I need help with the reliability solution.

A tension member of $A992(Fy=50$ksi$)$ material is to be used to resist the load cases shown below. Find

the area required for both the Allowable Stress Design $($ASD$)$ provisions and the Load and Resistance

Factor Design $($LRFD$)$ provisions for each load case. Show all work.

The nominal loads $($which are also mean loads$)$ are:

The following design equations control:

FOR ASD $,\frac{A{F}_y}{}{D}_n+L_n$

where $=1\mathrm{.}67$

FOR LRFD $,A{F}_y$max$(1\mathrm{.}4D_n,1\mathrm{.}2D_n+1\mathrm{.}6L_n)$

where $=0\mathrm{.}90$

DESIGN SOLUTION:

For each design above, find the safety index $$ and an approximate probability of failure $p{f}_f.$ Show all work.

Discuss implications on design from the results of the reliability analysis.

Mean Yield Stress $=55$ksi

$CO{V}_D=13\%$

$CO{V}_L=27\%$

$CO{V}_R=10\%$

$Z=R-D-L$

vec$(Z)\frac{?}{b}=ar(R)\frac{*}{b}ar(D)\frac{-}{b}ar(L)$

${}_{Z^2}^2-{}_D^2+{}_R^2+{}_L^2$

RELIABILITY SOLUTION: