A beam is being designed to support the loads shown in Figure. The four shapes proposed ar...

A beam is being designed to support the loads shown in Figure. The four shapes proposed are (a) a round bar, (b) a square bar, (c) a rectangular bar with the height made four times the thickness, and (d) the lightest American Standard beam. Determine the required dimensions of each proposed shape to limit the maximum stress due to bending to 80 MPa. Then compare the magnitude of the cross-sectional areas of the four shapes. Since the weight of the beam is proportional to its area, the one with the smallest area will be the lightest.