Civil Engineering Reference
In-Depth Information
Figure 3.25
Elastic analysis of cross-section of composite beam in
sagging bending
b
eff
h
2
/(2
n
)
A
a
(
z
g
−
h
c
)
<
(3.85)
The neutral-axis depth is then given by the usual 'first moments of area'
equation,
b
eff
x
2
/(2
n
)
A
a
(
z
g
−
x
)
=
(3.86)
and the second moment of area, in 'steel' units, by
x
)
2
b
eff
x
3
/(3
n
)
I = I
a
+
A
a
(
z
g
−
+
(3.87)
If Condition 3.85 is not satisfied, then the neutral-axis depth exceeds
h
c
,
as in Fig. 3.25, and is given by
A
a
(
z
g
−
x
)
=
b
eff
h
c
(
x
−
h
c
/2)/
n
(3.88)
The second moment of area is
x
)
2
(
b
eff
h
c
/
n
)[
h
2
/12
h
c
/2)
2
]
I = I
a
+
A
a
(
z
g
−
+
+
(
x
−
(3.89)
In global analyses, it is sometimes convenient to use values of
I
based
on the uncracked composite section. The values of
x
and
I
are then given
by Equations 3.88 and 3.89 above, whether
x
exceeds
h
c
or not. In sagging
bending, the difference between the 'cracked' and 'uncracked' values of
I
is usually small.
Stresses due to a sagging bending moment
M
are normally calculated in
concrete only at level 1 in Fig. 3.25, and in steel at levels 3 and 4. These
stresses are, with tensile stress positive:
σ
c1
=
−
Mx
/(
nI
)
(3.90)
