Knowing the total run of the hip rafter (21.21 feet)and the total rise (10 feet), you can figure the line lengthby applying the Pythagorean theorem. The line lengthis:To find the length of a hip rafter on the basis ofbridge measure, you must first determine the bridgemeasure. As with a common rafter, the bridge measureof a hip rafter is the length of the hypotenuse of a trianglewith its altitude and base equal to the unit of run and unitof rise of the rafter. The unit of rise of a hip rafter isalways the same as that of a common rafter, but the unitof run of a hip rafter is a fixed unit of measure, always16.97.The unit of run of a hip rafter in an equal-pitch roofis the hypotenuse of a right triangle with its altitude andbase equal to the unit of run of a common rafter, 12.Therefore, the unit of run of a hip rafter is:If the unit of run of a hip rafter is 16.97 and the unitof rise (in this particular case) is 8, the bridge measureof the hip rafter must be:This means that for every unit of run (16.97) therafter has a line length of 18.76 inches. Since the totalrun of the rafter is 21.21 feet, the length of the raftermust be the value of x in the proportional equation16.97:18.76::21.21:x, or 23.45 feet.Like the unit length of a common rafter, the bridgemeasure of a hip rafter can be obtained from the unitlength rafter table on the framing square. If you turnback to figure 2-16, you will see that the second line inthe table is headed LENGTH HIP OR VALLEY PERFT RUN. This means “per foot run of a common rafterin the same roof.” Actually, the unit length given in thetables is the unit length for every 16.97 units of run ofthe hip rafter itself. If you go across to the unit lengthgiven under 8, you will find the same figure, 18.76 units,that you calculated above.An easy way to calculate the length of anequal-pitch hip roof is to multiply the bridge measureby the number of feet in the total run of a common rafter,which is the same as the number of feet in one-half ofthe building span. One-half of the building span, in thiscase, is 15 feet. The length of the hip rafter is therefore18.76 x 15, or 281.40 inches—23.45 feet onceconverted.You step off the length of an equal-pitch hip roofjust as you do the length of a common rafter, except thatyou set the square to a unit of run of 16.97 inches insteadof to a unit of run of 12 inches. Since 16.97 inches is thesame as 16 and 15.52 sixteenths of an inch, setting thesquare to a unit of run of 17 inches is close enough formost practical purposes. Bear in mind that for any plumbcut line on an equal-pitch hip roof rafter, you set thesquare to the unit of rise of a common rafter and to a unitof run of 17.You step off the same number of times as there arefeet in the total run of a common rafter in the same roof;only the size of each step is different. For every 12-inchstep in a common rafter, a hip rafter has a 17-inch step.For the roof on which you are working, the total run ofcommon rafter is exactly 15 feet; this means that youwould step off the hip-rafter cut (17 inches and 8 inches)exactly 15 times.Suppose, however, that there was an odd unit in thecommon rafter total run. Assume, for example, that thetotal run of a common rafter is 15 feet 10 1/2 inches.How would you make the odd fraction of a step on thehip rafter?You remember that the unit of run of a hip rafter isthe hypotenuse of a right triangle with the other sideeach equal to the unit of run of a common rafter. In thiscase, the run of the odd unit on the hip rafter must be thehypotenuse of a right triangle with the altitude and baseequal to the odd unit of run of the common rafter (in thiscase, 10 1/2 inches). You can figure this using thePythagorean theoremor you can set the square on a true edge to 10 1/2 incheson the blade and measure the distance between themarks. It comes to 14.84 inches. Rounded off to thenearest 1/16 inch, this equals 14 13/16 inches.To layoff the odd unit, set the tongue of the framingsquare to the plumb line for the last full step made andmeasure off 14 13/16 inches along the blade. Place thetongue of the square at the mark, set the square to thehip rafter plumb cut of 8 inches on the tongue and17 inches on the blade, and draw the line length cut.2-21

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