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高強度鋼筋混凝土梁之高強度鋼筋混凝土梁之裂縫發展與控制裂縫發展與控制
邱建國Associate Professor,Department of Civil and Construction Engineering,Taiwan-TECH.
Life-Cycle ofStructure Engineering
2015/12/11
ContentContent
Destination
D i C dDesignCodes
Experimentp
ShearCrackControl
FlexuralCrackControl
ConclusionsConclusions
1
DestinationDestinationDestinationDestination
l l k lPerformance
① FlexuralCrackControl(ACI318)
② ShearCrackControl(AIJ2010)
③ Damage Evaluation
Service-ability
Repar-abilitySafety
③ DamageEvaluationCrackWidthsandDeformation
Crack widthExperiment
Design Damage Evaluation
Ref:日本建築學會‧鋼筋混凝土建築物之耐震性能評價指針,2004,5.梁部材の性能評価法,pp.129~168 2
Shear Crack ControlShear Crack ControlAllowable shear force corresponding to
Shear Crack ControlShear Crack ControlAIJ(2010)
i fAllowableshearforcecorrespondingtoserviceabilityensuring
Reinforcement
Allowableshearforcecorrespondingtoreparabilityensuring
Concrete
3
Shear Crack ControlShear Crack ControlShear Crack ControlShear Crack ControlAIJ(2010)According the research conducted by Simazaki (2009), if the long-termg y ( ), gloading is less than VAL1, the maximum shear crack width can becontrolled within 0.3 mm. If the short-term loading of a medium-magnitude is less than VSL1, the residual maximum shear crack widthcan be controlled within 0.3 mm.
4
Flexural Crack ControlFlexural Crack ControlFlexural Crack ControlFlexural Crack ControlACI-318 (2005) 280380( ) 2.5 cs cf
Ref Robert J Frosch (1999)
280300( )
s
s
f
sf
(1) Model:
Ref.RobertJ.Frosch (1999)
fsc s c c
s
fw S SE
CrackwidthgrowslinearlyN.A
h
c
dd c
1max c c
h cw w wd c
2
Ref:Robert J. Frosch, 1999, Another Look at Cracking Control in Reinforced Concrete, ACI Structural Journal 5
Flexural Crack ControlFlexural Crack ControlFlexural Crack ControlFlexural Crack ControlACI-318 (2002&2005)
(2) Crackspacing
Ref.RobertJ.Frosch(1999) Fromthebarcentertothefarthest
concrete element
d *d2*dC
concreteelement
sh c fw S * 2 21 c cd d d
d1*2dC
sControl !
maxs
cw cS
d E* 2 22 ( )2c
sd d
Control !
f s2 22 ( )2
smax c
s
f sw dE
Ref:Robert J. Frosch, 1999, Another Look at Cracking Control in Reinforced Concrete, ACI Structural Journal 6
Flexural Crack ControlFlexural Crack ControlC 318 2002 & 200ACI-318 (2002&2005)
Cs s
250 300 252s 380 ‐ 2.5Cf f
0280 300 28380 2 5C
0.41 mm
0 41 0 53
(3) Crackcontrol
Ref.RobertJ.Frosch (1999) Cs ss 380 ‐ 2.5C
f f 0.41‐0.53 mm
2 22 ( )2
smax c
s
f sw dE
2 22 ( )2max s
cw Es d
f
2 sf
Crackwidth:0.41 mmTensilestressofmainbars:0.6fy
Ref:Robert J. Frosch, 1999, Another Look at Cracking Control in Reinforced Concrete, ACI Structural Journal
cC 代替 cd7
Experiment Experiment ppSpecimenDesign
Chiuetal.(2013)Yielding stress 685、785MPaReinforcement size D32(#10)、D25(#8)
Stirrup ratioStirrup ratio
2000 mm2000 mm
2000 mm
Hinge
Roller
Number:10Concretecover:4cm
Compressive strength 70、100MPaSection size
Chiuetal.(2015) Chiuetal.(2014)
N b
Shear span to depth ratioShear span to depth ratioConcrete coverConcrete cover
Chengetal.(2014)400~2000Hinge
Roller Number:10Concretecover:4cm
g2000 mm
Number:3
Number:2Concretecover:2、3cm
Cyclic loadingCyclic loading
u be :3Concretecover:3cm
8
Experiment Experiment ppMeasurementsystem
1. Crackmeasurement 2. NDI
