b

c

d

Imperfection factor a

0,13

0,21

0,34

0,49

0,76

Table 6.5. Selection of buckling curve for a cross-section (Table 6.2 of EN 1993-1-I)

Table 6.5. Selection of buckling curve for a cross-section (Table 6.2 of EN 1993-1-I)

The choice as lo which buckling curve (imperfection factor) to adopt is dependent upon the geometry and material properties of the cross-section and upon the axis of buckling. The appropriate buckling curvc should be determined from Table 6.5 (Table 6.2 of EN 1993-1-1), which is equivalent to the 'allocation of strut curve' tabic (Table 23) of BS 5950: Part 1.

Non-dimensional slenderness for various buckling modes Clause 6.3.1.3 EN 1993-1-1 provides guidance for flcxural (clause 6.3.1.3), torsional (clause 6.3.1.4) and Clause 6.3.1.4 flexural-torsional (clause 6.3.1.4) buckling modes. For standard hot-rolled and welded structural cross-sections, flcxural buckling is the predominant buckling mode, and hencc governs design in the vast majority of eases.

Buckling modes with torsional components are generally limited to cold-formed members for two principal reasons:

♦ cold-formed cross-sections contain relatively thin material, and torsional stiffness is associated with the material thickness cubed

• the cold-forming process gives a predominance of open sections because these can be easily produced from flat sheet. Open sections have inherently low torsional stiffness.

Flcxural buckling of a compression member is characterized by excessive lateral deflections in the plane of the weaker principal axis of the member. As the slenderness of the column increases, the load at which failure occurs reduces. Calculation of the non-dimensional Clause 6.3.1.3 slenderness for flexural buckling is covered in clause 6.3.1.3.

The non-dimensional slenderness A is given by

A= I—— = —^—• for Class 1, 2 and 3 cross-sections VN„ i A,

where

for Class 4 cross-sections

is the buckling length of the compression member in the plane under consideration, and is equivalent to the effective length Lz in BS 5950 (buckling lengths are discussed in the next scction)

is the radius of gyration about the relevant axis, determined using the gross properties of the cross-section (assigned the symbols rx and in BS 5950 for the radius of gyration about the major and minor axes, respectively)

Clearly, the BS 5950 definition of slenderness (A = /-E/r.) is already 'non-dimensional', but the advantage of the Eurocode 3 definition of 'non-dimensional slenderness' A, which includes the material properties of the compression member through A„ is that all variables affecting the theoretical buckling load of a perfect pin-ended (Euler) column arc now present. This allows a more direct comparison of susceptibility to flexural buckling lo be made for columns with varying material strength. Further, A is useful for relating the column slenderness to the theoretical point at which the squash load and the Euler critical buckling load coincide, which always occurs at the value of non-dimensional slenderness A equal to 1.0.

As stated earlier, flcxural buckling is by far the most common buckling mode for conventional hot-rolled structural members. However, particularly for thin-walled and open sections, the designer should also check for the possibility that the torsional or torsional-flexural buckling resistance of a member may be less than the flexural buckling resistance. Torsional and torsional-flexural buckling are discussed further in Section 13.7 of this guide.

Table 6.6. Nominal buckling lengths Lcr for compression members | ||

End restraint (in the plane under consideration) |
Buckling length, Lcr | |

Effectively held in position at both ends |
Effectively restrained in direction at both ends |
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