Q$7\mathrm{.}4\mathrm{.}1$ A simply supported beam $AB$ of length $l$ is under a concentrated load $P$ at its mid$-$span, as shown in Fig. $7\mathrm{.}4\mathrm{.}1.$ Using the Macaulay function method, determine the angle of rotation at support ${}_A$ and maximum deflection $v_{\text{m}\text{a}\text{x}}$ of the beam. $($N$.$B$.$ This is the same question as Q$7\mathrm{.}2\mathrm{.}1,$ which you are asked to solve using the direct integration method$).$

$3.7\mathrm{.}4\mathrm{.}1$

Answers: $,\frac{P{l}^2}{16EI}$ and $\frac{P{l}^3}{48EI}.$

Q$7\mathrm{.}4\mathrm{.}2$ Re$-$work Q$7\mathrm{.}2\mathrm{.}2$ using the Macaulay function method.

Q$7\mathrm{.}4\mathrm{.}3$ Re$-$work Q$7\mathrm{.}3\mathrm{.}1$ using the Macaulay function method.