Second Moment of Area Made Easy

Bending I-beam

Illustration of I-beam under a Bending Moment

There are several factors that determine the strength of a given beam or structural element. Sheer cross sectional size may be the first thing many of us will accredit to a beam’s structural strength. – Or perhaps the beam’s material makeup. But there is what’s called the beam’s “second moment of area”. Maybe you’ve heard of this, maybe not!

A particular object’s second moment of area is used to predict its resistance to bending or deflection – simply put. So besides a beam’s cross sectional area and material makeup, what other major factor is used to determine its strength? As you’ve probably guessed, it’s the shape or geometry of the beam’s cross section.

So what this second moment of area is saying, in essence, is that not only is the cross sectional area important, but the shape of this area is as well. Take 2 example beams, both with equal cross sectional area. The cross section of one is square, and the other is in the shape of an “I”. Hmm, which one do you think has a higher second moment of area?

Again, you’ve probably guessed right in that the I-beam has a considerably higher second moment of area. Due to its shape, it has a higher resistance to bending than a solid square. One thing to keep in mind however, is that although structural elements with high second moments of area such as I-beams are often exceptionally strong in bending and shear, they aren’t as strong in torsion.

Torsion is the twisting of an object via an applied torque, and this can be countered with shapes such as circles. Circles or pipes however, aren’t particularly favored as structural elements because though they may have high resistance to torsion, they don’t have a high second moment of area. Perhaps the most well-known use of pipes in construction is steel scaffolding. Pipes are strong to direct impact, such as that received through being dropped roughly or when stacked and clamped with high torque, etc.

Various types of Steel and their Cross SectionsThere are other shapes and cross sections that are made with their individual characteristics making them ideal for a given situation such as the “Z”, “T”, angle, and channel. The HSS shape, standing for hollow structural section, is any shape with a hollow center. This can be square, rectangular, circular, or elliptical.

“C” channels for example, are often used as smaller horizontal framing welded onto vertical I-beam columns. The exterior siding is secured to the C-channels on the outside. Besides its reasonable second moment of area, C-channels work as a “channel” of sorts through which the building’s power and other cables can run safely and in an organized fashion – two reasons that make them fairly popular.

(See How to Calculate Second Moment of Area for calculation specifics.)

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