urnbsr of stories, r,t

Figure 5.16. Global buckling due to bending and coefficient for buckling load. Constant stiffness and equal increment of vertical load per storey.

The coefficient £,0 according to the upper curve in Figure 5.16 can be approximated by

where ns = number of storeys Combining expressions (3-4) to (3-6) gives

00,4 • Ecd ' Ic — 0 312 • ns • 'c — Q • Ecd 'c

L2 ' ns+1,6 L2 where 0,312 = 7,8- 0,1- 0,4 and ß = 0,312- ns /(ns + 1,6)

1 The ratio 0,5 between the stiffnesses for cracked and uncracked sections is of course a rough simplification. The ratio should depend on the reinforcement and the normal force, and with a normal force there is a more or less smooth transition between the two stages. However, since this is about cases where second order effects are more or less negligible, a simple rule is acceptable.

This is the background to expression (5.18). Compare the ENV formulation (see 3.3.1 above):

Expression (5.18) can be formulated in the same way (substituting Ecd with Ecm and explicitly including partial factor ycE = 1,2 on the right hand side):

In Figure 5.17 the two corresponding parameters $1,2 (EN) and a2 (ENV) are compared.

For the EN, curves for both cracked and uncracked sections are shown. The ENV gives no values for cracked section, therefore there is no comparison for this case.

The comparison shows that for uncracked section, the two models give rather similar results, although the ENV is often much more conservative.

Q5, ß!

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