How this instrument works
Pull a bar and it lengthens. Push its top sideways while its base stays put and it leans instead, tracing a parallelogram where a rectangle used to be. Shear modulus, written G, measures how stubbornly a solid refuses that second insult — shape changing while volume stays roughly constant. Divide shear stress by lean angle and you have it. Magnitudes worth carrying around: near 79 GPa for structural steel, 45 for copper, 26 for aluminium and for window glass, about 12 for concrete, near 4 for a glass-filled engineering polymer, and something like 0.0005 for soft rubber — five orders of magnitude separating hardware-store elastic from girder steel.
Charles-Augustin de Coulomb got here first, by twisting wires rather than shoving blocks. His 1784 memoir on torsion reported restoring torque rising with twist angle and with diameter to a fourth power, falling with wire length — shear stiffness measured cleanly, decades before anybody wrote a letter G. What followed was a fight worth remembering. Navier and Poisson, reasoning from central forces between molecules, deduced that every isotropic solid must show Poisson's ratio of exactly one quarter, which pins G at two fifths of E for everything. Wertheim's careful measurements through the 1840s kept refusing to cooperate, George Green's energy argument of 1837 showed two independent constants were required rather than one, and the multi-constant camp won. Steel sits at ν ≈ 0.30, not 0.25.
Three things quietly wreck a block measurement. Simple shear assumes a squat specimen: build one tall and slender and most of what your gauge reads is bending, which grows with height cubed while genuine shear grows only with height. Small angles are assumed too, since γ is properly the tangent of lean — faithful below a few degrees, worthless for elastomers distorted by tens of percent, territory where hyperelastic models take over. Isotropy is the third assumption. Timber carries three separate shear moduli depending on which pair of axes gets skewed, spanning more than tenfold; fibre laminates answer differently in every plane. Fluids mark the far edge of the range with a static G of exactly zero, which is roughly what being fluid means.
- Enter Shear force — load acting along the sheared face, parallel to it, never across it. Newtons, kilonewtons or pounds-force.
- Put the loaded or bonded face into Area resisting shear. A 50 mm by 20 mm face is 1000 mm²; switch that field's units instead of converting by hand.
- Give Sideways deflection, how far the moving face travels relative to the fixed one, and Height of the block, measured between those two faces.
- Read Shear modulus in Pa, MPa, psi or ksi. Shear strain appears beside it as a pure ratio — for small leans, that ratio is the angle in radians.
Worked example — 5 kN across a polymer block
A block of glass-filled nylon sits in a shear rig, 50 mm tall, bonded top and bottom over a face of 1000 mm² — call it 50 mm by 20 mm. A ram drives the upper platen sideways with 5 kN while a dial gauge watches the top edge, and it travels 62.5 micrometres. Enter 5000 into Shear force, 0.001 m² into Area resisting shear, 0.0000625 m into Sideways deflection, 0.05 m into Height of the block.
Strain arrives first: γ = 6.25 × 10⁻⁵ ⁄ 0.05 = 0.00125. Then stress: τ = 5000 ⁄ 0.001 = 5 × 10⁶ Pa, a round 5 MPa. Their quotient is what you came for — G = 5 × 10⁶ ⁄ 0.00125 = 4 × 10⁹ Pa, four gigapascals. Note what that strain figure really is: 0.00125 radians of lean, which converts to 0.0716°, roughly 4.3 arcminutes off vertical. Nobody would see it across a room.
Swap the polymer for steel and this rig goes blind. At G near 79 GPa, that same 5 MPa produces only 63 microstrain, moving the top face about 3 micrometres across 50 mm of height — smaller than the flex in most fixtures and well past what a dial gauge should be trusted to report. Stiff metals surrender G to torsion instead, where a long slim specimen piles up twist angle you can genuinely resolve.
Questions
What units does G use, and what unit does shear strain use?
G inherits units of stress — pascals — because shear strain is a bare ratio contributing none of its own. Handbooks list gigapascals for readability, since 79 GPa beats writing 79000000000 Pa, and US sources often use ksi or Msi. Shear strain γ carries no units at all. For deformations small enough that a tangent equals its angle, γ is simply the lean in radians, so 0.00125 means 0.0716 degrees. Quote it as a decimal, as microstrain, or as a percentage — but keep degrees out of the ratio itself.
How does shear modulus relate to Young's modulus and Poisson's ratio?
By G = E ⁄ [2(1 + ν)] in any isotropic material. With ν around 0.30, typical of metals, that factor is 1/2.6 and rigidity lands near 38% of tensile stiffness — steel's 200 GPa becomes roughly 79 GPa. Cork, whose ν sits close to zero, gives half of E. Rubber, nearly incompressible at ν ≈ 0.4999, gives a third. Any two elastic constants determine every other one for an isotropic solid, which is why a datasheet listing E and ν feels no obligation to print G as well.
My block test gives half the published value — what went wrong?
Bending, most likely. A loaded block shears and bends at once, and bending deflection scales with height cubed while shear deflection scales only with height, so a tall specimen quietly hands you extra travel that the formula reads as softness. Bond lines creeping, platens slipping and load frames flexing all push the same direction. Keep specimens squat, measure Sideways deflection between the two faces themselves rather than from crosshead travel, and where the number matters use torsion — ASTM E143 exists because shoving blocks sideways is genuinely hard to do cleanly.
Do liquids and gases have a shear modulus?
Zero, under static load — that is close to a working definition of a fluid. Apply any shear stress to still water, however gentle, and it keeps moving instead of settling into a distorted shape; what pushes back is viscosity, which resists rate of shearing rather than amount. Seismology reads this straight off the record. Shear waves need non-zero G to travel, and they disappear into a shadow zone beyond about 103 degrees of arc from a quake. Richard Oldham spotted that gap in 1906, and it remains how we know Earth's outer core is molten.
Is this the same as modulus of rigidity, or as shear strength?
Modulus of rigidity is just an older name for the identical quantity, still preferred in some British texts and standards. Shear strength is something else entirely — the stress at which material tears along a plane, not how far it skews on the way there. Structural steel pairs G near 79 GPa with shear yield near 145 MPa. Stiffness predicts deflection and twist; strength predicts the moment a bolt shank or rivet lets go. Confusing them sizes a shaft for the wrong failure.
Where does shear modulus actually earn its keep?
Anywhere twist or distortion governs. Drive shafts and torsion bars resist rotation in proportion to G. Coil spring rate depends on G, not on E, which surprises people the first time they derive it. Rubber engine mounts and elastomeric bridge bearings are specified around a deliberately low G so a deck can breathe with temperature. Thin-walled chassis boxes get their torsional rigidity from it, quoted in newton-metres per degree. And S-wave speed in rock is set by G together with density.