Class __Zr Book JIM. CoB'rigtitN"____lM CORsRIGHT DEPOSIT. Rn, SHEET- METAL WORK A MANUAL OF PRACTICAL SELF-INSTRUCTION IN THE ART OF PATTERN DRAFTING AND CONSTRUCTION WORK IN LIGHT- AND HEAVY-GAUGE METAL, INCLUDING SKYLIGHTS, ROOFING, CORNICE WORK, ETC. WILLIAM NEUBECKER INSTRUCTOK, SHEET-METAL DEPARTMENT NEW YORK TRADE SCHOOL ILLUSTRATED AMERICAN TECHNICAL SOCIETY CHICAGO 1919 COPYRIGHT, 1917, 1919. BY AMERICAN TECHNICAL SOCIETY COPYRIGHTED IN GREAT BRITAIN ALL RIGHTS RESERVED ^0-1^^^ JAN -2 1920 (^;u.Arii;i2 8.i. AVo I ci cr INTRODUCTION THE importance of sheet-metal work in modern manufactur- ing developments is vastly greater than those not actually in ■^ touch with the work would imagine. Its use in building sky- lights, roofs, and cornices are visible and obvious applications of the industry, but there are countless operations in pressed metal manufacturing where the principles discussed herein find their most important application, and it is to help those who are actually working in this field that this volume has been printed. The sheet-metal draftsman has a very different problem in many respects from that of the mechanical draftsman. The mechanical draftsman has to deal, in the main, with square or circular shapes, and he has perfectly definite plans or elevations to fashion from the specifications given. His surfaces also are flat, spherical, or cyUndrical and will be shaped by the various machines found in a well-equipped machine shop. f The sheet-metal draftsman, on the other hand, nmst have a deeper understanding of geometrical principles, of the areas of sur- faces, and many other matters not considered by the mechanical draftsman. He must be able, in addition to the simple drawing of the object, to make accurate developments of complex surfaces and do this so accurately that the sheet-metal form, made from his drawing, can be put together without waste and without ■distortion of the shape intended. ^ The author of this book has had years of practical experience in sheet-metal work of all classes as well as abundant oppor- tunity to apply his experience in teaching the subject. All the studies worked out are typical and the details are so clearly pre- sented as to make the volume valuable for the beginner as well as for the most experienced metal worker. CONTENTS PAGE Tools and methods of obtaining patterns 3 Material of construction 3 Shop tools 4 Intersections and developments 5 Parallel-line development 5 Development by triangulation 15 Approximate developments 22 Workshop problems 26 Sink drainer 26 Conical boss 28 Hip bath 30 Bathtub 32 Funnel 36 4 Strainer pail 36 Emerson ventilator 42 Elbows 44 Ship ventilator 57 Weights of cast and wrought iron >. . . . 62 Copper 62 Lead 62 Brass 62 Zinc 62 Weights of sheet copper and zinc 63, 64 Standard gauge for sheet iron and steel 65 Weight of flat rolled iron 66-71 Weights of square and round iron bars 72, 73 W^eights of angle and tee iron 74 Problems for Ught-gauge metal 75 Oblique piping 75 Rain-water cut-off 77 Transition piece in rectangular pipe 80 Curved rectangular chute 82 Hopper register box 85 Transition piece in circular pipe 86 Pipe offset connection 88 Three-way branch 90 Two-branch fork 94 Tapering flange 97 Cylinder intersecting furnace top 100 Coppersmith's problems 105 Sphere 105 Circular tank 107 Curved elbows. , 113 CONTENTS PAGE Workshop problems (continued) Brewing kettle 115 Problems for heavy metal 116 Boiler shells and stacks 117 Moulded cap for stack 117 Three-pieced elbow 122 Pipe interesections 124 Gusset sheet on locomotive 126 Scroll sign 128 Skylights 133 Skyhght bars 133 Reinforcing strips 133 Core-plate 134 Cap 134 Weight of glass 135 Tools 136 Shapes of bars and curbs 136, 137 Raising sash 139 Condensation gutters 140 Single-pitch and double-pitch skylights 141, 142 Ventilation 141 Hip monitor skylight 142 Photographer's skylight 142 Flat extension skyhght 142 Hipped skyhght without monitor 143 Skyhght of long span 143 Gearings 144 Development of patterns for hipped skylight 144 Rules for obtaining length of ventilator 156 Ridge 156 Hip 157 Jack 157 Roofing 158 Metal roofs 158 Tin 158 Copper 158 Galvanized iron 158 Building paper 158 Tables of quantities 160 Weights 161 Gauges 161 Metal 162 Slates : 162 Shingles 162 Hip coverings 162 Roofer's tool 163 Roof mensuration . 163 CONTENTS PAGE r.oofing (continued) Flat-seam roofing 167 Gutters 168 Flashings 169 Sheet lead 170 Soldering 172 Covering a conical tower 174 Standing-seam roofing 177 Corrugated iron roofing and siding 182 Measurements 184 Deflection under loads 184 Distances of supports 184 Laying corrugated roofing and siding 185-190 Cornice work 193 Members of a cornice or entablature 193 Cornice 194 Dentil and modillion courses 194 Bed and crown mould 194 ModiUion band and mould 194 Dentil band and mould 194 Panel mould 195 Stop blocks 195 Raking mouldings 196 Miter 196 Drawings and tracings 197 Methods of obtaining patterns 200 Shapes of mouldings 202 Problems in miter cutting 204 Six-pointed star 236 Eyebrow dormer 243 . Development of blanks for curved mouldings 249 Shop tools 250 Approximate blanks 250 Hand and machine hammering 258 Index 263 SHEETxMETAL WORK. PAET I. The sheet-metal worker of today who wishes to succeed must gnow far more than was necessary years ago. There are many good, practical sheet-metal workers in the trade who are handi- capped because they are unable to lay out the patterns that arise in their daily work. Notwithstanding the introduction of labor- saving machinery, the demand for good workmen has increased. While most sheet-metal workers acquire practical knowledge in the shop, they lack the technical education necessary to enable them to become proficient as pattern cutt€>rs and draftsmen. In this course, special attention is given to the fundamental principles tJiat underlie the art and science of pattern drafting. Practical workshop problems will be presented, such as arise in everyday practice, thus giving the student the practical experience that usually comes only after long association with the trade. CONSTRUCTION. In constructing the various articles made from sheet metal, various gauges or thicknesses of metal are used. For all gauges from No. 20 to No. 30 inclusive, we assume in the development of the pattern, that we are dealing with no thickness, and we make no allowance for bending or rolling in the machine. But where the metal is of heavier gauge than No. 20, allowance must be made for shrinkage of the metal in the bending and rolling operations, which will be explained in connection with development in heavy sheet-metal work. Certain instructions for wiring, seaming, and transferring patterns are not given here as they more properly belong to tinsmithing work. It is sometimes the case that the capacity of a vessel or article must be determined, when the rules given in Mensuration should be followed. When figuring on sheet-metal work, the specifications sometimes call for various metals, such as galvanized sheet iron or steel, planished iron, heavy boiler plate, 4 SHEET-METAL WORK band iron, square or round rods for bracing, etc., zinc, copper, or brass; and the weight of the metal must often be calculated together with that of stiffening rods, braces, etc. On this account it is necessary to have tables which can be consulted for the various weights. TABLES. There is a wide difference between gauges in use, which is very annoying to those who use sheet metal rolled by different firms according to the various gauges adopted. It would be well to do away with gauge numbers, and use the micrometer caliper shown in Fig. 1, which determines the thickness of the metal by the decimal or fractional parts of an inch. Pig.L This is the most satisfactory method for the average mechanic who works sheet metal manufactured by firms using different gauges. The tables on pages 61 to 74 can be consulted whan occasion arises. SHOP TOOLS. In allowing edges for seaming and wiring, we must bear in mind that when a seam is to be grooved by hand or machine the allowance to be made to the pattern should conform to the rolls in the machine or the hand tools in use. The edges of the pattern are usually bent on the sheet-iron folder, or brake, while the seam oan be seamed or grooved with the hand groover or giant grooving machine. Where round pipe work is done in lengths up to 3 feet, the slip roll former is used, while square or rectangular pipes are bent up on the brake in 8-foot lengths. Where pipes, elbows, SHEET-METAL WOKK 5 stove bodies, furnace shells, metal drums, etc., are made, the sheets are cut square on the large squaring shears, rolled, grooved, and stiffened, by beading both ends in the beading machine, using ogee rolls. There is also a special machine for seaming the cross seams in furnace pipes, also a set of machines for the manufacture of elbows used in sheet-metal work. As before mentioned, if these machines are at hand, it will be well to make slight modifications in the patterns so that both the machines and iDatterns may work to advantage. PATTERNS OBTAINED BY VARIOUS METHODS. In this course will be explained the four methods used in developing patterns for sheet-metal work, namely, parallel line, radial line, triangulation, and approximate developments. Further- more, practical problems illustrating these methods will be carefully worked out in every detail. INTERSECTIONS AND DEVELOPMENTS. The following problems on parallel line developments have been selected because they have a particular bearing on pipe work arising in the sheet-metal trade. All of the problems that will follow should be carefully studied, drawn on cheap paper, and proven by cardboard models. These models will at once show any error in the patterns which might otherwise be overlooked. As only the Examination Plates are to be sent to the School, the student should draw all the other plates given in this course. The first problem to be drawn is shown in Fig. 2, being the intersection between a cylinder and octagonal prism. In drawing these problems for practice, make the cylinder and octagonal prism both 2 inches in diameter. The height of the cylinder from B to E should be 4^ inches ; and the length of the prism from G to H, 3 inches. Let A represent the plan of the cylinder, shown in elevation by B D E ; and F, the section of the prism, shown in plan by G H I J. Number the comers of the section F as shown, from 1 to 4 on both sides ; and from these points draw horizontal lines intersecting the plan of the cylinder at 2 '3' and 1'4' on both sides as shown. Establish a convenient intermediate point of intersection between the corners of the prism, as a and a in A, from SHEET-METAL WORK which draw horizontal lines intersecting the section F at a' , a' ^ a' ^ and a ' . Take a tracing of the section F with its various inter- sections, and place it in its proper position as shown by F\ in the ELEVATION 4 3o' 4 center of the cylinder B C D E, allowing the section to make a quarter turn, and bringing the points h' h' at the top and bottom on a vertical line, while in the section F, 5' h' are on a horizontal SHEET-METAL WORK 7 line. From the various intersections in F\ draw horizontal lines intersecting vertical lines drawn from similarly nmnbered inter- sections in the plan A, as shown in elevation. A line drawn through these points will represent the joint between the cylinder and prism. For the development for the prism, extend the line H I in plan as N K, upon which place the stretchout of all the points contained in the section F, as shown by similar figures and letters on N K. Through these points, at right angles to N K, draw lines which intersect with lines drawn from similarly numbered points and letters in plan, at right angles to J I. Trace a line through points thus obtained, and K L M N will be the desired pattern. To obtain the development for the opening in the cylinder, extend the line D E in elevation as S 0, upon which place the stretchout of all the points contained in the half -circle A, as shown by similar numbers and letters on S O. At right angles to S O and through these points, draw lines intersecting horizontal lines drawn from inter- sections having similar numbers and letters in elevation, thus obtaining the intersections shown by T U V W, which will be the shape of the opening to be cut into one-half of the cylinder. In Fig. 3 is shown the intersection between a hexagonal and quadrangular prism, the hexagonal prism being placed in elevation at an angle of 45° to the base line. When drawing this problem for practice, make the height of the quadrangular prism 4J inches, and each of its sides 2 inches. Place the hexagonal prism at an angle of 45° to the base line, placing it in the center of the quadrangular prism in elevation as shown; and inscribe the hex- agonal section in a circle whose diameter is 2^ inches. Let A represent the plan of the quadrangular prism placed diagonally as shown, above which draw the elevation BODE. In its proper position and proper angle, draw the outline of the hexagonal prism as shown by 1^ 1" 4" 4^; and on 1" 4" draw the half section as shown by F, numbering the comers 1" 2" 3" and 4". From the corner 1 ' in the plan A, draw the center line 1 ' 4. Take a tracing of the half section F, and place it as shown by F^, placing the points 1" 4'^ in F on the center line in F^ as shown. From the comers 1, 2, 3, and 4, draw lines parallel to the center line, intersect- ing the two sides of A (h V and V a)a.i 2' 3^ and 1 ' 4', as shown. From SHEET-METAL WORK these iDterBections draw vertical lines, which intersect by linee drawn parallel to 4* 4^ from comers having similar numbers in B, thus obtaining the points of intersection 1^ 2^ 3' and 4^ Dropping vertical lines from the intersections on the plane 1" 4" in elevatiotk, and intersecting similarly numbered lines in r)lan, will give the horizontal section of 1' 4*, aa shown by 1** 2° 3' and 4*^. '-^1 X r- \vOli F ^i3" /» It Por the development of the hexagonal prism, extend the line i' 1* as shown by H J, upon which place the stretchout of twice the number of spaces contained in the half section F, as shown by similar figui-es on the stretchout line H J. Prom these points, at right angles to H J, draw lines as shown, which intersect by lines drawn at right angles to the line of the prism from intersections l"* to 4^, thus obtaininpr the points of intersection 1^ to 4^. Lines SHEET-METAL WORK \) traced from point to point as shown by J K L H, will be the required development. The shape of the opening to be cut into the quadrangular prism, is obtained by extending the line D E ija elevation as N O, upon which place the stretchout of one-half the section A, with the various points of intersection, as shown by similar figures on O N. At right angles to O N erect lines from these points, which intersect by lines drawn from similarly numbered intersections in elevation at right angles to the quad- rangular prism, thus obtaining the points of intersection 1'" to 4"' on both sides. Then NOPE, will be the half development. Fig. 4 shows the intersection between two cylinders of equal diameters at right angles. Make the height of the vertical cylinder 3 inches, that of the horizontal cylinder IJ inches, and the diameters of both 2 inches. Let A represent the plan of the vertical cylinder, and B its elevation. Draw the plan of the horizontal cylinder C, shown in elevation by D placed in the center of the vertical cylinder. Draw the half section E in plan and divide it into equal parts, as shown from 1 to 3 to 1. In a similar manner draw the half section E' in elevation, which also divide into the same number of spaces as E, reversing the numbers as shown. The following suggestions are given to avoid confusion in numbering the points or comers of irregular or round sections in plan and elevation. If the half section E were bent on the line 1-1 and turned upward toward the reader, and we should view this section from the front, the point 3 would be at the top, or, if bent downward, would be at the bottom; therefore the points 3 and 3 in elevation are placed at top and bottom. Now if the section E^ in elevation were bent on the line 3-3 either toward or away from the reader, the point 1 when looking down would show on both sides as shown in plan, which proves both operations. No matter whether the form is simple, as here shown, or complicated as that which will follow, the student should use his imaginative power. Study the problem well; close your eyes and imagine you see the finished article before you, or, failing in this, make a rough model in the shop or a cardboard model at home, which will be of service. Now from the intersections in E, draw horizontal lines intersecting the circle A at 1', 2' and 3' on both sides. From these points erect perpendicular lines and intersect them with horizontal lines drawn 10 SHEET-METAL WORK Fig. 4. HJTKI^yr-METAL WORK 11 from similarly numbered intersections in E^. Lines traced through these points 3" 2" 1" and 1" 2" 3" will be straight because both branches are of equal diameters. For the development of the cylinder D in elevation, extend the line 3-3 as shown by F G, upon which place the stretchout of twice the number of spaces contained in E^, as shown by similar numbers 3° to 1° to 3° to 1° to 3° on the stretchout line F G. From these points, at right angles to G F, draw lines, and intersect them by lines drawn parallel to the cylinder B from similar numbers in the joint line. Trace a line through these points in the development, when F G H I will be the desired shape. For the opening to be cut into the cylinder B to receive the cylinder D, extend the base of the cylinder B as shown by 1^ 1% upon which place the stretchout of the half circle A in plan, as shown by similar figures on the stretchout line 1^ 1^. From these points erect perpendiculars, which intersect by lines drawn from similarly numbered intersections in elevation at right angles to the line of the cylinder B. Trace a line through the intersections thus obtained; J K L M will be the shape of the opening. Fig. 5 shows the intersection of two cylinders of unequal diameters at an angle of 45°. Make the diameters of the large and small cylinders 2 inches and 1^ inches respectively; the height of the large cylinder 3 inches ; and the length of the small cylinder measured from its shortest side in elevation, 1 inch, placed at an angle of 45° in the center of the cylinder B. A represents the plan of the large cylinder struck from the center a and shown in elevation by B. Draw the outline of the small cylinder C at its proper angle, and place the half section D in its position as shown; divide it into a number of equal spaces, as shown from points 1 to 5. Through the center a in plan, draw the horizontal line a 5 ; and with & as a center describe a duplicate of the half section D with the various points of intersection, as shown by D^, placing the points 1 and 5 on the horizontal line a 5. From the intersections in D^ draw horizontal lines intersecting the large circle A at 3 ' to 3 ' as shown, from which points erect perpendicidar lines ; intersect them by lines drawn parallel to the lines of the smaller pipe from similarly numbered intersections in D. A line 12 SHEET-METAL WORK traced through the points thus obtained will represent the inter- section or miter joint between the two pipes. These same principles are applicable no matter what diameters the pipes have, or at what angle they are joined, or whether th*» Fig.a pipe is placed as shown in plan or at one side of the center line. For the development of the small cylinder extend She line 5-1 in elevation as shown by F E, upon which place the stretchout SHEET-METAL WORK 13 of the circle D^ in plan, or twice the amount of D in elevation, as shown by similar figures on the stretchout line F E. At right angles to F E and through these small figures, draw lines which intersect with lines drawn at right angles to the lines of the small cylinder from similarly numbered intersections in the miter line in elevation. Trace a line through the points thus obtained; E F Gr will be the development for the cylinder C. To obtain the opening in the large cylinder extend the lines of the large cylinder in elevation as shown at the base by H J, upon which place the stretchout of the intersections contained in the circle A, being careful to transfer each space separately (as they are unequal) to the stretchout line H J. Through these points and at right angles to H J erect lines which intersect with horizontal lines drawn from similar points in the miter line in elevation A line traced through the points thus obtained, as shown by K L M N, will be the desired development. Fig. 6 shows the intersection between a quadrangular prism and sphere, the center of the prism to come directly over the center of the sphere. Make the diameter of the sphere 2^ inches, the sides of the prism IJ inches, and the height from / to c' 2§ inches. Draw the elevation of the sphere A which is struck from the center a, from which erect the perpendicular a h. With any point, as c, as a center and using the same radius as that used for A, describe the plan B. Through c draw the two diagonals at an angle of 45°, and draw the plan of the prism according to the measurements given. Now draw the elevation of the prism/* c' and/' . In a similar manner, from the intersection in elevation draw a horizontal line intersecting the center line x y a.t d. Then using y as center and y das radius, describe an arc intersecting the sides of the prism at e and/! E Fjfe will show the development for either side of the prism shown in plan by D A and A B. By connecting the points G and f }t will be found that the line is a true horizontal line, which proves Fig. 7. ELBOW PATTERNS* In all elbow work the difficulty lies in obtaining the correct rise of the miter line. By the use of a protractor this is overcome and thus the necessity of drawing a complete quadrant is avoided. Following the rule given in the illustration the rise can be easily found, when the throat and diameter of the pipe is known. In the upper table are shown various pieced elbows, having different degrees when finished, and the various miter lines. There are six miter pat- terns shown, the first for a 6-pieced elbow having 90° when completed; the second for a 4-pieced 90° elbow; the third for a 3-pieced 90° elbow; the fourth for a 2-pieced 70° elbow; the fifth for a 2-pieced 90° elbow, and the sixth for qi 2-pieced lOS*^ elbow. No matter what size of throat the elbow may have, or what diameter or number of pieces, always follow the rule given in the illustration and obtain the miter line ; then place the half profile in its proper position and place the full girth of the pipe on the line shown in the pattern by similar numbers. By reversing the cut opposite the line 1-7-1 the pattern for the middle pieces is obtained, after which one cut can be placed into the other as shown on Page 48 . * The illustration referred to will be found on the back of this page. SHEET-METAL WORK 15 the two developments. Should the plan of the prism be so placed on the sphere that all sides would be different, then two elevations would be necessary so that the intersections of all the sides could be shown. Developments by Triangulation. In developing sheet-metal work of irregular forms, patterns are required which cannot be developed by either the parallel or radial-line methods. These irregular shapes are so formed that although straight lines can be drawn upon them the lines would not run parallel to one another, nor would they all incline to a common center. In the methods previously described, the lines in parallel developments run parallel to one another, while in radial-line developments all the lines meet at a common center. Hence in the d,evelopment of any irregular article, it becomes necessary to drop all previous methods, and simply proceed to measure up the surface of the irregular form, part by part, and then add one to another until the entire surface is developed. To accomplish this, we have merely to make use of one of the simplest of all geometrical problems, namely, to construct a triangle having given the three sides. This problem is solved very early in Mechanical Drawing. To carry out this method it is necessary only to divide the surface of the plan or elevation of any irregular article into a number of equal parts. Use the distances in plan as the bases of the triangles, and the distances in elevation as the altitudes or heights of the triangles, or vice versa; and then find the hypothenuse by connecting the two given lengths. To illustrate this simple principle Fig. 8 has been prepared. Let A B O D represent the plan of a plane surface, shown in elevation by A^ B^. We know that the true length of the plane is equal to A^ B^ and the true width is equal to A D or B in plan. We also know that the vertical height from the bottom of the plane A^ to the top B' is equal to B' h as shown. But suppose we want to obtain the true length of the diagonal line B D in plan on the developed plane. To obtain this it will be necessary only to take the length of B D, place it from h to D\ and draw a line as shown from B^ to D^, which is the length desired. While this may look very simple, it is all that there is to triangulation, and if the student thoroughly understands the simple principle and studies the problems which will follow, he will have 16 SHEET-METAL WORK no trouble in applying this principle in complicated work. To make it still clearer we will prove the length of the line B' D^. Take the distance of A^ B^, place it in plan as shown by A B^, and complete the rectangle A B^ C^ D. Draw the diagonal B^ D, being the length sought, which will be found to equal B^ D^ in elevation. When drawing this problem in practice, make the plan 4 by 6 inches and the vertical height in elevation 5 inches. In obtaining developments by triangulation. the student should !ise all of his conceptive powers as previously explained. Before ^B* making any drawing, he must ^^^ I see the article before him in his y.^/^ mind's eye, so to speak, before ^^^/^ I he can put it down on paper. rt^C 1 to 2^ in plan and place it on the line 3-2 extended in elevation, as shown from 2 to 1°, and draw a line from 1° to 2\ which is the desired length. For the pattern, proceed as is shown in Fig. 10. Take the distance of any one of the sides in the triangle, as 1-2 in Fig. 9, and place it on the horizontal line a^ elevation 2 * 1-2 in Fig. 10. Then using 1 and 2 as centers, with 1° 2^ in elevation in Fig. 9 as radius, describe the arcs in Fig. 10 intersecting each other in 2\ Then 1 2 2^ will be the pattern for one of the sides shown in plan in Fig. 9 by 1 2 2^. Proceed in this manner in Fig. 10 as shown by the small arcs; or a tracing may be taken of the one side 1 2 2^5 and traced as shown until six sides are obtained, which will be the full pattern and which is numbered to correspond to the numbers in plan. In Figs. 11, 12, and 13 are shown the methods used in develop ing a scalene cone. The method of obtaining the development of any scalene cone, even though its base is a perfect circle, is g vemed by the same principle as employed in the last problem on triangu- Fig. 9. Fig. m lation It is well to remember that any section of a scalene cone drawn parallel to its base will have the same shape (differing of course in size) as the base. This is equally true of articles whose 18 SHEET-METAL WORK bases are in the shape of a sqiiare, rectangle, hexagon, octagon, or any other polygon. What has just been explained will be proven in connection with Fig. 11, in which ABC represents a side elevation of a scalene cone, whose plan is shown by 1 4^ 7 4 O^. Draw any horizontal line, as A D, on which set off the distances '^: o r »l^\^s (0 HI _l o ^E ^ G in plan at N. Then with G as center strike the quarter circle N O. Now using M as center and M J as radius, strike the arc J P. Then on this arc, starting from J, lay off 4 times the stretchout of N O in plan for the full pattern. It should be understood that when stretching the cove A E, the point J remains stationary and the metal from J to L and from J to K is hammered respectively toward J A and J E. For this reason is the stretchout obtained from the point J. PRACTICAL WORKSHOP PROBLEMS. In presenting the 32 problems which follow on sheet-metal work, practical problems have been selected such as would arise in every-day shop practice. In this connection we wisK to im- press upon the student the necessity of working out each and every one of the 32 problems. Models should be made from stiff cardboard, or, if agreeable to the proprietor of the shop, the patterns can be developed at home, then cut out of scrap metal in the shop during lunch hour, and proven in this way. Our first problem is shown in Fig. 19, and is known as a sink drainer. It is often the case that the trap under the kitchen sink Fig. 19, SHEET-METAL WOKK 27 is choked or blocked, owing to a collection of refuse matter. To avoid this a sink drainer is used, and is fastened in position through the wire loops a, b and c* The refuse matter is poured into the drainer, from which it is easily removed after the fluid has passed through the perforations. These drainers may be made of tin or of black or galvanized iron, but where a good job is wanted 16 -ounce C5opper should be used. To obtain the pattern for any sized drainer, proceed as follows: First draw the plan of the drauier A B O in Fig. 20, making A B and B C each two inches and forming a right angle. Then using B as center and A B as radius, draw the arc A C. In its proper posi- tion above the plan construct the side elevation, making E D 2 inches high, and draw the line F D. Then will F E D be the side elevation. Divide the arc A into equal spaces as shown by the small figures 1 to 5. For the pattern nse F D as radius, and with ^ D in Fig. 21 as center strike the arc 1 5. From 1 draw a line to D and step off on 1-5 the same number of spaces as contained in A C in plan in Fig. 20, as shown by similar figures in Fig. 21. Draw a line from 5 to D. Then will 1-5-D be the pattern for the front of the strainer, in which per- forations should be punched as shown. Fig. 20. To join the sides of this pattern, use 1 and 5 as centers, and with either F E or A B in Fig, 20 as radius, describe the arcs E and E^ in Fig. 21. Now using D as center and D E in Fig. 20 as radius, intersect the arcs E and E^ as shown in Fig. 21. Draw lines from 1 to E^ to D to E to 5, which completes the pattern, to which edges must be allowed for wiring at the top and seaming at the back. When joining a faucet or stop cock to a sheet-metal tank it is usual to strengthen the joint by means of a conical "boss," which J8 SHEET-METAL WORK IS indicated by A in Fig. 22. In this problem the cone method is employed, tising principles similar to those used in developing a frustum of a cone intersected by any line. Therefore in Fig. 23 let A B represent the part plan of the tank, portion of the faucet extending back to the tank line, and F G H I the conical "boss" to fit around a faucet. When drawing this problem make the radius of the tank D A equal to 3J inches, and from D draw the vertical line D E. Make the distance from G to H equal to 2| inches, the diameter of the faucet F I 1 J inches and the vertical height K C IJ inches Draw a line from G to H inter- secting the center line D E at K. Then using K as center describe the half section G J H as shown. Divide J H into equal parts shown from 1 to 4, from ^^* * which drop vertical lines intersecting the line G H as shown, from which draw radial lines to the apex E cutting the plan line SHEET-METAL WORK 2^ of the tank A B as shown. From these intersections draw hori. zontal lines intersecting the side of the cone H I at 1, 2', 3', and 4', ^ow use E as center, and with radius equal to E 1 describe the Fig. 23. aro 1**-1« as s^own. Draw a line from 1° to E, and starting from 1" set off on 1°-1^ four times the number of spaces contained in 60 SHEET-METAL WORK J H in plan, as shown by cimilar numbers on 1° 1^. Draw a line from 1^ to E, and with E I as radius describe the arc N L inter, secting the radial lines 1° E and 1^ E at N and L respectively. From the various numbers on the arc 1° l'^ draw radial lines to the apex E; and using E as center and with radii equal to E 4', E 3 ' , and E 2 ' , draw arcs intersecting similarly numbered radial lines as shown. Trace a line through points thus obtained; then will N 1° 1 1^ L be the pattern for the "boss." In Fig. 24 is shown what is known as a hip bath. In drawing out the problem for practice the student should remember that it is similar to the preceding one, the only difference being in the outline of the cone. Make the top of the cone I B in Fig. 25 equal to 3J inches, the bottom C D If inches, the vertical height from K to 5 ' 2J inches, the diameter of the foot E F 2J inches, and the vertical height 5'-5'' J-inch. Through the center of the cone draw the center line K L, and at pleasure draw the outline of the bath as shown by A J B. It is imma- terial of what outline this may be, the principles that follow being applicable to any case. Thus, in the side elevation, extend the lines B C and A D imtil they •intersect the center line at L. In Fig. 24. similar manner extend the sides of the foot piece E D and F until they intersect the center line at R. Now with 5' as center and with radius equal to 5' D or 5 ' C, describe the halt section C H D, which divide into equal spaces as shown by the small figures 1 to 9. From the points of division erect vertical lines meeting the base line of the bath D C at points 1, 2', 3', etc., to 9. From the apex L and through these points draw radial lines intersecting the outline B J A, from which horizontal lines are drawn intersecting the side of the bath B C as shown from 1 to 9. For the pattern for the body use L as center, and with L C as radius draw the arc F L^. Now starting at any point, as 1, set off on F L^ twice the stretchout of D H C as shown by similar numbers on the arc F L\ From tlie aj)ex L and through the small figures draw radial lines, which intersect by arcs 8HEET-METAL WORK 31 struck from L as center with radii equal to similarly numbered intersections on B C. Trace a line through points thus obtained, and L^ M N P F will be the pattern for the body of the bath. to which laps should be added at the bottom and sides for seaming. Pig. 25. The pattern for the foot is obtained by using as radii R D and R E. and striking the pattern using R^ as center, the half pattern being shown by E^ T E^ D^ T>\ and the distance D^ D^ being equal to the stretchout of the half section D H O in side elevation 82 SHEET-METAL WORK It is usual to put a bead along the edges of the top of a bath as shown at a and h in Fig. 24. For this purpose tubing is sometimes used, made of brass, zinc, or copper and bent to the required shape; or zino tubes may be rolled and soldered by hand, filled with heated white sand or hot rosin, and bent as needed. The tube or bead can be soldered to the body as shown in (A) in Fig. 25. Here a represents the bead, in which a slot' is cut as c, and which is then slipped over the edge of the bath and soldered. Another method is shown in (B), in which the bath body 5 is flanged over the bead a and soldered clean and smooth at c, being then scraped and sandpapered to make a smooth joint. A wired edge is shown at c in Fig. 24, for which laps must be allowed as shown in Fig. 25 on the haK pattern for foot. In Fig. 26 is shown the perspective view of a bath tub; these tubs are usually made from IX tin or No. 24 galvanized iron. The bottom and side seams are locked and thoroughly soldered, while the top edge is wired with handles riveted in position as shown at A. The method used in de- veloping these patterns will be the cone method and triangula- Fig. 26. "^^ tion. In drawing this problem for practice (Fig. 27), first draw the center line W 8 in plan ; and using a as center with a radius equal to \\ inches draw the semicircle C-12 D. Now make the distance aioh ^ inches; and using h as center with a radius of If inches draw the semicircle E-7-H. Draw lines from E to D and from C to H. D E 7 H 012 D will be the plan of the bottom of the bath. In this case we assume that the flare between the top and bottom of the narrow end of the bath should be equal; therefore using a as center and with a radius equal to 1| inches draw the semicircle A W B. At the upper end of the bath the flare will be unequal; therefore from 5 measure a distance on line W 8 of 1 inch and obtain c?, which use as center, and with a radius equal to 2 inches describe the arc F 8 G. Draw lines from F to A and from B to G; and A F 8 G B W A will be the plan of the top of the bath. Now project the side elevation from the plan as shown by the dotted lines, making the slant height from I to R 2J inches and from J to K 3 J inches ; draw a line SHEET-METAL WORK 33 from K to R, and J K R I will be the side elevation of the bath tub. In constrticting the bath in