Use the finite element approach $($the "element formulation" approach$)$ to solve for displacements

and stresses in the structure shown in Figure $1.$ All dimensions are in inches. Young's modulus

of the material is $E=30{10}^{6}l\frac{b}{i}{n}^2.$ The left end face of the structure is fixed in space, and the

right end face is loaded with a force of $10,000lbf$ in the $+x$ direction. The structure is modeled as

a connected spring system in Figure $2.$ Use the node and element numberings in Figure $2.($Node

numbers in circles, element numbers in square.$)$

Report the following:

a$)$ List the element stiffness matrices for all elements.

b$)$ List the global stiffness matrix before imposing the displacement boundary conditions.

c$)$ List the global stiffness matrix after imposing the displacement boundary conditions.

d$)$ List the global force vector after imposing the displacement boundary conditions.

e$)$ List the nodal displacement solutions.

f$)$ Calculate the stresses for all elements.

g$)$ Fill in the blanks in the following table:

Hints:

After the nodal displacements are obtained, use the $2$ nd element stiffness equation to calculate

the force $f_{\text{r}\text{i}\text{g}\text{h}\text{t}\text{n}\text{o}\text{d}\text{e}}$ on each spring from the right end node. The axial stress in the element

$($spring$)$ is simply

$=\frac{f_{\text{r}\text{i}\text{g}\text{h}\text{t}\text{n}\text{o}\text{d}\text{e}}}{A}$

The answers can be all done in excel, please show the spreadsheet with the excel doc and formulas used.