Member AB:
$\Sigma M_A = 0$
$3P_{al} = 6P_{st}$
$P_{al} = 2P_{st}$
By ratio and proportion:
$\dfrac{\delta_B}{6} = \dfrac{\delta_{al}}{3}$
$\delta_B = 2 \delta_{al} = 2 \left[ \dfrac{PL}{AE} \right]_{al}$
$\delta_B = 2 \left[ \dfrac{P_{al} \, (2000)}{500(70\,000)} \right]$
$\delta_B = \frac{1}{8750} P_{al} = \frac{1}{8750} (2P_{st})$
$\delta_B = \frac{1}{4375} P_{st}$ → movement of B
Member CD:
Movement of D:
$\delta_D = \delta_{st} + \delta_B = \left[ \dfrac{PL}{AE} \right]_{st} + \frac{1}{4375} P_{st}$
$\delta_D = \dfrac{P_{st} \, (2000)}{300(200\,000)} + \frac{1}{4375} P_{st}$
$\delta_D = \frac{11}{42\,000} P_{st}$
$\Sigma M_C = 0$
$6P_{st} = 3P$
$P_{st} = \frac{1}{2} P$
By ratio and proportion:
$\dfrac{\delta_P}{3} = \dfrac{\delta_D}{6}$
$\delta_P = \frac{1}{2} \delta_D = \frac{1}{2} (\frac{11}{42\,000} P_{st})$
$\delta_P = \frac{11}{84\,000} P_{st}$
$5 = \frac{11}{84\,000} (\frac{1}{2} P)$
$P = 76\,363.64 \, \text{N} = 76.4 \, \text{kN}$ answer
