Problem $3\mathrm{.}2$: SL S Design

The beam shown in Figure $1$ carries a uniformly distributed live load $Q=4k\frac{N}{m}$ and a superimposed dead load $G=5k\frac{N}{m},$ in addition to its self$-$weight. Moreover, a $75$ kN permanent point load P from a brick wall is applied at mid$-$span. The width and the total depth of the beam are $250$ mm and $550$ mm respectively. The effective span $L$ is equal to $6$ m $.$ The tensile reinforcement is composed of $3$ N $24$ steel bars ; fsy $=500$MPa $).$ The effective depth d is $485$ mm $.$

The beam is exposed to an exterior environment in Sydney. Calculate the final total shrinkage strain of concrete.

Short term deflection using clause $8\mathrm{.}5\mathrm{.}3\mathrm{.}1$ and Equation $8\mathrm{.}5\mathrm{.}3\mathrm{.}1($I$)-$ Effect of concrete shrinkage will be ignored:

$2.$ Calculate the design service bending moment $M^{*}$ ser for short$-$term.

$3.$ Calculate $I_8.$

$4.$ Calculate $I_c.$

$5.$ Calculate the effective moment of inertia $I_{cf}$ and the short$-$term mid$-$span deflection of the beam using clause $8\mathrm{.}5\mathrm{.}3\mathrm{.}1$ and Equation $8\mathrm{.}5\mathrm{.}3\mathrm{.}1(1).$

Long term deflection using clause $8\mathrm{.}5\mathrm{.}3\mathrm{.}1$ and Equation $8\mathrm{.}5\mathrm{.}3\mathrm{.}1($I$)-$ Effect of concrete shrinkage will be included.

$6.$ Calculate the design service bending moment $M^{*}$ ser for long$-$term.

$7.$ Calculate the effective moment of inertia lef using clause $8\mathrm{.}5\mathrm{.}3\mathrm{.}1$ and Equation $8\mathrm{.}5\mathrm{.}3\mathrm{.}1(1)$ and the long$-$term mid$-$span deflection of the beam.

$8.$ Deduce the total deflection $($short $+$ long terms$)$ and compare with AS$3600$ Service Limit State. Is the beam meeting AS$3600-2018$ SLS requirement for control of deflection?