A roof structure consists of plywood and roofing material

Chapter 5, Problem 5.94

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A roof structure consists of plywood and roofing material supported by several timber beams of length L = 16 m. The dead load carried by each beam, including the estimated weight of the beam, can be represented by a uniformly distributed load \(w_D = 350 \text{ N/m}\). The live load consists of a snow load, represented by a uniformly distributed load \(w_L = 600 \text{ N/m}\), and a 6-kN concentrated load P applied at the midpoint C of each beam. Knowing that the ultimate strength for the timber used is \(\sigma_U = 50 \text{ MPa}\) and that the width of the beam is b = 75 mm, determine the minimum allowable depth h of the beams, using LRFD with the load factors \(\gamma_D = 1.2\), \(\gamma_L = 1.6\) and the resistance factor \(\phi =0.9\).