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009955
2024-03-15

VE9955 | Verzweigungslastfaktor und Knicklängen eines Rahmentragwerks

Description

A restrained frame with two additional hinged columns is loaded by vertical concentrated loads. The governing critical load factor must be calculated for the structural system and the respective effective lengths must be determined for the restrained frame posts.

Eingabeparameter and structural System

Modulus of Elasticity< style="font-family:Arial, sans-serif;font-size:16px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden; break:normal;background-color:#bfcfeb" rowspan="2">Cross-Section Parameters style="font-family:Arial, sans-serif;font-size:16px;padding:10px 5px;border-style:solid;border-width:1px;overf." low:hidden;word-break:normal;background-color:#cbdbf2">Bending Stiffness - Beam font-size:16px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal">kNcm2Height style="font -family:Arial, sans-serif;font-size:16px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;background-color:#cbdbf2"> Hinged Column 1
Material ParametersE210000N/mm2 EIS 8045,1kNcm2 EIR 1825,53
GeometryspanlR m
l=l1 =l2 4.5m
LoadsStrain 1Nle 120kN
Stainless Steel 2Nre 80F1 50kN
Hinged Column 2F2 60kN

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 allowable.

Compar Analytical Solution with RFEM Solution

Analytical Solution overflow:hidden;word-break:normal;background-color:#bfcfeb">RFEM 6Ratio
f10.252410.085 Lcr,li 8.0336 m8,100 mLcr,re 9,8392 m9.920 m''' td>0.992

The results between the manual calculation and RFEM 6 correspond very well. The relative deviations are less than 2%.

References

[1] ALBERT, Andrej; ua: Construction tables for engineers – with calculation notes and
examples. 23 ed. Nördlingen