ / \/ b a / Plan Joint Joint correct direction of the tangents' as required on the face-mould to square joints, in all cases of practical work where one tangent of a wreath is level and the other tangent is inclined, a condition usually met with in level-landing stairways. Fig. 90 exhibits a condition of tangents where the two are equally inclined. The plan here also is taken from Fig. S6. The inclination of the tangents is made equal to the inclination of tangent h in Fig. 86, as shown at w in Figs. 87, 88, and 89. In Fig. 91, a view of Fig. 90 is given, showing clearly the inclination of the tangents c" and d" over and above the plan tangents c and d. The central line of the wreath is shown extending along the sectional plane, over and above its plan lines, from one joint to the other, and, at the joints, made square to the inclined tangents c" and d" . It is evident from the view here given, that the condition necessary to square the joint at each end would be to find the true angle between the tangents c" and d" , which would give the correct direction to each tangent. In Fig. 92 is shown how to find this angle correctly as required on the face-mould to square the joints. In this figure is shown the same plan as in Figs. 90 and 9L and the same inclination to the tangents as in Fig. 90, so that, except for the portion marked "Section," it would be similar to Fig. 90. To find the correct angle for the tangents of the face-mould, draw the line m from d, square to the inclined line of the tangents c' d"; revolve the bottom inclined tangent c' to cut line m in n, where the joint is shown fixed ; and from this point draw the line c" to vj. The intersection of this line with the upper tangent d" forms the correct angle as required on the face-mould. By drawing the joints square to these two lines, they will butt square with the rail that is to connect Fig. 89. Finding Angle between Tangents. 199 48 STAIR-BUILDING Joint Fig. 90. Two Tangents Equally Inclined. FiR. 91. Plan T^lne.s Projeeteci into Oblique Plane Inclined to Two Sides. with them, or to the joint of another wreath that may belong to the cyhnder or well-hole. Fig. 93 is another view of tlie.se tangents in position placed over and above the plan tangents of the well- hole. It will be observed that this figure is made up of Figs. 88 and 91 com-, billed. Fig. 88, as here ]iresented, is shown to con- nect with a level -lajiding rail at a. The joint having been made square to -the level tangent, a will butt .square to a square end of the level rail. The joint at // is shown to connect the two wreaths and is made Fig. 92. Finding Angle between Tangents. Square tO the mciiued tan- 200 STAIR-BUILDING 40 gent?/i of the lower wreath, and also square to the inclined tangent d' of the upper wreath ; the two tangents, aligning, guarantee a square butt-joint. The upper joint is made square to the tangent d" , which is here shown to align with the rail of the connecting flight; the joint will consequently butt square to the end of the rail of the flight above. The view given in this diagram is that of a wreath starting from a level landing, and winding around a well-hole, connecting the landing with a flight of stairs leading to a second story. It is presented to elucidate the use made of tangents to square the joints in wreath construction. The wreath is shown to be in two sections, one extending from the level-landing rail at a to a joint in the center of the well-hole at h, this section having one level tangent a and one inclined tangent m; the other sec- tion is shown to extend from h to n, where it is butt-jointed to the rail of the flight above. This figure clearly shows that the joint at a of the bottom WTeath— owing to the tangent a being level and there- fore aligning with the level rail of the landing— will be a true butt-joint; and that the joint at li, which connects the two wreaths, will also be a true butt- joint, owing to it being made square to the tangent m of the bottom wreath and to the tangent c" of the upper wreath, both tangents having the same inclination; also the joint at viwill butt .square to the rail of the flight above, ,# Pig. 93. Laying Out Line of Wreath to Start from Level-Land- mg Rail, Wind around ^yell-Hole, and Connect at Landing w?th Flight to Upper Story. 201 50 STAIR-BUILDING owing to it being made square to the tangent d", which is shown to have the same incHnation as the rail of the flight adjoining. As previously stated, the use made of tangents is to square the joints of the wreaths; and in this diagram it is clearly show^n that the way they can be made of use is by giving each tangent its true direc- tion. How to find the true direction, or the angle between the tangents Fig. 91. Tangents Unfolded to Find Their Inclination. a and m shown in this diagram, was demonstrated in Fig. 89; and how to find the direction of the tangents c" and d" was shown in Fig. 92. Fig. 94 is presented to help further toward an understanding of the tangents. In this diagram they are unfolded; that is, they are stretched out for the purpose of finding the inclination of each one over and above the plan tangents. The side plan tangent a is shown stretched out to the fl(X)r line, and its elevation a' is a level line. 'J^hc side plan tangent d is also stretched out to the floor line, as shown by the arc n' in'. By this process the plan tangents are now in one straight line on the floor line, as shown from w to m'. Upon each one, erect a perpendicular line as shown, and from m' measure to n, the height the wreath is to ascend around the well-hole. In 202 STAIR HALL OF HOUSE IN URBANA, ILL. 1 - ' 3 i^. 1 1 y i HB Si i' " ^T^^^B™ i LIVING ROOM OF HOUSE IN URBANA, ILL. "White & Temple, Architects, University of Illinois For Exterior and Plans, See Page 266. STAIR-BITILDING 51 practice, the number of risers in the well-hole will determine this height. Now, from point 11, draw a few treads and risers as shown; and along the nosing of the steps, draw the pitch-line; continue this line over the tangents d", c", and m, down to where it connects with the hot om level tangent, as shown. This gives the pitch or inclination to the tangents over and above the well-hole. The same line is shown in Fig. 93, folded around the w e 1 1-h o 1 e, from ?i, where it connects with the flight at the up- per end of the well-hole, to o, where it connects with the level- landing rail at the bottom of the well-hole. It will be observed that the upper portion, from ■joint n to joint h, rig. 95. WeU-Hole Conneoting Two Flights, with Two Wreath- Pieces, fiacli Coutiduing Portions of Unequal Pilch. over the tangents c" and d", coincides with the pitch-line of the same tangents as presented in Fig. 92, where they are used to find the true angle between the tangents as it is required on the face-mould to square the ioints of the wTcath at h. In Fig. 89 the same pitch is shown given to tangent m as in Fig. 94; and in both figures the pitch is shown to be the same as that over and above the upper connecting tangents c" and r/", which is a neces- sary condition where a joint, as shown at h in Figs. 93 and 94, is to connect two pieces of wreath as in this example. In Fig. 94 are shown the two face-moulds for the wreaths, placed 203 52 STAIR-BUILDIXG upon tlie pitch-line of the tangents over the well-hole. The angles between the tangents of the face-moulds have been found in this figure by the same method as in Figs. 89 and 92, which, if compared with the present figure, will be found to correspond, excepting only the curves of the face-moulds in Fig. 94. The foregoing explanation of the tangents will give the student a fairly good idea of the use made of tangents in wreath construction. Tiie treatment, however, would not be complete if left off at this point, as it shows how to handle tangents under only two conditions — namely, first, when one tangent inclines and the other is level, as at a and m; second, when both tangents incline, as shown at c" and cV. In Fig. 95 is shown a well-hole connecting two flights, where two Tangent Tangent i Fig. '.1(3. Finding Anglo be- tween Tangents for Uottom Wreath of Fig. 95. Joint Joint 1^ 6 4 Tangent Fig. 97. Fimiing Angle be- tween Tangents for Upijer Wreath of Fig. 95. portions of unequal pitch occur in both pieces of wreath. The first piece over the tangents a and h is shown to extend from the square end of the straight rail of the bottom flight, to the joint in the center of the well-hole, the bottom tangent a" in this wreath inclining more than the upper tangent h". The other piece of wreath is shown to connect with the bottom one at the joint h" in the center of the well- hole, and to extend over tangents c" and d" to connect with the rail of the upper flight. The relative inclination of the two tangents in this wreath, is the reverse of that of the two tangents of the lower wreath. In the lower piece, the bottom tangent a", a.s previously stated, inclines con.siderably more than does the upjX'r tangent h"; while in the upper piece, the bottom tangent c" inclines considerably less than the upper tangent d". The question may arise: What cafises this? Is it for variation in the inclination of the tangents over the well-hole? It is simply owing to the tangents being u.sed in handrailing to s(juare the joints. The inclination of the bottom tangent u" of the bottom wreath 204 STAIR-BUILDING 53 JOlMt is clearly shown in the diagram to be determined by the inclination of the bottom flight. The joint at a" is made square to both the straight rail of the flight and to the bottom tangent of the wreath ; the rail and tangent, therefore, must be equally inclined, otherwise the joint will not be a true butt-joint. The same remarks apply to the joint at 5, where the upper wreath is shown jointed to the straight rail of the upper flight. In this case, tangent d" must be fixed to incline conform- ably to the in- clination of the upper rail ; other- wise the joint at 5 will not be a true butt-joint. The same principle is ap- plied in deter- mining the pitch or inclination over the crown tangents h" and c". Owing to the necessity of joint- in g the two wreaths, as shown at h, these two tangents must have the same inclination, and therefore must be fixed, as shown from 2 to 4, over the crown of the well-hole. The tangents as here presented are those of the elevation, not of the face-mould. Tangent a" is the elevation of the side plan tan- gent a; tangents h" and c" are shown to be the elevations of the plan tangents h and c; so, also, is the tangent d" the elevation of the side plan tangent (/. If this diagram were folded, as Fig. 94 was shown to be in Fig. 93, the tangents of the elevation— namely, a", h", c", r/"— would stand over and above the plan tangents a, h, c, d of the well-hole. In prac- tical work, this diagram must be drawn full size. It gives the correct Fig. 98. Diagram of Tangents and Face-Mould for Sta'r with Well-Hole at Upper Landing. 205 54 STAIR-BUILDING Joint Fig. 99. Draw- init; Mould when One Tan{;ent i.s Level and One Inclined o v o r Kigh t- Angled Plan. length to each tangent as reciuired on the face-mould, and furnishes also the data for the lay-out of the mould. Fig. 96 shows how to find the angle between the tangents of the face-mould for the bottom wreath, which, as shown in Fig. 95, is to span over the first plan quadrant a h. The elevation Joint tangents a" and h", as shown, will be the tangents of the mould. To find the angle between the tangents, draw the line ah in Fig. 96; and from a, measure to 2 the length of the bottom tangent a" in Fig. 95; the length from 2 to h, Fig. 96, will equal the length of the \ipper tangent h", Fig. 95. From 2 to 1, measure a distance equal to 2-1 in Fig. 95, the latter being found by dropping a perpendicular from 10 to meet the tangent h" extended. Upon 1 , erect a perpendicular line; and placing the dividers on 2, extend to a; turn over to the perpendicular at a"; con- nect this point with 2, and the line will be the bottom tangent as required on the face-mould. The upper tangent will be the line 2-h, antl the angle between the two lines is shown at 2. iNIake the joint at h square to 2-h, and at a" sfjuare to a"-2. The mould as it appears in Fig. 96 is complete, except the curve, which is comparatively a small matter to put on, as will be shown further on. The main thing is to find the angle between the tan- gents, which is shown at 2, to give them the direction to square the joints. In Fig. 97 is shown how to find the angle between the tangents c" and d" shown in Fig. 95, as required on the face-mould. On the line /i-5, make h-A ecjual to the length of the bottom tangent of the wreath, as shown at /i"-4 in Fig. 95; anil 4-5 equal to the length of the upper tangent d". Measure from 4 the distance shown at 4-6 in Fig 95, and place it from 4 to 6 as shown in Fig. 97; upon 6 erect a CJ 5 o Newel Fig. 100. Plan of Curved Steps and Stringer at Bottom of Stair. 206 STAIR-BUILDING 55 .Joint Level Tangent Floor Line'' b Tangent PiicVi- board perpendicular line. Now place the dividers on 4; extend to k; turn over to cut the perpendicular in h"; connect this point with 4, and the angle shown at 4 will be the angle required to square the joints of the wreath as showni at h" and 5, where the joint at 5 is shown drawn square to the line 4—5, and the joint at h" square to the line 4 h". Fig. 98 is a diagram of tangents and face-mould for a stairway having a well-hole at the top landing. The tangents in this example will be two equallyinclined tan- gents for the bot- tom wreath ; and for the top wreath, one inclined andonelev- el, the latter align- ing with the level rail of the landing:. The face-moidd, as here presented, will further help toward an under- standing of the lay- out of face-moulds as shown in Figs. 96 and 97. It will be obsers'ed that the pitch of the bottom rail is con- tinued from a" to h", a condition caused by the necessity of jointing the wreath to the end of the straight rail at a", the joint being made square to both the straight rail and the bottom tangent a". From h" a line is drawn to d", which is a fixed point determined by the number of risers in the well-hole. From point d", the level tangent d" 5 is drawn in line with the level rail of the landing; thus the pitch-line of the tangents over the well-hole is found, and, as was shown in the explanation of Fig. 95, the tangents as here presented will be those required on the face-mould to square the joints of the wreath. In Fig. 98 the tangents of the face-mould for the bottom wreath are shown to be a" and h". To place tangent a" in position on the face-mould, it is revolved, as shown by the arc, to m, cutting a line Fig. 101. NJewel Finding Angle between Tangents foi* Squaring Joints of Ramped Wreath. 207 56 STAIR-BUI rJ)IXG Newel Fig. 103. Bottom Steps \vith Obtuse Angle Plau. previously drawn from ?/' square to tlie tangent h" extended. Then, by connecting m to h", the bottom tangent is placed in position on the face-mould. The joint at m is to be made square to it; and the joint at c, the other end of the mould, is to be made square to the tangent b". The upper piece of wreath in this example is shown to have tangent c" inclining, the inclination being the same as that of the upper tangent b" of the bottom wreath, so that the joint at c", when made square to both tangents, will butt square when put together. The tangent d" is shown to be level, so that the joint at 5, when squared with it, will butt square with the square end of the level-landing rail. The level tangent is shown revolved to its position on the face-mould, as from 5 to 2. In this last position, it will be observed that its angle with the inclined tangent c" is a right angle; and it should be remembered that in every similar case where one tangent inclines and one is level over a square-angle plan tangent, the angle between the two tangents will be a right angle on the face-mould. A knowledge of this principle will en- able the student to draw the mould for this wreath, as shown in Fig. 90, by merely drawing two lines perpen- dicular to each other, as d" 5 and d" c" , equal respectively to the level tangent d" 5 and the inclined tangent c" in Fig. 98. The joint at 5 is to be made square to d" 5; and that at c" , to d" c". Comparing this figure with the face- mould as shown for the upper wreath in Fig. OS, it will be observed that both are alike. In practical work the stair-builder is often called upon to deal with cases in which the conditions of tangents differ from all the examples thus far given. An instance of this sort is shown in Fig. 100, in which the angles between the tangents on the plan are acute. ■"X^ ^y^' / Pitch- Face Mo<. board ^^^.^ '7y — Riser "1^^ — Riser '- ,'\w b rioor Line '¥ Plan NewelN Fig. 103. Developing Face -Mould, Obtuse-Angie Plan. 208 STAIR-BUILDIXG 57 Fig. 105. Wreath Twisted, Ready to be Moulded. In all the preceding examples, the tan- gents on the plan were at right angle.s; that is, they were square to one another. Fig. 100 is a plan of a few curved steps placed at the bottom of a stairway with a curv'ed stringer,which is struck from a center o. The plan tangents a and b Fig. m. ciitMnc^ Wreath from ^^j.^ gj^Qwu to form an acute angl-e with each other. The rail above a plan of this design is usually ramped at the bottom end, where it intersects the newel post, and, when so treated, the bottom tangent a will have to be level. In Fig. 101 is shown how to find the angle be- tween the tangents on the face-mould that gives them the correct direction for squaring the joints of the ^^Teath when it is determined to have it ramped. This figure must be drawn full size. Usually an ordinary drawing-board will answer the purpose. Upon the board, reproduce the plan of the tangents and curve of the center line of rail as shown in Fig. 100. Pleasure the height of 5 risers, as shown in Fig. 101, from tlie floor line to 5 ; and draw the pitch of the flight adjoining the wreath, from 5 to the floor line. From the newel, draw the dotted line to iv, square to the floor line; from IV, draw the \meivm, square to the pitch-line h'\ Now take the length of the bottom level tangent on a trammel, or on dividers if large enough, and extend it from n to?H, cutting the Fig. 106. T^^^isted Wreath Raised to Position, with i • J j-awn Dreviouslv from Sides Plumb. ^ tr >^ 209 58 STAIR-BUILDING w, at m. Connect m to n as shown by the hne a". The intersection of this hne with //'determines the angle between the two tangents a" and 6" of the face-mould, Avhich gives them the correct direction as required on the face-mould for squaring the joints. The joint at iii'is made square to tangent a"; and the joint at 5, to tangent h". In Fig. 102 is presented an example of a few steps at the bottom of a stairway in which the tangents of the plan form an obtuse angle with each other. The curve of the central line of the rail in this case will be less than a quadrant, and, as shown, is struck from the center o, the curve covering the three first steps from the newel to the springing. In Fig. 103 is shown .how to develop the tangents of the face- mould. Reproduce the tangents and FiK. 107. VincUiii: Hovel, not- torn TaiiK<'iit Indinetl, Top One Level. Fig. 108. Application of Bevels In Fitting Wreath to Kail. curve of the plan in full size. Fix point 3 at a height equal to 3 risers from the floor line; at this point place the pitch-board of the flight to determine the pitch over the curve as shown from 3 through b" to the floor line. From the newel, draw a line to w, square to the floor line; and from v\ square to the pitch-line h'\ draw the line w m; connect m to //. This last line is the development of the bottom plan tangent a; and the line h" is the development of the plan tangent 210 STAIR-BUILDING 50 Fig. 109. Face-Mould imd Bevel for Wreath, Bottom Tangent Level, Top One Inclined. b; and the angle between the two hnes a" and h" will give each line its true direction as required on the face-mould for squaring the joints of the wreath, a d / as shown at m to connect square with the newel, and at 3 to con- nect square to the rail of the conn cctin g flight. The wreath i n this e x- ample follows the nosingline of the steps without being ramped as it was in the examples shown in Figs. 100 and 101. In those figures the bottom tangent a was level, while in Eig. 103 it inclines equal to the pitch of the upper tangent 6" and of the flight adjoining. In other words, the method shown in Fig. 101 is applied to a construction in which the wreath is ramped ; while in Fig. 103 the method is applicable to a ground wreath following Line the nosing line all along the curve to the newel. The stair-build- er is supposed to know how to con- struct a wreath under both conditions, as the conditions are usually determined by the Architect. a. o Fig. 110. Finding Bevels for Wreath with Two Equally Inclined Tangents. 211 60 STAIII-BUILDIXG The foregoing cxcamples cover all conditions of tangents that are likely to turn up in practice, and, if clearly understood, will enable the student to lay out the face-moulds for all kinds of curves. Bevels to Square the Wreaths. The next process in the construc- tion of a wreath that the handrailer will be called upon to perform, is to find the bevels that will, by being applied to each end of it, give the correct angle to square or twist it when winding around the well- hole from one flight to another flight, or from a flight to a landing, as the case may be. The wreath is first cut from the plank square to its surface as shown in Fig. 104. After the application of the bevels, it is twisted, as shown in Fig. 105, ready to be moulded; a n d w hen in position, ascending from one end of the curve to the other T- end, over the in- clined plane of the section around the well-hole, its sides will be plumb, as Fig. 111. Api)Iicatlon of Bevels to Wreath Ascending on Phiiio luclint'il J'^iuiiUy in Two Directions. Fig. 112. Finding Bevel Where Upper Tanu'ciit Inrliiics More Thau Lowtr One. shown in Fig. 106 at h. In this fig- ure, as also in Fig. 105, the wreath a lies in a horizontal position in which its sides appear to be out of plumb as much as the bevels ieiie STAIR-BUILDING 61 are out of pluml). In the upper part of the figure, the wreath b is shown placed in its position upon the phms of the section, where its sides arc seen to be pkunb. It is evident, as shown in the relative posi- tionof the wreath in this figure, that, if the bevel is the correct angle of the plane of the section whereon the wreath h rests in its ascent over the well- a o hole the Fig. 113. Finding Bevel Where Upi)er Tangent Inclines Less ' Than Lower One. wreath will in that case have its sides plumb all along when in position. It is for this purpose that the bevels are needed. A method of finding the bevels for all wreaths (nhich is considered rather difficult) will now be explained : First Case. In Fi^. 