Chapter III: Part 3

Jacques Demoux, Winnipeg, Man., wants to know how to lay out braces, regular and irregular by the use of the Steel Square.

Answer: Braces and trusses are something like rafters and when the run is known, there should be no difficulty in getting the lengths and proper bevels.

In the first place it is always best to make a pattern and then mark out the timber work from the pattern. Suppose we want braces having a “four-foot run”—that is, the brace is to form a diagonal from points four feet from the post and four feet from the girt. Take a piece of stuff already prepared, six feet long, four inches wide and half-inch thick, gauge it three-eighths from jointed edge.

Take the square as arranged at Fig. 71, and place it on the prepared stuff as shown at Fig. 72. Adjust the square so that the twelve-inch line coincide exactly with the gauge line o, o, o, o. Hold the square firmly in the position now obtained, and slide the fence up the tongue and blade until it fits snugly against the jointed edge of the prepared stuff, screw the fence tight on the square, and be sure that the 12-inch marks on both the blade and the tongue are in exact position over the gauge-line.

We are now ready to lay out the pattern. Slide the square to the extreme left, as shown on the dotted lines at x, mark with a knife on the outside edges of the square, cutting the gauge line. Repeat this process four times, marking the ends, and you have the length and bevels. Square over at each end from the gauge line and you have the toe of the brace. The lines ss, Fig. 72, show the tenons left on the end of the braces.

The cut at Fig. 73, shows the brace in position, on a reduced scale. The principle on which the square works in the formation of a brace can easily be understood from this cut, as the dotted lines show the position the square was in when the pattern was laid out.

It may be necessary to state that the “square,” as now arranged, will lay out a brace pattern for any length, if the angle is right, and the run equal. Should the brace be of great length, however, additional care must be taken in the adjustment of the square, for should there be any departure from truth, that departure will be repeated every time the square is moved, and where it would not affect a short run, it might seriously affect a long one.

To lay out a pattern for a brace where the run on the beam is three feet, and the run down the post four, proceed as follows:

Prepare a piece of stuff, same as the one operated on for four feet run; joint and gauge it. Lay the square on the left-hand side, keep the 12-inch mark on the tongue, over the gauge-line; place the 9-inch mark on the blade, on the gauge-line, so that the gauge-line forms the third side of a right angle triangle, the other sides of which are nine and twelve inches, respectively.

Now proceed as on the former occasion, and as shown at Fig. 74, taking care to mark the bevels at the extreme ends. The dotted lines show the position of the square, as the pattern is being laid out.

Fig. 75 shows the brace in position, the dotted lines show where the square was placed on the pattern. It is well to thoroughly understand the method of obtaining the lengths and bevels of irregular braces. A little study will soon enable any person to make all kinds of braces.

If we want a brace with a two-foot run, and a four-foot run it must be evident that, as two is the half of four, so on the square take 12 inches on the tongue, and 6 inches on the blade, apply four times, and we have the length, and the bevels of a brace for this run.

For a three by four foot run, take 12 inches on the tongue and 9 inches on the blade, and apply four times, because, as three feet is ¾ of four feet, so 9 inches is ¾ of 12 inches.

A young carpenter, Toronto, wants to know how to find the center of a circle by aid of the Square.

Answer: In Fig. 76 is shown how the center of a circle may be determined without the use of compasses; this is based on the principle that a circle can be drawn through any three points that are not actually in a straight line. Suppose we take A, B, C, D for four given points, then draw a line from A to D, and from B to C; get the center of these lines, and square from these centers as shown, and when the square crosses the line, or where the lines intersect, as at x, there will be the center of the circle. This is a very useful rule.

Ed. McDonald, Cincinnati, Ohio, says: “I want to know how much can be done with the square towards setting out stair railing?”

