12.3 Stress, strain, and elastic modulus  (Page 6/26)

Shear stress, strain, and modulus

The concepts of shear stress and strain concern only solid objects or materials. Buildings and tectonic plates are examples of objects that may be subjected to shear stresses. In general, these concepts do not apply to fluids.

Shear deformation occurs when two antiparallel forces of equal magnitude are applied tangentially to opposite surfaces of a solid object, causing no deformation in the transverse direction to the line of force, as in the typical example of shear stress illustrated in [link] . Shear deformation is characterized by a gradual shift $\text{Δ}x$ of layers in the direction tangent to the acting forces. This gradation in $\text{Δ}x$ occurs in the transverse direction along some distance $L_0.$ Shear strain is defined by the ratio of the largest displacement $\text{Δ}x$ to the transverse distance $L_0$

Shear strain is caused by shear stress. Shear stress is due to forces that act parallel to the surface. We use the symbol $F_{\parallel }$ for such forces. The magnitude $F_{\parallel }$ per surface area A where shearing force is applied is the measure of shear stress

The shear modulus is the proportionality constant in [link] and is defined by the ratio of stress to strain. Shear modulus is commonly denoted by S :