107 is shown a case where the bottom tangent of a ^Teath is inclining, and the top one level, similar to the top wreath shown in Fig. 98. It has already been noted that the plane of the section for this kind of WTcath inclines to one side only; therefore one bevel only will be required to square it, which is shown at d, Fig. 107. A view of this plane is given in Fig. 108; and the bevel d, as there shown, indicates the angle of the inclination, which also is the bevel required to square the end d of the wreath. The bevel is shown applied to the end of the landing rail in exactly the same manner in which it is to be applied to the end of the wreath. The true bevel for this wreath is found at the upper angle of the pitch-board. At the end a, as already stated, no bevel is required, owing to the plane inclinino: in one direction onlv. Fig. 109 shows a face-mould and bevel for a wreath with the bottom tangent level and the top tangent inclining, such as the piece at the bottom connecting with the landing rail in Fig. 94. 213 02 STAIR-BUILDIXG Sccoml Case. It may be rc(|uirc(l to find the bevels for a wreath having two equally inclined tangents. An example of this kind also is shown in Fig. 04, where both the tangents c" and d" of the upper Fig. 114. FindiusUevel Whore Tiiiitreuts In- cline Kqually over Obtuse-Angle Plan. Fig. 115. Pa mo Plan as in Fig. Ill, but with Bottom Tangent Level. wreath incline equally. Two bevels are required in this case, because the plane of the section is inclined in two directions; but, owing to the inclinations being alike, it follows that the two will be the same. Thev are to be applied to both ends of the wreath, and, as shown in. Fiff. 105, in the same direction — namelv, toward the inside of the wreath for the bot- tom end, and toward the outside for the upper end. In Fig. 110 the method of finding the bevels is shown. A line is drawn from w to c", square to the pitch of the tangents, and turned over to the ground line at h, which point is con- nected to a as shown. The bevel is at h. To show that equal tangents have equal bevels, the line m is drawn, having the same inclination as the bottom tangent c", but in another direction. Place the dividers on o', and turn to touch the lines d" and m, as shown by the semicircle. The line from o' to n is equal to the side plan tangent Fig. 116. Finding IJevels for Wreath of Fig. 115. 214 STAIR-BUILDING 03 w a, and both the bevels here shown are equal to the one already found. They represent the angle of inclination of the plane where- on the wreath ascends, a view of which is given in Fig. Ill, where the plane is shown to incline equally in two directions. At both ends is shown a section of a rail ; and the bevels are applied to show how. by means of them, the wreath is squared or twisted when winding around the well-hole and ascending upon the plane of the section. The view given in this figure will en- able the student to understand the nature of the bevels found in Fig. 110 for a wreath having two equally inclined tangents; also for all other wreaths of equally inclined tangents, in that every w r e a t h in such case is assumed to rest upon an in- clined plane in its ascent over the well- hole, the bevel in every case being the angle of the inclined plane. Third Case. In this example, two unecjual tangents are given, the upper tangent inclining more than the bottom one. The method shown in Fig. 110 to find the bevels for a wreath with two equal tan- gents, is applicable to all conditions of variation in the inclination of the tangents. In Fig. 112 is shown a case where the upper tangent d" inclines more than the bottom one c". The method in all cases is to continue the line of the upper tangent d" , Fig. 112, to the ground line as shown at n; from n, draw a line to a, which will be the horizon- tal trace of the plane. Now, from o, draw a line parallel to a n, as shown from c to d, upon d, erect a perpendicular line to cut the tangent d", -as shown, at m; and draw the line m u o" . INIake u o" equal to the length of the plan tangent as shown by the arc from o. Put one Pis', in Upper Tangent Inclined. Lower Tangent Level, Over Acute- Angle Plan. 215 64 STATR-BUILDING m Finding Bevels for Wreatii of Plan, Fig. 117. leg of the dividers on u; extend to touch the upper +angent d", and turn over to 1 ; connect 1 to o"; the bevel at 1 is to be applied to tangent d". Again place the dividers on u; extend to the line h, and turn over to 2 as shown; connect 2 to o", and the bevel shown at 2 will be the one to apply to the bottom tangent c". It will be observed that the line Ji represents the bottom tangent. It is the same length and has the same inclination. An example of this kind of wreath was shown in Fig. 05, where the upper tangent d" is shown to incline more than the bot- tom tangent c" in the top piece ex- tending from h" to 5. Bevel 1 , found in Fig. 112, is the real bevel for the end 5; and bevel 2, for the end //" of the wreath shown from h" to 5 in Fig. 95. Fourth Case. In Fig. 113 is shown how to find the bevels for a wreath when the upper tangent inclines less than the bottom tangent. This example is the reverse of the preceding one; it is the condition of tangents found in the bottom piece of w^reath shown in Fig. 95. To find the bevel, continue the upper tangent h" to the ground line, as shown at n; connect ?«. to a, which will be the horizontal trace of the plane. From o, draw a line parallel to n a, as shown from o to d; upon d, erect a perpendicular line to cut the continued portion of the upper tangent h" in m; from m, draw the line m u o" across as shoMu. Now place the dividers on w; extend to touch the upper tangent, and turn over to 1 ; connect 1 to o" ; the bevel at 1 will be the one to ap})ly to the tangent h" at //-, where the two wreaths are shown connecteil in Fig. 95. Again place the dividers on u; extend to touch the line c; turn over to 2; connect 2 to o" ; the bevel at 2 is to be applied to the bottom tangent o!' at the joint where it is shown to connect with the rail of the flight. F////i Case. In this case we have two equally inclined tangents over an obtuse-angle plan. In Fig. 102 is shown a plan of this kinil ; and in Fig. 103, the development of the face-mould. In Fig. 1 14 is shown how to find the bevel. From a, draw a line to a', square to the ground line. Place the dividers on a'; extend to KIR STAIR-BUILDING 65 touch the pitch of tangents, and turn over as shown to m; connect m to a. The bevel at m will be the only one required for this wreath, but it will have to be applied to both ends, owing to the two tangents being inclined. Sixth Case. In this case we have one tangent inclining and one tangent level, over an acute-angle plan. In Fig. 115 is shown the same plan as in Fig, 114; but in this i.\ ^ Directing Ordinate "• ^ Of Section ^-^ \ ^x ^^ Directing Ordinate Of Base \L_^o Fig. 119. Laying Out Cui'ves on Face-Mould with Pins and Sti'lng. case the bottom tangent a" is to be a level tangent. Probably this condition is the most commonly met with in wreath construction at the present time. A small curve is considered to add to the appear- ance of the stair and rail; and consequently it has become almost a "fad" to have a little curve or stretch-out at the bottom of the stairwav, and in most cases the rail is ramped to intersect the newel at right angles instead of at the pitch of the flight. In such a case, the bottom tangent a" will have to be a level tangent, as shown at a" in Fig. 115, the pitch Off the flight being over the plan tangent b only. 217 66 STAIR-BUILDING To find the bevels when tangent h" inchnes and tangent a" is level, make a c in Fig. 110 equal to a c in Fig. 115. This line will be the base of the two bevels. Upon a, erect the line a w m at right angles to a c; make a IV equal to ou'in Fig. 115; con- nect w and c; the bevel at w will be the one to apply to tan- gent h" at n where the wreath is joined to the rail of the flight. Again, make a m in Fig. 116 equal the distance shown in Fig. 115 between w and m, which is Fig. 120. Shaple Method of Drawing Curves the full height OVer which tan- on Face-Mould. ^^^^ jy, j^ inclined ; connect m to c in Fig. 116, and at m is the bevel to be applied to the level tangent a". Seventh Case. In this case, illus- trated in Fig. 117, the upper tangent b" is shown to in- cline, and the bot- tom tangent a" to be level, over an acute - angle plan. The plan here is the same as that in Fig. 100, where a curve is shown to stretch out from the Section ■^.( -BeveM %s ^N Mirror \ ' X x/ 1 3- « V r^N Plar. / / / / / y y o line of the straight stringer at the bot- tom of a flight to a newel, and is large a- ^ 1 , . . Fig. 121. Tangents, Bevels, MoTild-Curves, etc., from Bottom enOUgll to contain Wroalh of Fig. H.'), in which Upper Tangent Inclines Le.ss „ , 1 • 1 than Lower One. nve treads, which are yracefullv rounded to cut the curve of the central Hue of rail in 1, 2, 3, 4. This curve also may be used to connect a landing rail to a 218 >• < a z ce u O !* J >» bb hi 3 : o d ^ ^ s ce ^ < a © M H H 3 = f O -^ H CA Q Z < Q oe O U p STAIR-BUILDING 67 flight, either at top or bottom, when the plan is acute-angled, as will be shown further on. To find the bevels — o] Major* for there will be two bevels necessary for this wreath, owing to one tangent b" being inclined and the other tangent a" being level — make a c, Fig. 118, equal to ac in Fig. 117, which is a line drawn square to the ground line from the ne\yel and shown in all preceding figures to have been used for the base of a triangle containing the bevel. Make a lO in ^'S- 123. Developed Section of Plane Inclining Un equally ni Two Directions. Fig. 118 equal to -mj in Fig. 117, which is a line drawn square to the inclined tangent h" from w; connect w and c in Fig. 1 IS. The bevel shown at w will be the one to be applied to the joint 5 on tangent h", Fig. 117. Again, make am Fig 123. Arranging Risers around Well-Hole on Level-Landing Stair with Radius of Central Line of Kail One-Halt Width of Tread. in Fig. 118 equal to the distance shown in Fig. 117 between the line representing the level tangent and the line m' 5, which is the height that M9 68 STAIR-BUII.DING Riser Riser tangent b" is shown to rise; connect to to c in Fig. 1 18; the bevel shown at m is to be applied to the end that intersects with the newel as shown at m in Fig. 117. The wreath is shown developed in Fig. 101 for this case; so that, with Fig. 100 for plan, Fig. 101 for the development of the wreath, and Figs. 117 and 118 for finding the bevels, the method of handling any similar case in practical work can be found. How to Put the Curves on the Face- Mould. It has been shown how to find the angle between the tangents o f the faccrmould, and that the angle is for the purpose of squaring the joints at the -ends of the wreath. In Fig. 119 is shown how to lay out the curves by means of pins and a string — a very common practice _, among; stair-build- e r s . In this example the face- mould has equal tangents as shown at c" and d". The angle between the two tangents is shown at m as it will be required on the face-mould. In this figure a line is drawn from wparallel tothe line drawn from /i,which is marked in the diagram as "Directing Ordinate of Section." The line drawn from m will contain the minor axes; and a line draw'n through the corner of the section at 3 will contain the major axes of the ellipses that will consti- tute the curves of the mould. The major is to be drawn square to the minor, as shown. Place, from point 3, the circle shown on the minor, at the same distance as the circle in the plan is fixed from the point o. The diameter Riser Fig. 124. Arrangement of Risers Around Well-Hole with Rad- ius Larger Than One-Half Width of Tread. 820 STAIR-BUILDING 60 of this circle indicates the width of the cun'e at this point. The width at each end is detennined bv the bevels. The distance a b, as shown Fig. 125. AiTangement of Risers around Well-Hole, with Risers Spaced Full Width of Tread. upon the long edge of the bevel, is equal to | the width of the mould, and is the hypotenuse of a right-angled triangle whose base is ^ the width of the rail. By placing this dimension on each side of n, as shown at 6 RisoT- r ^ Blaer Rlser- Riser Fig. 126. Plan of Stair Shown in Fig. 123. Fig. 127. Plan of Stair Shown in Fig. 124. Fig. 128. Plan of Stair Shown in Fig. 125. and b, and on each side of h" on the other end of the mould, as sho'^Ti also at b and b, we obtain the points 6 2 6 on the inside of the cun-e, and 221 70 STAIR-BUILDIXG the points h ] h on the outside. It will now be necessary to find the clliptic-al curves (hat will contain these points; and before this can be done, the exact length of the wmor and major axes respectively must be deter- mined. The length of the minor axis for the inside curve will be the dis- tance shown from 3 to 2; and its length for the outside will be the distance shown from 3 to 1 . Pitch '^^ ^"*^^ ^^^^ length of the major axis 'Board for the inside, take the length of half the minor for the inside on the dividers: place one leg on h, extend to cut the major in z, continue to the minor as shown at k. The distance from h to ^* will be the length of the semi-major axis for the inside curve. To draw the curve, the points or foci w^here the pins are to be fixed must be found on the major axis. To find these points, take the length of b k (which is, as previously found, the exact length of FiR. 129. Drawing Face-MonUl for Wreath from Pitch-Board. Landinq Rail Fig. 130. Development of Face-Mould for Wreath Connecting Rail of Flight with Level- Landing Kail. the semi-major for the inside curve) on the dividers; fix one leg at 2, and describe the arc Y, cutting the major where the pins are shown fixed, at and o. Now take a piece of string long enough to form a 2^2 STAIR-BUILDIXG loop around the two and extending, when tight, to 2, where the pencil is placed ; and, keeping the string tight, sweep the curve from btob. Step Step Step Step ^^T^ Joint Fig. 131. Arranginji Risers iu Quarter-Tnrn between ° .Two Fllght-s. The same method, for finding the major and foci for the out-side curve, is shown in the diagram. The line drawn from h on the outside of the joint at n, to ic, is the semi-major for the out,si(le curve; and the Ffiser Fig. 132. Arrangement of Risers aronnil Quarter-Turn Giv- ing Tangent*; Ecjual Pitch with Connecting Flight. points where the outside pins are shown on the major will be the foci. To draw the curves of the mould according to this method, which 223 72 STAIR-BUILDING 1 m" is a scientific one, may seem a complicated problem; but once it is understood, it becomes very simple. A simpler way to draw them, however, is shown in Fig. 120. The witlth on the minor and at each end will have to be determined by the method just explained in connection with Fig. 119. In Fig 120, the points b at the ends, and the points in which the circumference of the circle cuts the minor axis, will be points contained in the curves, as already explained. Now take a flexible lath; bend it to touch h, z, and b for the inside curve, and b, w, and b for the outside curve. This method is handy where the curve is comparatively flat, as in the example here shown; but where the mould has a sharp curva- Fig. 133. Finding Bevil for Wreath of Plan, Fig. 133. Fig. 134. Well-Hole with Riser in Center. Tangents of Face-Mould, and Central Line of Rail, Developed. ture, as in case of the one shown in Fig. 101, the method shown in Fig. 119 must be adhered to. With a clear knowledge of the above two methods, the student will be able to put curves on any mould. The mould shown in these two diagrams, Figs. 119 and 120, is for the upper wreath, extending from h to n in Fig. 94 A practical h.mdrailcr would draw only what is shown in Fig. 120. He would 224 \ STAIR-BUILDIXG 73 take tlie lengths of tangents from Fig. 94, and place them as shown at hm and m n. By comparing Fig. 120 with the tangents of the upper wreath in Fig. 94, it ^^^ll be easy for the student to understand Fig. 135. Arrangement of Risers in Stair with Obtuse-Angle Plan. Fig. 136. Arrangement of Risers in Obtuse- Angle Plan. Giving Equal Pitch over Tan- gents and Flights. Face-Mould Developed. the remaining lines shown in Fig. 120. The bevels are shown applietl to the mould in Fig. 105, to give it the twist. In Fig. 106, is shown how, after the rail is t\A'isted and placed in position over and above the quadrant c d in Fig. 94, its sides will be plumb. In Fig. 121 are shown the tangents taken from the bottom wreath in Fig. . 95 It was shown how to develop the section and find the angle for the tan- gents in the face-mould, Fig. 137. m Fig. 113. The method shown in Fig. 119 for putting on the curs^es, would be the most suitable. Fig. 121 is presented more for the purposes of study than as a method of construction. It contains all the lines made use of to find Arrangement of Risers in Flight with Curve at Landing. 225 74 STAIR-BUILDING /I ^N Landing Rail 1 \\m 1 , ^^ 1 ',^^ Landing Flooi' ^ 1 I f Plan /^ * N Fig. 138. Development of Face-Moulds for Plan, Fig 137. the developed section of a plane inclining unequally in two different directions, as shown in Fig. 122. Arrangement of Risers in and around Well-Hole. An important matter in wreath construction is to have a knowledge of how to arrange the risers in and around a well-hole. A great deal of labor and material is saved through it; also a far better appc^araiice to the finished rail may be secured. In level-landing stairways, the easiest example is the one shown in Fig. 123, in which the radius of the central line of rail is made equal to one-half the width of a tread. In the diagram the radius is shown to be 5 inches, and the treads 10 inches. The risers are placed in the springing, as at a and a. The elevation of the tangents by this arrangement will be, as shown, one level and one inc^lined, for each piece of wreath. When in this position, there is no trouble in finding the angle of the tangent as required on the face-mould , owing to that angle, as in every such case, being a right angle, as shown at w; also no special bevel will have to be found, because the upper bevel of the pitch-board contains the angle required. The same results are obtained in the example shown in Fig. 124, in which the radius of the well-hole is larger than half the width of a tread, by placing the riser a at a distance from c equal to half the width of a tread, instead of at the springing as in the preceding example. In Fig. 125 is shown a case where the risers are placed at a dis- tance from c equal to a full tread, the effect in respect to the tangents of the face-mould and bevel being the s£|,me as in the two preceding examples. In Fig. 126 is shown the plan of Fig. 123; in Fig. 127, the plan of Fig. 124; and in Fig. 128, the plan of Fig. 125. For the wreaths shown in all these figures, there will be no necessity of spring- ing the plank, which is a term used in handrailing to denote the twisting of the wreath; and no other lievel than the one at the upper end of the pitch-board will be required. This type of wreath, also, is the one that is required at the top of a landing when the rail of the flight intersects with a level-liuidinij rail. 226 STAIR-BUILDING 75 In Fig. 129 is shown a very simple method of drawing the face- mould for this wreath from the pitch-board. ^Nlake a c equal to the radius of the plan central line of rail as shown at the curve in Fig. 130. From where line c c" cuts the long side of the pitch-board, the line c" a" is drawn at right angles to the long edge, and is made equal to the length of the plan tangent a c, Fig. 130. The curve is drawn by means of pins and string or a trammel. In Fig. 131 is shown a quarter-turn between two flights. The correct method of placing the risers in and around the curve, is to put the last one in the first flight one-half a step from springing c, and the first one in the second flight one-half a step from a, leaving a space in the curve equal to a full tread. By this arrangement, as shown in Fig. 132, the pitch-line of the tangents will equal the pitch of the connecting flight, thus securing the second easiest condition of tan- gents for the face-mould — namely, as shown, two equal tangents. For this wreath, only one bevel will be needed, and it is made up of the radius of the plan central line of the rail o c, Fig. 131, for base, and the line 1-2, Fig. 132, for altitude, as shown in Fig. 133. The bevel shown in this figure has been previously explained in Figs. 105 and 106. It is to be applied to both ends of the wreath. The example shown in Fig. 134 is of a well-hole having a riser in the center. If the radius of the plan central line of rail is made equal to one-half a tread, the pitch of tangents will be the same as of the flights adjoining, thus securing two equal tangents for the two sections of wreath. In this figure the tangents of the face-mould are developed, and also the central line of the rail, as shown over and above each quadrant and upon the pitch-line of tangents. The same method may be employed in stairways having obtuse- angle and acute-angle plans, as shown in Fig. 135, in which two flights are placed at an obtuse angle to each other. If the risers shown at a and a are placed one-half a tread from c, this will produce in the elevation a pitch-line over the tangents equal to that over the flights adjoining, as shown in Fig. 13G, in which also is shown the face-mould for the wreath that will span over the curve from one flight to another. In Fig. 137 is shown a flight having the same curve at a landing. The same arrangement is adhered to respecting the placing of the risers, as shown at a and a. In Fig. 13S is shown how to develop the face-moulds- 227 HOUSE IN THE WHITE MOUNTAINS, NEW HAMPSHIRE The Boulders, which ai-e Plentiful inlhis Region, have been Used to Good Advantage, HOUSE NEAR PHILADELPHIA, PA. It is Verily a Part of the Landscape. ESTIMATING PART I * Introductory. The ability to estimate may be considered as the dividing line between the journeyman and the master builder, for, no matter how skilful a mechanic mav become, he can never "han^y out his shingle" and invite patronage in his distinctive line of work, unless he becomes able to make reliable estimates of material and labor to be furnished. To do this something more than mere accuracy and quickness in figures or a mastery of mathematics is needed; namely: experience and judgment, an understanding of the more or less complicated details which go to make up a building, and a knowl- edge of current