G. Hanswille/M. Bergmann/R. Bergmann · Design of composite columns with cross-sections not covered by Eurocode 4
Fig. 2. Safety concept for non-linear design of composite columns [2], [3]
tion. As shown in Fig. 2, it is necessary to determine the interaction curves for Rpl,m using the mean fi,m or nominal value fi,R of the material strength as well as the curve for the design value Rpl,d using the design values according to Eurocode 4. The partial factors 1.5 for concrete, 1.1 for structural steel and 1.15 for reinforcement have to be used for the interaction curve based on design values. For a given combination of internal forces NEd and MEd, the safety factor LR is then given by the ratio of the vectors Rpl,m and Rpl,d. In a second step, an incremental finite element analysis has to be performed using an initial geometrical bow imperfection and considering residual stresses. It has to be verified that the amplification factor Mu related to the design action effects is greater than the global factor LR according to Fig. 2. The verification has to be performed for the relevant critical cross-section. The stress-strain relation based on the nominal or mean strength values fc,R " fc,m and fs,R " fs,m for concrete and reinforcing steel respectively should be used in the analysis. When calculating LR according to Fig. 2, for simplicity, fc,R may be assumed as being equal to fck for concrete up to strength class C50/60. For determining the mean yield strength of structural steel, fy,R and fs,R may be taken as equal to fyk and fsk respectively. It should be mentioned that in Eurocode 4-1-1 the structural steel contribution ratio I has to be in the range between 0.2 and 0.9 for the general and the simplified methods. This limitation was originally introduced for the simplified method only in order to distinguish composite columns from steel and concrete columns. Using the general method, the I limitation is unnecessary.
2.2 Simplified design method The scope of the simplified method is limited to members with a doubly symmetrical and uniform cross-section over
the member length with rolled, cold-formed or welded steel sections. The method is not applicable if the structural steel component consists of two or more unconnected sections. Furthermore, the relative slenderness λ is limited to 2.0 and the structural steel contribution ratio I has to be in the range 0.2 f I f 0.9. In addition, the method applies to columns and compression members with steel grades S235 to S460 and normal-weight concrete of strength classes C20/25 to C50/60. The resistance to bending can be determined on the basis of the full plastic interaction curve according to Fig. 3, where factor FM mainly takes into account the effects of the reduction in the full plastic resistance to bending due to the strain limitations for concrete. The internal forces have to be determined based on second-order theory using an equivalent elastic flexural stiffness of the cross-section (see Fig. 3). The influence of geometrical and structural imperfections (residual stresses due to welding or rolling) is taken into account by equivalent geometrical bow imperfections according to Fig. 4. Fig. 5 shows a comparison between the resistance determined by the general and the simplified methods for concrete-filled tubes with different relative slenderness values. The figure illustrates that the simplified method leads to results that are in very good agreement with the results of the general method.
3 Typical applications for general method 3.1 General The development of the simplified method in Eurocode 4 was based on columns with cross-sections according to Fig. 1. If the scope of the method is to be extended further to other types of doubly symmetrical cross-sections, some additional aspects should be considered. There are mainly two reasons why the simplified method – even in case of doubly symmetrical cross sections – is not always applica-
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