Q$2)(45$P$)$ Consider the following limit state equation involving resistance $R,$ dead load effect $D,$ and live load effect $L$ :

$G(R,D,L)=R-(D+L)=R-D-L$

A possible corresponding design equation to this limit state equation, in LRFD format is:

$R_n{}_D{D}_n+{}_L{L}_n$

where $R_n,D_n$ and $L_n$ are nominal values of the loading. Given the following parameters, determine the partial safety factors to achieve $=4$ :

$R$ is lognormal $V_R=12\%,{}_R=1\mathrm{.}20$

$D$ is normal $V_D=10\%,{}_D=1\mathrm{.}10$

$L$ is normal $V_L=18\%,{}_L=1\mathrm{.}25$