Civil Engineering Reference
In-Depth Information
Taking moments about the line of action of the force in the slab,
M
pl,Rd
=
A
a
f
yd
(
h
g
+
h
t
−
x
c
/2)
(3.57)
where
h
g
defines the position of the centre of area of the steel section,
which need not be symmetrical about its major (
y-y
) axis.
(2) Neutral axis within the steel top flange
If Equation 3.56 gives
x
c
>
h
c
, then it is replaced by:
N
c,f
=
b
eff
h
c
(0.85
f
cd
)
(3.58)
This force is now less than the yield force for the steel section, denoted by
N
a,pl
=
A
a
f
yd
(3.59)
so the plastic neutral axis is at depth
x
c
h
t
, and is at first assumed to lie
within the steel top flange (Fig. 3.15(c)). The condition for this is
>
N
ac
=
N
a,pl
−
N
c,f
≤
2
bt
f
f
yd
(3.60)
The distance
x
c
is most easily calculated by assuming that the strength of
the steel in compression is 2
f
yd
, so that the force
N
a,pl
and its line of action
can be left unchanged. Resolving longitudinally to determine
x
c
:
N
a,pl
=
N
c,f
+
N
ac
=
N
c,f
+
2
b
f
(
x
c
−
h
t
)
f
yd
(3.61)
Taking moments about the line of action of the force in the slab,
M
pl,Rd
=
N
a,pl
(
h
g
+
h
t
−
h
c
/2)
−
N
ac
(
x
c
−
h
c
+
h
t
)/2
(3.62)
t
f
,
the plastic neutral axis lies within the
steel web, and
M
pl,Rd
can be found by a similar method.
If
x
c
is found to exceed
h
t
+
(3) Partial shear connection
The symbol
N
c,f
was used in paragraphs (1) and (2) above for consistency
with the treatment of composite slabs in Section 3.3.1. In design, its value
is always the lesser of the two values given by Equations 3.56 and 3.58. It
is the force that the shear connectors between the section of maximum
sagging moment and each free end of the beam (a 'shear span') must be
designed to resist, if full shear connection is to be provided.
Let us suppose that the shear connection is designed to resist a force
N
c
,
smaller than
N
c,f
. If each connector has the same resistance to shear, and