practice, seams are located at H G, F E, PATTERN \ \ \ \ \ \ \ \\ , FOR A-B-C-0 \^ \ \ V \ \ \ \1 ' IN PLAN \ \, \ \ \ \ \ \\ I \\\\\\\Vi a\\v\\\U ■'^xvy s' 7" Nd r»e^ Fig. 27. DIAGRAM OF TRIANGLI^ A D. a»d O B in plan, thus making the tub in four pieoM 84 SHEET-METAL WORK The lower end of the bath will be developed by the cone method as in the last two problems. From the center a droi? a line indefinitely as shown. Extend the side R I of the side elevation until it meets the center line a d ^i d. Now divide the quarter circle 12-9 in plan into equal spaces as shown by the small figures 9, 10, 11, and 12, from which drop vertical lines (not shown) intersecting the bottom of the bath tub in elevation from 9 ' to 12 ' . Then through these points from d draw lines intersecting the top line of the bath R K as shown, from which draw horizontal lines intersecting the side I-R extended as I X at points 9" to 12". Then using d as center and ^ I as radius, describe the arc I M, upon which place the stretchout of D 12 C in plan, as shown by similarly numbered points on L M. Through these points from d draw radial lines, which intersect by arcs drawn from similarly numbered intersections on I R extended, using d as center. Trace a line as shown, and L M N P will be the pattern for the lower end of the tab A B C D in plan. Laps should be alk wed for wiring and seaming. As the patterns for the upper end and sides will be developed by triangulation, diagrams of triangles must first be obtained, for which proceed as follows : Divide both of the quarter circles H 7 and G 8 in plan into the same number of spaces as shown respec- tively from 1 to 7 and from 2 to 8. Connect these numbers by dotted lines as shown from 1 to 2, 2 to 3, 3 to 4, etc. From the various points 2, 4, 6, and 8 representing the top of the bath, drop lines meeting the base line J/* in elevation at 2^^', 4^, 6^, and 8^, and cutting the top line of the bath at 2', 4', 6', and 8'. Then will the dotted lines in plan represent the bases of the triangles, which will be constructed, whose altitudes are equal to the various heights in elevation. Take the various distances 1 to 2, 2 to 3, 3 to 4, 4 to 5, etc., in plan up to 8, and place them on the vertical line l"-8" in (B) as shown from 1" to 2", 2" to 3", 3" to 4", 4" to 5", etc., up to 8". For example, to obtain the true length of the line 6-7 in plan, remembering that the points having even numbers represent the top line of the bath and those having uneven numbers the base line, draw at right angles to l"-8" in (B), from 6", a line equal in height to &M3' in elevation, and draw a line from C*" to 7" in (B), which is the length desired. For the true SHEET-METAL WORK 35 length of 6-5 in plan it is necessary only to take this distance place it from 6" to 5" in (B) and draw a line from 6^ to 5". In this way each altitude answers for two triangles. In plan draw a line from 1 to 0. Then will two more triangles be necessary, one on the line 1-0, and the other on B Gr or 0-2. From 2' in elevation draw a horizontal line, as 2' e^ intersecting the vertical line dropped from at 6. Now take the distances 1 and 2, and place them in (A) as shown by the horizontal lines 0"-l" and 0^2^ respectively. At right angles to both lines at either end draw the vertical lines 0"-0'" and 0-^0^ equal in height respectively to C^O' and eO' in elevation. Draw in (A) lines from 2^ to O^and from 1" to 0'", which are the desired lengths. Before proceeding with the pattern, a true section must be obtained on 2 '-8' in side elevation. Take the various distances 2' to 8' and place them on the line 2 '-8' in Fig. 28. At right angles to 2'-8' and through the small figures draw lines as shown. Now measuring in each and every instance from the center line in plan in Fig. 27, take the various distances to points 2, 4, and 2' 6 and place them on similarly num- Fig. 28. bered lines in Fig. 28, measuring in each case on either side of the line 2 '-8', thus obtaining the intersections 2-4-6. A line traced through these points will be the true section on 2 '-8' in elevation in Fig. 27. For the pattern for the upper end of the tub proceed as follows: Take the distance of 7 "-8^ in (B) and place it on the vertical line 7-8 in Fig. 29. Then using 8 as center and with a radius equal to 8 '-6 in Fig. 28, describe the arc 6 in Fig. 29, which intersect by an arc struck from 7 as center and with 7 "-6^ in (B) in Fig. 27 as radius. Then using 7-5 in plan as radius, and 7 in Fig. 29 as center, describe the arc 5, which intersect by an arc struck from 6 as center and with 6^-5" in (B) in Fig. 27 as radius. Proceed in this manner, using alternately as radii first the divisions in Fig. 28, then the length of the slant lines in (B) in Fig. 27, the divisions on 7 H in plan, then again the slant lines in B, until the line 1 -2 in Fig. 29 is obtained. Trace a line through points thus obtained, as shown by 2-8-7-1. Trace this opposite the line 8-7, as shown 86 SHEET-METAL WORK by 2' 1', Then will 2-8-2'-l'-7-l be the desired pattern, to which laps must be allowed. For the pattern for the side of the bath draw any line 9-^1 in Fig. 30 equal to 9-1 in plan in Fig. 27. Now with a radius equal Pig.29L to 9-P in the pattern X and with 9 in Fig. 80 as a center, desoribe the arc 0, which intersect by an arc struck from 1 as center and with l"-0'" in (A) in Fig. 27 as radius. Now taking a radius equal to 0^-2^ in (A) with in Fig. 80 as center, describe the arc 2, which iZ intersect by an arc n ~ — ■ ^ // struck from 1 as center, PATTERN FOR // ^nd with 1-2 in Fig. 29 as radius. Draw lines from comer to comer in Fig. 30, which gives the desired pattern, to ^^ which laps are added pig. 3a ' for seaming and wiring. In Fig. 81 is shown a perspective view of a funnel strainer paiL These pails are usually made from IX bright tin, and the same principles as are used in the development of the pattern are applicable to similar forms, such as buckets, coal hods, chutes, etc. This problem presents an interesting study in triangulation, the principles of which have been explained in previous problems. First draw the center line C I in Fig. 32, at right angles to whicb SHEET-METAL WORK 37 draw H E and H F each equal to 1^ inclies. Make the vertical height H 3 J inches and C D 2 inches. Now make the vertical heights measuring from C G, to A, and to P respectively ij inches, and IJ inches. Make the horizontal distance from C to G 2J inches, the diameter from G to A If inches, and from A to B f -inch, and draw a line from B to C. Con^ect points by lines ; then will ABCDEFGbe the side elevation of the pail. In its proper position below F E, with J as center, draw the plan K L M N. Also in its proper position draw the section on A G as O P R S. Now draw the rear elevation making G^ U and G^ V each equal to H E, and 1" T and 1"-!' each equal to C D. Project a line from B in side, intersecting the center line in rear at 4'. Then through the three points 1' 4' T draw the curve at pleasure, which in this case is struck from the center a* W Y X Z represents the opening on G A in side obtained as shown by the dotted lines but having no bearing on the patterns. Pails of this kind are usually made from two pieces, with seams at the sides, as in Fig. 81. The pattern then for the back shown by C D E H in side elevation in Fig. 32 will be obtained by the cone method, struck from the center I, the stretchout on E^ E^ in the pattern being obtained from the half plan. The pattern f or C D E H is shown with lap Fig. 31. and wire allowances by D^ D^ E^ E^ and needs no further explanation. The front part of the pail shown by A B C H F G will be developed by triangulation, but before this can be done a true section must be obtained on B C, and a set of sections developed as follows: Divide one-half of 1' 4' T in rear elevation into equal parts as shown from 1' to 4', from which draw horizontal lines intersecting the line B G as shown. From these intersections lines are drawn at right angles to B C equal in length to similarly numbered lines in rear as S'-S", 2'-2'', and l'~l". Trace a line as shown, so that C 1'" 2"' 3'" 4'" will be the true half section on B C. To avoid a confusion of lines take a tracing of A B C H F G 38 sheet-m]^:tal work and place it as shown by similar letters in Fig. 33. Now take tracings of the half sections in Fig. 32, as H E D C, C 1'" B, P O S, and the quarter plan N J M, and place them in Fig. 33 on similar lines on which they represent sections as shown respectively by H 9' 8' C, C 8 B, A 3 G, and F 9 H. Divide the half section CO j± ^51 r:r^:^^ A 3 G into 6 equal parts as shown by the small figures 1 to 5. As this half section is divided into 6 parts, then must each of the sections B 8 C and F 9 H be divided into 3 parts as shown respec- tively from 6 to 8 and 9 to 11. As C 8' and H 9' are equal respectively to C 8 and H 9 they are numbered the same as shown. SHEET-METAL WORK P>9 Now at right angles to G A, B C, C H, and H F, and from the various intersections contained in the sections G 3 A, B 8 C, 08' 9 ' H, and H 9 F, draw lines intersecting the base lines of the sections G A, B C, C H, and H F at points shown from 1/ to 11'. Now draw dotted lines from B to 5 ' to 6 ' to 4 ' to 7 ' to E to C, and then from H to E to 10' to 2', etc until all the points are "^^ Fig. 33. connected as shown. These dotted lines represent the bases of the sections whose altitudes are equal to similar numbers in the various sections. In order that the student may thoroughly understand this method of triangulation as well as similar methods that will follow 40 SHEET-METAL WORK in other problems, the model in Fig. 84 has been prepared, which shows a perspective of Fig. 33 with the sections bent up in their proper positions. This view is taken on the arrow line in Fig. 33, the letters and figures in both views being similar. For the true sections on the dotted lines in E A B in Fig. 33, take the lengths of the dotted lines C E, E 7', 7' 4', etc., and place them on the horizontal line in Fig. 35 as shown by similar letters and figures. From these small figures, at right angles to the horizontal line, erect the vertical heights C 8, E 8, 7' 7, etc., equal to similai Fig- 34. vertical heights in the sections in Fig. 33. Connect these points in Fig. 35 by dotted lines as shown, which are the desired true distances. In Fig. 36 are shown the true sections on dotted lines in G E H F in Fig. 33, which are obtained in precisely the same manner, the only difference being that one section is placed inside of £inother in Fig. 36. For the pattern proceed as is shown in Fig. 37. Draw any vertical line as G F equal to G F in Fig. 33. With radius equal to G 1 and with G in Fig. 37 as center describe the arc 1, which intersect by an arc struck from F as center and SHEET-METAL WORK 41 with a radius equal to F 1 in Fig. 36. Now with F 11 in Fig. 33 as radius and F in Fig. 37 as center, describe the arc 11, which is intersected by an arc struck from 1 as center and with 1-11 In Fig 36 as radius. Proceed in this manner until the line 3-9 in Fig 37 has been obtained. Then using 8 '-9' in Fig 33 as radius and 9 in Fig. 37 as center, describe the arc 8, which is intersected by an arc struck from 3 as center and with 3-8 in Fig. 8 T '^.^ — T^* % E 7^ Fig. 35. 4' 6' 35 as radius. Now use alternately as radii, first the divisions in B 8 in Fig. 33, then the length of the slant lines in Fig. 35, the divisions in E 3 A in Fig. 33, and again the distances in Pig. 35, until the line B A in Fig. 37 has been obtained, which is obtained from B A in Fig. 33. Trace a line through points thus obtained in Fig. 37 as shown by A B 8 9 F G A. Trace this half pattern opposite the line G F. Then will B A G A* B^ 8> E£' 1 1 10 Pig.sa POMi 9» F 9 8 be the pattern for the front half of the pail. If for any reason the pattern is desired in one piece, then trace one- half of D^ D2 E2 EMn Fig. 32 on either side of the pattern in Fig. 37 as shown by the dotted lines 8' D^ E* 9' and 9 E D 8. Allow edges for wiring and seaming. Fig 38 shows the method for obtaining the pattern tor an Emerson ventilator shown in Fig. 39. 42 SHEET-METAL WORK -«r While the regular Emerson ventilator has a flat disc for a hood it is improved by placing a cone and deflector on the top "as shown. To make the patterns, proceed as shown in Fig. 38. First draw the center line a h, on either side of which lay off SHEET METAL WORK 48 1-|- inches, making the pipe A, 3 inches in diameter. The rule usually employed is to make the diameter of the lower flare and upper hood twice the diameter of the pipe. Therefore make the diameter of s d 6 inches. From s and d, draw a line at an angle of 45° to inter- sect the line of the pipe at t and i; this completes B. Measure 2 inches above the line t i and make tc tn the same diameter as s d. Draw the bevel of the deflector so that the apex will be ^ inch above the line t i and make the apex of the hood the same distance above ^t m as the lower apex is below it. Then draw lines as shown which complete C and D. Fig. 39. Now with c as a center and radii equal io c e and c d draw the quarter circles ef and d A respectively, which represent the one- HALF PATTERN FOR ,\\ HOOD AND DEFLECTOR Fig. 40. quarter pattern for the horizontal ring closing the bottom of the lower flare. For the pattern for the hood, use I as a center and Ityi as a radius. Now draw the arc mm'. Take the stretchout 44 SHEET-ME'^fAL WORK of the quarter circle 1 to 6 on ^ A, and place twice this amount on mm' as shown from 1-6-1. Draw a line from 1 to ^. Then m' 6 ml, will be the half pattern for the hood. As the deflector has the same bevel as the hood, the hood pattern wiU also answer for the deflector. When seaming the hood and deflector together as shown at n, the hood o is double-seamed to the deflector at y, which allows the water to pass over; for this reason allow a double edge on the pattern for the hood as shown, while on the deflector but a single edge is required. Edges shonld also be allowed one d hf» For the pattern for the lower flare, extend the line d i until it intersects the center line at^\ Then with radii equal t-o^« i andjd and with j in Fig. 40 as center describe the arcs * *' and dd\ On one side as d draw a line toj. Then set off on the arc d d' Pig. 41. ijwice the number of spaces contained in ^ A in Fig. 38 as shown in Fig. 40. Draw a line from d' to i and allow edges for seaming. Then d d' i' i will be the hali pattv^m for the lower flare. The braces or supports E and F, Fig. 38, are usually made of galvanized band iron bolted or rivetea to hood and pipe. The hood D must be water tight or tht? water will leak into the deflector, from which it will drip fiom the apex inside the building. Elbows. There is no other article in the sheet-metal worker's line, of which there are more made in practice than elbows. On this account rules will be given for constructing the rise of the miter line in elbows of any size or diameter, also for elbows whose sections are either oval, square or round, including tapering elbows Before taking up the method of obtaining the patterns, the rule will be given for obtaining the rise of the miter line for any size SHEET-METAL WORK 45 or number of pieces. No matter how many pieces an elbow has, they join together and form an angle of 90°. Thus when we speak of a two-pieced, three-pieced, four, five or six-pieced elbow, we understand that the right-angled elbow is made up of that number of pieces. Thus in Fig. 41 is shown a two-pieced elbow placed in the quadrant C B, which equals 90° and makes C A B a right angle. From A draw the miter line A ^ at an angle of 45° to the base line A B. Then parallel to A B and A C and tangent to the quadrant at C and B draw lines to intersect the miter line, as shown. Knowing the diameter of the pipe as C D or E B draw lines parallel to the arms of the pipe, as shown. Then C B E D will be a two-pieced elbow, whose miter line is an angle of 45°. In a similar manner draw the quadrant B C, Fig. 42, in which it is desired to draw a three-pieced elbow. Now follow this simple Fig. 4a Fig. 44. rule, which is applicable for any number of pieces: Let the top piece of the elbow represent 1, also the lower piece 1, and for every piece between the top and bottom add 2. Thus in a three-pieced elbow: Top piece equals 1 Bottom piece equals 1 One piece between 2 Total equals 4 Now divide the quadrant of 90° by 4 which leaves 22^". As one piece equals 22|°, draw the lower miter line A ^ at that angle to the base line A B. Then as the middle piece represents two by the above rule and equals 45°, add 45 to 22^ and draw the second miter line A J, at an angle of 67^** to the base line A B. Now tangent to the quadrant at C and B draw the vertical and 46 SHEET-METAL WORK horizontal lines shown, until they intersect the miter lines, from which intersections draw the middle line, which will be tangent to the quadrant at F. CD and B E show the diameters of the pipe. which are drawn parallel to the lines of the elbow shown. Fig. 43 shows a four-pieced elbow, to which the same rule is applied. Thus the top and bottom piece equals 2 and the two middle pieces equal 4; total 6. Now divide the quadrant of 90° by 90 6. — ^ = 15. Then the first miter line A a will equal 15°, the second A I 45°, the third A c 75°, and the vertical line A C 90°. The last example is shown in Fig. 44, which shows a five- pieced elbow, in which the top and bottom pieces equal 2, the 3 90 middle pieces 6; total 8. Divide 90 by 8. — ^ = W\. Then the first miter line will equal 11J°, the second 33J°, the third 56^°, and the fourth 781°. By using this method an elbow having any num- ber of pieces may be laid out. When draw- ing these miter lines it is w^ell to use the pro- tractor shown in Fig. 45, which illustrates how to lay out a three-pieced elbow. From the center point A of the protrac- tor draw lines through Fig. 45. 224°,and674°. Now set off A a, and the diameter of the iDipe a h. Draw vertical lines from a and 1) to the miter line at c and d. Lay off similar distances from A to «' to 5' and draw horizontal lines intersecting the 67^^ miter line at c' and d' . Then draw the lines ^c?' andcc' to comjplete the elbow. In practice, however, it is not necessary to draw out the entire view of the elbow; all that is required is the first miter line, as will be explained in the following problems. SHEET-METAL WORK :4il EXERCISES FOR PRACTICE. 1. Make the diameter of the pipe If inches and the distances from A to E 1| inches in Figs. 41 to 44 inclusive. To obtain the pattern for any elbow, using but the first miter Pig. 46. line, proceed as follows: In Fig. 46 let A and B represent respect- ively a two- and three-pieced elbow for which patterns are desired First draw a section of the elbow as shown at A in Fig. 47 which r""Et L. U_| I 1- Fig. 47. is a circle 3 inches in diameterj divide the lower half into equal spaces and number the points of division 1 to 7. Now follow -thq rule r)reviously given: The top and bottom piece equals 2.^ thBQ 48 SHEET-METAL WORK for a two-pieced elbow divide 90 by 2. In its proper position below the section A draw BODE making ED 45°. From the various points of intersection in A drop vertical lines intersecting E D a€ ELEVATION Fig. 48. •hown. In line with B draw K L upon which place twice the number of spaces contained in the section A as shown by similar figures on K L; from these points drop perpendiculars to intersect SHEET-METAL WOKK 49 with lines drawn from similar intersections on E D, parallel to K L. Trace a line through points shown; then K L O N M will be the pattern. To this laps must be allowed for seaming. Now to obtain the pattern for a three- pieced elbow, follow the rule. Top and bottom pieces equal 2, one middle piece equals 2; total 4. — 7 == 22|. Therefore in line with the section A below 4 the two-pieced elbow draw F Gr J H, making H J at an angle of 22f ° to the line H 5. Proceed as above using the same stretchout lines; then U P R S T will be the desired pattern. It should be understood that when the protractor is used for obtaining the angle as shown in Fig. 45, the heights a o and h d measured from the horizontal line form the basis for obtaining the heights of the middle pieces, inasmuch as they represent one-half the distance; for that reason the middle pieces count 2 when using the rule. Therefore, the distances F H and Gr J (Fig. 47), represent one-half of the center piece and U T S R P one-half the pattern for the center piece of a three-pieced elbow. Fig. 48 shows how the patterns are laid into one another, to prevent waste of metal when cutting. In this example we have a three-pieced elbow whose section is 2 X 2 inches. It is to be laid out in a quadrant whose radius is 5 inches. Use the same principles for square section as for round; number the corners of the section 1 to 4. In line with S t draw D E upon which place the stretchout of the square section as shown by similar numbers on D E; from which draw horizontal lines which intersect lines drawn parallel to D E from the intersections 1' 2' and 3' 4' in A in elevation, thus obtaining similar points in the pattern. Then A^ will be the pattern for A in elevation. For the pattern fc r B simply take the distance from 2' to J and place it on the line 4 4' extended in the pattern on either side as shown by 4' 4'' on both sides. Now reverse the cut 4' 2' 4' and obtain 4" 2'^ 4''. By measurement it will be found that 4' 4" is twice the length of 2' 2 as explained in connection with Figs. 45 and 47. Make the distance from 1" to ^' the same as j to « in and draw the vertical line 5' I' intersecting the lines 4 4" extended on both sides. Then A^ B^, and C* will be the patterns in one piece minus the edges r^^:. 50 SHEET-METAL WORK seaming which must be allowed between these cuts ; this would of course make the lengths b' 4", 4" 4' and 4' 4 as much longer as the laps would necessitate. This method of cutting elbows in one piece, from one square is applicable to either round, oval or square sections. In Figs. 49 and 50 are shown three-pieced elbows such as are Fig. 49. Fig. 50. KJ... used in furnace-pipe work and are usually made from bright tin. Note the difference in the position of the sections of the two elbows. In Fig. 49 « 5 is in a vertical position, while in Fig. 50 it is in a horizontal position. In obtaining the patterns the same ^ — s^ — 1 ~7\ ^^^^ ^^ employed as in pre- ' ^ / ^ vious problems, care being taken when developing the patterns for Fig. 49 that the section be placed as in Fig. 51 at A; and* when developing the patterns for Fig. 50, that the section be placed as shown at A in Fig. 52. Fig. 51. Fig. 53 shows a taper- ing two-pieced elbow, round in section. The method here shown is short and while not strictly accurate, gives good results. It has been shown in previous problems on Intersections and Developments that an oblique section through the opposite SHEET-METAL WORK 51 sides of a cone is a true ellipse. Bearing this in mind it is evident that if the frustum of the cone H I O N, Fig. 54, were a solid and cut obliquely by the plane J K and the several parts placed side by side, both would present true ellipses of exactly the same size, and if the two parts were placed together again turning the upper piece half-way around as shown by J W M K, the edges Pig. 52. of the two pieces from J to K would exactly coincide. Taking advantage of this fact, it is necessary only to ascertain the angle of the line J K, to produce the required angle, between the two pieces of the elbow, both of which have an equal flare. The angle of the miter line, or the line which cuts the cone in two parts, must be found accurately so that when joined together an elbow will be formed having the desired angle on the line of its axis. Therefore draw any vertical line as A B. "With C as a center describe the plan of the desired diameter as shown by E D P B. At right angles to A B draw the bottom line of the elbow H I equal to E F, or in this case, 3 inches. Measuring from the line H I on the line A B the Fig. 53. height of the frustum is 5 inches. Through X' draw the upper diameter O N, IJ inches. Extend the contour lines of the frustum imtil they intersect the center line at L. Divide the half plan E D F into a nxunber of equal parts as shown; from these points urect lines intersecting the base line H I from which draw lines to the apex L. As the elbow is to he in two pieces, and the axis at right angles, draw the angle T K S, 52 SHEET-METAL WORK bisect it at U and draw the line R V. No matter what the angle of the elbow, use this method. Now establish the point J at some convenient point on the cone, and from J, parallel to R V, draw the miter line vJ K intersecting the radial lines drawn through the cone; from these points and at right angles to the center line A B draw lines intersecting the side of the cone J H from 1 to 7. If it is A I ELEVATION W Fig. 54, aesired to know how the side of the tapering elbow woidd look, take a tracing of N O K J, reverse it and place it as shown by J WMK. For the pattern proceed as follows: With L as a center and L H as a radius describe the arc 1 1. Starting from 1 set off on SHEET-METAL WORK 53 this arc twice the stretchout of 1 4 7 in plan, as shown by similar figures on 1 1, from which draw radial lines to the apex L. Again using L as center with radii equal toLN,Ll,L2toL7, draw arcs as shown intersecting radial lines having similar numbers. Through these intersections draw the line J' L'. Then O' N' J' K' L' or A will be the pattern for the upper arm (A) in elevation, and P ' K ' T ' X Y or B the pattern for the lower arm (B) in elevation. /'! j V\\\ \ \ \ X " ' ^ \ \ \ \ ^ ' ( I I \\\ \ \ N \ y I Fig. 55. The pattern should be developed full size in practice and then pricked from the paper on to the sheet metal, drawing the two patterns as far apart as to admit allowing an edge to A at «^; also an edge at J to B for seaming. When a pattern is to contain more than two pieces the method of constructing the miter lines in the elevation of the cone is 51 SHEET-METAL WOEK slightly different as shown in Fig. 55. Assume the bottom to be 3 inches in diameter and the top 1^ inches. Let the vertical height be 4 inches. Iii this problem, as in the preceding, the various pieces necessary to form the elbow are cut from one cone whose dimensions must be determined from the dimensions of the required elbow. The first step is to determine the miter lines, which can be done the same as if regular pieced elbows were being developed. As the elbow is to consist of four pieces in 90°, follow the rule given in connection with elbow drafting. The top and bottom 90 piece equal 2; the two middle pieces equal 4; total 6. 6 15 Lay off A B C D according to the dimensions given, and draw the half plan below D C ; divide it into equal parts as shown. From the points of division erect perpendiculars intersecting D C, from which draw lines meeting the center line E 4 at F. b-c SLIGHT BEN03 Fig. 56. Fig. 57. We assume that the amount of rise and projection of the elbow are not specified, excepting that the lines of axis will be at right angles. Knowing the angle of the miter line, it becomes a matter of judgment upon the part of the pattern draftsman, what length shall be given to each of the pieces composing the elbow. Therefor establish the points G, I and K, making D G, G I, IK and K A \, 12, f and 1 inch respectively. From G, I and K draw the hori^ zontal lines G 1", I 1° and K 1^. To each of these lines draw the lines G H, I J and K L respectively at an angle of 15° intersecting the radial lines in the cone as shown. From these intersections draw horizontal lines cutting the side of the cone. Then using F as a center, obtain the various patterns O, P, R and S in the manner already explained. SHEET-METAL WORK 55 In Fig. 56 is shown a side view of the elbow, resulting from preceding operations; while it can be drawn from dimensions obtained in Fig. 55, it would be impossible to draw it without first having these dimensions. In Fig. 57 is shown a perspective view of a tapering square elbow of square section in two pieces. This elbow may have any given taper. This problem will be developed by triangulation and parallel lines; it is an interesting study in projections as well as in developments. First draw the elevation of the elbow in Fig. 58 making 1-6 equal to 3J inches, the vertical height 1-2, 4J inches, and 6-5, 2^ inches; the projection between 1 and 2 should be I inch and between 5 and 6, § inch. Make the horizontal distance ELEVATION 2* & PLAN ° « OEVELOPEMENTS Fig. 58. from 5 to 4, 2 inches, and the rise at 4 from the horizontal line J inch, and the vertical distance from 4 to 3, IJ inches. Then draw a line from 3 to 2 to complete the elevation. In its proper position below the line 1-6, draw the plan on that line, as shown by 1' 1' 6' 6'. Through this line draw the center line A B. As the elbow should have a true taper from 1 to 3 and from 4 to 6, we may develop the patterns for the top and bottom pieces first and then from these construct the plan. There- fore, take the distances from 1 to 2 to 3 and from 4 to 5 to 6 in elevation and place them on the line A B in plan as shown respec- tively from 1° to 2° to 3° and from 4° to 5° to 6°; through these points draw vertical lines as shown. "While the full developments r>(> SHEET-METAL WORK E and D are shown we shall deal with but one-half in the explana- tion which follows. As the elbow is to have the same taper ou either side, take the haK distance of the bottom of the elbow 1-6 and place it as shown from l°-6° to l"-6", and the half width of the top of the elbow 3-4 and place it as shown from 3° to 3" and 4'^ to 4". Then draw lines from 3" to 1" intersecting the bend 2° at 2", and a line from 4" to 6" intersecting the bend 5° at 5". Trace these points on the opposite side of the line A B. Then 1" 3" ah will be the pattern for the top of the elbow and 6" 4" c h the pattern for the bottom. From these various points of intersection draw horizontal lines to the plan, and intersect them by lines drawn from similarly nxmibered points in the elevation at right angles to A B in plan. Draw lines through the points thus p^^^g.pj^ PQj, obtained in plan as shown by 1 ' , 2 ' , 3 ^ 4 ' , -^^T; \3 5 ' and 6 ' which will represent the half plan view. For the completed plan, trace these ,"4 lines opposite the line A B as shown. It will be noticed that the line 3^ in eleva- tion is perpendicular as shown by 3 ' 4 ' in plan while the points 2 ' and 5 ' project from it, showing that the piece 2-3-4-5 Fig. 59. in elevation must be slightly twisted along the line 5-3 when forming the elbow. Similarly slight bends will be required along the lines 1-5 and 5-2. It will now be necessary to obtain the true lengths or a diagram of triangles on the lines 1-5, 5-2 and 5-3. Connect similar numbers in plan as shown from 1' to 5', 5' to 2' and 5' to 3', the last two lines being already shown. From similar points in eleva- tion draw horizontal lines as shown by 2-A, 3-f, 5-e and 6-^. Take the distances from 1 ' to 5 ' , 5 ' to 2 ' and 5 ' to 3 ' in plan and place them on one of the lines having a similar number in eleva- tion, as shown respectively by 1^ 5^, 5^ 2^^ and 5^ 3^. From the points marked 5^^ draw vertical lines intersecting the horizontal line drawn from 5 at 5^^, 5^^ and 5^ respectively. Now draw the true lengths 1^ 5^, 2^^ 5^, and 3^ 5^. For the pattern draw any line as 1-6 in Fig. 59 equal to 1-6 in Fig. 58. Now with 6" 5" in D as a radius and 6 in Fig. 59 as a center, describe the arc 5 which is intersected by an arc struck from 1 as a center and the true length SHEET-MBTAL WORK 57 1* 5^ in Fig. 58 as radius. Then using the true length 5^ 2* as radius and 5 in Fig. 59 as center, describe the arc 2, which is intersected by an arc struck from 1 as center and 1" 2" in E in Fig. 58 as radius. Using the true length 5^ 3^ as radius and 5 in Fig. 59 as center, describe the arc 3, and intersect it by an arc struck from 2 as center and 2" 3" in E in Fig. 58 as a radius. Now with 5" 4" in D as a radius and 5 in Fig. 59 as a center, describe tht arc 4, and intersect it by an arc struck from 3 as center and ^4 in the elevation in Fig. 58 as a radius. Draw lines from point to point in Fig. 59 to complete the pattern. Laps should be allowed on all patterns, for seaming. Slight bends will take place as shown on the pattern, also as is shown hy ah and g in Fig. 57. If the joint is to be on the line 2-5 in elevation in Fig. 58, the necessary pieces can be joined together. In Fig. 60 is shown a perspective view of a five-piece tapering elbow, having a round base and an elliptical top. This form is generally known as a ship ventilator. The principles shown in this problem are applicable to any form or shape no matter what the respective profiles may be at the base or top. The first step is to draw a correct side view of the elbow as shown in Fig. 61. The outline A B C D E F can be drawn at pleasure, but for practice, dimensions are given. First draw the vertical line A F equal to 4 J inches. On the same Fig. 60. line extend measure down 1 J inches to y and draw the horizontal line H B. Fromy* set off a distance of IJ inches at G, and using G as a center and G F as a radius describe the arc F E intersecting H B at E, from which draw the vertical line E D equal to 1 inch. Draw D C equal to If inches, then draw C B. From B lay off 5| inches, and using this point (H) as a center and H B as a radius describe the arc B A. The portion shown B E D C is a straight piece of pipe whose section is shown by I J K L. Now divide the two arcs B A and E F into the same number of parts that the elbow is to have pieces (in this case four) and draw the lines of joint or miter lines as shown by U V, etc. 58 SHEET-METAL A\ ORK Bisect each one of the joint lines and obtain the points ah od and e. Then A B C D E F will be the side view. The patterns will be developed by triangulation, but before this can be done, true sections must be obtained on all of the lines in side elevation. The true sections on the lines B E and D are shown by I J K L. The length of the sections are shown by the joint lines, but the width must be obtained from a front outline of the elbow, which is constructed as follows: In its proper relation to the side elevation, draw the center line M R upon which draw FRONT OUTLINE Fig. 61. the ellipse M N O P (by methods already given in Mechanical Drawing) which represents the section on A F in side. Take half the diameter I K in section and place it on either side of the center line M R as R T or R S. Then draw the outline O S and T N in a convenient location. While this line is drawn at will, it should be understood that when once drawn, it becomes a fixed line. Now from the various intersections ah c d and e in the side elevation, draw lines through and intersecting the front outline as shown on SHEET-METAL WORK 59 (M one side by O, 5', g\ d' and e'. Then these distances will repre- sent the widths of the sections shown by similar letters in side. For example, the method will be shown for obtaining the true section on U V, and the pattern for piece 1 in side elevation. To avoid a confusion of lines take a tracing of A F V U and place it as shown by 1, 13, 12, O in Fig. 62. On 1-13 place the half profile M N P of Fig. 61. Bisect 0-12 in Fig. 62 and obtain the point 6; at a right angle to 0-12 from 6 draw the line 6 6' equal to l' h" in front outline in Fig. 61. Then through the three points O, 6' and 12 in Fig. 62, draw the semi-ellipse, which will represent the half section on U V. The other t t - / Of C0|- / I h\- ©^ ^v \ I I \ \ \ \ I I I "cat a> (0 in s o 13 Fig. 62. sections on the joint lines in side elevation are obtained in the same manner. If the sections were required for piece 2 in side it would be necessary to use only O 6' 12 in Fig. 62 and place it on U V in Fig. 61, and on a perpendicular line erected from c, place the width g' g" shown in front and through the three points obtained again draw the semi-elliptical profile or section. Now divide the two half sections (Fig. 62) into equal parts as shown by the small figures, from which at right angles to 1-13 and 0-12 draw lines intersecting these base lines from 1-13. Connect opposite points as 1 to 2 to 3 to 4 to 5, etc., to 12. Then these lines will represent CM 00 SHEET-METAL WORK the bases of sections whose altitudes are equal to the heights in the half section. For these heights proceed as follows: Take the various lengths from 1 to 2, 2 to 8, 8 to 4, 4 to 5, etc., to 11 to 12 and place them on the horizontal line in Fig. 63 as shown by similar figures; from these points erect vertical lines equal in height to similar figures, in the half section in Fig. 62 as shown by similar figures in Fig. 68. For example: Take the dis- tance from 7 to 8 in Fig. 62 and place it as shown from 7 to 8 in Fig. 68 and erect vertical lines 7-7', and 8-8' equal to 7-7' and 8-8' in Fig. 62. Draw a line from 7' to 8' in Fig. 68 which is the true length on 7-8 in Fig. 62. For the pattern take the distance of 1-0 and place it as shown by 1-0 in Fig. 64. Now using O as a center and O 2' in Fig. 62 as a radius, describe the arc 2 in Fig. 64 Fig. 64. and intersect it by an arc struck from 1 as a center with 1-2' in Fig. 68 as a radius. Now with 1-8' in Fig. 62 as a radius and 1 in Fig. 64 as a center, describe the arc 8, and intersect it by an arc struck from 2 as center and 2'-8' in Fig. 68 as a radius. Proceed thus, using alternately as radii, first the divisions in 0-6-12 in Fig. 62, then the proper line in Fig. 68, the divisions in l-7'-18 in Fig. 62 and again the proper line in Fig. 68, until the line 12-18 in Fig. 64 is obtained, which equals 12-18 in Fig. 62. In this manner all of the sections are obtained, to which laps must be allowed for wiring and seaming. SHEET-METAL WORK 61 TABLES. The following tables will be found convenient for the Sheet-Metal Worker: TABLES PAGE. Weight of Cast Iron, Wrought Iron, Copper, Lead, Brass and Zinc 62 Sheet Copper 63 Sheet Zinc 64 Standard Gauge for Sheet Iron and Steel 65 Weights of Flat Eolled Iron 66-71 Square and Round Iron Bars 72-73 Angles and Tees ... * ,.,.., 74 62 SHEET-METAL WORK i o z < CD < o < UJ & a o z © H C a :3 o Q Z < o U. o o < c U. o 2 ^ " iHiHtHrH lO lO lO lO vO lO . t-LO CO O t- tH O t'TH iH J 0il6c6d>c6 CO* CO rH rH Co' 05 (N t-< tH iH iH iH * lO CD 00 Oi rH -<*i 00 I llOOSCQCOQ-^C-THlOOi (M(MC0C0^'<^rt- 00 QO Ot Oi 02 Oi00tr-CDiO">*C0' 05 iH Tti CO OO' tH CO lO 00 Q (M* lO t-' iHtHTHTH(M o m be •i-t o o o a> p 4-> bfl 2 H O ;2; SHEET-METAL WORK 6S SHEET COPPER. Official table adopted by the Association of Copper Manufacturers of the United States. Rolled copper has specific gravity of 8.93. One cubic foot weighs 558.125 pounds. One square foot, one inch thick, weighs 46.51 pounds. s '*^ s • S) S n .5 a a w « n ?? * - S =^ w F ^ z. •^ rt .Si - C/3v5 H Q. 35 00537 33 00806 31 0107 29 0134 27 0161 26 0188 24 0215 23 .0242 22 .0269 21 0322 19 0430 18 .0538 16 0645 15 0754 14 0860 13 095 12 109 11. 