In
engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
, shear strength is the strength of a material or component against the type of
yield or
structural failure
Structural integrity and failure is an aspect of engineering that deals with the ability of a structure to support a designed structural load (weight, force, etc.) without breaking and includes the study of past structural failures in order t ...
when the material or component fails in
shear. A shear load is a
force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
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
Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, ...
, 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
Reinforced concrete (RC), also called reinforced cement concrete (RCC) and ferroconcrete, is a composite material in which concrete's relatively low ultimate tensile strength, tensile strength and ductility are compensated for by the inclusion ...
beam, the main purpose of
reinforcing bar (rebar) stirrups is to increase the shear strength.
Equations
For
shear stress
Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
applies
:
where
:
is major principal stress and
:
is minor principal stress.
In general: ductile materials (e.g. aluminum) fail in shear, whereas brittle materials (e.g. cast iron) fail in tension. See
tensile strength
Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or F_\text within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials ...
.
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 (
) is:
:
For average shear stress
where
:
is the average shear stress,
:
is the shear force applied to each section of the part, and
:
is the area of the section.
Average shear stress can also be defined as the total force of
as
:
This is only the average stress, actual stress distribution is not uniform. In real world applications, this equation only gives an approximation and the maximum shear stress would be higher. Stress is not often equally distributed across a part so the shear strength would need to be higher to account for the estimate.
Comparison
As a very rough guide relating tensile, yield, and shear strengths:
USS: Ultimate Shear Strength, UTS: Ultimate Tensile Strength, SYS: Shear Yield Stress, TYS: Tensile Yield Stress
There are no published standard values for shear strength like with tensile and yield strength. Instead, it is common for it to be estimated as 60% of the ultimate tensile strength. Shear strength can be measured by a torsion test where it is equal to their torsional strength.
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 B769, B831, D732, D4255, D5379, and D7078. Internationally, ISO testing standards for shear strength include ISO 3597, 12579, and 14130.
[S. Grynko, "Material Properties Explained" (2012), , p. 38.]
See also
*
Shear modulus
*
Shear stress
Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
*
Shear strain
*
Shear strength (soil)
*
Shear strength (Discontinuity)
*
Strength of materials
The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the re ...
*
Tensile strength
Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or F_\text within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials ...
References
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Mechanical engineering
Structural engineering