# What is Thermal Stress in Strength of Materials?

In this article we will learn about what is thermal stress and formula of thermal stress and strain.

## What is Thermal Stress?

Stress which is induced in a body due to change in the

temperature is known as thermal stress and the corresponding strain is called thermal strain.

Thermal stress induces in a body when the temperature of

the body is raised or lowered and the body is not allowed to expand or contract

freely. No stress will be induces in a body, when it is allowed to expand

or contract freely.

the body is raised or lowered and the body is not allowed to expand or contract

freely. No stress will be induces in a body, when it is allowed to expand

or contract freely.

Considered a body (for

example a rod) which is heated to a specified temperature?

example a rod) which is heated to a specified temperature?

Let

L = Original length of the rod,

T = Rise in temperature,

E = Young’s modulus,

α = Coefficient of linear expansion and

dL = Extension produced in the rod

Due to the increase in the temperature, there is an

extension produced in the rod. When the rod is allowed to expand freely, the

extension produced in the rod is given by

extension produced in the rod. When the rod is allowed to expand freely, the

extension produced in the rod is given by

This is shown in the diagram given above,

here AB is the original length of the rod, and BB’ is the extension produced in

the rod. Suppose a compressive load P is applied at the end BB’, Due to this

compressive load, there is a decrease in the length of the rod from (L + dL) to L. Compressive stress and strain is produced in the rod and is given by

here AB is the original length of the rod, and BB’ is the extension produced in

the rod. Suppose a compressive load P is applied at the end BB’, Due to this

compressive load, there is a decrease in the length of the rod from (L + dL) to L. Compressive stress and strain is produced in the rod and is given by

Thrust or load on the rod is given by

Formula of the Thermal Stress and Strain

When the ends of the rod is rigidly fixed

with the supports and the rod is heated to a certain temperature, here the

extension in the rod is prevented because we have rigidly fixed it’s both the

ends. Stress and strain is setup in the rod. The stresses and strain setup in

the rod is known as thermal stresses and strains.

with the supports and the rod is heated to a certain temperature, here the

extension in the rod is prevented because we have rigidly fixed it’s both the

ends. Stress and strain is setup in the rod. The stresses and strain setup in

the rod is known as thermal stresses and strains.

Thermal strain is given by

Thermal stress induced is given by

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**Stress and Strain When the Supports Yield**

If the supports at the ends yield by an

amount equal to the δ, then

amount equal to the δ, then

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