Opening your learning space
Starting the app …
Opening your learning space
Starting the app …
In the linear-elastic range, shear modulus is the ratio of shear stress to engineering shear strain.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
G and τ in Pa; γ dimensionless (rad)
| Symbol | Meaning | Unit |
|---|---|---|
| Material shear modulus | Pa | |
| Shear stress | Pa | |
| Engineering shear strain or small shear angle | dimensionless |
G=\frac{\tau}{\gamma}The constitutive law τ=Gγ applies to small elastic shear deformation. For isotropic linear-elastic materials, G=E/[2(1+ν)]; anisotropic materials may couple normal and shear response. The relation does not remain linear after yielding or under large nonlinear deformation. Shear strain is an angle in radians and is dimensionless.
The constitutive law τ=Gγ applies to small elastic shear deformation. For isotropic linear-elastic materials, G=E/[2(1+ν)]; anisotropic materials may couple normal and shear response. The relation does not remain linear after yielding or under large nonlinear deformation. Shear strain is an angle in radians and is dimensionless.
In the linear-elastic range, shear modulus is the ratio of shear stress to engineering shear strain.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Shear modulus and shear law” and check its unit and magnitude.
For τ=24 MPa and γ=3×10−4, G=24×106/(3×10−4)=80 GPa.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: G and τ in Pa; γ dimensionless (rad).
Formula cluster
In the linear-elastic range, shear modulus is the ratio of shear stress to engineering shear strain.
For τ=24 MPa and γ=3×10−4, G=24×106/(3×10−4)=80 GPa.
Model elastic shear deformation and torsional stiffness of materials.
Here is how to work through a typical Shear modulus and shear law (G = τ/γ) task step by step:
Task
Work through the numerical example for “Shear modulus and shear law” and check its unit and magnitude.
Solution path
For τ=24 MPa and γ=3×10−4, G=24×106/(3×10−4)=80 GPa.
G measures how strongly a material resists elastic shear deformation. At the same shear stress, a larger G produces a smaller shear strain γ. The relation is analogous to E=σ/ε but connects shear quantities rather than axial normal stress and tensile strain. It is a material property within the stated range. Determine shear modulus only in the small-strain linear-elastic range and use shear stress and angular strain from the same test. Units check: Pa divided by dimensionless γ gives Pa. For isotropic materials, G=E/[2(1+ν)] relates shear and tensile properties. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
For isotropic linear-elastic materials, G=E/[2(1+ν)]. If E=200 GPa and ν=0.25, then G=80 GPa. The relation follows from isotropic elasticity and is not universal for every material. For anisotropic materials, use measured direction-dependent shear properties. Determine shear modulus only in the small-strain linear-elastic range and use shear stress and angular strain from the same test. Units check: Pa divided by dimensionless γ gives Pa. For isotropic materials, G=E/[2(1+ν)] relates shear and tensile properties. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Engineering shear strain is, for small angles, lateral displacement divided by element height, a ratio of lengths. It may also be stated as an angle in radians, which is dimensionless. Do not insert degree values directly into a linear stress relation without converting them to radians. Determine shear modulus only in the small-strain linear-elastic range and use shear stress and angular strain from the same test. Units check: Pa divided by dimensionless γ gives Pa. For isotropic materials, G=E/[2(1+ν)] relates shear and tensile properties. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Write the quantity and unit from the variable list next to every value: G and τ in Pa; γ dimensionless (rad). Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For τ=24 MPa and γ=3×10−4, G=24×106/(3×10−4)=80 GPa. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Determine shear modulus only in the small-strain linear-elastic range and use shear stress and angular strain from the same test. Units check: Pa divided by dimensionless γ gives Pa. For isotropic materials, G=E/[2(1+ν)] relates shear and tensile properties. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
The background states this starting condition: The constitutive law τ=Gγ applies to small elastic shear deformation. For isotropic linear-elastic materials, G=E/[2(1+ν)]; anisotropic materials may. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Determine shear modulus only in the small-strain linear-elastic range and use shear stress and angular strain from the same test. Units check: Pa divided by dimensionless γ gives Pa. For isotropic materials, G=E/[2(1+ν)] relates shear and tensile properties. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Quanta exam set
Curated exam set for "Shear modulus and shear law":
Question (front)
Which formula describes Shear modulus and shear law?
Answer in your set
Question (front)
How do you rearrange Shear modulus and shear law for Base equation for the target quantity?
Answer in your set
Question (front)
Which common mistake happens with Shear modulus and shear law?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
Create a curated FSRS exam set for G = τ/γ: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential