(Solved): The maximum pressure of air in a 20-in. cylinder (double-acting air compressor)is 125 psig. What sho ...

Expert Answer

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To determine the diameter of the piston rod, we need to use the maximum stress formula for a rod under axial loading:    where ?_max is the maximum stress, F is the axial force, d is the diameter of the rod. We can assume that the axial force is equal to the pressure times the area of the piston, so:    where P is the maximum pressure, and A is the area of the piston. We can calculate the area of the piston using the diameter of the cylinder:    So, the axial force is:    Now, we can substitute this value into the maximum stress formula and solve for the diameter:       where N is the endurance limit factor, S is the allowable stress for AISI3140 at the given temperature, and FS is the factor of safety. We can look up the allowable stress for AISI3140 at 1000 F and find that it is 12,000 psi. Let's assume a factor of safety of 2.5: N = 75.1 S = 12,000 psi FS = 2.5 Then, we can solve for the diameter: