Dimensions of Strain

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What is Strain?

It is the response of any system to the stress applied to it. When a material is given some force, it tends to produce stress which then causes the material to deform. The amount of deformation in the direction of applied force divided by the earlier length of the material is called engineering strain. It results in a unitless number which is often also left in non-simplified form like inches per inch or meters per meter. 

In the case of stress, the distribution of strain may or may not be uniform in a complex structural element, also depending on the nature of the loading condition.

Let’s understand with an example where the strain in a bar which is being stretched in tension is the amount of elongation or change in length that is divided by its original length. On the other hand, if we talk about stress here, the strain may/may not be uniform in a complex structural element depending on the nature of the loading condition.

Strain= Elongation / Original Length

It can be represented by, Strain = ∆L/L⁰

Further, we can know that if the stress is small on the material, it may only strain by a small amount and return to its original size after the release of stress. It is called elastic deformation because similar to elastic, it returns to its unstressed state. Elastic deformation is known to occur in a material when stresses are lower than critical stress (also known as yield strength). If the material is stressed further to its elastic limit, the material remains in a deformed condition after the removal of the load and this is called plastic deformation.

True strain measures account for changes in cross-sectional area by using the instantaneous values of the area.


Dimensional Formula of Strain

The dimensional formula of Strain is represented as:

[M⁰L⁰T⁰]

Where,

  • M = Mass

  • L = Length

  • T = Time


Derivation

Strain = Change in dimension × [Original dimension]-1 . . . . . (i)

The dimensional formula of length = [M⁰L¹T0] . . . . . (ii)

On substituting equation (ii) in equation (i) we get,

Strain = M⁰L¹T0 × [M⁰L¹T0]⁻¹ = [M⁰L0T0]

Therefore, the dimensional formula of strain represented as [M⁰L0T0], which is a Dimensionless Quantity.

FAQ (Frequently Asked Questions)

Q1. What is Strain?

Ans: Strain is the response of a system when stress is applied. When force is applied to a material, it produces stress and causes the material to deform. Linear strain takes place when there is a change in the object’s length. Linear strain is produced by tensile stresses or compressive stresses. Shear strain is the result of a change in the object molecule’s orientation.

Q2. Differentiate between Stress and Strain.

Ans: Stress is known to cause strain as it is the force acting on an object per unit area. Strain is the change in size or shape resulting from all applied forces causing deformation. It's easier to understand if we say rocks only strain when those are placed under stress. Strain is denoted by a change in length of an object divided by its original length.