Let us consider the following structures:

 

 

In calculation we assume that

 

Now let’s assume that the forces change in 5%.

 

P1= P1 ± 2.5%

P2= P2 ± 2.5%

P3= P3 ± 2.5%

 

If we calculate the relative error of axial forces

 

 

then we will get the following results:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


We can see that in some cases the relative error

of calculation is grater than 100%.

 

The extreme values of axial forces can be calculated using the following ANSYS APDL files:

 

truss1.lgw (results are in the following file: axial1.lis)

 

truss2.lgw  (results are in the following file: axial2.lis)

 

truss3.lgw (results are in the following file: axial3.lis)

 

The results for the cross-section A=0.0025 [m^2]

 

 

 

 

Stress

 

 

 

 

 

Case1 [Pa]

Case2 [Pa]

Case3 [Pa]

Min [Pa]

Max [Pa]

Width [Pa]

Relative error %

1

-6.48E+05

-3.13E+05

-9.83E+05

-9.83E+05

-3.13E+05

6.70E+05

1.03E+02

2

-2.72E+05

-1.71E+05

-3.74E+05

-3.74E+05

-1.71E+05

2.04E+05

7.47E+01

3

-3.27E+05

-3.75E+05

-2.78E+05

-3.75E+05

-2.78E+05

9.68E+04

2.97E+01

4

-9.29E+05

-1.12E+06

-7.34E+05

-1.12E+06

-7.34E+05

3.89E+05

4.19E+01

5

3.79E+05

3.45E+05

4.13E+05

3.45E+05

4.13E+05

6.76E+04

1.78E+01

6

-7.31E+05

-4.98E+05

-9.63E+05

-9.63E+05

-4.98E+05

4.65E+05

6.37E+01

7

-2.09E+05

-1.13E+05

-3.05E+05

-3.05E+05

-1.13E+05

1.92E+05

9.20E+01

8

-2.63E+05

-3.17E+05

-2.09E+05

-3.17E+05

-2.09E+05

1.08E+05

4.10E+01

9

-9.35E+05

-1.02E+06

-8.51E+05

-1.02E+06

-8.51E+05

1.69E+05

1.80E+01

10

3.43E+05

3.12E+05

3.73E+05

3.12E+05

3.73E+05

6.05E+04

1.77E+01

11

-7.60E+05

-6.34E+05

-8.86E+05

-8.86E+05

-6.34E+05

2.52E+05

3.32E+01

12

-2.21E+05

-1.25E+05

-3.18E+05

-3.18E+05

-1.25E+05

1.94E+05

8.74E+01

13

-2.76E+05

-3.29E+05

-2.22E+05

-3.29E+05

-2.22E+05

1.07E+05

3.87E+01

14

-8.88E+05

-8.67E+05

-9.10E+05

-9.10E+05

-8.67E+05

4.29E+04

4.82E+00

15

3.12E+05

2.82E+05

3.42E+05

2.82E+05

3.42E+05

6.06E+04

1.94E+01

16

-8.38E+05

-8.18E+05

-8.58E+05

-8.58E+05

-8.18E+05

4.05E+04

4.84E+00

17

-1.65E+05

-69155

-2.62E+05

-2.62E+05

-6.92E+04

1.92E+05

1.16E+02

18

-2.20E+05

-2.74E+05

-1.66E+05

-2.74E+05

-1.66E+05

1.08E+05

4.91E+01

19

-8.90E+05

-7.62E+05

-1.02E+06

-1.02E+06

-7.62E+05

2.56E+05

2.88E+01

20

6.46E+05

6.13E+05

6.79E+05

6.13E+05

6.79E+05

6.68E+04

1.03E+01

21

-5.03E+05

-5.92E+05

-4.13E+05

-5.92E+05

-4.13E+05

1.79E+05

3.56E+01

22

-6.94E+05

-5.93E+05

-7.95E+05

-7.95E+05

-5.93E+05

2.02E+05

2.92E+01

23

-7.48E+05

-7.97E+05

-6.99E+05

-7.97E+05

-6.99E+05

9.80E+04

1.31E+01

24

-4.77E+05

-2.47E+05

-7.08E+05

-7.08E+05

-2.47E+05

4.61E+05

9.66E+01

25

-2.55E+06

-2.55E+06

-2.55E+06

-2.55E+06

-2.55E+06

6.90E+03

2.71E-01

26

-1.12E+05

-1.74E+05

-49399

-1.74E+05

-4.94E+04

1.24E+05

1.11E+02

27

-1.30E+06

-1.39E+06

-1.21E+06

-1.39E+06

-1.21E+06

1.75E+05

1.35E+01

28

1.58E+05

2.46E+05

69861

6.99E+04

2.46E+05

1.76E+05

1.11E+02

29

4.87E+05

6.16E+05

3.58E+05

3.58E+05

6.16E+05

2.57E+05

