Q$4.$ A simply supported beam with a span of $8m$ has a uniformly distributed load of $20k\frac{N}{m}$ from

the left support to middle of the span and a concentrated moment of $40kNm($clockwise$)$ at $2m$

from support $B($point $C)$ as shown in Figure Q$4.$ Please take $E=210$GPa and $I=5{10}^{-5}{m}^4.$

Please do the following:

$($a$)$ Obtain the reaction forces at the supports, clearly stating the direction of these.

$($b$)$ Using the Macaulay's function determine the slope of the beam at both supports, and the

vertical deformation at midspan, clearly stating the direction of the slopes and the

deformation in each case.