• Why are shear stress equations necessary?
• This article looks at some examples of shear stress equations: average shear stress, beam shear.

What are the basics of shear stress?

Whenever two materials rub against or slide over each other, there is shear. While normal stress results from the force applied perpendicular to the surface of a material, shear stress occurs when force is applied parallel to the surface of the material. A common example include the cutting of paper with scissors.

Shear stress differs across materials and cross-sections, and is measured using a set of formulas called the shear stress equations.

Why are shear stress equations necessary?

Shear stress occurs whenever there is contact between two materials or components. Examples include stress exerted on a set of cantilever beams (with or without adhesion between layers), horizontal beams used in construction, pipelines carrying flowing fluids, soil when it is subjected to loads from the top surface etc. Shear stress equations help measure shear stress in different materials (beams, fluids etc.) and cross-sections, which play an important part in the design of engineering structures, to determine the load that can be carried. Most engineering structures are designed for both normal stress and shear stress limits.

Average shear stress equation

General shear stress, represented by the Greek letter tau, τ, is given by the ratio of force applied to the area on which it acts.

Where,

• τ = shear stress
• F = force applied
• A = cross-sectional area of the material

Notes:

• Shear stress is the same irrespective of the direction in which it occurs, i.e., left to right or right to left.
• The above formula gives the average shear stress. In practical applications, shear stress is seldom uniform throughout the surface.

Beam shear stress equation

Beam Shear is the internal shear stress that occurs on a beam when it is subjected to a shear force.

Where,

• τ = beam shear stress
• V = shear force
• Q = static moment of the area (which is the summation of all areas multiplied by the distance from a particular axis)
• I = second area moment of the cross-section
• t = thickness of the material

Conclusion

Shear stress occurs almost everywhere around us. More so in engineering structures, which comprise of a variety of components that are subjected to different kinds of loads. The measurement of shear stress, using the shear stress equations, thus forms an integral part of the design of these structures.