(a) Condition: Pst = 2Pbr
$\Sigma F_V = 0$
$2P_{st} + P_{br} = 40$
$2(2P_{br}) + P_{br} = 40$
$P_{br} = 8 \, \text{kips}$
$P_{st} = 2(8) = 16 \, \text{kips}$
$\delta_{br} = \delta_{st}$
$\left( \dfrac{PL}{AE} \right)_{br} = \left( \dfrac{PL}{AE} \right)_{st}$
$\dfrac{8000 \, L_{br}}{1.5 (12 \times 10^6)} = \dfrac{16000 \, (3 \times 12}{1.0 (29 \times 10^6)}$
$L_{br} = 44.69 \, \text{in}$
$L_{br} = 3.72 \, \text{ft }$ answer
(b) Condition: σst = 2σbr
$\Sigma F_V = 0$
$2P_{st} + P_{br} = 40$
$2(\sigma_{st} \, A_{st}) + \sigma_{br} \, A_{br} = 40$
$2 \, [ \, (2 \sigma_{br}) \, A_{st} \, ] + \sigma_{br} \, A_{br} = 40$
$4 \sigma_{br} (1.0) + \sigma_{br} (1.5) = 40$
$\sigma_{br} = 7.27 \, \text{ksi}$
$\sigma_{st} = 2(7.27) = 14.54 \, \text{ksi}$
$\delta_{br} = \delta_{st}$
$\left( \dfrac{\sigma L}{E} \right)_{br} = \left( \dfrac{\sigma L}{E} \right)_{st}$
$\dfrac{7.27(1000) \, L_{br}}{12 \times 10^6} = \dfrac{14.54(1000)(3 \times 12)}{29 \times 10^6}$
$L_{br} = 29.79 \, \text{in}$
$L_{br} = 2.48 \, \text{ft}$ answer