Strain Formula

Strain Formula

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What is Strain?

Strain is the amount of deformation that an object experiences as a result of the application of stress. Simply put, stress refers to the internal force, whereas strain refers to the physical effect of that force on the object. Strain is a measure of the amount of deformation that occurs on an object as a result of force. Longitudinal strain, shearing strain, and volumetric strain are the three major types of strain.

Strain is a quantity that has no units. This is due to the fact that the values in the numerator and denominator are always in the same units. Furthermore, strain is a deformation description in terms of the relative displacement of particles in a specific body.

This description, however, excludes rigid body motions. Different equivalent choices for the expression of a strain field are certainly possible. Furthermore, this is dependent on whether it is defined with respect to the body’s final or initial configuration.

Strain Formula and Derivation

The strain formula is: S = ΔxX

Here,

S = strain (it is unitless)

Δx = change in dimension

X = original dimension

An important thing to consider is the dimensional representation of strain which takes place as [M0L0T0]

Here,

M = Mass

L = Length

T = Time

Therefore, one can derive the following formula of strain from the above formula or equation:

[M0L0T0] = M0L1T0×[M0L1T0]−1

Now from the above, one can derive the dimensional formula of length = [M0L1T0]

Finally, the formula of strain is = changeindimensionoriginalvalueofdimension

Types of Strain

The Strain Formula is critical because it discusses a variety of topics. It is a novel concept that is introduced to students in upper-level school classes. Not all students may be prepared for this level of complexity, and it may also intimidate some. There is nothing to be afraid of in the topic or the subject. It’s straightforward, and students can learn about it in their textbooks. Studying the topic can be made easier with the Extramarks platform. Students can access multiple study guides. Apart from study guides, students can also take free demo to analyse the level of teaching of the platform. The platform helps students in identifying their weak points. This allows students to discuss on the important parts of the learning and discuss on the topics among themselves. This boosts their confidence and allows them to write exams in a better and more precise manner. This results in better performance in the examination and better grades.

Solved Example on Strain Formula

Q1 Heating results in the expansion of metals. A hot liquid enters through a copper pipe 10.00 m long. This causes an increase in length to 10.17 m. Calculate the longitudinal strain?

A1 The longitudinal strain refers to the change in length divided by the original length. The change in length refers to the difference between the final length (l2) and the length which is initial(l1). Now one can find the strain:

S = ΔxX

S = Δll1

S = l2−l1l1

S = 10.17–1010

S = 0.1710

S = 0.017

Hence, the longitudinal strain is 0.01.