The RC beam section shown is singly$-$reinforced with one layer of tension steel. The specified

compressive strength of concrete is $4\mathrm{.}5$ksi and the steel yield stress is $60$ksi.

a$)$ Determine the balanced steel ratio, ${}_b$

b$)$ Determine the maximum and minimum steel areas allowed by ACI.

c$)$ If $A_s$ consists of $(4)$ #$8$ bars, answer the following:

i$.$ Is the reinforcement within the allowable limits set by ACI?

ii$.$ Determine the nominal flexural strength, $M_n$

iii. Determine the design flexural strength, $M_{n..}$ Verify the $$ value.

iv$.$ If the section is used on a $30-$ft$-$span simply supported beam with two

concentrated live loads of $25$ kips, each symmetrically placed at one$-$third from

the end of the beam, determine whether the beam is adequate or not.