Stress and strain produced by a force tangential to the surface of a body are known as shear stress and shear strain
Shear Stress Shear
stress exists between two parts of a body in contact, when the two parts exert equal and opposite force on each other laterally in a direction tangential to their surface of contact.
Figure shows a section of rivet subjected to equal and opposite forces P causing sliding of the particles one over the other.
From figure it is clear that the resisting force of the rivet must be equal to P. Hence, shearing stress τ is given by
τ = total tangential force/(Surface Area)
= P/A ; A = Π.d.t
The tensile stress and compressive stress are also known as “direct stresses" and shearing stress as "tangential stress”.
The common examples of a system involving shear stress are riveted and welded joint, towing device, punching operation etc.
Shear Strain
In case of a shearing load, a shear strain will be produced which is measured by the angle through which the body distorts.In Fig. is shown a rectangular block LMNP fixed at one face and subjected to force F. After application of force, it distorts through an angle Φ and occupies new position LM’N’P. The shear strain (es ) is given by
es = NN’/NP = tanΦ =
Φ (radians) ...... since Φ is very small.
The above result has been obtained by assuming NN’ equal to arc (as NN’ is small) drawn with centre P and radius PN
