Solution to Problem 233 Statically Indeterminate

$\delta = \delta_{cast \,\, iron} = \delta_{steel} = 0.8 \, \text{mm}$
 

$\delta_{cast \,\, iron} = \dfrac{P_{cast \, \, iron}(2000)}{[ \, \frac{1}{4} \pi (60^2 - 50^2) \, ] (100\,000)} = 0.8$

$P_{cast \, \, iron} = 11\,000 \pi \, \text{N}$
 

$\delta_{steel} = \dfrac{P_{steel}(2000)}{[ \, \frac{1}{4} \pi (50^2) \, ] (200\,000)} = 0.8$

$P_{steel} = 50\,000 \pi \, \text{N}$
 

$\Sigma F_V = 0$

$P = P_{cast \, \, iron} + P_{steel}$

$P = 11\,000 \pi + 50\,000 \pi$

$P = 61\,000 \pi \, \text{N}$

$P = 191.64 \, \text{kN}$           answer