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

Figure

Part A

If $P=150kN,$ 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.

$d=$

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$1$ of $1$