Part (a)
$EI \, t_{A/B} = (Area_{AB}) \, \bar{X}_A$
$EI \, t_{A/B} = \frac{1}{2}(\frac{1}{2}L)(\frac{1}{2}Lbw_o)(\frac{1}{3}L) - \frac{1}{3}(b)(\frac{1}{2}b^2w_o)\frac{1}{4}(2L - b)$
$EI \, t_{A/B} = \frac{1}{24}L^3bw_o - \frac{1}{12}Lb^3w_o + \frac{1}{24}b^4w_o$
$EI \, t_{A/B} = \frac{1}{24}w_ob (L^3 - 2Lb^2 + b^3)$
$EI \, \delta = \frac{1}{2} (EI \, t_{A/B})$
$EI \, \delta = \frac{1}{2} [ \, \frac{1}{24} w_ob (L^3 - 2Lb^2 + b^3) \, ]$
$EI \, \delta = \dfrac{w_ob}{48}(L^3 - 2Lb^2 + b^3)$ answer
Part (b)
$EI \, \delta = EI \, \delta_1 + EI \, \delta_2$
$EI \, \delta = \frac{1}{48} w_o b_1 (L^3 - 2L{b_1}^2 + {b_1}^3) + \frac{1}{48} w_o b_2 (L^3 - 2L{b_2}^2 + {b_2}^3)$
$EI \, \delta = \frac{1}{48} (800)(1) [ \, 6^3 - 2(6)(1^2) + 1^3 \, ] + \frac{1}{48} (800)(2) [ \, 6^3 - 2(6)(2^2) + 2^3 \, ]$
$EI \, \delta = 3416.67 + 5866.67$
$EI \, \delta = 9283.34 \, \text{ N}\cdot\text{m}^3$ answer
