Problem$1$: For the given doubly reinforced beam section and strain diagram below, $f{c}^{\text{'}}=4000,fy=60,000,$ please answer the following questions and provide solution procedures.

A

$($a$)$ section

$($b$)$ strain

$($c$)$ stress

$($d$)$ force

When reinforced concrete beam starts failure, $($a$)$ what is the maximum strain in the concrete compression zone, and $($b$)$ what is the real maximum stress in the concrete beam compression zone, and $($c$)$ draw the real compressive stress distribution in the concrete compression zone $(4$ points$).$

What is the compression zone depth, $c,$ when the beam starts failure? And indicate $c$ in the above Fig $(4$ points$).$

What is the strain of tensile reinforcement steel when the beam starts failure? Does the tensile reinforcement yield when the beam starts failure? $(4$ points$).$

What is the strain of compressive reinforcement steel when the beam starts failure? Does the compressive reinforcement yield when the beam starts failure? $(4$ points$).$

What is the nominal moment of the beam $?$ and What the design moment capacity of the reinforced concrete beam $(4$ points$)?$