Handed Out:2/12/96
Due: 2/19/96
1. A plate (thickness h, bending stiffness D, Poisson's ratio n) is simply supported on all edges (x = ±a/2, y = ±b/2), and has a transverse pressure p = -(po/a)(x-a/2) applied. Sketch the plate and the load. What physical problems might this model? (big hint: what if x is the vertical axis on the earth's surface, and plate has water on one side?) Solve for the deflection w using a series solution- calculate at least 3 terms. Do you think the series solution for w has converged acceptably after 3 terms? What about the solution for Mx? Sketch the w solution.
2. The plate in problem 1 is redesigned so that the edges y = ±b/2 are now clamped. The loading is the same. Find the deflection w to reasonable accuracy, and sketch it. Hint: move the origin to a more convenient place.
3. The sluice gate of a 8' high dam (filled all the way to the top with water on one side) is made of a 4' wide, 1/4" thick piece of steel (E = 28 Msi), supported loosely at the top and bottom (assume simple support). The side supports, depending on the design selected, can be anywhere from simple supports to clampscheck both extremes. Find the maximum deflection and the maximum stress for each of the two extreme cases.
4. A rather large person (300# total load) stands on one foot (assume
very small foot print) in the middle of a 4' x 8' piece of 5/8" thick
plywood (E = 2 Msi) supported loosely (by laying on underlying, assumed-to-be-rigid
roof beams) on all edges. Find the maximum deflection and maximum stress.