120* 10 134 9....... .148 8 165 7 180 6 203 5....... .220 4 238 3 2.59 2....... .284 1 300 340 '2 •t3 b a 6 a .-§ (0 ^ o ^§ S o ^§ g2§ u ii a X a X Q. M a >« o. 2 ' B * c ^ a " a * c o. ^•z s5 ^•- V « Xi iS-fi m js CO J3 W J3 o tJ.S? "S 5f «.Sf «.£? •S.Sf V lU • 82 128 184 246 177 • • • • 88.1^ 338 199 266 193 • • • • 96 151 217 289 2n .... 105^ 166 238 317 223 • . . • lllVa 126Vi 174 251 335 253 • •• • 196 285 3$0 64 SHEET-METAL WORK CO c6 (M CO 00 52^ isS CO tH £2^ (M o Oi g 00 1^ c ^5^ ^ ^ *?^ H W W CO W Oh H O W X o Oh Ph < ; 05 CO CO ' lO t-^ C^ (M (M rH 05 rH rH CO CO rH CO tH CO LO Q LO oi CO CO CO -^ '^ CO LO rH CO rH CI 00 rH rH 00 S 8 rH LO 00 lO (M 00 05 lO LO rH (M CO CO CD rH(MrHC0rHc4G;LO00 t-^t^0d0J0iOO(?4rHS^rt CS m < o W o o ril d o o 3 O le standards in accordance herewith. r u p^^'% That in the practical use and application of the standard gauge hereby estab- lished a variation of two and one-half per cent either way may be allowed. Approved, March 3, 1893. M SHEET-METAL WORK WEIGHTS OP PLAT ROLLED IRON PER UNEAR FOOT. Iron weighing 480 pounds per cubic foot. Thickness ia Inches. A t I 1^ If 1^ 1'' .208 .417 .625 1.04 1.25 1.46 1.67 1.88 2.08 2.29 2.50 2.71 2.92 3.13 3.33 3.54 8.75 3.96 4.17 4.37 4.58 4.79 5.00 5.21 5.42 5.63 5.83 6.04 6.25 6.46 6.67 IK" 260 .521 .781 1.04 1.30 1.56 1.82 2.08 2.34 2.60 2.86 3.13 3.39 3.65 3.91 4.17 4.43 4.69 4.95 5.21 5.47 5.73 5.99 6.25 6.51 6.77 7.03 7.29 7.55 7.81 8.07 8.33 IK" IH" .313 .625 .938 1.25 1.56 1.88 2.19 2.50 2.81 3.13 3.44 3.75 4.06 4.38 4.69 5.00 5.31 5.63 5.94 6.25 6.56 6.88 7.19 7.50 7.81 8.13 8.44 8.75 9.06 9.38 9.69 10.00 2" .365 .729 1.09 1.46 1.82 2.19 2.55 2.92 3.28 3.65 4.01 4.38 4.74 5.10 5.47 5.83 6.20 6.56 6.93 7.29 7.66 8.02 8.39 8.75 9.11 9.48 9.84 10.21 10.57 10.94 11.30 11.67 .417 .833 1.25 1.67 2.08 2.50 2.92 3.33 3.75 4.17 4.58 5.00 5.42 5.83 6.25 6.67 7.08 7.50 7.92 8.33 8.75 9.17 9.58 10.00 10.42 10.83 11.25 11.67 12.08 12.50 12.92 13.33 2K" .469 .938 1.41 1.88 2.34 2.81 3.28 3.75 4.22 4.69 5.16 5.63 6.09 6.56 7.03 7.50 7.97 8.44 8.91 9.38 9.84 10.3i 10.78 11.25 11.72 12.19 12.66 13.13 13.59 14.06 14.53 15.00 2H" .521 1.04 1.56 2.08 2.60 3.13 3.65 4.17 4.69 5.21 5.73 6.25 6.77 7.29 7.81 8.33 8.85 9.38 9.90 10.42 10.94 11.46 11.98 12.50 13.02 13.54 14.06 14.58 15.10 15.63 16.15 16.67 2K" .573 1.15 1.72 2.29 2.86 3.44 4.01 4.58 5.16 5.73 6.30 6.88 7.45 8.02 8.59 9.17 9.74 10.31 10.89 11.46 12.03 12.60 13.18 13.75 14.32 14.90 15.47 16.04 16.61 17.19 17.76 18.33 12'' 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 I SHEET-METAL WORK e7 WEIGHTS OF FLAT ROLX£D IRON PER LINEAR POOT. (Continued) Thickness is Inches. 3'' 3K'' 3H" SK" 4." .885 4^K" ^X" 12'' ^ .62'5 .677 .729 .781 .833 .938 .990 2.5d i' 1.25 1.35 1.46 1.56 1.67 1.77 1.88 1.98 5.00 Ji^ 1.88 2.03 2.19 2.84 2.50 2.66 2.81 2.97 7.50 i 2.50 2.71 2.92 8.13 3.33 3.54 3.75 3.96 lO-OOf ^^ 3.13 3.39 3.65 8.91 4.17 4.43 4.69 4.95 12:50 3.75 4.06 4.38 4.69 5.00 5.31 5.63 5.94 15.00 Te 4.38 4.74 5.10 5.47 5.83 6.20 6.56 6.93 17.50 ¥ 5.00 5.42 5.83 6.25 .6.67 7.08 7.50 7.92 20.00 1^ 5.63 6.09 6.56 7.03 7.50 7.97 8.44 8.91 22.50 f 6.25 6.77 7.29 7.81 8.33 8.85 9.38 9.90 25.00 ft 6.88 7.45 8.02 8.59 9.17 9.74 10.31 10.89 27.50 1 7.50 8.13. 8.75 9.38 10.00 10.63 11.25 11.88 30.00 if 8.13 8.80 9.4S 10.16 10.83 lT.51 12.19 12.86 32.50 Y 8.75 9.48 10.21 10.94 11.67 12.40 13.13 13.85 85.00 A 9.38 10.16 10.94 11:72 12.50 13.28 14.06 14.84 37.50 1 10.00 10.83 11.67 12.50 13.33 14.17 15.00 15.83 40.00 ItV 10.63 11.51 12.40 13.28 14.17 15.05 15.94 16.82 42.50 1? 11.25 12.19 13.13 14.06 15.00 15.94 16.88 17.81 45.00 ■lA 11.88 12.86 13.85 14.84 15.83 16.82 17.81 18.80 47.50 u 12.50 13.54 14.58 15.63 16.67 17.71 18.75 19.79 50.00 itV 13.13 14.22 15.31 16.41 17.50 18.59 19.69 20.78 52.50 1? 13.75 14.90 16.04 17.19 18.33 19.48 20.63 21.77 55.00 llv 14.3P> 15.57 16.77 17.97 19.17 20.36 21.56 22.76 57.50 u 15.00 16.25 17.50 18.75 20.00 21.25 22.50 23.75 60.00 1t\ 15.63 16.93 18.23 19.53 20.83 22.14 23.44 24.74 62.50 If i6.25 17.60 18.96 20.31 21.67 23.02 24.38 25.73 65.00 tft 16.88 18.28 19.69 21.09 22.50 23.91 25.31 26.72 67.50 If- 17.50 18.96 20.42 21.88 23.33 24.79 26.25 27.71 70.00 m 18.13 19.64 21.15 22.66 24.17 25.68 27.19 28.70 72.50 H 18.75 20.31 21.88 23.44 25.00 26.56 28.13 29.69 75.00 m 19.38 20.99 22.60 24.22 25.83 27.45 29.06 30.68 77.50 2 20.00 21.67 23.33 | 25.00 26,67 28.33 30.00 31.67 80.09 J , i 1 ( i 1 68 SHEET-METAL WOKK WEIGHTS OF FLAT ROLLED IRON PER LINEAR FOOT. (Continued) Thickness in laches. 5'' 1.04 1.09 5H" 1.15 5^" 1.20 6" 1.25 6K" e'A" 6^" 1.41 12'' tV 1.30 1.35 2.50 i 2.08 2.19 2.29 2.40 2.50 2.60 2.71 2.81 5.00 tV 3.13 3.28 3.44 3.59 3.75 3.91 4.06 4.22 7.50 i 4.17 4.38 4.58 4.79 5.00 5.21 5.42 5.63 10.00 A 5.21 5.47 5.73 5.99 6.25 6.51 6.77 7.03 12.50 1 6.25 6.56 6.88 7.19 7.50 7.81 8.13 8.44 15.00 tV 7.29 7.66 8.02 8.39 8.75 9.11 9.48 9.84 17.50 i 8.33 8.75 9.17 9.58 10.00 10.42 10.83 11.25 20.00 tV 9.38 9.84 10.31 10.78 11.25 11.72 12.19 12.66 22.50 1 10.42 10.94 11.46 11.98 12.50 13.02 13.54 14.06 25.00 H -11.46 12.03 12.60 13.18 13.75 14.32 14.90 15.47 27.50 f 12.50 13.13 13.75 14.38 15,00 15.63 16.25 16.88 30.00 H' 13.64 14.22 UM 15.57 16.25 16.93 17.60 18.28 32.50 f 14.58 15.31 16.04 16.77 17.50 18.23 18.96 19.69 35.00 if 15.63 16.41 17.19 17.97 18.75 19.53 20.31 21.09 37.50 1 16.67 17.50 18.33 19.17 20.00 20.83 21.67 22.50 40.00 iiV 17:71 18.59 19.48 20.36 21.^5 22.14 23.02 23.91 42.50 u 18.75 19.69 20.63 21.56 22.^,0 23.75 23.44 24.38 25.31 45.00 ItV 19.79 20.78 21.77 22.76 24.74 25.73 26.72 47.50 u 20.83 21.88 22.92 23.96 25.00 26.04 27.08 28.13 50.00 ItV 21.88 22.97 24.06 25.16 26.25 27.34 28.44 29.53 52.50 If 22.92 24.06 25.21 26.35 27.50 28.65 29.79 30.94 55.00 ItV 23.96 25.16 26.35 27.55 28.75 29.95 31.15 32.34 57.50 li 25.00 26.25 27.50 28.75 30.00 31.25 32.50 33.75 60.00 lA 26.04 27.34 28.65 29.95 81.25 32.55 33.85 85.16 62.50 u 27.08 28.44 29.79 31.15 32.50 33.85 35.21 36.56 65.0^ IH 28.13 29.53 30.94 32.34 33.75 35.16 36.56 37.97 67.50 ll 29.17 30.63 32.08 33,54 35.00 36.46 37.92 39.38 70.00 IH 30.21 31.72 33.23 34.74 36.25 37.76 89.27 40.78 72.50 U 31.25 32.81 34.38 35.94 37.50 39.06 40.63 42.19 75.00 1^^ 32.29 33.91 35.52 37.14 38.75 '40.36 41.98 43.59 77.50 8 33.33 35.00 36.67 38.33 40.00 41.67 43.33 45.00 80.00 ; . 1 > . SHEET-METAL WORK d9 WEIGHTS OF FLAT ROLLED IRON PER LINEAR FOOT (Continued) iji£Bohe& t ■A i if }T7 U u JA }^ u lA If 7// 1.46 7H" 7M'' •JK" 8" 6'A" SK" SK" 1.61 1.66 1.61 1.67 1.72 1.77 1.82 2.92 3.02 8.13 3.23 8.33 3,44 3.54 3.65 4.38 4.53 4.69 4.84 5.00 5.16 6.31 5.47 6.83 6.04 6.26 6.46 6.67 6.88 7.08 7.29 7.29 7.65 7.81 8.07 8.33 8.59 8.85 9.11 8.76 9.06 9.38 9.69 10.00 10.31 10.63 10.94 10.21 10.57 10.94 11.30 11.67 12.03 12.40 12.76 11.67 12.08 12,60 12.92 13.33 13.75 14.17 14.58 13.13 13.59 14.06 14.63 15.00 15.47 15.94 16.41 14.58 15.10 16.63 16.15 16.67 17.19 17.71 18.23 16.04 16.61 17.19 17.76 18.33 18.91 19.48 20.05 17.50 18.13 18.76 ,19.38 20.00 20.63 21.25 21.88 18.96 19.64 20.31 20.99 21.67 22.34 23.02 23.70 20.42 21.15 21.88 22.60 23.33 24.06 24.79 25.52 21.88 22.66 23.44 24.22 25.00 25.78 26.56 27.34 23.33 24.17 25.00 25.83 26.67 27.50 28.33 29.17 24.79 ^.68 26.66 27.45 28.33 29.22 30.10 30.99 26.26 27.19 28.13 29.06 30.00 30.94 31.88 32.81 27.71 28.70 29.69 30.68 31.67 32.66 33.65 84.64 29.17 30.21 31.25 32.29 33.38 34.38 35.42 36.46 30.62 31.72 32:81 ^3.91 SS^.OO 36.09 37.19 38.28 32.08 33.23 34.38 35.52 36.67 37.81 38.96 40.10 33.54 34.74 35.94 37.14 38.33 39.53 40.73 41.93 35.00 36.25 37.50 38.75 40.00 41.25 42.60 43.76 36.46 37.76 89.06 40.36 41.67 42.97 44.27 46.67 37.92 39.27 40.63 41.98 43.33 44.69 46.04 47.40 '39.38 40.78 42.19 43.59 45.00 46.41 47.81 49.22 40.83 42.29 43.75 45.21 46.67 48.13 49.58 61.04 42.29 43.80 45.31 46.82 48.33 49.84 51.35 52.86 43.75 45.^1 46.88 48.44 50.00 51.56 53.13 54.69 45.21 46.82 48.44 50.05 51.67 63.28 54.90 56.51 46.67 48.33 50.00 51.67 53.33 55.00 56.67 58.33 . ' I IC^ 2.60 5.00 7.50 10.00 12.60 15.00 17.50 20.00 '22.60 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 62.60 65.00, 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 70 SHEET-METAL WOKK WEIGHTS OF FLAT ROLLED IRON PER LINEAR FOal^ (Continued) Thickness in Inches. 9" 9M" 1.93 9H" 1.98 9K" 2.03 10" 2.08 lOi" 2.14 2.19 lOf'' 2.24 12" tV 1.88 2.50 i 3.75 3.85 3.96 4.06 4.17 4.27 4.38 4.48 5.0O ^F 6.63 5.78 5.94 6.09 6.25 6.41 6.56 6.72 7.50 i 7.50 7.71 7.92 8.13 8.33 8.54 8.75 8.96 10.00 t\ 9.38 9.64 9.90 10.16 10.42 10.68 10.94 11.20 12.50 f 11.25 11.56 11.88 12.19 12.50 12.81 13.13 13.44 15.00 1^ 13.13 13.49 13.85 14.22 14.58 14.95 15.31 15.68 17.50 i 15.00 15.42 15.83 16.25 16.67 17.08 17.50 17.92 20.00 T^^ 16.88 17.34 17.81 18.28 18.75 19.22 19.69 20.16 22.50 1 18.75 19.27 19.79 20.31 20.83 21.35 21.88 22.40 25.00 H 20.63 21.20 21.77 22.34 22.92 23.49 24.06 24.64 27.50 1 22.50 23.13 23.75 24.38 25.00 25.62 26.25 26.88 30.00 if 24.38 25.05 25.73 26.41 27.08 27.76 28.44 29.11 32.50 1 26.25 26.98 27.71 28.44 29.17 29.90 30.63 31.35 35.00 if 28.13 28.91 29.69 30.47 31.25 32.03 32.81 33.59 37.50 1 30.00 30.83 31.67 32.50 33.33 34.17 35.00 35.83 40.00 ItV 31.88 32.76 33.65 34.53 35.42 36.30 37.19 38.07 42.50 ti 33.75 34.69 35.63 36.56 37.50 38.44 39.38 40.31 45.00 lA 35.63 36.61 37.60 38.59 39.58 40.57 41.56 42.55 47.50 U 37.50 38.54 39.58 40.63 41.67 42.71 43.75 44.79 50.00 lA 39.38 40.47 41.56 42.66 43.75 44.84 45.94 47.03 52.50 tf 41.25 42.40 43.54 44.69 45.83 46.98 48.13 49.27 55.00 1/^ 43.13 44.32 45.52 46.72 47.92 49.11 50.31 51.51 57.50 U 45.00 46.25 47.50 48.75 50.00 51.25 52.50 53.75 60.00 lA 46.88 48.18 49.48 50.78 52.08 53.39 54.69 55.99 62.50 U 48.75 50.10 51.46 52.81 54.17 55.52 56.88 58.23 65.00 Hf 50.63 52.03 53.44 54.84 56.25 57.66 59.06 60.47 67.50 If 52.50 53.96 55.42 56.88 58.33 59.79 61.25 62.71 70.00 IH 54.38 55.89 57.40 58.91 60.42 61.93 63.44 64.95 72.50 U 56.25 57.81 59.38 60.94 62.50 64.06 65.63 67.19 75.00 m 58.13 59.74 61.35 62.97 64.58 66.20 67.81 69.43 77.50 2 1 60.00 61.67 63.33 65.00 66.67 68.33 70.00 71.67 80.00 SHEET-METAL WORK n WEIGHTS OP FLAT ROLLED IRON PER LINEAR FOOT. (Concluded) Thickness in Inches. 11' * t ■& -T5 t'i ^ f^ 1t^ If if 2.29 4.58 6.88 9.17 11.46 13.75 16.04 18.33 20.63 22.92 25.21 27.50 29.79 32.08 34.38 36.67 38.96 41.25 43.54 45.83 48.13 50.42 52.71 55.00 57.29 59.58 61.88 64.17 66.46 68.75 71.04 73.33 Hi" 2.34 4.69 7.03 9.38 11.72 14.06 16.41 18.75 21.09 23.44 25.78 28.13 30.47 32.81 35.16 37.50 39.84 42.19 44.53 46.88 49.22 51.56 53.91 56.25 58.59 60.94 63.28 65.63 67.97 70.31 72.66 75.00 11^'/ 2.40 4.79 7.19 9.58 11.98 14.38 16.77 19.17 21.56 23.96 26.35 28.75 31.15 33.54 35.94 40.73 43.13 45.52 47.92 50.31 52.71 55.10 57.50 59.90 62.29 64.69 67.08 69.48 71.88 74.27 76.67 111'' 2.45 4.90 7.34 9.79 12.24 14.69 17.14 19.58 22.03 24.48 26.93 29.38 31.82 34.27 36.72 39.17 41.61 44.06 46.51 48.96 51.41 53.85 56.30 58.75 61.20 63.65 66.09 68.54 70.99 73.44 75.89 78.3? 12" 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 12|" 2.55 5.10 7.66 10.21 12.76 15.31 17.86 20.42 22.97 25.52 28.07 30.63 33.18 35.73 38.28 40.83 43.39 45.94 48.49 51.04 53.59 56.15 58.70 61.25 63.80 66.35 68.91 71.46 74.01 76.56 79.11 81.67 i 12^" 12|" 2.60 5.21 7.81 10.42 2.66 5.31 7.97 10.63 13.02 15.63 18.23 20.83 13.28 15.94 18.59 21.25 23.44 26.04 28.65 31.25 23.91 26.56 29.22 31.88 33.85 36.46 39.06 41.67 34.53 37.19 39.84 42.50 44.27 46.88 49.48 52.08 45.16 47.81 50.47 53.13 54.69 57.29 59.90 62.50 55.78 58.44 61.09 63.75 65.10 '67.71 70.31 72.92 66.41 69.06 71.72 74.38 75.52 78.13 80.73 83.33 1 77.03 79.69 82.34 85.00 1 Q Ui Weight of □ Bar One Foot long. .013 .052 .117 .208 .326 .469 .638 .833 1.055 1.302 1.576 1.875 2.201 2.552 2.930 3.333 3.763 4.219 4.701 5.208 5.742 6.302 6.888 7.500 8.138 8.802 9.492 10.21 10.95 11.72 12.51 13.33 14.18 15.05 15.95 16.88 17.83 18.80 19.80 20.83 21.89 22.97 24.08 ■Weight of O Bar One foot long. .010 .041 .092 .164 .256 .368 .501 .654 .828 1.023 1.237 1.473 1.728 2.004 2.301 2.618 2.955 3.313 3.692 4.091 4.510 4.950 5.410 5.890 6.392 6.913 7.455 8.018 8.601 9.204 9.828 10.47 11.14 11.82 12.53 13.25 14.00 14.77 15.55 16.36 17.19 18.04 18.91 Area of □ Bar in sq. inches. Area of O Bar in sq. inches. .0039 .0156 .0352 .0031 .0123 .0276 .0625 .0977 .1406 .1914 .0491 .0767 .1104 .1503 .2500 .3164 .3906 .4727 .1963 .2485 .3068 .3712 .5625 .6602 .7656 ,8789 .4418 .5185 .6013 .6903 1.0000 1.1289 1.2656 1.4102 .7854 .8866 .9940 1.1075 1.5625 1.7227 1.8906 2.0664 1.2272 1.3530 1.4849 1.6230 2.2500 2.4414 2.6406 2.8477 1.7671 1.9175 2.0739 2.2365 3.0625 3.2852 3.5156 3.7539 2.4053 2.5802 2.7612 2.9483 4.0000 4.2539 4.5156 4.7852 3.1416 3.3410 3.5466 3.7583 5.0625 5.3477 5.6406 5.9414 3.9761 4.2000 4.4301 4.6664 6.2500 6.5664 6.8906 7.2227 4.9087 5.1572 5.4119 6.6727 Circumference of O Bar in inches. .1963 .3927 .5890 .7854 .9817 1.1781 1.3744 1.5708 1.7671 1.9635 2.1598 2.3562 2.5525 2.7489 2.9452 3.1416 3.3379 3.5343 3.7306 3.9270 4.1233 4.3197 4.5160 4.7124 4.9087 5.1051 5.3014 5.4978 5.6941 5.8905 6.0868 6.2832 6.4795 6.6759 6.8722 7.0686 7.2649 7.4613 7.6576 7.8540 8.0503 8.2467 8.4430 ttHEET.MBTAL WORK 78 5QOARB AND ROUND IRON BARS. (Concluded) Thickness or Diameter in Inches. J,6. I I ii ♦ 8 XL 16 I H Weight of □ Bar One Foot long. 25.21 26.37 27.55 28.76 30.00 31.26 32.55 33.87 35.21 36.58 37.97 39.39 40.83 42.30 43.80 45.33 46.88 48.45 50.05 51.68 53.33 55.01 56.72 68.45 60.21 61.99 63.80 65.64 67.50 69.39 71.30 73.24 75.21 77.20 79.^2 81.26 83.33 Weight of O Bar One Foot long. 19.80 20.71 21.64 22.59 23.56 24.55 25.57 26.60 27.65 28.73 29.82 30.04 32.07 33.23 34.40 35.60 36.82 38.05 39.31 40.59 41.89 43.21 44.55 45.91 47.29 48.69 60.11 61.55 63.01 64.50 66.00 67.52 69.07 60.63 62.22 63.82 Area of QBar in s^. inches. 7.5625 7.9102 8.2656 8.6289 9.0000 9.3789 9.7656 10,160 10.563 10.973 11.391 11.816 12.250 12.691 13.141 13.598 14.063 14.535 15.016 15.504 16.000 16.504 17.016 17,535 18.063 18.598 19.141 19.691 20.250 20.816 21.391 21.973 22.563 23.160 23.766 24.379 Area of O Bar in s^s2^xA 5 «34«2^x>^ 4J^ 2 s2 s^ S^Lbib m^m^^ m • l^xl^x^ 2 • IMxlMx^ -...IM • 1 xl xM... 1 • Ms Mx^ H " i s8 s^ T xe xM. e x3 x^, 4 x4 xH. TEE IRON. Weiglit Per Linear Foot. .30 .30 .14 Lbs. M 8^13^x1^ 12^ 8 x3 7M 2Hz2HxH 8 8>4x2HxA 5 2U^2}ixU 4 2 x2 xU 3}i mxi%xu 3 IMxl^xM 2M l}ixl}ixU 2H 1 xl x^ 1 Ms M&^ H UbB m « « : GOHSTRUCTION DRAWlHa ^MEET /AETAL mun AMD VEMTILATOU IH VEHTlLATIOn WOHK Iron Bt*a^ce>: T.ZZZ-Z. Joint between Vent, a^nd. I)r>um. >"R\vet nin^< Section Xhoufeh A-B. '^ Se^ctionesl view showiTn^ ventilaJtion pipes connected to dTum in eJtic a^lso stea>-m coils in drum to crea^te sucTion. 5HEET METAL WORK. PAKT II. ELEVATION PROBLEHS FOR LIGHT GAUGE HETAL. It is often the case that the siieet metal worker receives plans for vent, heat, or blower pipes to be constructed, in which the true lengths and angles are not shown but must be obtained from the plans or measurements at the building. Figs. 65 and 66 show the prin- ciples employed for obtaining the true angles and lengths in oblique piping, it being immaterial whether the piping is round, square, or oval in section. The only safe way in obtaining these angles is to use the center line as a basis and after this line has been obtained, build the pipe around it, so to speak. In Fig. 65 let A B C represent the eleva- tion of the elbow shown in plan by D E. Through the center of the pipes draw the center line abed which intersect the center lines of the pipe in plan at e andy. In ele- vation the rise of the middle piece B on the center line is equal to h e and projects to the right a distance equal to h A, shown in plan by^y*; this same pipe projects forward in While the miter lines in elevation tj PLAN Fiff. 65, plan a distance equal to e a. 76 SHEET METAL WORK and h I have been drawn straight, they would in reality show curved lines; those lines have not been projected as there is no necessity for doing so. ^ With the various heights and projections in plan and eleva- tion the true length and true angles are obtained as shown in Fig. TRUE LENGTH AND ANGLES Fig. 66. 66, in which draw the horizontal line ^y equal to ^yin plan in Fig. 65. Take the height from A to o and place it from y to c in Fig. 66 on a vertical line erected from f. Draw a line from e to c which is the true length on the center line of the pipe shown by B in elevation in Fig. 65. From the points c and e in Fig. ^^ draw perpendicular lines, making Y ^ X and X c Z = the true angles shown by t^ J X and IL c d respectively in Fig. 65. On either side of the center line in Fig. 66 lay off the half diameter of the pipe as shown, and in its proper position draw the profile W. SHEET METAL WORK 77 Divide this into equal spaces and obtain the pattern A B D E C/ in the usual manner. As both angles are similar the miter cut C E D can be used for all of the patterns. In drawing this prob- lem for practice make the diameter of the pipe 2 inches, the height from A to c 3£ inches in Fig. 65, the projection h to h 3|- inches, and the projection in plan e to a ^^ inches. Our next problem is that of a rain-water cut-off, a perspective view of which is shown in Fig. 67. While the miter cuts in this prob- lem are similar to elbow work the intersection between the two beveled arms, and the cut-off or slide on the inside require atten- tion. Make the diameter of the three openings each 2 inches; A to B (Fig. 68) 14 inches. From B at an angle of 45° draw B C 3^ inches and C D 2 inches. From G draw the vertical miter line G h. Make the distance from B to T J inch. Place the line d e of the cut-off ^ inch above the line T U as indicated at a and the line e cto the right of h G, as indicated by h, a distance of -j-V inch. Parallel to G H draw e d giving slight play room between G H, intersecting e d and e csitd and c respectively. From e at right angles to d c, draw a line as shown, intersecting A G at y, which is the pivot on which the cut-off c d e will turn either right or left. The angles of the pipes on opposite sides are constructed in similar manner; ABCDEFGHIJKLM will be the elevation, IST, the section on A M and O P B. S the section on I J. B T U L shows how far the upper tube projects into the body under which the scoop e d G turns right and left to throw the rain water into either elbow as desired. The pattern for the upper piece A T U M is a straight piece of metal whose circumference is equal to N. For the pattern for (A), divide the half section O P R into equal spaces as shown, from which erect lines intersecting the miter line H K as shown, and from which, parallel to K L and B. vr, draw lines intersecting the joint lines G A L as shown. As none of the T^i ig. 67. 78 SHEET METAL WORK lines just drawn intersect the corner A, it will be necessary to ob- tain this point on the half section OPE, from which the stretch- out of the pattern is taken. Therefore from /i, parallel to L K draw A A' intersecting H K at A', from which, parallel to K J, drop a line intersecting the profile O P E. S at A". At right angles to L K draw stretchout of O P R S as shown by similar numbers on T^ U^, through which at right angles to T^ U^ draw lines which are intersected by lines drawn at right angles to L K from similar in- Fig. 68. tersections on G A L and H K. A line traced through points thus obtained as shown by X Y Z V "W wdll be the pattern for (A). From/* in the elevation at right angles to L K project a line inter- secting the miter cut X Y Z at /" and/*". Aty and/*" holes are to be punched in which the pivot y of the scoop c\d e in elevation will turn. While the pattern for (B) can be obtained as that for (A) was obtained, a short method is to take the distance K to J and plac(^ SHEET METAL WORK 79 it as shown from W to J' and V to J' on the lines of the pattern X W and Z Y respectively extended. W Y J^ J^ will be the pat- tern for B. To avoid a confusion of lines in the development of the scoop or cut-off c d e. this has been shown in Fior, 69 in which dec is a reproduction of d e o in Fig. 68. A true section of the scoop must now be drawn on x e in Fig. 69 so that its dimensions will allow it to turn easily inside of the joint line G li in elevation in Fig. 68. Therefore draw any horizontal line as 4 5 in Fig. 69, at right angles to which from /draw a vertical line intersecting 4 5 at /l Now take a distance -^^ inch less than one-half the diameter of O li in Fig. 68, and place it in Fig. 69 on either side of the line 4 5 on the vertical line just drawn as shown from f to 2 and f to 2'. Extend d c till it intersects 4 5 at 4. Draw a line from 4 to 2'; by bisecting this line we obtain the line a h intersect- ing 4 5 at i. Then with i as center and^* 2' as radius, describe the arc 2' 2. From 2 and 2' draw horizontal lines equal to f e as shown by 2 1 and 2' 1'. Then will 1 4 1' be the true section on x e. Divide the half section into equal spaces as shown from 1 to 4, from which erect lines intersecting c e and e d. Extend x e SiS xj^ upon which place the stretchout of 1 4 1' as shown by similar numbers on xj, through which draw vertical lines. These lines intersect with hori- zontal lines drawn from similar intersections on d e c. Through points thus obtained draw the line 1 n V iii which is the desired pattern. As the pivot hole /'falls directly on line 2, then f"'f" will be the position of the holes in the pattern. Laps must be allowed to all patterns. In putting up rectangular hot air pipe it is often the case that the pipe will be placed in the partition of one story, then has to fall forward and twist one quarter way around to enter the par- tition of the upper story which runs at right angles to the lower one. A perspective view showing this condition is shown in Fig. 70, where the upper opening turns one quarter on the lower one Fig. 69. 80 SHEET METAL WORK and leaning to the right as much as is shown in Fig. 71 in plan. This problem is known as a transition piece in a rectangular pipe. Full size measurements are given in Fig. 71 which should be drawn one-half size. The height of the transition piece is 1 foot 8 inches, the size of the openings, each 4 X 10 inches turned as shown, two inches to the left and two inches above the lower section as shown. From the plan construct the front and side elevations as shown by the dotted lines. A B C D and E F G H will then be the front and side elevations of the transition piece respectively FRONT ELEVATION S PLAN Fig. 70. Fig. 71. equal to 20 inches or 10 inches for practice. Number each side of the plan (a), (b), (c), and [d). Through the front and side elevations draw the vertical and horizontal lines S T and U V respectively at pleasure. These lines are only used as bases for measurements in determining the patterns. For the pattern for the side marked (a) in plan take the length of B C and place it on the vertical line B C in Fig. 72. Through the points B and C draw the horizontal lines E F and H G, making B F and B E, and C G and C H equal respectively to the distances measured from the line U V in Fig. 71 to points F, E, G, H. Draw lines from E to H and F to G in Fig. 72, which is the pattern for (a). SHEET METAL WORK 81 For the pattern for (b) in Fig. 71 take the distance of A D, and place it as shown by A D in Fig. 72; through A and D draw E F and H G, making A F and A E, and D G and D H equal respectively to the distances measured from the line U V in side elevation in Fig. 71 to points F, E, G, H. Draw lines from E to H and F to G in Fig. 72, which will be the pattern for (b). In similar manner obtain the patterns for (c) and (d) in plan in Fig. 71. The lengths of E H and F G are placed as shown by similar letters Fig. 73. Pig. 74. in Fig. 72, while the projections to A, B, G, D are obtained from A, B, C, D in front elevation in Fig. 71, measuring in each instance from S T. If desired the top and lower flange shown in the perspective in Fig. 70 can be added to the patterns in Fig. 72. Laps are allowed to the patterns to allow for double seaming at corners, if, however, the pattern should be required in one piece, it would only 82 SHEET METAL WORK be necessary to join the various pieces in their proper positions as shown bj a d h in Fig. 73, which would bring the seam on the line J N in plan in Fig. 71, In Fig. 74 is shown a per- spective view of a curved rectancrular chute the con- struction of which arises in piping and blower work. The problem as here presented shows the sides a and a in vertical planes having the same height, while the bot- tom h has more width than the top c. The top opening is to rise above the bottom opening a given distance equal to C. First draw the plan and elevation as shown in Fig. 75, make A B equal to 2 inches, B 8 2^ inches; with a radius equal to J inch, with a as center draw the quarter circle 8 2. From 2 draw the vertical line 2 C equal to 1§ inches and draw C D equal to 1^ inches. Make D 1 equal to C 2 and using a as center and a 1 as radius draw the arc 1 h. From A draAv a line tangent to 1 ^ as A 7» A B C I) wall be the plan of the chute. In line with A B draw the section S T U V. In line wdth D C draw the ^ y ^ section EFI H as show^i. Place the desired rise of the ^^' ''^" chute as shown by F i in ele- vation and from i draw a horizontal line as ^K, w^hich intersect by SHEET METAL WOKK 83 a line drawn from A B in plan as shown. Make K J equal to F E and draw the lines F K, K I, and E J, J H. F E J K is the eleva- tion of the outside curve, H I K J the inside curve, F I K the bottom, and E II J the top. Having the plan and elevation in position we will first draw the pattern for the two vertical sides. For the pattern for the side of the chute shown by B C in plan proceed as follows: Divide the inner curve 2 to 8 into equal parts as shown by 2-4-6 and 8, from w^hich points drop lines intersecting the inside of the chute in plan FIJ K las shown. At right angles to J K draw LM, upon which place the stretchout of B C in plan as shown by similar letters and numbers on L M, through which draw vertical lines which inter- sect lines drawn parallel to L M from H J. Through points thus obtained draw the line E 2^ 4^ 6^ 8^N. The same method can 2' 3' 4 --^-- ^5' ^^ 6' --^^7"_,_^ 8' 2345676 A Fig. 76. be employed for the curve P O, but as the height H I and J K are equal, having a common profile B C, take the height of H I or J K and place it on vertical lines as R P and N O and trace the curve R N as shown by P O. JN O P R is the pattern for C B in plan ; To obtain the pattern for the outside curve divide the curve 1-7 into equal parts as shown, from which drop vertical lines inter- secting similar points in E J K F, in elevation at right angles to E F draw W X, upon w^hich place the stretchout of D A in plan as shown. From the divisions on W X drop vertical lines, which intersect by lines drawn from similar numbered intersections on E J. Trace a line through these points as shown by of and draw d e as explained in connection with the inside pattern, c d ef\^ the pattern for the outside of the chute shown in plan by D A. As both the top and bottom of the chute have the same bevel, the pattern for one will answer for the other. Connect opposite points in plan as shown from C to 1 to 2 to 3 up to 8, then to A. In similar manner connect similar points on the bottom in eleva- tion as shown from 1 to 2 up to K. The lines in plan represent 84 SHEET METAL WORK the bases of the sections whose altitudes are equal to the various heights in elevation, measured from i K. Take the various lengths from 2 to 3 to 4 to 5 to 6 to 7 to 8 to A in plan and place them as shown by similar numbers on the horizontal line a h (Fig. 76); through a h draw vertical lines, equal in height to similar numbers in ele- vation, in Fig. 75, measured from the line i K. For example take the distance 4 5 in plan and place it as shown by 4 5 in Fig. 76. Erect perpendiculars 4 4' and 5 5' equal to 4" 4 and 5" 5 in eleva- tion in Fig. 75. Draw a line from 4' to 5' in Fig. 76, which is the true length of 4 5 in plan in Fig. 75. Proceed in similar manner for the balance of the sections. Take a tracing of 1 2 C D in plan and place it as shown by 1, 2, C, D in Fig. 77. Now using 1 as jj '^ PATTERN FOR TOP OR BOTTOM A-B-O-D IN FIG.75 Pig. 77. Fig. 78. center and 1^ 3"^ in (a?), in Fig. 75, as radius, describe the arc at 3, in Fig. 77, which is intersected by an arc, struck from 2 as center, and 2' 3', in Fig. 76, as radius. Now with radius equal to 2V 4V in (^Y) in Fig. 75 and 2 in Fig. 77 as center, describe the arc at 4 which is intersected by an arc, struck from 3 as center and 3' 4', Fig. 76, as radius. Proceed in this manner, using alternately as radius, first the divisions in the pattern (X), Fig. 75, then the slant lines in Fig. 76, the divisions in the pattern (Y), Fig. 75, then again the lines in Fig. 76 until the line 7 8, Fig. 77, has been obtained. Then using? as center, with a line equal to 7^ in (X), Fig. 75, as radius, describe the arc A, Fig. 77, which is inter- sected by an arc struck from 8 as center and 8' A, Fig. 76, as radius. Then with radius, equal to 8"^ N in (Y), Fig. 75, and 8, Fig. 77, as center, describe the arc B, which is intersected by an arc, struck from A as center and A B in plan in Fig. 75 as radius. Trace lines* through points thus obtained in Fig. 77, SHEET METAL WORK 85 and A B C D will be the desired pattern. Laps must be allowed on all patterns for double seaming the corners. In Fig. 78 is shown a perspective view of a hopper register box usually made from bright tin or galvanized iron in hot air piping. In drawing this problem, the student should first draw the half plan, making the semi- circle 3| inches diameter, and placing it directly in the center of the rectangular top, which is B| inches wide and 5| inches long. Draw the elevation from the plan as shown by A B C D E F G H, making the vertical height V W, 2J inches, and the flanges at the top and bottom each ^ inch. I K L M in plan is the horizontal section on A B in elevation and OPE. the sec- tion on E F. The pattern will be devel- oped by triangulation, and the first step is to develop a set of triangles. Divide the quarter circle O R into equal spaces, as shown by the numbers 1 to 7 in plan, from which draw lines to the apex M. These lines represent the bases of triangles whose vertical height is equal to V W in elevation. Therefore, in Fig. 80, draw any horizontal line as T U, upon which place the various lengths M 1, M 2, M 3, etc.) Fig. 79) as shown by similar numbers on T U. From T U erect the line T S equal to the vertical height Y W (Fig. 79). Then draw the hypotenuses SI, S 2, S 3, etc., it: Fig. 80, which represent the true lengths of similar numbered lines in plan in Fig. 79. For the half pattern with seams on I O and P K in plan, take a tracing of D Y W in elevation and place it as shown by D Y 7 in Fig. 81. JSTow using D as center, and with radii equal to the variouts slant lines in Fig. 80 from S 1 to S 7 strike small arcs as shown from 1 to 7 in Fig. 81. Set the dividers 34e5l6 Fig. 80. 86 SHEET METAL WORK equal to the spaces contained in O R, in Fig. 79, and starting from point 7, in Fig. 81, step from one arc to another until 1 is obtained. Then using 1 as center and E D (Fig. 79) as radius describe the i\G D' in Fig. 81. With D as center and M I in plan in Fig. Fig. 81. 79 as radius, draw another arc intersecting the one previously drawT\ at D'. Draw a line froml to D' to D in Fig. 81, 7 1 D' D Y is the quarter pattern, and the left-hand side of the figure may be made by tracing the quarter pattern reversed as shown by Y C D" 1 7. Take the distance of the flange D A in elevation in Fig. 79 and place it at right angles to the line D' D, D C, C D" as shown respectively by A" A', A A<^ and A^ A-^, which completes the half pattern with laps allowed as shown The pattern for the collar E F G H in elevation in Fig. 79 is simply a straight strip o£ metal, equal to the circumference of O P R in plan. It is often the case that two unequal pipes are to be connected by means of a transition piece as shown by A in Fig. 82, the ends of the pipes being cut at right angles to each other. As the centers of both pipes are in one line when viewed in plan, making both halves of the transition piece equal, the problem then consists of developing a transition piece, from a round base to a round top placed vertically. Therefore in Fig. 83 draw 1 5 equal to 2^ inches, and at an angle of 45° draw 5 6 1| inches. At right angles to 1 5 draw 6 10 4 inches long and draw a line from 10 to 1. On 1 5 draw the semicircle 1 3' 5, and on 6 10 draw the semicircle 6 8' 10. Fig. 82. SHEET METAL WORK 87 Divide both of these into equal spaces as shown, from which draw lines perpendicular to their respective base lines. Connect opposite points as shown by the dotted lines, and construct a diagram of 3'^— I tf ff ^"^ ^-^-^C s.-s*--"— ■=»4l — »^ ^ 2 3 45 9» 7 6 9 10 Fig. 83. Fig. 84. sections as shown in Fig. 84 whose bases and heights are equal to similar numbered bases and heights in Fig. 83. For example, take the distance 4 8 and place it as shown by 4 8 in Fig. 84, from which points erect the "^^^vtical lines 4 4' and 8.8' equal to 4 4' and 8 8' in Fig. 83. Draw a line trom 4' to 8', Fig. 84, which is the true Fig. 86. length on similar line in Fig. 83. For the pattern take the dis- tance of 1 10 and place it as shown by 1 10 in Fig. 85. Using 1 as center, and 1 2', Fig. 83, as radius, describe the arc 2 in Fig. 85( intersect it by an are struck from 10 as center and 10 2', Fig. 84, as radius. Then using 10 9' in Fig. 83 as radius, and 10, Fig. 85, as 88 SHEET METAL WOliK center, describe the arc 9, and intersect it by an arc struck from 2 as center, and 2' 9', Fig. 84, as radius. Proceed in this manner using alternately as radii, first the divisions in the half profile 1 3' 5, Fig. 83, then the length of the proper hypotenuse in Fig. 84, then the divisions in 6 8' 10 in Fig. 83; then again the hypot- enuse in Fig. 84 until the line 5 6 in Fig. 85 has been obtained, which is equal to 5 6 in Fig. 83. Laps should be allowed for riveting and seaming as shown. 