A manure spreader tank is shown in Figure P12-15. The tank is 90 in. long. The bottom axle is 12 in. long measured along the tank axis direction and located in the middle. The single front end coupling is 6 in. in length measured along the axis of the tank. The pressure is a variable surface pressure extending from the top edge to bottom and given by the function shown with a maximum pressure of 11.6 psi at the center of the tank. (The density of manure is taken as 8.3 lbf / gallon or 0.0359 lbf / in.3). Other dimensions are shown in the figures. Assume the tank is made of plate steel with modulus of elasticity of 29 × 106 psi and Poisson's ratio of 0.29. Determine the von Mises stress throughout the tank and the maximum displacement. (This problem by Justin Hronyk.)
Figure P12-15 Manure spreader tank showing dimensions (in.) and pressure load variation (By Justin Hronek)

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O 36.000 45 20 Axle Cylinder 11.6 9.3 7.0 4.7 2.3 0.0 -18.0 18.0 -10.8 -3.6 3.6 10.8 (in.) Variable surface traction Pressure psi 000'I 12.000 in. Coupling