SITUATION $01-$ A reinforced concrete rectangular beam has a width of $310$ mm and an effective depth of $490$ mm $.$ Concrete compressive strength $f{c}^{\text{'}}=30$MPa and steel yield strength $fy=415$MPa.

What is the balanced steel area?

a$.,4611m{m}^2$

b$.4690m{m}^2$

c$.3458m{m}^2$

d$.2926m{m}^2$

What is the steel area when the beam is singly reinforced and has a reduction factor of $0\mathrm{.}90?$

a$.,3458m{m}^2$

b$.2926m{m}^2$

c$.4611m{m}^2$

d$.512m{m}^2$

What is the ultimate strength if the steel area is $3457m{m}^2?$

a$.,457KN-m$

b$.572KN-m$

c$.515KN-m$

d$.372KN-m$