等剪力段 等彎矩段Moment-equivalentShear-
l等剪力段 等彎矩段
剪力裂縫量測處regionequivalent
region
撓曲裂縫量測處3. Strainofreinforcement
9
Shear CrackExperimental DataExperimental DataShearCrack
TensileStrengthofConcrete
ShearCrackStrengthofC tConcrete
10
Shear CrackExperimental DataExperimental DataShearCrack
UltimateShearStrengthofConcrete
11
Shear CrackExperimental DataExperimental DataShearCrack
12
Shear Crack ControlShear Crack ControlDesign FormulaDesign Formula
10
Averageshearstress andMaximum Shear crack width
v/v c
r
MaximumShearcrackwidth(Reinforcement785MPa)
1v
1
1E-008 1E-007 1E-006 1E-005 0.0001(wps,max/d)*(pw)
1313
Shear CrackExperimental DataExperimental Data
AllowableShearStress(Maximum shear crack width0 3 mm)
ShearCrack
1.2
(Maximumshearcrackwidth0.3 mm)
1
0.6
0.8
P wf s
0.4P
0.2
140 0.004 0.008 0.012pw
0(MPa)
Shear CrackExperimental DataExperimental DataShearCrack
Allowable Shear Stress Allowable Shear StressAllowableShearStress(Maximumshearcrackwidth 1.0 mm)
AllowableShearStress(Maximumresidual
shear crack width 0 415
shearcrackwidth 0.4mm)
Shear Crack ControlShear Crack ControlDesign FormulaDesign Formula
Performance Allowable shear stress (MPa)
Long- Serviceability
Shear crackstrength
-term
ServiceabilityMaximumMaximum shearshear
crackwidthcrackwidth0 40 40.4mm0.4mm
ShortR bilit
Maximum sheark idth-
termReparability crackwidth
1.0mm
16
Shear Crack ControlShear Crack ControlDesign Formula
1.8
2.0
pwu,b/D=0.50pwu,b/D=0.55
Design Formula
1 4
1.6
pwu,b/D=0.60pwu,b/D=0.65pwa,b/D=0.50pwa,b/D=0.55
Serviceability
1.2
1.4
Rat
io(%
) pwa,b/D=0.60pwa,b/D=0.65
0.8
1.0
Stir
rups
R
SeismicDesign
:2.5%685
Assumption
f MP
0.4
0.6
S 6850.125 ( 785 )550
y
sa yt yt
f MPaf f f MPaf MPa
0.22
2
5501300 /1000 1.2 300 /
su
a
u
f MPaw kgf mw kgf m
0
10 11 12 13 14 15 16 17 18
Ln/D 17
Shear Crack ControlShear Crack ControlDesign FormulaDesign Formula
0 4 mmb/D:0.45-0.55B/L: 0.5-1.0
Randomvariables
0.4 mm B/L:0.5 1.0DeadLoad:800-1100kgf/mLiveLoad:200-400kgf/m2
fy:685Mpafyt:785Mpaf 550 MP
0.3 mm
fsu:550MPafsa:0.125or0.15fyt
L/DMCSmax (L/D) = 12max (L/D) = 12 (0.9997, 0.40mm)(0.9997, 0.40mm)
Reliability
18
Flexural Crack ControlFlexural Crack Control
'0 35 0 33 f A f手冊建議, 4.3.2
'0.351.5
c v sserw
f A fvb s
0.35 0.331.5
c v sserw
f A fvb s
f為剪力鋼筋之容許應力,最大值為0 15f[解說]設計剪應力之計算可參考ACI318之建議,v=V/(bwd)。計算梁構件於靜載重與活載重下之斷面剪應力時,不須考慮兩載
fs為剪力鋼筋之容許應力,最大值為0.15fyt
重之載重放大因子。式(4.3.1)之前項為混凝土之容許應力,依實驗結果可知,其與構件之剪力跨距與深度比有密切相關,就一
般中長梁而言則建議採用0.35[3]。由式(4.3.1)可知,梁構件可藉由剪力鋼筋之用量以提升其容許應力。若梁構件之跨深比增加,
為有效控制靜載重與活載重下之剪力裂縫,則具所需之剪力鋼
筋用量亦會增加,並會大於耐震設計下剪力鋼筋量;反之,若
19
能將梁構件之跨深比降至12以下,則耐震設計下剪力鋼筋需求會主控設計,而不須檢核本節規定[3]。
Experimental DataExperimental DataExperimental DataExperimental DataFlexuralCrack
600
700
(MPa
) Flexural crack
400
500
stre
ss f
s(
200
300
rcem
ent s
本研究試體
102年試體[17]
103年試體[18]
0
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Rei
nfor 103年試體[18]
文獻[21]
Maximum crack width (mm)
Crack width is proportional to reinforcement stress
20
Experimental DataExperimental DataExperimental DataExperimental DataStable →Crack number not increased →Crack spacing turns to be constantFlexuralCrackStable →Crack number not increased →Crack spacing turns to be constant
400
500
acin
g
2C100
400500
acin
g
3C100
0
100
200
300
Avg.
