Solution to Problem 676 | Midspan Deflection

$EI \, t_{A/C} = (Area_{AC}) \, \bar{X}_A$

$EI \, t_{A/C} = M \left( \dfrac{L}{4} \right)\left( \dfrac{3L}{8} \right)$

$t_{A/C} = \dfrac{3ML^2}{32EI}$
 

$\delta_{midspan} = \frac{1}{2} t_{A/C}$

$\delta_{midspan} = \dfrac{1}{2} \left( \dfrac{3ML^2}{32EI}\right)$

$\delta_{midspan} = \dfrac{3ML^2}{64EI}$           answer