Problem 1 (20 Points)
Let’s use an overly simplified model to investigate the difference in side impact safety between a convertible and a regular car. Specifically, we consider the side panels and the roof panel as beams, each with length $l$, second-area moment $I$, cross-section area $A$, and Young’s modulus $E$.
- Derive the spring rate $k$ for the convertible. ($k=F/\delta$, where $\delta$ is the deflection due to $F$.) (5 Pts)
- Derive the free-body diagram for the regular car. (5 Pts)
- Derive the spring rate for the regular car, by assuming that the horizontal beam does not buckle. (10 Pts) Note: Need to take into account the compression of the horizontal beam.
Problem 2 (80 Points)
Consider the bridges in the figure. Assume all joints are frictionless (truss element). Find the deflections at the loading point given the loading and the truss members’ Young’s modulus and cross section area. If truss members fail due to large tensional stress, which bridge is a better design?
