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Problem $04\mathrm{.}131-$ Consider a hydraulic cylinder operates at a pressure of $1500$ psi

The hydraulic cylinder shown in the figure has a $2-$in bore and is to operate at a pressure of $1500$ psi. With the clevis mount shown, the piston rod should be sized as a column with both ends rounded for any plane of buckling. The rod is to be made of forged AISI $1030$ steel without further heat treatment.

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Problem $04\mathrm{.}131.$a $-$ Select the diameter of a long piston rod

Use a design factor $n_d=2\mathrm{.}5$ and select a preferred size for the rod diameter if the column length is $50$ in $.($Round the final answer to three decimal places.$)$

The preferred size for the diameter of the rod is $$ in$.$