A cantilever beam is subjected to a parabolically varying end shear stress resulting in...

A cantilever beam is subjected to a parabolically varying end shear stress resulting in a load of P N and a linearly distributed load p N/cm (Fig. P7.42). Dividing the beam into two triangles as shown, calculate the stresses in the member. The beam is made of a transversely isotropic material, in which a rotational symmetry of properties exists within the xz plane:

Here is associated with the behavior in the xz plane, and with the direction perpendicular to the xz plane. Now the elasticity matrix, Eq. (7.54), becomes