Cra
ck S
pa
0100200300
0 2 4 6 8 10 12 14 16 18 20Avg.
Cra
ck S
pa
300ng
175R100500g
275R100500
325R70
0 2 4 6 8 10 12 14 16 18 20Av
Cuvature : rad/m ()0 2 4 6 8 10 12 14 16 18 20Av
Cuvature : rad/m ()
0100150200250300
Cra
ck S
paci
n
100
200
300
400
500
Cra
ck S
paci
ng
200
300
400
500
rack
Spa
cing
A k i C k b /S f h i l i
050
0 2 4 6 8 10 12 14
Avg.
C
Cuvature : rad/m (‰)
0
100
0 2 4 6 8 10 12 14 16 18 20Avg
. C
Cuvature : rad/m ()0
100
0 3 6 9 12 15 18 21 24 27 30Avg
. Cr
Cuvature : rad/m ()
Average crack spacing=Crack numbers/Span of the moment-equivalent region
21
AverageAverage CCrack Spacingrack SpacingAverage Average CCrack Spacingrack SpacingCrack width=(strain)(crack spacing)
ACI 318(2002&2005)
AIJ-2010(附錄)
JSCE-2007
CEB-FIP
Broms
趙唯堅與丸山
22
Fl l C k A C k S i
Experimental DataExperimental Data
ACI-318: 2 2( )sd * *1 2[ ]
Flexural Crack-Average Crack Spacing
ACI 318:
本研究試體 文獻[17] 文獻[18] 文獻[21] 本研究試體 文獻[17] 文獻[18] 文獻[21]
( )2c
d 1 2[ , ]
140
160
180
paci
ng(m
m)
140
160
180
g. S
paci
ng ModifiedUnconservative
80
100
120
rim
ent A
vg. S
p
80
100
120
xper
imen
t Avg
6060 80 100 120 140 160 180E
xper
ACI -318 Avg. Spacing
6060 80 100 120 140 160 180
Ex
ACI -318 Avg. Spacing (Modified)
d1*d2*dC
s 23
Fl l C k A C k S i
Experimental DataExperimental Data
AIJ 2010 (附錄) JSCE 2007
Flexural Crack-Average Crack Spacing
AIJ-2010 (附錄) JSCE-2007
本研究試體 文獻[17] 文獻[18] 文獻[21] 本研究試體 文獻[17] 文獻[18] 文獻[21]
140
160
180
Spac
ing
[ ] [ ] [ ]
140
160
180
Spac
ing
[ ] [ ] [ ]
80
100
120
erim
ent A
vg.
60
80
100
120
rim
ent A
vg.
60
80
60 80 100 120 140 160 180
Exp
e
AIJ - 2010 Avg. Spacing
40
60
40 60 80 100 120 140 160 180Exp
erJSCE -2007 Avg. Spacing
24
Fl l C k A C k S i
Experimental DataExperimental Data
180.
本研究試體 文獻[17] 文獻[18] 文獻[21]
Flexural Crack-Average Crack Spacing
CEB-FIP100120140160
peri
men
t Avg
.Sp
acin
g
6080
60 80 100 120 140 160 180
Exp
Model Code 2010 Avg. Spacing
Broms 趙唯堅與丸山
160180
vg.
