Bending moment in class 3 sections S235

The results for the maximum bending moment capacity were plotted against the increasing slenderness for flange and web in Figure 49, and Figure 50 respectively. The graphs of the total test population were presented in APPENDIX XXIII. In Figure 49, the increasing flange slenderness showed a quadratic decline up to the border of class 3 (λf=10), and subsequently, appeared to continue to decline linearly.

Figure 49-Limit values of the bending moment capacity for increasing λf in S235

In Figure 50, the increasing web slenderness caused a steep decline for the bending moment capacity between λw=35 and λw=72. Subsequently, the steep decrease appeared to level out between λw=82 and λw=121. In contrary to the quadratic shape for λf in Figure 49, the shape of the graphs for λw in Figure 50 were more similar to a cubic function.

Figure 50-Limit values of the bending moment capacity for increasing λw in S235

The graphs of Figure 49 and Figure 50 both illustrate that the bending moment capacity was dependent on a combination of λw λf, and cannot be determined with a single slenderness parameter. If the bending moment capacity is determined with a single slenderness nonetheless, both Figure 49 and

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Comparison with design rules with a single slenderness parameter λ in class 3

To compare the results for the bending moment capacity with EN 1993-1-1, CL. 5.5 and AM-1-1-2012-02 the bending moment capacity was rescaled with (M-Mel)/(Mpl-Mel). This scale is based on Mel=0 to Mpl=1. First, the results with a single slenderness parameter in the class 3 range were evaluated.

Both Figure 51 and Figure 52 indicate EN 1993-1-1, CL. 5.5 is a conservative method, except for (λw=72 λf=14). Moreover EN 1993-1-1, CL. 5.5 does not seem to describe the physical behavior of buckling, and confirms AM-1-1-2012-02 was correct to propose an alternative method. However, except from λf=4, AM-1-1-2012-02 does not lead to safe design capacities. Moreover, the linear interpolation from Mpl to Mel does not fit the curves of the results either. The results in both Figure 51 and Figure 52 illustrate both slenderness parameters influence the bending moment capacity, even though one of them is not class 3. Physically this is a logical result, i.e., even though a class 1 or 2 plate might not buckle itself, it restrains the plate that does buckle. Both slenderness parameters contribute to the overall buckling resistance of a member. Therefore, both AM-1-1-2012-02 and EN 1993-1-1, CL. 5.5 are unsuitable methods to describe the physical behavior of buckling properly.

Figure 51- Limit values of the bending moment capacity reduced for λf compared to design codes Class in 3

Figure 52-Limit values of the bending moment capacity reduced for λw compared to design codes Class in 3 -0,2

Comparison with design rules with both slenderness parameter λf and λw in class 3

The results for λf and λw both in class 3 and corresponding design codes are illustrated in Figure 56 and Figure 57. Both figures illustrate EN 1993-1-1, CL. 5.5 overall gives conservative results if either λf or λw

is in the class 3 range, similar to Figure 51, and Figure 52. However, if λf and λw are both in the class 3 range the elastic bending moment capacity is not achieved and EN 1993-1-1, CL. 5.5 overestimates the bending moment capacity. As was stated in the problem statement, Eurocode 3 defines Class 3 sections as:

‘class 3 cross-section are cross-sections in which the elastic moment can be reached, yet local buckling prevents the development of a plastic moment’

According to this definition, the borders of class 3 for λw and λf are currently overestimated. In AM-1-1-2012-03 it was already proposed to reduce the border of λw, class4 from 124, to 121. However, the results in Figure 57 indicate λw=121 does not ensure the elastic bending moment is obtained either.

Therefore, the proposal in AM-1-1-2012-03 cannot be regarded as a safe limit value. To ensure an elastic bending moment is obtained for class 3 sections, either the boundaries for class 3 must be reduced to λf=9 and λw=65, as is illustrated in Figure 56 and Figure 57. Or alternatively, the class 3 border must be described by a combination of λf λw.

To illustrate this effect the results were 3D plotted on a scale of (M-Mel)/(Mpl -Mel), for λw and λf. Subsequently, the graph is cut of at Mel, representing the border of class 3 to 4. In Figure 55 the cutting plane of Mel is visible in the upper right corner. The actual border of class 3-4 seems to be a convex function for λw and λf. Points on these cutting planes can be subsequently curve fitted to define the boundaries of class 3.

The border of class 2-3, i.e., the slenderness for which a plastic moment can be obtained seems to be defined by a similar convex function. However, it passes through the range that is currently defined as class 2 which was not in the test population. Therefore, too little data was available to confirm this assumption.

From Figure 55 it could be concluded that the class 3 border was best described by both λw and λf. The use of both slenderness parameters would lead to a more economic design compared to straightforwardly using λf=9 and λw=65.

Figure 53-Limit values for the bending moment with respect to λf λw with class 3 borders and Mel 3D view

Figure 54-Limit values for the bending moment with respect to λf λw S235 top view

Figure 55-Limit values for the bending moment with respect to λf λw in S235 cut of at Mel top view

Furthermore, the linear interpolation method proposed in AM-1-1-2012-02 uses the governing slenderness λ, therefore, it does not incorporate the composite effect of λf or λw on the bending moment capacity either. Consequently, if both λf or λw are in the class 3 range the interpolation method overestimates the bending moment capacity even worse compared to EN 1993-1-1, CL. 5.5. From these results it was concluded both EN 1993-1-1, CL. 5.5 and AM-1-1-2012-02 do not lead to safe limit values.

Therefore, an alternative design rule for local buckling of class 3 steel I sections that incorporates both λf and λw was required.

Figure 56-Bending moment capacity reduced for λf with λw in class 3 compared to design codes

Figure 57-Bending moment capacity reduced for λw with λf in class 3 compared to current design codes -1