Yesterday I made an I beam out of cardboard and compared it against just 6 strips of cardboard. The I Beam held up more weight than the pieces of cardboard. I don’t have anything else to say so I did some more research on the I beam and found out that there is a formula to figure out how strong the I Beam will be compared to other shapes. This is called area moment of inertia, and, yes I memorized this, the formula for an I beam is, assuming the I beam is on it’s x axis (I’ll put a picture down below of the I beam) is : I sub x = (a h^3/12) + (b/12)(H^3-h^3). If on the y axis, then it is : I sub y = (a^3h/12) + (b/12)(H-h). The number you get at the end is just a representation that you can use to compare with other shapes. The a is the width of the web, h is the height of the web, H is height of the whole thing, and B is the width of the flanges. Why 12? It’s derived from physics, and I’m not going try to figure that out. The rectangle cardboard is more simple it is I sub x = bh^3/12 and I sub y is b^3h/12. b and h is base and height. The higher the number you get, the more weight the beam can withstand. The website I learned this from is called Engineeringtoolbox.com and it has lots of other interesting stuff about engineering.

I beam picture

Very impressive, Peter. Moments of inertia is a complex topic! There are actually several different types (basic, product, polar, etc.) This is why the height of the web has a big influence on the strength of a beam. In physics, inertia is a measure of an object’s resistance to change. Scientists studying the mechanics of materials will be most concerned with area moment of inertia, or the second moment of area. This number (represent by “I”) describes the shape of the beam, specifically, the distribution of material in the shape. The area of the simple beam was similar to the area of the I-Beam but they behaved differently because of the distribution of the material in each example. The second moment of area increases as the area of the beam under maximum tension and compression gets farther from the neutral axis. If you increase the area of the beam under maximum tension/ compression and the distance from the neutral axis, you have a higher second moment of area. Beams with higher area moments of inertia deflect less. It is not an easy topic! Kudos for going deeper!