Answer: In a previous page a few remarks on this subject will be found and the following is further submitted:

Fig. 77 shows a plan of a stair well having three winders. The rail in this case will have two different pitches. These rails are a little more complicated than those having equal pitches, as in the latter the major axis is parallel off the diagonal line B D (Fig. 77). When the pitches differ the major axis ceases to be parallel; and the greater the difference in the pitches, the greater will be the difference in the axis and diagonal line. This fact can be easily demonstrated by cutting a model bed block out of 2-inch by 2-inch stuff to equal pitches. Procure a board, and draw a parallel line, say 8 inches off the edge. Now square over a line to cut the first line; set the bed block on, with the back corner touching the intersection of the lines. Lay a piece of cardboard on the inclined face of the bed block, and let it slide down until it touches the board. Make a mark along this edge, and it will be seen, on removing the card, that this line is equidistant from the corner (see Fig. 78). In Fig. 78 the cardboard is shown as though it were transparent. What has just been done is that the plane in which the rail lies has been projected to intersect the horizontal plane which contains the plan of the wreath. The name by which this line is generally known is the horizontal trace (shown at C, Figs. 78 and 79). The minor axis (Figs. 78 and 79) is always parallel off this, and always touches A as in Fig. 77. The major axis (Figs. 78 and 79) also touches this point A, and is always square off the minor axis and off the horizontal trace. It will be seen by this that the rail is pitched equally both ways; therefore the face mold will be of equal width at the ends.

When rails are cut by bandsaw on bed blocks, bevels are not necessary, as they can always be obtained by applying a bevel as shown at Fig. 80. The stock should lie solid on the block and square off the sides. When the block is thin it is best to apply the bevel near the corner, when a greater surface is obtained. These bevels are applied after the joint is squared off the tangent lines. To demonstrate a rail with unequal pitches, cut another piece of stuff 2x2 inches, as shown in Fig. 79, repeat the process with the cardboard as before. It will be found that the horizontal trace has departed from the angle of 45 degrees (see Fig. 79) and has approached nearer one corner and gone farther away on the other. The major axis B will have done likewise, as it is always square off the horizontal trace C. The wreath having two pitches, the face mold will obviously be wider at one end than at the other; and if bevels are required, they must be set off on the face of each side of the block. The width of the face mold is to be applied on the tangent line; this makes it slightly in excess on the joint, but it is better to have a little margin in thickness for working. Where thickness of stuff is a secondary consideration, it is preferable to take the rail out of stuff which is as thick as the diameter of a circle that will enclose the section of rail; the corners will then be left complete.

The following method shows the least thickness the rail can be cut out of, and also gives width of face molds on the joint. Set the bevel to the bed block as shown at Fig. 80, and apply at the side of the block. Draw a section of rail level; apply the bevel again, touching the bottom corner of the section. The distance between the marks is the thickness, a plumb line marked on shows the width of the face mold on the bevel line. Where the pitches are different the foregoing method has to be applied to each side of the bed block.

The bevels may be also obtained by the steel square. Take the width of prism face (shown by dotted lines) by laying the square with blade on the line C D (Fig. 82) and tongue, cutting at the center A. Note the length on the tongue of the square. Make a mark of this length on the edge of board. Now take the width of A to D (Fig. 84) which is 6 inches off the blade; keep this 6-inch mark fair at the end of this line made on the board (Fig. 81) and push on square until the tongue touches the end of the line; mark by the tongue, and this gives the bevel required.

To obtain an example of unequal pitches refer to Fig. 84. To set this out, run a line parallel off the edge of the board, and off this line square another. With the intersection A as a center, describe a semi-circle of 6 inches radius. This indicates the center of the rail. Run lines radial from A as shown; these are the riser lines. Draw the lines B C and C D, which are the tangents. Draw the diagonal B D. To make the bed blocks, procure a piece of one inch stuff; take it to the width shown at B C; square on a mark about 3 inches from the end (this is to allow for the shank to clear the saw table; the block is shown at Fig. 83 without the 3-inch allowance). Take on the steel square the rise on tongue and going on blade of the straight flight of stairs; mark on the inch board at tongue; this is pitch of the first tangent. Take the height at D, which is one and a half risers—10½ inches; deduct the height of the first tangent from 10½ inches; take the difference on the tongue and width from C to D on the blade; the tongue gives the cut for the second tangent. Mark the pitch of the first tangent on the edge of the second and cut to this; the pitch of the second tangent gives the edge cut of the first. Cut and fix together with stretcher as previously described.

