The shearing in a piece of structural steel is 100 MPa. If the modulus of rigidity G is 85 GPa, then the shearing strain is equal to _________ × 10^{-3}.

This question was previously asked in

PGCIL DT Civil 2018 Official Paper

Option 3 : 1.17

__Concept:__

Modulus of rigidity or shear modulus

The ratio of shear stress to the corresponding shear strain within the elastic limit, is known as Modulus of Rigidity or Shear Modulus. It is denoted by C or G or N.

∴ \(C\left( {or\;G\;or\;N} \right) = \frac{{Shear\;stress}}{{Shear\;strain}} = \frac{\tau }{\phi }\)

**Calculation:**

Given:

Shearing stress, τ = 100 MPa

Modulus of rigidity, G = 85 GPa = 85 × 10^{3} MPa

\(G = \frac{{Shear\;stress}}{{Shear\;strain}} = \frac{\tau }{\phi }\)

Shearing strain = \(\frac{100}{85\ × \;10^3}\) = 1.17 × 10^{-3}

Modulus of Elasticity or Young's Modulus

The ratio of tensile stress or compressive stress to the corresponding strain is a constant. This ratio is known as Young’s Modulus or Modulus of Elasticity and is denoted by E.

∴ \(E = \frac{{Tensile\;stress}}{{Tensile\;strain}}\;or\;\frac{{Compressive\;stress}}{{Compressive\;strain}}= \frac{\sigma }{e}\)

Bulk modulus (K)

It is the ratio of direct stress to volumetric strain.

\(K = \frac{{direct\;stress}}{{volumetric\;strain}} = \frac{\sigma }{{{e_v}}} = \frac{\sigma }{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\)