Strain is the measure of deformation occurred in a material due to applied force with respect to some reference length. Strain may also be called the displacement in the particles of a body. There are two forms of strain such as shear strain and normal strain. The most basic form of strain is normal strain. This article on how to calculate strain will help you in calculating strain required to deform a body.
- Strain is a dimensionless quantity and is the ratio of changed dimension of an object to its original dimension. Strain within an object is caused due to the stress applied to the object. It is the measure of a material resistance to the force applied to it.
- Normal strain within a body is the ratio of change in length of a body to the original length of the body.
- Shear strain within a body is defined as the change in angle between two orthogonal material lines.
Calculating strain
Strain is given by the formula:
Strain = P × L/ (A × E)
In the above formula,
- P is the force applied to deform the object.
- L is the original length of the object before applying any force.
- A is the length of the deformed object or the changed length of the object when force P is applied to the object.
- E is the elasticity constant or modulus of elasticity for the material. This modulus of elasticity is different for different materials. You can get this value from many sources such as books and online sources.
The values of modulus of elasticity are different in case of normal strain and shear strain for a same material.
Example for calculating strain
Consider an aluminum rod, whose length has changed from 2.1 m to 2.2 meter when a force of 25 N is applied.
Now, to calculate strain in the rod, locate the modulus of elasticity for aluminum either from the books or from the data available online.
You will find that the modulus of elasticity is 10.2 lb-in2 × 106
Now, substituting the values in the above formula
Strain = P × L/ (A × E)
Strain = 25 ×2.1/2.2 × (10.2 × 106)
Strain = 243. 40 × 10-6
Strain = 2.43 × 10 -8
While calculating the strain in the object experimentally, you need to measure the original length of the object before applying any force to the object and the length of the object after applying the force to the object.
You also need to measure the force applied to the body and note down the modulus of elasticity for that particular object.
Strain rate is also one of the important concepts related to the strain. Strain rate of an object is defined as the velocity at which the deformation within the object. Strain rate is given by the formula:
E = (L – L0)/Lo × t
- L is length of the object on deformation
- L0 is the original length of the object
- t is the change in time or time taken for the deformation
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