ABC of the Steel Square and Its Uses

by Fred. T. Hodgson

ROOF FRAMING.

Roof framing can be done about as many different ways as there are mechanics. But undoubtedly the easiest, most rapid and most practical is framing with the “square.” The following cuts will illustrate several applications of the square as applied to roof framing, and all who are interested in the subject can, by giving it a careful study, be able to frame any ordinary roof the mechanic comes in contact with.

[Fig. 33] is an illustration that could well be given much thought and study. It not only gives the most common pitches, but also gives the degrees.

Most carpenters know that half-pitch is 45 degrees, yet few know third pitch is nearly 34, and quarter-pitch about 27 degrees.

A building 24 feet wide (as the rafters come to the center) has a 12-foot run and half-pitch the rise would also be 12 feet, and the length of the rafter would be 17 feet (the diagonal of 12). Length, cuts, etc., could all be figured from the one illustration.

Fig. 33.

Fig. 34.

[Fig. 34] illustrates a way to cut rafters with the square.

A roof 14 feet wide would have a run of 7 feet, third-pitch would rise 8 inches to every foot run. Therefore, place the square on 8 and 12 seven times, and you have length and cuts.

[Fig. 35]. For the octagon rafter, proceed same as common rafter, only use 13 for run (in place of 12 for common rafter).

Fig. 35.

[Fig. 36], hip or valley rafter. As these rafters run diagonal with the common rafter and as the diagonal of 1 foot is practically 17 inches, use 17 for run, and proceed same as common rafter.

Fig. 36.

Length of jacks. If there are to be five, divide the common rafter into six equal parts, use that for a pattern, and it gives the length very nicely. But that will not always work. To get all the different lengths might at first look difficult even to many good mechanics, but it is very simple as illustrated in [Fig. 37]. If the first jack was one foot from corner apply the square same as for common rafter, and it gives length and cut (mark the length for starting point on next), and if it is 17 inches from the other move the square up to 17, if the next is 15 move up to 15 and so on.

Fig. 37.

[Fig. 38]. The side cut of jack to fit hip, if laid down level would, of course, be square miter, but the more the hip rises the sharper the angle. Measure across the square from 8 to 12, and it is nearly 14½, which is the length of rafter to one foot of run. Length and run, cut on length, gives the cut.

Fig. 38.

Fig. 39.

[Fig. 39], octagon jack. As the octagon miter on level surface is 5 and 12, it must raise same as common jack, and is, therefore, raised to length, or 14½, and 5 cut on length.

Fig. 40.

[Fig. 40], hip rafter, is also length and run, cut on length.

Fig. 41.

[Fig. 41]. To bevel top of hip take length and rise and mark on rise.

[Fig. 42] is another practical way, which is simply to lay the square on heel or hip. The illustration, explains itself.

Fig. 42.

Perhaps the most practical way of all to frame a roof, the simplest to understand, easiest to remember, and most rapid to apply is simply to always take the rise and run, measure across the square which gives length. Rise and run give cuts, so you have it all.

Fig. 43.

[Fig. 43] illustrates a roof 25 feet wide and a rise 10 feet, 9 inches, run 12 feet, 6 inches. Measuring across the square from 10¾ to 12½ gives 16½, or 16 feet, 6 inches is the length of rafter.

[Fig. 44]. If the run of common rafter is 12½, the run of the hip will be diagonal of 12½ which is 17 8-16, as is plainly illustrated.

Fig. 44.

[Fig. 45]. As the rise is 10¾ and run 17 8-12, the length will be 20 feet, 2 inches.

Fig. 45.

[Fig. 46]. When a roof must go to a certain height to strike another building at a given point, as in additions, porches, etc., don’t forget in getting the rise from plate to given point to allow the squaring up of heel as illustrated; and also remember to allow for ridge whenever one is used.

Fig. 46.

[Fig. 47] illustrates the cut of top of quarter-pitch rafter to lay on top of roof just mentioned. To apply the square first lay it on 12 and 6, which is quarter-pitch, and gives plumb-cut. From plumb-cut lay off pitch of main roof 10¾ and 12½, which gives cut.

Fig. 47.

Anyone that has studied this with determination will have no trouble in framing any ordinary roof, as the general principles apply to all roofs, pitches, etc. So I will not take up any more space with roof framing at this time, but remember all sheathing, studding, cornice, etc., are made on the same cuts. In fact a hopper is also exactly on the same principle.

Division B.
SOME POINTERS ON ROOF FRAMING.

