In Consteel, the calculation of cross sectional interaction resistance for Class 3 and 4 sections is executed with the modified Formula 6.2 of EN 1993-1-1 with the consideration of warping and altering signs of component resistances. Let’s see how…

Application of EN 1993-1-1 formula 6.2

For calculation of the resistance of a cross section subjected to combination of internal forces and bending moments, EN 1993-1-1 allows the usage -as a conservative approximation- a linear summation of the utilization ratios for each stress resultant, specified in formula 6.2.  

$$\frac{N_{Ed}}{N_{Rd}}+\frac{M_{y,Ed}}{M_{y,Rd}}+\frac{M_{z,Ed}}{M_{z,Rd}}\leq 1$$

As Consteel uses the 7DOF finite element and so it is capable of calulcating bimoment, an extended form of the formula is used for interaction resistance calculation to consider the additional effect.

$$\frac{N_{Ed}}{N_{Rd}}+\frac{M_{y,Ed}}{M_{y,Rd}}+\frac{M_{z,Ed}}{M_{z,Rd}}+\frac{B_{Ed}}{B_{Rd}}\leq 1$$

Formula 6.2 ignores the fact that not every component results the highest stress at the same critical point of the cross-section.

In order to moderate this conservatism of the formula, Consteel applies a modified method for class 3 and 4 sections. Instead of calculating the maximal ratio for every force component using the minimal section moduli (W), Consteel finds the most critical point of the cross-section first (based on the sum of different normal stress components) and calculates the component ratios using the W values determined for this critical point. Summation is done with considering the sign of the stresses caused by the components corresponding to the sign of the dominant stress in the critical point.

(For class 1 and 2 sections, the complex plastic stress distribution cannot be determined by the software. The Formula 6.2 is used with the extension of bimoments to calculate interaction resistance, but no modification with altering signs is applied)

Example

Let’s see an example for better explanation.

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Did you know that you could use Consteel to calculate effective cross-section properties for Class 4 sections?

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Did you know that you could use Consteel to draw a user-defined cross section and calculate its section properties?

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Did you know that you could use Consteel to include in your model a wide range of cold-formed macro sections?

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Good model and result visualization leads to better understanding and correct interpretation of any data model compared to texts or tables. With the help of Coloring by section feature, you will be able to switch to a new model view where the members get colours from their cross-section type. Watch the feature preview below and learn how to use the Coloring to make your model more perscpicuous.

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