5.3.3 Imperfection for analysis of bracing systems (1) In the analysis of bracing systems which are required to provide lateral stability within the length of beams or compression members the effects of imperfections should be included by means of an equivalent geometric imperfection of the members to be restrained, in the form of an initial bow imperfection:

e0 = αm L / 500 (5.12) where L is the span of the bracing system

and

+=α

m115,0m

in which m is the number of members to be restrained. (2) For convenience, the effects of the initial bow imperfections of the members to be restrained by a bracing system, may be replaced by the equivalent stabilizing force as shown in Figure 5.6:

0d 2q 8 q

Ed

eN

Lδ+

= ∑ (5.13)

EN1993-1-1 Clause 5.3.3: Imperfection for analysis of bracing systems©

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where δq is the inplane deflection of the bracing system due to q plus any external loads calculated from

first order analysis

NOTE δq may be taken as 0 if second order theory is used. (3) Where the bracing system is required to stabilize the compression flange of a beam of constant height, the force NEd in Figure 5.6 may be obtained from: NEd = MEd / h (5.14) where MEd is the maximum moment in the beam and h is the overall depth of the beam.

NOTE Where a beam is subjected to external compression NEd should include a part of the compression force.

(4) At points where beams or compression members are spliced, it should also be verified that the bracing system is able to resist a local force equal to αmNEd / 100 applied to it by each beam or compression member which is spliced at that point, and to transmit this force to the adjacent points at which that beam or compression member is restrained, see Figure 5.7. (5) For checking for the local force according to clause (4), any external loads acting on bracing systems should also be included, but the forces arising from the imperfection given in (1) may be omitted.

e0 imperfection qd equivalent force per unit length 1 bracing system

The force NEd is assumed uniform within the span L of the bracing system.

For non-uniform forces this is slightly conservative.

Figure 5.6: Equivalent stabilizing force

E N 1 9 9 3 - 1 - 1 C l a u s e 5 . 3 . 3 : I m p e r f e c t i o n f o r a n a l y s i s o f b r a c i n g s y s t e m s

©

Co

py

ri

gh

t

BS

I,

2

00

5

NEd

Ed

Ed

Ed

EdN

N

N

Φ

Φ

Φ

Φ

Φ2 N

1

2

Φ = αm Φ0 : Φ0 = 1 / 200

2ΦNEd = αm NEd / 100 1 splice 2 bracing system

Figure 5.7: Bracing forces at splices in compression elements

EN1993-1-1 Clause 5.3.3: Imperfection for analysis of bracing systems©

Cop

yrig

ht B

SI,

2005