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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.