solids bodies. In this chapter, we shall study the . Introduction . Stress and strain .
Hooke’s law . Stress-strain curve . Elastic moduli . Applications of elastic behaviour of materials Summary Points to ponder Exercises .
STRESS AND STRAIN When forces are applied on a body in such a manner that the body is still in static equilibrium, it is deformed to a small or large extent depending upon the nature of the material of the body and the magnitude of the deforming force. The deformation may not be noticeable visually in many materials but it is there. When a body is subjected to a deforming force, a restoring force is developed in the body. This restoring force is equal in magnitude but opposite in direction to the applied force.
The restoring force per unit area is known as stress. If F is the force applied normal to the cross–section and A is the area of cross section of the body, Magnitude of the stress = F / A ( . ) The SI unit of stress is N m – or pascal (Pa) and its dimensional formula is [ ML – T – ]. There are three ways in which a solid may change its dimensions when an external force acts on it.
These are shown in Fig. . . In Fig.
. (a), a cylinder is stretched by two equal forces applied normal to its cross-sectional area. The restoring force per unit area in this case is called tensile stress . If the cylinder is compressed under the action of applied forces, the restoring force per unit area is known as compressive stress .
Tensile or compressive stress can also be termed as longitudinal stress. In both the cases, there is a change in the length of the cylinder. The change in the length ∆ L to the original length L of the body (cylinder in this case) is known as longitudinal strain . Longitudinal strain ∆ ( .
) However, if two equal and opposite deforming forces are applied parallel to the cross-sectional area of the cylinder, as shown in Fig. . (b),