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REINFORCED AND PRESTRESSED CONCRETE I C6-
Reinforced and Prestressed ConcreteReinforced and Prestressed
Concrete -- CC 66 --
Milwaukee Art Museum, USA
Santiago Calatrava
Jubilee Church - Rome, Italy
Richard Meier
Dubai Arch Bridge 20 12
2
Flanged Section in Bending
T-sections and L-sections, having their flanges in compression,
can both be designed or
analyzed in a similar manner,
the flanges generally provide a large compressive area.
FLANGED
SECTIONS
Double
Reinforced
Singly
Reinforced
fhx
fhx >
fhx >
and lims 1
and lims >1
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fhx >Singly Reinforced Flanged Section
if , then:fhx >
>
=
d
h.
d
h
b
b
fdb
M ff
wcdw
Ed 5012
21 ,Rd,RdEd MMM +=
21111 ,s,ss AAA +=
21
xdz
=
22
fhdz =
==
2111
xdfxbzFM cdwc,Rd
( )
==
2222
fcdfwc,Rd
hdfhbbzFM
and lims 1
6
fhx >Singly Reinforced Flanged Section
( )
==
221
fcdfwEd,RdEd,Rd
hdfhbbMMMM
cdw fdb
2
1
( )
cdw
fcdfw
cdw
Ed
cdw
,Rd
fdb
hdfhbb
fdb
M
fdb
M
= 2221 2
=
d
h.
b
b
d
h f
w
fs 50111
and lims 1
Double Reinforced
Section
Singly Reinforced
Sectionlims 1
lims >1
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we check if the tension steel yields:
lims 1
if , then the flanged section is simply reinforced:
0111 = ,c,s FF yd,scdw fAfxb = 11
yd
cdw
yd
cdw,s
f
fdb
f
fdb
d
xA =
= 11
0221 = ,c,s FF ( ) yd,scdfw fAfhbb = 21
( )yd
cdfw,s
f
fhbbA = 21
( )yd
cdfw
yd
cdw,s,ss
f
fhbb
f
fdbAAA +=+= 21111
yd
cdw
f
ws
ffdb
dh
bbA
+= 11
x
xd
cu
s =3
1
s
ydydcucus
E
f. =
=
=
=
100350
11
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8
fhx >Double Reinforced Flanged Section and lims >1
321 ,Rd,Rd,RdEd MMMM ++=
3121111 ,s,s,ss AAAA ++=
21
xdz
=
22
fhdz =
23 ddz =
==
2111
xdfxbzFM cdwc,Rd
( )
==
2222
fcdfwc,Rd
hdfhbbzFM
( )22323313 ddfAzFzFM ydss,s,Rd ===
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if , then the flanged section is double reinforced, and :lims
>1
cdwlim,Rd fdbM =2
1
( )
=
22
fcdfw,Rd
hdfhbbM
213 ,Rd,RdEd,Rd MMMM =
( ) ( ) ( )fcdfwcdwlimEdyds h.dfhbbfdbMddfA = 502
22 cdw fdb
2
1
( ) ( )
cdw
fcdfw
cdw
cdwlim
cdw
Ed
cdw
yds
fdb
h.dfhbb
fdb
fdb
fdb
M
fdb
ddfA
=
22
2
22
22 50
( )
=
d
h.
d
h
b
b
fdb
ddfA ff
w
lim
cdw
yds5011
2
22
( ) yd
cdw
ff
wlim
sf
fdb
dd
d
h.
d
h
b
b
A
= 22
2
5011
ydsyd,s fAfA = 231
231 s,s AA =
10
( ) cdlimwyd,s fdbfA = 11 ( )yd
cdlimw,s
f
fdbA = 11
( ) cdfwyd,s fhbbfA = 21 ( )yd
cdfw,s
f
fhbbA = 21
3121111 ,s,s,ss AAAA ++=
( ) 21 syd
cdfw
yd
cdlimws A
f
fhbb
f
fdbA ++=
( )[ ] 21 sfwlimwyd
cds Ahbbdb
f
fA ++=
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yd
cdw
f
ws
f
fdb
d
h
b
bA
+= 11
12
Effective width of flanges
The effective flange width of T beams,depends on:
the web and flange dimensions,
the type of loading, the span,
the support conditions,
the transverse reinforcement.
The design of the effective flange width is
based on the distance l0 between points ofzero moment if:
1,effl 2,effl 3,effl
10 850 ,effl.l =
210 150 ,eff,eff ll.l +=
20 70 ,effl.l =
320 150 ,eff,eff ll.l +=
Section 1-1
23321
/.../l
l
i,eff
i,eff =+
23 50 ,eff,eff l.l
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