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 so much that they no longer have enough strength to withstand the forces while elongated.

### Items you will need

- Calculator
- Ruler
- Bar
- Elasticity Constant Table

## How to Calculate Elongation

Step 1Determine the length of the bar by measuring it with the ruler. The bar may be 10 inches long. This will be L in the formula.

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 multiply by pi. For example, if the diameter is 2 inches, divided by two to get a 1-inch radius, square it and get 1 inch squared, and multiple by pi to get 3.14 inches squared. This will be A in the formula.

Look up the elasticity constant for the bar's material. A bar may have an elasticity of 12 pounds of force per inch squared. This is E in the equation.

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 the values into the equation: Elongation = P * L / (A * E) In the example, multiply 10 times five to get fifty and multiply 3.14 times 12 to get 37.68. Divide 50 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.

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#### Warning

- Always use the same units. For example, don't use metrics for force and English units for length.