ࡱ> Fq 3$bjbjt+t+ "VAAJ]VVVV8,V^FZH(^^^^^^^$ `br^^H ZH H H d^@@^H H NPF ^>ܿVV. []0ERRATA #1: Residential Structural Design Guide 2000 Edition June 2000 Replace Example 5.11 with the following: EXAMPLE 5.11Hip Rafter XE "Rafter"  DesignGivenOne-story building Hip rafter and roof plan as shown below Rafters are 2x8 No. 2 Hem-Fir at 16 in on center Loading (see Chapter 3) Dead = 10 psf Snow = 10 psf Wind (90 mph, gust) = 4 psf (inward) = 10 psf (uplift) Live (roof) = 15 psf  Hip Rafter XE "Rafter"  Framing and Tributary Load AreaFind1. Hip rafter design approach for conventional rafter-ceiling joist roof framing. 2. Hip rafter design approach for cathedral ceiling framing (no cross-ties; ridge beam and hip rafter supported by end-bearing supports). Solution1.Evaluate load combinations applicable to the hip rafter design (see Chapter 3, Table 3.1) By inspection, the D + Lr load combination governs the design. While the wind uplift is sufficient to create a small upward bending load above the counteracting dead load of 0.6 D, it does not exceed the gravity loading condition in effect. Since the compression edge of the hip rafter is laterally braced in both directions of strong-axis bending (i.e., jack rafters frame into the side and sheathing provides additional support to the top), the 0.6 D + Wu condition can be dismissed by inspection. Likewise, the D + W inward-bending load is considerably smaller than the gravity load condition. However, wind uplift should be considered in the design of the hip rafter connections; refer to Chapter 7.2.Design the hip rafter for a rafter-ceiling joist roof construction (conventional practice). Use a double 2x10 No. 2 Hem-fir hip rafter (i.e., hip rafter is one-size larger than rafters - rule of thumb). The double 2x10 may be lap-spliced and vertically braced at or near mid-span; otherwise, a single 2x10 could be used to span continuously. The lap splice, when used to allow for shorter members, should be about 4 feet in length and both members face-nailed together with 2-10d common nails at 16 inches on center. A vertical brace to framing below (ceiling joists and walls) must be located at or near to the lap-splice. Design is essentially by conventional practice. Note: The standard practice above applies only when the jack rafters are tied to the ceiling joists to resist outward thrust at the wall resulting from truss XE "truss"  action of the framing system. The roof sheathing is integral to the structural capacity of the system; therefore, heavy loads on the roof before roof sheathing installation should be avoided, as is common. For lower roof slopes, a structural analysis (see next step) may be warranted because the folded-plate action of the roof sheathing is somewhat diminished at lower slopes. Also, it is important to consider connection of the hip rafter at the ridge. Usually, a standard connection using toe-nails is used, but in high wind or heavy snow load conditions a suitable connector or strapping should be considered.3. Design the hip rafter by assuming a cathedral ceiling with bearing at the exterior wall corner and at a column at the ridge beam intersection a. Assume the rafter is simply supported and ignore the negligible effect of loads on the small overhang with respect to rafter design. b. Determine the hip rafter loading based on the tributary loads from each supported jack rafter (see figure above): Hip rafter horizontal span =  EMBED Equation.3  = 19.4 ft Determine the span, L, of the tributary load (1/2 of the jack rafter span) at the top of the rafter: L = 1/2 (13.71 ft) = 6.86 ft Determine the maximum value of the uniform triangular line load at the top end of the hip rafter (bottom end is 0 plf): W = 2L(uniform roof design load) = 2(6.86 ft)(25 psf) = 343 plf Draw an approximate free body diagram for the hip rafter as follows:  c. From beam equations in Appendix A, determine reactions, maximum shear, and maximum moment on the hip rafter:  EMBED Equation.3   EMBED Equation.3  The value of R2 is appropriate for the determination of connection or support loads at the end of the hip rafter. For the design of the hip rafter itself, the load for a distance equal to the depth of the member from its end may be discounted when evaluating horizontal shear stress (see NDS(3.4.3). Thus, for design of the hip rafter member, the maximum design shear load is determined as follows:  EMBED Equation.3   EMBED Equation.3  (uniform load at a distance of member depth from the end)  EMBED Equation.3  The maximum moment is determined as follows:  EMBED Equation.3  d. Determine the required bending stress value, grade, and species if a continuous double 2x12 member (no splice) is to be used. Section Modulus of 2-2x12s, S = 63.3 in3  EMBED Equation.3  Set fb,reqd equal to Fb and solve for the tabulated unadjusted bending stress value (NDS(Supplement) as follows: Fb = Fb(CD)(Cr)(CF)(CL) 1,570 psi = Fb(1.0)(1.2*)(1.0)(1.0) * Cr = 1.2 is chosen (see Table 5.4) Fb = 1,308 psi This stress value would require the use of Select Structural Hem-fir 2x12s which is not an economical solution. Even with Southern Pine lumber, a No. 1 Dense grade would be required which is still uneconomical, particularly considering that the members are more than 19 ft long. Therefore, a more viable solution using an engineered wood member (i.e., laminated veneer lumber, etc.) should be considered. The reader is alerted to the fact that system effects from the sheathed roof assembly and the folded-plate action at the hip are not considered. Such system effects may significantly contribute to the bending capacity of the hip member and to load sharing in a manner different from that implied by the free body diagram used for the purposes of this illustration. e. Check horizontal shear: fv =  EMBED Equation.3  =  EMBED Equation.3  = 85 psi fv << Fv' = (75 psi)(2.0) = 150 psi (based on Hem-fir with CH = 2.0) f. Consider deflection: Deflection XE "Deflection"  is OK by inspection. No method exists to accurately estimate deflection of a hip rafter that is subject to significant system stiffness because of the folded-plate action of the roof sheathing diaphragm.ConclusionFor a cathedral ceiling application, an engineered wood member should be selected from the manufacturers data to meet the loading requirements. Since data to consider system effects in the design of a hip rafter is not currently available, there is an unnecessarily large discrepancy between the solution by conventional practice relative to the engineered solution. However, a cathedral ceiling with a hip roof is not a common occurrence. For traditional rafter-ceiling joist roof construction, a hip rafter one or two sizes larger than the rafters may be used. With a ceiling joist or cross-ties, the ridge member and hip rafter member need only serve as plates or boards that provide a connection interface, not necessarily a beam support, for the rafters. Thus, interconnection of rafters and cross-ties are the most critical design considerations. Deflection was not checked in this example and it, too, is significantly affected by the presence of the roof sheathing and the stiffening effect of the folded-plate action not considered in the engineering analysis. Replace Figure A.4 of Appendix A with the following: R1 = V1 =  EMBED Equation.3  R2 = V2 =  EMBED Equation.3  Vx =  EMBED Equation.3  Mmax (at x =  EMBED Equation.3 ) =  EMBED Equation.3  Mx =  EMBED Equation.3 (L2-x2) (max (at x = 0.52L) = 0.0065  EMBED Equation.3  (x =  EMBED Equation.3  [3x4-10x2L2+7L4]Figure A.4 - Simple Beam - Load Increasing Uniformly to One End NAHB Research Center, Inc. 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