Shear strength

In engineering, shear strength is the strength of a material or component against the type of yield or structural failure where the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear.

In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.g. beams, plates, or bolts). In a reinforced concrete beam, the main purpose of reinforcing bar (rebar) stirrups is to increase the shear strength.

For shear stress $\tau$ applies

$\tau = \frac {\sigma_1 - \sigma_3}{2} ,$

where

$\sigma_1$ is major principal stress and

$\sigma_3$ is minor principal stress.

In general: ductile materials (e.g. aluminium) fail in shear, whereas brittle materials (e.g. cast iron) fail in tension. See tensile strength.

To calculate:

Given total force at failure (F) and the force-resisting area (e.g. the cross-section of a bolt loaded in shear), ultimate shear strength ($\tau$) is:

$\tau = \frac {F}{A} = \frac {F}{\pi r_{bolt}^2} = \frac {4F}{\pi d_{bolt}^2}$

Comparison

As a very rough guide relating tensile, yield, and shear strengths:

Material	Ultimate Strength Relationship	Yield Strength Relationship
Steels	USS = approx. 0.75*UTS	SYS = approx. 0.58*TYS
Ductile Iron	USS = approx. 0.9*UTS	SYS = approx. 0.75*TYS
Malleable Iron	USS = approx. 1.0*UTS
Wrought Iron	USS = approx. 0.83*UTS
Cast Iron	USS = approx. 1.3*UTS
Aluminiums	USS = approx. 0.65*UTS	SYS = approx. 0.55*TYS

USS: Ultimate Shear Strength, UTS: Ultimate Tensile Strength, SYS: Shear Yield Stress, TYS: Tensile Yield Stress

Material	Ultimate stress (Ksi)	Ultimate stress (MPa)
Fiberglass/epoxy (23 o C)	7.82	53.9

When values measured from physical samples are desired, a number of testing standards are available, covering different material categories and testing conditions. In the US, ASTM standards for measuring shear strength include ASTM B831, D732, D4255, D5379, and D7078. Internationally, ISO testing standards for shear strength include ISO 3597, 12579, and 14130.

See also

• Shear modulus
• Shear stress
• Shear strain
• Shear strength (soil)
• Shear strength (Discontinuity)
• Strength of materials
• Tensile strength