Degree of $M/EI = n$
Moment reaction = $M_R$
Maximum rotation, $EI ~ \theta = \dfrac{M_R L}{n + 1}$
Maximum deflection, $EI ~ \delta = \dfrac{M_R L^2}{n + 2}$
| CASE | n, MR, θ, δ |
|---|---|
 |
$n = 0$
$M_R = M$ $EI ~ \theta = \dfrac{M_R L}{1}$ $EI ~ \delta = \dfrac{M_R L^2}{2}$ |
 |
$n = 1$
$M_R = PL$ $EI ~ \theta = \dfrac{M_R L}{2}$ $EI ~ \delta = \dfrac{M_R L^2}{3}$ |
 |
$n = 2$
$M_R = \dfrac{w_o L^2}{2}$ $EI ~ \theta = \dfrac{M_R L}{3}$ $EI ~ \delta = \dfrac{M_R L^2}{4}$ |
 |
$n = 3$
$M_R = \dfrac{w_o L^2}{6}$ $EI ~ \theta = \dfrac{M_R L}{4}$ $EI ~ \delta = \dfrac{M_R L^2}{5}$ |