prices and discounts in the trade. It is the object of this paper to point the way toward the acquirement of such of these needs as may be imparted by words or figures; that is, to put in con- densed form some of the common methods by which estimates are made up, and to point out some of the things which are to be avoided. Prices. As prices of labor and materials are constantly shifting, those quoted in this paper must be taken only as proportionate, to be used in comparison with known quantities and methods. All prices given are as current in Boston, Mass., in December, 1906, and are subject to immediate change. On account of the varia- bleness in price of labor and materials, it is better, in general, to make estimates on the basis of days or hours, and quantities of materials, so that they may be used for comparison in future work. To this end all estimates should be carefully labelled and filed away for future reference. This should be done whether the bids were successful or otherwise. If a successful bid, there will arise a good opportunity to compare the estimates of cost of the different items, with the actual cost of execution; and if a bid fails to win the job, satisfaction and experience may be gained by noting the items which may have been priced too high or too low. This data may be of great service in preparing future estimates, especially in the comparisons between estimated and actually executed work. * There is no such a thing as a universal or permanent standard price for anything. Prices vary in different localities at the same time, and in the same locality at different times. The estimator must therefore acquaint himself with local market conditions in every case. 229 ESTIMATING Catalogues. Catalogues and price lists of all standard articles are easily obtained and should be kept at hand, properly indexed, for ready reference, as they contain a great deal of specific information. For close figuring, however, it will not do to rely upon these prices, as the amounts of trade discounts are not always included. These vary greatly from time to time, and often there are two or more dis- counts, a trnde discount, a cash discount, and a variation in discounts made by different merchants, all of which the contractor must become aware of to obtain bctt.om prices. All data of this sort should be carefully tabulated for constant reference, in such a form thai I* may be easily revised and kept, so far as possible, up to date. The manner and time of payments is a matter to be considered in this connection, as it will permit the contractor to take advantage of cash discounts, which often make a great difference in the cost of certain materials. Profit. To the actual price of labor and materials must be added the profit and this will need careful consideration. A common method is to add a lump sum to the estimated cost of labor and materials, varying with locality and customer, with the probable sharpness of competition and the circumstiinces of the contractor. This is a care- less method, as it leaves no means for future comparison and no cer- tain knowledge of just what the profits of a given job are. Percentage. A better way is to base the profits upon a per- centage of the estimated cost. This will vary, in ordinary cases, from ten to fifteen per cent, ten per cent being the least that should be expected on any work, and this is not enough for small contracts of two or three thousand dollars; but for large work, where there is a great duplication »f parts and processes, it will be enough in most cases. Some contractors, whose workmen are required to perform especially skilful labor, figure fifteen per cent on all labor and ten Dcr cent on materials. Duplicate Parts. The matter of duplication is an important factor in estimating, as a considerable saving is often made if large quantities of material, cither worked or unworked, are required; this is especially true in manufactured parts, such as doors and windows, columns, balustrades, etc. Modern machines are capable of dupli- cation with astonishing rapidity, and workmen can put together 230 ESTIMATING similar parts more quickly and cheaply than variable members. Transportation. The distance of the work from the shop of the contractor, or from centers of manufacture, will fiflect the cost to a marked degree, as much time is consumed in ceaming and especially in handling material a number of times. If communication between the works and the building site can be established by water, it will usually save considerable expense for freight and handling, with perhaps less risk of damage, and conse- quently less expense for crating and boxing. A careful study should be made of the means of transportation to each different building site from the shop, the office, and the mill, and the data kept for future reference, subject to varying rates and conditions, to change of seasons, and amounts to be transported. These are some of the more important matters which require preliminary consideration as affecting all estimates, and are only a small part of the real questions involved, as different localities and customs require different treatment, and numerous questions will arise to confront the contractor, all of which may be successfully met, as we have seen, by the exercise of care and judgment. Methods. Estimates are formed by many and varying methods, depending upon the degree of accuracy required, the capability of the contractor, and the character of the building. A broad division may be made between approximate estimates and accurate detailed estimates, only the latter of which should be considered when it is the intention to actually carry out the work under a definite contract. Approximate Estimates. Approximate estimates are obtained with varying degrees of accuracy by several methods, the most con- venient and reliable of which is the system of cubing; i.e., the cubical contents of the proposed building is obtained and multiplied by a given price per cubic foot. This rate is obtained by careful com- parison of the plans and requirements with similar buildings which have been erected under conditions as like as possible to the con- ditions under which the proposed building can be erected. Several methods are used to determine the cubical units, de- pending upon the size and shape of the proposed building. One method is to multiply the square feet in the plan of the building by the height from half-way the depth of foundations to half-way up the roof. Another system uses the height from the bottom cf the 231 ESTIMATING foundation, and another obtains the actual cubical contents. Any of these may be used if the data for comparison is obtained in the same way, but all are subject to important variations which experience and judgment alone will determine. For instance, if the contour of the building is very uneven, with low portions, such as porches and sheds, and high portions, such as towers and cupolas, these must either be omitted from the whole and compared separately, or a lump sum be added or subtracted according to the size and elaboration of these members. Another variation arises in the size of rooms, giving a ratio of partitions and division walls which is not constant, and of course a large building with many duplicate parts will require a different rating from a smaller one, so that the method of estimating by cubing is at best approximate, and its degree of accuracy depends largely upon the experience and judgment of the contractor. Even long experience will afford no safe-guard against unusual elaboration of interior or exterior, so that cube rates can only be applied to buildings of ordinary character, and comparisons are only reliable between buildings of like description and uses, as the treatment of even the same materials will vary largely in buildings of varying uses. The height of the building will not increase the cube rate pro- portionately, unless the internal voids are alike, although it is cer- tain that the higher one builds from the ground, the more time and expense it requires to put the material in place, to say nothing of thicker walls and necessarily heavier construction. Estimating by the Square. A convenient method of estimating is by the square of one hundred surface feet. This is especially applicable to office buildings, schools, mills, stables, and all buildings where the floors are few in number or similar in plan. For one story buildings the price per square is taken to include the roof, walls, floor, and foundations, but for buildings of two or more stories the price per square should be taken separately for each floor, the lower floor being priced to include the foundations and the top floor to include the roof. This method of estimating by the square is not so accurate as by cubical contents, but the results are often more convenient and adaptable, because the tabulation of the square area of the various floors may be easily reduced to terms of accommodation for public 882 ESTIMATING 5 buildings or shops. For instance, a given floor area in a school house means accommodation for a certain number of pupils; in a church, a certain number of sittings; in factories for the manufacture of staple goods, a certain number of machines and operatives. This unit of accommodation is sometimes carried further, and, by the reverse process, made the basis of another method of estimating the approximate cost of such buildings as the above mentioned, i.e., schools, churches, factories, hospitals, etc. This is also a method by comparison, the known data being supplied by previous experience or calculation, and it is often valuable as a means of determining the approximate cost of buildings necessary to accommodate a given number of individuals or machines, even before any definite plans have been drawn. All of these methods are approximate, with varying degrees of accuracy, and should never be advanced as accurate, or used as the basis of a contract, unless the contractor has had a long and varied experience and feels absolutely certain of his judgment, or unless a proper margin is added for possible variations. Estimating by Quantities. The only sure and correct method of estimating is by taking off the actual quantities in detail and carry- ing out the prices accurately with the cost of labor, the percentage for profit, and contingencies added. For this, accurate and complete drawings and specifications are necessary to give the absolute quantity and quality of materials and labor. The various items are then taken off, similar portions grouped, the amount of labor estimated, and a complete and classified schedule prepared and priced at current rates; the cost of transportation, board of men, and any other contingencies noted, a percentage of profit added, and a sum total reached which should be correct if faithfully done. This, of course, takes considerable time, but is well worth the expense and trouble if a definite contract is to be made. Preparation. In order to estimate to a sufficient degree of accuracy, some things other than the possession of plans and speci- fications are necessary. A visit to the site should be made, to ascer- tain the nature of the soil, the levels of the lot, the distance from rail- road or wharf, the condition of the roads, if a long haul is necessary, and the preparation of the site necessary to receive and dispose of materials. Some knowledge should be obtained of the nature of 233 ESTIMATING the sub-soil, the presence of ledges or water below the surface which will require especial or costly treatment, etc. Often a deposit of sand will be found upon the site which will not only save carting away of material excavated, but, if of proper quality, it may be used for the work. Such items are constantly occurring so that a knowledge of existing conditions will be of great advantage to the estimator. Regarding underground conditions, there is always an element of chance, as the most thorough examination will not always reveal hidden perils; the author knows of a case where a mason had con- tracted for the building of a sewer, and was in a fair way to make a good profit, when a narrow vein of quicksand was uncovered, to over- come which not only took away all the anticipated profit but caused a severe loss to the contractor besides. Ground water is another source of danger and it will be well for the contractor to closely examine his contract, to see to what extent he is to furnish protection from this source, as a vein of water which may have been temporarily stopped or diverted by the operation of building, will sometimes unexpectjly make its presence known during or after the completion of the work, when it may become a source of great annoyance and expense to the contractor if he has agreed to insure a waterproof job. Numerous illustrations could be given of the danger from unforeseen causes which can at best be only partially obviated by the most careful examination. In order to accurately take off a building either by quantities, square or cube, a good knowledge of arithmetic is necessary; and, while we may assume that the reader already possesses this know- ledge, it may be well to include some of the essential rules of that branch of arithmetic which is known as mensuration. This consists primarily in the science of obtaining definite data regarding given figures or surfaces, such as areas, solids, capacity, linear dimensions, and comparisons of bodies. Definitions. The area, or superficial dimension of any figure is the measure of its surface, without regard to its thickness or any other dimension. The cubical contents of any figure is the measure of its solidity, or whole capacity, and has reference to the three dimensions, length, breadth, and thickness. 234 RESIDENCE FOR MRS. THOS. G. GAGE, ROGERS PARK, CHICAGO, ILL. John B. Fischer, Architect, Chicago, IlL View Looking Southeast. Lower Story Cement, Rough Sand Finish; Second Story Finish Shingles Stained a Warm Brown; Woodwork around Windows and Gable .Stained a Few Shades Darker than Shingles; Roof Shingles Stained a Dull Red. For Interiors, See Page S.'Sl. Cost of House: Excavation $ 27.50 Masonry 477 20 Carpentry. 2,S?.'S. lo Sheet-Metal Work. 70.00 Plastering 430 00 Plumbing and Gas fitting 4.50 00 Heating (Hot- Water) 449.40 Tile Work (3 Mantels, and Bath- room Floor) IM 60 Painting and Glazing 212.00 Hardware 60. 00 Decorating. 70 00 Electric Wiring 80 00 Electric and Gas Fixtures 88 20 Window Screens 20 00 Storm Sash. ."iO 00 Window Shades 19 00 Cement Walk 23 00 Grading, Trees and Shrubs 72.00 TotaL *5,162.00 Built in 1903. POBXIM »' - 17' ,»a.-7 rSRST FLCCE PLAN 1*5 ei Jj if? iT 1 lit p '\^^ wm PV^' RESIDENCE FOR MRS. THOS. G. GAGE. ROGERS PARK, CHICAGO, ILL. John B. Fischer, Architect, Chicago The Porch Faces East toward Lake Michigan. 'OECOND rLODB PLAN . ESTIMATING If the figure is considered as hollow, then the cubical contents becomes its capacity or capability of containing matter. The linear dimension of a figure is expressed by its length in a direct line in any direction and has no regard to breadth or thickness. Units. The application of these dimensions is made by fixing a unit by which the figure may be compared and the required dimen- sion obtained; thus, for calculating the area of a figure the unit is usually a square, one side of which is the unit of length, and the area becomes the square measure of the figure. This is expressed in common terms by square inch, square foot, square yard, or any other given unit and the measure of the surface is computed by obtaining the number of these square units which are contained in the figure, the process being called squaring. In a similar manner the cubical contents or solidity of a figure is obtained by computing the number of cubical units which it con- tains, which is called cubing it. Rules. Numerous rules have been adopted for obtaining these dimensions when given dimensions are known, and a tabulation of some of the more important and useful of these follows, by means of which it is hoped that the student may be able to solve most of the ordinary problems which will arise in common practice. RULES AND TABLES TABLE OF MULTIPLES Circumference of a circle Ai'ea of a circle Area of a circle Area of a circle Area of a circle Radius of a circle Radius of a circle Diameter of a circle Diameter of a circle Side of an inscribed square Side of an inscribed square Side of an equal square Area of a triangle diameter X 3.1416 square of the radius X 3.1416 square of the diameter X 0.7854 square of the circumference X 0.07958 half the circumference X half the diameter circumference X 0.159155 square root of the area X 0.56419 circumference X 0.31831 square root of area X 1.12838 diameter X 0.7071 circumference X 0.2251 diameter X 0.8862 base bv i the altitude 235 8 ESTIMATING Area of an ellipse = Surface of a sphere == Surface of a sphere = Surface of a sphere = Solid contents of a sphere = Solid contents of a sphere = Diameter of a sphere = Diameter of a sphere = Circumference of a sphere = Solid contents of a cone or pyramid = Surface of a cube = Area of trapezoid = Note— Volumes of similar their similar lines. product of both diameters X •/' circimiference X diameter square of the diameter X 3.1416 scjuare of the circumference X 0.3183 surface X ^ of its diameter cube of diameter X 0.5230 square root of surface X 0.60419 cube root of solidity X 1.2407 cube root of solidity X 3.8978 area of base X I altitude six X area of one side altitude X 2 sum of parallel sides solids are to each other as the cubes of MEASURE OF LINES AND SURFACE 1. To find the area of a parallelogram: Rule — Multiply the length by the breadth or perpendicular height. See Fig. 1 Are■ v-;- Total cost per perch $4 . 24 A perch of rubble wall laid in Portland cement moxta|^ 1 to 3, will cost: j^ < ^ * 1 perch of stone $1 . 25 ^ barrel Portland cement at $2. 10 1.05. i load sand at $1.75 .29 ^ day, mason at 4 . 50 1 . 50 ^ day, laborer at 2.40 .80 Total cost per perch $4.89 Cut Stone. Cut stonework is figured by the cubic foot, the prices differing according to the amount of labor involved in the cutting; and this will depend somewhat upon the nature of the stone, a hard stone being more expensive to prepare than a soft one. The principal kinds of stone used in building are granite, limestone, sandstone, marble, and bluestone. Granite. Granite is one of the hardest stones to quarry and prepare, and, on account of its cost it is not so freely used as lime- stone or marble. Granite in rough blocks from the quarry will cost 45 to 60 cents a cubic foot, the cutting of beds and joints w'ill cost 25 cents for each square foot of surface so treated. If the face is pitched off to a line with rock face, it will cost 25 cents per square foot, while hammering in 8-cut work will cost 70 cents per square foot. Quincy granite will cost, in the rough, about double this, or $1.20 per cubic foot; the cutting will cost one-third more. From this data we may deduce the following scale: Granite, in rough blocks at quarry, per cu. ft. $0.60 Add for beds and joints per sq. ft. .25 Add for rock face, pitched off to a line, per sq. ft. .25 Add for 8-cut work v per sq. ft. .70 Hence the facing of an average wall with 8 inches of granite V/> 244 ESTDIATING 17 will cost, if the stones arc about 2 feet x 3 feet, or G surface feet in each block: Stock, 4 cu. ft. at .60 $2.40 Beds and end joints -21 sq. ft. at .25 .67 -' i Rock face 6 sq. ft. at.. 25 1.50 J Cost of 6 superficial ft. or 76|^cents per square foot. $4.57 If the same were finished in 8-cut work, the cost of finishing the .surface wquld be 70 cents a square foot instead of 25 cents, making the cost per square foot 45 cents more, or about SI. 21 a square foot. Limestone. Limestone is used to a large extent, especially in conjunction with brick, for trimmings for various kinds of buildings. I/imestone will cost at the quarry about .30 cents a cubic foot ; this will apply to Indiana limestone only. Lake Superior redstone will cost 35 cents; Ohio sandstone, 50 cents. In estimating, ^.^ ^, Liu,estone window set. about 20 per cent should be added for waste, 5 per cent quariy waste, and 15 per cent for cutting waste: * Prices of Common Shapes of Limestone Water table, 8 in. x 12 in. per lineal foot $1 .50 Steps, 7 in. x 14 in. without nosing, per lineal foot 1 .50 Steps, 7 in. x 14 in. with nosing per lineal foot 2.50 Door sills, 8 in. x 12 in. per lineal foot 1 .25 ^ Window sills, 5 in. x 12 in. per lineal foot 1 .00 Window sills, 5 in. x 8 in. per lineal foot .75 Window caps, 4 in. x 10 in. per lineal foot .70 Window caps, 8 in. x 12 in. per lineal foot 1 .00 Wall coping, 5 in. x 20 in. per lineal foot 1 .50 Platforms and large slabs, 6 in. thick, per sq. ft. 2.00 * Window Sets. A common use of limestone is in the fomi of window sets, consisting of a flat arch in three pieces with keystone, and a light sill, as shown in Fig. 12. * These prices are based on a freight charge of $0.55 per cu. ft. to Boston. The freight on I^ake Superior stone is .55 The freight on Ohio stone ,41 245 18 ESTIMATING The rise of these caps is about 10 inches, and the rise of the sill 5 inches. These sets for an average sized window, say 4-foot opening, will cost for a 4-inch reveal $10, and for an eight-inch reveal S15. Sandstone. The cost of dressed sandstone is about 10 per_^ cent more than that of limestone. Setting. The cost of setting cut stone may be taken at 15 cents a running foot for window trimmings and ashlar vrork, and Fig. 13. Seam-Paced Granite Wall. 20 cents for platforms, water table, steps, etc. Trimming and fit- ting at the building will cost about 10 cents per cubic foot. The foregoing prices are based upon quarry-men's wages at $2.50 per day, and stone cutters' wages at $4.00 per day. ]\Iuch of the cutting and finishing of stone is done by machin- ery, so that the question uf wages will not enter into the prepara- tion of the stock so largely as in many other branches. Marble. A more expensive stone to use is marble, which can be obtained in a variety of colors, in diflVrent parts of the country. The price of marble differs in different localities but for general purposes 246 ESTIMATING 19 may be taken as about double the figures which we have quoted for hmestone. Bluestone. Bhiestone is used in the East mainly for flagging, cop- ings, etc., but is used to a considerable extent for building, in Central and Western sections. The price of bluestone flagging 3 inches thick with trimmed joints and face planed and dressed, will be 65 cents a square foot; with natural face, 35 cents to 45 cents. Bluestone ashlar 8 inches thick w^ith natural face and dressed joints, will cost $1.00 per square foot, and 15 cents a square foot for setting. Seam-Faced Granite. In some localities granite, lying in up- turned strata with open weathered seams, is to be obtained. This is used for facing walls in ashlar work, being set oh edge in the wall with the seam-face showing; this will cost, in place, 4-inch to 8-inch thick, from 60 cents to 75 cents a superficial foot. See Fig. 13. BRICKWORK Brickwork is usually estimated by the thousand bricks, but is sometimes priced by the cubic foot at 40 cubic feet to a thousand. A mason in one day will lay from 800 to 1,000 common bricks, or 300 to 400 face bricks. The number of bricks in a wall may be found by multiplying the superficial area by 7^ for each 4 inches of the thickness of the wall. Openings of the size of ordinary windows are generally deducted, but A-ery small openings will cost more to make than the deduc- tion. An allowance for breakage should be made of 5 pef cent. Mortar. Bricks are laid in mortar made of lime or cement, according to the strength required. Lime mortal* should not be used in damp situations, or where great strength is required. The dif- ference in cost of lime and cement mortar is so little that cement mortar is generally used. The building laws of some cities require brick work to be laid in cement mortar for a certain part of the height. Cement mortar makes a darker joint, but where a white joint is required it can be obtained, without loss of strength, by using Port- land cement and lime mortar. Cost. The cost of brickwork by the thousand in various kinds of mortar may be analyzed as follows: 247 20 ESTIMATING III 1 - 3 lime mortar, 1,000 bricks $0.00 3 bu. lime at $.36 per bu. 1 08 \ load of sand at $ 1 . 