本研究試體 文獻[17] 文獻[18] 文獻[21]
140160180
Avg.
g
本研究試體 文獻[17] 文獻[18] 文獻[21]
80100120140
Exp
erim
ent A
vSp
acin
g
6080
100120140
Exp
erim
ent
Spac
ing
6060 80 100 120 140 160 180
E
Broms. 研究建議 Avg. Spacing
6060 80 100 120 140 160 180趙唯堅與丸山久一研究建議 Avg. Spacing
25
Fl l C k Width
Experimental DataExperimental DataFlexural Crack Width
ACI 318 (2002 & 2005)
ACI 318
4
5
h R
atio
ode)
ACI - 318
4
5
h R
atio
ode)
ACI - 318 (Modified)
Modified. 1.15ExpCode
wAvg
W . 1.06Exp
Code
wAvg
W
1
2
3
Cra
ck W
idth
(Exp
. / C
o
1
2
3
Cra
ck W
idth
(Exp
. / C
o
Unconservative
0
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f / fd2* using
0
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
fs / fyusing max{d1*,d2*} fs / fy fs / fy
26
Fl l C k A C k S i
Experimental DataExperimental Data
AIJ-2010(附
Flexural Crack-Average Crack Spacing
(錄)JSCE-2007
5
o
AIJ - 2010
h 0 0002
5
o
JSCE - 2007
h 0 0002
2
3
4
k W
idth
Rat
ioE
xp. /
Cod
e)
εsh=0.0002εsh=0.0004
2
3
4
k W
idth
Rat
ioE
xp. /
Cod
e)
εsh=0.0002εsh=0.0004
0
1
2
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1
Cra
ck (E
0
1
2
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1C
rack (E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
fs / fy
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
fs / fy
Good prediction Good prediction in low stress0.002, . 0.87Expsh
Code
wAvg
w
Good prediction generally
Good prediction in low stress0.004, . 0.68Expsh
Code
wAvg
w
27
Fl l C k A C k S i
Experimental DataExperimental Data
CEB-FIP 5CEB-FIP 2010
Flexural Crack-Average Crack Spacing
CEB-FIP
2
3
4
Wid
th R
atio
p. /
Cod
e)
0
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cra
ck
(Ex
fs / fy
Broms 趙唯堅與丸山fs fy
4
5
Rat
iode
)
Broms. 相關研究
4
5
atio
)
趙唯堅 & 丸山久一相關研究
εsh=0.0002εsh=0 0004
0
1
2
3
Cra
ck W
idth
R(E
xp. /
Cod
1
2
3ra
ck W
idth
Ra
(Exp
. / C
ode) εsh=0.0004
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
C
fs / fy
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cr
fs / fy 28
Flexural Crack ControlFlexural Crack ControlDesign Formula
Problems: 5
o
ACI - 318
0 4 0 88Expswf f A
Design Formula
2
3
4
k W
idth
Rat
ioE
xp. /
Cod
e)(1) Low stress level
(2) Section parameter
0.4 , . 0.88Exps yy code
f f Avgf w
0
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cra
ck (E
d * d
Improving:Crack spacing
Assumption:Bi linear fs / fyd2* used
275R100
Bi-linearAverage stress:263MPa
300
400
500
ack
Spac
ing
3
ϕ209sf MPa
0
100
200
0 2 4 6 8 10 12 14 16 18 20
Avg.
