Hip Roof Framing

In Fig. 49 is shown another method of finding the bevels of the purlins at the hip or valley.

Let ABC be the eaves of roof, DF and FE the ridges, BF the valley or plan, HE the rise and BE the pitch of roof. Mark the purlin IJK to a large scale—full size if possible—and draw IL, JM, and KN all parallel to EF ; make SO equal to JK; draw OP, and draw NP parallel to DF; join MP; and the bevel SMP will apply on the side of purlin. Make RS equal to JI; draw LR; and the bevel SMR will apply on top of purlin.

Illustration of Roof Pitches.

Mr. Woods' ill ustration in Fig. 49a, contains a whole volume in roof framing. His explanation of the figure is as follows: In this illustration we show a line for every inch on the blade; or, in other words, for each inch in rise to one foot of run. Twelve on the tongue represents unity, because 12 inches is one foot; and since the run is 12 inches, the span must be double the run, or 24 inches, which is the length of the blade of the square. Then the first inch in rise on the blade must be that pro portion to its own length, and produces one twenty-fourth pitch, the second inch, one-twelfth pitch, the third one-eighth pitch, and continue to the twenty-fourth inch, when it becomes full. The twenty-fifth inch rise would therefore be one and one-twenty-fourth pitch, which is simply a repetition of the above pitches with a one pre fixed till it gets up to 48 inches, when it takes on another pitch and represents two pitches, and continues on and on, getting fuller and fuller, but would never stand straight up, because the run remains the same.

The fractional pitch lines for the common rafter are shown for each inch in rise up to the full pitch, and their lengths are expressed in decimal figures to the one-hundredth part of an inch, while to the right of the blade the same is expressed for the corresponding octagon and for the common hip or valley for a square-cornered building, which are reckoned from 13 and 17 on the tongue respectively. However, neither is absolutely correct, though near enough as far as the cuts are concerned. The greater deviation

being in the hip for the square-cornered building. It lacks .0295 of being 17 inches and represents the run of the hip to a 12-inch run of the com mon rafter. Its true length being 16.9705 inches, this is the length from which we have reckoned for the lengths of the hips instead of 17, as is the usual custom. This may seem a trifling difference, and so it is in a short run and low pitches; but suppose it is for iron construction. To begin with, the shortage of each foot in run with the common rafter is .0295 of an inch; added to this the gain it would have in the pitch, which would be .015 of an inch by the time it got up to the full pitch for the common rafter; and this added to the .0295 to start with would be a difference of .0445 of an inch to the foot in run with the common rafter. Now supose the run to be 18 feet ; 18 x .0445 = .8+, or 19-24 of an inch dif ference; or, if no account was made of the gain in pitch, the .0295 of an inch in the run would amount to over half an inch in the length of the hip alone. This is a common error and while it is not much and probably would never be noticed in wood construction, it is well to know this discrepancy and guard against it when the occasion demands, and for that reason we give the correct amounts. The shortage in the octagon is not so pronounced. Instead of it being in the run, it is the tangent that is lacking the same amount, it being 4.9705 instead of 5 inches. This coming as it does can not affect the length of the rafter nearly so much as in the above.

We explain this shortage better by referring to that part of the illustration in Fig. 49a showing the plan of a combination square and octagon frame with the heel of the steel square resting at the center. From this it will be seen that the two outer circles catch the corners of the frame and seemingly intersecting the tongue at 13 and 17 and represent the figures to use on that mem ber for the seat cuts, but the true length of the run of the hip is 16.9705 and that for the tangent of the octagon is 4.9705.