Summary for the value of end moments and deflection of perfectly restrained beam carrying various loadings. Note that for values of EIy, y is positive downward.
Case 1: Concentrated load anywhere on the span of fully restrained beam
End moments
$M_A = -\dfrac{Pab^2}{L^2}$
$M_B = -\dfrac{Pa^2b}{L^2}$
Value of EIy
$\text{Midspan } EI\,y = \dfrac{Pb^2}{48}(3L - 4b)$
Problem 726
A beam of length L, perfectly restrained at both ends, supports a concentrated load P at midspan. Determine the end moment and maximum deflection.