A square plate of a width b and thickness t is loaded by normal forces P x and P y and by shear forces V, as shown in the figure. These forces produce uniformly distributed stresses acting on the side...

A square plate of a width b and thickness t is loaded by normal forces P_x
and P_y
and by shear forces V, as shown in the figure. These forces produce uniformly distributed stresses acting on the side faces of the plate.

(a) Calculate the change DV in the volume of the plate and the strain energy U stored in the plate if the dimensions are b = 600 mm and t = 40 mm; the plate is made of magnesium with E = 41 GPa and v = 0.35; and the forces are P_x
= 420 kN, P_y
= 210 kN, and V = 96 kN.

(b) Find the maximum permissible thickness of the plate when the strain energy U must be at least 62 J. [Assume that all other numerical values in part (a) are unchanged.]

(c) Find the minimum width b of the square plate of thickness t = 40 mm when the change in volume of the plate cannot exceed 0.018% of the original volume.