(Solved): a) Write the flexure formula and general shear formula. (20) b) A timber beam AE of span \( 32 \mat ...

a) Write the flexure formula and general shear formula. (20) b) A timber beam AE of span \( 32 \mathrm{ft} \) is to support the two concentrated loads and a uniformly distributed load shown. Knowing that for the grade of timber used, allowable bending stress \( \sigma_{\text {all }}=1400 \mathrm{psi} \) and allowable shear stress \( \tau_{\text {all }}=120 \mathrm{psi} \). Determine the minimum required depth \( \mathbf{d} \) of the beam. \[ \left(\text { Hint: } \sigma_{a l l}=\frac{M_{\max }}{S}, \tau_{a l l}=\frac{1.5 V_{\max }}{A}\right) \]