Expression for normal and shear stress:

Derive expression for normal and shear stress on the plane AE inclined at an angle B with AB subjected to the direct stresses of compressive nature (both) of σ_x and  σ_y on 2 mutually

perpendicular stresses as shown in the figure given below.
 
Sol.: Consider unit thickness of element. Applying the equations of equilibrium to free body diagram of wedge ABE.

Let σ_n and  τ be normal and shear stresses on plane AE.
 
By multiplying the equation (iii) by sin θ, (iv) by cos θ and subtracting
 
Also by multiplying equation (iii) by cos θ and 4 by sin θ and then adding.