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where

1 + 0,7k k = ^^ (same definition as for isolated members, see 3.2) L/EI v '

6= rotation for bending moment M (compare figure 5.13) The factor S1 is an approximation, which has been derived by calibration against accurate numerical calculation for different numbers of storeys, see figure 5.18. The product S0S1 corresponds to S in expression (H.2) in EN annex H. Figure 5.18. Effect of flexibility of end restraint for bracing units. Solid curves represent the "exact" solution, dashed curve the approximation according to expression (3-12)

The effect of flexible moment restraint is not covered in the ENV, therefore no comparison can be made.

Effect of global shear deformations a) Shear deformations only (see Figure 5.19):

The (hypothetical) buckling load for shear deformations only is:

Fv,bs = S (or ES for more than one bracing unit) (3-13)

Here S is the shear stiffness (= shear force giving a shear angle = 1; see figure H-1 in the EN).

5.8.4 Creep Figure 5.19. Hypothetical buckling due to global shear deformations only

Figure 5.19. Hypothetical buckling due to global shear deformations only b) Combined bending and shear:

The combined buckling load, taking into account bending and shear deformations, can be expressed as

1 fvbb fvbb yFV,BB+yFV,BS 1 + FV,BB/FV ,BS 1 + FV,BB/ ^S

Expression (3-14) can be derived analytically for simple cases like isolated members with constant normal force. By numerical calculations, it can be verified also for bracing units with vertically increasing axial load and significant global shear deformations (e.g. shear walls with large openings).

The basic criterion for neglecting second order effects is the same as before:

which leads to expression (H.6) in Annex H.

This case is not covered in the ENV, therefore no comparison can be made. C5.8.4. Effective creep ratio 5.8.4.1 General

The ENV stated that creep should be considered in connection with second order effects, but gave no information on how. In the EN, on the other hand, practical models for taking into account creep are given, based on the so called "effective creep ratio".

A general approach would be to first calculate creep deformations under long-term load, then to analyse the structure for the additional load up to design load. With the effective creep ratio, the analysis can instead be made directly for the design load in one step. Figure 5.20 illustrates a hypothetical load history and the corresponding deformations. The total load is assumed to consist of one Long-term part Ql (corresponding to the quasi-permanent combination) and one additional short-term part up to the Design load Qd, applied after a "long time".2 The total load history can then be divided into three parts:

1. AB - long-term load Ql giving an elastic deformation

2. BC - constant load Ql giving a creep deformation based on full creep coefficient 9