Question

Explain the concept of Complementary shear stress.

Answer 1

It states that a set of shear stresses across a plain is always accompanied by a set of balancing shear stresses across the plane and normal to it. 

Shear force on face AB = τ.AB 

Shear force on face CD = τ.CD ...(i) 

These parallel and equal forces form a couple. 

The moment of couple = τ.AB.AD or τ.CD.AD ...(ii)

For equilibrium they must be a restoring couple. 

Shear force on face AD or BC = τ^l.AD or τ^l.BC ...(iii) 

They also form a couple as 

= τ^l.AD.AB or τ^l.BC.AB ...(iv) 

The moment of two couple must be equal; 

τ.AB.CD = τ^l.AD.AB or τ = τ^l 

τ^l is called complementary shear stress