Case 04 — Statically Indeterminate Truss Under Concentrated Loads
A symmetrical planar truss structure is subjected to vertical loads applied at selected joints. The structure is supported at both ends and modeled using truss elements only. This verification case validates the correct calculation of internal axial forces in truss elements subjected to symmetrical vertical loading.
Description
Consider the symmetrical truss shown in the figure. The structure is subjected to two equal vertical loads P=120 kN applied at the indicated joints. All members have the same axial stiffness EA.
Determine:
- Axial forces in all truss members.
Structural scheme
Geometry, boundary conditions, and load applications used in the verification model.
Model parameters
| Parameter | Value |
|---|---|
| Element type | Truss element |
| Material | Steel |
| Young's modulus | 2.0 × 10⁸ kN/m² |
| Section properties | A = 0.1 m² |
| Boundary conditions | Node 0: Ux, Uy restrained; Node 6: Uy restrained; Node 4: Uy restrained |
| Loads | Concentrated load −120 kN applied at nodes 5 and 7 in the Y direction |
Numerical results
Axial Forces
Table results from RodX
Comparison (kN)
| Rod | Analytical solution | RodX | Midas/Civil |
|---|---|---|---|
| 1 | 63.710 | 63.849 | 63.849 |
| 2 | 63.710 | 63.849 | 63.849 |
| 3 | 63.710 | 63.849 | 63.849 |
| 4 | 63.710 | 63.849 | 63.849 |
| 5 | 32.430 | 32.303 | 32.303 |
| 6 | 32.430 | 32.303 | 32.303 |
| 7 | -79.750 | -79.811 | -79.811 |
| 8 | -120.250 | -120.189 | -120.189 |
| 9 | -120.250 | -120.189 | -120.189 |
| 10 | -79.750 | -79.811 | -79.811 |
| 11 | 120.000 | 120.000 | 120.000 |
| 12 | 0.0 | 0.0 | 0.0 |
| 13 | 120.000 | 120.000 | 120.000 |
The numerical results obtained with RodX are in agreement with the analytical solution and reference FEA results.
Reference
- Karnovsky I.A, Lebed O. Advanced Methods of Structural Analysis, Springer, 2010, p. 235.