Shear Modulus (G = τ/γ)

G = \frac{\tau}{\gamma}

Worked example: 60 MPa at 800 microstrain shear → G = 75 GPa — press Try an example to run it live, then adjust anything.

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Shear Modulus (G = τ/γ) explained

Shear strain γ is not a stretch but a change of angle: push the top of a block sideways by Δx while its height stays h, and γ = Δx/h, the small angle in radians by which the originally square corner has been racked out of true. The shear modulus is the stress needed per unit of that racking. Charles-Augustin de Coulomb measured it first, in the 1784 torsion-balance experiments that also gave him the law of electrostatics — he twisted fine wires and timed their oscillations. Steel runs G ≈ 77 GPa (11 600 ksi), aluminium ≈ 26 GPa. A shear stress of 60 MPa producing γ = 0.0008 rad implies G = 60 ÷ 0.0008 = 75 000 MPa = 75 GPa.

The trap is treating G as an independent property to look up separately: for an isotropic material it is locked to E and Poisson's ratio by E = 2G(1 + ν), so with ν ≈ 0.3 you always get G ≈ 0.385 E. Enter γ as a plain ratio (radians), not degrees — a shear strain of 0.001 is a milliradian, about 0.057°, and mixing the two inflates G by a factor of 57.

Shear Modulus (G = τ/γ) formula

G = \frac{\tau}{\gamma}

Where

$G$ = Shear modulus (kPa)
$\tau$ = Shear stress (kPa)
$\gamma$ = Shear strain (radians) (m/m)

Missing one of these? Work it out first, then come back

Shear modulus — Relation Between E, G and ν, Angle of Twist (φ = TL/JG)
Shear stress — Average Shear Stress (τ = V/A), Torsional Shear Stress (τ = Tr/J)
Shear strain (radians) — Normal Strain (ε = δ/L), Young's Modulus (E = σ/ε)

Part of these formula sets

Stress, strain and the elastic constants

9 formulasNormal and shear stress, strain, axial deformation, and the four elastic constants E, G, K and ν that link them.

Torsion of shafts

4 formulasTwisting a round shaft: the polar moment of inertia, the shear stress it produces, and how far the far end rotates under load.