Changes in Shape

Here we consider changes in the shape of an object caused by pushing its top and bottom surfaces in opposite directions as shown in Fig. 9.2.

  

Figure 9.2: Shear strain

Definitions:

• Shear Stress is the force per unit area exerted on the top and bottom of solid. (Note that the surface whose area we need to consider is parallel to the force in this case.)
• Shear Strain is the distance the top surface has moved relative to the bottom surface, divided by the perpendicular distance between them.
• Shear modulus ( S ) is the ratio of the shear stress to the shear strain:

  $${\frac{{\:\rm shear\ stress}}{{\:\rm shear\ strain}}} {\frac{F/A}{\Delta x/h}}$$ (3)

  where F is the applied force, A is the area, $\Delta$x is the distance the top surface has moved relative to the bottom surface, and h is the perpendicular distance between the top and bottom surfaces. Notice that S has S.I. units of N/m ².