5.29E+01

30

-1.12E+05

-1.74E+05

-49399

-1.74E+05

-4.94E+04

1.24E+05

1.11E+02

31

-1.36E+06

-1.34E+06

-1.38E+06

-1.38E+06

-1.34E+06

3.79E+04

2.78E+00

32

-2.22E+06

-2.06E+06

-2.37E+06

-2.37E+06

-2.06E+06

3.15E+05

1.42E+01

33

6.12E+05

5.18E+05

7.07E+05

5.18E+05

7.07E+05

1.89E+05

3.09E+01

34

-1.46E+06

-1.52E+06

-1.41E+06

-1.52E+06

-1.41E+06

1.14E+05

7.81E+00

35

-8.66E+05

-8.31E+05

-9.02E+05

-9.02E+05

-8.31E+05

7.09E+04

8.19E+00

36

-1.46E+06

-1.36E+06

-1.57E+06

-1.57E+06

-1.36E+06

2.02E+05

1.38E+01

37

-2.22E+06

-2.28E+06

-2.15E+06

-2.28E+06

-2.15E+06

1.32E+05

5.97E+00

38

6.12E+05

6.57E+05

5.68E+05

5.68E+05

6.57E+05

8.88E+04

1.45E+01

39

-1.36E+06

-1.44E+06

-1.28E+06

-1.44E+06

-1.28E+06

1.59E+05

1.16E+01

40

4.87E+05

3.86E+05

5.88E+05

3.86E+05

5.88E+05

2.01E+05

4.14E+01

41

-1.12E+05

-48622

-1.75E+05

-1.75E+05

-4.86E+04

1.26E+05

1.13E+02

42

-1.30E+06

-1.20E+06

-1.40E+06

-1.40E+06

-1.20E+06

1.96E+05

1.51E+01

43

1.58E+05

68762

2.47E+05

6.88E+04

2.47E+05

1.78E+05

1.13E+02

44

-2.55E+06

-2.56E+06

-2.54E+06

-2.56E+06

-2.54E+06

1.43E+04

5.61E-01

45

-1.12E+05

-48622

-1.75E+05

-1.75E+05

-4.86E+04

1.26E+05

1.13E+02

46

-4.77E+05

-6.32E+05

-3.23E+05

-6.32E+05

-3.23E+05

3.09E+05

6.47E+01

47

-6.94E+05

-7.73E+05

-6.15E+05

-7.73E+05

-6.15E+05

1.58E+05

2.28E+01

48

-7.48E+05

-6.95E+05

-8.02E+05

-8.02E+05

-6.95E+05

1.07E+05

1.43E+01

49

-5.03E+05

-4.08E+05

-5.97E+05

-5.97E+05

-4.08E+05

1.89E+05

3.76E+01

50

6.46E+05

6.62E+05

6.31E+05

6.31E+05

6.62E+05

3.11E+04

4.82E+00

51

-8.90E+05

-9.53E+05

-8.26E+05

-9.53E+05

-8.26E+05

1.27E+05

1.42E+01

52

-1.65E+05

-2.41E+05

-89929

-2.41E+05

-8.99E+04

1.51E+05

9.13E+01

53

-2.20E+05

-1.62E+05

-2.77E+05

-2.77E+05

-1.62E+05

1.14E+05

5.21E+01

54

-8.38E+05

-8.40E+05

-8.36E+05

-8.40E+05

-8.36E+05

3.87E+03

4.62E-01

55

3.12E+05

3.25E+05

2.99E+05

2.99E+05

3.25E+05

2.64E+04

8.47E+00

56

-8.88E+05

-8.58E+05

-9.19E+05

-9.19E+05

-8.58E+05

6.15E+04

6.92E+00

57

-2.21E+05

-2.97E+05

-1.46E+05

-2.97E+05

-1.46E+05

1.52E+05

6.85E+01

58

-2.76E+05

-2.19E+05

-3.32E+05

-3.32E+05

-2.19E+05

1.14E+05

4.12E+01

59

-7.60E+05

-8.56E+05

-6.65E+05

-8.56E+05

-6.65E+05

1.91E+05

2.51E+01

60

3.43E+05

3.56E+05

3.29E+05

3.29E+05

3.56E+05

2.66E+04

7.76E+00

61

-9.35E+05

-8.11E+05

-1.06E+06

-1.06E+06

-8.11E+05

2.49E+05

2.66E+01

62

-2.09E+05

-2.85E+05

-1.33E+05

-2.85E+05

-1.33E+05

1.51E+05

7.23E+01

63

-2.63E+05

-2.06E+05

-3.20E+05

-3.20E+05

-2.06E+05

1.14E+05

4.34E+01

64

-7.31E+05

-9.20E+05

-5.41E+05

-9.20E+05

-5.41E+05

3.79E+05

5.19E+01

65

3.79E+05

3.94E+05

3.64E+05

3.64E+05

3.94E+05

2.96E+04

7.82E+00

66

-9.29E+05

-7.09E+05

-1.15E+06

-1.15E+06

-7.09E+05

4.40E+05

4.73E+01

67

-2.72E+05

-3.50E+05

-1.94E+05

-3.50E+05

-1.94E+05

1.56E+05

5.73E+01

68

-3.27E+05

-2.72E+05

-3.81E+05

-3.81E+05

-2.72E+05

1.09E+05

3.35E+01

69

-6.48E+05

-9.29E+05

-3.66E+05

-9.29E+05

-3.66E+05

5.63E+05

8.69E+01