bond requirements of straight beam bars passing through ... · 美國混凝土學會(aci) 352...

高強度鋼筋混凝土之梁柱接頭設計

李宏仁

高強度鋼筋混凝土(New RC)結構設計與施工技術研討會2016.12.09

國立雲林科技大學營建工程系副教授營建材料暨技術服務中心主任(TAF認證實驗室主管)

美國混凝土學會(ACI) 352 梁柱接頭委員會委員

ACI-ASCE Committee 352, "Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures (ACI 352R-02)," American Concrete Institute, Farmington Hills, MI, 2002, pp. 38.

Key reference

-

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

5,000,000

-

50

100

150

200

250

Usage License by Story, Above 21 story buildings and floor area

Buildings Total floor areas (m²)

2016

(Buildings)(m2)

1995 2005

2

資料來源：內政部統計處核發建築物使用執照按層數別分21層以上棟數及總樓地板面積註：2016年至9月底止227棟今年是歷史新高點….

Background

TaipeiTokyo

集中在新北市、台北市、台中市及高雄市等都會

3

New RC 預鑄工法

參考日本都市更新經驗

The Tokyo Towers, 2008年完工時為日本最高(58F, 192m)之New RC住宅

(都市再生開發案)

Emulative Precast Beam-Column

Connections

Cast-in-place concrete

Column unit

Grouted coupling sleeve

Beam unit

Grout

Column unit Roughened surface

Beam unit

• 現場只澆置接合部及樓板混凝土• 快速、高品質• “Emulation” of monolithic concrete structures

(亞利預鑄)

Advantages

20層樓案例比較

ACI 318

Joint Design Problems

1000x1000-mm Column

600-mm beam width (TYP.)

𝑉𝑛 = 𝛾 𝑓𝑐′𝐴𝑗

𝛾 =? 𝛾 =? 𝐴𝑗 =?

(40x48-in.)

(24-in.)

Plan view of connection

• Development Length

• Anchorage Length

• Confinement

• Joint Shear Strength

• Mechanical Splices…

Challenge for Connection Design

using SD690 reinforcing steel bars

Development length requirement at

interior joint

ACI 318-1420

b

c

d

h

MPa420 20

y

b

cf

d

h ACI 352-02

Zhu and Jirsa (1983) evaluated the

test results of 18 interior beam–

column joints and concluded that a

minimum column depth of 20 to

22𝑑𝑏 is appropriate to avoid bondfailure at an interstory drift of 3%

for Grade 420 bars and a concrete

strength of 28 to 35 MPa.

Code background

Laboratory Specimen under Cyclic Deformation Loading

Axial Load

6 m

3.2 m +─ +

─

P

Lateral Load Q

Laboratory testing

“J” failure versus “B” failure

32/600/

729/103/

30.1/,

bc

yac

nmjh

dh

ff

VV

61/450/

508/61/

95.0/,

bc

yac

nmjh

dh

ff

VV

04.0/ cg fAP 00.0/ cg fAP

“BJ” failure versus “BJa” failure

25/005/

470/56/

08.1/,

bc

yac

nmjh

dh

ff

VV

19/004/

347/31/

78.0/,

bc

yac

nmjh

dh

ff

VV

06.0/ cg fAP 10.0/ cg fAP

13

Video of Specimen EW0 beyond 2% drift

19/004/

347/31/

78.0/,

bc

yac

nmjh

dh

ff

VV

Bond failure along beam bars in beam-column joint (BJa failures)

