Imperfections According to EN 1993-1-1 Clause 5.3.2: Bow 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, Clause 5.3, specifies basic imperfections for the global analysis of frames as well as member imperfections.

Structural analysis

Although the influences of precambers are already included in the equations for the stability analyzes of structural components according to clause 6.3, a precamber has to be considered in the structural analysis if there is a structural or structural component that is sensitive to precamberes. This is governed by DIN EN 1993‑1‑1: 2010‑12 clause 5.3.2 (6).

Figure 01 - Example

The definition as to whether a component is sensitive to precambers is defined by Equation (5.8):
$\begin{array}{l}\overline{\mathrm\lambda}\;>\;0,5\;\cdot\;\sqrt{\frac{\mathrm A\;\cdot\;{\mathrm f}_\mathrm y}{{\mathrm N}_\mathrm{Ed}}}\\\mathrm{mit}\\\overline{\mathrm\lambda}\;=\;\sqrt{\frac{{\mathrm N}_\mathrm{pl}}{{\mathrm N}_\mathrm{cr}}}\;=\;\mathrm{Schlankheitsgrad}\;\mathrm{des}\;\mathrm{Bauteils}\;\mathrm{in}\;\mathrm{der}\;\mathrm{betrachteten}\;\mathrm{Ebene},\\\mathrm{der}\;\mathrm{mit}\;\mathrm{der}\;\mathrm{Annahme}\;\mathrm{beidseitig}\;\mathrm{gelenkiger}\;\mathrm{Lagerung}\;\mathrm{ermittelt}\;\mathrm{wird},\\\mathrm{und}\\\;N_\mathrm{cr}\;=\;\frac{\mathrm\pi²\;\cdot\;\mathrm E\;\cdot\;\mathrm I}{{\mathrm s}_\mathrm k²}\\\mathrm{ergibt}\;\mathrm{sich}\;\mathrm{die}\;\mathrm{bekannte}\;\mathrm{Abgrenzung}\;\mathrm{über}\;\mathrm{die}\;\mathrm{Stabkennzahl}\;\mathrm{aus}\;\mathrm{der}\;\mathrm{DIN}\;18800:\\\;s_\mathrm k\;\cdot\;\sqrt{\frac{{\mathrm N}_\mathrm{Ed}}{\mathrm E\;\cdot\;\mathrm I}}\;=\;\mathrm\varepsilon\;>\;0,5\;\cdot\;\mathrm\pi\;\approx\;1,6\end{array}$

Component imperfections

Flexural buckling
According to DIN EN 1993‑1‑1: 2010‑12, clause 5.3.2 (3), Table 5.1, the recommended precamber values are as follows:

Buckling curve according to
DIN EN 1993‑1‑1: 2010‑12,
Table 6.2
Cross-section check
Elastic e 0, d/L Plastic 0, d/L
a 0 1/350 1/300
1/300 1/250
B 1/250 1/200
C 1/200 1/150
[SCHOOLTRAINING.NUMBEROFSTUDENTS] 1/150 1/100

If the internal forces are determined according to the elasticity theory and the cross-section design is performed with a linear cross-section interaction according to DIN EN 1993‑1‑1: 2010‑12 Para. 6.2.1 (7) Equation (6.2), Table NA.2 of DIN EN 1993‑1‑1/NA: 2015‑08 [2] apply:

Buckling curve according to
DIN EN 1993‑1‑1: 2010‑12,
Table 6.2
Cross-section check
Elastic e 0, d/L Plastic 0, d/L
a 0 1/600 As for
Elastic,
however
M pl/M el times
1/550
B 1/350
C 1/250
[SCHOOLTRAINING.NUMBEROFSTUDENTS] 1/150

Flexural-torsional buckling
According to DIN EN 1993‑1‑1: 2010‑12, clause 5.3.4 (3), imperfection as a precamber about the minor axis with the value k ∙ e 0, d ( e 0, d see bending buckling). The value of k = 0.5 is recommended. It is not necessary to apply any further torsional imperfection.

An economical approach is possible according to DIN EN 1993‑1‑1/NA: 2015‑08 for I-sections. According to NDP Re 5.3.4 (3), the imperfection can be applied instead of k ∙ e 0, d with the values of Table NA.3.

Cross-section Dimensions Elastic
Cross-section
utilization
0, d/L
Plastic
Cross-section
utilization
0, d/L
Rolled
I-sections
h/w ≤ 2.0 1/500 1/400
h/w> 2.0 1/400 1/300
Welded
I-sections
h/w ≤ 2.0 1/400 1/300
h/w> 2.0 1/300 1/200

The specified values must be doubled in the range 0.7 ≤ λ LT ≤ 1.3. This requirement stems from a dissertation at the Ruhr-Universität Bochum from 2008 and has also been included in the revised DIN 18800: 2008‑11.

Reference

[1]   Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1: 2010‑12
[2]  National Annex - Nationally determined parameters - Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; DIN EN 1993‑1‑1/NA: 2015‑08
[3]  Training Guide EC3. Leipzig: Dlubal Software, September 2017

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