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Steel Designers' Manual - 6th Edition (2003)
fcu is the cube strength of concrete
py is the design strength of the steel
fy is the yield strength of the reinforcement.
In BS 5400: Part 5 a factor of 0.91 (corresponding to a material factor of 1.1) is
used to modify the term Aspy. This formula is restricted to concrete contribution
factors, defined as 0.45fcuAc/Pu, between 0.15 and 0.8. In order for any reinforcement
to contribute to the axial load resistance of the column, shear links of not less than
5 mm diameter should be provided at not more than 150 mm spacing. The value of
Ar should not exceed 0.03Ac.
Limits on the proportion of the cross section 3 are that the concrete casing should
provide a minimum cover to the steel section of 40 mm, and that the dimensions of
the concrete section used in determining Pu should not exceed 1.8 ¥ b or 1.6 ¥ D
(where b is the flange width, and D is the depth of the steel section).
The relative slenderness of a composite column of length L is defined by the
slenderness factor:
L Ê Puˆ
l =
p Ë EsSI¯ Design of encased composite columns 655
(22.2)
where SI is the combined second moments of area of the concrete, steel section and
reinforcement expressed in steel units. To do this, the second moment of area of the
concrete is divided by the modular ratio Es/(450fcu), where Es is the elastic modulus
of steel in N/mm2 .
The slenderness factor l,
converted to an effective slenderness l by multiplying
l by p ( E / P ) , can then be used to determine the design stress, pc, for the steel
s y
section. The selection of the appropriate column design curve in BS 5950: Part 1
depends on the steel section used (i.e. Tables 24(a)–(d) in BS 5950: Part 1).
The design stress pc divided by py is then taken as a resistance reduction factor
K1 to be applied to all the components of Pu in Equation (22.1). Hence, this method
can be used to determine the axial resistance of a composite column, which is K1Pu
in the absence of applied moment. This method can be used for slenderness factors
less than 2.0, as proposed in Eurocode 4; 3 for greater slendernesses second-order
effects are underestimated. Columns of slenderness factor less than 0.2 may be
taken as ‘stocky’ (i.e. K1 = 1.0).
In BS 5400: Part 5, 1 short columns are defined as those where the ratio of the
length L to the least lateral dimension bc of the composite column does not exceed
12. Where short columns are not designed to be subject to significant applied
moment, the axial resistance may be taken as 0.85K1Pu, in which the factor 0.85
allows for slight eccentricity of axial load.
Slender columns are those where L/bc exceeds 12. In design to BS 5400: Part 5, 1
l
the analysis of the member should consider a minimum additional moment given
by the axial load times an eccentricity of 0.03bc. This, together with any further
applied moments, may be treated as in the following section.