During the design process for this truss an alternative 'Configuration II$\text{'}$ was also considered. For this truss,

nodes $1,2,3$ and $4$ were pinned to the ceiling and nodes $5$ and $6$ both are are loaded symmetrically by a hopper

weighing $90$ kN as shown in the figure

Figure $2$: Truss Configuration II

Dimensions of truss members:

$\frac{?}{{?}_{215}}\frac{?}{{?}_{346}}==60\frac{,}{{?}_{523}}\frac{?}{{?}_{632}}=\frac{?}{{?}_{25}}==90$

$l(\frac{?}{\text{b}\text{a}\text{r}}(15))=l(\frac{?}{\text{b}\text{a}\text{r}}(23))=l(\frac{?}{\text{b}\text{a}\text{r}}(56))=l(\frac{?}{\text{b}\text{a}\text{r}}(46))=7m$

$A_{\frac{c}{s}}=0\mathrm{.}01m^2$

Elastic Modulus of Truss Members

$E=210$GPa

a$)$ Construct the System Free Body Diagram for the truss $(1$ pts$)$

b$)$ Construct the Elemental Free Body Diagrams for Elements $4,5$ and $6.$ Find the corresponding elemental

stiffness matrices $(3pts)$

c$)$ Find the displacement of the hopper due to deformation of the truss$(1pts)$

d$)$ Find the reaction forces at Nodes $1,2,3$ and $4($in x and y directions$)(2$ pts$)$

e$)$ Find the maximum stress in the truss $(2$ pts$)$