CIVL491 – Applied Finite Element Analysis for Civil Engineers

Practice Problem # 1

Introduction to the Finite Element Method: Spring Elements

The basic concept of the finite element method stems from determining the global stiffness

matrix of a structural system, applying forces and solving for displacements. A structure built

of spring elements can provide a simple, yet instructive way to illustrate this basic concept.

In this assignment, for the spring assemblage shown, apply the finite element method

(manually) to determine the following response parameters:

A. The displacements of all nodes

B. The reaction forces

C. The internal forces in each spring

Then, develop the STRAND7 model to obtain:

D. A printout of the displacements of all nodes

E. A printout of the reaction forces

For the list of students and the problem parameters, see page 2.

Due: This is a non-assessable task

A/Prof Alex Remennikov

2

Results

Student k1

(N/m) k2 k3 F1 (N) F2 F3 Max d Nax N

1 1000 750 500 400 300 200 0.46 290.63

2 1000 750 600 500 300 200 0.35 296.55

3 1000 750 700 600 300 200 0.28 301.60

4 1000 750 800 400 300 200 0.44 261.39

5 1000 750 500 500 300 200 0.38 309.38

6 1100 750 600 600 300 200 0.31 316.93

7 1100 750 700 400 300 200 0.43 272.16

8 1100 750 800 500 300 200 0.35 279.02

9 1100 750 500 600 300 200 0.34 331.21

10 1100 750 600 400 300 200 0.43 281.79

11 1200 850 700 500 300 300 0.41 313.41

12 1200 850 800 600 300 300 0.35 318.93

13 1200 850 500 400 300 300 0.56 319.67

14 1200 850 600 500 300 300 0.46 325.54

15 1200 850 700 600 300 300 0.38 330.61

16 1000 850 800 400 300 300 0.46 318.87

17 1000 850 500 500 300 300 0.53 333.52

18 1000 850 600 600 300 300 0.44 337.11

19 1000 850 700 400 300 300 0.48 309.44

20 1000 850 800 500 300 300 0.39 303.45

21 1100 750 500 600 400 200 0.46 390.75

22 1100 750 600 400 400 200 0.66 340.58

23 1100 750 700 500 400 200 0.56 346.59

24 1100 750 800 600 400 200 0.48 351.79

25 1100 750 500 400 400 200 0.70 352.60

26 1200 750 600 500 400 200 0.55 360.71

27 1200 750 700 600 400 200 0.46 365.75

28 1200 750 800 400 400 200 0.61 323.71

29 1200 750 500 500 400 200 0.56 374.19

30 1200 750 600 600 400 200 0.45 378.57

31 1100 850 700 400 400 300 0.67 352.03

32 1100 850 800 500 400 300 0.57 357.81

33 1100 850 500 600 400 300 0.57 416.30

34 1100 850 600 400 400 300 0.70 363.56

35 1100 850 700 500 400 300 0.58 368.93

36 1300 850 800 400 300 300 0.42 310.95

37 1300 850 500 500 300 300 0.52 342.09

38 1300 850 600 600 300 300 0.42 346.82

39 1300 850 700 400 300 300 0.44 301.50

40 1300 850 800 500 300 300 0.37 305.40

41 1100 750 600 500 400 200 0.57 358.15

42 1100 750 700 600 400 200 0.47 362.88

43 1100 750 800 400 400 200 0.62 321.44

44 1100 750 500 500 400 200 0.58 371.68

45 1100 750 600 600 400 200 0.47 375.72