75 per loai I . 88 10 hours, mason at $.00 per hour G . 00 10 hours, tender at $.30 per hour 3 . 00 $19.90 In 1-3 Rosendale cement mortar: 1,000 bricks $9.00 1.V bbl. Rosendale cement at $1.20 1 . 80 ^ load sand .88 10 hours, mason at $.60 per hour 6 . 00 10 hours, tender at $.30 per hour 3 . 00 $20.68 In 1-3 Portland cement mortar : 1,000 bricks 11 bbl. Portland cement at $2.10 ^ load sand at $1.75 10 hours, mason at $.60 per hoifr 10 hours, tender at $.30 per hour $ 9.00 2.62 .88 6.00 3.00 $21.50 From these tables we may deduce an approximate estimate in round numbers as follows : 1 ,000 bricks laid in 1 - 3 lime mortar $20 . 00 1 ,000 bricks laid in.l - 3 cement mortar 21 . 00 1 ,000 bricks laid in 1 - 3 Portland cement mortar 22 . 00 So that, on a job of ordinary size, the difference between lime and cement mortar ought not to be considered, where cement mortar will give assurance of greater stability. Face Bricks. Face bricks in great variety, are to be had either plain or moulded, and in a variety of colors. On ordinary face brickwork a mason with tender will lay about 300 to 400 bricks in a day. 248 ESTDIATING 2i Faced bricks cost from $25.00 to $50.00 per thousand; a good average brick can be secured for S32.00. This will make the price for a thousand, laid, about as follows: 1,000 face bricks $32.00 U bu. lime at $.36 .45 ^ load fine sand at $1 .75 .88 3 days, mason at $4.80 14.40 H days, tender at S2.40 3.60 $51.33 From this we find that 1,000 face bricks can be laid in the wall for $51.33 of which $33.33 goes for stock and $18.00 for labor. Enameled bricks are to be had in various colors, white and buff beino- the most common. These bricks cost from $50.00 to $60.00 per M. Concrete. Concrete is used to a great extent now for footings, walls, piers, etc. The cost of concrete is not a great deal different from stone for foundations and if there is uncovered a deposit of suitable sand and gravel, as is sometimes the case, it can be put in at a less price than a granite footing. Concrete with a reinforcement of steel is used in various forms for piers, floors, and walls. The cost of a cubic yard of concrete, using the proportion of 1-3 and 6, may be summarized as follows: 1 bbl. Portland cement $2.10 3 bbl. sand .75 6 bbl. broken stone 2.00 Mason, 2 hours at $.60 per hour 1 . 20 Laborer, 4 hours at $.30 per hour 1-20 $7.25 Cellar concrete 3 inches thick will cost S.60 to $.75 per square yard in place. Concrete of Rosendale cement can be put in at less cost, being for foundation walls about $6.00 per cubic yard; for piers $6.50 per cubic yard. 249 22 ESTIMATING MISCELLANEOUS DATA CHIMNEYS Chimneys may be quickly estimated by the lineal foot of height, as follows: 1 flue 8 in. X 8 in. per xoot $0.90 wfth flue lining $1.10 1 " 8 in. X 12 in. per foot 1.00 " " " 1.25 1 " 12 in. X 12 in. per foot 1.20 " " " 1.50 2 flues 8 in. X 8 in. per foot 1.40 " " " 1.80 2 '' 8 in. X 12 in. per foot 1.75 " " " 2.20 FLUE LINING Net price per foot, outside dimensions. ^ in.x 8^ inches $.10 8^ in. x 17^ inches $.32 4^ in.x 13 " .16 13 in.x 13 " .30 Sh in.x 8| " .16 13 in.x 18 " .42 8.i in.x 13 " .22 18 in.x 18 " .70 For openings add one-third. MASONS' SUPPLIES Portland Cement ■ Ro.sentlale Cement Extra Lime for Skimming No. 1 Lime for Mortar Vermont Lime Plaster, 250 lb. bbls. Mortar Color, Red, in bbls. Mortar Color, Red, in 100 or 200 lb. keg Mortar Color, black Philadelphia Pressed Brick, for fireplaces 35.00 per M. Fire Brick 35.00 " " Best Plastering Hair .25 per bush. Mortar Hods 1.50 each Brick Hods 1.25 " 10-in. Mortar Hoes .50 " Good No. 2 Shovels, square point, plain back . 75 ". Sand Screens, wood leg 6.00 " Bolted Dump Barrows 2.00 " 2 .10 per bbl ,20 <( .15 li .05 <( .20 <( .60 (( Oil per lb. .ou (( (I .03i in. ; 8 in. x 5^ in. = 44 sq. in. ; = 327. 2 44 sq. in. In measuring a slate' roof it is usual to allow an extra width of from 6 inches to a foot, according to localities, on hips, valleys, eaves, and wall cuttings, to allow for the extra work involved. Extra charge should be made for towers and all varied forms of roof. Quantities. The number of slates required .to cover a square of roofing is given for various sizes in the following table: 10 x 20 165 11 X 22 138 12 X 24 114 14 X 28 83 The cost of slating per square is as follows : Slates 10 in. X 16 in. .$ 7.50 Labor 1 day, slater 3 . 50 Nails .15 Roofing paper ' .50 Labor on paper .15 $11.80 Tin roof per sq. ft., average $0.11 Gutters per ft., galv. iron .90 Galv. iron conductors per ft., put up . 18 to .25 Copper roof, plain per square 40.00 Copper roof, with battens per square 50.00 Gravel roofing, 5-ply per square (>.00 Zinc flashing, \\ cent per inch of width, per foot. 6 X 12 533 7 X 14 377 8 X 16 277 9 X 18 214 272 ESTDIATIXG • 45 Tiles. Where a special feature is to be made of the roof, tiles are often used but these are found in t,ach a variety of shapes, sizes, and prices, that a roof of this sort should always be given to a roofer to estimate. Metal Roofs. Copper or tin is generally used for roofs where a metal covering is desired. Copper roofs, if steep enough to show as a feature of the building, are usually laid with ribs over battens. This makes a handsome and durable roof the cost being not greatly in- creased. Copper roofing will cost from S35.00 to S40.00 per square. Flashings around skylights and balustrades, 30 to 50 cents a lineal foot. For a cheaper metal roof, tin is generally used ; this may be used on steep or flat roofs. Tin for roofing should be painted on the under side and carefully soldered on the top. Tin roofing will cost from SIO.OO to S12.00 a square. Composition Roofs. For flat roofs, a composition of tar and paper in layers finished with a protective coat of gravel, is often used; the cost of this depends upon the number of layers of paper and "moppings" of tar required, but a 5-ply roof will give good service and will cost about S6 . 00 a square. Gutters and Conductors. Gutters and conductors are both made of wood or metal, metal being preferred in all cases. For metal gutters copper and galvanized iron are used. Copper gutters will cost about §1 .25 a lineal foot. Copper conductors .50 to .75 a foot Goosenecks 5 . 00 to 1 . 00 each ]Moulded conductor heads 4 . 00 to 1 . 00 each Straps 1 00 each Galvanized iron gutters will cost about 90 cents a lineal foot, and conductors, 18 to 25 cents a foot according to size. PLASTERING Plastering is measured by the square yard and is usually done in 2-coat or 3-coat work. In taking off plastering it is customary' to deduct only one-half of the area of openings to allow for the extra work of plastering to the grounds. 273 46 ■ ESTDIATIXG In some localities no openings are deducted unless more than 7 yards in area, but in close figuring this is not generally followed. Narrow strips, such as chimney breasts, if less than a foot wide, are generally called a foot. Round corners, beads, and arrises must be taken separately by the lineal foot. Raking surfaces require additional work and should be taken at about one-half more than plain work. Circular or elliptical work should be charged at two prices and domes, groins, and intersecting soffits, at three prices. Cornices are taken by the square foot of girth with enrichments charged separately by the lineal foot. Lathing. Lathing is generally included in the plasterer's price although put up by a different set of men. Lathing is estimated by the square yard or by the thousand laths, the price being $2.75 to $3.25 a thousand. Labor. 1 wo plasterers requiring one helper will do from 40 to 50 square yards of three-coat plastering, or GO to 70 square yards of two-coat work, in a day of 8 hours, and 1,200 to 1,500 laths makes a day's work for one lather. 100 sq. yds. of lath and plaster will cost about as follows, for two-coat work: 1,500 laths at $4.75 per M $ 7.12 10 lbs. 3d. nails at $3.20 per cwt. . 32 Labor on laths 4 . 50 10 bushels lime at . 48 per bu. 4 . 80 G lbs. hair at .04 .24 1 load sand 1 . 80 Plasterer 3 days at $5.00 15.00 Helper lir day sat $3.00 4.50 Cartage 1.00 $39.28 Cost of a square yard of two-coat work, $39.28 -=- 100 = 39 to 40 cents. This is a price which is on the increase and, while plastering is done in the country towns as low as 35 cents per yard it will not be safe to use this price any length of time. 274 ESTIMATING 47 For three-coat work we may take the following schedule: Laths and putting on, as above $11 . 94 13 bush, lime at . 48 6 . 24 • 81bs. hairat .04 . .32 1^ loads sand at $1 .80 2 . 70 1 bbl. plaster Paris 1 . 70 Plasterer 4 days at So.OO 20 . 00 Helper 2 days at S3. 00 6 . 00 Cartage " 1.00 $49.90 Cost of a sq. yd. of three-coat work, $49.90 -^ 100 = 50 cents. Rules. In some portions of the country a set of rules has been adopted governing the valuing of plasterer's work which are in the main as follows: " First Measure on all walls and ceilings the surface actually plastered, without deducting any grounds or any openings of less extent than seven superficial yards. Second. Returns of chimney-breasts, pilasters, and all strips of plastering less than twelve inches in width, measure as twelve inches wide; and where the plastering is finished down to the base, surbase, or wainscoa^ing, add six inches to height of walls. Third. In closets, add one-half to the measurement. Raking ceilings and soflBts of stairs, add one-half to the measurement; cir- cular or elhptical work, charge two prices; domes or groined ceilings, three prices. Fourth. For each twelve feet of interior work done farther from the ground than the first twelve feet, add five per cent; for outside work, add one per cent for each foot that the work is done above the first twelve feet." Stucco-work is generally governed by the following rules; viz., "Mouldings less than one foot girt are rated as one foot, over one foot, to be taken superficial. When work requires two moulds to run same cornice, add one-fifth. For each internal angle or mitre, add one foot to length of coi-nice, and, for each external angle, add two feet. All small sections of cornice less than twelve inches Ioul'' measure as twelve inches. For raking cornices, add one-half; circu- lar or elliptical work double price; domes and groins, three prices. 275 48 ESTIMATIXG For enrichments of all kinds a special price must be charged. The higher the work is above ground, the liigher the charge must be; add to it at the rate of five per cent for every twelve feet above the first twelve feet." PAINTING Painting is estimated by the yard, doors and windows being taken solid to make up for the extra labor of cutting in the sashes and mouldings. Railings, fences, grilles, and similar surfaces are taken solid. A painter in one day w'ill cover 100 yds. of outside work one priming coat, or 80 yds. of the second coat. Ten pair of blinds will make a day's work. On first coat, one pound of paint will cover about 4 sq. yds. and 6 sq. yds. on the subsequent coats. One pound of putty for stopping will cover 20 yds. Shingle stains require a gallon for every 500 shingles if dipped two-thirds in, and for a brush coat after laying, a gallon will cover about 200 feet of surface, or 1500 shingles. 1 gallon of priming color will cover 50 yards 1 gallon of zinc white will cover 50 yards ' 1 gallon of white paint will cover 44 yards 1 gallon of black paint will cover 50 yards 1 gallon of stone color will cover 44 yards 1 gallon of yellow paint will cover 44 yards 1 gallon of green paint will cover 45 yards 1 gallon of emerald green will cover 25 yards 1 gallon of bronze green will cover 75 yards The following table gives the comparative covering of paints by w^eight on various surfaces. COVERING OR SPREADING POWER OF TYPICAL PAINTS* ON WOOD First Coat Seconp Coat Red lead 112 252 White lead 221 324 *The figures represent square feet, covered by 100 lbs. of paiut of the usual con Bistency, applied evenly with a brush. 276 ESTBIATING 49 First Coat Second Coat Oxide of zinc 378 453 Red oxide 453 540 Raw linseed oil 756 872 Boiled linseed oil ON METAL 412 540 Red lead 477 White lead 648 Oxide of zinc 1134 Red oxide 870 Raw linseed oil 1417 Boiled linseed oil ON PLASTER 1296 Red lead 324 White lead (on sized wall) 362 Oxide of zinc 594 Raw hnseed oil (unsized wall) 55 99 Cost. The cost of painting varies under different conditions but in general the following table will be found an average price: INSIDE WORK 1 coat per sq. yd. $0.12 2 coats per sq. yd. .20 3 coats per sq. yd. .25 1 coat shellac per sq. yd. . 10 1 coat size and 2 coats paint .20 1 coat size and 3 coats paint stipple .30 INSIDE FINISH 1 coat liquid filler, 1 coat varnish 10.20 1 coat " filler, 2 coats varnish .25 1 coat " filler, 3 coats varnish .30 1 coat paste filler, 1 coat varnish .25 1 coat " filler, 2 coats varnish .30 1 coat " filler, 3 coats varnish .35 277 50 ESTIMATING Tinting walls in distemper will cost 15 cents per sq. yd. for small amounts and 10 cents per sq. yd. for 50 yds, or more. Finishing hard wood floors with filler, shellac, and 2 coats of varnish or wax finish will cost 30 cents per sq. yd. OUTSIDE PAINTING SO. 10 .18 .25 $0.28 .35 ,50 1 coat new work per sq. yard 2 coats new work per sq, yard 3 coats new work per sq, yard SANDING 2 coats paint, 1 coat sand per sq. yd. 3 coats paint, 1 coat sand per sq. yd. 3 coats paint, 2 coats sand per sq. yd. Painting on brick will cost 12 cents per yard for the first coat, but subse(juent coats will cost no more than on wood. Tin roofs can be painted one coat for 5 cents a yard. 1000 shingles dipped two-thirds of their length will cost $3.00 and a brush coat in addition costs 50 cents. Blinds are rated at $1 .50 per pair for an average size. HEATING The heating of a building is generally made the subject of a special contract. The three usual methods for hou.se heating are, the Hot Air Furnace, the Hot Water Boiler, or the Steam Boiler. Sometimes a combination svstem of hot air and steam, or hot air and hot water is used. Estimates of the cost of heating should be obtained from con- tractors Avho follow this particular branch of construction. In general, for an ordinary class of building such as residences, apartments, stores, etc., the heating will range according to the system used, from 6% to 12% of the cost of the building, as follows: Hot air furnace 6 to 7 per cent. Steam 8 to 10 per cent. Hot water 10 to 12 per cent. 878 ESTIMATING 51 These figures are approximate and the only reliable way to obtain the actual cost is by taking off the items and figuring each job by it- self. Quantities. The hot air heating of an ordinar}^ house can be approximated closely by the builder on the basis of cubic con- tents to be heated; and the area of piping and capacity of the furnace can be approximated by means of the following general rules : To determine the size of pipe for any room, find the cubic con- tents of the room in cubic feet and divide this by 25 for rooms on the first floor, and by 35 for rooms on the second and third floors. ]Make the cold air box at least | of the combined area of pipes, none of which should be smaller than 7 inches in diameter. Example. For a small house of seven rooms the quantities may be as follows: FIRST FLOOR Parlor 12x 15 x 9 ft. high 1624 cu. ft. divided by 25 = 65 sq. in. or 9 in. pipe Hall 8 x 20 X 9 ft. high 1440 cu. ft. divided by 25 = 58 sq. in. or 9 in. pipe Add 40% for second storv- hall space making 81 sq. in. = 10 in. pipe Dining Room 14 x 15 x 9 ft. high 1890 cu. ft. divided by 25 = 76 sq. in. or 10 in. pipe SECOND FLOOR Chamber 13 x 15 x 8h = 1658 cu. ft. ^ 35 = 48 sq. in. or 8 in. pipe Chamber 11 x 12 x 8h =-- 1122 cu. ft. ^ 35 = 32 sq. in. or 7 in. pipe Chamber 14 x 16 x 8^ = 1904 cu. ft. -h 35 = 55 sq. in. or 8 in. pipe Bath Room 8 x 10 x 8\ - 680 cu. ft. ^ 35 = 20 sq. in. or 7 in. pipe Total pipe area : 2-10 in. pipes 78 sq. in. each 156 sq. in, 1 - 9 in. pipe 64 sq. in. 64 sq. in. 2 - 8 in. pipes 50 sq. in. 100 sq. in. 2 - 7 in. pipes 38 sq. in. 76 sq. in. Total pipe area 396 From this scale we can determine the size of the furnace and the cost of piping. 279 52 ESTIMATING A furnace to carry say 400 to 500 sq. feet of pipe area would cost, set in place, from $100 to $125. The labor on pipes, registers, and furnace $20 to $24. The cost of piping will depend on the distances to run but the material can be estimated as follows: ■ Round tin pipes will cost; from A. A. charcoal plates, as follows: Size of Pipe 6" .09 1'? 7" .10 .12 .10 .15 8" .12 .12 .10 .18 9" ■ 14 .15 .12 .20 10- .16 .15 .12 .25 11" .18 .15 .14 .30 12" .23 .18 .18 .35 13" .25 .18 .18 .40 14" .27 .18 .18 .45 15" .28 .20 .20 .50 16" .30 .20 .20 .60 18" Per P oot .32 Hot Air DaiUDer .25 Furuace Collars. 10 .25 Tiu Elbows .12 .70 * REGISTERS Size 6x10 .50 .38 .14 05 7x10 .52 .42 .16 .05 1.15 8x10 .52 .44 .17 .06 1.19 8x12 9x12 10x14 1.08 .70 .27 .07 2.12 .12x15 12x16 14x18 2.74 1.50 .38 .10 4.72 16x20 Black Reurister .58 .50 .20 .06 1.34 .64 .63 .23 .07 1.57 1.37 .93 .33. .08 2.71 1.70 1.00 .35 .08 3.13 3.75 Slate Stoue 2.35 Register Box .50 Nettiug .12 1.07 Totals 6.V2 ♦ July, 1906.— Add one-third. Galvanized smoke pipe will cost 9c per lb. and will weigh per lineal foot as follows: Size No. 4" 5" 6" 7" 8" 9" 10" 11" 12"- 13" 14" 22 24 If 2i If n 3 ' 2i 31 24 3i 21 3 4i 31 5 3f 5i 3i 5i 4i GALVANIZED ELBOWS Size 4" 1 i'A" 5" 5/2" If .25 6" .28 7" 2i .32 8" Pouud u .23 31 Cost. ...'.'.'.'.'. .18 .20 .35 Tin, per Sheet DC 12^x17 .05 IX 14 x20 .07 IXX 14, x20 .08 IX 20 x23 .12 IX 20 x 26 .13 IX 20 x 29iV .16 IX 20 x32i .17 Miscellaneous Data Galvanized sheet iron per lb. Common sheet iron per lb. $0.05 .04 280 ESTDIATIXG 53 Zinc per lb. SO . 10 Wrought iron per lb. . 04 Galvanized piping per lb. . 09 Gahiinized cold air box per lb. . 09 Galvanized furnace shields per sq. ft. .08 Register box netting per sq. ft. . 05 Asbestos paper at 1 h lbs. per sq. yd, . 05 Figure cold air supply f combined area of piping. Register grilles take up ^ of area of register. Locate registers nearest convenient point to furnace, inside part of room preferred. Locate furnace so that all pipes will be as nearly equal in length as possible. Estimate pipes by lineal foot, but elbows and dampers sepa- rately, also registers with boxes and borders. Allow from SLOO to SL25 for flange connection of cold air box to furnace casing. Cover all risers with asbestos paper in partitions. HOT WATER AND STEAM HEATING In estimating for heating with hot water, all pipes and fittings must be taken off and listed, all standard radiators priced by the square foot of radiation, and special radiators listed separately, also tanks, valves, hangers, etc. Radiators are listed in the trade catalogues, together with the number of square feet in each section. These prices are subject to varying discounts which can be obtained of the manufacturers. Radiation. The amount of radiation necessars^ for each room depends upon so many var}4ng conditions that all rules are in a way approximate. Certain formulae may be used, which will give good results in ordinary cases, but just what allowances are necessar}' must be determined by the heating engineer. The same is true of making the estimates of hot water or steam and the contractor should in all cases have the job figured by an expert. In ordinary cases the amount of radiation may be determined 281 54 ESTIMATING from the cubic contents of the rooms to be heated by the following tables which give the proportions of one square foot of radiating surface to the cubic contents of the various rooms in cubic feet. STEAM One Square Foot of RadiationWill Heat dwellinos, Cubic Feet HaLI,8, Stores, Etc. Cubic Feet Churches AND Auditoriums, Cubic Feet By direct radiation — Ou first floor 35 to 60 50 to 80 75 to 100 125 to 200 Ou upper floors By indirect radiation — Ou first floor 25 to 40 40 to 50 50 to 70 80 to 135 On upper floors HOT WATER One Square Foot of^R adiation Will Heat Dwellings, Cubic Feet Halls, Stores. Etc. Cubic Feet Churches and Auditorium*, Cubic Feet By direct radiation — Ou first floor 15 to 25 25 to 40 30 to 45 50 to 85 On upper floors By indirect radiation — On first floor 17 to 40 25 to 35 45 to 65 80 to 125 Ou upper floors Having determined 'the amount of radiation, piping, and fit- tings, the labor may be obtained by adding about 20 per cent to the cost of materials. PLUMBING So wide a range is possible in the selection and price of plumb- ing fixtures that no very useful data can be given for a complete installation. For instance, in one house the price of a single bathroom, fitted up to meet the fancies and purse of the owner, may cost more than the whole plumbing outfit of his more modest neighbor. Nevertheless, it is a fact that the plumbing of a house is a poor place to practice economy, as no part of the construction of a build- ing needs more careful attention in execution or in selection. In general, a good job of plumbing will cost about 10 per cent of the cost of the building, and of this outlay about 30 per cent will represent the labor. In taking off plumbing the contractor should begin at tHe sewer 282 HOUSE AT WASHINGTON, ILL. Herbert Edmund Hewitt, Architect, Peoria, IIL Walls of Cement on Metal T.ath. Roofs Covered with Shingles Stained Green. All Outside Woodwork Stained Dark Urowu. No Paint on Outside except on Sash. Verand/v WW w fic^T TiooQ. Plan ^LcoND liooB Ran HOUSE AT WASHINGTON, ILL. Herbert Edmund Hewitt, Architect, Peoria, 111. Built In 1904. Cost, about ?4. 