To get out the face mold, procure a piece of thin stuff. Three-ply wood is excellent, as though it is liable to warp it does not shrink perceptibly. Shoot on edge and gauge on a center line; take the distance from B to D (Fig. 84) (the hypothenuse of 6 and 6) on the blade and the rise (10½) at D on the tongue; lay on the edge of the board to this. Lay off this length on the three-ply at B D (Fig. 82); take the width B C (Fig. 84) on the blade, rise at C on the tongue; find the hypothenuse, and apply with a pair of compasses at Fig. 82 with B as a center cutting at C. Then apply at D as a center, cutting at A. Now find the hypothenuse C to D (Fig. 84), and apply the compasses as before, with D and B as centers, cutting at A and C. Connect up the points where the arcs intersect to B and D; this is the face of the inclined prism, and contains the true shape of rail. Continue the tangent line C B, 3 inches or whatever is required for the shank, and square the joints of the lines B and D. In order to locate the major axis the horizontal trace is now required. Stand the bed block on the plan (see Fig. 83). Run the blade of the square down until it touches the board; mark this, and remove the block. It will be seen that the bed block has not got the 3 inches allowed at the bottom, but the horizontal trace is as easily found with as without the allowance; all that is required in the former case being to turn the blade to B (still keeping the heel at the top of the bed block), make a mark where the square touches and lay on the square as shown at Fig. 83. Mark at the blade, and slide back the square until the tongue touches at B, and also at the center A. This gives the true horizontal trace and major axis. Note the size indicated by the arrow lines on the tongue (from heel to B). Transfer the square to the three-ply board (Fig. 82), placing it as shown, with the blade touching A, and the distance of the arrow lines at B. Mark along the inside of the blade of the square and slide the square back until the tongue cuts at A. This gives the minor axis. Now continue this line downwards to guide the position of the square shown at Fig. 84. Describe a circle as wide as the rail on the minor axis (Fig. 82). The distance from A (Fig. 84) to the center of the rail is the distance to apply at Fig. 82 for the center of the rail, as this is the point where the center of the rail is fair with the plank. Obtain the width of the face molds, and apply at B and D; lay the square on the major and minor axis as shown at Fig. 84. Lay a lath on the square, with the point touching the outside of the circle at C; drive in a nail at the heel of the square; shift the lath until the point lies at B, and drive in another nail at the side of the square. This trammel is now ready to sweep the outside of the mold, which is done by reversing the square, as shown by dotted lines. Pull out the nails and repeat the process for the inside of the mold.

Now run parallel lines off the tangent B for the shank; this completes the face mold, which is now ready for the face of the plank. Wreaths for stairs with flights which stand at either acute or obtuse angles to each other may be set out by the methods that have been here described. The only difference, practically, is that the bed block is made acute or obtuse to suit plan of tangents. The device shown at Fig. 85 has been found to answer excellently for striking out ellipses. To make this, procure two screws ¾ inches long, also a piece of brass tube that will just slip on the plain part of the screw without shaking. Counter sink out the ends until the screw heads are flush; cut two pieces off the tube three-sixteenths and file up true—these pieces are best held by sinking them with a bit in a piece of hardwood. Now when about to strike an ellipse, drive these screws in with the collars on to half major and minor, measured from the point of the trammel to the inside of the collar for the major, and to the outside of the collar for the minor. It will be found that if the collar has been made true, the trammel will slip around the curve without causing the square to slip about, the collars acting as rollers.

W. T. Jones, Boise City, Idaho, would like to know of a ready way to frame hip roofs and roofs of irregular or different pitches with the steel square, including lengths and bevels of all rafters.

Answer: These problems along with many others are discussed and explained at length in my larger works on the Steel Square, but the following, which is somewhat condensed, does to some extent cover Mr. Jones’ inquiries:

Suppose A, B, C, D, Fig. 86, to represent one end of a hip roof with a span of 24 feet and a 10-foot rise. The side rafter I D shown in top sketch will have a run of 12 feet. The common rafter at the end of building, I L, has a run of 16 feet, with the same rise, so that the ends and sides of the roofs have different pitches. The lengths and cuts of the common rafters are obtained as shown in Fig. 87, by taking 12 on the blade and 10 on the tongue of the square and measuring across, giving the length of the side rafter, from which one-half the thickness of the ridge, measured square back from the plumb cut, must be deducted. The blade gives the foot cut and the tongue the plumb cut. The length of the end rafter is obtained by taking 16 on the blade and 10 on the tongue, which will of course give the respective cuts also. The same results may be obtained by applying the square to a straight edge and marking along the blade and tongue, which will give a gauge line to which a bevel may be set. By taking 16 on the blade and 12 on the tongue, as shown in Fig. 90, the run of the hip rafters, 20, is obtained.

