QUESTION $2(25$ marks$)$

For the beam shown in Figure $2($with the couple acting at B$)$:

a$)$ calculate the reactions and draw the shear force and bending moment diagrams

b$)$ if the beam in has a square cross$-$section, find the smallest allowable cross$-$

sectional dimensions when the maximum allowable stresses are $20$MPa in

bending and $2\mathrm{.}5$MPa in shear