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-- 2011 -
129
*
****
.
:
. .
.
.
[1-2-3-4-9]
.
[8].
.
:.
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***-
130
:
.
(deflections)
:
1- --
.
.
.
.
2-
.
)(
.
)Long-Term deflection(
).(
ACI 435R-95
[2]
ACI 209.2R-08 [3]
)Short-Term Deflection(
.
)Creep
and Shrinkage(.
.
[1]
ACI-318R-08[9].
:
--
.
.[6-10-11]
.
.
.
-- 2011 -
131
ACI 435R-95
sustLLT . %
)20-40(
[2]
.
.
:
:
-
.
-
.
- .
-
)
(4.0'cf
4.0'cf
)Long-Term
Deflection(:
)Long-Term Deflection (
ACI-318R-08 [1] ACI-435R-95 [2]
t:
)1(. sustLLT
:
L
sus )
(
t
t
)2('501t
'
.
:
25.
1.41.
1.26.
13.
)1(
.
132
)1(:
ACI-318R-08
-
- .
)
(
:
) CEB MC90 Model , GL2000 Model , ACI209
Model , B3 Model ([3-4]
.
)2 (
)3(
.
),( 0ttJ
),,( 0 ssh ttt
.
)3(),()(1
),( 000 tttnE
ttJC
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0
00 t
ttE
ci
cC
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t
0t
st
),( 0tt
)( 0tc
)( 0tci)(
)(
-- 2011 -
133
)2(:[3-4]
)3(:[3-4]
134
)Long-Term
Deflection ([9] :
ACI-
318R-08 :
)6(
.'
501db
A s
:
c
tc
c
c
E
f
E
)(,
dtEdt
tdf
tEdt
td
c
ttc
c
ct
0.)(
)(
1.
)(
0
0
00
0
0
)7()(
s
s
E
t
ACI-318R-08
23
25
1.41
1.41
1.20.5
1.20.5
11
1
3
:
.
Ec
Es
s(t) t
c(t)t
t t
t0 t0
:
.
:
1-
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(
2-
3-
4- cf `
0t
5- NM
6-
[3-4])
(
7-
-- 2011 -
135
8-
9-
t
:
:
)10(.)(
,
)()( 0 t
tE
tt
tEt shi
10-
.
-
cf `4.0
CEB MC90
Model [4]
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5.1exp.),( 0c
o ftt
-
NfixMfix
.
.
-
.
-
t.
- it.
-
:
1- it
)(.
2- 2/2100 cmkgf y
2/4200 cmkgf y
)(.
)4(
.
)9()(.)(
, 0icr f
tE
tt
)8()(
, 0icr tE
tt
136
)4(:
-- 2011 -
137
:
[8]
cmaa
cmHcmB
1'
20,10
:
181,81' TAA ss
:
10,/10.2,/200' 252 ncmkgEcmkgf cc
:cmL 220
:dayst 280
: mtM .8.4
)5(:
[4] CEB-MC90-99
)6(
:
- 1st .
- RN , :.
- %70RH .
10,/10.2,/200' 252 ncmkgEcmkgf cc
- .
- cmH 20.
[4] CEB-MC90-99 .
:
5.2
6
100'6
100'.10.700
c
c
f
fsh
62.0 10.88.6711. te
)12(.
1400100'.11.0 cf
s
s ett
tt
B=10 cm
H=20cm
8
T 18
L=220c
138
:
.1.0
1*7207.8),(
2.00 ttt
)13(35.1984
3.0
0
0
tt
tt
)6(:
[4]
)Step-by-Step (
[4] CEB-MC90-99
.
)7(
[8].
[1] ACI-318R-08
270
20.%
ACI-318R-08.
)7( :
[1]ACI-318R-08
] 8[
)8 (
.
)8(:
)(
)
(
)
(
)(
)(
-- 2011 -
139
'
ACI-318R-08
)9(
27%28
7.
)9(:
33 %
2.0''
)10 (
.
)10(:
)11(
.
)11(:
)12 (
4.0'cf
)(
140
)12(:
4.0'cf
:
:
22 60,20' cmAcmA ss
:
10,/10.2,/200' 252 ncmkgEcmkgf cc
:cmL 1200
: dayst 280
: mtM .100
)13(:
cmaa
cmLcmLL
cmHcmBcmBB
5'
60,20
100,15,40
231
231
)14(
80kg/cm2
0.4
.
L=1200
cmmm
-- 2011 -
141
)14 (
:
)
(
.
)(
.
.
)(
.
)ACI-318R-
08(
.
(Deflection)
.
142
1. ACI-318R-08 Building Code Requirements for Structural Concrete (ACI 318-08)and
Commentary ACI committee318 January
2008 2. ACI 435R-95 Guide Control of Deflection in
Concrete Structuresin hardened concrete ACI
committee435 Reapproved 2000 Appendix B
added 2003 3. ACI209.2R-08 Guide for modeling and
calculating shrinkage and creep in hardened
concrete ACI committee209 May 2008
4. CEB-FIP Model Code 1990, CEB Bulletin
d Information, No. 213/214, Comité Euro-
International du Béton, Lausanne, Switzerland, 1990.
5. H.S. Muler, C. H. Kuttner, V. Kuitsel «Creep and Shrinkage Models for Normal and Unified Code-Type Approach», eds. F.J. ulm, M. Prat, J. A. Calgaro and I Card Revue Francaise de Hernes Science, Publication, Paris 1999, Génie Civil. P 15-19. PP. 113-132
6. Long-term deflections in cracked reinforced concrete flexural members- Antonio R. Mar _, Jes s M. Bair n, Noemi Duarte-Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain-2010.
7. Simplified procedures for calculation of instantaneous and long-term deflections of reinforced concrete beams - José Milton de Ara jo- Department of Materials and
Construction, University of Rio Grande
FURG- Campus Carreiros, Av. It lia, 96203-000, Rio Grande, RS, Brazil-2005.
8. . .
-
" " 1967.
9.
2004
14/11/2010
10.
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-
-1997
11.
-
:
-2007