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Figure  2-30.—Equal-pitch  hip  roof  framing  diagram. HIP Most hip roofs are equal pitch. This means the angle of slope on the roof end or ends is the same as the angle of slope on the sides. Unequal-pitch hip roofs do exist, but they are quite rare. They also require special layout methods.  The  unit  length  rafter  table  on  the  framing square  applies  only  to  equal-pitch  hip  roofs.  The  next paragraphs  discuss  an  equal-pitch  hip  roof. The  length  of  a  hip  rafter,  like  the  length  of  a common rafter, is calculated on the basis of bridge measure multiplied by the total run (half span). Any of the methods previously described for a common rafter may be used, although some of the dimensions for a hip rafter are different. Figure 2-30 shows part of a roof framing diagram for an equal-pitch hip roof. A roof framing diagram may be included among the working drawings; if not, you should lay one out for yourself. Determine what scale will be used, and lay out all framing members to scale. Lay the building lines out first. You can find the span and the length of the building on the working drawings.  Then,  draw  a  horizontal  line  along  the center of the span. In an equal-pitch hip roof framing diagram, the lines indicating the hip rafters (AF, AG, BI, and BK in figure 2-30) form 45° angles with the building lines. Draw these lines at 45°, as shown. The points where they meet the center line are the theoretical ends of the ridge piece. The ridge-end common rafters AC, AD, AE, BH, BJ, and BL join the ridge at the same points. A line indicating a rafter in the roof framing diagram is  equal  in  length  to  the  total  run  of  the  rafter  it represents. You can see from the diagram that the total run  of  a  hip  rafter  (represented  by  lines  AF-AG-BI-BK) is the hypotenuse of a right triangle with the altitude and base equal to the total run of a common rafter. You know the total run of a common rafter: It is one-half the span, or one-half the width of the building. Knowing this, you can find the total run of a hip rafter by applying the Pythagorean  theorem. Let’s suppose, for example, that the span of the building is 30 feet. Then, one-half the span, which is the same as the total run of a common rafter, is 15 feet. Applying the Pythagorean theorem, the total run of a hip rafter  is: What is the total rise? Since a hip rafter joins the ridge at the same height as a common rafter, the total rise for a hip rafter is the same as the total rise for a common rafter. You know how to figure the total rise of a common rafter. Assume that this roof has a unit of run of 12 and a unit of rise of 8. Since the total run of a common rafter in the roof is 15 feet, the total rise of common rafter is the value of  x in  the  proportional equation  12:8::15:x,  or 10 feet. 2-20

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