Question

The state of stress in two-dimensionally stressed body at a point is as shown in Fig. (a). Determine the principal planes, principal stresses, maximum shear stress and their planes

Answer 1

Let x and y directions be selected as shown in the figure. Then 

p_x = – 100 N/mm² , p_y = – 75 N/mm² , q = – 50 N/mm²

= – 87.5 – 51.54 

i.e., p₂ = – 139.04 N/mm²

Let principal plane of p₁ make angle θ with x-axis. Then

The planes of maximum shear stresses are at 45° to the principal planes. These planes are shown in Fig. (b).