Referring to Fig. 88, it will be seen that 20 on the blade and 10 on the tongue give the seat and plumb cuts of the hip together with the length, after one-half the thickness of the ridge has been deducted from the side cut. The side cut is found in a slightly different way from that of a regular hip or valley on an ordinary roof. The common method is to take the length of the hip on the blade and run on the tongue, but this will not work in this case, as the run of the hip does not be at an angle of 45 degrees as in ordinary roofs. The line B J in Fig. 86 must first be obtained, as shown in Fig. 89. Joint one edge of a board and square up the line B L. Measure one-half the width of building—in inches—on this line, 12 in this case, and with the heel of the square at the point B, move the square until 20 on the blade touches the edge of the board at E. The tongue will then give the point J 15 inches; which is the length of the line required.

Then take this line on the tongue and the length of the hip on the blade, Fig. 90, and the blade will give the bevel of the hip to lie against the ridge. As a general rule, hip rafters are not backed, but if such is desired the lines for backing can be found by setting it to the foot cut of the hip rafter. Make O R square with S O and gauge back as shown in the diagram A. Do the same on the other side, using the distance T R instead of P S. The point O is of course at the center of the line T P.

For lengths and bevels of jacks, proceed as follows: For end of roof, and set 2 feet on centers, take a board and apply the square to it, as shown in Fig. 91, with the length of the end rafter on the blade and the run of the side rafter on the tongue. Space off 2, 4, 6, 8 and 10 in. on the tongue after marking along both blade and tongue. The lines, AA, BB, CC, DD, EE, will give the length of the jacks, as well as the side cut to fit the side of the hip, the square being moved down along tongue line, while the run of the end rafter on blade and its rise on tongue will give the seat and plumb cuts. For the side jacks, Fig. 92 gives the same method, only that the length of the side rafter is taken on the blade and the run of the end rafter on the tongue. If it is so desired, the length of the jack rafter A¹ A¹ may be deducted from the length of the common rafter, which will give the difference in the lengths of the jacks.

The rules and diagrams, given herewith will apply to valley as well as hip rafters, and may be relied upon as being accurate if closely followed.

RULE—See Fig. 87.

Tongue. Blade.
12″ 16″ gives run of hip.
10″ 12″ gives length of side rafter.
10″ 16″ gives length of end rafter.
10″ 20″ gives length of hip rafter.

RULE—See Fig. 91.

Blade. Tongue.
Common End Rafter 19″ 12′
Longest Jack “ 15 10/12″ 10′
4th “ “ 12 8/12″ 8′
3d “ “ 9 6/12″ 6′
2d “ “ 6 4/12″ 4′
Shortest “ “ 3 2/12″ 2′

Blade gives Side Cut of Jacks.

RULE—See Fig. 92.

Blade. Tongue.
Common Side Rafter 15′ 7½″ 16′
Longest Jack “ 13′ 8″ 14′
6th “ “ 11′ 8½″ 12′
5th “ “ 9′ 9″ 10′
4th “ “ 7′ 9½″ 8′
3d “ “ 5′ 10″ 6′
2d “ “ 3′ 10½″ 4′
1st “ “ 1′ 11″ 2′

Blade gives Cut of Jacks, also Sheathing.

These matters have been discussed at length, in trade journals and also in my larger volumes on The Practical Uses of the Steel Square, but the foregoing treatment of the subject is on somewhat different lines and will prove interesting.

John Wilberforce, Toronto, Ont., wants to know if a wreath piece for a single-pitch rail with level landing can be set out with the Steel Square.

