How to Calculate the Moment of Area of a Beam

Calculating the moment of area of a beam

The moment of area, also sometimes called the second moment of inertia, is an important geometric property of objects. The moment of area of an object can be used to determine the deflection or torsion of a beam when a shear or tensile stress is applied to the beam. This is useful for determining if a beam will be able to withstand the forces applied to it in the course of its lifetime. The moment of area of a rectangular beam -- a common geometric shape for beams -- can be done in a few simple steps.

Instructions

1. Cube the height of the beam; i.e., multiply the beam by itself twice. For example, if the beam is 0.5 meters (m) high, cubing this number gives 0.125 meters cubed (m^3).

2. Multiply the cubed height of the beam by the width of the beam. For example, if the width of the beam is 0.75 m, then multiplying this by 0.125 m^3 gives 0.094 meters to the fourth (m^4). Call this result A.

3. Divide result A by 12. In our example, dividing 0.094 m^4 by 12 gives 7.81 times 10 to the power of -3 meters to the fourth, or 7.81 x 10^(-3) m^4. This is the moment of area of the beam.

Tips & Warnings

• The moment of area of a beam is dependent on the geometric shape of the beam. There are a number of different equations which can be used, or derived from first principles.

References

• eFunda: Rectangular Area
• Engineering Toolbox: Area Moment of Inertia for some common Cross Sections
• Indian Institute of Technology: Simple Bending Theory OR Theory of Flexure for Initially Straight Beams