Stress is proportional to strain within its elastic limit. This law is known as Hooke‟s law. The material will not return to original shape if the applied stress is more than E.
Stresses are three types tensile, compressive, and shear stress. Moment and torsion will produced any of these stresses. Strain is nothing but deformation (change in length, breadth, height, diameter, therefore area or volume) of the body or material due to load. Therefore strain is change in dimension to the original dimension. It may be length or volume.
Therefore by substituting the value of ζ and ε in the Hook’s law. Change in length is
This is the fundamental equation to find change in length of any type of section or step section using principle of superposition method of varying load, length, area, and material. The change in length due to compressive load is taken as negative and positive for tensile load.