A timber beam AB of length L and rectangular cross-section carries a single concentrated load P at its midpoint C. (a) Show that the ratio τ m / σ 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 = 2 m, P = 40 kN, τm = 960 kPa, and σm = 12 MPa.
