Comparing the Stability Analysis of a Column Containing Internal Forces from Load Combinations with an Enveloping Result Combination

Technical Article

This example will show what you should consider when you perform column design for bending and compression with regard to the internal forces from load combinations and result combinations.

General

Calculating structures as 3D models is the general practice in today's structural analysis and design. It considers many variable loads such as wind, snow, imposed loads, and possibly alternative moving loads. This generates a large number of load combinations, which also have to be considered for the stability analysis of a steel column.

The following example compares the results of the stability analysis "Bending and compression" according to EN 1993-1-1 Chapter 6.3.3 with regard to the internal forces from load combinations and an enveloping result combination. The different options available in the RF-/STEEL EC3 add-on module will be explained.

A corner column of a steel hall will be designed. The hinged column has a height of 10.85 m and receives horizontal loads from connected trusses at a height of 8.20 m. Only three load combinations from seven load cases and one result combination will be considered.

The original structural model has more than 340 load combinations for the ultimate limit state. Not all seven load cases will be listed separately. They were determined as governing from the entire structural analysis and are contained in the attached example file. To simplify, partial safety factors and combination factors have been deliberately omitted. The loads have to be considered as design loads.

Cross-section:
2IK HEM 800 + HE M 800 | - + DIN 1025-4:1994

Material:
Steel S 355 | DIN EN 1993-1-1:2010-12

CO1 = LC1 + LC2 + LC3
CO2 = LC1 + LC4 + LC5
CO3 = LC1 + LC6 + LC7

Result combination:
RC1 = CO1/s or CO2/s or CO3/s

Figure 02 shows the internal forces N, My, and Mz of CO2. According to EN 1993-1-1 Chapter 6.3.3, Equation 6.6.2, these three internal forces result in the maximum design ratio of 92%. In this stability analysis on the equivalent member, interaction factors are used. According to [1] Chapter 6.2.2 (2) Note 1, the interaction formulas are based on the model of a single-span beam with lateral and torsional restraints, with or without intermediate support, which is subjected to compression forces, boundary moments, and/or lateral loads. By applying Table A.2 of [1], the actual moment distribution is taken into account when determining the interaction factors.

Figure 03 shows how the moment distribution for My and Mz of CO2 is classified in RF- STEEL EC3 and the equivalent moment factors Cmi,0 are determined according to Table A.2 of [1].

Looking at the detailed results evaluation for the stability analysis in Figure 04, it is clearly evident that the axial force hardly plays a role and the bending moments are decisive for the maximum design ratio.

Stability Analysis with Result Combination (Envelope)

To save time during the calculation, you can set the type of calculation for result combinations of the type OR to the second option in the "General" tab at "Details" in RF-/STEEL EC3 during the design phase. It should be clarified here that the enveloping internal forces are used for performing the stability analysis when this option is selected. Figure 05 shows the governing max./min. results for the result combination 1.

Another important point is the determination of interaction factors. Since the moment distribution of an enveloping result combination represents a maximum or minimum value for each x-location, no real moment distribution can be expected here. Therefore, a linear moment distribution with ψ = 1 will be used. See also Figure 06.

The detailed result evaluation of the stability analysis for the result combination 1 as an envelope shows an obvious disadvantage of this method. Since the absolute extreme values are assumed for the bending moments and not the corresponding moments, this result falls well within the safe range. The maximum My = 1,752.42 kNm belongs to CO2 and the minimum Mz = -2,543.51 kNm belongs to CO3. The conservative solution with the envelope results to a ratio of 131%.

Stability Analysis with Result Combination (Default)

If you set the type of calculation for result combinations of the type OR to the first option, which is also the default setting, at "Details" in the "General" tab of RF-/STEEL EC3, the results are comparable to those of the individual LCs.

Summary

The example shown here is a practical example and has the aim to explain the options for a quick calculation, but also what are the limitations when using enveloping results.

Reference

 [1] Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12