Question $1)(40$p$)$: Consider a simply supported reinforced concrete beam. The load$-$carrying

capacity is:

$A_s{F}_y(d-\frac{a}{2})$

where variables $A_s,F_y,$ and $(d-\frac{a}{2})$ are all random variables. The statistics for these parameters

are given in the table below. The mean moment due to the total load is known to be $125k-ft,$

and the COV is $13$ percent. The load effect due to the total load is normally distributed.

Calculate the reliability index of the beam via Hasofer$-$Lind reliability index method

$($matrix procedure$).$

Question $2)(40$p$)$: Calculate the reliability index of the beam stated in Question $1$ by the use of

same statistical parameters via Rackwitz$-$Fiessler reliability index method.