Civil Engineering Reference
In-Depth Information
Verification, for uni-axial bending
The column is strong enough if its cross-section can resist the combina-
tion of
M
Ed
with
N
Ed
. The bending resistance
M
Rd
in the presence of axial
compression
N
Ed
is found from the interaction diagram, explained in
Section 5.6.4.
A correction is required for the unconservative assumption that the
rectangular stress block for concrete extends to the plastic neutral axis
(Section 3.5.3.1). It is made by reducing the bending resistance, so that
the verification condition is
M
Ed
≤
α
M
M
Rd
(5.31)
where
355 N/mm
2
for
sections of thickness up to 40 mm. It is reduced to 0.8 for stronger steels,
to take account of the adverse effect of their higher yield strain on the
load at which concrete begins to crush.
α
M
=
0.9 for steel grades up to S355, for which
f
y
=
5.6.5.2
Bi-axial bending
It has to be decided in which plane of bending failure is expected to
occur. This is usually obvious. The bending moment
N
Ed
e
0
is included
only for this plane. The axial load
N
Ed
and the maximum design bending
moments about both axes,
M
y,Ed
and
M
z,Ed
, are found, as in Section 5.6.5.1.
The verification consists of checking Expression 5.31 separately for each
axis and, in addition, satisfying Expression 5.32:
M
y,Ed
/
M
y,Rd
+
M
z,Ed
/
M
z,Rd
≤
1.0
(5.32)
5.6.6
Transverse and longitudinal shear
For applied end moments
M
1
and
M
2
, as defined in Section 5.6.1, the
transverse shear in a column length is (
M
1
M
2
)/
L
. An estimate can be
made of the longitudinal shear stress at the interface between steel and
concrete, by elastic analysis of the uncracked composite section. This
is rarely necessary in multi-storey structures, where these stresses are
usually very low.
Higher stresses may occur near joints at a floor level where the axial
load added to the column is a high proportion of the total axial load. Load
added after the column has become composite,
N
Ed
say, is assumed to
be transferred initially to the steel section, of area
A
a
. It is then shared
between the steel section and its encasement on a transformed area basis:
−
N
Ed,c
=
N
Ed
(1
−
A
a
/
A
)
(5.33)
