The main system adopted for a lecture hall is composed of DT precast beams that span $26m.$ The

floor is subjected to SID$=1\mathrm{.}0k\frac{N}{m^2}$ and aLL$=2\mathrm{.}0k\frac{N}{m^2}.$

Question $1$

Assuming that the DT is a precast reinforced concrete beam reinforced with $32$ no $20$ and having

$f_{EL}=40$MPa and $F_Y=400$MPa,

Find:

a$.$ the location of the CG of the uncracked section,

b$.$ the moment of inertial about the major axis of the uncracked section and

c$.$ the section modulus $($w$.$r$.$t$.$ the top and bottom fibres$)$ of the uncracked section.

Calculate:

a$.$ the cracking moment of the section,

b$.$ the nominal moment of the section,

c$.$ the load acting on the section $)$ due to its own weight, SID, and $LL,$

d$.$ the maximum factored $($ultimate$)$ moment acting on the section $($you may use a

load factor of $1\mathrm{.}5),$

e$.$ the moment of resistance of the section $($according to the EGP and the ACI$)$; then

decide if the section is safe or not to use for this hall.