Imperfections According to EN 1993-1-1, Section 5.3.2: Global Initial Sway Imperfection

Technical Article

According to EN 1993-1-1 [1], it is necessary to use the equivalent geometric imperfections with values that reflect the possible effects of all types of imperfections. EN 1993-1-1, Section 5.3, specifies basic imperfections for global analysis of frames as well as member imperfections.

In the case of structures with a mode shape, which is characterized by a lateral displacement, the effect of imperfections can be considered for the structural calculation by a global initial sway imperfection (and individual bow imperfection, if necessary).

The global initial sway imperfection Φ is determined according to Equation (5.5):
Φ = Φ0 · αh · αm

The resulting basic value Φ0 is equal to 1/200, as specified in DIN 18800, and can be reduced by two factors. These factors take into account the favourable effects of very high columns as well as several supporting columns in a row. The background to this is that the imperfections are structurally distributed and thus very unlikely to be unfavourable on all components.

αh is the reduction factor for height h applicable to columns
$$\frac23\;<\;{\mathrm\alpha}_\mathrm h\;=\;\frac2{\sqrt{\mathrm h}}\;<\;1.0$$

Figure 01 - Reduction Factor αh (Blue Line)

αm is the reduction factor for the number of columns in a row
m is the number of columns in a row with a vertical load > 50% of the average value of the column

$${\mathrm\alpha}_\mathrm m\;=\;\sqrt{0.5\;\cdot\;(1\;+\;\frac1{\mathrm m})}$$

Figure 02 - Reduction Factor αm

Compared to DIN 18800, there are greater sway imperfections in the case of a larger number of columns m and higher columns resulting from the calculation according to EN 1993-1-1.

Reference

[1]  Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings; EN 1993-1-1:2010-12
[2]  Training Manual EC3. (2017). Leipzig: Dlubal Software.

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