# Modulus of rigidity

by chandran
Tags: modulus, rigidity
 P: 541 There are three moduli of rigidity: 1. Young's Modulus 2.Bulk Modulus 3.Shear Modulus Modulus is generally defined as Stress/Strain 1.Young's Modulus is generally used for solid materials( In problems, for wires..) $Y= \frac{Longitudinal Stress}{Longitudinal Strain}$ 2. Bulk Modulus is generally used for Liquids and Gases $B= \frac{Volumetric Stress}{Volumetric Strain}$ 3. Shear Modulus is used where tangential stress is applied and the object bends or tangentially bends making some angle with vertical. I assume you know what stress and strain is.
 HW Helper P: 2,277 Rigidity is the required force to produce a unit incrementum of length. In prismatic beams, the product of EA is known as axial rigidity. $$\delta = \frac{PL}{EA}$$ where $\delta$ is the change in length, P is the force applied at the centroid, L is the original length, E is the modulus of elasticity (assuming the material is at the elastic-linear region) and A is the cross sectional area. Of course this is for Homogenous materials. In general the rigidity will be a measure of a structural member "opposing the change in length", with rigidity it's often used flexibility, which is inverse to the rigidity.
 HW Helper P: 2,277 Modulus of rigidity Maybe you are refering to the modulus of elasticity in shear stress, also know as modulus of rigidity. According to Hooke's Law in shear (elastic-linear region) $$\tau = G \gamma$$ where $\tau$ is the shear stress, G is the modulus of rigidity or elasticity in shear and $\gamma$ is the angle of distorsion or the unit deformation. The rigidity here is about measuring the structural element resistance to the "change of its shape".