$3\mathrm{.}2$ The continuous beam shown in Fig. $1$ is part of a beam$-$and$-$slab floor system of an

office building and is typical of a series of beams spaced at $4$ m intervals. In addition to the

dead load, the live load on the floor is $3$ kPa $.$ Using $f^{\text{'}}c=32$MPa,$N32$ bars for main

reinforcement,

a$)$ Find the maximum positive and negative moments using the AS$3600$ simplified

method.

b$)$ Design the beam cross$-$section for the maximum amount of tensile steel required

at $($i$)$ interior supports, and $($ii$)$ mid$-$span. In both cases use singly reinforced design.

Fig. $1$a $($Continuous beam profile$)$

Fig. $1$b $($Typical Section$)$