Part 4

For a full pitch use the decimal 1.12, and as in the preceding mentioned pitch, and it will be found so near correct that it can be practically used in all cases.

It will be noticed that I have not made any allowance for projection of rafters over the plate. In this case gauge from the crowning side of your rafter the thickness of your projection; allow enough for the latter, and find the lower bevel according to the way you described in your last; measure the length of your rafter from where this bevel crosses the gauge line.

A little practice will enable the mechanic to lay off a rafter in a very short time. I have used the above myself, and have no trouble whatever. While I have no fault to find in your methods, as I know them to be correct, yet it is just as well that workmen should know other methods, as there are many occasions when the “only method” he possesses cannot be applied. Hence I submit the foregoing, at your request.

W. H.”

All this is very true, and right as far as it goes, but it so happens that many workmen do not have the necessary learning to work out these problems in footing on the lines laid down by W. H., but, in order to meet conditions of this kind I have prepared a series of tables which is inserted in the larger volumes, giving the length of rafters for any building having a width of from five to sixty feet and a rise of roof of from one to eighteen feet to ridge. This will cover the whole ground, and form a ready table for the estimator to take his quantities from.

I may be pardoned for again showing the common and simplest method of laying out an ordinary rafter, for notwithstanding all I have said and described and explained on this subject, there will always be some persons who will not be able to grasp the method, unless it is put to them in some other light. I am sure of this from the long experience I have had in the answering of questions of this kind through the columns of different building journals. This is no doubt owing to some constitutional peculiarities of both the person who makes the inquiry and the person who attempts to answer it. This is one of the main reasons why I have admitted into this work various methods and descriptions of others than myself, so that readers will have the same methods described and explained to them in several different ways by several writers.

Let us take the diagrams shown at Fig. 49, which shows a portion of a roof having a quarter pitch. CEB showing the height, and AB the length and inclination of rafter. D shows the foot of the rafter on the plate, cut “flat foot” and the line EC the plumb cut. This is quite plain. The building may be any width, let us say in this case, that it is 30 feet wide from A to O. That will make the distance from A to C 15 feet.

A method of obtaining the bevels for this rafter is given in Fig. 50 where the steel square is shown laid on the pattern with the points 16 inches on the blade and 8 inches on the tongue applied to the edge of the stuff. The line HO on the blade gives the bevel for the foot of the rafter AC. The line OP, Fig. 50 gives the bevel for the top of the rafter or the plumb cut, as most workmen call it. Now, there is nothing in this diagram, which is from Bell’s Carpentry, an excellent work—from which the workman can get the length of his rafter, without complicating matters. Had the figures 12 inches and 6 inches on the square been employed instead of 16 and 8, then the distance across the diagonal from these two points would have equalled on the rafter, one foot on the base line or seat of the rafter, so that 15 times that length would have been the total length of the rafter. Better still, however, would have been the application of the square 15 times on the edge of the rafter pattern with the points 12 and 6 on gauge points, then both length and bevels would have been obtained at one operation.

Of course, the expert workman will often invent, or discover, methods of using the square in certain phases of roof framing, that can not be found in books, or that cannot be taught because of the peculiar circumstances of the particular case. Having a fair knowledge of the uses of the steel, the workman will seldom be overtaken by difficulties he cannot overcome if he studies the problems before him and then employs his knowledge of the square to their solution, as a little application on this line will remove all possible troubles.

Every carpenter knows, or ought to know, that the run and rise of the rafter taken on the square will give the seat and plumb cuts, but inasmuch as buildings are not all of the same width, it requires a different set of figures for each run, and as it requires an extra calculation to first find the run of the hip or valley, it is better to use the full scale for a one-foot run of the common rafter which answers for any run.

Referring to Fig. 51, we show a square bounded by A, B, C, D, the sides of which are 12 inches. E is at a point 5 inches from B, and C 12 inches from B. B-A represents the run of the common rafter. E-A represents the run of the octagon hip or valley, and C-A the same for the common hip or valley, their lengths, being 12, 13, and 17 respectively. Now since 12, 13, and 17 are fixed numbers, we take them on the tongue of the square, as shown in Fig. 52. Now suppose we want to find the lengths and cuts of the rafters for the ⅜ pitch. We take 9 on the blade. Why? Because the run being 12 inches, the span must be two times 12, which equals 24, and since the pitch is reckoned by the span, we find that ⅜ of 24 is 9, which represents the rise of the foot run. Then 12 and 9 give the seat and plumb cuts for the common rafter, 13 and 9 for the octagon hip or valley, and 17 and 9 gives the same for the common hip or valley. In Fig. 53 I show each separately.

The measurement line of hips and valleys is at a line along the center of its back, and just where to place the square on the side of the rafter so as to make the cuts and length come right at that point is a question that taxes the skill of most carpenters, especially so when the rafters are so backed. In Fig. 54 I have tried to make the above points clear.

