# Shear Stress

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Any structure experiences stress during the application of load. When the load has any angular direction over an area that stress is termed **shear stress**. Generally, shear stress is caused between two adjacent layers either of the same material or in different materials.

In this article, we will discuss the nature and application of shear stress and how it causes the deformation into the prismatic or non-prismatic beam section or any structural member and also we get to know about the single shear stress and double shear stress.

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Table of content

## Shear Stress Definition

Shear stress is the force that will occur due to the application of force in the direction of the material layers or material planes that are joined layer by layer. Like in earthquakes when two adjacent layers of earth mass slip over each other the stress generated between them is called shear stress. Generally in our subjects, shear stress is expressed as a symbol tau (τ).

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## Shear Stress Formula

In context with the shear stress, the load is the basic component that acts on a particular area. When any external force is applied a deflection is developed and to resist that deflection, that resistance is developed between two parallel layers of material causing shear between them and when resistance obtained within the particular area causes shear stress.

Shear stress = Shear Force/ Resisting area of cross-section

τ = P/A

## Shear Stress Unit

Generally, the shear stress unit is similar to the stress unit in general. In SI units of shear stress is N/mm^{2} or Mpa or pascal termed as Pa. In the case of the CGS system the unit of shear stress is dyne/cm^{2 }is taken.

- SI unit system: Unit of shear stress = N/mm
^{2}or Mpa or Pascal - CGS unit system: Unit of shear stress = dyne/cm
^{2}

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## Shear Stress and Shear Strain

Shear stress and shear strain are related to each other in the context of shear modulus. Shear stress is the term used to describe intensity of load per unit area of a member that can be use to perform the operations.

While the shear strain is used to define Shear strain occurs when a sideways force is applied to a medium. A shear force wave can travel in the direction of the applied force. The direction of propagation is related to the motion of the shear wave.

## Analysis of Shear Stress

When a material surface is applicable by any projected load to the projected surface, this event causes a failure of the member block, this failure causes a shear off failure, such action is demonstrated as a small arrow. This phenomenon is termed a shear failure and responsible stress is called shear stress.

τ = Shear Force/ Resisting area of cross-section

τ = P/A

Shear stress is classified into two categories as-

- Single shear stress
- Double shear stress

**Single shear:** When Shear stress developed on the single plane through the member coinciding with the plane of the other contacting surfaces. It means only a single plane takes charge of a shear force called a single shear force.

Example: In lap joints of a steel member occur in the single side of a plane through the rivet connection to the connecting surface. The shear stress expressed in the formula as-

τ = 1.P/ A

**Double shear:** When two plates are joined in such a way that forces acting on the two contact surfaces their shear stress develops over the two surface planes through the member connecting with two surfaces of other attaching surfaces. The whole area is just double the net cross-sectional area of the member.

Example:- In double cover lap joint failure will occur on the double planes through the rivet coinciding with the contacting surfaces. Hence shear stress is expressed as;

τ = 1.P/ 2A

## Shear Stress in Fluids

Shear stress is developed between layers of fluids, when fluid flows in contact with the boundary of solid shear stress is developed between a thin fluid layer and the boundary of a solid. According to the depth of fluid, different layers have different velocities, but at the same level of layer molecules flowing in the same direction have similar velocity as well as similar shear stress.

But when layers are different the velocity may differ and the pressure from top to bottom also may vary as per depth variation by this the shear stress also varies. In liquid shear stress is directly proportional to the rate of shear strain with constant viscosity.

## Shear Stress Examples

In our daily life, many factors occur by shear stress phenomenon that we are not considered normal. This is just because shear stress is the minimal property of any action; without this, we can not perform those activities. Some of the activities are like-

- Cutting anything obtains shear stress between the cutter and objects.
- Rubbing marbles with each other.
- Shaving gel application on the face.
- Sliding on the surface.
- Brushing the pains over the surface.
- Painting on a wall or canvas.
- Tyre contact with the earth’s surface.
- Writing with pen or chalk on paper or blackboard.
- Move or stop anything with the use of friction.
- Chiselling the wood to refine the shape.
- Cleaning something to use shear stress, etc.