Civil Engineering Reference
In-Depth Information
The coefficient
k
in Equation (3.36) is determined from Equation (3.31). In the absence of
compression steel (
0), Equation (3.36) degenerates into Equation (3.27).
The cracked moment of inertia can be written simply as
I
cr
=
β
c
=
K
i
2
bd
3
, where
K
i
2
denotes
the expression in the bracket in Equation (3.36).
K
i
2
is a function of
n
β
c
and
d
/
ρ
,
d
and is
tabulated in ACI Special Publication SP-17(73).
3.1.3.3 Flanged Sections
A typical flanged section (T-section) is shown in Figure 3.4(a), together with the transformed
area in Figure 3.4(b). Comparing this transformed area for the T-section with the transformed
area for the doubly rectangular reinforced section in Figure 3.3(d), we observe that they are
identical except for two minor differences. First, the area of the top flange is (
b
−
b
w
)
h
f
rather
than
mA
s
. Second, the centroidal axis of the top flange is located at a distance
h
f
/
2fromthe
top surface rather than at a distance
d
.
Therefore, the formulas for cracked moment of inertia of doubly reinforced sections (Equa-
tions 3.36 and 3.31), are also applicable to T-sections, if these two differences are taken care
of as follows:
(1) Redefine the original definition of the symbol
β
c
in Equation (3.30) by substituting
ρ
:
(
b
−
b
w
)
h
f
/
b
w
d
for
m
(
b
−
b
w
)
h
f
β
c
=
(3.37)
(
n
ρ
)
b
w
d
(2) Replace
d
d
h
f
2
d
by
In conclusion, the cracked moments of inertia
I
cr
for flanged sections are calculated by
Equations (3.36) and (3.31), with the symbol
β
c
defined by Equation (3.37) and the ratio
d
/
d
replaced by
h
f
/
2
d
.
Figure 3.4
Cracked flanged sections
