5216x

001635

Dipl.-Ing. (FH) Stefan Frenzel

2020-05-26

Calculating Effective Lengths on Example of Double-Story Frame

With the RF-STABILITY and RSBUCK add-on modules for RFEM and RSTAB, it is possible to perform eigenvalue analyses for member structures in order to determine the effective length factors. The effective length coefficients can then be used for the stability design.

The following example determines the effective lengths for a double-story frame. These coefficients will be compared to the manual calculation. To do this, an example from technical literature will be used.

In this example, the structure consists of a frame structure where all beams should consist of one HEB 300 and all columns of one HEB 200 for simplification.

Model Description

To determine the effective lengths, we use the effective length table from the German book Statik und Stabilität der Baukonstruktion [1]. The input parameters for using this table are determined below.

y = 6 \cdot \frac{I_{Beam}}{I_{Column}} \cdot \frac{l_{Column 1}}{l_{Beam}} = \frac{25, 170}{5, 700} \cdot \frac{5.00}{10.00} = 13.23; \frac{1}{y} = 0.076 \approx 0.1

χ = E \cdot \frac{I_{Column 1}}{I_{Column 2}} \cdot \frac{l_{2}}{l_{1}} = 1 \cdot \frac{4.00}{5, 00} = 0.80

κ = \frac{N_{2}}{N_{1}} \cdot \frac{l_{2}}{l_{1}} = \frac{80}{200} \cdot \frac{4.00}{5.00} = 0.320

Input parameters for determination of effective lengths

For equally high loading of both columns, the table shows a β' of 1.1. We now have to convert this value to the individual columns by means of weighting factors.

m = \frac{160}{200} = 0.80

β_{1} = \sqrt{0.5 \cdot (1 m)} \cdot β' = \sqrt{0.5 \cdot (1 0.80)} \cdot 1.1 = 1.05

β_{2} = \frac{β_{1}}{\sqrt{χ \cdot κ}} = \frac{1.05}{\sqrt{0.80 \cdot 0.32}} = 2.07

Weighting Factors

If you now calculate this structure with RF-STABILITY or RSBUCK, you also get the effective length factors in the module for the individual columns in the first mode shape.

Results

Knowledge Base

KB 001635 | Calculating Effective Lengths on Example of Double-Story Frame

Author

Mr. Frenzel is responsible for developing products for dynamic analysis. He also provides technical support for customers of Dlubal Software.

Links

Stability Analysis Software

References

Osterrieder, P., & Richter, S. (2002). Kranbahnträger aus Walzprofilen, (2nd ed.). Wiesbaden: Vieweg & Sohn.
Petersen, C. (1982). Statik und Stabilität der Baukonstruktionen, (2nd ed.). Wiesbaden: Vieweg.

Downloads

Model of Technical Article | RFEM 5 File

536 KB

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