Linear Stress˗Strain Model for Material Response for Members inTorsion

Key Concept: One model to represent the property of a given material response is to assume a linear relationship between stress and strain. The slope, G, for this model is the Shearing Modulus of Elasticity or also called the Modulus of Rigidity. See the figure below.

In a Nut Shell: The equation relating stress and strain for the linear model is as follows:

τ = G γ

where τ is the shearing stress (lb/in², mPa, N/mm²)

γ is the shearing strain (in/in, mm/mm, microstrain)

G is the Shearing Modulus of Elasticity (a material property ˗ psi, GPa)

Material	Value of Shearing Modulus of Elasticity, G
Mild Steel	11 x 10^6 psi	77 GPa
Aluminum	4 x 10^6 psi	27 GPa

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