How to Calculate Stress in a Beam

A beam bends or deforms by sagging when an external perpendicular load is applied.

A beam is a long structural member that reacts to any applied loads by bending. Beams are classified with respect to how they are supported. A simple beam is supported at both ends with no overhang. Continuous beams have more supports throughout the length of the beam. A cantilever beam is supported only at one end, which is built into a wall in such a manner that prevents it from rotating.

Instructions

1. Draw a diagram of the loads applied to the beam. This bending or deflection of the beam is a direct result of the stresses applied by the loading forces. The equation is: Stress = Force/Area.

2. Measure the height and width of the beam to calculate the cross-sectional area. For a rectangular beam cross-section, the area is equal to the height times the width (A = HW).

3. Calculate the perpendicular magnitude of the applied force. If the force acts directly at a 90-degree angle to the beam, the entire force causes the stress. However, if the force acts at an angle to the beam, only part of that force acts directly in a normal direction. Use the trigonometric sine function to determine what part of the force actually acts on the beam.

4. Compute the stress applied to the beam using the equation for calculating stress. Make sure that the units represented are consistent in the same measuring system, either English or metric. For example, in the metric system, stress is represented in units of Newtons/meter^2, which is force in Newtons divided by the cross-sectional area of the beam.

References

• Engineering Toolbox: Beam Support Force Calculator
• University of Washington: Beams: Strain, Stress, and Deflections
• Online Easy Solver: Bending Stress Calculator

Resources

• Calculator Edge: Calculating Stress