EGM$3520-$ Class Activity #$6$: A reinforced concrete pier is used to support the stringers for a bridge deck. The pier loading can be modeled as in the figure, and it can be assumed that columns at A and B exert only punctual vertical loads on the pier. The cross sectional area of the concrete pier is rectangular, uniform between columns, and it is reinforced with $3$ rebars having $25mm$ diameter each. Take $E_{\text{s}\text{t}\text{e}\text{e}\text{l}}=200$GPa,$E_{\text{c}\text{o}\text{n}\text{c}\text{r}\text{e}\text{t}\text{e}}=25$GPa, distance $d=800mm,$ side $b=300mm.$

A$.$ Draw the moment diagram

B$.$find the moment of inertia of the equivalent section made of concrete in mm$^4$

C$.$ What is the maximum compressive stress of the concrete and steel?

D$.$ Knowing that the stress limits are the yield stress for steel, sy$($steel$)=250$ MPa, andthe ultimate stress for concrete Su$($concrete$)=40$ MPa, the factor of safety of the reinforced concrete pier is nearly what?