Shear strength

Shear strength in engineering is a term used to describe 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/construction of the component (e.g. beams, plates, or bolts) In a reinforced concrete beam, the main purpose of stirrups is to increase the shear strength.

For shear stress τ applies

$\tau = \frac {\sigma_1 - \sigma_2}{2} ,$

where

σ₁ is major principal stress

σ₂ is minor principal stress

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

To calculate:

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

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

As a very rough guide:

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

See also

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