500. House was Built for a Summer House, ba' Constructed the Same as if for All Year-Round Use, and Provided with Heating Plant. ESTniATlNG 55 or cesspool, if the drains are included, or, if not, at the outer end of the soil pipe, and take off carefully every pipe with its fittings, which should be itemized carefully as this data will be useful in getting at the amount of caulking, fitting, etc. Soil Pipes. Soil pipes should be estimated by the lineal foot, allowing in each joint | of a pound of lead for every inch in diameter of the pipe. List prices of pipe and fittings can be obtained from the dealers, which are subject to discount; these vary from time to time, but the present discounts will be found to bring the prices of the more com- mon materials about as follows: DRAINAGE 4-in. extra heavy soil pipe per ft. .$ .30 3-in. extra heavy soil pipe per ft. .22 2-in. extra heavy soil pipe per ft." . 15^ For fittings add 3-5 per cent to the cost of pipe. 4-in. running trap 2.00 4-in. brass ferrule cleanout .50 4-in. lead bend 1 . 50 4-in. brass ferrule .50 2-in. brass ferrule .20 Solder per lb. .22 WATER SUPPLY 40 gal. galvanized boiler and stand S15.00 1-in. brass pipe per ft. .60 1-in. galvanized pipe per ft. .09 f-in. galvanized pipe per ft. .06 i-in. galvanized pipe per ft. .05 1-in. stop and waste cock 1 .50 |-in. stop and waste cock .90 ^-in. stop and waste cock . 80 Sill cock 1 . 00 For fittings, add 30 per cent to cost of pipes. WATER 1 cu. ft. 7.48 gallons 1 cu. ft. 29.92 quarts 283 56 ESTIMATING 1 cu. ft., 62.321 lbs. 1004 oz. 1 cu. yd. 1692 lbs. 1 gal., 231 cu. in. • 8J lbs. 1-foot cylinder 49 . 1 lbs. 1-inch cylinder .028 lbs. Pressure per sq. in. = depth in feet x 433. Each 27.72 inches of depth gives a pressure of 1 lb. to a square inch. A barrel Slh gal. Contents in cu. ft. x 2375 = barrels. Head of water = pressure in lbs, per sq. in. x 2.31. Number of gallons in a foot of pipe = Diam. in. inches 2 x .04. Supply for one person is 15 gallons a day. Actual use 6 gallons to 12 gallons. Water 34 feet high has a pressure of 15 lbs. per sq. in. equal to atmosphere. CAPACITY OF CISTERNS In Qallons, for Each Foot in Depth Diameter in Feet Gallons iDlAMETER IN FeET Gallons 2. 23.5 9. 475.87 2.5 36.7 9.5 553.67 3. 52.9 10. 587.5 3.5 71.96 11. 710.9 4. 94.02 12. 846.4 4.5 119. 13. 992.9 5. 146.8 14. 1,151.5 5.5 177.7 15. 1,321.9 6. 211.6 20. 2,350.0 6.5 248.22 25. 3,570.7 7. 287.84 30. 5,287.7 7.5 330.48 35. 7,189. 8. .376. 40. 9,367.2 8.5 424.44 45. 11,893.2 The American Standard Rallon contains 21!! cnbic inche.s, or S'/i pound.s of pure water. A cvibic foot eontains 62.3 pounds of water, or 7.48 frallons. Pressure per square inch Is equal to the depth or head In feet multiplied by .433.^^Each 27.73 inches of depth gives a pressure of one pound to the square inch. For tanks that taper, take diameter ,\ from large end. FIXTURES 3-ft. .soapstone sink complete $30.00 to $40.00 14-in. X 17-iii. lavatory with marble slab and back piece fitted complete $35.00 to $50.00 284 ESTIMATING 57 Enamelled iron lavatory complete $25.00 to S40. 00 5-ft. 6-in. enamelled iron bath complete S60 . 00 to $100.00 Bath tub only $25.00 to $35.00 Soapstone laundry trays complete One part $15.00 to $18.00 Two parts $30.00 to $35.00 Three parts $45.00 to $60.00 List prices of fittings may be obtained from all dealers, subject to large discounts, which should be considered frequently as they are constantly changing. Labor. Having made a complete list of pipe, fittings, and fixtures, the labor of construction of an ordinary job of plumbing will run from 20 to 40 per cent of the cost of materials. GAS FITTING As in plumbing so in gas fitting, the wide range of selection and cost in fixtures, makes it impossible to give satisfactory data in regard to cost. The piping only, of an ordinary house will cost from $1.75 to $2.00 an outlet, and the whole outfit should cost from 3 to 5 per cent of the cost of the house. Pipes of usual size cost as follows: l-in. gas pipe per foot $0 . 03 ^-in. gas pipe per foot . 04 |-in. gas pipe per foot . 05 H-in. main .08 Fittings 25 per cent of cost of pipe. ELECTRIC WORK The original contract for a house usually provides for the wiring for electric lighting and bells, but fixtures are generally left to be provided for by a later agreement, as there is such a great latitude in selection and cost. For electric light wiring one of two systems is usually employed : the conduit .system, where the wires are all run in pipes or conduits, and the knob and tube system, where the wires are run in the clear space between timbers, secured to porcelain knobs, or passing through short tubes of the same material. 285 58 ESTIMATING In general, the rough wiring of a liouse may be reckoned at S4.00 per outlet for conduit work, and S2.00 per outlet for knob and tube work. This is for every time the wires are broufjht to the surface, whether for switches, cutouts, or fixtures. Another way is to allow $1.50 for each lamp or switch. Switches, ^^arious kinds of switches are used, the two principal kinds being the push button, and the rotary switch. These vary in price according to make and finish. A good rotary switch can be had at from 90 cents to $1.00. Push button switches from $1.00 to $1.10. Snap switches from 30 to 40 cents. Wires are sold in coils which are marked with the gauge and manufacturer, and should bear the label of inspection accej)table to the local Insurance board. The cost of wire will vary with the gauge and the insulation but for usual house work should cost, for No. 14 wire, 2 cents a foot. It is well to remember that, in electric wiring, the larger the house, the more per outlet the weiring will cost. This seems contrary to expectation but is occasioned by the smaller percentage of lights to length of wire. Bells. The number of call bells in a dwelling will vary according to the plan and choice of the owner. For an ordinary house the number would range from six to ten, and the cost should be from $18.00 to $25.00 or about $3.00 per bell. 286 W -J Sou K '^ U O ►J . £ " w .:^ o a o 2 « o w ESTIMATING PART II The taking-off of ciuantities and making-up of an actual estimate, is the end toward which our efforts are now directed. This is done, as has been said, in a number of ways, no two persons arriving at the same conchision or following exactly the same methods. To give the student a practical idea of howestimates are made, M'e shall now demon- strate the method of procedure in an actual instance. For this purpose, we shall take the case of the wooden Colonial residence of which the plans and working drawings, and the method of making these, are fully described in the course on "Architectural Drawing," and of which the details are also described to a certain extent in the chapters on "Building Superintendence;" and shall proceed at once to take off the quantities and make up an estimate of cost. Method. The usual method followed is to take off the quantities in the order in which they occur in the specification or in the operation of building, beginning with the Excavation and ending with the Painting. Tw^o methods of procedure are open to the Contractor, which he may avail himself of according to his experience or confidence. He may take off simply his own particular branch of the work, relying on each sub-contractor to give him a price for the detailed portions of the work; or, if he is a general contractor, he may, with the requisite knowledge of general building operations, take off all the quantities, pricing them according to his knowledge, and may submit his prop- osition on the basis of his own figures. The latter method requires great experience, and is followed generally by large contractors, who have in their employ men whose business is mainly to take off quantities and make up estimates. The following estimate has been carefully made up on the basis of the data given in Part I as to prices of materials and labor. In actual practice, details of more or less importance will vary in dif- ferent localities and among different contractors; but the example here given illustrates the process fully. fS69 uJ .,2 < 62 ESTIMATING ESTIMATE OF RESIDENCE AT RIDGEDALE, MO. FOR GEORGE A. JONES, ESQ. Staking-out and setting batter-boards $15.00 Water supply during construction 10.00 S25.00 EXCAVATION Note. — Excavation is priced by the cubic yard; and in this regard, the distance to which the excavated material must be carted will be an important consideration. In the present case, the material is to be carried only a short distance, so that no unusual conditions will have to be considered. As before mentioned, it is usually well to dig a cellar at least a foot larger all around than the sill line, so that plenty of room may be afforded to the mason to plaster the outside of the wall. This should be done without regard to the specifications. As this extra excavation lies entirely outside the line of the house, it may be well to take it off separately, remembering that it will extend down into the trench below the wall, making about 8 feet of height. Quantities — Cu. Ft. 42 ft. in. X 8 ft. in. X 1 ft. in 336 34 ft. in. X 8 ft. in. X 1 ft. in 272 10 ft. 4 in. X 8 ft. in. X Ift.Oin -. . 83 17 ft. 6 in. X 8 ft. in. X Ift.Oin 140 68 ft. in. X 8 ft. in. X 1 ft. in 544 41 ft. in. X 8 ft. in. X 1 ft. in 328 Cellar Excavations — 28 ft. in. X 43 ft. in. X 5 ft. in 6,622 12 ft. 6 in. X 3 ft. in. X 5 ft. 6 in 206 26 ft. in. X 20 ft. 6 in. X 5 ft. 6 in 2,931 9 ft. in. X 6 ft. 6 in. X 5 ft. 6 in 322 « Carried J orward 11,784 cu. ft 292 R-EL^lDLiMCIL- AT - RlDGE-DAl^E. - /^ 1 ^v/ O UP^I-^o^- . I 1 1 • rT-ivrLV. At)ooT>xe- Arc Ki led m^j-on, E>oiWinft - bo/'ton.- =ffil^ -i^nf p- ^AJ.^^7f (y □ □ DCTAIL-OF FRO/^T^ LLLVATION- Fig. 3 04 ESTIMATING Brought forward 11,784 cu. ft. Miscellaneous Quantities — Piers 2ft. in. X 2 ft. in. X 3 ft. Gin. X 12 168 Trench 185 ft. in. X 1 ft. 8 in. X 1 ft. in 308 Area 14 ft. in. X 2 ft. 8 in. X 3 ft. (i in 129 Drains 123ft. in. X 3ft. Gin. X 1ft. Gin 645 Cesspools 5 ft. Gin. X 5 ft. 6 in. X 8 ft. in 242 10 ft. in. X 10 ft. in. X 8 ft. in SOO Dry Wells 6 X 2 ft. in. X 2 ft. in. X 5 ft. in._ J120 Total, 14,19G cu. ft. Total, 14,196 cu. ft., or 525 cu. yds., at 50 cents .... $262 . 50 STONEWORK Dry Walls in Trench — Cu. Ft. 16 ft. in, X 1ft. 8 in. X. Ift.Oin 27 left.Oin. X lft.8in. X Ift.Oin 27 12 ft. 6 in. X 1ft. 8 in. X Ift.Oin 20.8 3 ft. in. X 1ft. 8 in. X Ift.Oin. ... 5 23 ft. in. X 1 ft. 8 in. X 1 ft. in 38 16 ft. 6 in. X 1 ft. 8 in. X 1 ft. in 27.5 28 ft. in. X 1 ft. 8 in. X 1 ft. in 46 28 ft. in. X 1 ft. 8 in. X 1 ft. in 46 14 ft. 6 in. X 1ft. 8 in. X Ift.Oin 24 4 ft. 6 in. X 1ft. 8 in. X Ift.Oin 7.5 23 ft. in. X 1 ft. 8 in. X 1 ft. in __3S Total, 306.8 cu. ft. 307 cu. ft. -!- 25 == 12 perches of dry wall. Mortar Walls — 16 ft. in. X 6 ft. 7 in. X 1ft. 8 in 175 16 ft. in. X 6 ft. 7 in. X 1ft. 8 in 175 9 ft. 6 in. X 8 ft. 3 in. X 1ft. 8 in 130 Carried forward 480 cu. ft. 294 . ,7-6- - - R&J)DEJiCE-AT-RJDS£D*A,£-AQ- -PCai- G£QRGE.-A-JOAE0"-£JQ.-' -FRAnK-A- bOUC-r\E.- A32CHlTEC-r- g] il] •BE- [gj ;10TE- ALL PLCiA 6- ■PORCH PItIV TO- I r -EjVJtnENT- PiAN- o ia34-^sra o-t^oa-'le cj^ Il III I I I I I I /««.+*- Fig. 4. 66 ESTIMATING Brought forward 480 cu. ft. 23 ft. in. X 8 ft. 3 in. X 1 ft. 8 in 316 12 ft. in. X 6ft. Tin. X 1ft. 8 in 132 28 ft. in. X 8 ft. 3 in. X 1 ft. 8 in 385 6 ft. in. X 6 ft. 7 in. X 1ft. 6 in 59 10 ft. in. X 6 ft. 7 in. X 1ft. in 66 8 ft. 6 in. X 6 ft. 7 in. X 1 ft. 8 in 93 9 ft. in. X 8 ft. 3 in. X 1 ft. 8 in 123 25 ft. in. X 6 ft. 7 in. X 1 ft. 8 in 274 6 ft. in. X 6 ft. 7 in. X 1 ft. 8 in 66 23 ft. in. X 6 ft. 7 in. X 1 ft. 8 in 252 Piers — 2 ft. 6 in. X 5 ft. 6 in. X Ift.Oin 14 2 ft. 6 in. X 5 ft. 6 in. X Ift.Oin 14 2 ft. in. X 2 ft. in. X 1 ft. in 4 12 ft. in. X 3 ft. 6 in. X 2 ft. in 84 12 ft. in. X 3 ft. 6 in. X 2 ft. in. .. 84 Area — 14 ft. in. X 3 ft. 6 in. X 1 ft. 6 in 73 Total, 2,519 cu.fto 2,519 cu. ft -^ 25 = 101 perches of mortar wall. Underpinning — Cu. Ft. 16 ft. in. X 1ft. 8 in. X 1ft. 8 in 45 16 ft. in. X 1ft. 8 in. X 1ft. 8 in 45 6 ft. in. X 1ft. 8 in. X 1 ft. 8 in 17 12 ft. in. X 1ft. 8 in. X 1 ft. 8 in 34 6 ft. in. X 1 ft. in. X 1 ft. in 6 8 ft. 6 in. X 1ft. 8 in. X 1ft. 8 in 23 25 ft. in. X 1ft. 8 in. X 1 ft. 8 in 70 6 ft. in. X 1ft. 8 in. X 1ft. 8 in 17 23 ft. in. X 1 ft. 8 in. X 1 ft. 8 in 64 14 ft. in. X 2 ft. in. X 1ft. 6 in 42 Total, 363cu. ft. 363 cu. ft. H- 25 = 142 perches of underpinning. Summary of Stonework — 12 perches of dry wall, at $3.00 $ 36.00 Carried forward $ 36.00 296 ESTIMATING 67 Brought forward $ 36 . 00 101 perches of mortar walls, at $4.25 429 . 25 14^ perches of underpinning, at $6 . 50 94 . 25 Total cost of Stonework, $559 . 50 PLASTERING WALLS WITH CEMENT 192 ft. in. X 6 ft. 7 in. = 1,264 sq. ft. = 140 sq. yds., at $.40 $ 56.00 CESSPOOLS Leaching Cesspool — 23 ft. 6 in. X S ft. in. X 1 ft. 6 in. = 282 cu. ft. -^ 25 = 11^ perches. IH perches at $3.50 $39.65 Cover 2.50 42. 15 Tight Cesspool — 11 ft. 6 in. X 8 ft. in. = 92 sq. ft. X 15 bricks - 1,380 bricks. 1,380 bricks at $20.00 per M !. .$27.60 Iron cover 3 .00 30.60 DRY WELLS 2 ft. in. X 2 ft. in. X 5 ft. in. X 12 = 264 cu. ft. -- 25 = 1 1 perches 11 perches at $2.50 27.50 DRAINS 171 ft. at $.20 $34.20 14 bends at $.30 4.20 38.40 Total cost of Stonework, Cesspools, and Drains $754.15 BRICKWORK Note. — Find the number of bricks in a foot of height in each chimney or pier, reckoning five courses to the foot of height. Cellar — . 35 X 8 280 107^ X 8 860 55 X 8 ■ 44 Carried forward 1,580 bricks 297 'jr- s -KfJlDLMCE-AT 21DGLnALE.-AO- f OR, - GEOCGE,-A-JDnE.J- EJCL- ■J? t O 1 2 3 4- .3 6 C^ ■7^^- 1- •9'-0^ o iJi •PIM2A- ^ -^■G? Floor. f^ ■-0 0= W- "m LiviMG'Roon ■W'KJ CteV. tiiv.ik- ■Oov. riooi- 1 1 1 1 1 1 ' 1 1 J. 1 , \r^ — ' II •Hall- C.>i«T»5'.yin,liK- « ^ 5 /^ D ■i {(^"^ J ^ —- =4 I •PjrtiMG- ROO^\- g «•- a'-o" c g-^oj..~.«.o g In ■H'-e- • - 7-j' TTTp, U ^ feu •^g~ •V»TI6U1.E- \rio- •Parlor.- 0»V Floor-. •/+■-&•- .T ■p f— — 7^'': f- -•7-^5'- 'PLAM- or- ni^T- YlOOit' Fig. 5. s H I-] s H H pq H < M M s o 9B >« K H D O u o «« cu >- o H tfl H o «s be a sa O g m fl O d • o-S a> O 3 o s m'.9 H -t^ ■< O (d P. r/1 ft D o O a S o >« a tt 'is- H o 4-) o d o OS b. cu O >> 2 < C/3 PL, >- ^ K t» O H (A Q is o u u (A isai J lO «oj. ol ■I 00-1 N- 0- IQ- 0- w- (!) < I 10 i I W CI '. CO •—1 j^ "to- 'b 6 s ^ < VD- 10- ESTIiMATING 71 Brought forward 1,580 bricks Veranda Piers — 58* X 10 585 Chimneys — 107h X 6ft. 6in 700 105 X 11 ft. in 1,155 35 X 11 ft. in 385 35 X 4 ft. 6 in 157 127i X 5 ft. 6 in 701 35 X 19 ft. in 665 57;V X 4 ft. in 230 127i X IHt.Oin 1,402 7, 560 bricks Summary — 7,560 bricks at $20.00 per M., laid $ 151 . 20 3 fireplaces at S30.00 each 90 . 00 Flue Linings — 26 ft., 13 in. X 13 in., at $.35 9.10 36 ft., 9in. round, at $.30 10.80 68ft.,8J X 13,at$.30 20.40 Total cost of Brickwork and Flue Linings, $ 281 .50 CONCRETING Sq. Ft. 23 ft. in. X 38 ft. in 874 3 ft. in. X 9 ft. 6 in 28^ 15 ft. in. X 26 ft. in 390 4 ft. in. X 7 ft. in 28 1^20 sq. ft. Total, 1,320 sq. ft. = 147 sq. yds., at $.60 , . . $88 . 20 PLASTERING Note. — ^Take off square feet of plastered surfaces, and deduct one-half of the openings, after reducing to sq. yds. Cellar — Sq. Ft. 23 ft. in. X 38 ft. in 874 9ft. in. X 3 ft. in 28 Carried forward 902 sq. ft. 301 !l FOR,-GEOR.aE:-AJO;^Ev/'EiJa- • FrdTtK A- bourac- Ar(3iit«ct " bo/ton,- •56 Tllft/on, boildiag _/7li. "xs' '=_ 4U 4T^ t±I_ ^■;cs"- ^a-oc ^ ZK&-- 4*S, J-' 4^ 1 -0- t-TOfT ^. Z-^"^" >' 1 = =££ ^ s-"=>— 4 tr :^ t Brid^imq =3 -»<'0l c^ /4- a JNi_ s IT -4 ^' t ^'S "-"-I h— H — I lyr._5 <5lB.PEE^ POJT sxicr POJT a -yojT nr ■jftyr s'-^to- 1 * -a*x;o' T-di- - -l-i Bni>ftin% — ~i r -0- V9 - ^g A/O' 3' »sr-^ f r-lo- _L. -=i- TT^e-- ■FDJT TWD ^^xlo'^JSi;^o-g■ BRII7<^IKIi — « 1P»JT -«-== s— -09-0- ^ ■1 l-.-t h nb ALL FiiyT fiooR <^oi;rj- ■TO BE- 2A/0" ' -BepRooa- -^ -~--^. o IX ;+-« ■A1.COVE- _2 Q Bep- Rooa- ?> /4--0' P ROor D^Q: =0=Q I -PLAN-- Or-U'ZjC.O/AD-TiJDO^- ora34-307ss *-3"-l-|| XH r n.f.^x-'t-^*' v-7^^m|. 1234-v5e7S '^./c&.le. of !■ I ii I I I I I I /ee.t ^ Fig. 11. ESTDIATIXG Brought jorward $1,300.33 19 ft. in. X 6 ft. fi in 124sq. ft. 11 ft. in. X 5 ft. in GO " " 14 ft. in. X 9 ft. in J33 " " . 474 sq. ft. 474 sq. ft. at $20.92 per square $ 99 . IG Outside Walls, Studding and Boarding — 172 ft. in. X 20 ft in 3,440 sq. ft. G ft. G in. X 10 ft. in. X 2 sides 130 " " 3 ft. in. X 9 ft. in. X 2 sides 54 " " 3,G24 sq.ft. 3,G24 sq. ft. at $8.30 per square $ 300 . 79 Inside Studding — ISOft.Oin. X Oft.Oin l,G20sq.ft. 19Gft.0in. X 8ft. Gin 1,GGG " '' 28 ft. in. X Sft. in 224 " " 37510 sq. ft. 3,510 sq. ft., at $4.00 per square $ 140.40 Clapboarding — 44 ft. in. X 19 ft. in. X 2 sides . 1 , G72 sq. ft. G ft. in. X 8 ft. in. X 2 sides . 96 " " 2 ft. in. X 9 ft. in. X 2 sides . 3G " " 39 ft. in. X 19 ft. in. X 2 sides . 1,482 " " 3,28G sq. ft. 3,286 sq. ft. at $7.95 per square ... $261 . 23 Deduct for stock only, 36 windows - 54r, sq. ft., at $4.70 per square 25 . 38 $ 235 . 85 miscellaneous Dormers — 6, at $50 each $ 300.00 Main Cornice — 180 ft., at $1.25 per ft 225.00 B.\LUSTRADE ON RoOF — 96 ft., at $0.50 per ft $48.00 18 posts, at $1.50 each . 27.00 75. 00 Carried forward $2,676.53 808 ESTIMATING 79 Piazza Finish— Brought forward §2,676.53 Cornice — 102 ft., at $2.00 per ft 204.00 Columns — 9 in place, at SIO.OO each 90 . 00 Corner Pilasters — 2Hn place, at $8.00 each 20.00 Balustrade — 76 ft., at $.50 per ft $38 .00 Small Posts — SiatSl.OOeach 12.00 50.00 Outside Steps 25 .00 Lattice — 55 ft. in. X 1 ft. 6 in. = 82* sq. ft., at $.15 persq. ft 12.37 Porch Ceiling — 111 sq.ft., at $10.00 per square 11.10 Bulkhead Steps 25 . 00 corxer b0ards-7 252 ft. in. X 8 in, = 168 sq. ft., at .S.30 per sq. ft. 50.40 Water Table — 117Minearft.,at$.20perft 23.50 Windows and Frames — Attic— 4 windows, circular top, at $11 .20 each $ 44.80 4 ''.indows, square, at $5 . 25 each 21 . 00 Second Story — 8 windows, 3 ft. 6 in. X 5 ft. in., at $13.33 each $106.64 7 windows, 2 ft. 6 in. X 4ft. 6 in., at 811 .44 each 80.08 First Story — 1 window, 2 ft. 6 in. X 4 ft. 6 in $ 11 .44 2 windows, 2 ft. 6 in. X 5 ft. 6 in., at $12.00 each 24.00 2 windows, 2 ft. 6 in. X 3 ft. 9 in., at $11 . 00 eacli 22 . 00 2 pairs French windows (oak), . 4 ft. 6 in. X 7 ft. 6 in., at $18. 24 each 36.48 1 window, 3 ft. 4 in. X 5 ft. 6 in. (oak finish) . . . 16.57 Carried foncard $3,550.91 309 ■Plate (z) ij^^- BrIPCtING - 1^ !I M.P. LEPCitK- •BOARP- □ -4-^a ^1- ^=5^ s f E t H P ■URSER DOARO r^ tt JaL .4 .4" 4-xa tAR- OW- kx e- w I -^MDQiHCi- Pc -ov- -:r- BR- -^ -Qi PAX CAP 4^ 4 TC. i^ ^ N LBp- "HP. DD ^ £t ^^ ^^=6^ ^ -I!RIt>GlrtG Pi. ATE TWO i'^A-' '^' '^ H-P. -LEPCfR. BOARP. TJMniNG- PLAn - Or-THIRD- FLOOR ■ vJca^le of I I I 1 1 I I I I I I /r r t Fig. 12. ESTLAIATIXG 81 Brought forward §3,550.91 1 window, 3 ft. 4 in. X 5 ft. 6 in. (birch;finish) . . 16.57 1 window, 2 ft. 6 in. X 5 ft. 6 in. (birchfinish) . . 14.45 2 windows, 3 ft. 4 in. X 5 ft. 5 in. (whitewood), at S13.33each 26.66 4 windows, 2 ft. 6 in. X 4 ft. 6 in. (X. C. pine), at .S11.44each 45.76 Front Door, with side and top lights — 3 ft. 3 in. X 7 ft. 6 in 56 .33 Rear Door — 2ft. 10 in. X 7 ft. Gin 13.46 Cellar Sashes — 12, at S3.25 each. 39.00 Inside Finish — Coal bins in basement, 240 sq. ft. Studding 240 sq. ft. at $3 . 00 per square S 7 . 20 Boarding240 " "$4.75 " " 11.40 Labor on 2 doors, one day 3 . 25 21 . 85 Cold-Air Box — 3 ft. in. X 1 ft. in., 25 ft." long, at $.62 per linear ft 15 .50 Basement Partitions — 46 ft. in. X 8 ft. in., 368 sq. ft., at $8.75 per square .... 32.20 3 doors, at $8.87 each 26 . 61 67^ ft. shelving, at $.15 per ft 10. 12 1 door to bulkhead 10 . 00 First Story — 1 door, 2 ft. 8 in. X 7 ft. 6 in. (whitewood and birch finish) 20 . 67 1 pair sliding doors (whitewood and birch finish) 53.52 40 ft. birch base at $. 20 per ft 8 .00 1 door, 3 ft. 3 in. X 7 ft. 6 in. (whitewood and oak) 22.67 1 door, 2 ft. 10 in. X 7 ft. 6 in. (whitewood and oak) 20 . 67 Wood Cornice in Dining Room — 56 ft., 6 in. X 6 in. (birch), at $.48 per ft $26.88 56 ft. picture moulding, at $.06 per ft 3 . 36 30 . 24 Wood Cornice in Library — 82 ft., 6 in. X 6 in. (oak), at $.48 per ft §39.36 Carried forward $39.36 $4,035.19 311 82 ESTIMATING Brought forward $39.36 $4,035.19 82 ft. picture moulding, at $.0G per ft 4.92 44 . 28 Oak Base — 72 ft. at $.20 per ft .' 14.40 1 door, 3 ft. in. X 7 ft. 6 in (whitewood) 1 2 . 59 Vestibule Door, side lights and top light, same as front door. 56 . 33 Whitewood Base, 101 ft., at $.10 per ft 10.10 5doors (N. C. pine), at $9.48each 47.40 China Closet Finish 100.00 Pantry 50.00 Kitchen and Back Entry Sheathing — 65hnearft.,at$.40perft 26.00 Mantels — Allowance $125.00 Labor of setting 6.50 $131 .50 Second Story — 1 6 doors stock, at $9.48 each $151 .68 larchinhall 10.00 2 wood columns, at $10.00 each 20.00 5 closets, at $3.50 each 17.50 1 Hnen closet .' 25.00 1 linen closet 20.00 Third Story — 2 doors, finishe;! one side, at $7.04 each $ 14 .08 1 closet door 7 . 04 Tank 10.00 Finished floor, lOOsq. ft 7.25 Base, 14 ft., at $.10 per ft 1 . 40 Conductors^ 120 ft., at $.13 per ft., put up $15.60 6 goosenecks, at $1.00 each 6.00 $ 21.60 Cutting and Fitting for Plumbing and Heating 35 . 00 Freight, Fares and Expenses ' 50.00 Insurance 10.00 Total cost of Carpenter Work $4,928 . 34 312 li B- ALU- AAin RAf TER5 TO BE 2X7'-20'-O-C •PORttER RAFTERS ZALlCfOC 4---^-k _.-._^ -FRAPMnG-PLAN- OT-IKXT- oia 34-.5ev* -Jca«.le. c/LLLLi_L_L_l_L_LJ/ee.t.- f ig. ii. 84 ESTIMATING STAIRS Front Stairs — 128 ft. spruce, at $30 per M 3.84 120 ft. whitewood, at S70 per INI 8 . 40 85 ft. quartered oak, at $150 per ]\I 12 . 75 . 30 ft. mahogany rail and turn 24.00 5 paneled posts at $5.00 each 25 .00 105 balusters at $.15 each 15 . 75 11 nosings at $.06 each -66 25 scotias at $.03 each 75 Nails, glue, etc 1-00 Labor •')6.00 $148.15 Back Stairs — First Flight— 55ft. spruce, at $30 per M $ 1 .65 105 ft N.C. pine, at $60 per M 6.30 16 scotias at $.03 each .48 Nails, etc 75 Labor IG^ 25.18 Second Flight — 54 ft. spruce, at $30 per ]\I $ 1 .62 110 ft. N.C. pine, at $60 per M 6.60 17 scotias at $.03 each 51 Nails, etc ' • ''^ 1 post •. • -75 4 ft. rail, at $.m per ft 50 12 balusters at $.06i each 75 Labor }l^ 28.48 Cellar Stairs — 40 ft. spruce, at $30 per M $ 1.20 75 ft. N. C. pine, at $60 per M 4.50 Post -50 Rail 1.20 Labor 5.00 12.40 $214.21 Framing 2 . 00 Total cost of Stairs $216.21 314 r/j?^T fLOOi^ rj./!/^ FIRST-FLOOR PLAN OF RESIDENCE FOR MR. HANS HOFFMAN, MILWAUKEE, WIS. COST OF HOUSE: Mason Work % 625.00 Carpentry 3,684 00 Tinning. 