How to Find a Moment of Inertia in a Steel Beam

Measure the volume of the steel beam, if you have not obtained the weight as part of a homework assignment or from the manufacturer you bought the beam from. If the beam is a simple rectangular one, measure the length, width and thickness. Then multiply the three of them together. If it is an I-beam, measure the length, width and thickness of the top and bottom sections and of the upright section connecting them together. Multiply the length, width and thickness of a section to get the volume of that section. Add the volumes of the three sections together to get the total volume of the beam. As an example, if you have a rectangular beam that is 10 feet long, 1 foot wide, and 4 inches, or 1/3 foot, thick, then the volume is 10 x 1 x 1/3, or 3.33 cubic feet.

Multiply the volume of the steel beam by the density of steel. Because steel consists of iron, carbon and sometimes other elements, it can vary in density from 480.5 pounds per cubic foot to 505.4 pounds per cubic foot. An average value is 493 pounds per cubic foot. Skip this step if you already know the weight of the beam. The 3.33 cubic foot rectangular beam would have a weight of 493 pounds per cubic foot times 3.33 cubic feet, or 1,641.69 pounds.

Multiply the length of the beam in feet by itself. Multiply the result by the weight of the beam in pounds. If the beam is supported in the center, divide the result by 12 to obtain the moment of inertia for the beam around this center support. If the beam is supported on one end, divide the result by 3. This result is the moment of inertia of the beam around the end. As an example, if your 3.33 cubic foot rectangular beam were supported at the center, its moment of inertia would be 1,641.69 pounds x 10 feet x 10 feet divided by 12, or 13,680.75 pound-feet squared.