Materials: $F^{\text{'}}C=250k\frac{g}{c}m2(E=$cte$)$;$Fy=4,200k\frac{g}{c}m2$; load combination: U$2=1\mathrm{.}2DL+1\mathrm{.}6LL$

lengths: Lab$=8m$;$Lbc=$Lcd$=9m$

Recessed A and D ends; articulated$/$roller supports B and C

SERVICE LOADS

DL:

$!$

Consider the maximum design moment from the moment diagram at $BC.$

Re$-$size the section with an alpha factor of $=0\mathrm{.}8$ and for an amount of $50\%$ of the balanced amount, $=0\mathrm{.}5bal.$

Use the maximum moment $M$ max of the analysis. Propose steel $($a rod bed$)$ for the newly sized section.

Calculate the required steel and provide reinforcement $($a bed of rod$)$ for the central and DER moments on member BC$,$ from

the resized section above $($for new $b$ and $d).$ Continue using the same coating $(h-d=6cm).$

Solve on paper. Comment on your results; Compare with respect to problem $1.$

Problem $2\mathrm{.}1))$ For the re$-$sized section of problem $2($for M max$),$ place $2$ more rods in the compression zone, that is$,$ provide $A^{\text{'}}$

$,$ of the same diameter as the proposed one. Check the new section with DOUBLE reinforcement, calculate the design capacity

Mn of the new section. Consider $d^{\text{'}}=6cm.$ Obtain the utilization ratio, ratio $=\frac{}{}Mn$ for this section.