First, I show the plan of the rafter. The cross lines on same represent an external corner for the hip and valley respectively. Above the plan is shown the elevation. The sections 1-2-3-4 represent the position of the rafters under the following conditions: No. 1 hip when not backed, No. 2 hip when backed, No. 3 valley when not backed, No. 4 valley when backed. No. 1 is outlined by heavy lines, and sets lower than the others. By tracing the bottom line of the sections down to the seat of No. 1, thence up to the second elevation will show just how deep the notching should be for each rafter. No. 1 cuts into the right hand vertical line from the plan, which would make it stand at the right height above the plate, but in order to make the seat cut clear the corner of plate, it is necessary to cut into the center line above the plan. No. 2 cuts into the same points as No. 1, but owing to its being backed, the seat cut drops accordingly. No. 3 cuts into the center vertical line, and in order to clear the edges of the plate must cut out at the sides to the left vertical line. No. 4 cuts in the same as the latter, but as much lower than No. 3 as No. 2 is below No. 1.

The outer vertical lines from the plan represent the width of the rafter. Therefore if the rafter be two inches thick, would be one inch apart, and this amount set off along the seat line (or a line parallel with it) will give the gauge point on the side of the rafter. To make this clearer refer to Fig. 53; 17 and 9 gives the cuts. Now leaving the square rest as it is, measure back from 17 one-half the thickness of the rafter, and this will be the gauge line point from which to remove the wood back to the center line of hip, and the measurement from the edge of the rafter taken vertically down to the gauge point set off on the plumb cut regulates how far apart the parallel lines of the seat cuts will be under the above conditions. This rule applies to any roof so long as the pitches are regular.

Proceed in like manner for the octagon hip, the variation, however, is practically one-half of the above results for the square cornered building.

Fig. 55 illustrates side cut of the jack, 12 on the tongue, and 15 (length of the common rafter) on the blade.

Fig. 56 illustrates side cut of the octagon jack, 5 on the tongue and 15 on the blade.

Fig. 57 illustrates the side cut of the hip or valley, 17 on tongue, 19¼ (length of the hip) on the blade giving the cut in each case.

The latter, however, is for the unbacked rafter. If it has been previously backed, then apply the square with the above figures on the lower edge at bottom of the plumb cut, or apply the square as for the jack, Fig. 56, to the backing line, which will give the same result as 17 and 19¼.

It is quite clear that when a workman cuts a common rafter, he is also cutting a timber that would answer for a hip for a building of less span having the same rise, only taking some adjustment of the top bevel to fit against a ridge. This is quite plain, and if we refer to Fig. 58, we find that the common rafter for a 1-foot run becomes a hip for an 8½-inch run, and that a hip for a 1-foot run of the building becomes a common rafter for a 17-inch run. Therefore, the rule that applies to the common rafter also applies to the hip rafter, _i. e._, the run and rise taken on the square will give the seat and plumb cuts. The run and length of the rafter taken on the square will give the side cuts, or taking the scale for a 1-foot run, Fig. 58, it is 12 on the tongue and the rise on the blade for the common rafter, and 17 on the tongue and rise on the blade for the hip. The tongue giving the seat cut and the blade the plumb cut. For the side cuts we take 12 on the tongue and 15⅝ inches on the blade, and the blade will give the side cut of the jack. Take 17 on the tongue and the length of the hip, 19¾ inches, on the blade and the blade will give the side cut of the hip. It would also be the side cut of the corresponding jack if it be a common rafter. Seventeen is used for a foot run of the hip rafter because the diagonal of a 12-inch square is practically 17 inches.

If we were to use 12 on the tongue for a foot run of the hip the rise to the foot would necessarily be less than 10 inches. In Fig. 59 I show what the difference is in rise to the foot.

From 12 to 12 is the length of the run of the hip would only have 10-17 of an inch to one run of the common rafter, and an equal rise of the common rafter, set off as at A, and a line from this to 12 on the tongue passes at 7 1-17 inches on the blade, because the common rafter having a rise of 10 inches to one foot, for one inch it would have 10-12 of an inch, while the hip would only have 10-17 of an inch to one inch and for 12 inches it would be 12 times 10-17 equals 120-17, or 7 1-17 inches. Therefore the figures given in the second illustration would give the same cuts as those in the first, but as the latter necessitates a calculation that ends in fractions—fractions not given on the square—and for that reason 17 is generally used for a foot run for the hips and valleys.

AN UNEQUAL PITCH.

