Q$7\mathrm{.}4\mathrm{.}4$ A simply supported beam ABC of length $l$ is under both concentrated load $P$ at the mid$-$

span and uniformly distributed load $q,$ as shown in Fig. $7\mathrm{.}4\mathrm{.}4.$ Using the Macaulay method,

determine the angle of rotation at a support ${}_A$ and maximum deflection $v_{\text{m}\text{a}\text{x}}.($N$.$B$.$ This is the

same question as Example $1\mathrm{.}3\mathrm{.}2$ in the Notes, which is solved using the superposition method$).$

Fig. $7\mathrm{.}4\mathrm{.}4$

Answers: $,\frac{P{l}^2}{16EI}+\frac{q{l}^3}{24EI}$ and $\frac{P{l}^3}{48EI}+\frac{5q{l}^4}{384EI}.$