Problem 2: FEA Truss (20 Points)

Consider the truss structure shown below. All truss members are considered linear elastic, with a

rod diameter of 40 mm. The material is steel (E = 210 GPa). Place the origin of coordinate system at

Node 1 with x to the right and y to the top. The structure is loaded with forces P1 = 20 kN at Node 7

and P2 = 10 kN at Node 5. Follow the same numbering scheme used for nodes and elements as show

in the figure. The nodal coordinate positions in meters:

b)

c)

d)

e)

3

f)

10 KN

11

(10)

20 KN

60⁰

Node

1

2

3

4

5

6

7

XOONNTT6

X

2

2

TO

Y

4.5

1.5

4.5

3

4.5

a) What is the total degree of freedom of the system? What is the size of the global stiffness

matrix and force vector?

44

4.5

Determine the stiffness matrix for element 10.

Assemble the stiffness matrix of element 10 into the global stiffness matrix (i.e., which rows

and columns do these components go?)

What are the known values of the global displacement vector d and force vector f?

Explain the procedure to obtain reduced stiffness matrix. What is the size of the reduced

stiffness matrix?

Briefly describe the steps to solve the system once you have reduced the stiffness matrix.

What are the unknowns that we solve for in FEA? How do we solve for the reaction forces?