Title 45 Steel - Purlins.pdf ✅

If there are sag rods at third points, consider a continuous beam with simple supports at the ends and at third points. Using three moment equation, M1L1 + 2M2 (L1 + L2 )+ M3L2 + 6A1a1 L1 + 6A2b2 L2 = 0 0+ 2M2 ( L 3 + L 3 ) + M3 ( L 3 ) + w 4 ( L 3 ) 3 + w 4 ( L 3 ) 3 = 0 By symmetry, M2 = M3 = M, 0 + 2M ( L 3 + L 3 ) + M ( L 3 ) + w 4 ( L 3 ) 3 + w 4 ( L 3 ) 3 = 0 M = − wL 2 90 The maximum moment in the y-direction is at third points and the maximum moment in the x-direction at midspan. The moments used for interaction must be computed at the same location. For the moment in the x-direction at third points, M = wL 2 ( L 3 ) − w ( L 3 ) ( 1 2 ) ( L 3 ) M = wL 2 9 Therefore, at third points, Mx = wxL 2 9 My = wyL 2 90 For the reactions on the y-direction, wL 2 90 + R1 ( L 3 ) = wL 3 ( 1 2 ) ( L 3 ) R1 = 2wL 15
By symmetry, 2R1 + 2R2 = wL 2 ( 2wL 15 ) + 2R2 = wL R2 = 11wL 30 For the moment in the y-direction at midspan, M = 2wL 15 ( L 2 ) + 11 30 ( L 6 ) − wL 2 ( L 4 ) = wL 2 360 Therefore, at midspan, Mx = wxL 2 8 My = wyL 2 360 4. Stresses After computing the moments, the flexural stress is computed using the flexure formula. f = Mc I In terms of section modulus, f = M S When the loads are acting on the top flange instead of on the centroid, the effective inertia or section modulus is halved. f = 2Mc I (loads acting on the top flange) f = 2M S (loads acting on the top flange) 5. Interaction From PSAD 44: Combined Axial and Bending, the interaction value is computed using: IV = fa Fa + fbx Fbx + fby Fby whenever the ratio fa Fa does not exceed 0.15. For purlins which experience only bending, fa Fa = 0. IV = fbx Fbx + fby Fby (for D + L combination) When the spacing is being found and the stresses are expressed in terms of spacing, fbx Fbx + fby Fby = 1 (for D + L combination) 203.4.2. Alternate Basic Load Combinations In lieu of the basic load combinations, specified in Section 203.4.1., structures and portions thereof shall be permitted to be designed for the most critical effects resulting from the following load combinations. When using these alternate load combinations, a one-third increase shall be permitted in the allowable stresses for all combination including W or E.