At joint D,the inclined member BD balances P with its vertical component,so its magnitude is P/sin60°. Horizontal equilibrium gives |CD|=Pcot60°=P/√3. Joint C similarly gives |BC|=P/√3. The BC limit therefore controls:P≤30√3=51.9615 kN;the CD limit would allow50√3. Thus Pmax=51.96 kN.
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