Civil Engineering Reference
In-Depth Information
when the condition in Equation (4.9) is satisfied. In this case, the cracked
moment of inertia can be computed as (Figure 4.14c):
3
(
)
b d
dd
+
eff
f
2
I
nA
f
1
f
2
(
1
k
)
(4.80)
=
+
−
cr
f
f tot
,
3
2
If Equation (4.9) is not satisfied (Figure 4.14d), the neutral axis depth is to
be computed by solving the following equation for the unknown neutral axis
depth,
x
=
c
cr
:
2
bx
2
bb
xt
)
(
)
dd
−
+
eff
(
slab
f
1
f
2
(4.81)
nA
x
−−
=
−
eff
w
f
f tot
,
3
2
2
Once the neutral axis depth is determined, the cracked moment of inertia
of a T-section with N.A. through the web can be determined as
3
)
(
)
2
bc
3
bb
c
t
dd
c
−
+
(
eff r
cr
slab
f
1
f
2
I
nA
(4.82)
=
−
−
+
−
cr
eff
w
f
f tot
,
cr
3
3
2
Gross moment of inertia
Cracked moment of inertia (Section A-A)
b
e
b
e
t
slab
A
f
t
slab
d
g
d
f
c
g
c
cr
b
w
b
w
(a)
(b)
Cracked moment of inertia (Section B-B)
or
Cracked moment of inertia (Section B-B)
b
e
b
e
c
cr
t
slab
c
cr
t
slab
d
f
2
d
f
2
d
f
1
d
f
1
A
f
A
f
b
w
b
w
(c)
(d)
Figure 4.14
Gross and cracked moments of inertia of a T-beam.
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