8 PLAN ^ Fig. 87. In Fig. 86 is show^n a perspective of an offset connecting a round pipe with an oblong pipe, having rounded corners. The first step is to properly draw the elevation and plan as shown in Fig. 87. Draw the horizontal line A B equal to one inch, B 5' one inch, and from 5' at an angle of 45° draw 5' 6' equal to 2 J inches and 6' C IJ inches. Make the diameter C D 2| inches and D /' 0' 1| inches. Make A 1' ^ inch and draw a line from 1' to SHEET METAL WORK 89 » 10' which completes the elevation. Directly above the line A B draw the section of the oblong pipe, making the sides 1 1 and 5 5 equal to 1^ inches, to which describe the semicircles on each end as shown. In similar manner draw the section on J) C, which is phown by G 8 10 8. A duplicate of the oblong pipe is also shown in plan by E F, showing that the centers of the pipe come in one line, making both halves symmetrical. The patterns for the pipes will first be obtained. Divide the semicircular ends of the oblong section into equal parts, in this case four, also each of the semicircles of the round pipe in similar number of pans as shown respectively from 1 to 5 and 6 to 10. Draw vertical lines from these intersections cutting the miter line of the oblong pipe at 1' 2' 3' 4' 5' and the miter line of the round pipe at 6' r 8' 9' and 10'. In line with A B draw B M, upon which place the stretchout of the oblong pipe as shown by similar num- 9L=. bers; from B M drop vertical lines inter- secting the lines drawn parallel to B M i09 from similarly numbered points on 1' 5'. Fig. 88. Trace a line through points thus obtained, and P N O will be the pattern for the oblong pipe. !Now take the stretchout of the round pipe, and place it on C H; erect vertical lines as shown intersecting the lines drawn parallel to C H from similar intersections on 6' 10'. I J H C is the pattern for the round pipe. The transition piece 1' 5' 6' 10' will be developed by triangu- lation, and it is usual to obtain true sections on the lines 1' 5' and 6' 10'; however, in this case it can be omitted because we have the true lengths of the various divisions on the lines 1' 5' and 6' 10' in the miter cuts in P and L respectively. The next step is to obtain a diagram of sections giving the true lengths, for which proceed as follows: Connect opposite points in elevation as shown from 1' to 9' to 2' to 8' to 3' etc., as shown. For example draw center lines through the oblong and round sec- tions as shown hj a b and c d respectively, and take the length of 1' 10' in elevation and place it as shown from 1 to 10 in Fig. 88. From 1 draw the vertical line 1 1' equal to the height of 1 in the oblong section in Fig. 87 above the center line a h. ' As point 10 in plan has no height, it falls on the center line c d in plan, then 90 SHEET METAL WORK draw a line from 1' to 10 in Fig. 88. Now take the distance from 1' to 9' in elevation, Fig. 87, and place it as shown from 1 to 9 in Fig. 88. Erect the lines 1 1' and 9 9' equal to points 1 and 9 in the oblong and round sections in Fig. 87, measured respectively from the lines a h and c d. Draw a line from 1' to 9' in Fig. 87. Proceed in this manner until all of the sections are obtained. For the pattern proceed as shown in Fig. 89, in which draw any verti- cal line as e 10 equal to 1' 10' in elevation in Fig. 87. Now, with one-half of 1 1 in pattern P as ^ 1 as radius, and e in Fig. 89 as center, describe the arc 1 which is intersected by an arc struck from 10 as center and 10 1', in Fig. 88 as radius. With radius equal to 10'' 9" in pattern L in Fig. 87, and 10 in Fig. 89 as center describe the arc 9, which is intersected by an arc struck from 1 as center and 1' 9', in Fig. 88 as radius. Now, using as radius 1" 2" in pattern P in Fig. 87 and 1 in Fig. 89 as center, describe the arc 2 which is intersected by an arc struck from 9 as center and 9' 2' in Fig. 88 as radius. Proceed in this manner, using alternately as radii, first the divisions in the pattern cut I J, Fig. 87, then the length of the slant lines in Fig. 88, the divisions in the cut O N in Fig. 87, then again the slant lines in Fig. 88 until the line 5 6 in pattern. Fig. 89, has been obtained. Then using 5 as center and 1 e in P, Fig. 87, as radius, describe the arc e in Fig. 89, and intersect it by an arc struck from 6 as center and 6' 5' in elevation in Fig. 87 as radius. Draw lines through the various intersections in Fig. 89; 10 6 6' 6 is the half pattern. By tracing it opposite the line e 10, as shown by e V 5' e" G' 10, the whole pattern, e' e e" 6' 10 6, is found. Laps should be allowed on all patterns for seaming or riveting both in Figs. 87 and 89. In Fig. 90 is shown a perspective view of a three-way branch round to round, the inlet A being a true circle, and the outlets B, C, and D also being true circles, the centers of which are in the same vertical plane, thus making both sides of the branch symmetrical. First draw the elevation and the various sections as shown in Fig. 91. Draw the center hne a h. From h draw the center line of the branch C at an angle of 68° as shown by h d. Make the center lines a h and b d each 3^ inches long. Make the half diameter of the branch B at the outlet |- inch, and the full diam- SHEET METAL WORK 91 eter of the branch C at the outlet IJ inches placed on either side of and at right angles to the center lines. Draw a line from e to/, and with i and h as centers and radii equal to | inch draw arcs intersecting each other at c. Draw lines from i to c to h. In similar manner obtain A and the opposite half of E. A B C is the elevation of the three branches whose sections on outlet lines are shown respectively by G F and E and whose section on the inlet line is shown by D. The next step is to obtain a true section on the miter line or line of joint b c. Knowing the height h c and the width at the Fig. 89 bottom, which is equal to the diameter of D, the shape can be drawn at pleasure as shown in Fig. 92, 3 c is drawn equal to h c, Fig. 91, while hd^nd.ha are equal to the half diameter D in Fig. 91. Now through aodm Fig. 92 draw the profile at pleasure as shown, which represents the true section on c h in Fig. 91. As the side branches A and C are alike, only one pattern will be required, also a separate pattern for the center branch both of which will be developed by triangulation. To obtain the measure- ments for the sections for the center branch B, proceed as shown in Fig. 93 where 1 4 5 8 is a reproduction of one-half the branch B in Fig. 91. As the four quarters of this center branch are alike oDly one quarter pattern will be developed; then, if desired, the quarter patterns can be joined together^ forming one pattern. Now 92 SHEET METAL WORK take a tracing oi c h a^ Fig. 92, and place it on the line 5 8 as shown in Fig. 93. Similarly take a tracing of the quarter profile F in Fig. 91 and place it on the line 4 1 in Fig. 93. Divide the two profiles 1' 4 and 5 8' each into the same number of spaces as shown respectively by points 1' 2' 3' 4 and 5 6' T 8', from which points at right angles to their respective base lines 1 4 and 5 8 draw lines intersecting the base lines at 1 2 3 4 and 5 6 7 8. Now draw solid lines from 3 to 6 and 2 to 7 and dotted lines from 3 to 5, 2 to 6, and 1 to 7. These solid and dotted lines represent Fig. 91. Fig. 92. Fig. d3. thu bases of the sections whose altitudes are equal to the varioiu lieights of the profiles in Fig. 93. Tlie slant lines in Fig. 94 rep- resent the true distances on similar lines in Fitr. 93, as those in Fig. 95 represent the true distances on dotted lines in Fig. 93. For the pattern take the length of 1' 8', Fig. 94, and place it as shown by 1 8 in Fig. 96, and using 8 as center and 8' 7' in Fig. 93 as radius draw the arc 7, which intersect by an arc struck from 1 as center and 1' 7' in Fig. 95 as radius. Then using 1' 2' in Fig. 93 as radius draw the arc 2, which intersect by an arc struck from 7 as center and 7' 2' in Fig. 94 as radius. Proceed iu this manner until the line 4 5 in Fig. 96 has been obtained SHEET METAL WORK 93 whicli equals 4 5 in Fig. 93. Trace a line through points thus obtained in Fig. 96, then will 14 5 8 1 give the quarter pattern. If the pattern is desired in one piece trace as shown by similar figures, to which laps must be allowed for riveting. As the two branches A and in Fig. 91 are alike, one pat- tern will answer for the two. Therefore let 1 7 8 11 14 in Fig. 97 be a reproduction of the branch C in Fig. 91. Now take a trac- ing oi a h c in Fig. 92 and place it as shown by 11' 11 8 in Fig. 97; also take a tracing of the half section E and the quarter sec- tion D in Fig. 91 and place them as shown respectively by 1 4' 7 and l3V. I I J I I 2 3 5 67 Fig. 96. Fig. 95. 11 11' 14 in Fig. 97. Now divide the two lower profiles 8 11 and 11' 14 each into 3 equal parts, and the upper profile 7 4' 1 into 6 equal parts as shown by the small figures 8 to 11', 11' to 14 and 1 to 7. From these points, at right angles to the various base lines, draw lines, intersecting the base lines as shown by similar num- bers. Draw solid and dotted lines as shown, and construct the sections on solid lines as shown in Fig. 98 and the sections on dotted lines as shown in Fig. 99 in precisely the same manner as described in connection with Figs. 94 and 95. In Fig. 100 is shown the pattern shape (to which laps must be allowed for riveting) obtained as was the development of Fig. 96. First draw the vertical line 1 14, Fig. 100, equal to 1 14 in Fig. 97. Then use alternately as radii, first the divisions in 1 4' 7 in Fig. 97, the proper slant line in Figs. 98 and 99 and the divisions in 11' 14 until the line 4 11, Fig. 100, is obtained. Starting from 94 SHEET METAL WORK the point 11 use as radii in their regular order the distances marked off between 11' and 8, Fig. 97, then the proper slant lines in Figs. 98 and 99, the distances shown in the semicircle, 1 4' 7, Fig. 97, until the line 7 8j Fig. 100, is drawn equal to 7 8, in Fig. 97. Then in I6'r, ■I I -L4-- I II 1 6 5 134 12 1234149 6 6 5 101342 Fig. 97. Fig. 98. Fig. 99. 1 7 8 11 14, Fig. 100, will be the half pattern. If the pattern is desired in one piece trace 1 7' 8' 11' 14 opposite the line 1 14 as shown. In Fig. 101 is shown a perspective view of a two-branch fork oval to round, commonly used as breeching for two boilers. As Fig. 100. Fig. 101. both halves of the fork are symmetrical the pattern for one will answer for the other. While the side elevation shown in Fig. 102 is drawn com. plete, it is only necessary in practice, to draw one half as follows, and then, if desired, tL'^ other half elevation can be traced opposite SHEET METAL WORK 95 to the center line E J. First draw J E, 1^ inches, equal to the half diameter of the outlet, and the vertical center height J Y, 2^ inches. Establish the height of the joint J E one inch, and the desired projection Y D on the base line 1^ inches. Draw the length of the inlet D C 2| inches, and draw a line from C to B and D to E. Draw a similar figure opposite the line J E, and A B C D E F G shows the side elevation of the fork. In their proper position below A B draw the sections M and N whose semicircular ends are struck from a h c and d with radii equal to ^ incho Now draw an end elevation in which the true section on o&-^ e li i END I ELEVATION Fig. 102. J E is obtained. Draw the center line y e and extend the lines A B and G C in elevation as A P and G S. Take the half diam- eter L J and place it on either side of ^y as shown by OP. In a similar manner take the half diameter of the section N as d i and place it on either side of ^y as shown by R S. Then O P S K shows the end elevation. Draw E T intersecting efB,i T. Now draw the curve O T P, which in this case is struck from the center U, being obtained by bisecting the line O T. It should be under- stood that the curve O T P, which represents the true section on J E, can be made any desired shape, but when once drawn, repre- sents a fixed line. 96 SHEET METAL WORK The pattern will be developed by triangiilation, for which diagrams of sections must be obtained from which to obtain meas- urements. These sections are obtained as follows: In Fig. 103 1 4 5 12 13 is a reproduction of J B C D E, Fig. 102. Keproduce the quarter profile H L I, the half profile O T, and the half profile m no as shown by 1' 1 4, 1" 13 1 and 12 9' 8' 5 in Fig. 103. Divide the round ends in a each into 3 parts and the profiles b and c also each into 3 spaces, as shown by the figures. Drop lines from these figures at right angles to the base lines from 1 to 15 as shown and draw solid and dotted lines in the usual manner. While in some of the previous problems only dotted lines were drawn, we -;-?: Fig. 103. 1231 1514 II 10 9 678 Fig. 104. _;2ii*^:fi - — III III 231514 I no 9 678 Fig. 105. have drawn both solid and dotted lines in this case, in order to avoid a confusion of sections. A diagram of sections on solid lines in Fig. 103 is shown in Fig. 104, the figures in both correspond- ing; while Fig. 105 shows the true sections on dotted lines. The method of obtaining these sections has been described in connection with other problems. For the pattern draw any vertical line as 4 5, Fig. 106, equal to 4 5 in Fig. 103. Then with 5 6', Fig. 103, as radius and 5 in Fig. 106 as center draw the arc 6, intersecting it by an arc struck from 4 as center and 4 6', Fig. 105, as radius. Then using 4 3', Fig. 103, as radius, and 4 in Fig. 100 as center, describe the arc 3^ intersecting it by an arc struck from 6 as center and (>' 3' in Fig. 104 as radius. Proceed in this manner, using alternately as radii, first the divisions in a in Fig. 103, then the slant lines in Fig. 105; the divisions in c in Fig. 103, then the slant lines in Fig. SHEET METAL WORK 97 104, until the line 1 8, Fi^. 100, is obtained, l^ow using 8 as center and 8' 9', Fig. 103, as radius draw the arc 9 in Fig. 106, intersecting it by an arc struck from 1 as center and 1" 9', Figo 104, as radius. Then starting at 1 in Fig. 106 use alternately as radii, iirst the divisions in h in Fig. 103, then the slant lines in Fig. 105, the divisions in a in Fig. 103, then the length of the slant lines in Fig. 104 until the line 12 13 is obtained in Fig. 106, which equals 12 13 in Fig. 103. Trace a line through points thus obtained in Fig. 106, then will 4 1 IB 12 9 8 5 be the half pattern. If the pattern is desired in one piece, trace this half opposite the line 4 5 as shown by 1' 13' 12' 9' 8', allowing laps for riveting. In Fig. 107 is shown a perspective view of a tapering flange around a cylinder passing through an inclined roof, the flange Fig. 107. being rectangular on the roof line. The problem will be developed by triangulation, a plan and elevation first being required as shown in Fig. 108. First draw the angle of the roof A B at an angle of 45°, through which draw a center line D. From the roof line A B on the center line set off a b equal to 4 inches and through b draw the horizontal line E F, making B F and B E each one inch. Through d on the center line draw the horizontal line G H, making d H and d G each two inches. From H and G erect perpendiculars intersecting the roof line at \\ and L. Then draw lines from E to K a d F to L, completing the elevation. Construct the square in ])lan uaking the four sides equal to G H. Bisect H I and draw the Cv nter line c e intersecting the vertical center at d' . Then with radiu equal to J F or ^ E in elevation and d' in plar. as center. 98 SHEET METAL WORK. draw the circle 14 7 4' representing the horizontal section on E F in elevation, while G H 1 J is the horizontal section on K L in elevation. As the circle in plan is in the center of the square making the two halves symmetrical it is only necessary to divide the semicircle into equal spaces as shown from 1 to 7 and draw lines 0— ' Fig. 108. from 1, 2, 3 and 4 to G, and 4, 5, 6 and 7 to H. Then will the lines in 1 G 4 and 4 H 7 represent the bases of triangles which will be constructed, whose altitudes are shown respectively by the vertical heights in K E and L F in elevation. Therefore draw hori- zontal lines through E F, K, and L as shown by F O, K N, and LM. From any point as K and T on F O, draw the perpendiculars R S and T U respectively, meeting the horizontal lines drawn from L and K, Now take the various lengths in plan as Gl, G2, G3, and SHEET METAL WOEK 99 G4 and place them on the line F O as shown by Tl, T2, T3 and T4, from which points draw lines to U which will represent the true lengths on similar lines in plan. In similar manner take the dis- tances in plan from H to 4, to 5, to 6, to 7, and place them on the line F O, from E- to 4, to 5, to 6, to 7, from which points draw lines to S which represent the true lengths on similar lines in plan. For the pattern take the distance F L in elevation and place it on the vertical line 7' L in Fig. 109. At right angles to 7' L draw L S equal to (? H or 6' I in plan, Fig. 108. Draw the dotted line from 7' to S in Fig. 109, which should be equal to S 7 in W in Fig. 108. Now with radii equal to S ^, and S |- and S, Fig. 109, as center, draw the arcs indicated by similar numbers. The dividers should equal the spaces in the semicircle in plan in Fig. 108, and starting at 7' in Fig. 109, step from arc to arc of corre- sponding numbers as shown by 6', 5', 4'. Draw a dotted line from 4' to S. Then using S as center and L K in elevation, Fig. 108, as radius, describe the arc U in Fig. 109, intersecting it by an arc struck from 4' as center and U 4, Fig. 108, as radius. Now using U J, and U § in X as radii, and U, Fig. 109, as center, describe arcs having similar numbers. Again set the dividers equal to the spaces in plan in Fig. 108, and starting from 4' in Fig. 109 step to corresponding numbered arcs as shown by 3', 2', 1'. 100 SHEET METAL WORK Draw a dotted line from 4' to U to 1'. With K E in elevation, Fig. 108, as radius, and 1' in Fig. 109 as center, describe the arc e intersecting it by an arc struck from U as center and G e in plan in Fig. 108 as radius. Draw a line connecting S, U, e^ and 1'. 7' 4' 1' ^ U S L 7' shows the half pattern, which can be traced opposite the line 7' L to complete the full pattern as shown by 7' 4" 1" e' U' S' L. One of the difficult problems often encountered by the sheet metal worker is that of a cylinder joining a cone furnace top at any angle. The following problem shows the principle to be applied, no matter what size the furnace top has, or what size pipe is used, or at what angle the pipe is placed in plan or elevation, the principles being applicable under any conditions. Fig. 110 shows a view of a cyl- inder intersecting a conical fur- nace top, the top being placed to one side of the center of the top. A B D represents a portion of the conical top, intersected by the cylinder E F G H, the side of the cylinder H I to intersect at a given point on the conical top as at H. This problem presents an interesting study in projections, intersections, and development, to which close attention should be given. In Fig. Ill first draw the center line A X. Then draw the half elevation A B C D, making A B 1| inches, C D 3^ inches and the vertical height A D 2J inches. Draw the line from B to C. Directly below C D draw the one-quarter plan using Z as center, as shown by Z C D^ and in line with A B of the elevation draw the quarter plan of the top as Z B^ A^. Let a in the eleva- tion represent the desired distance that the side of the cylinder is to meet the cone above the base line as H in Fig. 110. From «, parallel to C D in Fig. Ill, draw a h. Then from a drop a ver- tical line intersecting the line Z C^ in plan at a'. Then using Z as center and Z a' as radius, describe the quarter circle a' h'. Z a' b' Fig. 110. SHEET METAL WORK 101 in plan represents the true section on the horizontal plane a I in elevation. N^ow locate the point where the side of the cylinder as li in Fig. 110 shall meet the arc a' V in plan, Fig. Ill, as shown ONE HALF>! ^ ELEVATION \\>i; ] • I I ' I I . II ! Ill I Z' • 'ONE QUARTER I PLAN i i fe!llFf*l!Wj^ liila'lci Fig. 111. 102 SHEET METAL WORK At 3". Througli 3" draw the horizontal line intersecting the center line at K*, the outer arc at M* and extend it indefinitely to 3. From 3 erect the perpendicular equal to the diameter of the cylin- der, or 1| inches, bisect it and obtain the center c. Using c as center with > 6"* as shown by similar figures on C F as shown Pig. 112. SHEET METAL WORK 105 from 2^ to 6^. From these points draw radial lines to the apex E, and intersect them by arcs struck from E as center whose radii are equal to the various intersections on B C having similar numbers. Thus arc 4 intersects radial line 4^ at 4^; arcs 3, 5, and 2 intersect radial lines 3^, d^, and 2^ at 3^, 5^, and 2^, and so on. Trace a line through points thus obtained as shown from 1 -^ to 8^ which is the desired shape. If a flange is desired to connect with the cylin- der, a lap must be allowed along the inside of the pattern. COPPERSniTH'S PROBLEMS. In the five problems which will follow, particular attention i.a given to problems arising in the coppersmith's trade. While all the previous problems given in the course can be used by the cop- persmith in the development of the patterns where similar shapes are desired, the copper worker, as a rule, deals mostly with ham- mered surfaces, for which flaring patterns are required. The prin- ciples which will follow, for obtaining the blanks or patterns for the various pieces to be hammered, are applicable to any size or shape of raised work. The copper worker's largest work occurs in the form of brewing kettles, which are made in various shapes, to suit the designs of the different architects who design the work. In hammering large brewing kettles of heavy copper plate, the pieces are developed, hammered, and fitted in the shop, then set together in the building, rope and tackle being used to handle the various sections for hammering, as well as in construction at the building. While much depends upon the skill the workman has with the hammer, still more depends upon the technical knowledge in laying out the patterns. In all work of this kind the patterns are but approximate, but no matter what size or shape the work has, the principles contained in the following problems are applicable to all conditions. In Fig. 113 is shown a perspective of a sphere which is to be constructed of horizontal sections as shown in Fig. 114, in which for practice draw the center line A B, on which, using a as center, and with radius equal to 2^ inches, describe the elevation of the sphere B C D E. Divide the quarter circle D C into as many spaces as the hemi-sphere is to have sections, as shown by C F G D. From these points draw horizontal lines through rhe elevation, as 10« SHEET METAL WOKK shown by C E, r H, and G I. iSTow through the extreme points as E II, H I, and I D draw lines intersecting the Qenter line B A at J, K, and D respectively. For the pattern for the first section Z, take D I as radius, and using D^ in 7} as center, describe the circle shown. For the pattern for the second section Y, use K 1 and K H as ladii, and with K^ as center draw the arcs I^ P and ff Pig. 113. Fig. 114. W. From any point as H^ draw a line to the center K^ It now becomes necessary to draw a section, from which the true length of the patterns can be obtained. Therefore with (^ F as radius, describe the quarter circle F L, which divide into equal spaces, as shown by the figures 1 to 5. Let the dividers be equal to one of those spaces and startii\g at H^ on the outer arc in Y^ step off four times the amount contained in the quarter section F L.^ as shown from 1 SHEET METAL WORK 107 to 5 to 1 to 5 to 1 in Y\ From 1 or H^ draw a line to K^ Then will H^ P r H^ be the pattern for the section Y in elevation. For the pattern for the third section, use J as center, and with radii equal to J H and J E draw the arcs H H^ and E E\ IN'ow set the dividers equal to one of the equal spaces in F L and starting from H set off four times the amount of L F as shown from 1 to 5 to 1 to 5 to 1 on the inner curve H Jl\ From the apex J through W draw a line intersecting the outer curve at E\ E E^ H^ H shows the pattern for the center section. It will be noticed in the pattern X^ we space off on the inner curve, while on the pattern Y^ we space off on the outer curve. These two curves must contain the same amount of material as they join together when the ball is raised. To all of the patterns laps must be allowed for brazing or soldering. The patterns shown are in one piece ; in practice where the sphere is large they are made in a number of sections. In Fig. 115 is shown the per- spective view of a circular tank whose outline is in the form of an ogee. The portion for which the patterns will be described is indicated by A A, made in four sections, and riveted as shown hj a h G d. Fig. 116 shows how the pattern is developed when the center of the ogee is flaring as shown from 3 to 4 in elevatiouo First draw the elevation A B C D, making the diameter of A B equal to 7 inches, the diameter of D C 4 inches, and the vertical height of the ogee 1| inches. Through the center of the elevation draw the center liney A, and with any point upon it as i, draw the half plan through A B and C D in elevation as shown respectively by E F and H G. Now divide the curved parts of the ogee into equal spaces as shown from 1 to 3 and 4 to 6. Draw a line through the flaring portion until it meets the center line/* A atj. j will, therefore, be the center with which to strike the pattern. Take the stretchout of the curve from 3 to 1 and 4 to 6 and place it on the flaring line from 3 to 1' and 4 to 6' as shown by the figures. Then will 1' 6' be the stretchout for the ogee. It should be under- Fig. 115. 108 SHEET METAL WORK r ^tood that no haanmering is done to that part shown from 3 to 4. The portion shown from 3 to 1' is stretched to meet the required profile 3 2 1, while the low^er part 4 to 6' is raised to conform with the lower curve 4 5 6. Therefore, knowing that the points 3 and 4 are fixed points, then from either of these, in this case point 4, Fig. 116. drop a vertical line intersecting the center line E F in plan at a. Then with i as center and i a as radius, describe the quarter circle a e^ and space it into equal parts as shown by a^ h, e, d^ e, which represent tlie measuring line in plan on the point 4 in elevation. Using ;' as center, and j 6', j 4, j 3 and / 1' as radii, draw the arcs 1"-!'", 8"-3"', 4"-4'" and 6"-6"' as shown. From 1" draw a radial line to / intersecting all the arcs as shown. Now starting at 4" step off on SHEET METAL WORK 109 tbe arc 4" -4'" twice the stretchout of the quarter circle a e as shown by similar letters a io e io a' in pattern. From j draw a line through a' intersecting all of the arcs as shown. r'.l'"-6"'-6" shows the half pattern for the ogee. While in the previous problem the greater part of the ogee was flared, occasion may arise where the ogee is composed of two quarter cir- cles struck from centers as shown in Fig. 117. First draw the center line A B, then draw the half diameter of the top C^ C equal to 3^ inches and the half diameter E D 1| inches. Make the vertical height of the ogee 1^ inches, through the center of which draw the horizontal line a h. From C and D draw ver- tical lines intersecting the horizontal line aJ),2iia and h respectively. Then using a and h as centers with radii equal respectively to « C and h D draw the quarter circles shown completing the ogee. In the quarter plan below which is struck from the cen- ter F, G J and H I are sec- tions respectively on D E and C C^ in elevation. The meth- ods of obtaining the patterns in this case are slightly different than those employed in the previous problems. The upper curve shown from C to c will have to be stretched, while the lower curve shown from nary point 3 in elevation in Fig. 117, then set the dividers equal to the spaces 10 16 in plan and step off similar spaces in Fig. 118 on the arc 8 3', starting at 3 as shown by simi- lar numbers 16 to 10. Through 10 draw a line to the apex m, intersecting the inner curve at 5' and the outer curve at To 1 1' 5' 5 is the quarter pattern for the upper curve or half of the ogee, to which laps must be allowed for. riveting and brazing. For the pattern for the lower curve in elevation in Fig, 117 draw a line from c to D; bisect it at e and from e erect a perpen- dicular intersecting the curve at 7. From 7 draw a horizontal line intersecting the center line aty. Now the rule to be followed in "raising" is as follows: Divide the distance from ^ to 7 into as many parts, as the half diameter F 7 is equal to inches. In this case 7/* equals 2J inches; (any fraction up to the \ inch is not SHEET METAL WORK 111 taken into consideration, but over -J inch one is added). Therefore for 2| inches use 2. Then divide the distance from ^ to 7 into two parts as shown at i and through i parallel to c D draw a line as shown intersecting the center line at N. Now divide the curve (? to D into equal spaces as shown by the figures 5 to 9. Let off on either side of i the stretchout from 5 to 9 as shown from 5" to ^ \ PATTERN FOR LOWER / ^ \ HALF OF OGEE / \ \ ' / / '^ X / \ r / \ I / \ ! / n Fig. 118. 9'. From, i drop a vertical line intersecting F H in plan at 23. Then using F as center draw the arc 23 17 as show^n, which rep- resents the measuring line in plan on i in the stretchout. The student may naturally ask, why is i taken as the measuring line in plan, when it is not a stationary point, for when "raising" i will be bulged outward with the raising hammer until it meets the point 7. In bulging the metal outward, the surface at i stretches as much as the difference between the diameter at i and 112 SHEET METAL WORK 7. In other words, if the measuring point were taken on 7 it would be found that after the mould was " raised " the diameter would be too great. But by using the rule of dividing e 7 into as many parts as there are inches iny* 7 the diameter will be accurate while this rule is but approximate. In this case e 7 has only been divided into two equal parts, leaving but one point in which a line would be drawn througix parallel to c D. Let us suppose that the semi-diameter 7^ is ©qualto eleven inches. Then the space from ^ to 7 would be divided into just so many parts, <27?.<^ through the first part nearest the cove the line would be drawn parallel to c D and used as we have used i. !N^ow with radii equal to n 9', ni^ and ii 5" and n in Fig. 118 as center, describe the arcs 5" 5'" i i' and 9 9'. From any point as 5" draw a line to n intersecting all the arcs shown. Now take the stretchout from 17 to 23 in plan. Fig. 117, and starting from 17 in Fig. 118 mark off equivalent distances on the arc i i' as shown. Draw a line through 28 to the apex n, intersecting the inner and outer arcs at 9' and 5'". Then will 9 5" 5'" 9' be the greater pat- tern for the lower part of the ogee. Another case may arise where the center of the ogee is vertical as shown from c to d in Fig. 119 in A E. In this case the same principles are applied as in Fig. 117; the pattern for c d in Fig. 119 being a straight strip as high as c d and in length equal to the quarter circumference c c" in plan in Fig. 117 which is the section on c in elevation. These rules are applicable to any form of mould as shown in Fig. 119, by e,y*, /i, and^*. The bead i in j would be made in two pieces with a seam at i as shown by the dotted line, using the same method as explained in connection with c J) m elevation in Fig. 117. The coppersmith has often occasion to lay out the patterns for curved elbows. While the sheet metal worker lays them out Fig. 119. SHEET METAL WORK 113 in pieces, the coppersmith's work must form a curve as shown in Fig. 120 which represents a curved elbow of 45°. In Fig. 121 is shown how an elbow is laid out having 90°, similar principles being required for any degree of elbow. First draw the side elevation of the elbow as shown by A B C D, mak- Fig. 121. Fig. 120. ing the radius E J3 equal to dj inches and the diameter B C 2 inches. Bisect C B at K. Then with E as center and E K as radius draw the arc K J representing the seam at the sides. Draw the front view in its proper position as F G H, through which draw the center line F I representing the seam at back and front, thus making the elbow in four pieces. Directly below C B draw 114 SHEET METAL WORK the section of the elbow as shown hj a h c d struck from M as center. Through M draw the diameters h d and a c. The inner curve of the elbow a d c in plan will be stretched, while the outer curve ahem plan will be raised. Through M draw the diagonal 3 6 intersecting the circle at 3 and f respectively. Now draw a d; through/" parallel to a d draw a line intersecting the center line A E extended at O. On either side of/' place the stretchout of 6 a and 6 (^ as shown hjfa' andy^Z'. Then with radii equal to O d' and O a and with O on the line A B, Fig. 122, as center describe the arcs d d and a a. Make the length of d d equal to the inner curve D C in Fig. 121. From a and d in Fig. 122 draw lines to the apex O extending them to meet the outer curve at a and a. Then will a d d a\>Q the half pattern for the inner portion of the elbow for two sides. The radius for the pattern for the outer curve is shown in Fig. 121 by N c\ N b\ placing the SHEET METAL WORK iin stretchout of the curve on either side of the point e. hh c cm Fig. 122 shows the pattern for the outer curve, the length h h being obtained from A B in elevation in Fig. 121. In work of this kind the patterns are made a little longer, to allow for trimming after the elbow is brazed together. Laps must be allowed on all patterns for brazing. Fig. 123 shows a perspective view of a brewing kettle, made in horizontal sections and riveted. The same principles which were employed for obtaining the patterns for a sphere in Fig. 114 are applicable to this problem. Thus in Fig. 124, let A B C rep- resent a full section of a brewing kettle as required according to architect's design. Through the middle of the section draw the center line D E. Now divide the half section B to C into as many parts as the kettle is to have pieces as shown by ah and h a as shown. In precisely the same manner obtain the intersection c* and d' at the bottom. IS^ow through the intersections V ah a' and d' c d c' draw the curve as shown by bend- ing the straight-edge or any straight strip of wood placed on edge and brought against the various intersections, extending the curves at the ends and top and bottom indefinitely. Since the circumfer- ence of the circle is more than three times the diameter, and as we only have three times the diameter as shown from c to d' and h' to a\ then multiply .1416 times the bottom and top diameter d c and a h respectively, and place one-half of the amount on either side of the bottom and top curves as shown by e^ e\ and A, h', Now take one-half of seven times the thickness of the metal in use and place 122 SHEET METAL WOKK it on eitlier side on the bottom and top curves as shown hyj^^f and /, /', and draw a line from i to /and i' tof. To this lap must be allowed for riveting. Tiie desired pattern is shown by i iff. Fig. 131 shows a three-pieced elbow made from heavy metal, the two end pieces fitting into the center pieces, to which laps' are allowed for riveting. The principles which shall be explained to cut these patterns and make the necessary allowance for any thick- ness of metal is applicable to any elbow. In Fig. 132 draw as previously described the elbow ABC, below G H draw the section of the inside diameter as D which is struck from «, and divide into equal spaces as shown by the figures 1 to 5 on both sides. Through these figures draw vertical lines intersecting the miter line h 7 31,--?^ 1 1 1 1 1 |E 1 \ 1 2^- -1 1 1 1 1 1 • 1 1 1 1 1 1 I 2 3 4 5 6 7 6 5 4 3 2 e Fig. 140. any number of sides, in this case being C sides or a hexagon. The more sides the polygon has, the nearer to a true spiral will the figure be. Therefore number the corners of the hexagon 1 to WORK AND PLUMBING. 5 and draw out each side indefinitely as 1 «, 2 ^, 3 (?, 4 ^, 5 6, and 6y. Now using 2 as center and 2 1 as radius, describe the arc 1 A; then using 3 as center and 8 A as radius, describe the arc 130 SHEET METAL WORK A B, and proceed in similar manner using as radii 4 B, 5 C, 6 D. and 1 E, until the part of the spiral shown has been drawn. Then using the same centers as before continue until the desired spiral is obtained, the following curves running parallel to those first drawn. The size of the polygon a\ determines the size of the spiral. In Fig. 143 let A B C D represent the elevation of one corner of the flag sign shown in Fig. 141. In its proper position in Fig. 143 draw a section of the scroll through its center line in elevation as shown by a 17 to 1, which divide into equal spaces as shown from 1 to 17. Supposing the scroll is to be made of J inch thick Fig. 142. metal, and as the spiral makes two revolutions then multiply J by 14, w^hich would equal 1| inches. Then on E F in Fig 144 place the stretchout of the spiral in Fig. 143, as shown by similar numbers, to which add 17 E equal to 14 times the thickness of metal in use, and draw the arc E 17' in the usual manner and obtain the true stretchout with the various intersections as shown. Through the elevation of the corner scroll in Fig. 143 draw the center line E F, upon which place tlie stretchout of 17' E, Fig. 144, as shown by similar numbers on EF in Fig. 143. At right angles to E F, through land 17', draw 17^ 17^" equal to AB and I'' l'^ equal to the desired width of the scroll at that point. Then at pleasure draw the curve l'^ 17° on either side, using the straight- SHEET METAL WORK 131 n^. 143. 