What is "shear strength"

n. The resistance to forces that cause or tend to cause two contiguous parts of a body to slide relative to each other in a direction parallel to their contrast.

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 τ applies

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

where

σ
is major principal stress and

σ
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 (τ) is:

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

Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle contacts. Due to interlocking, particulate material may expand or contract in volume as it is subject to shear strains. If soil expands its volume, the density of particles will decrease and the strength will decrease; in this case, the peak strength would be followed by a reduction of shear stress. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. The theoretical state at which the shear stress and density remain constant while the shear strain increases may be called the critical state, steady state, or residual strength.

The volume change behavior and interparticle friction depend on the density of the particles, the intergranular contact forces, and to a somewhat lesser extent, other factors such as the rate of shearing and the direction of the shear stress. The average normal intergranular contact force per unit area is called the effective stress.

If water is not allowed to flow in or out of the soil, the stress path is called an undrained stress path. During undrained shear, if the particles are surrounded by a nearly incompressible fluid such as water, then the density of the particles cannot change without drainage, but the water pressure and effective stress will change. On the other hand, if the fluids are allowed to freely drain out of the pores, then the pore pressures will remain constant and the test path is called a drained stress path. The soil is free to dilate or contract during shear if the soil is drained. In reality, soil is partially drained, somewhere between the perfectly undrained and drained idealized conditions.

The shear strength of soil depends on the effective stress, the drainage conditions, the density of the particles, the rate of strain, and the direction of the strain.

For undrained, constant volume shearing, the Tresca theory may be used to predict the shear strength, but for drained conditions, the Mohr–Coulomb theory may be used.

Two important theories of soil shear are the critical state theory and the steady state theory. There are key differences between the critical state condition and the steady state condition and the resulting theory corresponding to each of these conditions.

The shear strength of a discontinuity in a soil or rock mass may have a strong impact on the mechanical behavior of a soil or rock mass. The shear strength of a discontinuity is often considerably lower than the shear strength of the blocks of intact material in between the discontinuities, and therefore influences, for example, tunnel, foundation, or slope engineering, but also the stability of natural slopes. Many slopes, natural and man-made, fail due to a low shear strength of discontinuities in the soil or rock mass in the slope. The deformation characteristics of a soil or rock mass are also influenced by the shear strength of the discontinuities. For example, the modulus of deformation is reduced, and the deformation becomes plastic (i.e. non-reversible deformation on reduction of stress) rather than elastic (i.e. reversible deformation). This may cause, for example, larger settlement of foundations, which is also permanent even if the load is only temporary. Furthermore, the shear strength of discontinuities influences the stress distribution in a soil or rock mass.