The rectangular R$/$C beam shown is singly$-$reinforced with one layer of tension steel. The

concrete compressive strength is $4500$ psi and the steel yield stress is $60,000$ psi.

a$)$ Determine the yield strain for the given yield stress.

b$)$ Use the idealized Stress$-$Strain relationship to determine the steel stress

corresponding to the following steel strain values:

i$.\backslash$epsi s $=0\mathrm{.}00140$

ii$.\backslash$epsi s $=0\mathrm{.}00350$

iii. $\backslash$epsi s $=0\mathrm{.}00735$

c$)$ Draw the strain profile at the strength limit state and determine the corresponding

neutral axis depth, c $,$ and the section curvature, $\backslash$phi $,$ if the strain in A s at the strength

limit state is $($strain values in part b$)$:

i$.\backslash$epsi s $=0\mathrm{.}00140$

ii$.\backslash$epsi s $=0\mathrm{.}00350$

iii. $\backslash$epsi s $=0\mathrm{.}00735$

d$)$ Determine the area of tension steel for the strength limit states considered in part $($c$)$

$$ Hint: use equilibrium of internal forces.

e$)$ Draw conclusions regarding the effect of the amount of tension steel on the neutral

axis depth, strain in tension steel, and curvature at the strength limit stateThe rectangular R$/$C beam shown is singly$-$reinforced with one layer of tension steel. The

concrete compressive strength is $4500$ psi and the steel yield stress is $60,000.$

a$)$ Determine the yield strain for the given yield stress.

b$)$ Use the idealized Stress$-$Strain relationship to determine the steel stress

corresponding to the following steel strain values:

i$.{}_s=0\mathrm{.}00140$

ii$.{}_s=0\mathrm{.}00350$

iii. ${}_s=0\mathrm{.}00735$

c$)$ Draw the strain profile at the strength limit state and determine the corresponding

neutral axis depth, $c,$ and the section curvature, $,$ if the strain in $A_s$ at the strength

limit state is $($strain values in part b$)$:

i$.{}_s=0\mathrm{.}00140$

ii$.{}_s=0\mathrm{.}00350$

iii. ${}_s=0\mathrm{.}00735$

d$)$ Determine the area of tension steel for the strength limit states considered in part $($c$)$

Hint: use equilibrium of internal forces.

e$)$ Draw conclusions regarding the effect of the amount of tension steel on the neutral

axis depth, strain in tension steel, and curvature at the strength limit state.