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Solved: A timber beam AB of length L and rectangular cross
Chapter 6, Problem 6.20(choose chapter or problem)
A timber beam AB of length L and rectangular cross section carries a uniformly distributed load w and is supported as shown. (a) Show that the ratio \(\tau_m/ \sigma_m\) of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 5 m, w = 8 kN/m, \(\tau_m = 1.08 \text{ MPa}\), and \(\sigma_m = 12 \text{ MPa}\).
Questions & Answers
QUESTION:
A timber beam AB of length L and rectangular cross section carries a uniformly distributed load w and is supported as shown. (a) Show that the ratio \(\tau_m/ \sigma_m\) of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 5 m, w = 8 kN/m, \(\tau_m = 1.08 \text{ MPa}\), and \(\sigma_m = 12 \text{ MPa}\).
ANSWER:
a) The maximum normal stress occurs at the top and bottom of the beam, where sm=w*L/2A, where A is the area of the beam and w is the uniform load. The maximum shear stress occur