
$EI ~ t_{A/B} = 0$
$(Area_{AB}) \cdot \bar X_A = 0$
$Mb(L - \frac{1}{2}b) - \frac{1}{2}L(RL)(\frac{2}{3}L) = 0$
$MbL - \frac{1}{2}Mb^2 - \frac{1}{3}RL^3 = 0$
$\frac{1}{3}RL^3 = MbL - \frac{1}{2}Mb^2$
$R = \dfrac{3Mb}{L^2} - \dfrac{3Mb^2}{2L^3}$
$R = \dfrac{3Mb}{2L^3}(2L - b)$ answer
$M_{wall} = M - RL$
$M_{wall} = M - \dfrac{3Mb}{2L^3}(2L - b)L$
$M_{wall} = M - \dfrac{3Mb}{2L^2}(2L - b)$ answer
When $b = L$
$R = \dfrac{3ML}{2L^3}(2L - L) = \dfrac{3M}{2L}$
$M_{wall} = M - \dfrac{3ML}{2L^2}(2L - L) = M - \frac{3}{2}M = -\frac{3}{2}M$
See Problem 707 for propped beam with moment load at the simple support for comparison.