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Mc Rd is the moment resistance of the cross-section given in 5.4.1(1)P; Vw Rd is the shear resistance of the web given in 5.8(1)P.

5.11 Combined bending moment and local load or support reaction

(1)P Cross-sections subject to the combined action of a bending moment AfSd and a transverse force due to a local load or support reaction FSd shall satisfy the following:

A*Sd/A*c,Rd * 1

... (5.26a)

^Sd^w.Rd - 1

... (5.26b)

MSà ^ FSd ^ ^

... (5.26c)

Mc Rd is the moment resistance of the cross-section given in 5.4.1(1)P;

*w Rd is the appropriate value of the local transverse resistance of the web from 5.9.

Page 62

ENV1993-1-3 s 1996 6 Buckling resistance 6.1 General

(1)P The design values of the internal forces and moments in each member shall not exceed its design buckling resistance to:

- axial compression, as given in 6.2;

- combined bending and axial compression, as given in 6.5.

(2)P In members with cross-sections that are susceptible to cross-sectional distortion, account shall be taken of possible lateral buckling of compression flanges and lateral bending of flanges generally, see 6.4.

(3)P The effects of local buckling shall be taken into account by using effective section properties determined as specified in Section 4.

(4)P The internal axial force in a member shall be taken as acting at the centroid of its gross cross-section.

(5) The resistance of a member to axial compression should be assumed to act at the centroid of its effective cross-section. If this does not coincide with the centroid of its gross cross-section, moments corresponding to the shift of the centroidal axes (see figure 6.1) should be taken into account, using the method given in 6.5.

(6)P Frame instability shall be taken into account as specified in ENV 1993-1-1.

Figure 6.1: Shift of centroidal axis

Figure 6.1: Shift of centroidal axis

6.2 Axial compression

6.2.1 Design buckling resistance

(1)P Unless determined by a second-order analysis of the member, see 6.2.2(6)P, the design buckling resistance for axial compression NbRd shall be obtained from:

the effective area of the cross-section, obtained from Section 4 by assuming a uniform compressive stress acom Ed equal to fyb/ym;

the area of the gross cross-section;

the appropriate value of the reduction factor for buckling resistance, in which the reduction factor 0A is given by:

(2)P The reduction factor x for buckling resistance shall be determined from:

with:

where:

a is an imperfection factor, depending on the appropriate buckling curve;

X is the relative slenderness for the relevant buckling mode.

(3)P The lowest value of x for flexuiral buckling of the member about any relevant axis, or for torsional or torsional-flexural buckling, shall be used.

(4)P The imperfection factor a corresponding to the appropriate buckling curve shall be obtained from table 6.1.

Table 6.1: Imperfection factor a

Buckling curve

a0

a

b

c

a

0,13

0,21

0,34

where:

Aef{ is

Ag is

X is

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ENV1993-1-3:1996 6.2.2 Flexural buckling

(1)P The design buckling resistance NbRd for flexural buckling shall be obtained from 6.2.1 using the appropriate buckling curve from table 6.2 according to the type of cross-section and axis of buckling.

(2)P The buckling curve for a cross-section not included in table 6.2 may be obtained by analogy.

(3)P The buckling resistance of a closed built-up cross-section shall be determined using either:

- buckling curve b in association with the basic yield strength fyb of the flat sheet material out of which the member is made by cold forming;

- buckling curve c in association with the average yield strength /ya of the member after cold forming, determined as specified in 3.1.2, provided that /?A = 1,0.

(4)P The relative slendemess X for flexural buckling about a given axis (Xy or Xz) shall be determined from the following:

with:

where:

i is the buckling length for flexural buckling about the relevant axis (ty or £z);

i is the radius of gyration about the corresponding axis (iy or ¿z), based on the properties of the gross cross-section.

(5) Reference should be made to ENV 1993-1-1 for information on determining the buckling length i for flexural buckling of a compression member, from its system length L .

(6)P As an alternative to (1)P, the design budding resistance NbRd for flexural buckling may be obtained from a second-order analysis of the member as specified in ENV 1993-1-1, based on the properties of the effective cross-section obtained from Section 4.

6.2.3 Torsional buckling and torsional-flexural buckling

(1)P For members with point-symmetric open cross-sections, account shall be taken of the possibility that the resistance of the member to torsional buckling might be less than its resistance to flexural buckling.

(2)P For members with mono-symmetric open cross-sections, see figure 6.2, account shall be taken of the possibility that the resistance of the member to torsional-flexural buckling might be less than its resistance to flexural buckling.

(3)P For members with non-symmetric open cross-sections, account shall be taken of the possibility that the resistance of the member to either torsional or torsional-flexural buckling might be less than its resistance to flexural buckling.

(4)P The design buckling resistance Nb Rd for torsional or torsional-flexural buckling shall be obtained from 6.2.1 using buckling curve b .

Table 6.2: Appropriate buckling curve for various types of cross-section

Type of cross-section

Buckling about axis

- y y-
- y

y - y z - z z rh any y-«H— y y-^ -1— y or other cross-section any

^ The average yield strength f should not be used unless Aeff = A%

.._t----y y— -J.----y y y---1-----y a—y m y y y—

Figure 6.2: Cross-sections susceptible to torsional-flexural buckling

(5)P The relative slenderness X for torsional or torsional-flexural buckling shall be obtained from:

with:

where:

a., t is the elastic critical stress for torsional buckling, see (6)P;

acr TF is the elastic critical stress for torsional-flexural buckling, see (7)P.

(6)P The elastic critical stress acr T for torsional buckling shall be determined from:

7cr,T

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