For the column cross section shown below, use a strain$-$compatibility solution to compute five points on the

nominal interaction diagram corresponding to points $1$ to $5$ in Fig. $11-22$ in the textbook $($also shown

below$).$ Plot the interaction diagram

Material strengths are Gr$.60$ steel and normal weight concrete with $f_c$ of $5000.$ Assume interior

exposure conditions. The points $1$ to $5$ are:

Point points$)$: Maximum axial load $($a uniform compressive strain$).$

Point $2(20$ points$)$: A strain diagram corresponding to incipient cracking, passing through a

compressive strain of $0\mathrm{.}003$ on the top face and zero strain on the bottom face.

Point $3(20$ points$)$: The limiting compression$-$controlled strain distribution, which has a

compressive strain of $0\mathrm{.}003$ on the top face and the yield tensile strain at the centroid of the

reinforcement layer nearest to the tensile face $($bottom$).$

Point $4(20$ points$)$: The limiting tension$-$controlled strain distribution, which has a compressive

strain of $0\mathrm{.}003$ on the top face and a tensile strain of $0\mathrm{.}003+e_{ty}$ in the reinforcement layer nearest

to the tensile face.

Point $5(20$ points$)$: A uniform tensile strain of ety in the steel with the concrete cracked.

Material strengths are Gr$.60$ steel and normal weight concrete with f$$c of $5000$ psi. Assume interior

exposure conditions. The points $1$ to $5$ are:

$$ Point $1(20$ points$)$: Maximum axial load $($a uniform compressive strain$).$

$$ Point $2(20$ points$)$: A strain diagram corresponding to incipient cracking, passing through a

compressive strain of $0\mathrm{.}003$ on the top face and zero strain on the bottom face.

$$ Point $3(20$ points$)$: The limiting compression$-$controlled strain distribution, which has a

compressive strain of $0\mathrm{.}003$ on the top face and the yield tensile strain at the centroid of the

reinforcement layer nearest to the tensile face $($bottom$).$

$$ Point $4(20$ points$)$: The limiting tension$-$controlled strain distribution, which has a compressive

strain of $0\mathrm{.}003$ on the top face and a tensile strain of $0\mathrm{.}003+$ ety in the reinforcement layer nearest

to the tensile face.

$$ Point $5(20$ points$)$: A uniform tensile strain of ety in the steel with the concrete cracked.

Solve all parts