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 |
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