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This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) 520 Members with compression and moments Fig. 18.9 Primary and secondary moments 2 Mm action: the combinations of F and M corresponding to the full strength of the cross-section. This is the ‘strength’ limit, representing the case where the primary moment acting in conjunction with the axial load accounts for all the cross-section’s capacity. The substance of Fig. 18.10 can be incorporated within the type of interaction formula approach of section 18.2 through the concept of equivalent uniform moment presented in Chapter 16 in the context of the lateral–torsional buckling of beams; its meaning and use for beam-columns are virtually identical. For moment gradient loading member stability is checked using an equivalent moment M = mM, as shown in Fig. 18.11. Coincidentally, suitable values of m, based on both test data and rigorous ultimate strength analyses, for the in-plane beam-column case are almost the same as those for laterally unrestrained beams (see section 16.3.6); m may conveniently be represented simply in terms of the moment gradient parameter b. The situation corresponding to the upper boundary or strength failure of Fig. 18. 10 must be checked separately using an appropriate means of determining crosssectional capacity under F and M. The strength check is superfluous for b =+1 as it can never control, while as b Æ-1 and M Æ M c it becomes increasingly likely that the strength check will govern. The procedure is: (1) check stability using an interaction formula in terms of buckling resistance Pc and moment capacity Mc with axial load F and equivalent moment M, (2) check strength using an interaction procedure in terms of axial capacity Ps and moment capacity Mc with coincident values of axial load F and maximum applied end moment M1 (this check is unnecessary if m = 1.0; M = M1 is used in the stability check). Consideration of other cases involving out-of-plane failure or moments about both axes shows that the equivalent uniform moment concept may also be applied. For simplicity the same m values are normally used in design, although minor
This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) 1.0 0,5 1.0 0. L/r = 40 0 0.5 cross—section interaction /= -1.0 = 0.0 M = 1.0 cross—section interaction = —1.0 0 0.5 = 0.0 Fig. 18.10 Effect of moment gradient on interaction Effect of moment gradient loading 521 = 1.0 M 1.0 1.0 ( ( 'F
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