14

G.L

Plastic

Hinge

ch

Bond stress

ch

bd

Pinching effect

Strength and stiffness degradation,

poor hysteresis behavior

Low residual stiffness at small displacement

Unlikely to repair

T1= As,topao fy

T2= As,botao fy

QCc2

Cc1

Cs2= As,topk2ao fy

Cs1= As,botk1ao fy

hcColumn depth

db

Average bond focres

Beam bar diameter

with flange in

compression

Typical As,top As,bot

and then k1 k2

(c)Q

1

221joint

b

ccb

sc

L

L

jd

hLQ

QCCTV

ka

a 14

2

yob

bpcb fd

uhd

bp

yos

bp

yo

b

c

u

fα

u

fα

d

h

a

a

a

k

44

1

Horizontal shear and bond forces acting on the joint concrete

jcjo AfV int

Comparison of the Overstrength Factors for International Design Criteria

Design codes and standards

Grade Yield strength, min (MPa)

Yield strength, max (MPa)

𝛼𝑜 factor

ACI 318 (2014)(ASTM A706-15)

420550

420550

540675

1.25

AIJ Guideline (1999)(Nishiyama 2009)

390490

590A590B685A685B

390490590590685685

510625675650785755

1.311.281.141.101.141.10

Eurocode 8 (2004) All - - 1.20NS 3101 (2006)(AS/NZS 4671:2001)

300E500E

300500

380600

1.25

Factor 𝜶𝒔 accounting for the bar stress level developed in the joint

bp

yos

b

c

u

fα

d

h

a

a

4

Available bond strength

Relative column dimension required by different codes and recommendations (1/2)

Relative column dimension required by different codes and recommendations (2/2)

Min. Col. Dimensions required by

different codes and recommendations

𝑓𝑐′(MPa) 35 35 35 70 70 70

Design Criteria 𝑓𝑦(MPa) 420 550 690 420 550 690

AIJ Guideline (1999) 29 37 44 18 23 28

Eurocode 8 (2004) 33 42 50 21 26 31

NZS 3101 (2006) 25 32 38 18 23 27

Brooke & Ingham (2013) 26 33 40 18 23 29

Li & Leong (2014) 28 35 43 20 25 31

Proposed Eq. 22 28 34 15 19 24

Kelly et al. (2014) 19 28 37 14 19 26

ACI 352R-02 20 26 33 20 26 33

Note: Reference beam-column joint with a column axial load of

0.2A𝑔𝑓𝑐′; bottom-to-top reinforcement ratio of 0.75; equal diameters for

top and bottom bars.

Comparison

• Recommended

cp

yos

b

c

f

fα

d

h

6a

aand 20

Kelly et al. (2014)c

y

b

c

f

f

d

h

3.1)(

4.22

1and 20

(SI unit)

Kelly, D.; Lepage, A.; Mar, D.; Restrepo, J.; Sanders, J.; and Taylor, A., "Use of

High-Strength Reinforcement for Earthquake-Resistant Concrete Structures,"

Tenth US National Conference on Earthquake Engineering, Anchorage, Alaska,

2014.

Lee, H.-J., Chen, H.-C., Tsai, T.-C., (2016), “Minimum column depth for

acceptable bond performance of straight beam bars in beam-column joints,” The

18th Japan-Korea-Taiwan Joint Seminar on Earthquake Engineering for Building

Structures (SEEBUS 2016), Tainan, Taiwan, December 2-3, 2016.

RC

New RC

Database construction

JP75%

US12%

TW7%

NZ5%

KO1%

• 357 test data published in Japan, US, NZ, and Taiwan

• Unified database for normal-strength and high-strength RC

• Beam-column joints without trans. beams/slabs, eccentricity

Column bar versusyf cf

Relations between failure modes, displacement

ductility, and the experimental-to-nominal shear

strength ratio for the 202 interior joints assembled

by Lee and Hwang (2013)

𝑉𝑗ℎ,𝑚𝑉𝑛

Displacement ductility ratio

Selected 59+6 = 65 interior joints

• Bar 𝑓𝑦 not less than 400 MPa

• A minimum of two cycles at the limiting drift ratio

• BJ or BJa failure

Evaluation of the hysteretic behavior at

the limiting drift cycle(>3.5% 2nd or 3rd)

