where

Mi, Mi... restraining moments in members 1, 2..., see Figure 5.15

Ma restraining moment in the adjacent column, see Figure 5.15, calculated without taking into account the axial force Na a = Na/Nea

Na axial force on the adjacent column

Nea buckling load of the adjacent column (can be estimated approximately, e.g. taking into account only the horizontal members adjacent to its nodes)

5.8.3.3 Global second order effects in buildings

C5.8.3.3 Global second order effects in structures 5.8.3.3.1 Background a) Model in ENV, A.3.2

According to the ENV, global second order effects may be ignored, and the structure may be considered as "non-sway", if

Where L total height of building (htot in the ENV) Fv total vertical load (FV in the ENV) EcmIc sum of bending stiffnesses of bracing members a 0,2 + 0,1ns < 0,6 (in the ENV, no particular symbol is used for this parameter) ns number of storeys (n in the ENV)

This criterion is valid only on certain conditions (not stated in the ENV):

1. No significant rotation at the base (rigid restraint / stiff foundation)

2. No significant global shear deformations (e.g. no significant openings in shear walls)

These conditions are not fulfilled for e.g. a bracing system including frames, shear walls with large openings and/or flexible foundations.

The criterion also explicitly requires that bracing members are uncracked. In practice, bracing members are often more or less cracked in ULS, due to high lateral and low vertical loadings (most of the vertical load is often carried by the braced members).

For the above reasons, ENV A.3.2 has a very limited field of application. Since the limitations of the applicability are not stated, and no information is given for the cracked stage, there is a also risk that it is used outside the scope, giving unsafe results.

b) New proposals

Due to the above shortcomings, the ENV criterion was not included in earlier drafts of the EN. After many requests to include something similar, two alternative proposals were presented to CEN TC250/SC2 (Berlin, May 2000), a "mini-version" and a "full version":

• "Mini-version": same scope as in ENV-A.3.2, and a criterion given in a similar closed form. However, the conditions and restrictions are clearly stated, and the criterion is improved to be less conservative and to take into account cracking in a simple way.

• "Full version": formulated in a more general and transparent way. Detailed information is given only for regular cases, but the formulation opens for general cases. A simple extension is given to cover the effect of global shear deformations.

In the final draft a somewhat extended "mini-version" is given in the main text, and further extension to the "full version" are given in Annex H.

5.8.3.3.2 No significant shear deformations, rigid moment restraint

The basic criterion "second order effects < 10% of first order effects" gives, together with the simplified magnification factor for bending moment in 5.8.7.3 (3):

This gives the following criterion for the vertical load, cf. expression (H.1):

FV,Ed < Fv,bb■ 0,1 / 1,1 « 0,1 Fv,bb Here Fv Ed total vertical load

Fv,bb nominal buckling load for global bending (no shear deformations) MoEd first order moment Med design moment The global buckling load for bending can be written

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