Solution to Problem 234 Statically Indeterminate

$\delta_{co} = \delta_{st} = \delta$

$\left( \dfrac{PL}{AE} \right)_{co} = \left( \dfrac{PL}{AE} \right)_{st}$

$\left( \dfrac{\sigma L}{E} \right)_{co} = \left( \dfrac{\sigma L}{E} \right)_{st}$

$\dfrac{\sigma_{co} L}{14000} = \dfrac{\sigma_{st} L}{200\,000}$

$100 \sigma_{co} = 7 \sigma_{st}$
 

When σ_st = 120 MPa
$100 \sigma_{co} = 7(120)$

$\sigma_{co} = 8.4 \, \text{ MPa} \gt 6 \, \text{ MPa}$       → (not okay!)
 

When σ_co = 6 MPa
$100(6) = 7 \sigma_{st}$

$\sigma_{st} = 85.71 \, \text{ MPa} \lt 120 \, \text{ MPa}$       → (okay!)
 

Use σ_co = 6 MPa and σ_st = 85.71 MPa.
 

$\Sigma F_V = 0$

$P_{st} + P_{co} = 300$

$\sigma_{st} \, A_{st} + \sigma_{co} \, A_{co} = 300$

$85.71A_{st} + 6 \, [ \, \frac{1}{4} \pi(200)^2 - A_{st} \, ] = 300(1000)$

$79.71A_{st} + 60\,000 \pi = 300\,000$

$A_{st} = 1398.9 \, \text{ mm}^2$           answer