The effective I $(I_{ef})$ value used for deflection calculations is:

$($a$)$ Less than $I_g$ because cracking increases the bending stiffness of the

beam.

$($b$)$ Less than $I_{rr}$ because cracking reduces the bending stiffness of the

beam.

$($c$)$ Greater than $I_g$ because the concrete in tension between the cracks adds

to the bending stiffness of the beam.

$($d$)$ Greater than $I_{cr}$ because the concrete in tension between the cracks

adds to the bending stiffness of the beam.

$($e$)$ None of the other answers is correct.

MPa

mm

When the cross$-$section shown above is subjected to a positive bending moment,

using $d_n=233mm,$ the value of $I_a$ is:

$($a$)$ None of the other answers is correct

$($b$)4502\mathrm{.}4{10}^6{m}^4$

$($c$)4502\mathrm{.}4{10}^{6}m{m}^4$

$($d$)3553\mathrm{.}75{10}^6{m}^4$

$($e$)3553\mathrm{.}75{10}^{6}m{m}^4$

$I_{ef}=1915{10}^{6}m{m}^4$

$Ec=30,100$MPa

$s=1\mathrm{.}0$ and $l=0\mathrm{.}6$

Permanent load $=16k\frac{N}{m}$

Imposed load $=10k\frac{N}{m}$

effective span of $5\mathrm{.}5$ m $.$ The total deflection at the midspan, the maximum allowable

deflection and the deflection decision is:

$($a$)$ Total deflection $=9\mathrm{.}8mm$; max. allowable deflection $=24mm$;

:$.$ deflection OK$.$

$($b$)$ Total deflection $=11\mathrm{.}7mm$; max. $.$ allowable deflection $=22mm$;

:$.$ deflection OK

$($c$)$ None of the other answers is correct

$($d$)$ Total deflection $=11\mathrm{.}7mm$; max. allowable deflection $=11mm$;

:$.$ deflection not OK

$($e$)$ Total deflection $=37\mathrm{.}9mm$; max. allowable deflection $=22mm$;

:$.$ deflection not OK