INSTRUCTION: SOLVE THE FOLLOWING PROBLEMS

SITUATION: A $350$ x $500mm$ rectangular beam is

reinforced for tension only with $5-28$ mm bars.

The beam has an effective depth of $446mm.$ The

beam carries a uniform dead load of $4\mathrm{.}5k\frac{N}{m}$

$($including its own weight$),$ a uniform live load

of $3k\frac{N}{m},$ and concentrated dead load of $P$ and

$2P$ as shown in the figure. Assume $fy=414$MPa,

$f{c}^{\text{'}}=34\mathrm{.}5$MPa. Calculate the following:

The depth of the compression block in $mm.$

a$.151\mathrm{.}3$

b$.146\mathrm{.}10$

c$.124\mathrm{.}19$

d$.123\mathrm{.}20$

The ultimate moment capacity of the section in $kN-m$

a$.450$

b$.430$

c$.420$

d$.440$

The maximum value of $P$ in $kN.$

a$.230$

b$.430$

c$.210$

d$.192$

A cantilever beam $300400mm$ deep is $3m$ long is designed with tension reinforcement only.

Superimposed dead load $=12k\frac{N}{m}$

Live load at free end $=20kN$

Concrete unit weight $=23\mathrm{.}5k\frac{N}{m^{{?}^{{?}^{?}}}}3$

Concrete $f^{\text{'}}C=30$MPa

Steel $f{y}_y=414$MPa

Assume $70mm$ concrete cover to the centroid of the tension reinforcement. Using reduction factor $=$

$0\mathrm{.}90,$ calculate the Ultimate strength in $kNm$ of the section if the tension reinforcement consists

of $4-25mm\frac{O}{?}.$

a$.230\mathrm{.}45kN-m$

b$.220\mathrm{.}67kN-m$

c$.202\mathrm{.}56kN-m$

d$.190kN-m$