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In constructions, flanged sections may occur in the forms of
monolithic beam-slab and T or L beams as
shown in Figure 2.6 below. The composite action between flange
and web resulting in the whole section
bend as one piece.
The design of the flanged section is divided into two groups,
depending on the depth of the compression or
stress bloc as shown below.
The depth of the compression !one reflects the concrete
resistance to the e"ternal design moment, M#d. Thus
the depth of the stress blocs, is determined by checing the
resistance of the fully compressed flange,Mf.
2.4.1 Design of Flange section - stress block within the
flange
19
bf
bw bw
hf hf
d d
Figure 2.6 Flanged sections.
$a% &onolithic beam-slab $b% T-beam $c% L-beam
h
slab
beam
bf
N.A
N.A
MEdMEd
$i% 'ompression()tress bloc within flange $ii%
'ompression()tress bloc in the web
FccFcc
Fst Fst
x
x ss
2.4 FLANGD !"#$%N
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Figure 2.* shows a flanged section with the stress bloc within
flange and stress-strains distributions.
"ondn
Mf&Md
( )fffckf h5,0dhbf567,0M = $2.+%
The section is designed as a ectang!la section ofb'bf" d.
(ef. "alculations %ut)ut
*a+)le 2.4.1(1)
erify that the neutral a"is of T-beam shown in the figure
below is within the flange if it is subected to an
e"ternalmoment of +2/ 0m.
1etermine the reinforcement area if the characteristiccylinder
strengthfck 23 0(mm
2andf"k 3// 0(mm2.
4mm5
20
Figure 2., Flanged section with stress block within flanges #
0.$x % hf.
x s # hf
As
bw
hf
bf
Fst
Fcc
0,567fckc!
"k
& # d ' hf()dM#d
bf# *00
hf
# +00
d# 50
bw
# )00
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The flange width bfin the design euations is the effective
flange width, beff. #'2 clause 3..2.+ specifies
beffas follow7
21
(ef. "alculations %ut)ut
-l. .).+.+/+
-l. .).+.+/
!olution
The moment of esistance of the flange
fffckf h5,0dhbf567,0M =
+00x5,050/+00x*00x)5x567,0 =
0mm+/"+,+8/ 6
=
Mf1 MEd stess block within the flange.
2esign as a ectang!la beam of bf"d3
)fck
Ed
dbf
Mk= )
6
50x*00x)5
+0x+)0k=
4k0.$,0 >=
o8ide 9)0 As# *) mm)
mm+5& =
*00+00
50
)00
:2/ *92 mm2
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i% beff beff,i: bwb for monolithic cast beam-slab.
where
beff,i 0,)bi; 0,+lothe minim!m of0,)loand bi
lois the distance between oints of &eo moments.
*)ee figures (2.8)and (2.
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2.4.2 Flange section with stress block in the web !ingl
reinforced
23
(ef. "alculations %ut)ut
5..).+
-l. .).+.+/+
-l. .).+.+/
!olution
a) Effective flnge width beff
beff +# beff )# 0,)bi; 0,+lothe minim!m of0,)loand bi
0,)bi; 0,+lo# 0,)/+000; 0,+/5$)5 # 7$),5 mm
0,)lo# 0,)/5$)5 # ++65 mm
b+# b)# +000 mm
beff +# beff )# 7$),5 mm
bf# beff# beff i: bw# 7$),5 : 7$),5 : )50 # +$+5 mm
b) Main reinforcement- MEd= 150 kNm
The moment of esistance of the flange
fffckf h5,0dhbf567,0M =
+00x5,0*50/+00x+$+5x0x567,0 =
0mm+/"+2,3 6
=
Mf1 MEd
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@hen the e"ternal bending moment, MEd is greater than the flange
resistance, Mf, the compression will
move into the web, figure 2.+/.
"ondn
Mf= MEd= Mf bal
)
fckflabf dbf>M =
f
wff
f
wf
b
b+67,0
d
h
d)
h+
b
b+567,0> +
=
( )f"kfwck
sh5,0df$7,0
h0,6ddbf+,0MA
+
2.4.5 Flange section with stress block in the web Doubl
reinforced
@henMis greater thanMbal, the section reuires compression
reinforcement. Figure 2.++ shows a doubly
reinforced flanged section with the neutral a"is in the web (x #
0,*5d)and stress-strains distributions.
)
fckflabf dbf>M =
f
wff
f
wf
b
b+67,0
d
h
d)
h+
b
b+567,0> +
=
( )
( )4ddf$7,0
MM4A
"k
labs
= dA should be taen as d?(xbal% 0,$
s"k
fwfckwck
s 4Af$7,0
hbbf567,0dbf)0*,0A +
+=
24
sx
bw
hf
bf
Fst
Fccf
0,567fckc!
"k
&w
Figure 2.10 !ingl reinforced flanged section with stress block
in the web.
d
M
Fccw &
f
As
As
sx
bw
hf
bf
Fst
Fccf
0,567fckc!
"k
&w
Figure 2.11 Doubl reinforced flanged section with stress block
in the web.
d
M
Fccw &f
Fsc
&sc
A?s
