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

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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.

For structures with an eigenmode characterized by a lateral displacement, the influence of imperfections for the structural analysis can be taken into account by a global initial inclination (possibly with precamber).

The global initial inclination Φ is determined according to Equation (5.5) as follows:
Φ = Φ 0 · α h · α m

The output value Φ 0 results, analogous to DIN 18800, to 1/200 and can be reduced by two factors. These factors take into account the favorable effects of very high columns as well as many supporting columns in a row. The background for this is that imperfections occur statistically distributed and thus very unlikely to have an unfavorable effect on all components.

α h = reduction factor for the height h of columns
$$\frac23\;<\;{\mathrm\alpha}_\mathrm h\;=\;\frac2{\sqrt{\mathrm h}}\;<\;1,0$$

Figure 01 - Reduction Factor αh

α m = reduction factor for the number of columns in a row
m = number of columns in a row with load> 50% of the average column load

$${\mathrm\alpha}_\mathrm m\;=\;\sqrt{0,5\;\cdot\;(1\;+\;\frac1{\mathrm m})}$$

Figure 02 - Reduction Factor αm

Compared to DIN 18800, there are larger inclinations according to DIN EN 1993-1-1 for a large number of columns m and high columns.

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 Guide EC3. Leipzig: Dlubal Software, March 2017

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