## Design of slender columns

As specified in section 9.2. a column is classified as slender if the slendcmcss ratio about either axis exceeds the value of A|itn. If A < A|¡„, then the column may be classified as short and the slenderness effect may be neglected.

A slender column with X > A¡¡m must be designed for an additional moment caused by its curvature at ultimate conditions. EC2 identifies four different approaches to designing slender columns:

1. A general method based on a non-linear analysis of the structure and allowing for second-order effects that necessitates the use of computer analysis.

2. A second-order analysis based on nominal stiffness values of the beams and columns that, again, requires computer analysis using a process of iterative analysis.

3. The 'moment magnification' method where the design moments are obtained by factoring the first-order moments.

4. The 'nominal curvature' method where second-order moments are determined from an estimation of the column curvature. These second-order moments are added to the first-order moments to give the total column design moment.

Only the fourth method, as given above, will be detailed here as this method is not greatly dissimilar to the approach in the previous British Standard for concrete design. BS8110. Further information on the other methods can be found in specialist literature.

The expressions given in FC2 for the additional moments were derived by studying the moment/curvature behaviour for a member subject to bending plus axial load. The equations for calculating the design moments are only applicable to columns of a rectangular or circular section with symmetrical reinforcement. A slender column should be designed for an ultimate axial load (A^d) plus an increased moment given by

en is an equivalent first-order eccentricity ea is an accidental eccentricity which accounts for geometric imperfections in the column fi is the second-order eccentricity.

where

The equivalent eccentricity en is given by the greater of

where eyi and <?02 are the first-order eccentricities at the two ends of the column as described above, and |eo21 is greater than |<?0i •

The accidental eccentricity is given by the equation k ea = V-

where In is the effective column height about the axis considered and 