132 SHEET ]V1ETAL WORK edge and bending it as required. Then will 1° 1° 17" IT be the pattern for the scroll using heavy metal. If it is desired to know how this scroll will look when rolled up, then at right angles to E F and through the intersections 1' to 17' draw lines intersecting the curves of the pattern 1°-17° on both sides. From these intersections, shown on one side only, drop lines intersecting similar numbered lines, drawn from the intersections in the profile of the scroll in section parallel to A B. To avoid a confusion of lines the points 1^, 3^, 5^, 7^, 10^, 12^, and 17^ have only been intersected. A line traced through points thus obtained as shown from 1^ to 17^ in elevation gives the pro- jections at the ends of the scroll when rolled up. SKYLIGHT WORK* The upper illustration shows the layout of a flat pitched skylight whose curb measures 6' — 0" X 7' — 6'', the run of the rafter or length of the glass being 6' 0" on a horizontal line. Five bars are required, making the glass 15 inches wide A working section through AB and CD is shown below. It will be noticed in the section through AB that the flashing is locked to the roofing and flanged around the inside of the angle iron construction; over this the curb of the skylight rests, bolted through the angle iron as shown, the bolt being capped and soldered to avoid leakage. The same construction is used in the section through CD, with the excep' tion, that when the flashing cannot be made in one piece, a cross lock is placed in the manner indicated, over the fireproof blocks. * The illustration referred to will be found on the back of this page. COri5TDUCTIOri DuAV/ina aHOWIMG LAYOUT OF FLAT aKVL^IGRT AJiB i^lETrtOD OF FA5TE:n.in.G FLAaamo on amgle. luon con5TR.ucTior\. •Ile>^s'hm^ Conde. n5 aj; i on. tube -Roof ^^^^ Section throao,h lower ena of ourb ^-B aection through u.ppe.r end of ot^rb C-D FOR EXPLANATION OF THIS PROBLEM SEE BACK OF PAGE SHEET METAL WORK PART III SKYLIGHT WORK Where formerly skylights were constructed from wrought iron or wood, to-day in all the large cities they are being made of galvanized sheet iron and copper. Sheet metal skylights, having by their peculiar construction lightness and strength, are superior to iron and wooden lights; superior to iron lights, inasmuch as there is hardly any expan- sion or contraction of the metal to cause leaks or breakage of glass; and superior to wooden lights, because they are fire, water and condensa- tion* proof, and being less clumsy, admit more light. The small body of metal used in the construction of the bar and curb and the provisions which can be made to carry off the inside con- densation, make sheet metal skylights superior to all others constructed from different material. CONSTRUCTION The construction of a sheet metal skylight is a very simple matter, if the patterns for the various intersections are properly devel- oped. For example, the bar shown in Fig. 145 consists of a piece of sheet metal having the required stretchout and length, and bent by special machinery, or on the regular cornice brake, into the shape shown, which rep- resents strength and rigidity with the least amount of weight. A A represent the condensation gut- ters to receive the condensation Fig. 145. Fig. 146. from the inside when the warm air strikes against the cold surface of the glass, while B B show the rabbets or glass-rest for the glass. In Fig. 146; C C is a re-enforcing strip, which is used to hold the 134 SHEET INIETAL WORK two walls O O together and impart to it great rigidity. When skylight bars are required to bridge long spans, an internal core is made of sheet metal and placed as shown at A in Fig. 147, which adds to its weight-sustaining power. In this figure B B shows the glass laid on a bed of putty with the metal cap C C C, resting snugly against the glass, fastened in position by the rivet or bolt D D. Where a very large span is to be bridged a bar similar to that shown in Fig. 148 is used. A heavy core plate A made of J-inch thick metal is used, riveted or bolted to the bar at B and B. In construction, all the various bars terminate at the curb shown at A B C in Fig. 149, which is fastened to Fig- 147. the wooden frame D E. The condensation gutters C C in the bar b, carry the water into the internal gutter in the curb at a, thence to the outside through holes provided for this purpose at F F. In Fig. 150 is shown a sectional view of the construction of a double-pitched skylight. A shows the ridge bar with a core in the center and cap attached over the glass. B shows the cross bar or clip which is used in large skylights where it is impossible to get the glass in one length, and where the glass must be protected and leakage prevented by means of the cross bar, the gutter of which conducts the water into the gutter of the main bar, thence outside the curb as before explained. C is the frame generally made of wood or angle iron and covered by the metal roofer with flash- ing as shown at F. D shows the skylight bar with core showing the glass and cap in position. 148. Fig E is the metal curb against which the bars terminate, the condensation being let out through the holes shown. In constructing pitched skylights having double pitch, or being hipped, the pitch is usually one-third. In other words it is one-third SHEET ]\IETAE WORK 135 of the span. If a skylight were 12 feet wide and one-third pitch were required, the rise in the center would be one-third of 12, or 4 feet. When a flat skylight is made the pitch is usually built in the wood or iron frame and a flat skylight laid over it. The glass used in the construction of metallic sky- lights is usually f-inch rough or ribbed glass; but in some cases heavier glass is used. If for any reason it is desired to know the weight of the various thickness of glass^ the following table will prove valuable. Weight of Rough Glass Per Square Foot. Thickness in inches. 3 1. Weight in pounds. Z% Ji~ot 0'9» o. 7. o^ 10. 12*. Fig. 149 Fig. 150. 136 SHEET METAL WORK SHOP TOOLS In the smaller shops the bars are cut with the hand shears and formed up on the ordinary cornice brake. In the larger shops, the strips required for the bars or curbs are cut on the large squaring shears, and the miters on the ends of these strips are cut on what is known as a miter cutter. This machine consists of eight foot presses on a single table, each press having a different set of dies for the purpose of cutting the various miters on the various bars. The bars are then formed on what is known as a Drop Press in which the bar can be formed in two operations to the length of 10 feet. METHOD EMPLOYED IN OBTAINING THE PATTERNS The method to be employed in developing the patterns for the various skylights is by parallel lines. If, however, a dome, conserva- tory or circular skylight is required, the blanks for the various curbs, bars, and ventilators are laid out by the rule given in the dis- cussion of circular mouldings beginning on page 249. VARIOUS SHAPES OF BARS In addition to the shapes of bars shown in Figs. 145 to 148 in- clusive, there is shown in Fig. 151 a plain bar without any condensation gutters, the joint being at A. BE represents the glass resting on the rabbets of the bar, while C shows another form of cap which covers Mswwmws imm\\^^^^ ?XL^ Fig. 152. Fig. 153. the joint between the bar and glass. Fig. 152 gives another form of bar in which the condensation gutters and bar are formed from one piece of metal with a locked hidden seam at A. Fig. 153 shows a bar on which no putty is required when glazing. It will be noticed that it is bent from one piece of metal with the seam at A, the glass B B resting on the combination rabbets and gutters C C. D is the cap which is fastened by means of the cleat E. These cleats are cut about i-inch wide from soft 14-oz, copper, and riveted to the top of the bar SHEET INIETAL \\ORK 137 at F; then a slot is cut into the cap D as shown from a to & in Fig. 154; then the cap is pressed firmly onto the glass and the cleat E turned down which holds the cap in position. When a skylight is constructed in which raising sashes are re- quired, as shown in Fig. 155, half bars are required at the sides A and B, while the bars on each side of the sash to be raised are so constructed that a water-tight joint is obtained when closed. This is shown in Fig. 156, which is an enlarged section tlii'ough A B in Fig. 155. Thus in Fig. 156, A A represents the two half bars with condensation gutters as shown, the locked seam taking place at B B. C C repre- sent the two half bars for the raising sash with the caps D D attach- ed to same, as shown, so that when the sash C C is closed, the caps Fig. 154. Fig. 155. D D cover the jomt between the glass E E and the stationary half bars. F F are the half caps soldered at a a to the bars C C which protect the joints between the glass H H and the bars C C. VARIOUS SHAPES OF CURBS In Figs. 157, 158 and 159 are shown a few shapes of curbs which are used in connection with flat skylights. A in Fig. 157 shows the curb for the three sides of a flat skylight, formed in one piece with a joint at B, while C shows the cap, fastened as previously described. ''A" shows the height at the lower end of the curb, wh^'ch is made as high as the glass is thick and allows the water to run over. In Fig. 158, A is 138 SHEET METAL WORK anothe/ form of skylight formed in one piece and riveted at B; a shows the height at the lower end In the previous figures the frame on which the metal curb rests is of wood, while in Fig. 159 the frame is Fig 157 Fig. 158 Fig. 159, of angle iron shown at A. in this case the curb is slightly changed as shown at B ; bent in one piece, and riveted at C. In Figs. 160, 161 , and 162 are shown var'ous shapes of curbs for pitched skylights in addition "o that shown in Fig. 149 A in Fig. 160 shows a curb formed in one piece from a to b with a condensation hole or tube shown at B. Fig. 160 Fig. 161. Fig. 162. In Fig. 161 is shown a slightly modified shape A, with an offset to rest on the curb at B. When a skylight is to be placed over an opening whose walls are brick, a gutter is usually placed around the wall, a& SHEET METAL \TORK 139 shown in Fig. 162, in which A represents a section of the wall on which a gutter, B, is hung, formed from one piece of metal, as shown from a to h to c. On top of this the metal curb C is soldered, which is also formed from one piece with a lock seam at i. To stiffen this curb a wooden core i END OF HOOD HALF PATTERN FOR EfsJD OF OUTSIDE VENT 2" 3" 4" H G B Fig. 179. Fig. 180. HALF PATTERN FOR END OF INSIDE VENT Fig. 181. stretchout oihijkl in Fig. 178 and place it on the vertical line A B in Fig. 180 as shown by similar letters, through which draw horizontal lines making them in length, measuring from A B, equal to similar letters in Fig. 178, also measuring from the center line A B. Connect the points as shown in Fig. 180 which is the desired half pattern. In Fig. 181 is shown the half pattern for the end of the inside ventilator, the stretchout of which is obtained from F V "2!' Z" ^' H G in Fig. 178, the pattern being obtained as explained in connection with Figs. 179 and 180. When a skylight is to be constructed on which the bars are of such lengths that the glass cannot be obtained in one length, and a cross bar or clip is required as shown by B, in Fig. 150, which miters against the main bar, the pattern for this intersecting cut is obtained as shown in 152 SHEET METAL WORK Fig. 182. Let A represent the section of the main bar, B the elevation of the cross bar, and C its section. Note how this cross bar is bent so that the water follows the direction of the arrow, causing no leaks be- cause the upper glass a is bedded in putty, while the lower light b is capped by the top flange of the bar C (See Fig. 150). Number all of the corners of the section C as shown, from 1 to 8, from which points draw horizontal lines cutting the main bar A at points 1 to 8 as showuo At right angles to the lines in B draw the vertical line D E upon wh?eh 1 2 u Ol^ -wmimmmm fc-_Z^^ 3 A- C 6'i PATTERN FOR CROSS BAR 8 Fig, 182. place the stretchout of the cross bar C, shown by similar figures, through which draw horizontal lines, intersecting them with lines drawn parallel to D E from similar numbered intersections against the main bar A, thus obtaining the points of intersections 1' to 8' in th^ pattern. Trace a line through points of intersections thus obtained which will be the pattern for the end cut of the cross bar. In Fig. 183 is shown a carefully drawn working section of the turret sash shown in Fig. 168 at A- These sashes are operated by SHEET METAL WORK 153 means of cords, chains or gearings from the inside, the pivot on which they turn being shown by R S in Fig. 183. The method of obtaining the patterns for these sashes will be omitted, as they are only square and butt miters which the student will have no trouble in developing, pro- viding he understands the construc- tion. This will be made clear by the following explanation : A B represents the upper part of the turret proper with a drip bent on same, as shown at B, against which the sashes close, and a double seam, as shown at A, which makes a tight joint, takes out the twist in bending, and avoids any soldering. This up- per part A B is indicated by C in Fig. 168, over which the gutter B is placed as shown by X U Y in Fig. 183. C D represents the lower part of the turret proper or base, which fits over the wooden curb W, and is indicated by D in Fig. 168. E in Fig. 183 represents the muUion made from one piece of metal and double seamed at a. This mullion is joined to the top and bottom. The pattern for the top end of the mullion would simply show a square cut, while the pattern for the bot- tom would represent a butt miter against the slant line i j. Before forming up this mulHon the holes should be punched in the sides to admit the pivot R S. These mullions are shown in position in Fig. 168 by E E, etc. F G in Fig. 183 represents the section of the side of the sash below the pivot T. Notice that this lower half of the side of the sash has a lock attachment which hooks into the flange of the mullion E at F. While the side of the sash is bent in one piece, the upper half, above tiie pivot T, has the lock omitted as shown by J K. Thus when the sash opens, the upper half of the sides turn towaru the inside as shown by Fig. 183. 154 SHEET METAL WORK the arrow at the top, while the lower half swings outward as shown by the arrow at the bottom. When the lower half closes, it locks as shown at F, which makes a water-tight joint; but to obtain a water-tight joint for the upper half, a cap is used, partly shown by L M, into which the upper half of the side of the sash closes as shown at M. This cap is fastened to the upper part of the muUion E with a projecting hood / which is placed at the same angle as the sash will have when it is opened as shown by e e' and d d! or by the dotted lines. The side of the sash just explained is shown in Fig. 168 at H. The pattern for the side of the sash has a square cut at the top, mitering with H I at the bottom, in Fig. 183, the same as a square miter. H I represents the section of the bottom of the sash. Note where the metal is doubled as at 6, against which the glass rests in line with the rabbet on the side of the sash. A beaded edge is shown at H which stiffens it. This lower section is shown in Fig. 168 by G and has square cuts on both ends. N O in Fig. 183 shows the section of the top of the sash shown in Fig. 168 by F. The flange N in Fig. 183 is flush with the out- side of the glass, thereby allowing the glass to slide into the grooves in the sides of the sash. After the glass is in position the angle P is tacked at n. A leader is attached to the gutter Y as shown by B° in Fig. 168. While the method of construction shown in Fig. 183 is generally employed, each shop has different methods; what we have aimed to give is the general construction in use, after knowing which, the student can plan his own construction to suit the conditions which are apt to arise. In the following illustrations. Figs. 184 to 187, it will be explained how to obtain the true lengths of the ventilator, ridge, hip, jack, and common bars in a hipped skylight, no matter what size the skylight may be. Using this rule only one set of patterns are required, as for example, those developed in connection with Figs. 178, 179, 180, and 181, vvhich in this case has one-third pitch. Tf, however, a skylight was required whose pitch was different than one- third, a new set of patterns would have to be developed, to which the rule above mention* SHEET METAL WOKK 155 ed would also be applicable for skylights of that particular pitch. Using this rule it should be understood that the size of the curb, or frame, forms the basis for all measurements, and that one of the lines or bendsof the bar should meet the line of the curb as shown in Fig. 178, where the bottom of the bar E in the half section meets the line of the curb c 4' at 4', and the ridge at the top at 4'. Therefore when laying 12 11 10 9 8 7 6 5 Fig. 185. out the lengths of the bars, they would have to be measured on the line 4 of the bar E from 4' to 4'' on the patterns, as will be explained as we proceed. The first step is to prepare the triangles from which the lengths of the common and jack bars are obtained, also the lengths of the hip bars. After the drawings and patterns have been laid out full size according to the principles explained in Fig. 178, take a tracing of the triangle in the half section D C 4' and place it as shown by A 12 O, in Fig. 184. Divide O 12, which will be 12 inches in full size, into quarter, half-inches, and inches, the same as on a 2-foot rule, as shown by the figures O to 12. From these divisions erect lines until they intersect the pitch A O which completes the triangle for obtaining the true lengths of jack and common bars for any size skylight. In similar manner take tracing of N R 4^ in the diagonal elevation in Fig. 178 and place it as shown by B 12 O in Fig. 185. The length 12 O then becomes the base of the triangle for the hip bar in a skylight whose base of the triangle for the common and jack bars measures 12 inches Fig. 186. 156 SHEET METAL \VOKJ> -.X as shown in Fig. 184, the heights A 12 in Fig. 184 and B 12 in Fig. 185 being equal. Now divide 12 O in 12 equal spaces which will represent inches when obtaining the measurements for the hip bar. Divide each of the parts into quarter-inches as shown. From these devisions erect lines intersecting the hypothenuse or pitch line B O as shown. To explain how these triangles are used in practice, Figs. 186 and 187 have been prepared, showing respectively a skylight without and with a ventilator whose curb measures 4 ft. x 8 ft. Three rules are used in connection with the triangles in Figs. 184 and 185, the comprehension of which will make clear all that follows. Rule I. To obtain the length of the ridge bar in a skyhght without a ventilator, as in Fig. 186, deduct the short side of the frame or curb from the long side. Example: In Fig. 186, take 8 feet (long side of frame)— 4 feet (short side of frame) = 4 feet (length of ridge bar a b). Rule 2. To find the length of the ventilator in a skylight deduct the short side of the frame from the long side and add the width of the desired ventilator (in this case 4 inches, as shown in Fig. 187). Example: In Figure 187 take 8 feet (long side of frame) — 4 feet (short side of frame) = 4 feet. 4 feet + 4 inches (width of inside ventilator) = 4 feet 4 inches, (length of inside ventilator a' 6'). To find the size of the outside ventilator h I and hood m p in Fig. 178 simply add twice the distance a b and a c respectively to the above size, 4 inches, and 4 feet 4 inches, which will give the widths and lengths of the outside vent and hood. Rule 3. To find the lengths of either common or hip bar (in any size skylight) deduct the width of the ventilator, if any, from the length of the shortest side of frame and divide the remainder by two. Apply the length thus obtained on the base line of its respective triangle for common or hip bars and determine the true lengths of the desired bars, from the hypothenuse. Example: As no ventilator is shown in Fig. 186, there will be nothing to deduct for it, and the operation is as follows: 4 feet (short- SHEET METAL WORK 157 est side of frame) -7-2=2 feet. We have now the length with which to proceed to the triangle for common and hip bars. Thus the length of the common bar c d will be equal to twice the amount of A O in Fig. 184, while the length of the hip bar b ein Fig. 186, will be equal to twice the amount of B O in Fig. 185. Referring to Figs. 186 and 187 the jack bars i j are spaced 16 inches, therefore, the length of the jack bar for 12 inches will equal A O in Fig. 184, and 4 inches equal to 4° O; both of which are added together for the full length. The lengths of the common and hip bars will be shorter in Fig. 187 because a ventilator has been used, while in Fig. 186 a ridge bar was employed. To obtain the lengths of the common and hip bars in Fig. 187 use Rule 3: 48 inches (length of short side) — 4 inches (width of inside ventilator) = 44 inches; and 44 inches -^ 2 = 22 inches or 1 foot 10 inches. Then the length of the common bar c' d' measured with a rule will be equal to A O in Fig. 184 and 10° O added together, and the length of the hip bar e^ f in Fig. 187 will be equal to B O in Fig. 185 and 10^ O added together. Use the same method where fraction- al parts of an inch occur. In laying out the patterns according to these measurements use the cuts shown in Figs. 178, 179, 180, and 181, being careful to measure from the arrowpoints shown on each pattern. It will be noticed in Fig. 178 we always meas- ure on line 4 in the patterns for the hip, common, and jack bars. This is done because the line 4 in the profiles E and E^ come directly on the slant line of the triangles which were traced to Figs. 184 and 185 and from which the true lengths were obtained. Where a curb might be used, as shown in Fig. 188, which would bring the bottom line of the bar 1^ inches toward the inside of the frame h, all around, then instead of using the size of 4 x 8 feet as the basis of measurements deduct 3 . inches on each side, making the basis of measurements 3 ft. 9 inches X 7 ft. 9 inches, and proceed as explained above. 158 SHEET METAL WORK ROOFING A good metal covering on a roof is as important as a good foun- dation. There are various materials used for this purpose such as terne plate or what is commonly called roofing tin. The rigid body, or the base of roofing tin, consists of thin sheets of steel (black plates) that are coated with an alloy of tin and lead. Where a first-class job is desired soft and cold rolled copper should be used. The soft copper is generally used for cap flashing and allows itself to be dressed down well after the base flashing is in position. The cold-rolled or hard cop- per is used for the roof coverings. In some cases galvanized sheet iron or steel is employed. No matter whether tin, galvanized iron, or copper is employed the method of construction is the same, and will be explained as we proceed. Another form of roofing is known as corrugated iron roofing, which consists of black or galvanized sheets, corrugated so as to secure strength and stiffness. Roofs having less than one-third pitch should be covered by what is known as flat-seam roofing, and should be cover- ed (when tin or copper is used) with sheets 10x14 inches in size rather than with sheets 14 x 20 inches, because the larger number of seams stiffens the surface and prevents the rattling of the tin in stormy weather. Steep roofs should be covered by what is known as standing- seam roofing made from 14^' x 20'' tin or from 20" x 28". Before any metal is placed on a roof the roofer should see that the sheathing boards are well seasoned, dry and free from knots and nailed close together. Bef or claying the tin plate a good building paper, free from acid, should be laid on the sheathing,or the tin plate should be painted on the under- side before laying. Corrugated iron is used for roofs and sides of buildings. It is usually laid directly upon the purlins in roofs, and held in place by means of clips of hoop iron, which encircle the purlins and are riveted to the corrugated iron about 12 inches apart. The method of constructing flat and double-seam roofing, also corrugated iron coverings, will be explained as we proceed. TABLES The following tables will prove useful in figuring the quantity of material required to cover a given number of square feet. SHEET MEl AL WORK 159 FLAT-SEAM ROOFING Table showing quantity of 14 x 20-inch tin required to cover a given number of square feet with flat seam tin roofing. A sheet of 14 x 20 inches with with ^-inch edges measures, when edged or folded, 13 x 19 inches or 247 square inches. In the following all fractional parts of a sheet are counted a full sheet. 100 no 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 r„ '^ -d No. of sq. ft. 59 330 193 65 340 199 70 350 205 76 360 210 82 370 216 88 380 222 94 390 228 100 400 234 105 410 240 111 420 245 117 430 251 123 440 257 129 450 263 135 460 269 140 470 275 146 480 280 152 490 286 1.58 500 292 164 510 298 170 520 304 175 530 309 181 540 315 187 550 321 5 6' en 78 49 15 16 4 48 83 33 109 50 16 17 4 79 84 23 28 51 16 18 4 110 85 23 59 52 16 19 5 29 86 23 90 53 16 20 n 60 87 24 9 54 17 21 5 91 88 24 40 65 17 22 6 10 89 24 71 56 17 23 6 41 90 24 102 57 18 24 6 72 91 25 21 58 18 25 fi 103 92 25 52 59 18 26 7 23 93 25 83 60 19 27 7 53 94 26 3 61 19 28 7 84 95 26 33 62 19 29 8 3 96 26 64 63 19 30 8 34 97 26 95 64 20 81 8 65 98 27 14 65 20 32 8 96 99 87 45 66 20 33 9 15 100 27 76 67 21 1 34 9 46 Size of sheet before working, 20 X 28 inches. Square inches per sheet exposed 479} inches. Exposed on roof 27X1 7f inches. Sheets per box 112. SITKKT AIKIWT. WORK IC)! NET WEIGHT PER BOX TIN PLATES Basis 14 X 20, 112 Trade term • • • 80-lb. 85-lb. 90-lb. 95-lb. 100-lb. IC IXL IX IXX IXXX IXXl 1 Weight per box, lb. 80 85 90 95 100 107 128 135 155 175 195 Size of Sheets sheets per box 80 85 90 95 100 107 128 135 155 175 10 X 14 225 195 14 X 20 112 80 85 90 95 100 107 128 135 155 175 195 20 X 28 112 160 170 180 190 200 214 256 270 310 350 390 10 X 20 225 114 121 129 136 143 153 183 193 221 250 279 11 X 22 225 138 147 156 164 172 184 233 234 268 303 337 WA X 23 225 151 161 170 179 189 203 343 255 393 331 368 12 X 12 225 82 87 93 98 103 110 133 139 159 180 201 12 X 24 112 82 87 93 98 103 110 133 139 159 180 301 13 X 13 225 97 103 109 115 121 129 154 163 187 211 235 13 X 26 113 97 103 109 115 121 129 154 163 187 311 235 14 X 14 225 112 119 136 133 140 150 179 189 317 345 273 14 X 28 112 112 119 126 133 140 160 179 189 317 245 273 15 X 15 225 129 137 U5 153 161 172 206 217 349 281 313 16 X 16 225 146 155 lo5 174 183 196 234 247 283 320 357 17 X 17 225 165 175 186 196 306 221 264 279 320 361 403 18 X 18 112 93 98 104 110 116 124 148 156 179 202 226 19 X 19 152 103 110 116 123 129 138 165 174 200 236 251 20 X 20 112 114 121 129 136 143 153 183 193 221 260 279 21 X 21 112 126 134 142 150 158 169 203 213 244 276 307 22 X 22 112 138 147 156 164 172 184 321 234 268 302 337 23 X 23 112 151 161 170 179 189 202 243 255 298 331 368 24 X 24 112 164 175 185 195 204 230 263 278 319 360 401 26 X 26 112 193 205 217 229 241 358 309 826 374 423 471 16 X 20 112 91 97 103 109 114 133 146 154 177 200 223 14 X 31 112 134 133 140 147 155 166 198 209 240 271 303 uy^-x 22Y^ 112 73 78 83 87 91 98 n\i X 1734 112 60 71 76 80 84 90 13K X 191^ 112 73 77 83 87 91 97 isy2 X 19^ 112 75 80 85 89 94 100 131/^ X 19% 112 76 81 86 90 95 103 14 X 18K 124 83 88 93 98 103 110 14 X 19K 120 83 88 93 98 103 110 14 X 21 112 84 89 95 100 105 113 14 X 22 112 88 94 99 105 110 118 14 X 225^ 112 89 95 100 106 111 119 15H X 23 113 103 108 115 121 137 136 STANDARD WEIGHTS AND GAUGES OF TIN PLATES Trade term Nearest wire gauge No. Weight, square foot, lb. Weight, box, 14 x 20, lb. 65-lb. 70^1b. 75-lb. 80-lb. 85-lb. 90-lb. 95-lb. 35 35 34 33 32 31 31 .298 .322 .345 .367 .390 .413 .436 65 70 75 80 85 90 95 100-lb. 30 .459 100 Trade term Nearest wire gauge No Weight, square foot, lb. Weight, box, 14 x 20, lb. , IC IXL IX 30 28 28 .491 .5»8 .619 107 128 135 IXX 27 .712 1.55 IXXX 26 .803 175 IXXXX 25 895 195 ixxxxx 24 .987 215 IC 14x20 IC 20 X 28 IX 14 X 20 IX 20 X 28 Black elates before coating . . weight per 112 sheets lb. 95 to 100 lb. 190 to 200 lb. 125 to 130 lb. 250 to 260 When coated the plates weigh per 112 sheets. 115 to 120 230 to 240 145 to 150 290 to 300 162 SHEET METAL WORK OTHER FORMS OF METAL ROOFING There is another form of roofing known as metal slates and shin- gles, pressed in various geometrical designs with water-tight lock attach- ments so that no solder is required in laying the roof. Fig. 189 shows the general shape of these metal shingles which are made from tin, galvanized iron, and copper, the dots a a a a representing the holes for nailing to the wood sheathing. In Fig. 190, A represents the side lock, showing the first operation in laying the metal slate or shingle on a roof, a representing the nail. B, in the same figure, shows the metal slate or shingle in position cover- ing the nail b, the valley c of the bottom ^^^- ^^^- slate allowing the water, if any, to flow over the next lower slate as in A in Fig. 189. In Fig. 191 is shown the bottom slate A covered by the top slate B, the ridges a a a keeping the water from backing up. Fig. 192 shows the style of roof on which these shingles are employed, that is, on steep roofs. Note the con- struction of the ridge roll, A and B in Fig. 192, which is first nailed in position at a a etc., after which the shingles B are slipped under the lock c. Fig. 193 shows sheathing board a roll hip covering which is laid from the -^^S- 190. top downward, the lower end of the hip having a projection piece for nailing at a, over which the top end of the next piece is inserted, thus 5HEATHING BOARD ^ Fig. 191. covering and concealing the nails. Fig. 194 represents a perspective view of a valley with metal slates, showing how the slates A are locked to the fold in the valley B. There are many other forms of suKF/r AiryrAj. work k; )6 metal shingles, but the shapes shown herewith are known as the Cortright patents. TOOLS REQUIRED Fig. 195 shows the various hand tools required by the metal roof- e)*; starting at the left we have the soldering copper, mallet, scraper, Fig. 192. stretch-awl, shears, hammer, and dividers. In addition to these hand tools a notching machine is required for cutting off the corners of the Fig. 193. sheets, and roofing folders are re- quired for edging the sheets in flat- seam roofing, and hand double seamer and roofing tongs for standing-seam roofing. The roofing double seamer and squeezing tongs can be used for ,,. , standing-seam roofing (in place of the Fig. 194. . hand double seamer), which allow the operator to stand in an upright position if the roof is not too steep. ROOF MENSURATION While some mechanics understand thoroughly the methods of 104 SHEET METAT. AYORK laying the various kinds of roofing, there are some, however, who do not understand how to figure from architects' or scale drawings the amount of material required to cover a given surface in a flat, irregular shaped, or hipped roof. The modern house with its gables and va- Fig. 195. rious ipicrsecting roofs, forming hips and valleys, render it necessary to give a short chapter on roof measurement. In Figs. 196 to 198 in- clusive are shown respectively the plans with full size measurements for a flat, irregular, and intersected hipped roof, showing how the length of the hips and valleys are obtained direct from the architects' scale drawings. The illustrations shown herewith are not drawn to a scale as architects' drawings will be, but the measurements on the diagrams are as- sumed, which will clearly show the principles which must be applied when figuring from scale drawings. Assuming that the plans from which we are figuring are drawn to a quarter-inch scale, then when measurements are taken, every quarter inch represents one foot. J inch = 6 inches, ^V inch = 3 inches, etc. If the drawings were drawn to a half-inch scale, then J inch ==12 inches, J inch = 6 inches, J inch = 3 inches, ^\ inch = 1} inches, etc. A B C D in Fig. 196 represents a flat roof with a shaft at one side as shown hy ab c d. In a roof of this kind we will figure it as if there was no air shaft at all. Thus 64 feet X 42 feet = 2,688 square feet. The shaft is 12.5 X 6 feet = 75 square feet; then 2,688 feet - 75 feet - Fig. 196. SHEET METAL WORK 105 B X- n o 9-0"k 0) 2,613 square feet of roofing, to which must be added an allowance for the flashing turning up against and into the walls at the sides. In Fig. 197 is shown a flat roof with a shaft at each side, one shaft being irregular, forming an irregular shaped roof. The rule for obtaining the area is sim- ilar to that used for Fig. 196 with the exception that the area of the irregular shaft a; rr a: a; in Fig. 197 is determined differently to that of the shaft hcde. Thus A B C D = 108 feet X 45 feet = 4,860 square feet. Find the area oi h c d e which is 9.25 X 39.5 - 365.375 or 365f square feet. To find the area of the irregular shaft, bisect xx and xx and obtain a a, measure the length of a a which is 48 feet, and multiply by 9. Thus 48 X 9 = 412, and 412 + 365.375 = 777.375. The entire roof minus the shafts = 4,860 square feet - 777.375 = 4,082.625 square feet of surface in Fig. 197. Fig. 197. In Figc 198 is shown the plan, front, and side elevations of an in- tersected hipped roof. A B C D represents the plan of the main build- i (0 c b . d e 9-3 'V A5-0"- SIDE ELEVATION Fig. 198. mg intersected by the wing E F G H. We will first figure the main roof as if there were no wing attached and then deduct the space taken 16G SHEET METAL WORK up by the intersection of the wing. While it may appear difficult to some to figure the quantities in a hipped roof, it is very simple, if the rule is understood. As the pitch of the roof is equal on four sides the length of the rafter shown from O to N in front elevation represents the true length of the pitch on each side. The length of the buildin j: at the eave is 90 feet and the length of the ridge 48 feet. Take 90 - 48 = 42, and 42 -f- 2 = 21. Now either add 21 to the length of t!ie edge or deduct 21 from the length of the eave, which gives 69 feet as shown from S to T. The length of the eave at the end is 42 feet ani it runs to an apex at J. Then take 42 feet -^ 2 = 21, as shown from T to U. If desired the hip lines A I, J B and J C can be bisected, obtain- ing respectively the points S, T, and U, which when measured will be of similar sizes; 69 feet and 21 feet. As the length of the rafter O N is 30 feet, then multiply as follows: 69 X 30 = 2070. 21 X 30 = 630. Then 630 + 2,070 = 2,700, and multiplying by 2 (for opposite sides) gives 5,400 square feet or 54 squares of roofing for the main building. From this amount deduct the intersection E L F in the olan as follows : The width of the wing is 24 feet 6 inches and it intersects the main roof as shown at E L F. Bisect E L and L F and obtain points W and V, which when measured will be 12 feet 3 inches or one half of HGj 24 feet 6 inches. The wing intersects the main roof from Y to F^ in the side elevation, a distance of 18 feet. Then take 18 X 12.25 = 220.5. Deduct 220.5 from 5400 = 5,179.5. The wing measures 33 feet 6 inches at the ridge L M, and 21 feet 6 inches at the eave F G, tlius making the distance from V to X =27 feet 6 inches. The length of the rafter of the wing is shown in front elevation by P R, and is 18 feet. Then 18 X 27.5 = 495, and multiplying by 2 (for opposite side), gives 995 sq. ft. in the wing. We then have a rooting area of 5,179.5 square feet in the main roof and 995 square feet in the wing, making a total of 6,174.5 square feet in the plan shown in Fig. 198. If it is desired to know the quantity of ridge, hips, and valleys in the roof, the following method is used. The ridge can be taken from the plans by adding 48' + 33'6'' = 81' - 6". For the true length of the hip I D in the plan, drop a vertical line from I* in the front elevation until it intersects the eave line P. On the eave line extended, place the distance I D in the plan as shown from 1° to D° and draw a line from D° to r which will be the true length of the hip I D in the plan. Multi- ply this length by 4, which will give the amount of ridge capping re- SHEET METAL WORK 167 quired. This length of hip can also be obtained from the plan by tak- ing the vertical height of the roof P I' in the elevation and placing it at right angles to I D in the plan, as shown, from I to P, and draw a line from P to D which is the desired length. For the length of the valley L F in the plan, drop a vertical line from F^ in the side elevation until it intersects the eave line at F°. Take the distance F L in the plan and place it as shown from F° to L°, and draw a line from L° to F^ which is the true length of the valley shown by L F in the plan. Multiply this length by 2, which will give the required number of feet of valley required. This length of valley can also be obtained from the plan by taking the vertical height of the roof of the wing, shown by F° F^ in the side elevation, and placing it at right angles to F L in the plan, from L to F^, and draw, a line from F^ to F which is the desired length similar to F^ L° in the side elevation. FLAT-SEAM ROOFING The first step necessary in preparing the plates for flat seam I'oofing is to notch or cut off the four corners of the plate as shown in Fig. 199 which shows the plate as it is taken from the box, the shaded corners a a a a representing the corners which are ^ notched on the notching machine or with the shears. 