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Nikita Parmar

Updated on 25th October, 2023 , 5 min read

Strain Formula: Definitions, Types, and Important Facts

Strain Formula Overview

People frequently worry about how an object will move once a specific force has been applied to it. But these people don't think about how the force can change the object's structure. Bridges are a great case in point. Due to their weight, automobiles on a bridge tend to move with a downward force. Stress tests are performed on the bridge to ensure that it can tolerate high pressure without failing. The internal force per unit area is undoubtedly what is meant by "stress." Most importantly, an object's level of strain is ultimately defined by the quantity of strain imposed on it.

What is Strain?

The degree of distortion an item experiences as a result of the application of stress is referred to as strain. Simply said, strain denotes the physical impact that a force has on an item whereas stress denotes the internal force. A measurement of the amount of force-induced deformation on an item is known as strain. The longitudinal strain, shearing strain, and volumetric strain are the three primary strain types. Strain is a quantity that has no units. This is due to the constant usage of the same units for both the numerator and denominator values. In addition, strain is a way of describing how a body deforms in terms of the relative displacement of its constituent parts. However, the stiff body movements are not included in this definition. There is undoubtedly a chance to select many equivalent options for the expression of a strain field. Additionally, this depends on whether it is defined in terms of the body's initial or ultimate configuration.

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Definition of Strain Formula

One definition of strain is- "The ratio of the amount of deformation a body experiences in the force's direction to the body's initial dimensions." The restoring force and the deforming force have the same magnitude even if their directions of action are reversed.

What is a Strain Formula?

In general, the strain formula for physics is as follows-

Strain Formula

Another way to express strain is as "Change in Body Dimension/Original Body Dimension." A dimensional analysis of strain may be done as follows-

[M0 L1 T0] / [M0 L1 T0]

= L/L

= M0 L1 T0 / M0 L1 T0

= M0 L0 T0

Thus, it is established that Strain [M = Mass, T = Time, L = Length] has no units.

Types of Strain

The three basic types of strain are as follows-

Longitudinal Strain

The effect of longitudinal stress is longitudinal strain. In this odd situation, the object's length determines how much stress or restoring force is applied per unit area. It implies that the length of the item will alter as a result of the deforming force that has been applied. Because the physical change in the item has happened along the dimensions of length, the strain that has been produced will be referred to as longitudinal. It can be either compressive (length decreases) or tensile (length increases). It is shown as-

Longitudinal Strain = Δ L/L

By deducting the initial length from the newly created length, one may determine the object's change in length or L. L is the true length of the item at its equilibrium condition before any tension is applied.

Strain Formula

Shearing Strain

Shearing strain results when the tension placed on the body seems to have a tangential effect on the item. The change in the body that happened tangentially on the body is what causes the shearing strain, which stems from tangential tension or shearing stress. Shearing Strain is denoted as Shearing Strain = Shearing/Stress Strain, therefore

Shearing Strain = Δ x/L = tanθ

Δ x represents the tangentially generated change.

L is the object's length.

θ is the object's angular displacement from its vertical location.

Strain Formula

Volumetric Strain 

When an item undergoes volume-based changes, this strain is specially created. Here, a type of stress termed hydraulic stress is used to compress the object's volume. Specifically fluid items were used in this instance (such as water, gas, or any substance that can be squeezed to change its volume). Therefore,

Volumetric Strain = Δ V/V 

Δ V is the volume change that results from hydraulic stress on the body's geometric shape.

V represents the body's actual volume before the application of hydraulic pressure or stress.

Strain Formula

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Important Facts of Strain Formula

The following are some of the important facts about strain formula-

  1. Even after a permanent deformation, the substance is still intact at this phase. 
  2. However, the material's flexibility has a limit. 
  3. If the applied stress crosses this line, the material will be irreversibly damaged due to elasticity loss.
  4. More stress, or even a little reduction force, will cause the tensile strength line to cross.
  5. Point D represents the material's tensile strength. 
  6. The capacity of a material to return to its original shape after being subjected to stress and strain is referred to as its elasticity. 
  7. The material's elasticity varies.
  8. This elasticity limit is the material's point of strength. 
  9. This is why Point E has a fracture where the material separates.
  10. When stress is applied, the elongation or decrease created as a result of the resultant strain returns to its original shape. 

Strain Formula

Conclusion

In the absence of rigid-body movements, deformation in terms of relative particle displacement in the body is referred to as strain. Deformation can be brought on by external loads, internal body forces like gravity or electromagnetic forces, variations in temperature, moisture content, or chemical reactions, among other things. A continuous body experiences a deformation field as a result of a stress field brought on by applied forces or as a result of variations in the body's internal temperature field. Numerous structural issues are resolved using constitutive equations, which show how stresses and induced strains relate to one another. 

Points to Remember 

  1. The amount of distortion that happens in a body when stress is applied is defined as strain.
  2. There are three forms of strain: longitudinal, shearing, and volumetric. 
  3. Each of them is caused by three types of stress: longitudinal, tangential, and hydraulic.
  4. Strain is a unitless quantity symbolized by the letter epsilon (ε).
  5. Strain formula = x/x, where x represents the change in body dimension and x = original body dimension.
  6. Strain develops as a result of the tension that is created. 
  7. The greater the strain, the greater the stress. 
  8. However, there comes a moment when the material's elasticity fails and no more strain is created even when greater tension is applied.

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Frequently Asked Questions

Is a coiled string's stretching dictated by its shear modulus?

Yes, the shear modulus of the coil string determines its stretching since only the length changes when the string is stretched or compressed. There is no influence on its bulk or length.

What is a Stress?

Ans. The internal force per unit area is undoubtedly what is meant by "stress."

What is a strain?

Ans. The degree of distortion an item experiences as a result of the application of stress is referred to as strain. Simply said, strain denotes the physical impact that a force has on an item whereas stress denotes the internal force.

Does strain have units?

Ans. Strain is a quantity that has no units.

What are the three types of strain?

Ans. Longitudinal, Shearing, and Volumetric are the three types of strain.

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