Mz=3.34KN.m [up lift]

My=0.9$\times\frac{wdy\times l^{2}}{8}=0.9\times\frac{0.19\times 4^{2}}{8}$

My-0.342 KN.M

using E=2G[1+$\mu$].....Take $\mu$=0.3]

2$\times 10^{5}$=2g[1+0.3]

G=76.92$\times 10^{3}N/mm^{2} $ Mpa

hy=[100-6.4]=93.6mm

$I_{b}=\sum\frac{b.t^{3}}{3}$

=$\frac{2\times500\times 6.4^{3}}{3}+\frac{93.6\times4^{3}}{3}$

It=10.73$\times 10^{3}$

Iw=[1-$\beta_{f}]\beta_{f}\times Iy\times hy^{2}..... \beta_{F}=0.5]$

=[1-0.5]$\times0.5\times24.8\times10^{4}\times93.6^{2}$

=543.18$\times 10^{6}$

LLT=4000mm

Mc0=$\sqrt{(\frac{\pi^{2}EIy}{(LLT)^{2}})[GIe+\frac{\pi^{2}EIw}{(LLT)^{2}}]}$

=5.23$\times10^{6}$ N...

$\lambda LT=\sqrt{\beta_{b}\times Z_{p}fy/Mcr}\leq \sqrt{1.2Z_{c}\times fy/Mcr}$

=1.35$\leq$1.37

safe

$\phi_{lt}=0..4[1+\alpha LT(\lambda LT-0.2)+\lambda LT^{2}]$=1.53

$\kappa_{LT}=\frac{1}{\phi_{LT}+[\phi^{2}_{LT}-\lambda^{2}_{LT}]^{0.5}}$=0.44

fing =$\kappa _{LT}\times\frac{fy}{\gamma mo}$=100MPa

Mdz=B$_{b}Z_{p}\times fdb$

=1$\times 3.809\times 10^{6}$ Nmm

=3.809$\times 10^{4}$ N.mm

using interaction equation

$\frac{Mz}{Mdz}+\frac{My}{Mdy}\leq$ 1

$\frac{3.34}{3.81}+\frac{0.342}{1.92}\leq$ 1

1.05$\leq$ 1 unsafe

C] Design of Bottom member [L$_{1}, L_{2}]$

Reaction

Using method of joint (L$_{1}, L_{2})$

=0($\uparrow$=$\downarrow$)

sin 30=1

=-10KN

EH=0$(\rightarrow)$

L$_{1}L_{2}$+L$_{1}U_{1}$

cos 30$^{\circ}$=0

L$_{1}L_{2}$=8.66 kN(T)

$\sum v=0(\uparrow=\downarrow)$

4.8+L$_{1}u_{1}sin 30^{\circ}$=0.8

L$_{1}u_{1}$=-8kN

$\epsilon H=0(\rightarrow=\leftarrow)$

L$_{1}L_{2}+L_{1}U_{1}cos 30^{\circ}$

L$_{1}L_{2}=6.93KN(T)$

$\sum V=0(\uparrow=\downarrow)$

L$_{1}U_{1} $sin 30 +1.62 30

60$^{\circ}$=13.60

L$_{1}U_{1}$=22.66K(T)

$\sum H=0(\rightarrow=\leftarrow)$

L$_{1}L=+L_{1}U_{1}$ cos 30=2.62 cos 30

L$_{1}L_{2}$=-18.32L[c}]