Civil Engineering Reference
In-Depth Information
Global analysis
It is assumed that the major-axis joints between the beams and the inter-
nal column are rigid and full-strength, and that the frame is braced against
sidesway. The uncracked unreinforced second moment of area of the beam,
with
n
=
20.2, is given in Table 4.5 as
I
=
636
×
10
6
mm
4
, so
(
EI
)
beam
=
636
×
210
×
10
6
=
1.34
×
10
11
kN mm
2
(5.56)
254 UC73 steel
section, encased to 400 mm square, and with longitudinal reinforcement
of six T20 bars. To obtain its stiffness, an effective modulus for the
concrete is required. A low value, relative to that for the beams, reduces
the bending moments in the column, so the creep coefficient
The column was at first assumed to have a 254
×
3.0, used
in Section 5.7.2 for resistance, may be too high. The design is relatively
insensitive to this assumption, so the value
n
ϕ
=
2
n
0
is now used for the
whole loading, as for the beams. For the Grade C25/30 normal-density
concrete used,
E
cm
=
=
31 kN/mm
2
, so
n
=
2
×
210/31
=
13.6. This leads to
(
EI
)
column
=
0.60
×
10
11
kN mm
2
(5.57)
The beam members in Fig. 5.19 are over twice as long as the column
members, so the stiffnesses (
EI
)/
L
of beams and columns at nodes C, D,
etc., are similar. Moment distribution for this limited frame gives the
bending moments shown in Fig. 5.19, plotted on the tension side of each
member.
For the beams, from Section 4.2.1.2, the bending resistance at the
internal column is
M
pl,Rd
=
510 kN m
Cracking and inelastic behaviour are assumed to reduce the beam moments
that exceed 510 kN m to that value, by redistribution of moments to mid-
span, without altering the column moments. This enables the shear force
in each beam at nodes C, D, etc., to be found, and hence, the total axial
load in the column just above node D, including its weight. The result is
N
Ed
=
5401 kN
(5.58)
Resistance of an internal column
Approximate calculations then showed that the initial column cross-
section was too weak. The larger doubly-symmetric cross-section shown
in Fig. 5.20 was assumed. Its resistance was checked by the methods used
in Section 5.7 for external columns, taking account of the single-curvature
