(a) Modulus of Rigidity or Shear Modulus
It is the ratio between shear stress(τ) and shear strain (es). It is denoted by G. It is the same as Shear modulus of elasticity
G = τ/es
(b) Hydrostatic Stress
When a body is immersed in a fluid to a large depth, the body gets subjected to equal external pressure at all points of the body. This external pressure is compressive in nature and is called hydrostatic stress.
(c) Volumetric Strain
The hydrostatic stress cause change in volume of the body, and this change of volume per unit is called volumetric strain ev.
Or, It is defined as the ratio between change is volume and original volume of the body, and is denoted by ev,
ev = change in volume/ original volume = δV/V
ev = ex + ey + ez
i.e., Volumetric strain equals the sum of the linear normal strain in x, y and z direction.
(d) Bulk Modulus or Volume Modulus of Elasticity
It may be defined as the ratio of normal stress(on each face of a solid cube) to volumetric strain. It is denoted by K. It is the same as Volume modulus of elasticity. K is a measure of the resistance of a material to change of volume without change of shape or form.
K = Hydrostatic pressure / Volumetric strain.
K = σn/ev =
(e) Poisson’s Ratio (µ)
If a body is subjected to a load, its length changes; ratio of this change in length to the original length is known as linear or primary strain. Due to this load, the dimensions of the body change; in all directions at right angles to its line of application the strains thus produced are called lateral or secondary or transverse strains and are of nature opposite to that of primary strains. For example, if the load is tensile, there will be an increase in length and a corresponding decrease in cross-sectional area of the body (Fig.). In this case, linear or primary strain will be tensile and secondary or lateral or transverse strain compressive
Poisson’s ratio is the ratio of lateral strain to the longitudinal strain. It is an elastic constant having the value always less than 1. It is denoted by ‘µ’ ( l/m)
Poisson’s Ratio (µ) = Lateral Strain / Longitudinal Strain; always less than 1.
Sl. No. |
Material |
Poisson’s ratio |
1 |
Aluminium |
0.330 |
2 |
Brass |
0.340 |
3 |
Bronze |
0.350 |
4 |
Cast iron |
0.270 |
5 |
Concrete |
0.200 |
6 |
Copper |
0.355 |
7 |
Steel |
0.288 |
8 |
Stainless steel |
0.305 |
9 |
Wrought iron |
0.278 |