Problem:

A $250mm600mm$ reinforced concrete beam cross$-$section is subjected to positive

bending moment. It is reinforced at the bottom with $2$ layers of steel: one

consisting of $3$ No$.14$ bars and another consisting of $3$ No $\mathrm{.}20$ bars. The material

properties are: $f^{\text{'}}{?}^c=40$MPa $($normal weight$)$ and $f_y=420$MPa.

a$)$ Calculate the nominal weight of the beam per unit length, $w_D($units $=k\frac{N}{m}).$

b$)$ Compute the centroid of the total tension steel area from the top, d $.$

c$)$ Verify that the steel is more than the minimum ACI code requirement.

d$)$ Check if the section is under$-$reinforced or over$-$reinforced.

e$)$ Determine the location of the neutral axis from the top, c$,$ at ultimate.

f$)$ Compute the strain in the top $(3$ No $\mathrm{.}14$ bars$)$ and also in the bottom $(3$ No $.$

$20$ bars$)$ layers of steel at ultimate condition.

g$)$ Calculate the nominal flexural strength of the section at ultimate, $M_n.$