Question $2-$ Beam Design $(25$marks$)$

The cross section of the continuous reinforced concrete beam with $3-28$mm diameter steel bars is shown in Figure $1\mathrm{.}1$ and Figure $1\mathrm{.}2$ below. The continuous beam has five supports $(2$ exterior and three interior supports$).$ The design parameters are $f{c}^{\text{'}}=25$MPa;$fsy=400$MPa $($main bars$)$; Es$=200,000$ MPa; unit weight of concrete $=24k\frac{N}{m}2.$ Answer the following:

a$.$ Determine if the steel yields prior to concrete reaching a strain of $0\mathrm{.}003$ using $(5$ marks$)$ the rectangular stress block of AS$36002009.$

b$.$ If the Live load $(Q)=9k\frac{N}{m},$ Dead load exclusive of self$-$weight $(G)=15k\frac{N}{m}(10$ marks$)$ determine the span length between supports that will safely carry the live load in the beam. Use combination factor $(w)=1\mathrm{.}2G+1\mathrm{.}5Q$

c$.$ Design the shear reinforcement of the beam. Use R$12$ reinforcement of $(10$ marks$)$ strength $300$MPa. Draw and detail the reinforcement.