This article explains how to calculate shear stress. Shear stress is responsible for the deformation of workpiece along the plane of cross section.

**When the stress acting on the surface of the work piece is acting parallel to the cross section of the work piece then the stress experienced by the work piece is called as shear stress. **

**How to calculate shear stress in a beam?**

When a beam is subjected to bending moment, M and shear force, V, the beam experiences shear stress along its central axis.

**The maximum shear stress for a rectangular beam is given as follows-**

Where,

tau is shear stress

The maximum shear stress for a circular beam is given as follows-

Where,

A is the cross section area of the beam

**How to calculate shear stress of bolt?**

Shear stress is simply the amount of shear force acting on unit area of the bolt. A bolt attached to a plate experiences shear stress when the ends of the plates are subjected with shear force.

**The shear stress acting on the bolt is given as below-**

where,

t1 and t2 are thicknesses of plates (for two plates)

d is the nominal diameter of the bolt

**How to shear stress from normal stress?**

Usually when a work piece is acted upon by some force, the work piece experiences both shear as well as norml forces. The normal stress can be found using the relation below

N = F/A x cos^{2}θ

where,

N is the normal stress

**The shear stress can be found using the relation below-**

S = F/A x sinθ

where, S is the shear stress

**Hence, if we want to write shear stress in terms of normal stress, then –**

S = N x tanθ

**How to calculate shear stress from torque?**

When a work piece undergoes torque then it experiences shear on the surface. This is a double shear that is acts on both sides from where the torque is produced.

**The formula for finding shear stress from torque is given below-**

**How to calculate shear stress in fluids?**

Shear stress in fluids occurs as a result of flow. The entire volume of the liquid can be considered as multiple thin layers of liquid sandwiched together. When the liquid flows, each layer moves with different velocity.

**This difference in velocity creates a rubbing action and gives rise to shear stress in fluids. To find the shear stress in fluids, we need to know dynamic viscosity, velocity of the layer and distance of that layer from the surface.**

Mathematically, the shear stress in fluids can be found using the relation below-

where mu is the dynamic viscosity

**How to calculate shear stress in torsion test?**

To check the for the shear strength of the work piece under torsional load, torsion test is performed. In this test, the ends of the work piece are twisted along the longitudinal axis of the work piece. This is the simplest practice to test the work piece under torsion.

**This test is performed to know whether work piece will work under specific torsional load conditions or not. If the work piece breaks then it is said to fail the torsion test and if it survives without necking then it is said to pass the test.**

The formula to calculate the shear stress from torsion is discussed in above sections and the same is used while performing the torsion test.

**How to calculate shear stress at a point?**

Till now all the formulae that we have discusses are used for finding shear stress at the surface. To find shear stress at a particular point there is a different practice.

**The formula for finding shear stress at a point is given below-**

where,

I is the moment of inertia

**What is stress concentration?**

When the work piece has sharp edges or turns or holes in it, the stress get accumulated locally. These stresses are not distributed across the surface due to sudden change in cross section. These weakens the work piece and has greater potential to fail.

**So, stress concentration is not desirable as the holes and sharp edges will become the weakest part of the entire work piece. We can calculate the strength of the work piece under stress concentration by using the relation below-**

*K _{t} = σ_{max}/σ*

**Image credits : Wikipedia**

**How to calculate shear stress at pipe wall?**

When a fluid flows inside a pipe, it follows a general relation from which we can find the shear stress at pipe walls. The relation is different for laminar and turbulent regions.

**The velocity profile of fluid flowing inside a pipe wall is parabolic and the resulting shear stress profile will be double triangles with zero shear stress at the center (maximum velocity is at the center due to this reason).**

The formula for finding shear stress is same as discussed in above sections. The velocity can be found using the formula given below-

*u/u _{max} = 1 – (2y/h)^{2}*

**What is shear strength?**

Strength is the amount of stress that a body can withstand. Shear strength is the amount of stress the body can bear without breaking.

**Values of shear strength depend on the material of the work piece and it is independent of the shape of the work piece. When shape of the work piece is critical then stress concentration takes place due to which a new concept of modified shear strength comes into play. However, we will limit the discussion up to shear strength only.**