Natural wood has a lower critical strength than most modern materials, and a lower elastic constant, yet it is the strongest material for some applications because it is remarkably light and remarkably cheap on a per-volume or weight. In some important applications, high strength per volume is the important measure, and in virtually every case high strength per dollar is relevant. Consider the table top: it should support a person standing on it, as one might do to change a lightbulb, and it should not weigh too much, or cost too much.

I’ve drawn a 9 foot by 4 foot table at left, with a 250 lb person in the center. Assuming that the thickness of the table is t, the deflection in the center, ∂, is found by the formula ∂ =FL³/4Ewt³. Here, F is the downward force, 250 lbs (a bit higher if we include the weight of the table), L is the length between the supports, 6 feet = 72 inches, E is the elastic constant of the table top, 2,300,000 psi assuming ash wood, w is the width of the table, 48″, and t is the thickness, let’s say 1″.

Using the formula above, we fid that the deflection of this tabletop is 0.211″ for a force of 250 lbs. That’s not bad. The weight of the 9′ table top is 125 lbs, which is not too bad either, and the cost is likely going to be acceptable: ash is a fairly cheap, nice-looking wood.

By comparison, consider using a 1/4″ thick sheet of structural aluminum, alloy 6061. The cost will be much higher and the weight will be the same as for the 1′ thick piece of ash. That’s because the density of aluminum is 2.7 g/cc, more than three times that of ash. Aluminum 6061is four times stiffer than ash, with an elastic constant of 10,000,000 psi, but the resistance to bending is proportional to thickness cubed; and 1/4 cubed is 1/64. We thus find that the 125 lb tabletop of Al alloy will deflect 3.11 inches, about 16 times more than ash, far too much to be acceptable. We could switch to thicker aluminum, 3/8″ for example, but the weight would be 50% higher now, the cost would be yet 50% higher, and the deflection would still be too high, 0.92 inches. Things get even worse with steel since steel is yet-denser, a 1/4″ sheet of steel would deflect about as much as the 3/8″ aluminum, but would weigh about twice as muc. For this application, and many others like it, wood is likely the best choice; its light weight per strength and low cost can’t be beat.

Robert E. Buxbaum, January 11, 2022