A beam can be subjected to multiple stresses at once—axial normal stress, bending normal stress, torsional shear, and transverse (horizontal) shear. In the linear-elastic range, evaluate each at the same point and add them (superposition) for the net state.
$$ \sigma = \frac{P}{A} $$
$$ f_b = \frac{M c}{I} $$
$$ \tau_{\text{torque}} = \frac{T r}{J} $$
$$ \tau_{\text{shear}} = \frac{V Q}{I b} $$
Problem: Cast-Iron with Axial and Bending Stresses
A cast iron is shown below. The allowable stresses are 30MPa in tension and 70MPa in compression.
a. Determine the safe value of P (in kN) based on the allowable tensile stress.
b. Determine the safe value of P (in kN) based on the allowable compressive stress.