Problem #$2$: $(45$ points$)$

You are asked to determine where to terminate reinforcing bars in a reinforced concrete beam. The beam shown below has $(4)$ #$8$ bars and you would like to terminate the middle two bars. Factored loads on the beam are shown in the figure below along with the stirrup size and spacing. Please assume these meet the ACI Requirements. Please use the material properties listed.

iMINATE

Concrete compressive strength $(f^{\text{'}})=4000$

Longitudinal reinforcement yield stress $(f_y)=60$ksi

Stirrup$/$Transverse reinforcement yield stress $(f_{yt})=60$ksi

Normal weight concrete

Beam is not exposed to weather or the ground

All bars are uncoated

a$)$ Using this information, calculate the cutoff location for the center $(2)$ #$8$ bars shown in the figure above. Use simplified equations where appropriate. Do not use reduction for $\frac{A_{s,\text{r}\text{e}\text{q}\text{u}\text{i}\text{r}\text{e}\text{d}}}{A_{s,\text{p}\text{r}\text{o}\text{v}\text{i}\text{d}\text{e}\text{d}}}.$ Ensure the cutoff location chosen meets ACI requirements and typical construction industry standards. Ignore the flexural capacity contribution of the top bars.

b$)$ Sketch an elevation of the beam showing the cut off location as measured from the support.

c$)$ Sketch the moment demand and capacity plots on the same curve. Label critical locations and use different line weights to indicate the different capacities and demands of the beam. $($Note this is similar to what you did in your Homework #$4).$