Civil Engineering Reference
In-Depth Information
The upper limit is to ensure that the bars are not too congested at overlaps.
The thickness of concrete cover to the steel section that may be used in
calculations has upper limits
c
y
0.3
h
. These relate to the
proportions of columns for which this design method has been validated.
The
steel contribution ratio
=
0.4
b
,
c
z
=
δ
and the
slenderness
l (Section 5.6.3.1) are
limited for the same reason.
The steel contribution ratio is defined by
δ
=
A
a
f
yd
/
N
pl,Rd
(5.18)
where
f
yd
is the design yield strength of the structural steel, with the
condition
0.2
≤
δ
≤
0.9
If
δ
<
0.2, the column should be treated as reinforced concrete; and if
δ
0.9, as structural steel. The term
A
a
f
yd
is the contribution of the struc-
tural steel section to the plastic resistance
N
pl,Rd
, given by Equation 5.24.
>
5.6.3
Properties of column lengths
The characteristic elastic flexural stiffness of a column cross-section about
a principal axis (
y
or
z
) is the sum of contributions from the structural
steel (subscript a), the reinforcement (subscript s) and the concrete (sub-
script c), and so has the format:
(
EI
)
eff
=
E
a
I
a
+
E
s
I
s
+
K
c
E
c,eff
I
c
(5.19)
where
E
is the elastic modulus of the material and
I
the second moment of
area of the relevant cross-section.
The elastic critical normal force is found from
N
cr
=
π
2
(
EI
)
eff
/
L
2
(5.20)
where
L
should be taken as the length between the lateral restraints in the
plane of buckling considered. The 'concrete' term in Equation 5.19 is
based on calibration of results from this method against test data. It was
found that
K
c
0.6 and that creep should be allowed for by reducing the
mean short-term elastic modulus for concrete,
E
cm
, as follows:
=
E
c,eff
=
E
cm
/[1
+
(
N
G,Ed
/
N
Ed
)
ϕ
t
]
(5.21)
where the symbols are defined after Equation 5.7.
