ANSWER

D bends the most, A bends the least. This is a question about bending MOMENTS. You can find these formulas in Architectural Graphic Standards or at the link above, or by googling.

The beam itself weighs 600lbs. A W12x30 is 12 inches tall and weighs 30 lbs per linear foot. (20ft x 30lbs/ft = 600lbs) I didn’t size this beam, so I don’t know if it could actually support any of these loads. In this question the size of the beam does NOT matter. You can see from the formulas that the bending moment doesn’t acount for any physical properties of the beam. It is only concerned with how much weight there is, what the span is and how much support there is. Watch the 2nd video link above for a good description of this stuff.

So do you actually have to memorize all the moment formulas? No, I don’t think so. But you should be familiar enough with them to know that a beam with a point load will generally bend more than a beam with a uniform distributed load, and a cantilever will bend more than a beam supported on both ends. I would feel most safe standing on the beam supported at both ends, and that’s the one that turns out to bend the least.

A: wl²/8 = 2,500 ft-lbs
B: PL/4 = 5,000 ft-lbs
C: wl²/2 = 10,000 ft-lbs
D: PL = 20,000 ft-lbs