In the matter of roofing over unequal pitches when there is no ridge and when all hips meet, the building being longer than it is wide, the backing of hips and their lengths and bevels would be a very easy matter if a drawing of the whole thing was made, but, to obtain these by the use of the square alone, is somewhat more difficult. Let us assume the building to be 18 feet wide and 28 feet long, and having a rise of 9 feet, then, by referring to Fig. 60, we show to one inch scale the length, run, rise, seat, and plumb cuts for the hip and common rafters as follows: The run of the long way of the building is 14, and 9 for the narrow way, which we take on the blade and tongue respectively, as shown on square No. 1, and to this apply square No. 2, as shown. AD equals the run of the hip. AE equals the rise and ED equals the length of the hip. The reader will notice that the letters A, B, C, D form a parallelogram, with side and ends equal to the runs of the common rafters. Therefore, by taking the runs on the tongue, as shown by the squares Nos. 3 and 4, will give their lengths, seat and plumb cuts.

In Fig. 61 is shown the intersection of the rafters at the peak and as the lengths of all rafters are scaled to run to a common center it is necessary that the common rafters must cut back so as to fit in the angle formed by the hips. The proper deduction for this is shown in Fig. 62 by placing two squares on the back of the rafter, with the heel or corner of the squares resting on the center line. The distance from the corner of the square to B measured square back (at right angles) from the plumb bevel, as shown in Fig. 61, will locate the point of the long common rafter at B in Fig. 61. Proceed in like manner for the short common rafter, taking the distance from the corner at C, and for the side cuts, take 14 on the tongue and the length of the short common rafter CE on the blade—the blade will give the cut at AC in Fig. 61. The reader will observe that this angle is the same as that for the side cut of the jack. Proceed in like manner for the long common rafter side, using 9 on the tongue and BE on the blade. These same figures will give the side cuts of the hip, provided hip has been previously backed. Taking the last for example the reader will observe that 9 on the tongue and BE on the blade the square would lay on the plane of the backing and the blade giving the cut along the line BB in Fig. 61, or these cuts may be found by measuring square back from a plumb bevel at points A and A, Fig. 62, the distance AC and AB, which will give the proper plumb cut at the sides and intersecting the line AA at the center. These same distances, AC and AB, but transferred to opposite sides, set off on the seat cut or a line parallel with it, will give the gauge points on the side of the hip for the backing.

The lengths of the jacks may be found by dividing the length of the common rafter by the number of the spacings for the jacks; the quotient will be the common difference.

END OF DIVISION B.

THE STEEL SQUARE AND ITS USES. DIVISION C. _Introductory._

During my long experience as Editor of several of the leading building journals in the United States and Canada, I have been asked and have answered thousands of questions regarding matters concerning building construction, builders’ materials, tools and processes, and particularly regarding the “Steel Square and its Uses,” and I have concluded that the publication of a few of these questions and answers, along with other matter, in this division will be appreciated by my readers, and to this end I insert a number of the most useful items in this manual.

Besides these questions and answers, I also publish other up to date matter, all of which will make this volume one of the most useful little works to the American carpenter and wood-worker ever published.

I open this division with a few hints regarding the construction, or rather the laying out of a Hip-Roof where the design has been furnished by an architect, and which, of course, shows the pitch and the lay of the timbers. We suppose the roof to have a span of 18 feet and a rise of 6 feet, thus giving the roof a one-third pitch. The fence is used in this example to its full extent, and when placed on the square and fastened, the line of fence shows the slope or pitch of roof. Fig. 64 shows the square set to the pitch of the hip rafter. The squares as set give the plumb and level cuts. Fig. 65 is the rafter plan of a house 18 by 24 feet; the rafters are laid off on the level, and measure nine feet from center of ridge to outside of wall; there should be a rafter pattern with a plumb cut at one end, and the foot cut at the other, got out as previously shown. When the rafter foot is marked, place the end of the long blade of the square to the wall line, as in drawing, and mark across the rafter at the outside of the short blade, and these marks on the rafter pitch will correspond with two feet on the level plan; slide the square up the rafter and place the end of the long blade to the mark last made, and mark outside the short blade as before, repeat the application until nine feet are measured off, and then the length of the rafter is correct; remember to mark off one-half the thickness of ridge-piece. The rafters are laid off on part of plan to show the appearance of the rafters in a roof of this kind, but for working purposes the rafters 1, 2, 3, 4, 5 and 6, with one hip rafter, is all that is required.

To proceed, we first lay off common rafter, which has been previously explained; but deeming it necessary to give a formula in figures to avoid making a plan, we take 1-3 pitch. This pitch is 1-3 the width of the building, to point of rafter from wall plate or base. For an example, always use 8, which is 1-3 of 24, on tongues for altitude; 12, ½ the width of 24, on blade for base. This cuts common rafter. Next is the hip-rafter. It must be understood that the diagonal of 12 and 12 is approximately 17 in framing work, and the hip is the diagonal of a square added to the rise of roof; therefore we take 8 on the tongue and 17 on the blade; run the same number of times as common rafter which gives the length of hip and plumb and level bevels.

