Description
A restrained frame with two additional hinged columns is loaded by vertical concentrated loads. It is necessary to calculate the governing critical load factor for the structural system and to determine the respective effective lengths for the restrained frame posts.
Eingabeparameter and Structural System
| Material Parameters | Modulus of elasticity | E | 210000 | N/mm² |
| Cross-Section Parameter | Bending stiffness of posts | E_IS | 8,045.1 | kNcm² |
| Bending stiffness of beam | E_IR | 1,825.53 | kNcm² | |
| Geometry | Span | l_R | 8.0 | m |
| Height | l=l1=l2 | 4.5 | m | |
| Loads | Post 1 | N_li | 120 | kN |
| Post 2 | N_re | 80 | kN | |
| Hinged Column 1 | F1 | 50 | kN | |
| Hinged Column 2 | F2 | 60 | kN |
Analytical Solution
The analytical solution uses the approximate formulas according to [1] for frames with restrained footings.
The critical load factor is greater than 10, so the calculation of internal forces according to the linear static analysis in compliance with EC 3‑1‑1 would be possible.
Vergleich Analytical Solution with RFEM-Lösung
| Comparison Value | Analytical Solution | RFEM 6 | Ratio |
|---|---|---|---|
| f | 10.2524 | 10.085 | 1.017 |
| Lcr,li | 8.0336 m | 8.100 m | 0.992 |
| Lcr,re | 9.8392 m | 9.920 m | 0.992 |
The results between the manual calculation and RFEM 6 correspond very well. The relative deviations are less than 2%.
References
[1] Albert, A., et al. (2018). Bautabellen für Ingenieure – mit Berechnungshinweisen und
examples, 23rd ed. Nördlingen.