The top crossbar for a gantry crane is to be constructed out…
The top crossbar for a gantry crane is to be constructed out of 6 × 2.034 channel (see table below for geometric properties) and with a length L = 7 feet. The channel is implemented as shown in the close-up so that it can be considered as a simply-supported beam that bends about the 1-1 axis. It is desired that the crane be used to repeatedly lift a weight at the midpoint of the crossbar. Consider the weight as a point force acting through the centroid of the channel that varies between 0 lbf and 8,000 lbf. The channel material is hot-rolled AISI 1045 (Sut = 82 ksi, Sy = 45 ksi), and you don’t need to consider any stress concentrations or the weight of the channel crossbar. Determine the following: The maximum bending stress (σmax) in the crossbar (the shear stress can be ignored in the analysis) The modified endurance limit (Se) for this application with 90% reliability The factor of safety with respect to infinite life (nf) using the Modified Goodman criteria The number of cycles (N) it is expected to last before fatigue failure Write down all your work to scan and submit, including a free-body diagram and bending moment diagram for the crossbar. σmax = ksi (round answer to 1 decimal place)Se = ksi (round answer to 1 decimal place)nf = (round answer to 2 decimal places)N = (round answer to nearest thousand; enter “infinite” if infinite life is predicted)