$[1]$ Problem $1$:

A $2$D truss has been built on a ceiling supporting a heavy industrial hopper The configuration I has three pinned

nodes $(1,2$ and $3).$ Nodes $4$ and $5$ are loaded symmetrically by a hopper weighing $90$ kN as shown in the figure

Figure $1$: iruss Conngurauon $1$

Dimensions of truss members:

$l(\frac{?}{\text{b}\text{a}\text{r}}(12))=l(\frac{?}{\text{b}\text{a}\text{r}}(23))=l(\frac{?}{\text{b}\text{a}\text{r}}(14))=l(\frac{?}{\text{b}\text{a}\text{r}}(24))=l(\frac{?}{\text{b}\text{a}\text{r}}(25))=l(\frac{?}{\text{b}\text{a}\text{r}}(35))=l(\frac{?}{\text{b}\text{a}\text{r}}(45))=7m$

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

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 $1,4$ and $7.$ Find the corresponding elemental

stiffness matrices$(3pts$

c$)$ Find the displacement of the hopper due to deformation of the truss$(2pts)$

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

e$)$ Find the elemental forces for Elements $1,4$ and $7(3$ pts$)$

f$)$ Find the maximum stress in the truss $(3$ pts$)$