5 Care must be taken when cutting off these corners not to cut off too little otherwise the sheets will not edge well, and not to cut off too much, otherwise a hole will show at the corners when the sheets are laid. To find the correct amount to be cut off proceed as follows: ^^' Assuming that a J-inch edge is desired, set the dividers at J inch and scribe the lines b a and a c on the sheet shown in Fig. 199, and, where the lines intersect at a, draw the line deal an angle of 45 degrees, which represents the true amount and true angle to be cut off on each corner. After all the sheets have been notched, they are edged as shown in Fig. 200, the long sides of the sheet being bent right and left, as shown at a, while the short side is bent as shown at 6, making the notched corner appear as at e. In some cases after the sheets are edged the contract requires that the sheets be painted on the underside before laying. This is usually done with a small brush, being careful that the edges of the sheets 32 too f 1 i •c i^; the corner is double seamed at ab. M shows a sectional view through the gutter showing how the tubes and leaders are joined. The tube N is flanged out as shown at i i, and soldered to the gutter; the leader O is then slipped over the tube N as shown, and fastened. In the section on Flat-Seam Roofing it was explained how a conical tower, Fig. 214, A^ould be covered. It will be shown now how this tower would be covered with stand- ing-seam roofing. As the circumference of the tower at the base is 396 inches, and assuming that 14 x 20-inch tin plate is to be used at the base of the tower, the nearest width which can be employed and which will divide the base into equal spaces is 17 /g- inches, without edges, thus dividing the cir- cumference into 23 equal parts. Then the width of ly^^g- inches and the length of the rafter A B or AC in elevation will be the ^ basis from which to construct the pattern for the standing seam strip, for which pro- ceed as follows : Let A B C D in Fig. 228 represent a 20-inch wide strip locked and soldered to the required length. Through the center of the strip draw the line E F. Now measure the length of the rafter A B or A C in Fig. 214 and place it on the line E F in Fig. 228 as shown from H to F. At right angles to H F on either side draw F O and F L making each equal to 8J| inches, being one half of the I7/3- above referred to. 182 SHEET METAL WORK From points L and O draw lines to the apex H (shown broken). At right angles to H L and H O draw lines H P equal to IJ inches and H S equal to 1 J inches respectively. In similar manner draw L D and O C and connect by lines the points P D and S C. Then will P S C D be the pattern for the standing seam strip, of which 22 more will be required. When the strips ai-e all cut out, use the roofing tongs and bend up the sides, after which they are laid on the tower, fastened with cleats, and double seamed with the hand seamer and mallet in the usual manner. If the tower was done m copper or galva- nized sheet iron or steel, where 8-foot sheets could be used, as many sheets would be cross- locked together as required; then metal could be saved, and waste avoided, by cutting the sheets as shown in Fig. 229 in which A B C D shows the sheets of metal locked together, and E and F the pattern sheets, the only waste be- ing that shown by the shaded portion. Where the finial D in Fig. 214 sets over the tower, the standing seams are turned over flat as much ^' ' as is required to receive the finial, or small notches would be cut into the base of the finial, to allow it to slip over the standing seams. Before closing the seams, they are painted with white lead with a tool brush, then closed up tight, which makes a good tight job. CORRUGATED IRON ROOFING AND SIDING Corrugated iron is used for roofs and sides of buildings. It is usually laid directly upon the purlins in roofs constructed as shown in Figs. 230 and 231, the former being constructed to receive sidings of corrugated iron, while in the latter figure the side walls of the building are brick. Special care must be taken that the projecting edges of the corrugated iron at the eaves and gable ends of the roof are well secured, otherwise the wind will loosen the sheets and fold them up. The cor- rugations are made of various sizes such as 5-inch, 2i-inch, IJ-inch and f-inch, the measurements always being from A to B in Fig. 232, and the depth being shown by C. The smaller corrugations give a SHEET METAL WORK 183 more pleasing appearance, but the larger corrugations are stiffer and will span a greacer distance,thereby permitting the purlins to be further apart. -=i^ Fig. 230. The thickness of the metal generally used for roofing and siding varies from No. 24 to No. 16 gauge. By actual trial made by The 231. Keystone Bridge Company it was found that corrugated iron No. 20, spanning 6 feet, began to give permanent deflection at a load of 30 lb. per square foot, and that ^ ^ \ /^<^ it collapsed with a load of 60 lb. per square foot. The distance ^^' between centers of purlins should, therefore, not exceed 6 feet, and preferably be less than this. 184 SHEET ]\IETAL AVORK TABLES The following tables will prove of value when desiring any infor- mation to which they appertain. MEASUREMENTS OF CORRUGATED SHEETS Dimensions of Sheets and Corrugations. o ^ o -a ^ O *j XJ ^ No. of corrugations to the sheet Covering width after lapping one corrugation Width of sheet after corrugated Length of the longest sheets furnished 5 inch. 5 inch. 1 inch. 6 24 inch. 27 inch. 10 feet. 2% inch. 2% inch. yitoYi inch. 10 24 inch. 26 inch. 10 feet. 1 1/ inch. 1 H inch. ^8 to Yi inch. 19^ 24 inch. 26 inch. 10 feet. 5i inch. % inch. 5i inch. 34^ 25 inch. 26 inch. 8 feet. RESULTS OF TEST of a corrugated sheet No. 20, 2 feet wide, 6 feet long between supports, loaded uniformly with fire clay. Load per sauare foot. lb. Deflection at center under load. Inches. Permanent Deflection, load removed. 5 1 2 10 15 1 20 li 25 ^ 30 13 4 35 2i h 40 2| 45 3i H 50 4 n 55 6i Not noted. 60 Broke down. i( u The following table shows the distance apart the supports should be for different gauges of corrugated sheets: Nos. 16 and IS 6 to 7 feet apart. Nos. 20 and 22 4 to 5 feet apart. No. 24 , , 2 to 4 feet apart. No. 28 , 2 feet apart SHEET ME'IWL WORK 185 The following table is calculated for sheets 30i inches wide before corrugating. No. by Birmingham gauge .r-4 '-f A «-( .a ^( and jrn-'- r > > / J / I > I // /^^/^ \ SECTION ^ ,0N ^ A B ---B Fig. 261. Fig„262. are often called working drawings. Tracings are duplicate drawings, made by tracing upon transparent cloth or paper placed over the orig- Fig. 263. inal drawing. Many other terms might be introduced here; but enough, we beUeve, ha ^e been presented to give the student the leading general points. 198 SHEET IMETAL WORK A few words are necessary on the subject of fastening the cornice to the wall. Sheet-metal cornices are made of such a wide range of sizes, and are required to be placed in so many different locations, that the methods of construction, when wooden lookouts are employed and Fig. 264. when the cornice is put together at the building in parts, are worthy of the most careful study. The general order of procedure in putting up, is as follows: The foot-moulding or architrave a b (Fig. 2G4) is set upon the wall finished up to /, the drip a being drawn tight against the w^all. The brickwork is then carried up, and the lookout A placed in position, the wall being carried up a few courses higher to hold the lookout in position. A board B is then nailed on top of the lookouts (which should be placed about three feet apart) ; and on this the flange of the foot-mould b is fastened. The frieze or panel 6 c is now placed into the lock B, which is clcsed and soldered; when the lookout C and the •board D are placed in their proper positions, as before described. SHEET METAL WORK 199 The planceer and bed-mould c d are now lov^ked and soldered at D, and the lookout E placed in position,, with a board F placed under the lookouts the entire length of the cornice; onto this board the plan- ceer is fastened. Having the proper measurements, the framer now constructs his lookouts or brackets G H I E, fastening to the beam at T, when the crown-mould d e\s fastened to the planceer, through the flange of the drip at d, and at the top at e. The joints between lengtns of mouldings, are made by lapping, riveting, or bolting, care being taken that they are joined so neatly as to hide all indications of a seam when finished and viewed from a short distance. '^ • ^ If brackets or modillions are to be placed in position, they are riveted or bolted in position; or sometimes the back of the cornice is blocked out with wood, and the brackets screwed in position through their flanges. While a galvanized-iron cornice thus constructed on wooden lookouts will resist fire for a long time, a strict- ly fireproof cornice is obtained only by the use of metal for supports and fastenings, to the entire exclusion of wood. This fireproof method of con- struction is shown in Fig. 265. In- stead of patting up in parts on the building, the cornice is con- structed in one piece in the shop or upon the ground, and hoisted to the top of the wall in long lengths easily handled. A drip a is used at the bottom of the foot-mould, and the joints made in the way in- dicated at h and c, with a lock at d. Band iron supports and braces are used, formed to the general contour of the parts as shown by A B C, and bolted direct to the cornice, as shown, before hoisting. When the cornice sets on the wall as at C, anchors are fastened to the main brace, as at D and E, with an end bent up or down for fastening. If the cornice sets perfectly plumb, the mason carries up his wall, which holds the cornice in a firm position. The top and back are then framed in the usual manner and covered by the metal Fig. 265. 200 SHEET METAL WORK roofer. In constructing cornices in this manner, the mouldings are run through solid, behind all brackets and modillions. The brackets and modillions are attached by means of riveting through outside flanges. SHOP TOOLS One of the most important tools In cornice or architectural sheet- metal working shop is the hrahe. On those operated by hand, sheets are bent up to 8 feet in one continuous length. Li the larger shops, power presses or brakes are used, in which sheets are formed up to 10 feet in length, the press being so constructed that they will form ogees, squares, or acute bends in one operation. Large 8- or 10-feet squaring shears also form an important ad- dition to the shop, and are operated by foot or power. When cornices are constructed where the planceer or frieze is very wide, it is usual to put crimped metal in, to avoid the waves and buck- les showing in the flat surface; for this purpose the crimping machine is used. In preparing the iron braces for use in the construction of fire- proof cornices, a punching machine and slitting shears are used for cutting the band iron and punching holes in it to admit the bolts. While braces are sometimes bent in a vise, a small machine known as a brace bender is of great value in the shop. In large fireproof building constructions, it is necessary that all doors, window frames, and even sashes be covered with metal, and made in so neat a manner that, when painted and grained, no differences will be apparent to Indicate whether the material is wood or metal, the smallest bends down to J inch being obtained. This, of course, cannot be done on the brakes just mentioned, but is done by means of the draw-bench, which is con- structed In lengths up to 20 feet and longer, operated by means of an endless chain, and capable of drawing the sheet metal over any shaped wood mould as tightly as if it were cast in one piece. The smaller tools In the shop are similar to those referred to on page 4 of this volume. METHOD EMPLOYED FOR OBTAINING PATTERNS The principles applied to cylinder developments, as explained on page 5 and following In the treatment of the Parallel- Line method of development, are also applicable for obtaining SHEET METAL WORK 201 the patterns for any moulding where all members run parallel; for it makes no difference what profile is employed, so long as the lines run parallel to one another, the parallel-line method is used. While this method h- chiefly employed in cornice work, other problems will arise, in which the "Radial-Line" and the "Triangulation" methods will be of service. The term generally used in the shop for pattern cutting on cornice work is miter cutting. To illustrate, suppose two pieces of mouldings are to be joined together at angle of 90°, as shown in Fig. 266. The first step necessary would be to bisect the given angle and obtain the miter- line and cut each piece so that they would miter together. If a ^^§- 266. carpenter had to make a joint of this kind, he would place his moulding in the miter-box, and cut one piece right and one piece left at an angle of 45°, and he would be careful to hold the moulding in its proper po- sition before sawing; or else he may, instead of having a return miter as shown, have a face miter as in a picture frame, shown in Fig. 267. The sheet-metal cornice- maker cannot, after his moulding is formed, place it in the miter- box to cut the miter, but must lay it out — or, in other words, develop it — on a flat surface or sheet of metal. He must also be \ '^Op Fig. 267. careful to place the profile in its proper position with the miter- line; or else, instead of having a return miter as shown in Fig. 266, he will have a face miter as shown in Fig. 267. If he lays out his work correctly, he can then cut two pieces, form one right and the other left, when a miter will result between the two pieces of moulding and will look as shown in Fig. 266. If, however, a face miter is desired, as shown in Fig. 267, which is used when miters are desired for panels and other purposes, the method of laying them out will be explained as we proceed. The same principles required for developing Figs. 266 and 267 are used, whether the mouldings are mitered at angles of 90° 202 SHEET INIETAL WORK or otherwise. The method of raking the mouldings — or, in other words, changing their profile to admit the mitering of some other moulding at various angles — will also be thoroughly explained as we proceed. VARIOUS SHAPES OF MOULDINGS The style of mouldings arising in the cornice shop are chiefly Roman, and are obtained by using the arcs of a circle. In some cases, Greek mouldings are used, the outlines of which follow the curves of conic sections; but the majority of. shapes are arcs of circles. In Fig. 268. Fig. 269. Figs. 268 to 272 inclusive, the student is given a few simple lessons on Roman mouldings, which should be carefully followed. As all pat- tern-cutters are required to draw their full-size details in the shop from small-scale drawings furnished by the architect, it follows that they must understand how to draw the moulds with skill and ease; other- Fig. 270. Fig. 271. wise freehand curves are made, which lack proportion and beauty. In Fig. 268, A shows the mould known as the cyma rectay known in the shop as the ogee, which is drawn as follows : Complete a square a h c d; draw the two diagonals a c and b d, intersecting each other at e. Through e, draw a horizontal line inter- secting a c? at / and 6 c at /t. Then, with / and h as centers, draw VQ- spectively the two quarter-circles a c and e c. SHEET METAL ^^'ORK 205 In Fig. 269, B shows the cyma reversa, known in the shop as the ogee, reversed. Complete a square abed, and draw the two diagonals b d and a c intersecting at e; through e, draw a vertical line intersecting abatf and c d nth, which points are the respective centers for the arcs a e and e c. C in Fig. 270 shows the cavetto, called the cove in the shop, which is drawn by completing a square abed. Draw the diagonal b d sit 45°, which proves the square; and, using cZ as a center, draw the quarter-circle a.c. In Fig. 271, D represents the ovolo or echinus, known in the shop as the quarter- round, which is constructed similarly to C in Fig. 270, with the exception that b in Fig. 271 is used to obtain the curve ac. E in Fig. 272 is known as the torus, known in the shop as a bead- moidd. A given distance a 6 is bisected, thus obtaining c, which is the center with which to describe the semicircle a b. All of these profiles should be drawn by the student to any de- sired scale for practice. In preparing mouldings from sheet metal, Fig. 272. cc^ocmaiaao Fig. 273. it is sometimes required that enrichments are added in the ogee, cove, and bead. In that case the mould must be bent to receive these en- richments, which are usually obtained from dealers in stamped or pressed sheet-metal work. Thus, in Fig. 273, F represents a front view of a crown mould whose ogee is enriched, th^ section of the en- 204 SHEET METAL WORK richmeiit being indicated by a 6 in the section, in which the dotted line d c shows the body of the sheet-metal moulding bent to receive the pressed work. In Fig 274, H represents part of a bed-mould in which Fig. 274. egg-and-dart enrichments are placed. In this case the body of the mould is bent as shown by c cZ in the section, after which the egg-and- dart is soldered or riveted in position. J in Fig. 275 represents part Fig. 275. of a foot-mould on which an enriched bead is fastened. The body of the mould would be formed as indicated by c in the section, and the bead a b fastened to it. This same general method is employed, no matter what shape the pressed work has. PRACTICAL MITER CUTTING Under this heading come the practical shop problems. The prob- lems which will follow should be drawn to any desired scale by the student, developed, and bent from stiff cardboard to prove the accu- racy of the pattern. If the student cannot use the small brake in the shop and test his patterns cut from metal, he can use the dull blade of a table knife, over which the bends can be made, when using cardboard patterns. This at once proves interesting and instructive not only from the purely manipulation standpoint but also from the fact that, in this manner, a check on the accuracy of one's work SHEET METAL WORK 205 will be obtained. While the problems selected cannot possibly cover the whole field, they have been chosen with care so as to illustrate sufficiently the basic principles involved. The first problem will be to obtain the development of a square return miter, such as would occur when a moulding had to return around the comer of a building, as shown in Fig. 276. In Fig. 277 are shown two methods of ob- taining the pattern. The first method which will be described is tlie ''long" method, in which are set forth all the principles applicable to obtaining pat- terns for mouldings, no matter what angle the plan may have. Fig. 276. The second method is the "short*^ ELEVATION in0^9^8^7^6^5Vy 2^ l' T~$ ^^tr =kr PATTERN PATTERN Fig, 277, 206 SHEET METAL WORK rule generally employed in the shop, which, however, can be used only when the angle H G F in plan is 90°, or a right angle. To obtain the pattern by the first method, proceed as follows: First, draw the elevation of the mould as shown by 1, B, A, 11, drawing the coves by the rule previously given. Divide the curves into equal spaces; and number these, including the corners of the fillets as shown by the small figures 1 to 1 1. In its proper position below the elevation, draw the soffit plan as shewn by C D E F G H. Bisect the angle H G F by the line G D, which is drawn at an angle of 45°. From the va- rious intersections in the elevation, drop fines intersecting the miter-line as shown. At right angles to H G, draw the stretchout line 1' IT, upon which place the stretchout of the mould 1 11 in elevation, as shown by similar figures on the line T 11'. At right angles to 1' 11', and from the numbered points thereon, draw fines, which intersect by lines drawn at right angles to H G from similarly numbered inter- sections on the miter-line G D. Trace a line through the intersections Fig. 278. thus obtained, as shown by J G. Then will 1' G J 11' be the desired pattern. This gives the pattern by using the miter-line in plan. In developing the pattern by the short method, on the other hand, the plan is not required. At right angles to 1 B in elevation, draw the stretchout line 1" 11", upon which place the stretchout of the profile 1 11 in elevation, as shown by similar figures on 1" 11", at right angles to which draw lines through the numbered points as shown, which intersect by lines drawn at right angles to 1 B from similarly numbered intersections in the profile in elevation. Trace a line through points thus obtained, as shown by G K. Then will G 1" 11" K be similar to J G V IV obtained from the plan. SIH^I'/r i\[F/rAL \\0\Us 207 In Fig. 278 is shown a horizontal moulding butting against a plane surface oblique in elevation. A miter cut of this kind would be required when the return moulding of a dormer window would butt against a mansard or other pitched roof. In this case we assume A to be the return butting against the pitched roof B. The method of PATTERN SECTION Fig. 279. obtaining a pattern of this kind is shown in Fig. 279. Let A B C D represent the elevation of the return, A D representing the pitch of the roof. In its proper position as shown, draw the section 1 11, which divide into equal spaces as shown, and from which, parallel to A B, draw lines intersecting the slant line A D from 1 to 11, as shown. At right angles to AB erect the stretchout line 1' 11', upon which place the stretchout of the section as shown by similar figures on 1' 11'. At right angles to V 11', and through the numbered points thereon, draw lines, which intersect by lines drawn at right angles to A B from similarly numbered intersections on the slant line A D. Through 208 SHEET METAL WORK the various intersections thus obtained, draw E F. Then will E F 11' 1' be the desired pattern. It is sometimes the case that the roof against which the moulding butts, has a curved surface either concave or convex, as shown by B C in Fig. 280, which surface is convex. Complete the elevation of the moulding, as D E; and in its proper position draw the section 1 9, which divide into equal spaces as shown by the small figures, from which draw horizontal lines until they intersect the curved line B C, which is struck from the center point A. At right angles to the line of the moulding erect the line 1' 9', upon which place the stretchout PATTERN SECTION C Fig. 280. of the section, as shown by the figures on the stretchout line. Through the numbered points, at right angles to V 9', draw lines, which intersect by lines drawn at right angles to 2 D from similarly numbered intersections on the curve B C, thus resulting in the intersections I" to 9" in the pattern, as shown. The arcs 2'' 3'' and 7" 8'' are simply repro- ductions of the arcs 2 3 and 7 9 on B C. These arcs can be traced by any convenient method; or, if the radius AC is not too long to make it inconvenient to use, the arcs in the pattern may be obtained as follows: Using A C as radius, and 7'^ and 8'' as centers, describe arcs intersecting each other at A^ ; in similar manner, using 2" and 3'' as centers, and with the same radius, describe arcs intersecting each SHEET METAL WORK 209 other at A^. With the same radius, and with A^ and A^ as centers, draw the arcs 8'' T and 3" 2" respectively. Trace a Une through the other various intersections as shown. Then will V V 9'' 9' be the desired pattern. In Fig. 281 is shown an elevation of an oblong or rectangular panel for which a miter-cut is desired on the line a h — known as a ^^panel" or ''face" miter. The rule to apply in obtaining this pattern is shown in Fig. 282. A shows the part elevation of the panel; a b and c d, the miter-lines drawn at angles of 45°. In its proper position with the lines of the mould- ing, draw the profile B, the curve or mould of which divide into equal spaces, as shown by the figures 1 to 7 ; and from the points thus obtained, par- allel to 1 b, draw lines inter- Fig. 281. Fig. 282. secting the miter-Hne a 6 as shown. From these intersections, par- allel to h d, draw Hues intersecting also c d. At right angles to b d draw the stretchout line V T, upon which place the stretchout of the profile B. At right angles to 1' 7', and through the numbered points of division, draw lines, which intersect by lines drawn at right angles to b d from similarly numbered intersections on the miter- lines a b and c d. Trace lines through the various points of inter- section in the pattern as shown. Then will C D E F be the required cut for the ends of the panel. The same miter-cuts would be employed for the long side a c k. 210 SHEET METAL WORK Fig. 281, it being necessary only to make D E in Fig. 282 that length when laying out the patttern on the sheet metal. Where the miter-cut is required for a panel whose angles are other than right angles, as, for example, a triangular panel as shown in Fig. 283, then proceed as shown in Fig. 284. First draw the elevation of the triangular panel as shown by A B C, the three sides in the case being equal. Bisect each of the angles A, B, and C, thus obtaining the miter-lines Ac, B 6, and C a. In line with the elevation, place in its proper position the profile E, which divide into equal spaces as shown; and from the numbered division points, parallel to A C, draw lines cutting the miter-line C a. From these intersec- tions, parallel to C B, draw lines intersecting the miter- line 6 B. At right angles to C B draw the stretchout line 1' 7', upon which place the ELEVATION FiS. 283. Fig. 284. stretchout of the profile E. Through the numbered points of divi- sion and at right angles to V 7\ draw lines as shown, which intersect by lines drawn at right angles to C B from intersections of similar numbers on the miter-lines a C and h B. Through the points thus obtained, trace the pattern F G H I. It makes no difference what shape or angle the panel may have; the principles above explained are applicable to any case. In ornamental cornice work, it often happens that tapering mould- ed panels are used, a plan and elevation of which are shown in Fig. 285. SHEET METAL WORK 211 By referring to the plan, it will be seen that the four parts ba,a 6', 6' a', and a' b are symmetrical ; therefore, in practice, it is necessary only to draw the one-quarter plan, as shown in Fig. 286, and omit the eleva- tion, since the height d e (Fig. 285) is known. Thus, in Fig. 286, draw the quarter-plan of the panel, no matter what is its shape, as shown Fig. 285. by a 1 5 6 9. Divide the curves from 1 5 and 6 9 into equa- spaces, indicated respectively by 1, 2, 3, 4, and 5, and 6, 7, 8, and 9. From these points, draw lines to the apex a. As the pattern will be de- veloped by triangulation, a set of triangles will be required, as shown in Fig. 286. Fig. 287, for which proceed as follows : Draw any horizontal line, as a 1; and from a erect the perpendicular a a' equal to the height the panel is to have. Now take the lengths of the various lines in Fig. 286 from a to 1, a to 2, a to 3, etc., to a to 9, and place them on the line a 1 in Fig. 287, as shown by similar numbers. Then using as radii the various 212 SHEET METAT. ^VOIU<: lengths a' 1, a' 2, a' 3, etc., to a' 0, and with any point, as a' in Fig. 288 as center, describe the various arcs shown from 1 to 9. From any point on the arc 1 draw a line to a' . Set the dividers equal to the spaces contained in the curve 1 5 in Fig. 286; and, starting from 1 in Fig. 288 step from one arc to an- othcx having similar num- bers, as shown from 1 to 5. In similar manner, take the distance from 5 to 6 and the spaces in the curve 6 Fig. 287. Fig. 288. in Fig. 286, and place them on corresponding arcs in Fig. 288, step- ping from one arc to the other, resulting in the points 5 to 9. Trace a line through the points thus obtained. Then will a' 1 5 6 9 a' be the quarter-pattern, which can be joined in one- half or whole pattern as desired. In Fig. 289 is shown a perspective of a mould- ing which miters at an angle other than a right angle. This occurs when a moulding is required for over a bay window or other structure whose angles vary. The rule given in Fig. 290 is applicable to any angle or profile. First draw a section or an elevation of the moulding as shown by A B 14 1. Directly below the moulding, from its extreme point, as 2 3, draw a plan of the desired angle as shown by C 2 D. Bisect this angle by using 2 as center and, with any radius, describing an arc meeting the sides of the angle at C and E. With the same or any other radius, and with C and E as centers, describe arcs intersecting each other in F. From the corner 2, draw a line through F. Then will 2 II be the Fig. 289. SFIEKT MKTAL WORK 213 miter-line, or the line bisecting the angle C 2 D. Now divide the profile 1 14 into equal spaces as shown by the figures, and from the points tlius obtained drop vertical lines intersecting the miter-line 2 2 1 D Fig. 290. H in plan from 1 to 14 as shown- At right angles to C 2, draw the line J K, upon which place the stretchout of the profile in elevation as shown by similar figures on the stretchout line, through which drop lines perpendicular to J K, which intersect with lines drawn parallel to J K from similarly numbered ^^' * points of intersection on the miter- line 2 H. Trace a line as shown by L M, which is the miter-cut desired. When two mouldings having different profiles are required to miter together as shown in Fig. 291, where C miters at right angles 214 SHEET METAL WORK with D, two distinct operations are necessary, which are clearly shown in Figs. 292 and 293. The first operation is shown in Fig. 292, in which C represents the elevation of an ogee moulding which is to miter at right angles with a moulding of different profile as shown at D. Divide the profile C into equal 2 spaces, from which points draw horizontal lines intersecting the moulding D from 1' to 10'. At right angles to the line of the moulding C, draw the line A B, upon which place the stretchout of the profile C as shown by simi- lar figures on A B. At right angles to A B, and through the ELEVATION PATTFRN FOR Fig. 292. points indicated by the figures, draw lines, which intersect with lines drawn parallel to A B from similarly numbered intersections in the profile D. Trace a line through the points thus obtained, as shown by E H. Then will.E F G H be the pattern for C in elevation. To obtain the pattern forD, draw the elevation of D (Fig. 293), which is to miter at right angles with a moulding whose profile is C. Proceed in precisely the same manner as explained in connection with Fig. 292. Divide the profile D in Fig. 293 into equal parts, as shown, from which draw horizontal lines cutting the profile C. At right angles SHEET METAL WOUK 215 to the lines of the moulding D, draw the stretchout line A B, upon which place the stretchout of the profile D. At right angles to A B, and through the numbered points of division, draw hnes as shown, which intersect by lines drawn parallel to A B from similarly numbered intersections in the profile C. Through these points of intersection draw F G. Then will E F G H be the desired pattern for D. It should be understood that when the patterns in Figs. 292 and 293 are foraied and joined together, they will form an inside miter, as is shown in Fig. 291. If, however, an outside miter were required, it would be necessary only to use the reverse cuts of the patterns in Figs. 292 and 293, as shown by E J H in Fig. 292 for the mould C, and F J G in Fig. 293 for the mould D. When joining a Fig. 294. curved moulding with a straight moulding in either plan or eleva- tion even though the curved or straight mouldings each have the same profile, it is necessary to establish the true miter-line before the pattern can be correctly developed, an example being given in Fig. 294, which shows an elevation of a curved moulding which is intersected by the horizontal mouldings A B. The method of ob- taining this miter-line, also the pattern for the horizontal pieces, is clearly shown in Fig. 295. First draw the profile which the horizontal moulding is to have, as 1 10. Let the distance 9 B be established. Then, with C on the center fine as center, and A C as radius, describe the arc B A. From any point on the line 9 B, as a, erect the vertical line a b. Through the various divisions in the profile 1 10, draw horizontal lines intersecting the vertical line a b from 1 to 10 as shown. From the center C, draw any radial line, as C d, cutting the arc B A at e. Now take the various divisions on a b, and place them from e to d sls shown by points V to 10'. Then, using C as center, with radii deter- mined by the various points on e d, d^'aw arcs intersecting horizontal lines of similar nun^bers drawn through the divisions owab. Through 216 SHEET METAL WORK these points of intersection, draw the miter-line shown. The student will note that this line is irregular. Having obtained the miter-Kne, the pattern is obtained for the horizontal moulding by drawing the stretchout line E F at right angles to 9 B. On E F lay off the stretchout of the profile 1 10; and through the numbered points and at right angles to E F, draw hori- zontal lines, which intersect with lines drawn at right angles to 9 B from similarly numbered in- tersections in the miter-line determined by horizontal lines already drawn through the vertical line a h. Trace a line through the points thus ob- tained, as shown by H I J K, which is the desired pattern. J Fig. 295. Fi?J^- ^*J0. In Fig. 290 is shown a shaded view of a gable moulding intersect- ing a pilaster, the gable moulding B cutting against the vertical pilaster A, the joint-line being represented hy ahc. To obtain this joint-line, without which the pattern for the gable moulding cannot be developed, an operation in projection is required. This is explained in Fig. 297, in which BCD shows the plan of the pilaster shown in elevation by E. In its proper position in plan, place the profile of the gable moulding, as shown by A, which divide into equal spaces as shown by the figures 1 to 8, through which draw horizontal lines intersecting the plan of the pilaster B C D as shown by similar figures. For convenience in pro- SHEET METAL WORK 217 jecting the various points, and to avoid a confusion of lines, number the intersections betv^een the lines drawn from the profile A through the wash B 2, '7°", ''4°", and '^3°". At the desired point H in eleva- tion, draw the lower line of the gable moulding, as H F. Take a tracing of the profile A in plan, with all of the various intersections on same, and place it in elevation as shown by A*, placing the line 1 8 at right angles to H F. Through the various in- tersections 1, 7°, 4°, 3°, 2, 3, 4, 5, 6, 7, and 8 in »AS and parallel to F H, draw lines indefinitely, which intersect by lines drawn at right angles to C B in plan from sim- ilarly numbered intersec- . tions in the pilaster C D B, thus obtaining the points of intersection P to 8^ in elevation. For the pattern, pro- ceed as follows: At right angles to H F, draw the stretchout line J K, upon which place the stretch- out of the profile A or AS with all the points of in- tersection on the wash 1 2. At right angles to J K, and through the numbered points, draw lines as shown, which intersect by lines drawn at right angles to H F from similarly numbered intersections in the joint-line 1^ 8^ Through the points thus obtained, trace the miter-cut M N O. Then will L M N O P be the pattern for the gable moulding. In Fig. 298 are shown gable mouldings mitering upon a wash. The 218 SHEET METAL WORK mouldings A A intersect at any desired angle the wash B. In this case, as in the preceding problem, an operation in projection must be gone through, before the pattern can be obtained. This is clearly shown in Fig. 299. Draw the section of the horizontal moulding B^ with the wash a b. From this section project lines, and draw the part elevation D C. Fig. 298. Knowing the bevel the gable is to have, draw C B, in this case the top line of the moulding. Draw a section of the gable mould, as A, which divide into equal parts as shown from 1 to 8; and through the point of division draw lines parallel to B C, indefinitely, as shown. Take a tracing of the profile A, and place it in section as shown by A^ Divide A into the same PATTERN SECTION ELEVATION Fig. 299. number of spaces as A; and from the various divisions in A^ drop vertical lines intersecting the wash a 6 as shown, from which points draw horizontal lines intersecting lines drawn parallel to B C through similarly numbered points in A, at 1° to 8°. Trace a line through these intersections as shown, which represents the miter-line or line of joint in elevation. For the