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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) 656 Composite columns 22.2.2 Combined axial load and bending moments The moment resistance of a composite column may be determined by establishing plastic stress blocks defining the resistances of the portions of the section under tension and compression. The plastic neutral axis depth y p is defined as below the extreme edge of the concrete in compression. Three cases of neutral axis position exist: in the concrete, through the steel flange, and in the web of the section. The position depends on the relative proportions of steel and concrete (see Fig. 22.2). Commonly, y p lies within the steel flange (i.e. y p ª (d c - D)/2) for major axis bending of a composite section. In this case: Ap s y Ê dc-Dˆ ≥ ¥ ( 045 . fcubc)≥ Awpy + Af( 045 . fcu) Ë 2 ¯ The moment resistance of the composite section is then given by: M = 05 . A p ( d -y )+ 05 . A ( 087 . f ) ( d - 2d ) pc s y c p r y c r (22.3) (22.4) where dc is the depth and b c is the breadth of the concrete section, d r is the cover to the reinforcement, D is the depth of the steel section, A w is the cross-sectional area of the web, A f is the cross-sectional area of the flange, and A r is the crosssectional area of any additional reinforcement. Other cases are defined in BS 5400: Part 5, Appendix C. 1 Because the above plastic stress block method slightly overestimates the bending resistance of the composite section, M pc is multiplied by 0.9 for design purposes. In the presence of axial load, the plastic neutral axis depth increases. For small to medium axial loads, the plastic neutral axis remains within the steel web, but for higher axial loads most of the section is in compression. A typical interaction diagram representing the variation of moment resistance with axial load is shown in Fig. 22.3. An interesting phenomenon is that there is a slight increase in moment resistance with increasing axial load (compression), and there is a certain axial load where the moment resistance of the section equals that in the absence of axial load (i.e. Mpc from Equation (22.4)). For simple design, the possibility exists of defining the interaction between moment and axial force in terms of three intercepts A, B and C on the moment and axial load axes, and also point D, which corresponds to the axial load at which the moment capacity remains unchanged. Therefore, a trilinear relationship AD, DC, CB closely models the real interaction diagram. It is normal practice to ignore the beneficial effect of axial load as it cannot always be assumed to be coincident with the applied moment. The curvature of the interaction diagram at higher axial loads can also be ignored without much loss of economy. The method developed by Basu and Sommerville 4 empirically follows the shape of the interaction diagram using coefficients K 1, K 2 and K 3 (see Fig. 22.3). The value of axial load P at which the moment resistance remains unchanged (point D) may be evaluated as follows.
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) axial load Tension Conipressi on Actual interaction Smniplified interaction Fig. 22.3 Interaction between moment and axial force Design of encased composite columns 657 D moment Determine the neutral axis depth yp for P of zero, corresponding to equal tension and compression forces across the composite section. Redefine a neutral axis depth, y¢p = dc - yp, which corresponds to an axis symmetrically placed with respect to yp around the centre of the section. The net compressive resistance of the section with neutral axis y¢p corresponds to no change in moment resistance because the net moment effect of the section contained between depths yp and y¢p is zero, as illustrated in Fig. 22.2. It may be shown that the axial resistance of the section (termed P0), corresponding to depth y¢p, is, in fact, the axial resistance of the concrete section ignoring the contribution of the steel member and the reinforcement. Hence, P0 = 0.45fcudcbc (22.5) Dividing by Pu from Equation (22.1) gives a non-dimensional ordinate on the moment/axial-force diagram, corresponding to the moment resistance of the composite section. This ordinate is also equivalent to the concrete contribution factor for major axis bending, and can also be used for minor axis bending. For stocky columns it also corresponds to the appropriate value of K2 in the Basu and Sommerville approach. 4 For slender columns, account is to be taken of the moments arising from eccentricity of axial load in addition to the applied moments. The Basu and Sommerville method4 has been codified in BS 5400: Part 5. 1 Because the method uses empirical formulae for K1, K2 and K3 as a function of the slenderness of the column, it appears to be relatively complicated, but it may be simplified by taking K3 as zero so that the moment resistance at any value of axial load is given by:
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