Answer: Yes, the problem can be solved as follows:

Set out on a board the plan of the wreath A (Fig. 94). Draw the outside circle and the inside and center line of same, showing also the joints. Set out the pitch off the shank; square up the center outside and inside lines from the plan on to the pitch. The thickness of the wreath piece is found by drawing a section of rail under the pitch line B. Set out again the half-width of the well; square off the pitch lines to the half width; this gives major and minor axes of the ellipse, as shown in the development (Fig. 94). Lay the square on the axis. Get a light piece of lath, drive in a nail at the half major, and one at the half minor; describe the inner ellipse line on the piece of timber from which the wreath is to be formed; pull out the nails, and repeat the process for the center and outside lines. Draw the shank and also the point as shown on the board.

Now cut at the joints, allowing an ⅛-inch for the fitting of the joint after the wreath is cut and roughed out. Use another piece of timber about 2 inches thick, to form the bed block, and cut it to the pitch accurate and square in thickness. Screw or pin it to the under side of the wreath piece (see Fig. 95), taking care to get it parallel with the shank, and the nails in clear of the saw. Then proceed to cut the wreath with the band saw, beginning at the circular part, and work it to the shank inside and outside. This operation should be performed most carefully with a narrow band saw, having a strong set and strained tight, feeding very slowly. The wreath should require hardly any spoke shaving. Knock off the block and draw a chalk mark across the table, just in front of the teeth. The use of this line is to assist the operator to get the outside of the wreath always touching this spot in front of the saw. He must carefully lower his hand until it is down level at the shank end. The top is cut first, and the saw should skim along the outside top arris, giving a sweep that cannot be excelled in graduation of curve. Then set a gauge to the thickness of the rail, mark a line on the inside of the wreath, and cut as before. With a little practice a wreath can be turned off the band saw ready for molding. When the shank is too long, it is always better to nail the bed block on top of the wreath, and cut it upside down, thus getting the curve portion near the table. Then the shank can be run in with the band saw when the block is knocked off. The foregoing is for a single-pitch wreath as used for stairs with level landings and narrow wells. Where the rails are pitched both ways, the bed block has to be cut at the double inclination. (See preceding answers.)

INDEX

A. B. C.
STEEL SQUARE—THE STEEL SQUARE AND ITS USES.

Division A.

Preface 1
Introductory remarks 3
Some useful advice 7
Framing posts, girts and braces 9
Testing a steel square 11
Practical uses of the steel square 13
Some rules for roof framing 16
Octagon rules 19
Lines on steel square explained 22
Varieties of squares 29
Bridge-builder’s square 31
Crenelated square 34
Test diagrams 37
Degrees on the square 44

Division B.

Introductory 47
Slotted fence 48
Laying out stairs 49
Laying out rafters 51
Metal fences 53
Fence adjusted for stair strings 55
Brace rules and diagrams 57
Regular and irregular runs 60
Roof framing 63
Cutting rafters 64
Octagon rafter bevels 65
Hip and valley rafters 65
Jack rafters 66
Bevels for hips, valleys and jack rafters 66
Measuring rafters 68
Different pitches for roofs 70
Some pointers in roof framing 72
Roof diagrams 79
Rise and run of rafters, hips and jacks 82
Cuts and bevels for rafters 86
Unequal pitches 91
Hip-roof with deck 96

Division C.

Introductory 97
Diagram of hip-roof 98
To cut jack rafters 100
Hopper miters 101
Questions and answers for correspondents 102
Joints for obtuse or acute angles 102
Drawing circle with square 104
Laying out stair wreath with square 105
Bevel for miter cap 105
Face mould by the square 106
Making pitch-board by the square 107
To lay out braces, girts and trusses 108
Braces, regular and irregular 109
Diagram of braces in position 112
Finding center of circles 113
Stair with three windows 114
Pitches and bevels for hand-rail 115
Traces for hand-rail bevels 116
Cutting out rails with band saw 118
Diagram of hand-railing 119
Tangents in hand-railing 121
Getting horizontal trace of hand-railing 122
Instrument for laying out hand-rails 124
Framing a hip-roof 125
Diagram of hip and rafter lines 126
Rafter measurement on the square 127
Bevels and cuts of roof 128
Plumb and horizontal cuts for hips 129
Length of rafters, hips and jacks on square 131
Rules for cutting rafters 133
Stair wreath for level landing 133
Wreath for single pitch rail 134
Block for cutting wreath 135
Square and plumb 136

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