Construction beam masses vary depending on their volume and density. Density is the compactness of a given material. For example, an iron beam has a higher density than a wooden one; therefore, two beams of the same volume will differ in mass if constructed of unlike materials. It is important to note that mass and weight are different quantities. Mass is the amount of matter in an object while weight is the force required to lift the object. Weight is determined from mass.

Measure the length of the beam in centimetres. For example, say the length is 300.0cm. Notice that the I-beam is composed of three long metal sheets. The top and bottom of the "I" have the same width, while the central part of the "I" might have a different width. Measure the width and thickness of the three parts of the I-beam in centimetres. As an example, say the central part has a width of 10.0cm and a thickness of 1.5cm. The top and bottom parts of the "I" both have a width of 12.0cm and a thickness of 1.0cm.

Multiply the length, width and thickness together for each part of the "I" to get its volume. Performing this step for the top and bottom of the "I" leads to 300.0cm times 12.0cm times 1.0cm, or 3600.0 cubic cm. The middle bar has a volume of 4500.0 cubic cm from multiplying 300.0cm times 10.0cm times 1.5cm.

Add together the three volumes to get the total volume in grams per cubic centimetre. Performing this operation leads to 3600.0 cubic cm plus 3600.0 cubic cm plus 4500.0 cubic cm which equals 11,700 cubic cm.

Multiply the total volume by the density of the I-beam to get mass. Now you have, assuming an iron I-beam, 7.8g per cubic cm times 11,700 cubic cm, or 91,260g.

Convert the mass to weight in pounds by dividing by 453.6. Completing the illustration you arrive at 91,260 cubic cm divided by 453.6g per lb which equals 91.3kg.

Measure the length, width and thickness of the beam in centimetres. As an example, use a length of 100.0cm, a width of 10.0cm and a thickness of 5.0cm.

Multiply the length, width and thickness together to obtain the volume in cubic centimetres. Performing this step yields 100.0cm times 10.0cm times 5.0cm, or 5000.0 cubic cm.

Multiply the volume by the density of the beam material in grams per cubic centimetre to obtain mass. Assuming the beam is made of iron, with a density of 7.8g per cubic cm, you have 7.8g per cubic cm times 5000.0 cubic cm which equals 39,000g.

Divide the mass by 453.6 to get weight in pounds. Completing the exercise leads to 39,000g divided by 453.6g per lb, or 39kg.

#### References

- Georgia State University: HyperPhysics: Density
- "Physics for Scientists and Engineers with Modern Physics"; Raymond A. Serway and John W. Jewett; 2009
- Georgia State University: HyperPhysics: Mass and Weight
- Georgia State University: HyperPhysics: Densities of Common Substances
- Engineering Toolbox: Mass and Weight