pattern, draw any Hne as E F, at right angles to B C, upon which place the stretchout of the profile A, as shown by similar figures on the stretchout line E F. Through the numbered points of division and at right angles to E F, draw lines as sliown, which intersect by SHEET METAI. WORK 219 Fig. 300. lines drawn at right angles to B C from similarly numbered intersec- tions on 1° 8^ and on the vertical line B D. A line traced through points thus obtained, as shown by G H I J, will be the desired pattern. In Fig. 300 is shown a front view of a turret on which four gables are to be placed^, as shown by A A; also the roofs over same, as shown by B B. The problem con- sists in obtaining the developments of the gable mouldings on a square turret. In developing this pattern, the half-elevation only is required, as shown in Fig. 301, in which first draw the center line E F; then establish the half-width of the turret, as C D, and draw the rake B C. At right angles to the line B C, and in its proper position as shown, draw the profile A, which divide into equal spaces as shown by the figures 1 to 6, through which, parallel to B C, draw lines intersecting the center line F E as shown; and extend the lines below C, indefinitely. Now take a tracing of the profile A, and place it in position as shown by AS being careful to have it spaced in the same number of divisions, as shown from 1 to 6, through which, parallel to D C, erect lines intersecting similarly numbered lines drawn through the profile A, thus obtaining the intersections 1° to 6°, through which a line is traced, which represents the line of joint at the lower end between the two gables. For the pattern, take a stretchout of A, and place it on the line J K drawn at right angles to B C, as shown by the figures 1 to 6 on J K. At right angles to J K, and through these points of division, draw lines, which intersect by lines drawn from similarly numbered intersections on F B and 1° 6°. Trace a line through the points thus obtained, as shown by F° B° C° 6°, which is the desired pattern, of which eight are required to complete the turret, four formed right and four left. If the roof shown by B in Fig. 300 is desired to be added to the pattern in Fig. 301, then, at right angles to F° 6°, draw the line F° F^ equal to F H in the half-elevation, and draw a line from F^ to 6° in the pattern. In Fig. 302 is shown front view of an angular pediment with hori- zontal returns at bottom A and top B. In this problem, as in others which will follow, a change of profile is necessary before the correct 220 SHEET METAL WORK pattern for the returns can be developed. In other words, a new pro- file must be developed from the given or normal profile before the pat- terns for the required parts can be developed. It should be under- stood that all given profiles are always divided into equal spaces; there- fore the modified profiles will contain unequal spaces, each one oi HALF D .ELEVATION Fig. 301. which must be carried separately onto the stretchout line. Bearing\ this in mind, we shall proceed to obtain the modified or changed pro- files and patterns for the horizontal returns at top and foot of a gable moulding, as at B and A in Fig, 302, the given profile to be placed in the gable moulding C. In Fig. 303, let C represent ihe gable moulding SHEET METAL WORK 221 placed at its proper angle with the horizontal moulding G H. Assum- ing that 6^ 6° is the proper angle, place the given profile A at right angles to the rake, as shown; and divide same into equal spaces as shown from 1 to 10, through which points, parallel to 6^ 6°, draw lines towards the top and bottom of the raking moulding. Assuming that the length 6^ 6° is correct, take a tracing of the profile A, and place it in a ver- tical position below at A^ and above at A^, being careful to have the points and 6 in the profiles directly in a ver- ^^S- 303. tical position below the points 6^ and 6°, as shown. From the va- rious intersections in the profiles A^ and A^ (which must contain the same number of spaces as the given profile A), erect vertical lines intersecting lines drawn through the profile A, as shown at the lower end from P to 10^, and at the upper end from 1° to 10°. Trace a line through the points thus obtained. Then will P 10^ be the modified profile for the lower horizontal return, and 1° 10° the modified profile for the upper horizontal return. Note the difference in the shapes and spaces between these two modified profiles and the given profile A. It will be noticed that a portion of the gable moulding miters on the horizontal moulding G H from 6^ to 10'. For the pattern for the gable moulding, proceed as follows: At right angles to E F, draw the stretchout line J K, upon which place the stretchout of the given profile A, as shown by the figures 1 to 10 on J K. Through these figures, at right angles to J K, draw lines as shown, which intersect with lines drawn at right angles to E F from similarly numbered intersections in 1° 10° at the top and P 0^ 10' at the lower end. Trace a line through the intersections thus ob- tained. Then will L M N O be the pattern for C. For the pattern for the horizontal return at the top, draw a side view as shown at B, making P R the desired projection, and the profile 1 10 on B, with its various intersections, an exact repmduction of 1° 10° in the elevation. Extend the line R T as R S; and, startmg from 10, lay off the stretchout of the profile in B as shown by the figures 1 to 10 on R S, being careful to measure each spac^e separately. At right angles to R S draw the usual measuring lines, which intersect 222 SHEET METAL ATORK by lines drawn parallel to S R from similarly numbered points in the profile in B. Trace a line through points thus obtained. Then will U V 10 1 be the pattern for the return B. In similar manner, draw the side view of the lower horizontal return as shown at D, making the projection W 10 equal to P R — CU rf> "t in «N» 0>5 h CO o CO ajfr)'r'''®N(0 o>S X in B. The profile shown from 1 to 10 in D, with all its divisions, is to be an exact reproduction of the profile 1^ to lO'^ in elevation. Extend the line A\' X as X Y, upon which lay off the stretchout of the profile 1 10 in D, being careful that each space is measured separately, as they are all unequal. Tliiough the figures on X Y draw lines as SHEET METAL WORK 223 shown, which intersect by Hnes drawn parallel to W Y from the various intersections in the profile in the side D. A line traced through points thus obtained, as shown by Z V, will be the desired cut, and 1 Z V 10 the pattern for the return D. In Fig. 304 is shown a front view of a segmental pediment with upper and lower horizontal returns. This presents a problem of obtaining the pattern for horizontal returns at top and foot of a segmental pediment, shown respectively at A and B, the given profile to be placed in C. The ^^S- ^^^• principles used in obtaining these patterns are similar to those in the preceding problem, the only difference being that the mould- ing is curved in elevation. In Fig. 305 the true method is clearly given. First draw the center line B D, through which draw the horizon- Fig. 305. tal line C O. From the line C C^ establish the height E ; and with the desired center, as B, draw the arc E C intersecting the line C^ C at C. In its proper position on a vertical line F G, parallel to D B, draw the given profile of the curved moulding as shown by A, which divide into equal spaces as shown from 1 to 10. Through these figures, at right angles to F G, draw lines intersecting the center line D B as shown. 224 SHEET MF/rAL WORK Then, using B as center, with radii of various lengths corresponding to the various distances obtained from A, describe arcs as shown, ex- tending them indefinitely below the foot of the pediment. The point C or 6'' being established, take a tracing of the profile A, with all the various points of intersection in same, and place it as shown by A^, being careful to have the point 6 in A^ come directly below the point 6" in elevation in a vertical position. Then, from the various inter- sections in A^ erect vertical lines intersecting similarly numbered arcs drawn from the profile A. Trace a line as shown from 1" to 10'', which is the modified profile for the foot of the curved moulding. Establish at pleasure the point V at the top, and take a tracing of the given profile A, placing it in a vertical position below 1', as shown by A^ From the various intersections in A^ erect vertical lines intersecting similarly num- bered arcs as before. Through these intersections, shown from 1' to 10', trace the profile shown, which is the modified profile for the top return. The curved moulding shown in elevation can be made either by hand or by machine. The general method of obtaining the blank or pattern for the curved moulding is to average a line through the extreme points of the profile A, as I J, extending it until it intersects a line drawn at right angles to D B from the center B, as B H, at K. We will not go into any further demonstration about this curved work, as the matter will be taken up at its proper time later on. To obtain the pattern for the upper and lower return mouldings, proceed in precisely the same manner as explained in connection with returns B and D in Fig. 303. In Fig. 306 are shown the plan and elevation of a gable moulding in octagon plan. This problem should be carefully followed, as it presents an interesting study in projections; and the principles used in solving this are also applicable to other problems, no matter what angle or pitch the gable has. By referring to the plan, it will be seen PLAN Fio;. 306. SHEET MEIWl, WORK 225 'that the moulding has an octagon angle in plan a h c, while similar points in elevation a' h' c' run on a rake in one line, the top and foot of the moulding butting against the brick piers B and A. The method of proceeding with work of this kind is explained in detail in Fig 307, where the principles are thoroughly explained. Let A B C D E represent a plan view of the wall, over which a gable moulding is to be placed, as shown by G H IJ, the given profile of the SOFFIT PUkN Fig. 307. m.oulding being shown by L M. Divide the profile into equal spaces as shown by the figures 1 to 8. Parallel to I H or J G, and through the figures mentioned, draw lines indefinitely as shown. Bisect the angle B C D in plan, and obtain the miter-line as follows : With C as center, and any radius, describe the arc N O. With N and O as centers, and any radius greater than C N or C O, describe arcs intersecting each other at P. From the point C, and through the intersection P, draw the miter-line C Q. Transfer the profile L M in elevation to the posi- 226 SHEET METATv WORK tion shown by R S in plan, dividing it into the same number of spaces as L M. Through the figures in the profile R S, and parallel to D C, draw lines intersecting the miter-line C Q, as shown. From the inter- sections on the miter-line, and parallel to C B, draw lines intersecting the surface B A. Now, at right angles to C D in plan, and from the SOFFIT PLAN Fig. 308. intersections on the miter-line C Q, draw vertical lines upward, inter- secting lines of similar numbers drawn from points in profile L M in elevation parallel to J G. A line traced through points thus obtained, as shown from 1' to 8', will be the miter-hne in elevation. For the pattern for that part of the moulding shown by C D E Q' in plan, and H G 8' 1' in elevation, proceed as follows: At right angles to 1 H in elevation, draw the line T U, upon which place the siii^:rt mrtat. work 227 stretchout of the profile L M, as shown by the figures 1 to 8. At right angles to T U, and through these figures, draw Hnes, as shown, which intersect with Hnes of similar number's drawn at right angles to 1 H from intersections on the miter-line V 8' and from intersections against the vertical surface ti G. Lines traced through points thus obtained, as shown by V W X Y, will be the pattern for that part of the gable shown in plan by C D E Q' of Fig. 307. In Fig. 308, on the other hand, the position of the plan is changed, so as to bring the line A Q horizontal. At right angles to B C draw the vertical line C E, on which locate any point, as E. In the same manner, at right angles to C B, draw the vertical line B J indefinitely. From the point E, parallel to B C, draw the line E 8'', intersecting the line J B, as shown. Now take the distance from 8'' to J in eleva- tion. Fig. 307, and set it off from 8'' toward J in Fig. 308. Draw a line from J to E, which will represent the true rake for this portion of the moulding. Now take the various heights shown from 1 to 8 on the line Z Z in elevation in Fig. 307, and place them as shown by Z Z in elevation, Fig 308, being careful to place the point 8 of the line Z Z on the line 8'' E extended. At right angles to Z Z, and from points on same, draw lines, which intersect with lines drawn at right angles to B C from intersec- tions of similar numbers on C Q in plan. A line traced through points thus obtained, as shown by D E in eleva- tion, will be the miter-line on C Q in plan. From the intersections on the miter-line D E, and parallel to E J, draw lines, which intersect with lines drawn from intersections of similar numbers on A B in plan at right angles to B C. A line traced through points thus obtained, as shown by F J, will be the miter-line -^^S- 309. or line of joint against the pier shown in plan by B A. Before obtaining the pattern it will be necessary to obtain a true section or profile at right angles to the moulding F D. To do so, pro- ceed as follows : Transfer the given profile L M in elevation in Fig. 307, with the divisions and figures on same, to a position at right angles to F D of Fig. 308, as shown at L. At right angles to F D, and from the intersections in the profile L, draw lines intersecting those of simi- lar numbers in F D E J. Trace a line through intersections thus ob- 228 SHEET INTETAT. WORK tained, as shown from 1 to 8, thus giving the profile M, or true sections at right angles to F D. For the pattern, proceed as follows: At right angles to F D, draw the line H K, upon which place the stretchout of the profile M, as shown by the figures. At right angles to H K, and through the figures, draw lines, which intersect with those of similar numbers drawn at Fig. 310. Fig. 311. right angles to F D from points of intersection in the miter-lines D E and J F, as shown. Lines traced through points thus obtained, as shown by N O P R, will be the pattern for the raking moulding shown in plan. Fig. 307, by A B C Q'. In Fig. 309 is shown a view of a spire, square in plan, intersecting four gables. In practice, each side A is developed separately in a manner shown in Fig. 310, in which first draw the center line through the center of the ^able, as E F. Establish points B and C, from which SITRRT jNIETAT. WOUK 229 draw lines to the apex F. At pleasure, establish A D. At right angles to F E, and from B and J, draw the lines B II and J K respectively. For the })attern, take the distances B K, K A, and A F, and place them as shown by similar letters on the vertical line B F in Fig. 311. At right angles to B F, and through points B and A, draw lines as shown, making B H and B H^ on the one hand^ and A N and A O on the other hand, equal respectively to B H and A N in elevation in Fig. 310. Then, in Fig. Fig. 312. Fig. 313. 311, draw lines from N to H to K to H' to O, as shown, which repre- sents the pattern for one side. In Fig. 312 is shown a perspective view of a drop B mitering against the face of the bracket C as indicated at A. The principles for developing this problem are explained in Fig. 313, and can be ap- plied to similar work no matter what the profiles of the drop or bracket may be. Let A B C D E represent the face or front view of the bracket drop, and F H G I the side of the drop and bracket. Divide one-half of the face, as D Cj into equal spaces, as shown by the figures 1 to 7 on either side, from which points draw horizontal lines crossing H G in side view and intersecting the face H I of the bracket at points 1' to 7'. In line with H G, draw the line J K, upon which place the stretch- out of the profile B C D, as shown by 1 to 7 to 7 to 1 on J K. x\t right angles to J K, draw the usual measuring lines as sho vvn. which inter- sect by lines drawn parallel to J K from similarly numbered intersec- tions on H I. Trace a line through the points thus obtained. Then 230 SHEET METAI. WOTJTC will J K L be the pattern for the return of the drop on the face of the bracket. In Fig. 314, A shows a raking bracket placed in a gable moulding. When brackets are placed in a vertical position in any raking moulding, they are called *'raking" brackets. B represents a raking bracket placed at the center of the gable. The patterns which will be develop- ed for the bracket A are also used for B, the cuts being similar, the only difference being that one-half the width of the bracket in B is formed right and the other half left, the two halves being then joined at the angle as shown. In Fig. 315 are shown the principles employed for obtain- ing the patterns for the side, face, sink strips, cap, and returns for a raking bracket These principles can be applied to any form or angle in the bracket or ELEVATION Fig. 314. gable moulding respectively. Let S U V T represent part of a front elevation of a raking cornice placed at its proper angles with any perpendicular line. In its proper position, draw the outHne of the face of the bracket as shown by E G M O. Also, in its proper position as shown, draw the normal profile of the side of the bracket, indicated by 6-Y-Z-15; the normal profile of the cap-mould, as W and X; and the normal profile of the sink strip, as indicated by 10 10' 15' 15. Complete the front elevation of the bracket by drawing lines par- allel to E O from points 7 and 9 in the normal profile; and establish at pleasure the width of the sink strip in the face of the bracket, as at J K and L Ho To complete the front elevation of the cap-mould of the bracket, proceed as follows : Extend the lines G E and M O of the front of the brackets, as shown by E 6 and O 6, on which, in a vertical position as shown, place duplicates (W^, W^) of the normal profiles W and X, divided into equal spaces as shown by the figures 1 to 6 in W^ and W^. From these intersections in W^ and W^, drop vertical lines, /hich intersect by lines drawn parallel to E O from similarly numbered intersections in X, and trace lines through the points thus obtained. Then will R E and O P represent respectively the true elevations, also SHEET METAL WORK 231 the true profiles, for the returns at top and foot of the cap of the raking bracket. Now divide the normal profile of the bracket into equal spaces, as shown by the figures 6 to 15, through which, parallel to E O, draw lines intersecting the normal sink profile from 10' to 15' and the face lines of the bracket EFG, JH, KL, and ONM, as shown. To obtain the PATTERN FOR RETURN R E ^n\ H\^y ^ PATTER M FOR SIDE BRACKET 6' ia)'yi2'>ATTEM' 1-^/3' FOR SINK STRIP PATTERN FOR C Fig. 315. true profile for the side of the bracket on the lines OM and GE, pro- ceed as follows: Parallel to OM, draw any line, as Y^ Z^; and at right angles to OM, and from the various intersections on the same, draw lines indefinitely, crossing to the line Y^ Z^ as shown. Now, measuring in each instance from the line YZ in the normal profile, take the various distances to points 6 to 15 and 15' to 10', and place them on similarly numbered lines measuring in each and every instance from the line Y* ZS thus obtaining the points 6' to 15' and 15" to 10", as shown. Trace a line through the points thus obtained. Then will Y^ 6' 7' 9' 10' 15' Z^ be the pattern for the side of the raking bracket, 232 SHEET METAL WORK and 10' 10'' 15" 15^ the pattern for the sink strip shown by the lines K L and H J in the front. For the pattern for the face strip B, draw any line, as A' B', at right angles to G M, upon which place the stretchout of 10 15 in the normal profile, as shown from 10 to 15 on A^ B^ Through these points, at right angles to A^ B^ draw lines as shown, which intersect with lines drawn from similar intersections on the lines F G and H J. Trace a line through points thus obtained as shown by F° G° H° J°, which will be the pattern for the face B, B. For the pattern for the sink-face C, draw C^ D^ at right angles to GM, upon which place the stretchout of 10' 15' in the normal profile as shown from 10' to 15' on C^ D^ through which, at right angles to C^ D\ draw lines, which intersect by lines drawn from similar intersections on K L and H J. Trace a line through the points so obtained as J° K° L° H°, which is the pattern for the sink- face C. The pattern for the cap D and the face A will be developed in one piece, by drawing at right angles to EO the line E^ F^. At right angles Fig. 316. Fig. 317. to E' F', and through the figures, draw lines, which intersect w^ith lines drawn at right angles to EO from similarly numbered intersections on REF and NOP. A line traced through the points thus obtained, as shown by R° E° F° and N° 0° P° will be the pattern for D and A. For the patterns for the cap returns R E and O P, draw any line at right angles to 1 1 in the nornial profile, as H^ G^ upon which place the stretchouts of the profiles R E and O P, being careful to carry each space separately onto the line H^ G*, as shown respectively by G^' P and 6^ 1^, Through these points draw lines at right angles to G^ IP, which intersect by lines drawn at right angles to 1 1 from SHEET METAL WORK 233 similar numbers in W and X. Trace lines through the points thus obtained. Then will N^ O^ R^ S^ be the pattern for the lower return of the cap, R E; while J^ M^ L^ K^ will be the pattern for the upper re- turn, P O. In Fig. 316 is shown a perspective view of a gutter or eave- trough at an exterior angle, for which an outside miter would be re- quired. It is immaterial what shape the gutter has, the method of obtaining the pattern for the miter is the same. In Fig. 317 let 1 9 10 represent the section of the eave-trough with a bead or wire .edge aiabc; divide the wire edge, including the gutter and flange, into an equal number of spaces, as shown by the small divisions cZ to 1 to 9 to 10. Draw any vertical line, as A B, upon which place the stretch- out of the gutter as shown by simi- lar letters and numbers on A B, through which, at right angles to A B , draw lines, which intersect by Fig. 318. Fig. 319. 'rofis drawn parallel to AB from similar points in the section. Trace i line through the points thus obtained. Then will C D E F be the pattern for the outside angle shown in Fig. 316. If a pattern is required for an interior or inside angle, as is shown in Fig. 318, it is necessary only to extend the lines C D and F E in the pattern in Fig. 317, and draw any vertical line, as J H. Then will J D E H be the pattern for the inside angle shown in Fig. 318. In Fig. 319 are shown a plan and elevation of a moulding which has more projection on the front than on the side. In other words, A B represents the plan of a brick pier, around which a cornice is to be constructed. The projection of the given profile is equal to C, the profile in elevation being shown by C^ The projection of the front in plan is also equal to C, as shown by C^. The projection of the left side of the cornice should be only as much as is shown by D in plan. This requires a change of profile through D, as shown by D^ To ob* 234 SHEET METAL WORK tain this true profile and the various patterns, proceed as shown in Fig. 320, in which A B C D represents the plan view of the wall, against which, in its proper position, the profile E is placed and divided into equal spaces, as shown by the figures 1 to 12. Through 1 2, par- allel to C D, draw G F. Locate at pleasure the projection of the re- PATTERW FOR FRO^^T II \2 M- !• S'3'4'5'6'7'8'd'l0' H' I I • I ri I » B' H PATTERN - FOR RETURN C (l> "I p-C PLAN ^ , , D Fig. 320. turn mould, as B H, and draw H G parallel to B C, intersecting F G at G. Draw the miter-line in plan, G C. From the various divisions in the profile E, draw lines parallel to C D, intersecting the miter-line C G as shown. From these intersections, erect vertical lines indefi- nitely, as shown. Parallel to these lines erect the line K J, upon which place a duplicate of the profile E, with the various divisions on same, as shown by E^ Through these divisions draw horizontal lines in* SHEET INIETAL WORK 235 tersecting the similarly numbered vertical lines, as shown by the in- tersections 1 to 12'. Trace a line through these points. Then will F^ be the true section or profile on H B in plan. For the pattern for the return H G C B in plan, extend the line B A, as B M, upon which place the stretchout of the profile F^ being careful to measure each space separately (as they are unequal), as shown by figures 1' to 12' on M B. At right angles to this line and through the figures, draw lines, which intersect by lines drawn at right angles to H G from similar points on C G. Trace a line through the points thus obtained. Then will H^ G^ O B' be the pattern for the return mould. The pattern for the face mould GCDF is obtained by taking a stretchout of the profile E and placing it on the TRUE PROFILE THROUGH 1" 7" IN PLAN 2' ELEVATION X Fig. 321. Fig. 322. vertical line P O, as shown by similar figures, through which, at light angles to P O, draw lines intersecting similarly numbered lines previously extended from C G in plan. Trace a line through these intersections. Then will 1 B^ C^ 12be the miter pattern for the face mould. In Fig. 321 is shown a perspective view of a gore piece A joined to a chamier. This presents a problem often arising in ornamental 236 SHEET METAI> ^^ORK PATTERN FOR GORE sheet-metal work, the development of which is given in Fig. 322. Let A B C D show the elevation of the corner on which a gore piece is re- quired. .H 7' E in plan is a section through C D, and E F G H is a section through X I, all projected from the elevation as shown. The profile 1 7 can be drawn at pleasure, and at once becomes the pattern for the sides. Now divide the profile 1 7 into an equal number of spaces as shown, from which drop vertical lines onto the side 7' E in plan, as shown from V to 7'. From these points draw lines parallel to F G, intersecting the opposite side and crossing the line 7' V (which is drawn at right angles to F G from 70 at V 2" Z" ^ 5'' 6^'. Draw any line parallel to C D, as K J, upon which place all the intersections contained on 7' V in plan, as shown by 1° to 7° on K J. From these points erect perpendicular lines, which intersect by lines drawn from simi- larly numbered points in elevation parallel to C D. Through the points thus obtained trace a line. Then will P to 7^ be the true profile on 7' V in plan. For the pattern for the gore, draw any vertical line, as A B in Fig 323, upon which place the stretchout of the profile F 7^ in Fig. 322, as shown by similar figures on A B in Fig. 323. At right angles to AB, and through the figures, draw lines as shown. Now, measuring in each instance from the line 7' V in plan in Fig. 322, take the various distances to points 1' to 7', and place them in Fig. 323 on similarly numbered lines, measuring in each instance from the line A B, thus locating the points Fig. 324. shown. Trace a line through the points thus obtained. Then will F G 7 be the pattern for the gore shown in plan in Fig. 322 by F G 7\ In Fig. 324 is shown a face view of a six-pointed star, which often arises in cornice work. No matter how many points the star has, the principles which are explained for its development are applicable to any size or shape. Triangulation is employed in this problem, as shown in Fig. 325. First draw the half-outline of the star, as shown by A B C D E F G. Above and parallel to the line AG, draw JH of similar length, as shown. Draw the section of the star on A G in plan, Fig. 823. * SHEET METAL AVORK 237 as shown by J K H. Project K into plan as shown at I, and draw the miter-hnes B I, C I, D I, E I, and FT As K H is the true length on I G, it is necessary that we find the true length on I F. Using I F as radius and I as center, draw an arc intersecting I G at a. From a erect a line cutting J H in section at b. Draw a line from h to K, which is the true length on I F. For the pattern, proceed as shown in Fig. 326. Draw any line, as K H, equal in length to K H in Fig. 325. Then, using K b as radius and K in Fig. 326 as center, describe the arc b b, which intersect at a and a by an arc G G struck from H as center and with F G in plan in Fig. 325 as radius. Draw lines in Fig. 326 from K to a to H to a to K, which will be the pattern for one of the points of the star of which 6 are required. When bending the points on the line HK, it is necessary to have a stay or profile so that we may know at what angle the bend should be made. To obtain this stay, erect from the corner B in Fig. 325 a line intersecting the base-line J H at c, from which point, at right angles to J K, draw c d. Using c as center, and c d as radius, strike an arc inter- secting J H at e. From e drop a vertical line meeting A G in plan at d\ Set off i B^ equal to i B, and draw a line from B to d' to B^ which is the true profile after which the pattern in Fig. 326 is to be bent. If the stay in Fig. 325 has been cor- rectly developed, then d' B^ or d^ B must equal earn Fig. 326 on both sides. In Fig. 327 is shown a finished elevation of a hipped roof, on the four corners of which a hip ridge A A butts against the upper base B and cuts off on a vertical line at the bottom, as C and C. To obtain the true profile of this hip ridge, together with the top and lower cuts and the patterns for the lower heads, proceed as shown in Fig. 328, where the front elevation has been omitted, this not being necessary, as only the part plan and diagonal elevation are required. First draw PATTERN FOR kK vCORNER Fig. 326. 238 SHEET METAL WORK the part plan as shown by A B C D E F A, placing the hip or diagonal line F C in a horizontal position; and make the distances between the lines F A and C B and between F E and C D equal, because the roof in this case has equal pitch all around. (The same principles, how- ever, would be used if the roofs had unequal pitches.) Above the plan, draw the line G H. From the points F and C in plan, erect the lines F G and C I, extending C I to C^ so that I C* will be the re- quired height of the roof above G I at the point C in plan. Draw a line "FRONT ELEVATION '"Xl ^^^^ ^ ^0 C\ and from ^. „^„ O draw a horizontal and Fig. 327, vertical line indefinitely, as shown. Then will I G C^ be a true section on the line of the roof on F C in plan. The next step is to obtain a true section of the angle of the roof at right angles to the hip line G C^ in elevation. This is done by drawing at right angles to F C in plan, any line, as a h, intersecting the lines F A and F E as shown. Extend a h until it cuts the base-line G I in elevation at c. From c, at right angles to G CS draw a line, as c dj intersecting G C^ at d. Take the distance c d, and place it in plan on the line F C, measuring from i to d\ Draw a line from a to d' to b, which is the true angle desired. On this angle, construct the desired shape of the hip ridge as shown by J, each half of which divide into equal spaces, as shown by the figures 1 to 6 to 1. As the line G C^ rep- resents the line of the roof, and as the point d^ in plan in the true angle also represents that line, then take a tracing of the profile J with the various points of intersection on same, together with the true angle a d' b, and place it in the elevation as shown by J^ and a' d" b\ being careful to place the point d'^ on the line G C\ making a' 6' parallel to G C^ From the various points of intersection in the profib J, draw lines parallel to F C, intersecting B C and A F at points from 1 to 6. as shown. As both sides of the profile J are symmetrical, it is necessary only to draw lines through one-half. SIIKET IMETATv WORK 230 In similar manner, in elevation, parallel to G C\ draw lines through the various intersections in J^, which intersect by lines drawn at right angles to F C in plan from similarly numbered points on A F PATTERN FOR HIP RIDGE W 214 3 6 34 12 5 5 PATTERN FOR LOWER HEAD Fig. 328. £tDd BC. Trace a line through the points thus obtained. Then will K L be the miter-line at the bottom, and M N the miter-line at the top. For the pattern, draw any line, as O P^ at right angles to G CS 240 SHEET METAL ^VORK upon which place the stretchout of J in plan or J^ in elevation, as shown by the figures 1 to 6 to 1 on O P; and through these numbered points, at right angles to O P, draw lines, which intersect by lines drawn at right angles to G C^ from similar intersections in the lower miter-line K L and upper miter-line N M. Trace a line through the points thus obtained. Then will R S T U be the desired pattern. In practice it is necessary only to obtain one miter-cut — either the top or the bottom— and use the reverse for the opposite side. In other words, U T is that part falling out of R S, the same as R S is that part which cuts away from U T. The upper miter-cut butts against B in Fig. 327; while the lower cut requires a flat head, as shown at C. To obtain this flat head, extend the line I G in Fig. 328, as I W, upon which place twice the amount of spaces contained on the line A F in plan, as 6, 3 — 5, 4, 1, 2, as shown by similar figures on either side of 6 on the line V W. From these divisions erect vertical lines, which intersect by lines drawn parallel to V W from similarly numbered intersections in the miter-line K L G. A line traced through the points thus obtained, as shown by X Y Z, will be the pattern for the heads. Where a hip ridge is re- quired to miter with the apron of a deck moulding, as shown in Fig. 329, in which B repre- sents the apron of the deck cornice, A and A the hip ridges mitering at a and a, a slighdy different process from that described in the preceding problem is used. In this case the part elevation of the mansard roof must first be drawn as shown in Fig. 330. Let ABC K represent the part elevation of the mansard, the section of the deck moulding and apron being shown by D B E. Draw E X par- allel to B C. EX then represents the line of the roof. In its proper position, at right angles to B C, draw a half-section of the hip mould, as shown by F G, which is an exact reproduction of B E of the deck mould. Through the corners of the hip mould at Y and G, draw lines parallel to B C, which intersect by lines drawn parallel to B A from V, W, and E in the deck cornice. Draw the miter-line H I, which completes the part elevation of the mansard. Fig. 329. SHEET METAT> WORK 241 Before the patterns can be obtained, a developed surface of the mansard must be dravvu. Therefore, from B (Fig. 330), drop a ver- tical line, as B J, intersecting the line C K at J. Now take the dis- tance of B C, and place it on a vertical line in Fig. 331, as shown by B C^ Through these two points draw the horizontal lines B A and C K as shown. Take the projection J to C in Fig. 330, and place it as PART ELEVATION OF MANSARD ROOF K PART PLAN \ \ TRUEs SECTION or HIP TRUE SECTION . ON 0-P' Rl Fig. 330. shown from C^ to C in Fig. 331, and draw a line from C to B. Then will A B C K be the developed surface of A B C K in Fig. 330. As both the profiles B V W E and F Y G are similar, take a tracing of either, and place it as shown by D and D^ respectively in Fig. 331. Divide both into the same number of equal spaces, as shown. Bisect the angle A B C by establishing a and b, and, using these as centers. 242 ^nv]v:r mktat. work by describing arcs intersecting at c; then draw d B, which represents the miter-Kne. Through the points in D and D^ draw hnes parallel to their respective moulds, as shown, intersecting the miter-linL B d and the base-line C C^ For the pattern for the hip, draw any line, as E F, at right angles to B C, upon which place twice the stretchout of D, as shown by the divisions 6 to 1 to 6 on EF. Through these divisions draw lines at PATTERN FOR nHIp ridge \a i^y/. L2 "iilZa. 