For all questions, $f{c}^{\text{'}}=28$MPa,${}_1=0\mathrm{.}85,fy=420$MPa,$$ concrete $=24K\frac{N}{m^3}(2\mathrm{.}4\frac{t}{m^3})$

Q$1.(30$ points$)$ For the beam shown, the factored dead load $=12\frac{t}{m}$ and the factored live load $=18\frac{t}{m}.$ Three cases of loading are analyzed and the bending moment diagrams are provided

a$)$ Knowing that the beam has sufficient rotation capacity, is it safe to reduce the design moments at the critical locations by $20\%?$

b$)$ If the answer is no$,$ what would be the maximum $\%$ safe reduction level.

Show your justification in full details.

$3$

Q$2.$ a$)(20$ points$)$ For the grid shown in Plan $1,$ determine $x$ and the maximum load that can be supported in $\frac{t}{m^2}$ units. The beams are all fully fixed into the walls. The beams are spaced at $1m$ center to center in both directions. $Mpx=30$ t$.$m$,Mpy=10$ t$.$m

$4$

b$)(15$ points$)$ For the beam layout shown in Plan $2,$ determine the maximum load that can be supported in $\frac{t}{m^2}$ units. The beams are all fully fixed into the walls. The beams are spaced at $1m$ center to center. $Mpx=30$ t$.$m$.$

c$)(5$ points$)$ Based on the results of parts a$)$ and b$),$ what are your conclusions.