Editing Shear modulus (section)

{{Short description|Ratio of shear stress to shear strain}}
{{Infobox Physical quantity
| bgcolour =
| name = Shear modulus
| image = 
| caption = Math
| unit = [[Pascal (unit)|Pa]]
| symbols = {{mvar|G}}, {{mvar|S}}, {{mvar|μ}}
| derivations = {{math|1=''G'' = [[Shear stress|τ]] / [[Shear strain|γ]] = [[Young modulus|''E'']] / [2(1 + [[Poisson's ratio|ν]])]}}
}}
[[File:Shear scherung.svg|thumb|right|Shear strain]]
In [[materials science]], '''shear modulus''' or '''modulus of rigidity''', denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the [[Elasticity (physics)|elastic]] shear stiffness of a material and is defined as the ratio of [[shear stress]] to the [[shear strain]]:<ref>{{GoldBookRef|title=shear modulus, ''G''|file=S05635}}</ref>
:<math>G \ \stackrel{\mathrm{def}}{=}\ \frac {\tau_{xy}} {\gamma_{xy}} = \frac{F/A}{\Delta x/l} = \frac{F l}{A \Delta x} </math>

where 
:<math>\tau_{xy} = F/A \,</math> = shear stress
:<math>F</math> is the force which acts
:<math>A</math> is the area on which the force acts
:<math>\gamma_{xy}</math> = shear strain. In engineering <math>:=\Delta x/l = \tan \theta </math>, elsewhere <math> := \theta</math> 
:<math>\Delta x</math> is the transverse displacement
:<math>l</math> is the initial length of the area.

The derived [[SI]] unit of shear modulus is the [[Pascal (unit)|pascal]] (Pa), although it is usually expressed in [[Pascal (unit)|gigapascal]]s (GPa) or in thousand [[pounds per square inch]] (ksi). Its [[dimensional analysis|dimensional form]] is M<sup>1</sup>L<sup>−1</sup>T<sup>−2</sup>, replacing ''force'' by ''mass'' times ''acceleration''.