# 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/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
$\sigma_3$ 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:[1]

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)[2] 7.82 2.6

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.[3]

## References

1. ^ http://www.roymech.co.uk/Useful_Tables/Matter/shear_tensile.htm
2. ^ Watson, DC (May 1982). Mechanical Properties of E293/1581 Fiberglass-Epoxy Composite and of Several Adhesive Systems (PDF) (Technical report). Wright-Patterson Air Force, Ohio: Air Force Wright Aeronautical Laboratories. p. 16. Retrieved 24 October 2013.
3. ^ S. Grynko, "Material Properties Explained" (2012), ISBN 1-4700-7991-7, p. 38.