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009955
2024-03-15

VE9955 | Critical Load Factor and Effective Lengths of Frame Structure

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.