Shear Stress and Strain 

When a body is subjected to two equal and opposite forces acting tangentially across the resisting section, as a result of which the body tends to shear off the section, then the stress induced is called shear stress.

The corresponding strain is known as shear strain and it is measured by the angular deformation accompanying the shear stress. The shear stress and shear strain are denoted by the Greek letters tau (τ) and phi (φ) respectively. Mathematically,

Shear stress, τ =Tangential force / Resisting area

 Consider a body consisting of two plates connected by a rivet as shown in Fig. (a). In this case, the tangential force P tends to shear off the rivet at one cross-section as shown in Fig.(b). It may be noted that when the tangential force is resisted by one cross-section of the rivet (or when shearing takes place at one cross-section of the rivet), then the rivets are said to be in single shear. In such a case, the area resisting the shear off the rivet,

A = (π/4) × d²

 and shear stress on the rivet cross-section,

       = P/A

 = (4P/ π d²)

 Shear Modulus or Modulus of Rigidity

 It has been found experimentally that within the elastic limit, the shear stress is directly proportional to shear strain. Mathematically

        ∝ φ

        = C . φ

      / φ = C

where

 τ = Shear stress,

φ = Shear strain, and

C = Constant of proportionality, known as shear modulus or modulus of rigidity. It is also denoted by N or G.

Working Stress

 When designing machine parts, it is desirable to keep the stress lower than the maximum or ultimate stress at which failure of the material takes place. This stress is known as the working