In this section we want to verify the WeStatiX’s accuracy solving the problem represented in the picture below. It consists of a beam structure with imposed displacement of a supported node.
The data you will need to build it are displayed in the following table. You can also read how to create it in our tutorials.
| Young’s modulus | E | 200000000 | kPa |
| Section | A | 0,04 | \(m^2\) |
| Length | L | 4,00 | m |
| Height | h | 3,00 | m |
| Moment of inertia | J | 1,00E-04 | \(m^4\) |
| Displacement | \(\delta\) | 0,001 | m |
Here is the model created in WeStatiX, as shown in the picture.
As usual you can solve the beam equation in order to find the expression for all the deflection, rotation and the internal forces. In the table below we compare the fundamental results obtained analytically with the numerical results obtained in WeStatiX.
| Description | Parameter | UM | Analytical solution | WSX | Error | |
|---|---|---|---|---|---|---|
| Horizontal reaction in A | \(H_A\) | kN | \(\) | 0,00 | 0,00 | 0,00% |
| Vertical reaction in A | \(V_A\) | kN | \(\) | 8,44 | 8,47 | 0,33% |
| Moment reaction in A | \(M_A\) | kNm | \(\) | 33,89 | 33,89 | 0,00% |
| Vertical reaction in C | \(V_C\) | kN | \(\) | 11,53 | 11,53 | 0,00% |
| Moment reaction in C | \(M_C\) | kN | \(\) | -46,11 | -46,11 | 0,00% |
| Normal force in beam 1 | \(N_1\) | kNm | \(\) | 5,08 | 5,08 | 0,06% |
| Shear force in beam 1 | \(T_1\) | kN | \(\) | -6,78 | -6,78 | 0,04% |
In the following pictures you can see all the numerical results.
