Suppose we have a $3$m simply supported beam which is under partially UDL of $33\mathrm{.}92$kN on $1\mathrm{.}5$m span of the beam. See attached photo for drawing and values.

Draw SFD and BMD

Find:

a$.$ Equation of shear force V$($x$)$ in terms of x

b$.$ Equation of bending moment M$($x$)$ in terms of x

c$.$ Equation of slope theta$($x$)$ in terms of x

d$.$ Equation of deflection of the beam y$($x$)$ in terms of x

Then from that, calculate:

e$.$ Max slope

f$.$ Max deflection