The figure shows a simply supported beam of length 10a, which is loaded by a transverse force P at the center of the beam. The cross-section is a double symmetric box profile with overall dimensions given in terms of a and wall thickness t. The profile is homogeneous and thin-walled with

a) Find the distribution of the internal forces and the moment Mz and shear force Qz at the section indicated by the dashed line immediately to the left of the force P.

b) Find the distribution of the normal stress σ and shear stress τ in the cross-section.

c) Determine the largest principal stress component σ₁ at point D in the cross-section, and find the orientation of σ₁ with respect to the longitudinal x axis.

d) Determine the von Mises stress at point D in the cross-section