36 00 Pluiubing 380.00 Plastering. 253.00 Heating {Furnace) $ 167.00 Painting. 325.00 Decorating 53.00 Total $4,523.00 Built in 1902. Oak Wainscoting and Ceiling in Dining Kooni; Oak Finish in Stair Hall and All Main Rooms on First Floor; Cypress iu Balance ol House. For Exterior, See Page 331. SECOND-FLOOR PLAN OF RESIDENCE FOR MR. HANS HOFFMAN, MILWAUKEE, WIS. First-Floor Plan Shown on Opposite Page. ESTIMATING 85 HARDWARE Note. — ^This estimate is based upon a fair quality of hardware, the butts being of bronze-plated steel, the knobs of struck-up bronze metal, with rose and escutcheon combined; the sash fasts of solid bronze metal, also lifts and catches. BASEMENT Bulkhead, Outside — 2 pairs extra heavy galv. T hinges, S-inch at $.85 each $1.70 2 hooks and staples, 5-inch, at $ . 10 each . 20 Labor 1 .00 Bulkhead, Inside — 1 pair heavy T hinges, 8-inch 15 1 thumb-latch 10 Labor 50 Three Doors — 3 pairs butts, Sj X S^Wnch, at $.15 each .45 3 sets locks at $ . 45 each 1 . 35 Labor 1 . 50 Hinged Windows — 12 pairs butts, IHnch, at $.06 each .72 12 hooks and eyes, at $ . 02 each . 24 12 buttons, at $.02 each .24 Labor 1 .50 $ 9.65 FIRST FLOOR Entrance Door — H pairs butts, 4-^- X 4^-inch, at $.38 each $ .57 1 set locks, bronze metal 9 . 50 Labor 2.00 Seven Inside Doors, Front — 7 pairs butts, 3^- X 3Wnch, at $.30 each 2. 10 7sets locks at $1.00each 7.00 Labor , 5 . 25 Carried forward $26 .42 $9 . 65 315 -DETAIU^OMHTCHLN^PANTKy- ETC^ -F052.-GED52jGL-A-JOnEJ - MQ- ,* ^ J L J L ] ■ ■- _ L J L 7 ^ n 1 — 1 ■ f 1 SECTION- THRO'- KITCHEN PANTRY •Scale- 12 6 o I I I I I I I SECTION- -THRO'- CHINA - CLOSET- -DflTAIL- or PANTRIES- _ -DETAIL" OF' LI I^N- CLOSET" OCALE.- . 12 9 6 3 O I I'll IIDOT. Fig. 14. ESTIMATING 87 Erought funvard $26 A2 $9.65 Side Entrance Door — Impairs butts, 4^- X 4i-inch, at S.38each .57 Isetlocks 2.25 Labor ^l.OO One Pair Sliding Doors, 5 ft. in. — 1 set hangers, 5 ft. in, Double 3 . 50 1 sets. D. locks : . . . 2.50 Labor 2.00 Six Inside Back Portions — 6 sets lock sat 1.45 each 2.70 6 pairs butts, 3^ X 3^>-inch, at $ .15 each . 90 Labor 4.00 Back Doors — H pairs butts, 4h X 4Hnch, at $ . 20 each . 30 Isetlocks 2.25 Labor 1.00 Ice-Chest Door — 1 pair butts, 3 X 3-inch .40 1 IH lever, galvanized .60 1 brass hasp and padlock 1 . 50 Labor .50 China Closet — 2 pairs glass doors — 2 pairs butts, 2^ X 2Hnch, at $ . 26 each . 52 2 elbow catches, at $ . 06 each . 12 2 cupboard catches, at . . S . 15 each . 30 1 pair cupboard doors — 2 pairs butts, 2h X 2Hnch, at -S . 10 each . 20 1 elbow catch .06 1 cupboard catch .15 20 dra\\er-pulls, at S . 06 each 1 . 20 Labor 2.50 Pantry — 4 cupboard doors — 4 pairs butts, 2^ X 2^-inch, at $ . 10 each .40 Carried forward $57.84 $9.65 317 88 ESTBIATING Brought forward $57.84 $9.05 4 cupboard catches, at $. 15 each .60 1 bl)l. swing .75 " 10 drawer-pulls, at $ . 06 each . 60 Labor 2.00 Windows — 15 sash fasts, at $.30 each 4.50 30 sash lifts, at $.06 each 1 .80 Labor 7 . 50 Casement "Windows, 4 pairs butts, 3 X 3-inc-h , at $ . 50 each 2 . 00 2 pairs flush bolts, at $1 . 00 each 2 . 00 2 casement fasts, at ' $ . 45 each . . 90 Labor 1.00 $81.49 SECOND FLOOR Sixteen Doors — 16 pairs butts, 3^ X SHnc'li, :»t ■■•• .$.30 each $ 4.80 16sets locks, at $.90each 14.40 Labor 10.40 Windows — 14 sash fasts, at.... $.30each 4.20 1 sash fast .35 28 sash lifts, at $.00 each 1 .68 2 sash lifts, at $.10each .20 Labor 7.00 Six Drawers in Linen Closet — 12 drawer-pulls, at $.06each .72 Labor .25 $44.00 Bathroom — 1 pair butts, 3^ X 3^-inch (nickel-plate) 40 1 set locks (nickel-plate) 1 . 25 Labor .75 $ 2.40 ATTIC Two Doors — 2 pairs butts, 3^ X 3Hnch,at . . . ..$.12 each. . . .$.24 2sets locks, at $.45 each 90 Labor 1.00 Carried forward $2.14 $137.54 318 Fig. 16. Fig. 16. ESTIMATING 91 Brought forward $2.14 §137.54 Two Low Doors — 2 pairs butts, 2h X 2.\-inch, at ,?.10 each 20 2 cupboard turns, at $.35 each 70 Labor .' 1 . 00 Windows — 8 sash fasts, at $.30 each. . . .2.40 16 sash Hfts, at $.06 each 90 Labor 4.00 6 doz. H. & C. hooks, 639^^, at ... . $.50 doz 3 . 00 3 doz. ba.se knobs, at $.35 doz 1 .05 Labor .2.50 $ 17.95 Total cost of Hardware put on $155 . 49 HEATING Furnace — 1 No. 28 Crawford furnace (28-in. firepot) . . $125 .00 ' 22 ft. S-in. galv. iron smoke-pipe, 55 lbs., at $.09 lb. 4.95 Registers — 1 14 X 18-in. register, stone, box and netting, 4.72 4 9 X 12-in. registers, stone, box and netting, at $1.57 each 0.28 4 8 X 10-in. registers, stone, box and netting, at $1.19 each 4.76 4 8 X 10-in. registers, stone, box and netting, at $1.15 each 4.60 Piping, including dampers, collars, and elbows — 12 ft. 14-in. tin pipe, at $.27 per ft.. . 3.24 64ft. 9-in. " " at $.16 " ".. 10.24 278 ft. 7-in. " " at $.10 " ".. 27. SO Covering for Risers (6 lbs. asbestos paper per pipe) — 5 risers, 30 lbs., at $.05 lb. 1 .50 Plastering Rings in Cellar — For 13 pipes at $.20 each 2.60 $ 195.69 Office expense and profit 48.92 $244.61 Carried forward $244 . 61 321 'PLUAblNG^PLAn^J-d/ -SECTION -ErjlOU^Ct- AT- EtotDAU, -/«o - >- roR.v GtoeGE-'A-joMEj- - £jQ^- • fKAMK AeOOUnt,' ARCH1T££.T- -/ujo«- 6Uil,£>ittG Borrow- P==cp rU ^P fiO. Porch- ^ Porch Rini^rRATCT. Zl CT PAnTRy 3 KITCHErt r'- ? CTT^ t Hall CHWA CLO/XT -y^T flALU ^ DI □ / \D CLO/ TLT 1 CHAr&!:R nR5T FLODR PLUMBFNG-PLAN oE(DND FLOOR. PLUMBING- N d*:;-'-'*^ ,*'■ c o BUI TRAP n IWihENT PLUMPING- D lAWPRy. yVoRC liOO, •■*v*Tory^ TWfr ^^ '• vim —A. tfOH pK — ^; ■sTtT.cxwixna-vrrK- riXTWRE V^ll- *"ci _ > TAr lin TOR Tvnmt Fig. 17. ESTIMATING 93 Brought forward $244. Gl Labor — INIeasurino- and laying out risers, man 1 day . $4 . SO Erecting risers, man 2 days, helper 1 day ... . 1 2 . 00 Laying out and erecting cellar pipes and fur- nace, inan 3 days, helper 2 days 19 .20 Finishing, man 1 day 4.80 Carting and expenses 10.00 50.80 Total cost of Heating Apparatus $ 295 .41 PLUMBING Waste and Soik Pipes — 2 4-in. lead Fends, at $1.10 each .^ $2 . 20 2 4-in. sleeves, at $.65 each .....:... 1 . 30 5 2-in. " ' at $.28each ..../.. 1 .40 2 3 X 2-in. sleeves, at $ . 45 each .90 1 1^-in. Penlberton trap ! . .^ 6.80 30 lbs. solder, wiping, at$.25 lb 7 .'50 2 trap plugs, at $.42 each .84 2 6-in. tra/s, at $2.35 each 4 . 70 1 6-in. cesspool 3 . 00 4 1^-inch solder nipples, at $ . 15 each .60 1 4-in. roof flashing 1 . 35 Soil pipe 47 . 87 15 ft. H-in. lead pipe. No. 55 3 .24 50 ft. 2-in. iron pipe | g ng 40ft. li-in. " " f Soil fittings, ^ cost of pipe 15 .96 Cast-iron fittings, 20 per cent 1-79 $ 108 .41 Miscellaneous Fittings — 3 4-in,b?ssCO $ 2.70 1 5-in. brass CO 1.50 Refrigerator waste 1 2 . 50 Local vents 12.00 1 ball-cock 1-25 2 sill cocks 2.00 Tank overflow 6 . 50 4|-inchS. &W. cocks 3.24 Carried forward $41.69 $108.41 323 04 ESTIMATING B roughf fonvcml S 4 1 . 69 $ 1 08 . 4 1 1 boiler valve and chain .70 25 lbs. tinned copper, at $.32 lb 8 . 00 6 3-part hangers, brass 6 . 30 2 ^-in. hose bibs 1 .50 3 |-inch plain bibs 2.10 Street connections 55 . 00 lib. putty 05 2 lb?, grafting wax .50 Calking lead, 380 lbs 22.80 Oakum 1.60 $ 140.24 FiXTURE.S — 1 3G X 24 X 8-in. sink, 12-in. back $11 .40 1 24 X 14-in. pantry sink 14.00 1 pair pantry cocks 3 .60 2 24 X 48-in. trays, 12-in. back 14. 10 1 5-ft. bathtub, complete 41 .00 1 lavatory, complete 32 . 50 1 water-closet, complete 60.00 1 40-gallon boiler 10.75 1 " " ." stand 85 . 12 lbs. fine solder 3 . 12 Clamps and hooks 2 . 70 Tinned tacks .15 Fuel 1.95 $ 202. 12 Supplies and IvAbor — 126 ft. |-inch galv. water pipe $4 .41 22ft. i-inch " " " .62 Fittings, ^ cost of pipe 1 .67 74 ft. ^in. brass $23.49 56 ft. Hn. " 16.24 39.73 Fittings, 20 per cent • 7 .95 Painting of iron pipes 9 . 75 Stop-cocks . 3 . 54 Sink and tray legs 4 . 72 Lead, oil, etc .165 Carried forward $ 7S .04: $450.77 324 ESTLMATIXG 95 Brought Jorward S 73.04 S 450.77 Clamping brass and screws .25 Cartage and fares 5 . 00 Labor, 40 days, at S6.00 per day 240 . 00 318 . 29 $ 769.06 Profit, 10 per cent 76 .90 Total cost of Plumbing S 845 .96 ELECTRIC WIRING 75 ft. No. 4 S. B. R.C. wire S 4.80 150 ft. No. 1 S. B. R. C. wire 4.26 40 Large porcelain tubes, 5 cents 2 . 00 30 " " knobs, 5 cents 1 .50 1 3-pole 50-amp. fused switch 1 .50 1 Main cabinet (meter) 3 . 50 1 8-circuit cut-out panel 16 .00 2,500 ft. No. 14 S.B. R.C. wire 28.60 500 ft. 1 4-in. circular loom 20.00 800 5^ knobs 3.20 1 ,600 5-in. porcelain tubes 4 . 00 100 Fire stops 9 .00 100 12-in. porcelain tubes 10.00 18 Ceiling boxes 1 . 80 30 Bracket boxes 3 .00 11 Switch boxes 2.20 11 " " 12.10 Labor on No. 14 wire 55 .00 "mains 15.00 " "finish.... 15.00 Teaming and freight 5 . 00 Sundries 5 . 00 Nails, leatherheads, etc 3 . 00 $ 22b AQ Office expense, 10 per cent 22 . 55 S 248.01 Profit, 20 per cent 49.60 Total cost of Electric Wiring % 297.61 325 Of) ESTIMATING Note. — This estimate is figured on outlet boxes at all outlets; and includes a main cabinet and main switch to connect with the meter and to cover the meter, on an eight-circuit panel-board, which allows one spare circuit. The panel-board is to be made of slate, with slate gutters and linings, with good wood door and trim. The labor is estimated on wages being $3.60 per day for a journey- man, and $2.00 per day for helper. This price is above that paid in small places, but is below what is paid in some cities. ELECTRIC LIGHTING FIXTURES Note. — While the electric lighting fixtures are not generally made a part of the building contract, it may be worth while to consider them in relation to the cost of the house; although, as has been stated, there is such a wide range in design and cost, as well as in personal prefer- ence, that any data given can be at best only approximate. The following estimate is based upon simple designs of moderate cost in "old brass" finish: FIRST STORY Living Room — ' 1 4-light electrolier $17 .50 4 1-light wall brackets, at $3.25 each 13 .00 Hall — 2 2-light ceiling pieces, at $2.50 each 5 . 00 Vestibule — 1 3-light cluster 5 .00 Porch — 1 1-light ceiling-piece 1 .75 Parlor — 1 4-light electrolier 1 7 . 50 2 1 " wall brackets 6.50 Dining Room — 1 4-light electrolier 10.00 2 1 " wall brackets 5 .00 China Closet, Rear Hall, Kitchen — 3 1-light ceiling-pieces, at $.75 each 2.25 2 1 " wall brackets, at $1.35 each 2.70 Carried forward $S6 .20 320 ESTIMATING 97 Brought forward $ 86 . 20 Pantky — 1 1-light ceiling-piece ■ '^ Entry — 11 " " " 1.35 Piazza — 11 " " " , 1.75 SECOND STORY Hall — 2 1-light ceiling-pieces, at $1.50 each $3 .00 Alcove — 2 1-light ceiling pieces, at $2.50 each 5.00 Bedrooms — 13 1-light brackets, at $2.50 each 32 .50 Bathroom — 1 1-light ceiling-piece 1-35 Rear Hall — 1 1-light bracket . 1 .35 THIRD STORY Hall — 1 1-light wall bracket • $1 .35 Attic — 1 3-ft. drop-cord -85 BASEMENT Laundry — 1 1-light wall bracket $1 . 15 Cellar — 4 3-ft. drop-cords, at$.85 each 3.40 $ 140.00 LABOR Installing above fixtures with all necessary trimmings . . . % 12.00 Total cost of Electric Lighting Fixtures in place .... $152 . 00 PAINTING Outside Painting — 17 pairs blinds, three coats painting, at $1.50 pair .... $ 25 .50 1,068 yds. three coats painting, windows and wood- work, at $.20 yd •• 213.60 Carried forward $239 . 10 327 98 ESTBIATING Brought jonvard $239.10 54 yds. two coats metallic paint, upper side tin roofs, at $.15 yd 8.10 62 yds. two coats oilingon floors, porch, and piazza, at S.lOyd ■ 0-20 Interior Painting-t- 16G yds. filling, staining, and shellacing, and two coats hard oil finish, at S . 20 yd $33 . 20 245 yds. filling and two coats spar varnish, first coat rubbed, at $.25 yd 61 .25 403 yds. one coat shellac, three of paint, two coats zinc and white varnish. Rubbed with pumice and water, ivory white finish, at $ . 80 yd 322 . 40 294 yds. treat with potash, one oil filler, clean, four coats shellac, last coat rubbed with pumice and oil, oak and birch, at $.35 yd. 102.90 109 vds. filling, four coats shellac, last coat rubbed with pumice and oil, floors at $.30 yd 32.70 114 yds. size and three coats paint, last coat with varnish, walls, at $.20 yd 22.80 5 yds. three coats paint and one enamel gloss, bath- tub, at $.25 yd 1.25 100 yds. three coats paint, last with zinc, flat, white- wood, at $.25 yd 25 .00 10 yds. one coat shellac on pipes, at $ . 10 yd 1 . 00 299 yds. size and tint in water-colors, ceilings, at $.15 yd 44.85 Total cost of Painting -. . .$ 900.75 GENERAL SUMMARY Batter-Boards and Water Supply $ 25 . 00 Excavation 262 . 50 Stonework, Cesspools, and Drains 754. 15 Chimneys and Brickwork 281 .50 Concreting 88.20 Plastering 544.40 Carpenter Work 4,928.34 Carried forward %Q,^^Am 328 DZmhJ^Of^ TRin^OI^^FIMT^ FLOOR' ■DODR- ,3CAli-K>RIXIVATlON^- ? . I . 1 I f DETAIL- OF TRIM- ■WINDOW-. -DGDR- ? 6 9} L-L-LJ [ 1 U -^GALE • FOR- PrTAlL^ - BASE- BOARD V^ctilc-o^- ? . ^ DETAIL- OF- £)aDKCA^£ ■ SHOWING- •5ECTiort "fitia TOP or CASE,- •5KLr ■SECTION ■ -SHOWlNff a ^ZCTiOrt OF3E.AT 5P' F 6 1 I pect-c?- Jncbs/-- Fig. 18. 100 ESTIMATING Brought forward $6,884.09 Stairs 216.21 Hardware 155.49 Heating 295.41 Plumbing 845 . 96 Electric Wiring 297 . 61 Electric Fixtures 152.00 Painting ^00^75 Total, '$9,747.52 SCHEDULES ANALYSIS OF CARPENTER WORK Following is a section devoted to the analysis of the different portions of carpenter work in the foregoing estimate. These show how the prices are obtained, and will be very useful for comparison, as the changes in cost of parts can be noted and kept up to date. First Floor, price per square of 100 sq. ft., including the floor beams, bridging, and under floors, but no furring for plaster — Joists, 2 X 10-in., 16 inches on centers $3.25 Labor 1.50 Nails 10 Bridging 50 Under floor, hemlock, at $24.00 : . 2 . 30 Waste, one-third 80 Labor 75 Nails .15 $ 9.35 Hard Pine Upper Floor, per s(juare of 100 sq. ft. — Stock $6.00 Waste, one-third 2 .00 Labor 2.25 Nails _25 $10.50 Quartered Oak Upper Floor, per square of 100 sq. ft. — Stock $10.00 Waste 3.30 Labor 6 . 50 Nails 25 $20.05 330 J) h U h i u OJ V c O t r H U < S 2 9 "K < X C i- - 1 O b U u z u o 1) ESTIMATING 101 Porch or Veranda Floor, per square of 100 sq. ft. — Joists, 2 X 8-in., 16 inches on centers .... !S!2 .60 Labor 1.00 Hard pine flooring, at $55 , 5 .50 Waste 1.80 Labor 1.25 Nails , 20 $12.35 Second Floor, per square of 100 sq, ft. — Joists, 2 X 10-in., 16 inches on centers .$3 25 Labor 1 . 50 Bridging 50 Furring 1 . 50 Under-floor stock 2 .30 Waste, one-third 80 Labor 75 Nails 15 Upper-floor stock 4 . 00 Waste 1.30 Labor 1 . 75 Nails ,. 20 $18.00 Third Floor, per square of 100 sq. ft. — Joists, 2 X S-in., 16 inches on centers $ 2.60 Labor 1 . 50 Under floor 4.00 Furring 1 . 50 Bridging -. . . .50 $10.10 Shingled Roof, per square of 100 sq. ft — Rafters, 2 X 7-in, 20 inches on centers $ 2. 17 Labor 2.25 Matched spruce boarding 2.50 Waste, one-third 80 Labor 1 .25 Nails 20 Shingles 4 . 00 Labor . 3 . 25 Nails 25 $16.67 331 102 ESTIMATING Tinned Roof, per square of 100 sq. ft. — Rafters, 2 X 7-in., 20 inches on centers $ 2. 17 Labor 1.50 Matched boarding, as above 4 . 75 Paper 50 Tinning 12.00 $20.92 Wall Frame and Boarding, per square of 100 sq. ft. — Studding, 2 X 4-in., 16 inches on centers S 4.00 Boarding 2 . 30 Waste.. ^ 80 Labor 1.00 Nails .20 8 8.30 Inside Studding, per square of 100 sq. ft. — Stock, 2x4-in., 16 inches on centers $ 1..30 Waste, one-half stock .65 Labor 1 . 50 Nails 15 Grounds and beads .40 $ 4.00 Clapboarding, per square of 100 sq. ft. — Clapboards, 80, at $.05 each $ 4.00 Labor 3 . 25 Paper 50 Nails .20 $7.95 Main Cornice, per linear foot — Gutter, perft $ .12 Upper fascia 03 Fillet 01 Lower fascia .04 Planceer 08 Bed-mould 02 Frieze 06 Architrave moulding .04 Brackets 25 Labor 50 Rough furring .10 $ 1 .25 Piazza Cornice, per linear foot — Upper fascia $ . 03 Carried forward $ . 03 832 DETAIL OF'GENEEAL'WINDOW-FRAMEJ' /: i!i|iiiii|i|irT r\ FLojKina o on 3 ijLud a«4 "Window JnzToe. Hcod livnie i-atK Architrave, W S JtuA Boarding Weighti E>ox 'JECTION-THKO^ 'WINDOW-! OX 'AT- JIDL- JECTION-THKO- \A/1ND0W-HEAD- OuUrudr ArchiLrave C>ackbDiul T JICTIQN'THED Fig. 19. 104 ESTIMATING Brought forward $ .03 Gutter 10 Lower fascia 03 Fillet 01 Planceer 08 Bed-mouia 02 Brackets 25 Frieze 15 Architrave mould 03 Soffit 05 Inside frieze 10 Labor... 1.00 Rough furring -15 $ 2.00 Attic Windows, circular top, each — Frame $ 6.00 Sash 2.50 Inside finish 1 . 00 Weights and cord 45 Labor 1.25 $11 .20 Second-Story Windows, 3 ft. in. X 5 ft., each — Frame S 3 . 50 Sashes, 17. V .sq. ft., at $ . 20 per sq. ft $ 3 . 50 Blinds 1.00 Blind fasts 15 Inside finish 1.19 Nails and screws 10 Weights and cord 64 Labor, 1 dav 3.25 $13.33 Inside Finish for Window, as above — Architrave, 21 ft., at $.03-^ per ft $ .73 Back-band, 21 ft., at $.03 " " 63 Beads, 17ft.,at$.02 " " ^M $1.70 30 per cent off .51 $1.19 Weights and Cord for Window, as above — Weights, 17^ ft.,21bs.per ft., 35 lbs., at $.0U per lb $ .44 Cord, 20 ft., at $.01 per ft 20 $ .64 334 ESTIMATING 105 Cost of Window, 2 ft. 6 in. x 4 ft. 6 in., each- Frame § 3 50 Window, Hi sq.ft., at $.20 per sq. ft 2.25 Blinds 75 Blind fastenings j5 Screws and nails. 20 Weight, 22Mbs., at S.OU per lb 28 Cord 15 Inside Casing, 18 ft., at 8.03^ per ft 03 Back-band, 18 ft., at $.03 per ft 54 Stop-beads, 14 ft., at $ . 02 per ft 28 Lal^oi- 3.25 $11 .88 French Windows, 4 ft. 6 in X 7 ft. 6 in., each— Fraiiie § 5 00 Sash, 4ft. 6 in. X 7 ft. G in., .34 .sq. ft., at $.20 per sq- ft 6.80 Astragal 50 Nails and screws 10 Inside finish ^ gg L'^^^or 4 §3 $18.24 Window, 3 ft. 4 in. X 5 ft. G in. (oak finish), each- Frame s 3 50 Window, 18 sq. ft., at S . 20 per sq. ft 3 . GO Blinds 1 00 Blind fasts 15 Nails and screws 10 ^^'eights 70 Finish (oak) 2 64 Labor, Udays 4,88 31657 Rear Door, 2 ft. 10 in. X 7 ft. 6 in.— Frame $4 00 Door,21sq. ft.,at$.25persq.ft 5.25 Finish gj Labor 3 25 ^^^'^ 05 $13.46 335 106 ESTIMATING Front Door, 3 ft. 3 in. X 7 ft. 6 in., with top and side lights— Frame — Sill, 7 ft., at S. 25 per ft $1.75 Jambs, 23 ft., at $.07 per ft 1.61 Mullions and transom bar, 20 ft., at $.10.V perft 2.10 Outside casing, 23 ft., at $.03.V per ft 81 Mullion casing, 20 ft., at $. O23V per ft 42 Labor, v price of stock 3 . 32 $10.01 Z)oor, 3 ft, 3 in. X 7 ft. () in.— ^1 sq. ft., at$.25persq. ft $5.25 Side-light panels, 6 ft., at $ . 25 per ft 1 . 50 3 sash rims, at $.50 each 1 .50 Leaded glass, 10| sq. ft., at $2 . 50 per sq. ft. . 27.00 $35.25 Inside Finish — Stop-beads - $ -28 Architrave, 24 ft., at $ . 04^ per ft 1 . 08 Labor, 3 days 9-75 $11.11 Total cost of front tloor and frame $56 .37 Door, 2 ft. 8 in. X 7 ft. 6 in. (N. C. pine)— Stockdoor $3.00 Frame 1-25 Threshold 15 Nails 05 Finish, 39.V ft., at $.04^ per ft. .... 1 .78 Labor 3.25 $9.48 Pair of Sliding Doors, ft. X 8 ft. (whitewood and birch)— Doors, 48 sq ft., at $ . 50 per sq. ft $24 . 00 Architrave, 24 ft., bn-ch 2 .34 24 ft., whitewood 1.05 Jambs, 22 ft., birch 1 .82 " 22 ft, whitewood 85 Grounds, 22 ft, birch . .50 Carried forward $30 . 56 336 ESTBIATING 107 Brought foncard S30.56 Grounds, 22 ft., whitewood 23 Chafing strip, 22 ft., birch 33 22 ft., whitewood 15 Astragal, birch and whitewood 1 .50 Sheathing pockets, 96 ft.; at S4.75 per square. 4 . 50 Labor, 5 days' work 16.25 $53.52 Schedule of Rooms, and Memoranda from which Heating Esti= mate is Made Up First Floor Rooms Size o >< n m Equals Size of Register < 128 Feet of Tin Pipe, includ- ing Elbows Living Room . 14x25x9 3,150 25 2 9-in. pipes 2 9x12 34 Hall 11x25x9 Add 40% for space above, 3,465 25 ,25 14-in. " 14x18 154 64 ' 12 Parlor 12x14x9 1,512 9-in. " 9X12 14 Dining Room. 12x14x9 1,512 25 35 35 35 9-in. •• 9x12 64 38 16 China Closet. 7x10x9 • • ■ • 7-in. " 7X10 24 Second Floor 8X10 Bedroom .... iixux" (A as u K s K M H >" CQ c/} M CC Pu, » 5' -S" ■-^ M D Bd H b O o K X to fa <1> "V3 s ^ >. "O c rt ^ n ix — rr '"»^ 4-^ o OJ o c/: a, • •k M W 3 U < PC >- Ol -a a> s tS o D K o ; 3 en S X -s! •IS u %^ z ^ «< rt f^ ^ o: H ^ ^ "^ >« ca X ■?, c« u ;J '^ « «i V) .. - K w •^^ HN o b. 0) ^ 4^ CO < 9 *S :as PS S H o 4^ ^ b a O O z <^ (i; u a r> o f« o »J < ce 3 H O s ce H W THE STEEL SQUARE INTRODUCTORY The Standard Steel Square has a blade 24 inches long and 2 inches wide, and a tongue from 14 to IS inches long and U inches wide. The blade is at right angles to the tongue. The face of the square is shown in Fig. 1. It is always stamped with the manufacturer's name and number. The reverse is the back (see Fig. 2). The longer arm is the blade; the shorter arm, the tongue. In the center of tlie tongue, on the face side, will be found two parallel lines divided into spaces (see Fig. 1); this is the octagon scale. The spaces will be found numbered 10, 20, 30, 40, 50, 60,. and 70, when the tongue is IS inches long. To draw an octagon of 8 inches square, draw a square S inches each way, and draw a perpendicular and a horizontal line through its center. To find the length of the octagon side, place one point of a com- pass on any of the main divisions of the scale, and the other point of the compass on the eighth subdivision; then step this length off on each side of the center lines on the side of the square, which will give the points from which to draw the octagon lines. The diameter of the octagon must equal in inches the number of spaces taken from the square. On the opposite side of the tongue, in the center, will be found the brace rule (see Fig. 3). The fractions denote the rise and run of the brace, and the decimals the length. For example, a brace of 36 inches run and 36 inches rise, will have a length of 50.91 inches; a brace of 42 inches nm and 42 inches rise, .'svill have a length of 59.40 inches; etc. On the back of the blade (Fig. 4) will be found the board measure, where eight parallel lines running along the length of the blade are sho\\Ti and divided at every inch by cross-lines. Under 12, on the outer edge of the blade, will be found the various lengths of the boards, as 8, 9, 10, 11, 12, etc. For example, take a board 14 feet long and 9 341 THE STEEL SQUARE =^ C\J i:^ O =- 0> E- «0 — r^ o _ G) CO _ r~ - CD CO in ^ ^ (0 ty 10 _ t - ro OJ ib] V fl O o O m n o ci 5- _ VI o s fee o H bO lililililililililili 842 THE STEEL SQUARE zr O) — 00 = r^ CVJ = CO = LO = ^ = 00 CO to 10 00 CD CD 05 CO 05 CD CO lO c^ ^(ocnycvj^io ^= o = 0) = oo: N = CO: lO== ^^ co=i (\J = — C\J "-- --CMCVJCVl 3 llllNlllllllllllll OOl in •a !-< ci O cq W PI o .