$4\mathrm{.}3.$ A typical cross$-$section of a reinforced concrete T$-$beam is shown in the figure below. The beam is reinforced with $6-25M$ bars in the tension zone. Use an effective depth of $600$ mm $.$ The material proper. ties are summarized below.

a$)$ Find the gross moment of inertia $(I_g)$ for the uncracked section, ignoring the effect of rein. forcement.

b$)$ Find the moment of inertia for the uncracked section using the transformed section properties $(I_{g,tr}).$

c$)$ Compare the results of the calculations performed in parts a$)$ and b$).$ Express the difference in the moment of inertia values as a percentage.

d$)$ Do you believe that the difference in moment of inertia values obtained in part c$)$ is significant from a practical design perspective? Explain.

Given:

$f_c^{\text{'}}=35$MPa $(normal-$density concrete$)$

$f_y=400$MPa

$E_s=200000$MPa$4\mathrm{.}3.$ A typical cross$-$section of a reinforced concrete T$-$beam is shown in the figure below. The beam is reinforced with $6-25M$ bars in the tension zone. Use an effective depth of $600$ mm $.$ The material proper. ties are summarized below.

a$)$ Find the gross moment of inertia $(I_g)$ for the uncracked section, ignoring the effect of rein. forcement.

b$)$ Find the moment of inertia for the uncracked section using the transformed section properties $(I_{g,tr}).$

c$)$ Compare the results of the calculations performed in parts a$)$ and b$).$ Express the difference in the moment of inertia values as a percentage.

d$)$ Do you believe that the difference in moment of inertia values obtained in part c$)$ is significant from a practical design perspective? Explain.

Given:

$f_c^{\text{'}}=35$MPa $(normal-$density concrete$)$

$f_y=400$MPa

$E_s=200000$MPa