Problem#$1.$ A six$-$meter$-$long cantilever column $($Column ab$)$ is connected to a "rigid leaning column" $($i$.$e$.,$ a rigid bar, $EA=)$ connected to the cantilevered column with another rigid bar with hinges at both ends$),$ as shown in Fig $1.$ The beam$-$column is made of W$360$x$110$ with are laterally braced in the perpendicular direction.

Load combinations to be considered: $1\mathrm{.}2D+1\mathrm{.}0W+1\mathrm{.}0L$ and $1\mathrm{.}2D+1\mathrm{.}6L$

Given: $W=150kN,P_{MF,D}=100kN,P_{MF,L}=50kN,P_{\text{L}\text{e}\text{a}\text{n}\text{i}\text{n}\text{g}\text{,}}=500kN,$ and $P_{\text{L}\text{e}\text{a}\text{n}\text{i}\text{n}\text{g}\text{,}L}=350kN$

$P_{MF,D}=$ Dead load acting on the cantilever $,P_{MF,L}=$ Live load acting on the cantilever

W$=$Wind load $,P_{\text{L}\text{e}\text{a}\text{n}\text{i}\text{n}\text{g}\text{,}}=$ Dead load acting on the leaning column

PLeaning. $L=$ Live load acting on the leaning column

Required:

Reduce the stiffness of the lateral force$-$resisting system;

Compute notional loads;

Conduct first and second$-$order analyses $($consider P$-$ effect only$)$;

Determine axial force and bending moment demands;

Determine capacities of members using $K=1\mathrm{.}0$;

Check if an additional stiffness reduction is required based on the axial force demand level;

Check if member ab is safe.

$\backslash$table$[[\backslash$table$[[$Lateral Deflection at Joint $b,{}_b=\frac{W{L}^3}{3EI}$