there is relative displacement between the opposite faces of the cylinder. The restoring force per unit area developed due to the applied tangential force is known as tangential or shearing stress . As a result of applied tangential force, there is a relative displacement ∆ x between opposite faces of the cylinder as shown in the Fig. .
(b). The strain so produced is known as shearing strain and it is defined as the ratio of relative displacement of the faces ∆ x to the length of the cylinder L . Shearing strain ∆ x L = tan θ ( . ) where θ is the angular displacement of the cylinder from the vertical (original position of the cylinder).
Usually θ is very small, tan θ is nearly equal to angle θ , (if θ = °, for example, there is only % difference between θ and tan θ ). It can also be visualised, when a book is pressed with the hand and pushed horizontally, as shown in Fig. . (c).
Thus, shearing strain = tan θ ≈ θ ( . ) In Fig. . (d), a solid sphere placed in the fluid under high pressure is compressed uniformly on all sides.
The force applied by the fluid acts in perpendicular direction at each point of the surface and the body is said to be under hydraulic compression. This leads to decrease (a) (b) (c) (d) Fig. . (a) A cylindrical body under tensile stress elongates by ∆ L (b) Shearing stress on a cylinder deforming it by an angle θ (c) A body subjected to shearing stress (d) A solid body under a stress normal to the surface at every point (hydraulic stress).
The volumetric strain is ∆ V/V, but there is no change in shape. elastic behaviour and mechanical properties of solids which would answer many such questions. in its volume without any change of its geometrical shape. The body develops internal restoring forces that are equal and opposite to the forces applied by the fluid (the body restores its original shape and size when taken out from the fluid).