No matter what people may say to the contrary, there is no method or methods that has ever been devised that is so effective in roof framing, or results so rapidly achieved, as those which are obtained by the use of the steel square. I have shown in some of the earlier pages of this work how rapidly the length, and bevels of any common rafter may be obtained by the simple application of the square, any determined number of times. Thus for a building of, say, 30 ft. in width, which is to have a roof of any given pitch, we arrange the pitch as I have shown, with so many inches on the blade for the run, and so many on the tongue for the rise. This settled, we apply the square fifteen times to the rafter, 15 being half of the width of the building. This then gives the length of the rafter, and a line drawn along the edge of the tongue of the square will give the proper bevel for the top or plumb cut. If there is to be a ridge board on the roof, then half the thickness of such board must be measured back on the line drawn, and the rafter must be cut at that point, this provides for the ridge board being nailed on the face of the cut without in the least changing the pitch.

A line along the edge of the blade, gives the proper bevel for the level or horizontal cut. If the bottom end of the rafter is to have a crow-foot cut on it to fit the plate, the workman will have no difficulty whatever in cutting the foot of the rafter to suit, as all the lines will be at right angles to each other, and a section of the plate may be made on the line of the bevel and the “cuts” laid off to suit the conditions.

In reviewing an article of mine on this method of laying out a rafter, an English carpenter took exceptions to it on the grounds that it would take too much time to lay out the rafters for a whole building by this “tiresome process,” as he called it. Now the Englishman was right from his point of view, but no American workman would ever think of laying out the rafters for a whole building by the process. He would simply make one rafter as I have shown, for a pattern, and use this pattern for laying out all the other rafters for that particular pitch and rise on the same roof. Most workmen, however, make a pattern from thin stuff of some sort, as it is lighter and easier handled. The reviewer suggested as a better way “that the pitch be arranged on the iron square, then measure across the angle from the points of run and pitch, and multiply this measurement by half the width of the roof to be covered.” Now this is all right, but, as a matter of fact, entails more labor of a “tiresome sort” and would use much more time than the method I have taught now for nearly forty years. The American workman, however, does not even require a suggestion as to the quicker method. He will see and adopt it at once without argument.

Fig. 48.

The method the Englishman would adopt is shown at [Fig. 48], where the points of pitch and run are shown at 12 and 8, which makes the diagonal line 14½ inches. To get the length of the rafter for our supposed building then, we must multiply this 14½ inches fifteen times, then we must use the square at the top and bottom of the timber to obtain the necessary bevels for the cutting lines.

Regarding this question of preparing rafters for a common roof, an “old hand” in the use of the steel square writes to me to say: “I do not think that any simpler method can be given for finding the bevels at the heel and point of rafters than that which you have explained in your books, but I do think that the following method for obtaining lengths of rafters, is somewhat better than yours, particularly when employed for estimating purposes. The most common width of buildings in my locality is 24 ft., and with your permission I purpose to take that width for the practical test of my method. As you have given several ways by which the same result can be obtained, I will ask you to compare them with mine.

Finding the length of the hypothenuse by the old rule, we obtain for one-quarter-inch pitch 13:4.99, or, as near as it can be used on the square 13 feet, 5 inches.

Allowing one inch to the foot and trying your method we find, as a result, 13 inches and 7-16 scant, or 13 feet, 5 inches. This is a very simple method, and when the rule is kept perfectly straight, the results are very satisfactory.

By my way I simply multiply the width of the building by the decimal .56, 24×.56=13.44, or as near as can be worked by the square, 13 feet, 5 inches.

Let us try the same rule for a greater width—say 60 feet. By finding the hypothenuse we find as near as can be used by the square, 33 feet, 6½ inches. By my method it would be 60×.56, or 33.60, equal to 33 feet, 7 inches full. By this method the rafters in wide buildings are a little long. Thus, if the building is 52 feet wide, by the hypothenuse it would be 29 feet, 1 inch; my way it would be 29 feet, 1½ inches. I consider this an advantage, as it leaves the point of the rafter very slightly open.

For one-third I follow the same plan, only using the decimal .6. Unlike the decimal used for a quarter pitch the lengths are a very small fraction short; as, for instance, a rafter for a building 60 feet wide, by finding the hypothenuse, would be 36 feet, 1-16 of an inch. By my way, 60×.6=36 feet. A slight difference, truly. If building is 48 feet wide, then by the first method we find 28 feet, 10 inches full; by my way, 28 feet, 9⅜ inches. A little practice will enable the mechanic to allow just enough to make up for the slight difference, so that when rafters are put together the fit will be perfect.

The one-half pitch can be found in the same manner by using the decimal .71. Taking the 24-foot building, length of rafters by the hypothenuse, we find 16 feet, 11 2-3 inches; my way they would be 17 feet full. Again, building 60 feet wide, rafters by the first method would be 42 feet, 6⅛ inches; by my way 60×.71=42 feet, 6 inches. By using this decimal, the length is so near practically correct, that it may be used in all cases.

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.

Fig. 49.

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.

Fig. 50.

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.

Fig. 51.

Fig. 52.

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.

Fig. 53.

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.

Fig. 54.

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.

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

Fig. 56.

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

Fig. 57.

[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.

Fig. 58.

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.

Fig. 59.

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.

Fig. 60.