=) a) pi a* "3 +J o o ho ■fc'? t 09 Bl 09 ffij 343 4: THE STEEL SQUARE Fig. 5. Use of Steel Square to Find Miter and Side of Pentagon. inches wide. To find the contents, look under 12, and find 14; then fol- low this space along to the cross-line un- der 9, the width of the board ; and here is found 10 feet 6 inches, denoting the contents of a board 14 feet long and 9 inches wide. To Find the Mi= ter and Length of Side for any Poly= gon, with the Steel In Fiff. 5 Square. is shown a pentagon figure. The miters of the pentagon stand at 72 degrees with each other, and are found by dividing 3G0 by 5, the number of sides in the pentagon. But the angle when applied to the square to obtain the miter, is only one-half of 72, or 36 degrees, and intersects the blade at 8f |, as shown in Fig. 5. By squaring up from G on the tongue, intersecting the degree line at a, the center a is determined either for the inscribed or the circumscribed di- ameter, the radii being a h and a c, respec- tively. The length of the sides will be 8|f inches to the foot. If the length of the inscribed diameter be 8 feet, then the sides- would 1 o V ^ o 9 Fig. 14. Diagram to Illustrate Use of Steel Square In Laying Out Timbers of Roofs of Equal Pitch. To understand this figure, it is necessary only to keep in mind that the pitch of a roof is reckoned from the span. Since the run iu each pitch as shown is 12 inches, the span is two times 12 inches, which 349 10 THE STEEL SQUARE equals 24 inches; hence, 12 on bhide to represent the foot run, and 12 on tongue to represent the rise over 2 the span, will be the figures on the square for a J-pitch roof. For the I pitch, the figures are shown to be 12 on tongue and 9 on blade, 9 being I of the span, 24 inches. The same rule applies to all the pitches. The ^ pitch is shown to rise 4 inches to the foot of run, because 4 inches is I of the span, 24 inches, the 3- pitch is shown to rise 8 inches to the foot of run, because 8 inches is ^ of the span, 24 inches; etc. The roof referred to in Figs. 16 and 17 is to rise 9 inches to the foot of run; it is therefore a f -pitch roof. For all the common rafters, the fig- ures to be used on the square will be 12 on blade to represent' the run, and 9 on tongue to represent the rise to the foot of run ; and for all the hips and valleys, 17 on blade to represent the run, and 9 on tongue to represent the rise of the roof to the foot of run. Why 17 represents the run for all the hips and valleys, will be understood by examining Fig. 19, in which 17 is shown to be the diag- onal of a foot square. In equal-pitch roofs the corners are square, and the plan of the hip or valley will always be a diagonal of a square corner as shown at 1, 2, 3, and 5 in Fig. 14. In Fig. 18 are shown ^ pitch, s pitch and i pitch over a square corner. The figures to be used on the square for the hip, will be 17 for run in each case. For the ^ pitch, the figures to be used would be 17 inches run and 4 inches rise, to correspond with the 12 inches run and 4 inches rise of the common rafter. For the | pitch, the figures to be, used for hip would be 17 inches run and 9 inches rise, to corre- CVJ "251 CM "2 "551 "Jo CM V -00 .A? I I I L^lTlO 19 18 |7 16 15 H 13 \Z |l X 12 i 24 CM 2 Pitch II 5 3 1 SA X A Fig. 15. Steel Square Giviug Various Pitches to Foot of Kuu. 350 THE STEEL SQUARE 11 spond with the 12 inches run and 9 inches rise of the common rafter; and for the 2 pitch, the figiu'es to be used on the square will be 17 inches run and 12 inches rise, to correspond with the 12 inches run and 12 inches rise of the common rafter. It will be observed from above, that in all cases where the plan of the hip or valley is a diagonal of a square, the figures to be used on , , , ^ , Top cut for 13ft. 6in. x^^Heel Cut Co-mrr>or. • Rafter ' Plumb Cut Fig. 16. Method of Layin^ Out Common Rafters of a J^-Pitch Roof. the square for run will be 17 inches; and for the rise, whatever the roof rises to the foot of run. It should also be remembered that this is the condition in all roofs of equal pitch, where the angle of the hip or valley is a 45-degree angle, or, in other words, where we have the diagonal of a square. It has been shown in Fig. 12 how other figures for other plan angles may be found; and that in each case the figures for rim vary Heel cut of hip T op cut for i3ft.ein. run of hip Top cut for 13 ft. run of hip Fig. 17. Method of Laying Out Hips and Valleys of a %-Pitch Roof. according to the plan angle of the hip or \alley, while the figure for the height in each case is similar. In Fig. 14 are shown a variety of runs for common rafters, but all have the same pitch ; they rise 9 inches to the foot of run. The main 351 12 THE STEEL SQUARE Pitch roof is shown to have a span of 27 feet, which makes the run of the common rafter 13 feet inclies. The run of the front wing is shown to be 10 feet 4 inches; and the run of the small gable at the left corner of the front, is shown to be 8 feet. Tiie diversity exhibited in the runs, and especially the fractional part of a foot shown in two of them, will afford an opportunity to treat of the main difficulties in laying out roof timbers in roofs of ecjual pitch. Let it be determined to have a rise of 9 inches to the foot of run; and in this connec- tion it may be well to re- member that the propor- tional rise to the foot run for roofs of equal pitch makes not the least dif- ference in the method of treatment. To lay out the common rafters for the main roof, which has a run of 13 feet G inches,pracced as shown in Fig. IC. Take 12 on the blade and 9 on the tongue, and step 13 times along the rafter timber. This will give the length of rafter for 13 feet of run. In this example, however, there is another 6 inches of run to cover. For this additional length, take 6 inches on the blade (it being ;V a foot run) for run, and take \ of 9 on the tongue (which is U inches), and step one time. This, in addition to what has already been found by stepping 13 times with 12 and 9, will give the full length of the rafter. The scjuare with 12 on blade and 9 on tongue will give the heel and plumb cuts. Another method of finding the length of rafter for the G inches is shown in Fig. 16, where the square is shown applied to the rafter Fig. 18. Method of Laying Out Hips and Rafters for Roofs of Various Pitches over Square Corner. 352 THE STEEL SQUARE 13 timber for the plumb cut. Square No. 1 is shown appHed with 12 on blade and 9 on tongue for the length of the 13 feet. Square from this cut, measure 6 inches, the additional inches in the run; and to this point move the square, holding it on the side of the rafter timber with 12 on blade and on tongue, as for a full foot run. It will be observed that this method is easily adapted to find any fractional part of a foot in the length of rafters. In the front gable, Fig. 14, the fractional part of a foot is 4 inches to be added to 10 feet of run; therefore, in that case, the line shown measured to 6 inches in Fig. 16 would measure only 4 inches for the front gable. Heel Cut of Common Rafter. In Fig. 1(3 is also shown a method to lay out the heel cut of a common rafter. The square is shown applied ^^^th 12 on blade and 9 on tongue; and from where the 12 on the square intersects the edge of the rafter timber, a line is drawn square to the blade as shown by the dotted line from 12 to a. Then the thickness of the part of the rafter that is to project beyond the plate to hold the cornice, is gauged to intersect the dotted line at a; and from a, the heel cut is drawn with the square having 12 on blade and 9 on tongue, marking along the blade for the cut. The common rafter for the front wing, which is shown to have a run of 10 feet 4 inches, is laid out precisely the same, except that for this rafter the square with 12 on blade and 9 on tongue will have to be stepped along the rafter timber only 10 times for the 10 feet of run; and for the fractional part of a foot (4 inches) which is in the run, either of the two methods already shown for the main rafter mav be used. The proportional figures to be used on the square for the 4 inches will be 4 on blade and 2\ on tongue; and if the second method is used, make the addition to the length of rafter for 10 feet, by drawing a line 4 inches square from the tongue of square No. 1 (see Fig. 16), instead of 6 inches as there shown for the main rafter. Hips. Three of the hips are shown in Fig. 14 to extend from the plate to the ridge-pole; they are marked in the figure as 1, 2, and 3 respectively, and are shown in |)lan to be diagonals of a square- measuring 13 feet 6 inches by 13 feet 6 inches; they make an angle, therefore, of 45 degrees with the plate. 353 ) 14 THE STEEL SQUARE In Fig. 18 it has been shown that a hip standing at an angle of 45 degrees with the plate will have a run of 17 inches for every foot run of the common rafter. Therefore, to lay out the hips, the figures on the square will be 17 for run and 9 for rise; and by stepping 13 times along the hip rafter timber, the length of hip for 13 feet of run is obtained. The length for the additional 6 inches in the run may be found by squaring a distance of 82- inches, as shown in Fig. 17, from the tongue of the square, and moving square No. 1 along the edge of the timber, holding the blade on 17 and tongue on 9, and marking the plumb cut where the dotted line is shown. In Fig. 18 is shown how to find the relative run length of a portion of a hip to correspond to that of a frac- tional part of a foot in the length of the common rafter. From 12 inches, measure along the run of the common rafter G inches, and drop a line to cut the diagonal line From m to a, along the diagonal line, will be the relative run 12 ^ / cu /V2' f Oj / e 6 a. Fig 19. Dinsvain Sliowint? Rclntive Leiij^tlis of K)in for Hips jiud Common Riifters in Kqual- • Pilch Roofs. m m. length of the part of hip to correspond with 6 inches run of the common rafter, and it measures 8 V inches. The same results may be obtained by the following method of figuring: As 12 :17 G G 12)102 8 G = 8^- In Fig. 19 is shown a 12-inch square, the diagonal vi being 17 inches. By drawing lines from the base a b to cut the diagonal line, the part of the hip to corre- spond to that of the common rafter will be indicated on the line 17. In this figure it is shown that a G-inch run on a h, which represents the run of a foot of a common rafter, will have a corresponding length of 80 £1 -^ FIr. 20. Mftliod of Determining Run of Viilley for Ailclitioniil Run in ("oi union Rafter. 354 THE STEEL SQUARE 15 inches run on the Hne 17, which represents the plan hne of the hip or valley in all equal-pitch roofs. In the front gable, Fig. 14, it is shown that the run of the common rafter is 10 feet 4 inches. To find the length of the common rafter, Fig. 21. Corner of S(iuare Building, Show- ing Plan Lines of Plates and Hip. Fig. 22. Corner of Square Building, Show- ing Plan Lines of Plates and Valley. take 12 on blade and 9 on tongue, and step 10 times along the rafter timber; and for the fractional part of a foot (4 inches), proceed as was shown in Fig. 16 for the rafter of the main roof; but in this case measure out square to the tongue of square No. 1, 4 inches instead of 6 inches. The additional length for the fractional 4 inches run can also be found by taking 4 inches on blade and 3 inches on tongue of square, and stepping one time; this, in addition to the length obtained by Heel cut of Valley Fig. 23. Use of Square to Determine Heel Cut of Valley. stepping 10 times along the rafter timber with 12 on blade and 9 on tongue, will give the full length of the rafter for a run of 10 feet 4 inches. In the intersection of this roof with the main roof, there are shown to be two valleys of different lengths. The long one extends from the plate at n (Fig. 14) to the ridge of the main roof at m; it has therefore 355 X 16 THE STEEL SQUAl^E a run of 13 feet G inches. For the length, proceed as for the hips, by taking 17 on blade of the square and 9 on tongue, and stepping 13 times for the length of the 13 feet; and for the fractional C inches, proceed precisely as shown in Fig. 17 for the hip, by squaring out from the tongue of square No. 1, 8-> inches; this, in addition to the length obtained for the 13 feet, will give the full length of the long valley n m. The length of the short valley a c, as shown, extends over the run of 10 feet 4 inches, and butts against the side of the long valley at c. By taking 1 7 on blade and 9 on tongue, and stepping along the rafter timber 10 times, the length for the 10 feet is found; and for the 4 inches, measure 5| inches square from the tongue of square No. 1, in the manner shown in Fig. 17, where the 8A inches is - /Bevel to fit hips "•^a.ga.in3t a deep Fig. 34. Steel Square Applied to Finding Bevel for Fitting Top of Hip or Valley to Kidge. roofer Tidc^eboard^hown added for the 6 inches addi- tional run of the •main roof for the hips. The length 5§ is found as shown in Fig. 20, by meas- uring 4 inches from a to m along the run of common rafter for one foot. Upon //i erect a line to cut the seat of the valley at c; from c to a will be the run of the valley to correspond with 4 inches run of the common rafter, and it will measure 5| inches. How to Treat the Heel Cut of Hips and Valleys. Having found the lengths of the hips and valleys to correspond to the common rafters, it will be necessary to find also the thickness of each above the plate to correspond to the thickness the common rafter will be above the plate. In Fig. 21 is shown a corner of a square building, showing the plates and the plan lines of a hip. The length of the hip, as already found, will cover the span from the ridge to the corner 2; but the sides 356 THE STEEL SQUARE 17 of the hip intersect the plates at 3 and 3 respectively; therefore the distance from 2 to 1, as shown in this diagram, is measured backwards from a to 1 in the manner shown in Fig. 17; then a plumb line is drawn through 1 to m, parallel to the plumb cut a-17. From m to o on this line, measure the same thickness as that of the common rafter; and through o draw the heel cut to a as shown. In like manner the thickness of the valley above the plate is fountl ; but as the valley a.s shown in the plan figure, Fig. 22, projects bevond point 2 before it intersects the outside of the plates, the distance from 2 to 1 in the case of the valley will have to be measured outwards from 2, as shown from 2tol in Fig. 23; and at the point thus found the thickness of the valley is to be measured to cor- respond with that of the com- mon rafter as shown at m n. In Fig. 24 is shown the steel square applied to a hip or valley timber to cut the bevel that will Bevel to fit bacK ' -I of jacks against hip or valley Fig. 25. Steel Square Applied to Jack Rafter to Find Bevel for Fitting against Side of Hip or Valley. fit the top end against the ridge. The figures on the square are 17 and 19j. The 17 represents the length of the plan line of the hip or valley for a foot of run, which, as was shown in previous figures, will always be 17 inches in roofs of equal pitch, where the plan lines stand at 45 degrees to the plates and square to each other. The 19j taken on the blade represents the actual length of a hip or valley that will span over a run of 17 inches. The bevel is marked along the blade. The cut across the back of the short valley to fit it against the side of the long valley, will be a square cut owing to the two plan lines being at right angles to each other. 357 r^ 18 THE STEEL SQUARE 8 In Fig. 25 is shown the steel square applied to a jack rafter to cut the back bevel, to fit it against the side of a hip or valley. The figures on the square are 12 on tongue and 15 on blade, the 12 repre- senting a foot run of a common rafter, and the 15 the length of a rafter that will span over a foot run; marking along the blade will give the bevel. The rule in every case to find the back bevel for jacks in roofs of equal pitch, is to take 12 on the tongue to represent the foot run, and the length of the rafter for a foot of run on the blade, marking along the blade in each case for the bevel. In a ^-pitch roof, which is the most common in all parts of the country, the length of rafter for a foot of run will be 1 7 inches ; hence '^ . . ^"f °^ .^'^I^®'' Fig. 26. Finding Length to Shorten it will be well to remember that 12 Rafters fm-^ Jacks per Foot on tongue and 17 on blade, marking along the blade, will give the bevel to fit a jack against a hip or a valley in a ^Vpitch roof. In a roof having a rise of 9 inches to the foot of run, such as the one under consideration , the length of rafter for one foot of run will be 15 inches. The square as shown in Fig. 25, with 12 on tongue and 15 on blade, will give the bevel by marking along the blade. To find the length of a rafter for a foot of run for any other pitch, place the two-foot rule diagonally from 12 on the blade of the square to the figure on tongue representing the rise of the roof to the foot of run ; the rule will give the length of the rafter that will span over one foot of run. The length of rafter for a foot of run will also determine the difi"erence in lengths of jacks. For example, if a roof rises 12 inches to one foot of run, Fig. 27. Finding Length of Jack . »^ ... , , <• i Kafier in }4-Pitch Koof. tile ratter ovcr this span has been round to be 17 inches; this, therefore, is the number of inches each jack is shortened in one foot of run. If the rise of the roof is S inches to the foot of run, the length of the rafter is found for one foot of run, by placing the rule diagonally from 12 on 358 THE STEEL SQUARE 19 Fig. 28. Findiua; Length of Jack Rafter in ;"s-Pitcii Roof. tongue to 8 on blade, which gives 142- inches, as shown in P^ig. 2G. Tliis, therefore, will be the number of inches the jacks are to be shortened in a roof rising 8 inches to the foot of run. If the jacks are placed 24 inches from center to center, then multiply 14^^ by 2 = 29 inches. In Fig. 27 is shown how to find the length with the steel square. The square is placed on the jack timber rafter with the figures that have been used to cut the common rafter. In Fig. 27, 12 on blade and 12 on tongue were the figures used to cut the com- mon rafter, the roof being ^ pitch, ri.sing 12 inches to the foot of run. In the diagram it is shown how to find the length of a jack rafter if placed 16 inches from center to center. The method is to move the square as shown along the line of the blade until the blade measures 16 inches; the tongue then would be as shown from w to m, and the length of the jack would be from 12 on blade to m on tongue, on the edge of the jack rafter timber as shown. This latter method becomes convenient when the space between jacks h less than 18 inches; but if used when the space is more than nn Ridge Plate Fig. 29. Method of Determining Length of Jacks Between Hips and Valleys; also Bevels for Jacks, Hips, and Valleys. 18 inches it will become necessary to use two squares; otherwise the tongue as shown at m would not reach the edge of the timber. In Fig. 28 the same method is- shown for finding the length of a jack rafter for a roof rising 9 inches to the foot of run, with the jacks placed 18 inches center to center. The square in this diagram is shown placed on the jack rafter timber with 12 on blade and 9 on 359 20 THE STEEL SQUARE tongue; then it is moved forward along the Hne of the blade to w. The blade, when in this latter position, will measure 18 inches. The tongue will meet the edge of the timber at m, and the distance from w on tongue to 12 on blade will indicate the length of a jack, or, in other words, will show the length each jack is shortened when placed Miter Bevel for Boards Bevel to_ cut the Bo^rd Back B#vel for Jacks Fig. 30. Method of Finding Bevels for All Timbers in Roofs of Equal Pitch. IS inches between centers in a roof having a pitch of 9 inches to the foot of run. When jacks are placed between hips and valleys as shown at 1, 2, 3, 4, etc., in Fig. 14, a better method of treatment is shown in Fig. 29, where the slope of the roof is projected into the horizontal plane. The distance from the plate in this figure to the ridge m, equals the length of the common rafter for the main roof. On the plate ann is made equal to a n n in Fig. 14. By drawing a figure like this to a scale of one inch to one foot, the length of all the jacks can be measured 360 THE STEEL SQUARE 21 lide cut of hip ainst the ridqe board and also the lengths of the hip and the two valleys. It also gives the bevels for the jacks, as well as the bevel to fit the hip and valley against the ridge; but this last bevel must be applied to the hip and valley when backed. It has been shown before, that the figures to be used on the square for this bevel when the timber is left square on back as is the custom in construction, are the length of a foot run of a hip or val- ley, which is 17, on tongue, and the length of a hip or valley that will span over 17 inches run, on blade — the blade giving the bevel. Fig. 30 contains all the bevels or cuts that have been treated upon so far, and, if correctly understood, will enable any one to frame any roof of equal pitch. In this figure it is shown that 12 inches run and 9 inches rise will give bevels 1 and 2, which are the plumb and heel cuts of rafters of a roof rising 9 inches to the foot of run. By taking these figures, therefore, on the square, 9 inches on the tongue and 12 inches on the blade, marking along the tongue will give the plumb cut, and marking along the blade will give the heel cut. Bevels 3 and 4 are the plumb and heel cuts for the hip, and are shown to have the length of the seat of hip for one foot run, which is 17 inches. By taking 17 inches, therefore, on the blade, and 9 inches on the tongue, marking along the tongue for the plumb cut, and along Fig. 31. Method of Fiuding Bevel .5, Fig. 30, for Fitting Hip or Valley Against Ridge when not Backed. Face cut ot TOOf bo&rd BacK bevel for jacKs Miter cut for too* board Fig. 33. Method of Finding Back Bevel 6, Fig. 30, for Jack Rafter.s, and Bevel 7, for Roof- Board. Fiu Determining Miter Cut for Roof- Board. the blade for the heel cut, the plumb and heel cuts are found. Bevel 5, which is to fit the hip or valley against the ridge when not backed, is shown from o w, the length of the hip for one foot of run, which is 19| inches, and from o s, which always in roofs of equal pitch will be 17 inches and equal in length to the seat of a hip or valley for one foot of run. 361 90 THE STEEL SQUARE iffures Laying Out Timbers of One-half Gable of %-Pitch Roof. These figures, therefore, taken on the square, 19^ on the blade, and 17 on the tongue, will give the bevel by marking along the blade as shown in Fig. 31, where the square is shown applied to the hip timber with 19^ on blade and 17 on tongue, the blade showing the cut. Bevels 6 and 7 in Fig. 30 are shown formed of the length of the rafter for one foot of run, which is 15 inches, and the run of the rafter, which is 12 inches. These applied on the square, as shown in Fig. 32, to a jack rafter tim- ber; taking 15 on the blade and 1 2 on the tongue, marking along the blade will give the back bevel for the jack rafters, and marking along the tongue will give the face cut of roof -boards to fit along the hip or valley. It is shown in Fig. 30, also, that by taking the length of rafter 15 inches on blade, and rise of roof 9 inches on tongue, bevel 8 will give the miter cut for the roof-boards. In Fig. 33 the square is shown applied to a roof-board with 15 on blade, which is the length of the rafter to one foot of run, and with 9 on tongue, which is the rise of the roof to the foot run; marking along the tongue will give the miter for the boards. Other uses may be made of these figures, as shown in Fig. 34, which is one-half of a gable of a roof ris- ing 9 inches to the foot run. The squares at the bottom and the top will give the plumb and heel cuts of the common rafter. The same figures on the square applied to the studding, marking along the tongue for the cut, will give the bevel to fit the studding against the rafter; and by marking along the blade we obtain the cut for the boards that run across the gable. By taking 19^ on blade, which is Backing of Fig. .