In this page we compare the analytical results with the ones obtained with WeStatiX for the system represented below: it is a continuous beam with constrained rotation and release of vertical displacement under a point load.
In the table you can read the data you need to build the model. We also explain hot to do it in our tutorials.
| Young’s modulus | E | 1,00 | kPa |
| Section | A | 0,01 | \(m^2\) |
| Length | L | 1,00 | m |
| Moment of inertia | J | 1,00 | \(m^4\) |
| Load | P | -1,00 | \(kN\) |
Here is the FE model: it can be found in the WeStatiX library
As in the previous examples we want to prove the accuracy of WeStatiX comparing the analytical solution (you can get with the beam equation) with the numerical one. We do it in the table below.
| Description | Parameter | UM | Analytical solution | Analytical solution | WSX | Error |
|---|---|---|---|---|---|---|
| Rotation in A | \(\phi_{A}\) | rad | \(3PL^2/28EJ\) | 0,10714 | 0,10715 | 0,00% |
| Rotation in B | \(\phi_B\) | rad | \(3PL^2/14EJ\) | -0,21429 | -0,21429 | 0,00% |
| Rotation in C | \(\phi_C\) | rad | \(5PL^2/14EJ\) | -0,35714 | -0,35716 | 0,01% |
| Vertical displacement in C (left) | \(v_c^{l}\) | m | \(31PL^3/84EJ\) | -0,36905 | -0,36906 | 0,00% |
| Vertical displacement in C (right) | \(v_c^{r}\) | m | \(5PL^3/28EJ\) | 0,17857 | 0,17860 | 0,02% |
| Bending moment in C | \(M_C\) | kNm | \(5PL/14\) | 0,35714 | 0,35713 | 0,00% |
| Shear force in A | \(T_A\) | kN | \(9P/14\) | 0,64286 | 0,64287 | 0,00% |
| Shear force in C | \(T_C\) | kN | \(1P/1\) | -1,00000 | -1,00000 | 0,00% |
Here are some screeshots of the results for you to see.
