The rigid beam is supported by the three posts $A,B,$ and C$.$ Posts A and $C$ have a diameter of $50$ mm and are made of aluminum, for which $E_{sl}=70$GPa and $({}_Y{)}_{al}=20$MPa. Post $B$ is made of brass, for which $E_{br}=100$GPa and $({}_Y{)}_{br}=590$MPa

Part A

If $P=120kN$ determine the largest diameter of post $B$ so that all the posts yield at the same time. $($Figure $1)$

Express your answer with the appropriae units.

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Figure

$1$ of $1$