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 σx and σy 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 σn 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.