^5. Finding Backing of Hip in Uablo Roof. 2B2 THE STEEL SQUARE 23 the len^-.th of the hip for one foot of run, and taking on the tongue the rise of il.. '^oof to the foot of run, which is 9 inches, and applying these as shcv:n in Fig. 35, we obtain the backing of the hip by marking along the tongue of the two squares, as shown. It will be observed from what has been said, that in roofs of equal pitch the figure 12 on the blade, and whatever number of inches the roof rises to the foot run on the tongue, will give the plumb and heel cuts for the common rafter; and that by taking 17 on the blade instead of 12, find taking on the tongue the figure representing the . rise of the roof to the foot run, the plumb and heel cuts are found for the hips and valleys. By taldng the length of the common rafter for one foot of run on blade, and the run 12 on tongue, marking along the blade will give 6 6 Fig. 36. Laying Out Timbers of Koof with Two Unequal Pitches. the back bevel for the jack to fit the hip or valley, and marking along the tongue will give the bevel to cut the roof-boards to fit the line of hip or valley upon the roof. With this knowledge of what figures to use, and why they are used, it will be an easy matter for anyone to lay out all' rafters for equal-pitch roofs. In Fig. 36 is shown a plan of a roof with two unec(ual pitches. The main roof is shown to have a rise of 12 inches to the foot run. The front wing is shown to have a run of 6 feet and to rise 12 feet; it has thus a pitch of 24 inches to the foot run. Therefore 12 on blade cf the square and 12 on tongue will give the plumb and heel cuts for the main roof, and by stepping 12 times along the rafter timber the length of the rafter is found. The figures on the square to find the heel and- 363 24 THE STEEL SQUARE plumb cuts for the rafter in the front wing, will be 12 run and 24 rise, and by stepping times (the number of feet in the nm of the rafter), the length will be found over the run of 6 feet, and it will measure 13 feet G inches. If, in place of stepping along the timber, the diagonal of 12 and 24 is multiplied by 6, the number of feet in the run, the length may be found even to a greater exactitude. Many carpenters use this method of framing; and to those who have confidence in their ability to figure correctly, it is a saving of time, and, as before said will result in a more accurate measurement; but the better and more scientific method of framing is to wor to a scale of one inch, as has already been explained. According to that method, the diagonal of a foot of run, and the number of inches to the foot run the roof is rising, measured to a scale, will give the exact length. For example, the main roof in Fig. 30 is rising 12 inches to a foot of run. The diagonal of 12 and 12 is 17 inches, which, considered as a scale of one inch to a foot, will give I ' Fig. 37. Finding- Length of Rafter for Front Wing in Hoof Shown in Fig. 36. Fig. 3». Laying Out Timbers of Roof Shown in Fig. Sfi, hy Projecting Slope of Koof into Horizontal Plane. 17 feet, and this will be the exact length of the rafter for a roof rising 12 inches to the foot run and having a run of 12 feet. The length of the rafter for the front wing, which has a run of G feet and a rise of 12 feet, may be obtained by placing the rule as shown 364 THE STEEL SQUARE 25 Elevation in Fig. 37, from on blade to 12 on tongue, whieh will give a length of 13^ inches. If the scale be considered as one inch to a foot, this will equal 13 feet 6 inches, which will be the exact length of a common rafter rising 24 inches to the foot run and having a run of 6 feet. It will be observed that the plan lines of the valleys in this figure in respect to one another deviate from forming a right angle. In equal-pitch roofs the plan lines are always at right angles to each other, and therefore the diagonal of 12 and 12, which is 17 inches, will be the relative foot run of valleys and hips in equal-pitch roofs. In Fig. 3G is shown how to find the figures to use on the square for valleys and hips when deviating from the right angle. A line is drawn at a distance of 12 inches from the plate and parallel to it, cutting the valley in m as shown. The part of the valley from m to the plate will measure ISo inches, which is the figure that is to be used on t\\3 square to obtain the length and cuts of the valleys. It will be observed that this equals the length of the common rafter as found by the square and rule in Fig. 37. In that figure is shown 12 on tongue and 6 on blade. The 12 here represents the rise, and the 6 the run of the front roof. If the 12 be taken to represent the run of the main roof, and the 6 to represent the run of the front roof, then, the diagonal 132 will indi- cate the length of the seat of the valley for 12 feet of run, and there- fore for one foot it will be 13 \ inches. Now, by taking 13^ on the blade for rim, and 12 inches on the tongue for rise, and stepping along the valley rafter timber 12 times, the length of the valley will be found. The blade will give the heel cut, and the tongue the plumb cut. In Fig. 3S is shov/n the slope of the roof projected into the hori- zontal plane. By drawing a figure based on a scale of one inch to one Plan Fig. "9. Method of Pindin^'- Length and Cuts of Octagon Hips luiersei-t- iiig a Roof. S6B 26 THE STEEL SQUARE foot, all the timbers on the slope of the roof can be measured. Bevel 2, shown in this figure, is to fit the valleys against the ridge. By drawing a line from w scjnare to the seat of the valley to vi; making - -^ .Ridge in 5econ d Po^sition Fig. 40. Showing How Cornice Aflects Valley.s unci Plates in Roof with Uni qiial Pitches. w 2 equal in length to the length of the valley, as shown, and by con- necting 2 and m, the bevel at 2 is found, which will fit the valleys against the ridge, as shown at 3 and 3 in Fig. 36. In Fig. 39, is shown how^ to find the length and cuts of octagon hips intersecting a roof. In Fig. 36, half the plan of the octagon is shown to be inside of the plate; and the hips o, z, o intersect the slope of the roof. In Fig. 39, the lines below x y are the plan lines; and those above, the elevation. From z, o. * o, in the plan, draw lines to x y, as shown from o to m and from z to m; from m and 7>i,draw the ele- vation lines to the apex o", inter- secting the line of the roof in d" and c". From (/" and c", draw the lines d" v" and c" a" parallel io X y; from c" , drop ji line to in- tersect the plan line a o in c. Make a iv equal in length to a''o" of the elevation, and connect w c; measure from w to n the full height of the octagon as shown from xy The length from ic to c is that of Plate of Na.TTOw Roof Plate of Ma.i-n Roof Lvvl 3 Fig. 41. Showing Relative Position of Plates in Koof with Two Un- equal Pitches. to the apex o" ; and connect c n. 366 THE STEEL SQUARE 27 the two hips shown at o o in Fig. 30, both being equal hips intersect- ing the roof at an equal distance from the plate. The bevel atwis the top bevel, and the bevel at c will fit the roof. Again, drop a line irom d" to intersect the plan line az'md. Make a 2 equal to v" o" in the elevation, and connect 2 d. JNIeasure from 2 to 6 the full height of the tower as shown from x tj to the apex o" in the elevation, and connect dh. The length 2 d' represents the w'^^^l^^Y^^^^X length of the hip z shown in Fig. 36; the bevel at 2 is that of the top; and the bevel at^, the one that will fit the foot of the hip to the intersecting roof. AA hen a cornice of any con- siderable width runs aroimd a roof of this kind, it affects the plates and the angle of the val- leys as shown in Fig. 40. In this figure are shown the same valleys as in Fig. 36; but, owing to the width of the cornice, the foot of each has been moved the distance a h along the plate of the main roof. Why this is done is shown in the drawing to be caused by the necessity for the valleys to intersect the corners c c of the cornice. The plates are also affected as shown in Fig. 41, where the plate of the narrow roof is shown to be much higher than the plate of the main roof. The bevels shown at 3, Fig. 40, are to fit the valleys against the ridge. In Fig. 42 is shown a very simple method of finding the bevels for purlins in equal-pitch roofs. Draw the plan of the corner as shown, and a line from m to o; measure from o the length x ij, representino- the common rafter, to w; from lo draw a line to m; the bevel shown at 2 will fit the top face of the purlin. Again, from o, describe an arc to cut the seat of the valley, and continue same around to S; con- nect S m; the bevel at 3 will be the side bevel. Fitr. i2. Method of Finding Bevels for Pur- lins in Equal-Pitcli Roofs. 867 REVIEW QUESTIONS. PRACTICAL TgST QUESTIONS. In the foregoing sections of this Cj^clopedia numerous ilhistrative examples are Avorked out in detail in order to show the application of the various methods and principles. Accompanying these are examples for practice Avhich will aid the reader in faxing the principles in mind. In the following pages are given a large number of test questions and problems which afford a valu- able means of testing the reader's knowledge of the subjects treated. They will be found excellent prac- tice for those preparing for College, Civil Service, or Engineer's License. In some cases numerical answers are given as a further aid in this work. 369 REVIEW QUESTIONS ON THE SUBJECT OF C A R P E ]Sr.T R Y . PART I. 1. Give a rule for squaring a log to get the strongest pos- sible timber out of it. 2. What is the "three-four-five rule," and how is it used? 3. Describe (and illustrate by a sketch) a splice suitable for a piece subjected to a bending stress. 4. Why is a " ledger-board " not as good as a " girt " for supporting the ends of floor joists ? 5. What are partition caps and soles? Wliat takes the place of the sole when there is a partition directly beneath the one which is beino;' built? 6. Show by a sketch what is meant by "sizing down" a joist onto a girder or sill. 7. What is the method employed for supporting a corner which has no direct support beneath it? Make a sketch of the framing for such a corner. 8. From what two classes of trees is most building lumber obtained ? 9. Give a brief description of the following varieties of timber :. a. Cypress d. Spruce 6. Ash e. Pine c. Poplar /. Oak 10. Name, and show by sketch, five kinds of joints used in carpentry. 11. What must take place before a "fished" splice for tension can be pulled apart? 12. What is a " raised girt ? " a " dropped girt ? " 871 CAKPENTIIY 13. How are furring walls around chimney breasts con- structed ? 14. Explain one method of framing joists into girders. Girders into sills. Illustrate with sketch. 15. How are floors " bridged ? " Which is the best method? Why? 16. What is the manner of growth of the trees named in Question 9, and in what other way do trees grow ? 17. What qualities are required in a wood to be used for light framing ? 18. Wliat is "ground water," and wh}^ must it be taken into account in tlie laying out of a building? 19. Show by sketch how the corner of a wooden building may be framed so as to give a nailing for the lathing. 20. At the point where a partition meets an outside wall, what sliould be the arrangement of the studding? Wliy? 21. Explain the method of framing around an opening in the floor frame for a chimney or staircase. Give clear definitions of the following: oo a. Pith e. Heai'twood h. Annual King f. Sapwood c. Medullary Ray g. Cross-grained Timber d. Heartshake h. Cupshake and AVindshako 23. Wliat is the '' heel " of a steel square? the "blade?" the " tongue?" 24. What are " batter-boards ? " Make a sketch of one form of batter-board. 25. How is a "key" employed in a splice for tension? What determines the distance between keys if there are more than one in a single splice ? 26. What is the function of the braces in braced frames? Show by a sketch one method of bracing a frame. 27. What is meant by "crowning?" Why is it necessary? 28. Explain the effect of the shrinkage of framing timber, and explain how unequal settlement (^due to such shrinkage) may be prevented. 29. What is the best method of cutting planks from a log? Why? 372 REVIE^V QtJESTIOXS 0>- THE StrUJECT OF CARF E X T R Y . PART II. 1. Give full description of the various forms of roofs, with sketches. 2. Give a rule for obtaining the rise of the rafter in a roof, the span of which is known. 3. Describe the method emploved in framintT a aanibrel J. •• DP roof. 4. What is the "run of a rafter"? AVhat is the rise? What is meant by the pitch ? 5. AVhat important property is characteristic of all lines in a roof surface which are parallel to the ridge line ? Tell in a general way how this fact is made use of in laying out the valley line. 0. What are the two distances which determine the posi- tion of the steel square in laying out valley rafters ? 7. AVhp.t is the principle used in finding the slope of the hip rafter in an "ogee-' roof? 8. What is the usual size of rafters for ordinary frame dwellinops ? o 9. Describe a hip rafter. What relation does it bear to a parallel valley rafter in the same roof surface? 10. What is the method of framing adopted for the valley when a small gable intersects a large roof ? 11. Describe the different kinds of jack rafters. 12. What must be done to studs formino- the framework of an attic partition in order to make them fit the under side cf the roof framincr ? 13. In what does "backiuo;" consist ? D 373 CARPENTKY 14. Describe two methods of forming the eaves on frame buildings 15. Describe the framing of a mansard roof. 16. What is the purpose of the ridge-pole and how is it usually made. 17. Describe two different kinds of dormer windows. 18. How are openings made in a roof frame for dormer windoM's, skylights, etc.? 19. When are trussed partitions used ? Describe in a gen- eral way their construction. 20. Describe two methods of constructing an " inclined floor". 21. AVhat is the difference between a '.' king-post trussed beam" and a "queen-post trussed beam"? 22. Describe the construction of a '* flitch plate girder ". 28. What are the different kinds of rafters used in a roof frame ? Describe each. 24. Give a rule for determining the general proportions of a gambrel roof. Illustrate by a sketch. 25. How are rafters of long span strengthened? What are "dwarf walls"? What is a collar beam? Make sketches of same. 20. Describe the construction of a "notched" beam. A "keyed" beam. 27. Explain the difference between a "king-post truss" and a " queen -post truss ". 28. How is the curved form given to a bell-shaped or concave tower roof ? 29. Is the stress in the king-post of a common king-post truss tension or compression ? Of what material is it ordinarily made ? 30. Describe or show by a sketch a method of framing a domical roof with provision for a lantern at the top. 81. What is a "groined" ceiling? 82. How far may a balcony or gallery be allowed to project beyond the line of supporting columns without the introduction of a brace ? 83. What is the difference between the two connections shown in Fig. 202 i What does each depend upon for its strength? 374 REVIKTV QUESTIOiSrS O >• THE SUBJECT O !•'• STAIR -BUILDIXG 1. Define staircase and stairway. 2. What is meant by the rise and run of a stairway? How measured ? 3. Define tread and riser. 4. How do treads and risers compare as to number? Why? 5. What is a string or string-board'! Describe the various kinds of strings. G. How are treads and risers fitted together and fastened in housed strings? 7. Describe the construction and use of a pitch-hoard. S. How are the rehitive dimensions of treads and risers deter- mined? 0. Are all the risers in a flight of stairs cut of uniform height? 10. Describe the use of 'flyers, ivinders, and dancing steps. 11. How are balusters fastened on strings? 12. How are strings fastened to newel-posts? 13. Describe methods of constructing buUnose steps and risers for same. 14." AMiat is the difference between a quarter-space landing and a half -space landing'! 15. Define the terms: well-hole; drum; cylinder; kerfng; geometrical staincay; carriage timber; wreath; tangent; crown tangent; springing of a well-hole; ground-line; swan-neck; face- mould; nosing; return nosing; spandrel; cove-moulding. 10. Describe the use of the face-mould. 17. When the face-mould is applied, and material for the wreath cut from the plank, how is the wreath-piece given its final shape? 375 STAIR-BUILDTXG 18. What is the use of tangents in handraiHng? What do the bevels represent? 19. What is an oblique plane'? 20. Are all wreaths assumed to be resting on an oblique plane? 21. In referring to jjn oblique plane, what do you understand by the expressions inclined in one direction only and inclined in tivo directions'^ 22. What is meant when two wreath tangents are said to be equally inclined'^ What, when unequally inclined"? 23. When an oblique plane is incUned in one direction c)nly, how many bevels will be needed to twist the wreath? 24. When the plane inclines in two directions, how many bevels are required? 25. When the inclination is equal in two directions, how many bevels are needed? 26. W^hen the plane is unetiually inclined in two directions, how many bevels are needed? 27. How can a stairway be reinforced? 28. How shoidd a scroll bracket be terminated against the riser? 29. When a plane is equally inclined in two directions, hov/ are the bevel or bevels to be applied to twist the wreath resting upon it in its ascent around the well-hole? 30. What is the difference between the plan tangents, pitch-line of tangents, and tangents of the ]ace-mouhVi 31. Why is it necessary to determine with exactness the angle between the tangents on the face-mould ? 32. What is the width of the face-mould to be, when laid out on the minor axis? 33. How is the width of the mould at the ends determined? 34. How do you find the minor axis and major axis of the mould curves? 35. Show how to find the thickness of the plank that will be recjuired for the wreath. 30. When the plan tangents are at a right angle to each other, and the pitch is equal, how are the bevels to be applied, (1) in relation to each other; (2) in relation to the sides of the wreath? 378 RKVTK^V QUT^STTOXS \0 yi T II K fS IT n .T K O T tJ K E S T I ]M A T I N O . PARTI 1. (a) What will a walk of bluestone flagging 4 ft. wide and 19 ft. long cost, complete? (b) Give cost of limestone coping for an 18- inch wall on one side of the path. 2. (a) About how many square yards of surface will four pounds of paint cover in two coats? (b) How much will it cost to paint a brick wall 8 ft. high and 15 ft. long with three coats of paint? 3. (a) How many feet B. M. in a 4-in. x 10-in. stick 22 ft. long? (b) How much lumber will it take to stud up a wall 12 ft. long and 9 ft. high with two windows in it? 4. Give aii analysis of one cubic yard of concrete. 5. What percentage of the cost of a building should be allowed for heating by furnace? How much of this goes to the labor? C. What will a square of slating cost? 7. Analyze the cost of a square of flooring. 8. (a) What will be the cost of a plain copper roof for a store 30 ft. X 40 ft.? (b) What will be the cost of a tin roof? 9. How many cubic feet of wall will a thousand bricks lay? 10. Give an analysis of the cost of 100 square yards of 2-coat plastering. 11. What gpecial data besides plans and specifications are necessary to figure a job for a contract? 12. How many square feet will 1000 shingles lay at 5 in. to the weather? 13. What will be the a{)prox!mate cost of a house 20 ft. X 30 ft. with an 8 ft. cellar and a half-pitch gable roof, at 12 cents per cubic foot? 377 ESTIMATING 14. How large .a furnace pipe must be run to a room 15 ft. X 20 ft. and 10 ft. high, and what will be the size of register? 15. Give a rule for finding the number of studs in a front if set 16 in. on centers. If set 12 in. on centers. 10. AVhat will be the cost of an ordinary flight of stairs of 17 risers for a $3000 house? How much should be allowed for the cellar stairs of 14 risers? 17. How much studding can two men set in one day? How much boarding? Shingles? Diagonal boarding? 18. (a) How many square yards of 2-coat plastering can a mason and helper put on in one day? (b) What will it cost? 19. (a) What will the newel of an ordinary staircase cost? (b) How much will the balusters of first run cost at two to a tread if the run is 8 risers high? 20. (a) How many bricks will be required to build a wall 10 ft. high, 30 ft. long, and 1 ft. thick, (b) What will it cost in 1 to 3 lime mortar? 21. What will it cost to put on 1000 laths? 22. In making repairs a man required the services of a carpen- ter for 5 hours, a plumber and helper 2 days, and an electrician for a day and a half, Avhat was his bill for labor? 23. What will it cost to dig out a cellar 18 ft. X 30 ft.; 4 ft. below grade at one end and G ft. the other? 24. (a) At a base price of $2.45 per cwt. what will three cwt. of 6-penny box nails cost? (b) What will 1 cwt. of 4-penny slating nai'ls cost? 25. (a) What per cent of the cost of a house will usually go to the plumbing? (b) What portion of this will represent the labor? 2G. (a) What is the relative cost of marble as compared with limestone? (I)) Of sandstone as compared with lime^stone? 27. (a) What is the usual cost of moulded finish in white wood or cypress? (b) What will the casings for both sides of a door 3 ft X 7 ft. cost, using a 5-inch casing with corner blocks? 28. (a) About how many cubic feet will one square foot of direct steam radiation heat, in the first story of a dwelling? (b) Direct hot water radiation? 20. What will be the area of a pyramidal roof 20 ft. square at the base and 15 ft. on the rafter line?. 378 ^aaW JS^ .^< l-_ ■v,) .rfl' ^y ii^ it 1^ 3?' .^r