Stress Strain & Thermal Stress (Stress and Strain Part-1)

Stress: When a body is subjected to an external force, resisting forces will be generated inside the body. This resisting force per unit area is stress.
It is denoted by σ

For e.g. spring is placed on your hand and you press it or stretches it, compression or tensile forces generate.

Strain: When a body is subjected to an external force. Then there will be change in the length of the body. So the strain is defined as

When F force is being applied to a body of length “l” and width “b” .

δl is linear change and δb is lateral change.

Or we can say that lateral strain and linear strain are perpendicular to each other.

 

Poisson’s Ratio: It is ratio of lateral strain to longitudinal strain. It is denoted by μ.

Note: Value of Poisson’s ratio cannot be negative.

 

So if the value is coming negative just multiply it by “-1” and that will be your answer.

Shear Strain: When we apply a force that is tangential to the element, its edge is displaced by some distance.

As it is seen the above figure when a Force F is applied at the top face, Box slide on the top side only by angle Φ.

 

“So shear strain is the ratio of displacement of one face with respect to other face and the distance between them.”

Volumetric Strain: It is the ratio of change in volume to initial volume.

Hook’s Law: In simple words Hook’s law says that

” In elastic limit Stress is Directly Proportional to Strain.”

Stress α Strain

σ α e

σ = Ee

Thermal Stresses

Whenever there is a change in the temperature of the material it either expands or contracts.

Findings have shown that Change in length is directly proportional to change in temperature. Also, change in length is proportional to the Initial length.

δl = α ΔT         where α is coefficient of  thermal expansion.

Now we will see general cases:

Case 1. If a bar is fixed at one end only.

δl = α ΔT  

and the stress is zero, σ = 0

Case 2. If the bar is fixed at both ends and the walls are exerting the same amount of force in such a way that it would expand same amount if it was free.

Here in this case change in length is stopped by the Force applied by the walls. So change in length due to thermal expansion will be equal to change in length due to resisting force. 

Case 3. If the bar is fixed at one end and the other wall is at some distance which is δ.

Now two conditions can occur: 

a) 

 In this case σ = 0, because expansion from thermal stresses is less than the gap between the walls. So if the body is not reaching another wall, there won’t be any resisting force.

Hence σ = 0  

b)

In this case thermal expansion will be greater than δ, So wall be provide resisting force & Stress will be 

σ = E α ΔT

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