How to Calculate Elongation

When objects are put under stress, they will stretch before breaking. If the stress is not great enough to break the object, the deformation is usually temporary and the object's original shape will return when the stress is removed. Knowing how an object will elongate is critical for designing machines that will operate under stressful conditions, such as airplanes and racing cars, so that they do not elongate too much that they no longer have enough strength to withstand the forces while elongated. Different levels of stress and strain on an object are measured with a tensile test showing how much the object will deform or elongate as defined in Hooke's Law and how much it will return to its original shape after the stress is removed.

Types of Stress

In determining elongation, types of stress applied to the object falls into three categories: tensile stress, compressive stress and shearing stress. Tensile stress stretches or elongates while compressive stress compresses or shortens the object. Shearing stress acts on the object by shearing the material.

Measure Length

To calculate elongation, you must first determine the length of the bar that you are stressing by measuring it with a ruler. As an example, the bar may be ten inches long. The bar's length would be labelled as L in the formula. Always use the same units when solving the elongation. For example, don't use metrics for force and English units for length.

Calculate Area

Next calculate the cross-sectional area of the bar. Measure the diameter of the bar and divide it by two to get the radius. Square this number and then multiply by pi. For example, if the diameter is two inches, divided by two to get a one inch radius, square it and get one inch squared, and multiple by pi to get 3.14 inches squared. This will be A in the formula.

Elasticity Constant

Determine the elasticity constant for the material being tested by referring to Young’s Modulus which is equal to longitudinal stress divided by the strain on the object. A bar may have an elasticity of twelve pounds of force per inch squared. That elasticity determination is E in the equation.

Determine Force Level

Determine how many pounds of force are being applied to the bar by multiplying the stress times the area. A bar may have a force of 5 lbf applied to it. This is P in the equation.

Insert Values and Solve

Insert the values into the equation: Elongation = P * L / (A * E)

In the example, multiple ten times five to get fifty and multiple 3.14 times twelve to get 37.68. Divide fifty by 37.68 and get an elongation of 1.33 inches. This means when the material is subjected to this amount of stress, it will stretch by 1.33 inches.