# Second-Order Analysis

### 词汇表条目

In the calculation according to the second-order analysis, the equilibrium on a deformed structural system is determined.

The calculation according to the second-order analysis (also: P‑delta) detects the deformation effects due to loading, which affect the distribution of internal forces. Axial forces in the structural system usually lead to an increase of bending moments. In the case of pressure-loaded members, additional moments arise and thus overlinear effects of loads and moments occur. On the other hand, tension forces have a positive effect.

In RFEM and RSTAB, it is possible to calculate load cases and load combinations according to the various methods of analysis (see Figure 01). However, result combinations superimpose the results of the calculated load cases and combinations, so that the method of analysis can only be controlled indirectly.

The calculation according to the second-order analysis examines stability problems, for example buckling. In the RF‑/STEEL EC3 add‑on module, you can also perform the stability analysis considering lateral-torsional (torsional-flexural) buckling. The module extension RF‑/STEEL Warping Torsion allows you to perform the analysis according to the second‑order theory with 7 degrees of freedom (warping torsion).

In the case of steel structures, the second-order analysis must be used if the compression force in a member exceeds 10% of the elastic critical buckling load [4]. For concrete structures, certain limiting slendernesses are governing. Timber structures are usually calculated according to the linear static analysis.

Chapter 7.2.1.1 of the RFEM [1] or RSTAB manual [2] contains further information about the methods of analysis.

In the attached example, a load is analysed according to the linear static analysis and the second-order analysis. A vertical load with a small horizontal load acts on the column head (see Figure 02). The axial force has no influence on the moment distribution My in LC 1. However, the additional moment according to the second-order analysis is clearly recognisable in LC 2. If the load is further increased (or the cross-section is reduced), the program will display a message about the instability.

#### 参考文献

 [1] Manual RFEM. (2018). Tiefenbach: Dlubal Software. [2] Manual RSTAB. (2013). Tiefenbach: Dlubal Software. [3] Roik, K.; Carl, J.; Lindner, J. (1972). Biegetorsionsprobleme gerader dünnwandiger Stäbe. Berlin: Ernst & Sohn. [4] Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12

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