To cut jack rafters, divide the number of openings for common rafters. Suppose we have five jacks, with six openings, our common rafter 12 feet long, each jack would be 2 feet shorter. The first, next the hip, 10 feet, the second 8 feet, third 6 feet, and so on. The top down cut same as down cut for common rafter. For the bevel, cut against hip. Take half the width of building on tongue and length of common rafter on blade, and blade gives the bevel. Now find diagonal of 8 and 12, which is 14 7-16 in. Take this length on blade and 12 on tongue, blade gives bevels. If the hip-rafter is beveled or “backed” to suit jacks, then take height of hip on tongue, length of hip on blade, and tongue gives bevel. These figures will cover all bevels for cutting, cornice and sheathing. For bed moulds for gable to fit under cornice, take half width of building on tongue, length of common rafter on blade; blade gives cut. To cut planceer to run up valley, take height of rafter on tongue, length of rafter on blade; tongue gives bevel. For plumb cut, take height of hip on tongue, length of hip on blade; tongue gives bevel.

These figures were specially prepared for a hip roof having a one-third pitch, but will suit other pitches equally well if the difference in height of ridge is considered.

For a hopper the mitre is cut on the same principle. To make a butt joint, take the width of side on blade, and half the flare on tongue: the latter gives the cut. You will observe that a hip-roof is the same as a hopper inverted. The cuts for the edges of the pieces of a hexagonal hopper are found this way. Subtract the width of one piece at the bottom from the width of same at top, take remainder on tongue, depth of side on blade; tongue gives the cut. The cut on face of sides: Take 7-12 of the rise on tongue and the depth of side on blade; tongue gives cut. The bevel of top and bottom: Take rise on blade, run on tongue; tongue gives cut.

SOME QUESTIONS AND ANSWERS FROM VARIOUS CORRESPONDENTS.

The following questions and answers from practical workmen are considered among the very best things regarding the use of the Steel Square, as they are from men who knew of what they were talking about. They are gathered from many sources, but chiefly from the columns of Technical Journals with which I have been connected, either as Editor or contributor.

Jas. Willis, Rochester, N. Y., asks: “How can I get the proper bevel for a butt joint on an obtuse or acute angle, by the use of the square only?”

Answer: Suppose Fig. 66 represents an obtuse angle formed by two parallel boards or timbers. To obtain the joint, A, space off equal distances from the point 1 to 3, 3, then square over from the lines, R, R, keeping the heel of the square at the points 3, 3. At the junction of the lines formed by the tongue of the square at 0 will be one point, and 1 will be the other by which the joint line, A, is defined.

To find the line of juncture for an acute angle, proceed as follows: Fig. 67 represents two parallel boards or timbers; 1 the extreme angle, 3, 3 equal distances from the angle 1 and are the points where the heel of the square must rest to form the lines 0, 3; 0 shows the junction of the lines formed by the blade of the square. Draw a line from 0 to 1, and the line, A, formed, is the bevel required.

It will be seen, by these two examples, that the bevel of a junction at any angle may be obtained by this method.

P. McVity, Milwaukee, asks: “How can I draw a circle with the Steel Square?”

Answer: A circle of any required diameter may be drawn by means of the square by using it as indicated in the accompanying sketch. Drive two pins or nails, A and B, Fig. 68, at whatever distance apart the circle is to have as its diameter. Bring the square against them, as shown, and use a pencil in the angle as indicated in the drawing. This rule is very convenient in many instances. Suppose A and B are two points through which a circle is required to be drawn. By bringing the square against pins or nails placed in the points, it may be described as indicated in the sketch.

A “Mechanic,” Tampa, Fla., asks: “Can the steel square be used in laying out a wreath for a handrail, and if so, please describe how?”

Answer: Some advance in this direction has been made, but not much, but the outlook is quite encouraging as many experts are trying to obtain all the lines required for forming circular handrails. It will be accomplished sooner or later. A few problems and solutions are given herewith: In getting out face-molds it has generally been considered necessary first to unfold the tangents and get the heights, and by construction get the bevels. The method shown is somewhat different, though results are the same, but are produced more rapidly. Take for illustration a side wreath mitered into a newel cap. This method will apply no matter where the newel is placed, or whether the easement is less or more than the one step of the example illustrated. What is meant by one step is, that the tangent of the straight rail continues to the point 2, Fig. 69. The tangent 2-1 is level.

To produce the face mould, lay the steel square in the position, indicated by the lines 1, 2, 3, 4, not the figure on the square at the points numbered, and transfer them to a piece of thin stuff, Fig. 70. Line 3-4 in Fig. 70 is indefinite. Now take the length of the long edge of the pitch board in the compasses, and with 2, Fig. 70, as a center, cut the line 3-4 in 4 and draw 2-4. Now 1-2 is the level, and 2-4 is the pitch tangent on the face mold.