In this page we use WeStatiX to calculate a beam resting on a Winkler soil and compare the results with analytical solution. In the Examples and Tutorials section you can find a description of the modeling procedure, together with the model file.
Description of the example
The analysed example is represented in the following figure:
Below are the diagrams obtained for various results.
In particular, the bending moment diagram:
The shear force diagram:
The vertical beam diplacements:
Rotations around cross – section horizontal axis:
Validation
The results obtained with WeStatiX have been validated by comparing them with the analytical solution of the analysed problem which is provided in the work of Colajanni et al. [1]. Below are the diagrams obtained from the analytical solution:
In the following tables the accuracy of the solution provided by WeStatiX is evaluated, checking result values in some significant points of the obtained diagrams:
| TYPE OF RESULT | TARGET VALUE | WESTATIX VALUE | RELATIVE ERROR |
|---|---|---|---|
| Vertical displacement at point B [m] | 0.000985 | 0.000983 | 0,20% |
| Type of result | TARGET value | WESTATIX value | relative error |
|---|---|---|---|
| Rotation at left side of point B [ – ] | 4.92e-4 | 4.91e-4 | 0,20% |
| Rotation at right side of point B [ – ] | 4.15e-4 | 4.11e-4 | 0,96% |
| TYPE OF RESULT | TARGET VALUE | WESTATIX VALUE | RELATIVE ERROR |
|---|---|---|---|
| Maximum negative bending moment [kNm] | 222.52 | 223.83 | 0,59% |
| Maximum positive bending moment [kNm] | 308.51 | 308.75 | 0,07% |
| Bending moment at point D [kNm] | 98.46 | 98.60 | 0,14% |
| TYPE OF RESULT | TARGET VALUE | WESTATIX VALUE | RELATIVE ERROR |
|---|---|---|---|
| Shear force at left side of point B [kN] | 215.02 | 214.32 | 0,33% |
| Shear force at right side of B [kN] | 239.38 | 239.80 | 0,18% |
| Shear force at point D [kN] | 76.96 | 77.07 | 0,14% |
From the comparison it can be seen that WeStatiX passed the validation in an excellent way.
References
[1] COLAJANNI P., FALSONE G., and RECUPERO A. – Simplified formulation for solution of beams on Winkler foundation allowing discontinuities due to loads and constraints, International Journal for Engineering Education, 25, 1, 75-83, 2009.