# Thermal Stress

Before we learn what is thermal stress, it is vital to understand the fundamentals of basic stress and how it is caused.

When an external force is applied to a body, there is a high chance it can get deformed to a certain extent. How much deformation will take place relies entirely on the nature of molecular attraction of the concerned body.

As the deformation takes place, several internal forces within the body act aggressively to bring the body back to its initial state.  More the deformation caused, higher will be the magnitude of these internal forces.

### What is Stress?

The internal restoring force acting per unit area of a distorted body is known as stress. At an equilibrium state, these internal forces of a distorted body are always equal and opposite to the deforming forces. If this deforming force is removed, the internal force of restitution brings back the body to its original shape.

Let’s say, for a body of Area A, an external force, F is applied which expands the length of the body L by a certain measure. Let this be ΔL. As a result, an internal force of the same magnitude is created, i.e. F in the opposite direction.

So, Stress = $\frac{F}{A}$.

### Define Thermal Stress

When the external force applied on a body which leads to any sort of deformity is caused due to change in temperature, the resultant stress thus created can be termed as thermal stress. In other words, thermal stress definition states that formation of corresponding stress takes place when a body acquires compressive strain due to any thermal expansion or contraction.

Example of Thermal Stress

A prime example of thermal stress is the gap maintained between the outer and inner ends of rail tracks. If two such steel rods (which are usually used as rails over which trains pass) are in contact with their inner and outer ends, a high magnitude of thermal stress generated due to friction and other temperature conditions will easily bend the rods.

Before we carry on with this discussion on what is thermal stress, brush up your memory on the following topics in the Q&A section given below.

• ### What are the Different Types of Stress?

Ans. There are various types of stress. Stress can be classified into 3 types based on the action of the deforming force and how it changes the orientation of a body.

These types are normal stress, tangential or shearing stress and hydrostatic or hydraulic stress. Normal stress can be further divided into tensile stress and comprehensive stress.

Moreover, this classification can be explained with this illustration given below

Check Out These Questions Below and Test Your Understanding.

• ### What are the CGS and SI units of stress?

Ans. As per Newton’s third law of motion, the internal force of restoration is equal and opposite to the deforming force at equilibrium during thermal expansion of a material.

Hence, thermal stress or any other stress is quantitatively equal to the force of deformation acting per unit area of the concerned body.

So, the dimensional formula of stress is [ML -1 T-2]. In that case, CGS and SI units of stress are dyne cm-2 and Nm-2, respectively.

• ### What is strain?

Ans. Due to any change in temperature, a material may undergo thermal expansion or contraction. When such a deformity takes place, the concerned material is said to be strained. It is measured as the ratio of change in orientation to the original orientation of a body.

Since strain is a ratio, it is dimensionless and therefore has no units. This is the main difference between thermal stress and strain.

### Thermal Stress Formula

Let us consider that a solid rod of area A has undergone thermal expansion and its original length L0 has increased to L.

The rise in temperature is known to be ΔT due to heat applied by a certain magnitude of a force, i.e. F.

One can observe that this linear thermal expansion is directly proportional to L0 and ΔT.

So, we can conclude that –

L – L0 = α ΔT, where α is the coefficient of linear expansion of the material.

In that case, L = L0 (1 + α ΔT)

Hence, thermal stress = $\frac{F}{A}$ = Y (L - L0) / L0 where Y is Young’s modulus of the given material.

This can be simplified into Y (α ΔT) / L0

This is considered as the thermal stress formula.

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1. What is the Definition of Thermal Stress?

Ans.  While understanding what is thermal stress, students must note that when a body is going through thermal expansion, a resultant internal force is formed which generates a particular stress. This kind of stress is called thermal stress.

2. What is the Difference Between Thermal Stress and Strain?

Ans. Thermal strain is dimensionless and thus has no units whereas thermal stress has a dimension and thus both CGS and SI units.

3. What is the Formula of Thermal Stress?

Ans. The formula of thermal stress is Y (α ΔT) / L0, where Y is Young’s modulus of the given material, ΔT is the change in temperature, α is the coefficient of linear thermal expansion of the given material and L0 is the original length of the material before the expansion.