Problem $3(20$pts$)$

For the $T-$ beam shown: $f_c^{\text{'}}=3,000$ and $f_y=50,000,$ Calculate the design capacity in flexure: $M_n=k-ft$

$(1)b=$ in$,b_w=$ in$,h_f=$ in$,d=$ in $,A_s=i{n}^2$

$(2)$ checking $A_{s-\text{m}\text{i}\text{n}}=q,i{n}^2$

$(3)$ Area of concrete in compression: $A_c=q,i{n}^2$

$(4)$ Solve for the depth of the stress block; $a=$ in

$(5.)(4)$ Determine tensile strain: $lo{n}_t=$

$(6)$ Determine the centroid of $A_c$ from top: $\frac{?}{\text{b}\text{a}\text{r}}(y)=$ in

$(7)$ calculate the design capacity in flexure: $M_n=$