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The $4-$mm$-$dlameter cable $BC$ is made of a steel with $E=200$ GPa. Knowing that the maximum stress in the cable must not

exceed $170$ MPa and that the elongation of the cable must not exceed $6$ mm $.$ If $a=4\mathrm{.}5m$ and $b=2\mathrm{.}5m,$ find the allowable

load $P$ that can be applied as shown.

we

Using the FBD$/$equilibrium equations for member ABC $,$ the tension in the cable BC can be written as $P_{BC}=$