Solution to Problem 626 | Moment Diagram by Parts

By symmetry
$R_1 = R_2 = \frac{1}{2}(400)(3)$

$R_1 = R_2 = 600 \, \text{lb}$

and

$(Area_{AB})\,\bar{X}_A = (Area_{AB})\,\bar{X}_B$
 

 

$(Area_{AB})\,\bar{X}_A = \frac{1}{2}(5)(1500)(\frac{5}{2}) - \frac{1}{3}(3)(450)(\frac{5}{2})$           answer

$(Area_{AB})\,\bar{X}_A = 8\,250 \text{lb}\cdot\text{ft}^3$
 

Thus,
$(Area_{AB})\,\bar{X}_B = 8\,250 \text{lb}\cdot\text{ft}^3$           answer