5 6 ^. DEVELOPCD SURFACE OF MANSARD ROOF K Fig. 331. right angles to E F, intersecting similarly numbered lines drawn at right angles to B C from the divisions on B c? and C C^ Trace a line through the points thus obtained. Then will G H J L be the pattern for the hip ridge. When bending this ridge in the machine, it is necessary to know at what angle the line 1 in the pattern will be bent. A true section must be obtained at right angles to the line of hip, for which proceed as shown in Fig. 330. Directly in line with the elevation, construct a part plan L M N O, through which, at an angle of 45 degrees (because the angle L O N is a right angle), draw the hip line O M. Establish at pleasure any point, as P^ on O M, from which erect the vertical line- into the elevation crossing the base-line C K at P and the ridge-line C B at R. Parallel to O M in plan, draw O^ P^ equal to O PS as shown. Extend P^ P^ as P^ R^ which make equal to PR in elevation. SriERT METAT. WORK 243 Draw a line from R^ to O^ Then O^ R^ P^ represents a true section on OP^ in plan. Through any point, as a, at right angles to OM, draw be, cutting L O and ON at b and c respectively. Extend b c until it intersects O^ P^ at d. From d, at right angles to O^ Ji\ draw the line d e. With d as center, and de as radius, draw the arc e e' , intersecting O^ P^ at e' , from which point, at right angles to OM in plan, draw a line intersecting OM at e" . Draw a lir? from b to c" to c, which repre- sents the true section of the hip after which the pattern shown in Fig. 331 is formed. The pattern for the deck mould D B in Fig. 330 is obtained in the same way as the square miter shown in Fig. 277; w^hile the pattern for the apron D^ in Fig. 331 is the same as the one-half pattern of the hip ridge shown by ?i H 1 6. In Fig. 332 is shown a front elevation of an eye-brow dormer. In this view ABC represents the front view of the dormer, the arcs being SECTION THROUGH H J Fig. 332. struck from the center points D, E, and F. A section taken on the Ime H J in elevation is shown at the right; L M shows the roof of the dormer, indicated in the section by N; while the louvers are sbown in elevation by O P and in section by RT. In Fig. 333 is shown how to obtain the various patterns for the various parts of the dormer. ABC represents the half-elevation of the dormer, and EFG a side view, of which EG is the line of the dormer EF that of the roof, and GF the line of the pitched roof against which tlie dormer is required to miter. The front and side views being placed in their proper relative positions, the first step is to obtain a true section at right angles to EF. Proceed as follows: Divide the curve A to B into a number of equal spaces, as shown from 1 to 9. At right angles to A C, and from the figures on A B, draw lines intersecting E G in side view as shown. 244 SIIEF/l^ MF/FAL WOUK From these intersections, and parallel to EF, draw lines intersecting the roof-line GF at P, 2-', 3^ etc. Parallel to EF, and from the point ONE HALF TRUE 9 PROFILE ON LINE E-H IN SIDEVIEW 9 7 6 5 4 3 2 1 ONE HALF PATTERN FOR SHAPE OF OPENING IN ROOF Fig. 33S. G, draw any line indefinitely, as G H. At right angles to EF, and from the point E, draw the line EH, intersecting lines previously drawn, SIIKI^ri^ MK/fAL WORK 245 at IS 2S 3S etc., as shown. Now take a duplicate of the hne E K, with the various intersections thereon, and place it on the center line AC extended as K J. At right angles to K J, and from the figures P, 2^ 3^ etc., draw lines, which intersect with those of similar numbers drawn at right angles to CB, and from similarly numbered points on the curve A B. Trace a line through the points of intersection thus obtained. Then KLMJ will be one-half the true profile on the lire E H in side view, from which the stretchout will be obtained in the development of the pattern. For the pattern for the roof of the dormer, draw at right angles to EF in side view the line N O, upon which place the stretchout of one-half the true profile on the line EH as shown by the small figures 1*, 2*, 3S etc. Then, at right angles to N O, and through the figures, draw lines, which intersect with those of similar numbers drawn at right angles to EF from intersections on EG and GF. Trace a line through the points thus obtained. Then will PRST represent one- half the pattern for the roof. To obtain the pattern for the shape of the opening to be cut into the roof, transfer the line GF, with the various intersections thereon, to any vertical line, as UV, as shown by the figures 1\ 2^ 3^ etc. In similar manner, transfer the line CB in front view, with the various intersections on same, to the Ijne ZW, drawn at right angles to UV, as shown by the figures 1, 2, 3, etc. At right angles to UV, and from the figures, draw lines, which in- tersect with those of similar num- bers drawn at right angles to YZ. Through these points, trace a line. Then will UXYZ be the half-pattern for the shape of the opening to be cut into the main roof. For the pattern for the ventilating slats or louvers, should they be required in the dormer, proceed as shown in Fig. 334. In this figure, A B C is a reproduction of the inside opening shown in Fig. 333. Let 1, 2, 3, 4, 5 in Fig. 334 represent the sections of the louvers which will be placed in this opening. As the methods of obtaining the pat- HALF PATTERN FOR LOUVRE ^4- F 24G STIERT METAL WORK terns for all louvers are alike, the pattern for louver No. 4 will illus- trate the principles employed. Number the various bends of louver No. 4 as shown by points 0, 7, 8, and 9. At right angles to A B, and from these points, draw lines intersecting the curve A C as 6^ 7^ 4^ 8*, and 9^ On B A extended as E D, place the stretchout of louver No. 4 as shown by the figures on ED. Since the miter-line AC is a curve, it will be necessary to introduce intermediate points between 7 and 8 of the profile, in order to obtain this curve in the pattern. In this instance the point marked 4 has been added. Now, at right angles to DE, and through the figures, draw lines, which intersect with those of similar numbers, drawn parallel to AB from intersections 6^ to 9^ on the curve AC. A line traced through the points thus obtained, as FKJH, will be the half-pattern for louver No. 4. The pattern for the face of the dormer is pricked onto the metal direct from the front view in Fig. 333, in which A 8 B C is the half-pattern. In laying out the patterns for bay window work, it often happens that each side of the window has an unequal projection, as is shown in Fig. 335, in which DEE shows an elevation of an octagonal base of a bay window having unequal projections. All that part of the bay above the Une AB is obtained by the method shown in Fig. 290, while the finish of the bay shown by ABC in Fig. 335 will be treated here. In some cases the lower ball C is a half-spun ball. A^ B^ F^ is a true section through A B. It will be noticed that the lines Ca, Cc, and Cd, drawn respectively at right angles to ab, be, and cd, are each of different lengths, thereby making it necessary to obtain a true profile on each of these lines, before the patterns can be obtained. This is clearly explained in connection with Fig. 336, in which only a half-elevation and plan are required as both sides are symmetrical. First draw the SHEET METAI. WORK 247 center line AB, on which draw the half-elevation of the base of the bay, as shown by CDE. At right angles to AB draw the wall line in plan, as FK; and in its proper position in relation to the line CD in elevation, draw the desired half-plan, as shown by GHIJ. From the corners H and I draw the miter-lines HF and IF, as shown. As DE HALF PATTETRN FOR 3 Fig. 336. represents the given profile through FG in plan, then divide the profile DE into an equal number of spaces as shown by the figures 1 to 13. From these points drop vertical lines intersecting the miter-line FH in plan, as shown. From these intersections, parallel to HI, draw lines intersecting the miter-Unes IF, from which points, parallel to IJ, draw lines intersecting the center fine FB. ' Through the various points of intersection in DE, draw horizontal lines indefinitely right and left as shown. 248 SHEET METAL WOIIK If for any reason it is desired to show the elevation of the miter- Hne FI in plan (it not being necessary in the development of the pat- tern), then erect vertical lines from the various intersections on FI, intersecting similar lines in elevation. To avoid a confusion in the drawing, these lines have not been shown. Trace a line through points thus obtained, as shown by D^ 13, which is the desired miter- line in elevation. The next step is to obtain the true profile at right angles to HI and IJ in plan. To obtain the true profile through No. 3 in plan, take a tracing of J F, with the various intersections thereon, and place it on a line drawn parallel to CD in elevation, as J^ F^, with the intersections 1 to 13, as shown. From these intersections, at right angles to J^ FS erect lines intersecting similar lines drawn through the profile DE in elevation. Trace a line through the points thus obtained, as shown by 1' to 13', which represents the true profile for part 3 in plan. At right angles to IH in plan, draw any line, as ML, and extend the va- rious lines drawn parallel to IH until they intersect LM at points 1 to 13, as shown. Take a tracing of LM, with the various points of intersection, and place it on any horizontal line, as L^ MS as shown by the figures 1 to 13, from which, at right angles to L^ M^ erect vertical lines inter- secting similarly numbered horizontal lines drawn through the profile DE. Trace a line through the points thus obtained. Then will r'— 13'' be the true profile through No. 2 in plan at right angles to HI. For the pattern for No. 1 in plan, extend the line FK, as NO, upon which place the stretchout of the profile DE as shown by the figures 1 to 13 on NO. At right angles to NO, and from the figures, draw lines, which intersect with lines (partly shown) drawn parallel to FG from similar intersections on the miter-line FII. Trace a line through the points thus obtained; then will 1 P 13 be the pattern for part 1 in plan. At right angles to H I, draw any line, as T U, upon which place the stretchout of profile No. 2, being careful to measure each space separately, as they are all unecjual, as shown by the small figures 1" to 13" on TU. Through these figures, at right angles to TU, draw lines as shown, which intersect by lines (not shown in the drawing) drawn at right angles to I H from similar points on the miter-lines HF and FI. SHEET METAF. W)RK 249 Trace a line through the points thus obtained. Then will \^ W X he the pattern for part 2 in plan. For the half-pattern for part 3 in plan, extend the center line A B in plan as B R, upon which place the stretchout of the true profile for 3, being careful to measure each space separately, as shown by the figures 1' to 13' on BR. At right angles to B R draw lines through the figures, which intersect by lines drawn at right angles to J I from similar points of intersection on the miter-line F I. A line traced through points thus obtained, as V S 13', will be the half-pattern for part 3. DEVELOPMENT OF BLANKS FOR CURVED MOULDINGS Our first attention will be given to the methods of construction, it being necessary that we know the methods of construction before the blank can be laid out. For example, in Fig. 337 is a part elevation of a dormer window, with a semicircular top whose profile has an ogee, fillet, and cove. If this job were undertaken by a firm who had no circular moulding machine, as is the case in many of the smaller shops, the mould would have to be made by harid. The method of construc- tion in this case would then be as shown in Fig. 338, which shows an enlarged section through a 6 in Fig. 337. Thus the strips a, b, and c in Fig. 338 would be cut to the required size, and would be nothing more than straight strips of metal, while d d' would be an angle, the low^er side d' being notched with the shears and turned to the required circle. The face strips e, /, and h would represent arcs of circles to correspond to their various diameters obtained from the full-sized elevation. These face and sink strips would all be soldered together, and form a succession of square angles, as shown, in which the ogee, as shown by i j, and the cove, as shown by vi, would be fitted. In obtaining the patterns for the blanks hammered by hand, the averaged lines would be drawn as shown by ^ / for the ogee and n for the cove. The method or principles of averaging these and other moulds will be explained as we proceed. In Fig. 339 is shown the same mould as in the previous figure, a different method of construction being employed from the one made by hand and the one hammered up by machine. In machine work this 250 SHEET METAL WORK mould can be hammered in one piece, 8 feet long or of the length of the sheets in use, if such length is required, the machine taking in the full mould from A to B. The pattern for work of this kind is averaged by drawing a line as shown by CD. This method will also be ex- plained more fully as we proceed. SHOP TOOLS EMPLOYED When working any circular mould by hand, all that is required m the way of tools is various-sized raising and stretching hammers square stake, blow-horn stake, and mandrel including raising blocks made of wood or lead. A first-rate knowledge must be employed by the mechanic in the handling and working of these small tools. In a thoroughly up-to-date shop will be found what are known as '^curved moulding" machines, which can be operated by foot or power, and which have the advantage over hand operation of saving time' and labor, and also turning out first-class work, as all seams are avoided. PRINCIPLES EMPLOYED FOR OBTAINING APPROXIMATE BLANKS FOR CURVED MOULDINGS HAMMERED BY HAND The governing principles underlying all such operations are the same as every sheet-metal worker uses in the laying out of the simple patterns m flaring ware. In other words, one who understands how to lay out the pattern for a frustum of a cone understands the principles of developmg the blanks for curved mouldings. The principles will be described in detail in what follows. Our first problem is that of obtaining a blank for a plain flare shown in Fig. 340. First draw the center line A B, and construct the half-elevation of the mould, as C D E F. Extend D E until it inter- SHEET iMETAL WORK 251 sects the center line A B at G. At right angles to A B from any point, as H, draw H 1 equal to C D, as shown. Using H as center, and with H 1 as radius, describe the quarter-circle 1 7, which is a section on C D. Divide 1 7 into equal spaces, as shown. Now using G as center, with radii equal to G E and G D, describe the arcs D 7' and E E°. From any point, as T, draw the radial line 1' G, intersecting the inner arc at E^. Take a stretchout of the quarter-section; place it as shown Fig. 340. Fig. 341. from r to 7'; and draw a line from7' to G, intersecting the inner arc at E°. Then will E^ V 7' E° be the quarter-pattern for the flare D E in elevation. If the pattern is required in two halves, join two pieces; if required in one piece, join four pieces. In Fig. 341 is shown a curved mould whose profile contains a cove. To work this profile, the blank must be stretched with the stretching hammer. We mention this here so that the student will pay attention to the rule for obtaining patterns for stretched moulds. First draw the center line A B; also the half-elevation of the moulding, as C D E F. Divide the cove E D into an equal number of spaces, as shown from 252 SHEET METAL WORK (7 to e. Through the center of the cove c draw a Hue parallel to e a, extending it until it meets the center line A B at G, which is the center point from which to strike the pattern. Take the stretchout of the cove c e and c a, and place it as shown by c e' and c a' . When stretch- ing the flare a! e' , c remains stationary, e' and a' being hammered to- wards e and a respectively. Therefore, from c erect a vertical line intersecting H 1 , drawn at right angles to A B, at 1 . Using H as center and H 1 as radius, describe the arc 1 7, which divide into equal spaces as shown. AVith G as center, and radii equal to G a\ Gc, and G c', describe the arcs c'' e^', 1' 7\ and a" a". Draw a line from e'^ to G, inter- secting the center and lower arcs at 1^ and a'\ Starting from T, lay oflp the stretchout of the quarter-section as shown from 1' to 7'. Through 7' draw a line towards G, intersecting the in- ner arc at a''; and, extending the line upward, intersect the outer arc at e'\ Then will a'' e" e^' a" be the quarter- pattern for the cove E D in elevation. If the quarter-round N O were re- quired in place of the cove E D, then, as this quarter-round would require to be raised, the rule given in the former Instruction Paper on Sheet Metal Work would be applied to all cases of raised mouldings. In Fig. 342 is shown a curved mould whose profile is an ogee. In this case as in the preceding, draw the center line and half-elevation, and divide the ogee into a number of equal parts, as show^n from a to h. Through the flaring portion of the ogee, as c e, draw a line, extending it upward and downward until it intersects the center line A B at G. Take the stretchouts from a to c and from eioh and place them re- spectively from c to a' and from e to h' on the line h! G. Then, in work- ing the ogee, that portion of the flare from c to e remains stationary; thepart from t to A/ will be stretched to fonii e h ; while that part shown from c to a' will be raised to fomi c a. From any point in the station- ary flare, as d, erect a line meeting the line H 1, drawn at right Fig. 342. SHEET METAL ^^OKK 253 angles to A B, at 1. Using H as center and H 1 as radius, describe the quarter-section, and divide same into equal spaces, as shown. With G as center and with radii equal to G a' , G d, and G h! , describe the arcs a" a", V 1\ and h" h". From h'' draw a line to G. Starting at V , lay off the stretchout of the section as shown from 1' to 7'. Through 7' draw a line to G, as before de- a' scribed. Then will ^a'^ a" If be the quarter-pat- tern for the ogee E D. In Fig. 343 is shown how the blanks are de- veloped when a bead moulding is employed. As before, first draw the center line A^ B^ and the half-elevation A B C D. As the bead takes up f of a circle, as shown by ' ^V^ a c e f, and as the pat- tern for / e will be the same as for e c, then will the pattern for c e only be shown, which can also be used for e j. Bisect a c and c e, obtaining the points 6 and d, which represent the stationary points in the patterns. Take the stretchouts of 6 to a and b to c, and place them Fig. 343. as shown from b to a' and from b to c'; also take the stretchouts oi d to c and d to e, and place them from d to c' and from d to e/ on lines drawn parallel respectively to a c and c e from points b and d. Extend the lines e' c' and c' a' until they intersect the center line A^ B* at E and F respectively. From the points b and d erect lines intersecting the line G 1, drawn at right angles to A^ 254 SHEET METAL WORK B', at 14 and 1 respectively. Using G as center, and with radii equal to G 14 and G 1, describe quarter-sections, as shown. Divide both into equal parts, as shown from 1 to 7, and from 8 to 14. With £ as center, and with radii equal to E c\ E d, and E e\ describe the arcs c" c", d' d', and e" e". From any point on one end, as e", draw a radial hne to E, intersecting the inner arcs at d' and c". Now take the stretchout of the section from 1 to 7, and, starting at d\ lay off the stretchout as shown from 1' to T. Through 7 draw a line towards E, intersecting the inner arc at c" and the outer one at e". Then will c" e" e" c" be the quarter-pattern for that part of the bead shown by c e, also for e /, in elevation. For the pattern for that part shown by a c, use F^ as center; and with radii equal to F a, F b, Fig. 344. and F c', describe the arcs a" a", b' b', and c" c". From any point on the arc b' b' , as 8', lay off the stretch- out of the quarter-section 8 14, as shown from 8' to 14'. Through these two points draw lines towards F^ in- tersecting the inner arcs at a" «"; and extend them until they intersect the outer arc at c" and c'. Then will c" a" a" c" be the desired pattern. In Fig„ 344 is shown an illustra- ® tion of a round finial which contains ^^S- 345. moulds, the principles of which have already been described in the preceding problems. The ball A is made of either horizontal or vertical sections. In Fig. 345 is shown how the moulds in a finial of this kind are averaged. The method of obtaining the true length of each pattern piece will be omitted, as this was thoroughly covered in the preceding problems. First draw the center line A B, on either side of which draw the section of the finial, as shown by C D E. The blanks for the ball a will be obtained as explained by the devel- opment shown on page 1C6 of this volume. The mould 6 is averaged as shown by the line e j\ extending same until it intersects the center line at h, e f representing the stretchout of the mould STIKET jMETAT. WORK 25; O.) obtained, as already explained elsewhere in the text. Using // as center, with h f and h e as radii, describe the blank h°. In the next mould, c c\ a seam is located in same as shown by the dotted line. Then average C by the line / j, extending same until it meets the center line at k; also average c' by the line / m, extending this also until the center line is intersected at n. Then i j and / m represent respectively the stretchouts of the mould c c\ the blanks c° and c^ being struck respectively from the centers k and n. The mould b' h" also has a seam, as shown by the dotted line, the moulds being averaged by the lines p o and s t, which, if extended, intersect the center line at r and u. These points are the centers, respectively, for striking the blanks 6° and h^. The flaring piece d is struck from the r 2:. 7 Fig. 346. center x, with radii equal to xw and x v, thus obtaining the blank dP. By referring to the various rules given in previous problems, the true length of the blanks can be obtained. The principles used for blanks hammered by hand can be applied to almost any form that will arise, as, for example, in the case shown in Fig. 346, in which A and B represent circular leader heads; or in that shown in Fig. 347, in which A and B show two styles of balusters, a and b (in both) representing the square tops and bases. Another example is that of a round finial, as in Fig. 348, A showing the hood which slips over the apex of the roof. TOiile these forms can be bought, yet in some cases where a special design is brought out by the architect, it is necessary that they be made by hand, especially when but one is required. The last problem on handwork is shown in Fig. 349 — that of obtaining the blanks for the bottom of a circular bay. The curved moulding A will be hammered by hand or by machine, as will be ex- ^r^c^ SHEET METAL ^Y()RK plained later on, while the bottom B is the problem before us. The plan, it will be seen, is the arc of a circle; and, to obtain the various blanks, proceed as shown in Fig. 350, in which ABC is the elevation of the bottom of the bay, I J K being a plan view on A C, showing the Fig. 347. curve struck from the center H. In this case the front view of the bottom of the bay is given, and must have the shape indicated by A B C taken on the line IJ in plan. It therefore becomes necessary to establish a true section on the center line S K in plan, from which to obtain the radii for the blanks or ^ Fig. 349. Fig. 348. patterns. To obtain this true section, divide the curve A B into any number of equal parts, as shown from 1 to 6. From the points of division, at right angles to A C, drop Hues as shown, intersecting the wall line I J at points 1' to 6'. Then, using H as center, and radii equal to H 6', H 5', H 4', H 3', and H 2', draw arcs crossing the center line D E shown from V to Cf. At any convenient point siiKRT Minwr. \v()i: 2f)7 opposite the front elevation draw any vertical line, as T U. Extend the lines from the spaces in the profile A B until they intersect the vertical line T II as shown. Now, measuring in every instance from the point S in j)lan, take the various distances to the num- TRUE SECTION , ON S-K K \ \ M \ \ In E Fig. 350. bered points in plan and place them upon lines of similar numbers, measuring in every instance from the line T U in section. Thus take the distance S K in plan, and place it as shown from the line T U to K^ ; then again, take the distance from S to 2" in plan, and place it as shown from the line T U to 2" on line 2 in section. Proceed in this manner until all the points in the true section have been obtained. Trace a line as shown, when V to 6'' to Y will be the true section on the line S K in plan. It should be understood that the usual method for making the bottom of bays round in plan is to divide the profile of the moulding into such parts as can be best raised or stretched. As- suming that this has been done, take the distance from 1'' in plan to the center point H, and place it as shown from \" to L in section. From the point L, draw a vertical line L M, as shown. For the pat- tern for the mould \" 2" , average a line through the extreme points, as shown, and extend the same until it meets L M at N. Then, with N as center, and with radii equal to N 2" and N \" , describe IM 258 STTRRT ATRTAT. WORK the blank shown. The length of this blank is obtained by measur- ing on the arc 1' V in plan, and placing this stretchout on the arc V of the blank. The other blanks are obtained in precisely the same manner. Thus P is the center for the blank 2'' 3''; R, for the blank 3'' 4"; O, for the blank 4'' 5^'; and M, for the blank 5'' 6''. The moulds V 2^ 2'^ 3'', and 3'' r will be raised; while the blanks ^ 5'' and 5^' 6'' will be stretched. APPROXIMATE BLANKS FOR CURVED MOULDINGS HAMMERED BY MACHINE The principles employed in averaging the profile for a moulding to be rolled or hammered by machine do not differ to any material extent from those used in the case of mouldings hammered by hand. Fig. 351 shows the general method of aver- aging the profile of a moulding in determin- ing the radius of the blank or pattern. It will be seen that A B is drawn in such a manner, so to speak, as to average the in- equalities of the profile D C required to be made. Thus distances a and b are equal, as are the distances c and d, and e and /. It is •c very difficult to indicate definite rules to be ^B observed in drawing a line of this kind, or, in other words, in averaging the profile. Nothing short of actual experience and intim.ate knowledge of the material in which the moulding is to be made, will enable the operator Fig. 351. SECTION Fig. 352. to decide correctly in all cases. There is, however, no danger of making very grave errors in this respect, because the capacity of the machines in use is such, that, were the pattern less advanta- geously planned in this particular than it should be, still, by passing it through the dies or rolls an extra time or two, it would be brought to the required shape. SlIERT MKTAT. WOlMv 2;7.) In Fig. 352 is shown a part elevation of a circular moulding as it would occur in a segmental pediment, window cap, or other structure arising in sheet-metal cornice work. B shows the curved moulding, joining two horizontal pieces A and C, the true section of all the moulds being shown by D. In this connection it may be proper to remark that in practice, no n. iters are cut on the circular blanks, the miter-cuts being placed on die horizontal pieces, and the circular moulding trimmed after it has l)een formed up. In Fig. 353 is shown the method of obtaining the blanks for mouldings curved. in elevation, no matter what their radius or profile Fig. 353. may be. First draw the center line A B, and, with thedesired center, as B, describe the outer cui^e A. At right angles to A B, in its proper position, draw a section of the profile as show^n by C D. From the various, members in this section, project Hues to the center line A B, as 1, 2, 3, and 4; and, using B as center, describe the various arcs and complete the elevation as shown by A B C in Fig. 352, only partly shown in Fig. 353. In the manner before described, average the profile C D by the line c d, extending it until it intersects the line drawn through the center B at right angles to A B, at E. Then E is the center from which to strike the pattern. Centrally on the section C D, estab- lish e on the line c d, where it intersects the mould, and take the stretchout from 6- to C and from e to D, and place it as shown respec- tivelv from e to c and from e to d on the line c d. Now, using E as 260 SlIKKT MF/lAL WOUK ^ ELEVATION ) Fig. 354. center, with radii equal to E c^, E e, and E c, describe the arcs d' df\ e' e", and c' c" . Draw a Hne from c' to E, intersecting the middle and inner arc at e' and d! . The arc e' e" then becomes the measuring line to obtain the length of the pattern, the length being measured on the arc 2 in elevation, which corresponds to the point e in section. In Fig. 354 is shown the elevation of a moulding A curved in plan B, the arc being struck from the given point a. This is apt to occur when the moulding or cornice is placed on a building whose corner is round. To ob- tain the pattern when the moulding is curved in plan, proceed as shown in Fig. 355. Draw the section of the moulding, as A B, A C be- ing the mould for which the pattern is desired. C B represents a straight strip which is at- tached to the mould after it is hammered or rolled to shape. In practice the elevation is not required. At pleasure, below the sec- tion, draw the horizontal line E D. From the extreme or outside edge of the mould, as 6, drop a line intersecting the horizontal line ED at E. Knowing the radius of the arc on h in section, place it on the line E D, thus ob- taining the point D. With D as center, describe the arc E F, intersecting a line drawn at right angle to V. D from D. Average a line through the section, as G H, intersecting the line D F, drawn vertical from the cen- ter D, at J. Establish at pleasure the stationary point a, from which drop a line cutting E D at a\ Using D as center, and with D a' as radius, describe the arc a' a", which is the measuring line when laying out the pattern. Now take the stretch- Fig. 3.55. SIIKF/r i\IF/l\\L v.omv 201 outs from a to h and from a to c, and place them on tl^e avera«^ed line from a to G and from a to H respectively. Using J as center, with radii extending to the various points G, a, and IT, describe th' arcs G G\ a a"\ and H H^ On the arc a' a!" , the pattern is measured to correspond to the arc o! a" in plan. In Fig. 356 is shown a front view of an ornamental bull's-eye window, showing the circular mould A B C D, which in this case we desire to lay out in one piece, so that, when hammered or rolled in the machine, it will have the desired diameter. The same principles can be applied to the upper mould E F, as were used in connection with Figs. 352 and 353. Fig. 356. To obtain the blank for the bull's-eye window shown in Fig. 35t^ proceed as shown in Fig. 357. Let A B C D represent the elevatio of the bull's-eye struck from the center E. Through E draw the hor HL H ELEVATION Fig. 357. zontal and perpendicular hues shown. In its proper position, draw a section of the window as shown by F G. Through the face of the mould, as H I, average the hne H^ I\ extending it until it intersects 262 SHEET METAL WORK the center line B D at J. Where the average Hne intersects the mould at a, establish this as a stationary point; and take the stretchouts from a to I and from a to II, and lay them off on the line H^ P from a to I' and a to PP respectively. As 1 5 in elevation represents the quarter-circle on the point a in section, divide this quarter- circle into equal spaces, as shown. Now, with radii equal to J P, J a, and J H^, and with J in Fig. 358 as center, de- scribe the arcs H H, a a, and I I. From any point, as H, on one side, draw a line to J, intersecting the middle and in- Fig. 358. ner arcs at a and I. Take the stretchout of the quarter-circle from 1 to 5 in elevation in Fig. 357, and place it on the arc a a as shown from 1 to 5. Step this off four times, as shown by 5', 5'', and 5'". From J draw a line through 5''', intersecting the inner and outer arcs at I and H. Then will H a a H be the full pattern. PRACTICAL PROBLEMS IN MENSURATION FOR SHEET METAL WORKERS. A square tank, Fig. 1, is required whose capacity should be 200 gallons, the sides h a and a c each to be 30 inches; liow high must c d be, so that the tank will hold the desired quantity ? Suppose the height 6' d is to be 51^ inches, and the tank is to c a ID ^^^ ^^ ) CAPACITY 200 GALLONS d / CAPACITY 510 GALLONS Fig. 1. Fi}?. 2- have similar capacity, and one side c a is to be 20 inches wide, how long must the alternate side a Ij be, so that the tank will hold 200 gallons ? A round tank. Fig. 2, is to be constructed whose capacity should equal 510 gallons, and be 5 feet high from c to a\ what must its diameter a h be, so as to hold the desired capacity ? Suppose the diameter of the tank is to be 50 inches as a h: what must its heiorht a e be, so that the tank will hold 510 gallons ? A large drip pan, Fig. 3, is to be constructed whose ca- pacity should be 165 gallons, and whose top measurements a 1) and b c are 60 X 40 inches respectively, and bottom measurements d e and Fiu-, PROBLEMS IN MENSUKATION eJ'S4: X 54 inches respectively; what iniist its height 7/i n be, so as to hold the desired volume ? A round tapering measure, Fig. 4, is to be constructed whose volume will equal 42 quarts; its bottom diameter a h is to be 14 Fig. 4. inches, its top diameter c d 18 inches; what must its height e/'hii to hold the desired quantity ? An elliptical tapering tank, Fig. 5, is to be constructed whose major axis vi h is 24 inches, and minor axis c dlii inches at the top, while at the bottom the major axis ef\^ 20 inches, and minor axis g h 10 inches; the capacity of the tank should equal 44 quarts; what must the height qu n be, so that the tank will hold the desired amount ? A tank. Fig. 6, is to be constructed with semicircular ends Fig. 6. Fig. 7. whose capacity should equal 30 gallons; the length a h to be 20 inches, and the diameters of c and d to be each 10 inches; what must the height ^'^be, so that the tank will hold the desired quantity? Suppose the height ^,/is to be 24 inches, the diameters c and d each 11 inches; what must the length of a h be, so that the tank will hold 30 gallons ? PROBLEMS IN MENSURATION 111 Fig. 7 IS shown a fitting used in ventilation piping; the diameter a h \^ 11^ inches and it is desired that the oblono- pipe on the opposite end shall have an area similar to the round pipe a h\ if ^ymust be 5 inches, what must c d be so that both areas are alike ? Suppose the pipe is to be square in place of oblong, what must the length of each side be, so that both ends have similar area? In Fig. 8, ah is 40. inches in diameter; and each one of the branches \)7 three-way branch !)() two-branch fork 04 M Mallet 163 Metal roofing 158 tables 159-161 tools 103 Metal slates and shingles ] 62 Micrometer caliper 4 Miter, definition of 196 Miter cutting 204 angular pediment with horizontal returns 219 eye-brow dormer 243 gable moulding intersecting a pilaster 216 gable moulding mitering on a wash 217 gable moulding in octagon plan 224 gore piece joined to a chamfer 235 gutter or eavetrough 233 hip ridge 237 horizontal moulding butting against pitched roof 207 moulding which miters at an angle other than right 212 panel or face miter 209 raking bracket in gable moulding 230 segmental pediment with upper and lower horizontal returns 223 six-pointed star 236 spire, square in plan, intersecting four gables 228 square return miter 205 turret with four gables 219 two mouldings having different profiles to miter together 213 Modillion course 194 Mouldings 202 cavetto 203 cyma recta 202 cyma reversa 203 echinus 203 torus 203 X Notching machine 163 O Oblique piping 75 P Panels 194 Pitched skylights 134 Planceer 194 260 INDKX Page Problems, coppersmith's ' . -. 105 Problems in heavy metal work IIG Problems in light gauge metal , 75 I'roblcMiis in sheet-metal work 26 bath tub ;-{2 elbows 44 Emerson ventilator 41 faucet, joining of to sheet-metal tank 27 funnel strainer pail 36 hip bath 30 sink drainer 26 R Rain-water cut-off 77 Raising sash 139 Raking mouldings 196 Roman mouldings 202 Roof mensuration 163 Roofing 158 corrugated iron 182 flat-seam 167 table 159 standing-seam 177 table 160 tin plate data 161 tools 163 Roofing folders 163 Roofing tin 158 S Scraper 163 Shears 163 Sheet-metal cornices 193 Sheet metal work coppersmith's problems 105 cornices 193 heavy metal problems 116 light gauge metal problems 75 miter cutting 204 plates \ 75-79, 133-135 roofing 158 skylights 133 Shop tools 4 Single-pitch skylight 141 Sink drainer 26 Skyhghts 133 bars, various shapes of 136 construction 1 33 curbs, various shapes of 137 INDEX 267 Skylights Page double-pitch 142 fiat extension 142 hipped 14;^ raising sash 189 shop tools 136 single-pitch 141 Soldering 172 Soldering copper 163 Standing-seam roofing 177 table 160 Stretch-awl 163 T Tables angle iron, weight of 74 cast iron, wrought iron, copper, lead, brass, and zinc, weight of . . . . 62 corrugated sheets, measurements of 184 flat rolled iron, weights of 66-71 flat-seam roofing 159 iron bars, square and round 72, 73 rough glass, weight of, per sq. ft 135 sheet copper 63 sheet iron and steel, standard gauge for 65 sheet zinc 64 standing-seam roofing 160 tee iron, weight of 74 tin plates, net weight per boK 161 tin plates, standard weights and gauges of 161 Terne plate 158 Tools required by metal roofers . . -. 163 Tools used in cornice work 200 Torus moulding 203 Triangulation, developments by 15 Turret sash 1 52 W Workshop problems 26