# Calculation of Effective Cross-Section Properties

### Technical Article

Prior to the analysis of steel cross‑sections, the cross‑sections are classified according to EN 1993‑1‑1, Chap. 5.5, with respect to their resistance and rotation capacity. Thus, the individual cross‑section parts are analysed and assigned to Classes 1 to 4. The cross‑section classes are subsequently determined and usually assigned to the highest class of cross‑section parts. If plastic resistance is to be applied to further design of cross‑sections of Class 1 and Class 2, you can analyse the elastic resistance of cross-sections as of Class 3. In the case of Class 4 cross‑sections, local buckling already occurs before reaching the elastic moment. In order to take this effect into account, you can use effective widths. This article describes the calculation of the effective cross‑section properties in more detail.

#### Calculation Process

In the first calculation step, the stress distribution is determined on a gross cross‑section. According to EN 1993‑1‑5, Chap. 4.4 [2], the buckling value kσ of the cross‑section parts subjected to compression can be determined by using the existing stresses. On the basis of the slenderness ratio at buckling λp and the resulting reduction factor ρ, the effective width beff of the cross‑section part is calculated. The resulting reduction is deducted from the entire cross‑section. This gives you the result of new cross‑section dimensions and properties.

At this point, the calculation is not yet complete. There is a further iteration step, where the new stress distribution with the existing internal forces is calculated on the basis of the reduced cross‑section. The following must be considered:

1. By reducing the cross‑section, the center of gravity is shifted. The possible acting normal forces generate an additional moment at the distance of the new center of gravity to the old one.
2. The cross‑section reduction may also have an effect on the rotation of the major axes. In such cases, the deviation moment Iyz must be taken into account.

After determining the stresses, the slenderness of the cross‑section parts subjected to compression is checked again. If more reductions are necessary, the iterative process continues as long as no significant cross‑section modifications occur. Only then is it possible to perform the corresponding designs of the effective cross‑sections.

#### Summary

The quick determination of effective cross‑sections performed initially may easily become a time‑consuming calculation due to several required iterations. By using the powerful program SHAPE‑THIN as well as the add‑on modules for structural steel analysis and design, you can easily avoid such difficulties.

#### Reference

 [1] Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings; EN 1993-1-1:2005 + AC:2009 [2] Eurocode 3: Design of steel structures - Part 1-5: Plated structural elements; EN 1993‑1‑5:2006 + AC:2009 [3] Kuhlmann, U. (Ed.): Stahlbau-Kalender 2013: Eurocode 3 - Anwendungsnormen, Stahl im Industrie- und Anlagenbau. Berlin: Ernst & Sohn, 2013