How to Calculate Shear Force in a Shaft

Written by william hirsch
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How to Calculate Shear Force in a Shaft
Shear forces can affect bricks in a wall. (Brick image by Luke Haverkamp from

A shear force deforms a rectangular shaft into the shape of a parallelogram. This is caused by a force being applied across the top surface of the rectangle while another force pushes the bottom surface the opposite direction. The volume of the shaft remains the same. The shear force is related to the top surface area of the shaft, the horizontal distance the sheared face moves, the height of the shaft and a constant called the shear modulus. Every material has its own unique shear modulus, or modulus of rigidity as it is named in engineering.

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  1. 1

    Find the shear modulus for the shaft from a table or handbook. For example, carbon steel has a shear modulus of 11.2 x 10^2.72 Kilogram per square inch.

  2. 2

    Measure the length and width in inches of the top surface of the rectangular shaft. For example, say the measurements are length = 10 inches and width = 20 inches.

  3. 3

    Calculate the area of the top surface of the rectangular shaft in square inches by multiplying length by width. This leads to 10 inches x 20 inches, or simply 200 square inches.

  4. 4

    Measure the height of the shaft in inches. In the example, assume a height of 5 inches.

  5. 5

    Measure the distance in inches the shaft is deformed horizontally when the force is applied. Use a deformation distance of 0.1 inch for the example calculation.

  6. 6

    Calculate the force "F" in pounds by applying the formula:

    F = (S x A x L)/H

    where "S" is the shear modulus, A is the area, L is the deformation distance and H is the shaft height. For the example, you have:

    F = (11.2 x 10^2.72kg/in^2) x (200 in^2) x (0.1 in)/(5 in)

    = 4.5 x 10^3.18kg.

    A force of 4.5 x 10^3.18 Kilogram has been applied to the shaft.

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