#$1$ A T$-$beam for a floor system has a slab thickness of $100mm$ and a total depth

of $550mm.$ It has a web thickness of $300mm.$ The T$-$beam is cast

monolithically with the slab. The beam has a simple span of $6m.$ with a

spacing of $2\mathrm{.}4m.$ center to center. The beam carries a live load moment of

$184$ kN$.$m and a dead load moment of $84$ kN$.$m$.f_c^{\text{'}}=20\mathrm{.}7$MPa,

$f_y=413\mathrm{.}7$MPa. Assume steel covering of $65mm.$

$(1)$ Determine the effective width of flange.

$(2)$ Determine the depth of compression block.

$(3)$ Determine the steel area required for tension only.

#$2$ A reinforced concrete T$-$beam has an effective depth of $600mm$ and is

reinforced with $8-28mm\frac{O}{?}$ bars. The web width is $300mm$ and has a

flange thickness of $90mm.$ The beam has a span of $5\mathrm{.}8m.$ and has a

spacing center to center equal to $1\mathrm{.}5m.f{c}^{\text{'}}=21$MPa and fy $=415$MPa.

$(1)$ Which of the following gives the effective width of the flange.

$(2)$ Which of the following gives the depth of the compression block.

$(3)$ Which of the following gives the nominal moment capacity of the beam.

#$3$ A T$-$section has a flange width of $750mm,$ thickness of flange is $50mm.$

Effective depth is $750mm$ with a width of web section of $350mm.$ The beam

is subjected to a factored moment $M_u=816kN.m.$

$f_c^{\text{'}}=20\mathrm{.}7$MPa,$f_y=276\mathrm{.}5$MPa.

$(1)$ Compute the nominal moment capacity of the overhanging portion of the

section.

$(2)$ Compute the depth of compression block.

$(3)$ Compute the area of reinforcement needed for the T$-$section.