Lesson plan
Shear modulus
In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to shear strain: \begin{align} G &:= \frac {\tau_{xy}} {\gamma_{xy}} = \frac{\frac{F}{A}}{\frac{\Delta x}{l}} = \frac{F l}{A \Delta x}\\ \tau_{xy} &= \frac{F}{A}\\ \gamma_{xy} &= \frac{\Delta x}{l} \end{align} where \tau_{xy} is the shear stress, \gamma_{xy} is the shear strain, F is the force, A is the area, \Delta x is the traverse displacement, l is the initial length or height. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M 1 L −1 T −2 , replacing force by mass times acceleration.
Article summary
In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to shear strain: \begin{align} G &:= \frac {\tau_{xy}} {\gamma_{xy}} = \frac{\frac{F}{A}}{\frac{\Delta x}{l}} = \frac{F l}{A \Delta x}\\ \tau_{xy} &= \frac{F}{A}\\ \gamma_{xy} &= \frac{\Delta x}{l} \end{align} where \tau_{xy} is the shear stress, \gamma_{xy} is the shear strain, F is the force, A is the area, \Delta x is the traverse displacement, l is the initial length or height. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M 1 L −1 T −2 , replacing force by mass times acceleration.
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Discussion questions
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