or in methods of checking resistance, as explained above.
Clause 5.3.1(2) Clause 5.3.1(2) requires imperfections to be in the most unfavourable direction and form. The most unfavourable geometric imperfection normally has the same shape as the lowest buckling mode. This can sometimes be difficult to find; but it can be assumed that this condition is satisfied by the Eurocode methods for checking resistance that include effects of member imperfections (see comments on clause 5.2.2).
5.3.2. Imperfections in buildings
Clause 5.3.2.1(1)
Generally, an explicit treatment of geometric imperfections is required for composite frames. In both EN 1993-1-1 and EN 1994-1-1 the values are equivalent rather than measured values (clause 5.3.2.1(1)), because they allow for effects such as residual stresses, in addition to imperfections of shape. The codes define both global sway imperfections for frames and local bow imperfections of individual members (meaning a span of a beam or the length of a column between storeys).
Clause 5.3.2.1(2)
The usual aim in global analysis is to determine the action effects at the ends of members. If necessary, a member analysis is performed subsequently, as illustrated in Fig. 5.1(a); for example to determine the local moments in a column due to transverse loading. Normally the action effects at members’ ends are affected by the global sway imperfections but not significantly by the local bow imperfections. In both EN 1993-1-1 and EN 1994-1-1 the effect of a bow imperfection on the end moments and forces may be neglected in global analysis if the design normal force NEd does not exceed 25% of the Euler buckling load for the
pin-ended member (clause 5.3.2.1(2)).
Clause 5.3.2.1(3) Clause 5.3.2.1(3) is a reminder that an explicit treatment of bow imperfections is always required for checking individual composite columns, because the resistance formulae are for cross-sections only and do not allow for action effects caused by these imperfections.
Clause 5.3.2.1(4) The reference to EN 1993-1-1 in clause 5.3.2.1(4) leads to two alternative methods of allowing for imperfections in steel columns. One method includes all imperfections in the global analysis. Like the method just described for composite columns, no individual stability check is then necessary.
The alternative approach is that familiar to most designers. Member imperfections are not accounted for in the global analysis. The stability of each member is then checked using end moments and forces from that analysis, with buckling formulae that take account of imperfections.
Do second-order global analysis
Note: These flow charts are for a particular load combination and arrangement for ultimate limit states, for a beam-and-column type plane frame in its own plane, and for global analyses in which allowances may be needed for creep, cracking of concrete, and the behaviour of joints. ‘EC3’ means EN 1993-1-1
Yes
Yes
Check beams for lateral–torsional buckling, using resistance formulae that include member imperfections (clauses 5.2.2(5) and 5.3.2.3(2))
Were member imperfections for columns included in the global analysis?
Is the member in axial compression only?
Verify column cross-sections to clause 6.7.3.6 or 6.7.3.7, from clause 5.2.2(6) Do second-order analysis for each column, with end action- effects from the global analysis, including member imperfections, from clause 5.2.2(6)
No
Use buckling curves that account for second-order effects and member imperfections to check the member (clause 6.7.3.5)
No Yes
Do first-order global analysis Determine frame imperfections as equivalent horizontal forces,
to clause 5.3.2.2, which refers to clause 5.3.2 of EC3. Neglect member imperfections (clause 5.3.2.1(2))
No
Note: for columns, more detail is given in Fig. 6.36 Go to Fig. 5.1(e), on methods of global analysis
For each column, estimate NEd, find l to clause 5.3.2.1(2). Determine member imperfection for each column (to clause 5.3.2.3) and where condition (2) of clause 5.3.2.1(2) is not satisfied, include these these imperfections in second-order analysis
Is second-order analysis needed for global analysis? Go to Fig. 5.1(b), on creep Go to Fig. 5.1(c), on cracking
Determine appropriate stiffnesses, making allowance for cracking and creep of concrete and for behaviour of joints
Go to Fig. 5.1(d), on joints
-
Fig. 5.1. Global analysis of a plane frame
Does clause 5.4.2.2(11), on use of a nominal modular ratio, apply? No Yes
For composite beams, assume an effective modulus (clause 5.4.2.2(11)) and determine a nominal modular ratio, n
For composite beams, determine modular ratios n0 for
short-term loading and nL for permanent loads. For a
combination of short-term and permanent loading, estimate proportions of loading and determine a modular ratio n from n0 and nL
For each composite column, estimate the proportion of permanent to total normal force, determine effective modulus Ec, eff (clause 6.7.3.3(4)), and hence the design
effective stiffness, (EI)eff, II, from clause 6.7.3.4(2)
Determine cracked stiffness for each composite column, to clause 6.7.3.4
Yes No
No Yes
Yes
No
Is the frame braced? Assume uncracked beams
Make appropriate allowances for creep (clause 5.4.2.2) and flexibility of joints (clause 8.2.2)
Analyse under characteristic combinations to determine internal forces and moments (clause 5.4.2.3 (2)) and determine cracked regions of beams
Do adjacent spans satisfy clause 5.4.2.3(3)?
Are internal joints rigid?
Assume cracked lengths for beams (clause 5.4.2.3(3))
Assign appropriate stiffnesses for beams
No
Yes Yes
No
Can the joint be classified on the basis of experimental evidence or significant experience of previous performance in similar cases? (See EN 1993-1-8 (clause 5.2.2.1(2))
In the model for the frame, assign appropriate rotational stiffness to the joint
Determine rotational stiffness ((clause 8.2.2 and EN 1993-1-8 (clause 5.1.2)) Determine classification by stiffness (clause 8.2.3 and EN 1993-1-8 (clause 5.2)) Calculate initial rotational stiffness, Sj, ini (clause 8.3.3, Annex B and EN 1993-1-8 (clause 6.3))
Is the joint nominally-pinned or rigid?
Fig. 5.1. (Contd)
(b) Supplementary flow chart, creep
(c) Supplementary flow chart, cracking of concrete
Global imperfections
Clause 5.3.2.2(1)
Clause 5.3.2.2(1) refers to clause 5.3.2 of EN 1993-1-1. This gives values for the global sway