Cra
1
0 0 4
ϕ
Cuvature : rad/m () 0 0.4fs / fy
29
Flexural Crack ControlFlexural Crack ControlDesign Formula
4
5
o
Modified
0 82Expw
Avg
Design Formula
Problems:
2
3
4
ck W
idth
Rat
iE
xp. /
Cod
e)
. 0.82Code
Avgw
( ) sma cf sw d 2 22
(1) Low stress level
0
1
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1
Cra
c (E
( ) max cs
w dE2 2
( / ), / . s y s yf f f f3 5 0 0 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
fs / fy(2) Section parameter0.8
d1*d2*dC :預測偏低
* *2 1d d
0.4
0.6
0.8
縫寬
度(m
m)
using d1*
s * *
( )
d dsd d d
2 1
2 2 2 20
0.2
0 100 200 300 400 500 600 700
最大
裂縫
ACI-318
30
( )
c c
c
c
d
d d
s
d
22
0 100 200 300 400 500 600 700最大鋼筋應力 (MPa)
Flexural Crack ControlFlexural Crack ControlDesign Formula
( ) smax cs
f sw dE2 22
2
Design Formula
Proposed formulap
. cs cf 280380 2 5
s
s
f
s f280300
31
s
Flexural Crack ControlFlexural Crack Control
280380 2 5 s C手冊建議, 4.3.2 300 280
s380 2.5 cs
s Cf
s
sf
fs為在使用載重下算得之鋼筋應力,若其小於0 4f時 須以0 4f取代之於0.4fy時,須以0.4fy取代之
[解說] 依現階段之實驗結果可知,梁撓曲裂縫控制可延用ACI318之規定。然[ ]而於使用載重下梁之鋼筋應力偏低,則依式計算所得之撓曲裂縫間距會有過
小之疑慮,而造成裂縫寬度之計算值亦偏小而不保守;因此,fs若其小於0.4fy時 須以0 4f代入式 以決定鋼筋中心距 之最大容許值[4]時,須以0.4fy代入式,以決定鋼筋中心距s之最大容許值[4]。
[解說] 依ACI318-02可知,式之成立條件為假設鋼筋中心距s之一半會大於撓曲受拉鋼筋中心至最近受拉面之距離 且依現階段之實驗結果可知 若鋼筋曲受拉鋼筋中心至最近受拉面之距離,且依現階段之實驗結果可知,若鋼筋
中心距s之一半小於撓曲受拉鋼筋中心至最近受拉面之距離時,則依式計算所得之撓曲裂縫間距會有過小之疑慮;因此,本手冊建議鋼筋中心距s之選取不
32宜小於2Cc[4]。
ConclusionsConclusions
( ) 280380 2 5
Spacingofreinforcement
( ) .
( )
cs
s cf
s f
380 2 5
280300
33
( )sf
Th kThank you
Life-Cycle ofStructure EngineeringStructure Engineering
34
Past ResearchesPast ResearchesFlexuralCrackPast ResearchesPast Researches
Bengt.B.Broms (1965)
Specimens
1.Stablestate:140~210MPa2 C k i 2d2.Crackspacing:2dc3.Crackwidthisproportionaltothesteelstress 35
文獻回顧撓曲裂縫發展
文獻回顧各國撓曲裂縫控制規範 剪力裂縫控制 損傷評估
美國ACI-318規範 歐洲EuroCode 2規範 日本AIJ-2010附錄 日本JSCE-2007
(1)滿足最小鋼筋量(2)應力限制(3)限制鋼筋直徑及間距
不計算裂縫寬度
鋼筋應力
(MPa) wk=0.4mm wk=0.3mm wk=0.2mm160 40 32 25
鋼筋最大直徑 (mm)鋼筋應力(MPa) wk=0.4mm wk=0.3mm wk=0.2mm
鋼筋最大間距 (mm)
160 40 32 25220 32 25 16240 20 16 12280 16 12 8320 12 10 6
160 300 300 200220 300 250 150240 250 200 100280 200 150 50320 150 100 -
360 10 8 5400 8 6 4450 6 5 -
360 100 50 -
36
文獻回顧撓曲裂縫發展
文獻回顧各國撓曲裂縫控制規範 剪力裂縫控制 損傷評估
美國ACI-318規範 歐洲EuroCode 2規範 日本AIJ-2010附錄 日本JSCE-2007
縫寬度
抗壓及抗拉 抗剪
SD295 195 195
長期容許應力鋼筋型號
裂縫寬度0.3~0.4mm 附錄鋼筋混凝土標準規範
SD295 195 195SD345 215(*195) 195SD390 215(*195) 195SD490 215(*195) 195SD785 580 580
以上之鋼筋為()內數值
可適用混凝土抗壓強度*D29以上之鋼筋為()內數值 60~100MPa
Ace=(2Cb+ϕ)b
xn
Ace (2Cb+ϕ)b
D sd
ϕ
cb
bcs
37