Problem $1$

A reinforced concrete beam has a rectangular cross$-$section as shown in Figure $1.$

a$)$ Calculate the steel reinforcement area.

b$)$ Calculate the steel reinforcement ratio.

Given:

$-$ Compressive strength, $\backslash ($ f$^\{\backslash$prime$\}$ c$=4,000\backslash$mathrm$\{$psi$\}\backslash )$

$-$ Rebar yield strength, $\backslash ($ f y$=60\backslash$mathrm$\{$ksi$\}\backslash )$

$-$ Rebars: $4$ No$.9$

Parameters:

$-\backslash ($ b$=12\backslash )$ in

$-\backslash ($ d$=17\backslash )$ in

$-$ clear cover, $\backslash (\backslash$mathrm$\{$cc$\}=2\backslash )$ in

Problem $2$

For the beam cross$-$section in Problem $1,$ determine:

a$)$ The minimum steel reinforcement area required by the ACl $318$ code.

b$)$ The minimum steel reinforcement ratio required by the ACl $318$ code.

c$)$ Does the provided reinforcement meet the code requirements?

Problem$3$

For the beam cross$-$section in Problem $1,$ determine:

a$)$ Whether the section is tension$-$controlled, or compression controlled.

b$)$ Strength reduction factor for bending.