Effective length
Figure 5 gives guidance on the effective length of the column. However, for most real structures Figures 5f) and 5g) only are applicable, and Eurocode 2 provides two expressions to calculate the effective length for these situations. Expression (5.15) is for braced members and Expression (5.16) is for unbraced members.
In both expressions, the relative flexibilities at either end, k1 and k2, should be calculated. The expression for k given in the Eurocode involves calculating the rotation of the restraining members, which in practice requires the use of framework analysis software. Alternatively, PD 6687: Background paper to the UK National annex8 provides a simplification, based on the stiffness of the beams attached to either side of the column. This relative stiffness, k, can therefore be calculated as follows (provided the stiffness of adjacent columns does not vary by more than 15% of the higher stiffness):
/c, Ib are the column and beam uncracked second moments of area lc, lb are the column and beam lengths
Once k, and k2 have been calculated, the effective length factor, F, can be established from Table 4 for braced columns. The effective length is then lo = Fl.
For a 400 mm square internal column supporting a 250 mm thick flat slab on a 7.5 m grid, the value of k could be 0.11, and therefore lo = 0.59l. In the edge condition k is effectively doubled and lo = 0.67l. If the internal column had a notionally 'pinned' support at its base then lo = 0.77l.
It is also generally accepted that Table 3.19 of BS 8110 may conservatively be used to determine the effective length factor. In the long term, Expressions (5.15) and (5.16) will be beneficial as they are particularly suitable for incorporation into design software.
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