Material fundamentals · Shear

Shear modulus and twisting

Why can a plate resist bending yet twist easily?

Shear deformation changes angles rather than only stretching a length. Wood needs separate shear properties for its three principal material planes.

Try the interactive demo

Start with something familiar

Place a stack of cards on a table, keep the bottom still and slide the top sideways. The outline becomes slanted. This illustrates shear geometry; real elastic wood deforms internally rather than freely slipping card by card.

Original shape

Angle changes under a sideways load

Under load

Angle changes under a sideways load

Diagram · A top face displaced sideways relative to the bottom. The dashed rectangle is the undeformed outline, not a separate material.

Notice what changes
Stretching changes a length along the load. Shearing mainly changes an angle. They are different deformation modes, so resistance to one does not completely describe resistance to the other.
Understand why
For the same applied shear stress, a larger shear modulus gives a smaller angle change. The teaching drawing magnifies that tiny angle so the difference is visible.
Connect it to wood and making
Wood has different shear planes. Twisting or coupled plate modes can involve these properties even when two specimens share the same longitudinal Young’s modulus.

Put names to the ideas

Stress and angular strain

In linear shear, τ = Gγ. Shear stress τ and modulus G use Pa; engineering shear strain γ is dimensionless and represents the small change in angle in radians.

Three shear planes

Orthotropic wood uses G_LR, G_LT and G_RT. The familiar isotropic relation between E, G and Poisson’s ratio cannot generally recover these values from a single longitudinal E.

A different vibration contribution

Twisting and coupled plate modes involve shear as well as normal elasticity. For short or thick beams, shear deformation can also make the simplest slender-beam inversion inadequate.

\tau_{LR}=G_{LR}\gamma_{LR}

τ is shear force per area; γ is angular shear strain; G is their ratio. At fixed τ, doubling G halves γ in this linear model.

A worked example

Two woods with similar E_L and density can still differ in twisting response. A plate model that uses only E_L and ρ cannot distinguish this difference.

Explore it yourself

Use a suitable torsion or multi-mode method when shear response matters; record the material plane and the model used for inversion.

Shear stress MPa

Shear modulus GPa

γ: 0.100 %

Hold stress fixed and double G: angular strain halves. The graphic magnifies deformation; no nonlinear or damage behaviour is modelled.

Check your understanding

At fixed shear stress, what happens if G doubles?It doublesIt halves