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

### Technical Article

001466

08/01/2017

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):

$$\mathrm\Phi\;=\;{\mathrm\Phi}_0\;\cdot\;{\mathrm\alpha}_\mathrm h\;\cdot\;{\mathrm\alpha}_\mathrm m$$

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 favorable 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 unfavorable on all components.

αh is the reduction factor for height h applicable to columns

$$\frac23\;<\;{\mathrm\alpha}_\mathrm h\;=\;\frac2{\sqrt{\mathrm h}}\;<\;1.0$$

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.

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

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.