Strain Formula with Examples

Deformation is the change of a body from a reference configuration to a current configuration in continuum mechanics. A configuration is a collection of all the locations of the body’s particles. External loads, intrinsic activity (e.g. muscular contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, among other things, can produce deformation.

Strain is associated with deformation in terms of relative particle displacement in the body, excluding rigid-body movements. Depending on whether the strain field is defined with regard to the initial or final configuration of the body, and whether the metric tensor or its dual is considered, several equivalent options for the formulation of the strain field may be made.

A deformation field occurs in a continuous body as a result of a stress field caused by applied forces or changes in the body’s temperature field.

Strain Formula

The Greek symbol epsilon (ε) represents the strain equation.

ε = Δx/x

Where,

Δx = Change in dimension

x = Original dimension

Derivation of Formula

The three-dimensional depiction of strain that occurs as [M⁰L⁰T⁰]

Here,

• M = Mass
• L = Length
• T = Time

As a result, the following formula for strain may be derived from the aforementioned formula or equation:

[M⁰L⁰T⁰] = M⁰L¹T⁰ × [M⁰L¹T⁰]⁻¹

The dimensional formula of length = [M⁰L¹T⁰]

Finally, the formula of strain is = Change in dimension/Original value of dimension

Sample Problems

Problem 1: Calculate the strain if the body’s original length is 10 cm and the length after stretching is 10.2 cm.

Solution

Here the original length is L = 10cm.

ΔL = 10.2 – 10 = 0.2 cm

Now the strain formula is given as follows:

ε_L= Change in length / Original length

= ΔL / L

Substituting the values we get,

ε_L= 0.2 / 10

= 0.02 cm

Therefore, the strain is 0.02 cm.

Problem 2: If the Body Strain is 0.0125 and the Original Length is 8 cm, then Calculate the Body’s Change in Length.

Solution

 Here the strain is ε_L= 0.0125.

The original length is L = 8 cm.

ε_L= Change in length / Original length

= ΔL / L

Substituting the values we get,

0.0125 = ΔL / 8

0.0125 x 8 = ΔL

ΔL = 0.1 cm

Therefore, the change in length of the body is 0.1 cm.

Problem 3: Calculate the body’s original length if the strain is 0.015 and the length change is 0.3 cm.

Solution

Here the longitudinal strain is ε_L= 0.015.

Change in length is ΔL = 0.3 cm

ε_L= Change in length / Original length

= ΔL/L

Substituting the values we get

0.015 = 0.3/ L

L = 0.3 / 0.015

L = 20 cm.

Therefore, the original length of the body is 20 cm.

Question 4: What is a Strain?

Answer

The term “strain” is used to describe the outcome of a stressful situation. The strain is a measurement of how much the body has warped as a result of the force’s action in contrast to its initial shape. The Greek letter epsilon (ε) is used to designate the strain.

Problem 5: A force pulls a string with an original length of 100 cm. The chord length changes by 2 mm. Identify the strain

Solution

Original length (L) = 100 cm = 1 m

The change in length (ΔL) = 2 mm = 0.002 m

ε_L= Change in length / Original length

= ΔL/L

=0.002/1

=0.002 m