1

19.0PPD EE

10.0)(4

1

s

Deq

E

E

DE

PPE

%33

%36

iKoK

01.0io KK

sE

StrengthStiffnessEnergy dissipation

𝑄 ≥ 0.75𝑄𝑚

𝐾𝑜 ≥ 0.05𝐾𝑖

Τ𝐸𝐷 𝐸𝑃𝑃 ≥ 0.125

ACI 374.1-05

𝜉𝑒𝑞 ≥ 0.125

Energy dissipation Index

Provided-to-required development length ratio

cp

yos

b

c

f

f

d

h

6a

aa

cp

yos

b

c

f

f

d

h

6a

aa

𝐸𝐷𝐸𝑃𝑃

𝜉𝑒𝑞

Strength and stiffness degradation

Provided-to-required development length ratio

cp

yos

b

c

f

f

d

h

6a

aa

cp

yos

b

c

f

f

d

h

6a

aa

mQ

Q

i

o

K

K

Performance Evaluation

n

mjh

V

V ,

cp

yos

b

c

f

f

d

h

6a

aaProvided-to-required

development length ratio

Final Recommendations

20 and 6

oflarger thecp

yos

b

c

f

fα

d

h

a

a

os

tops

o

sA

A

aaa

11

7.01

,

where

20.10.29.0

cg

PfA

Pa

Brooke and

Ingham (2013)

NZS 3101 (2006)

Omitting tfaa

cp

yos

f

f

5a

aa

cp

yos

b

c

f

f

d

h

6a

aa

20 ,

6max

cp

yos

b

c

f

f

d

h

a

aa

n

mjh

V

V ,

設計手冊𝑓𝑐′ SD420 SD550 SD690

𝑘𝑔𝑓

𝑐𝑚2𝑀𝑃𝑎 α𝑠 =1.80 α𝑠 = 1.56 α𝑠 =1.83 α𝑠 = 1.58 α𝑠 = 1.87 α𝑠 = 1.61

280 28 25 21 32 27 39 34350 35 22 20 28 25 35 30420 42 20 20 26 22 32 27490 49 20 20 24 21 29 25560 56 20 20 22 20 28 24630 63 20 20 21 20 26 22700 70 20 20 20 20 25 21770 77 20 20 20 20 23 20840 84 20 20 20 20 22 20900 90 20 20 20 20 22 20

1000 100 20 20 20 20 21 20

註：本表適用於內柱軸力大於0.15𝐴𝑔𝑓𝑐′。

Seismic Testing for Interior Beam-

Column Joints500x600-mm Beam6-D32 top and bot.

600x600-mm Col. 16-D32

USD685 bars

21 6

cp

yos

b

c

f

fα

d

h

a

a

Test results

𝑓𝑐′ = 100(132) 𝑀𝑃𝑎

𝑓𝑦 = 685(697) 𝑀𝑃𝑎

Design equation

𝑃 = 0.05𝐴𝑔𝑓𝑐′

𝛼𝑜 = 1.15

19 mm 32

mm 600

b

c

d

h

Provided0.88

,

n

mjh

V

V

4%-drift PerformanceRating = 3 Acceptable



• Confinement





Anchorage Length for Headed Bars

ℓ𝑑𝑡 ≥ 0.192𝑓𝑦𝑑𝑏

𝑓𝑐′

ACI 318-14, 8𝑑𝑏 , 150 𝑚𝑚 (MPa unit)

ℓ𝑑𝑡 ≥ 0.06𝑓𝑦𝑑𝑏

𝑓𝑐′

(kgf/cm2 unit) ℓ𝑑𝑡 ≥ 0.016𝑓𝑦𝑑𝑏

𝑓𝑐′

(psi unit)

(a)value of 𝑓𝑐′ ≤ 6000 psi (42 MPa);

(b)bar specified 𝑓𝑦 ≤ 60 ksi (420 MPa);

(c)bar size ≤ No. 11 (D36);

(d)net bearing area of head 𝐴𝑏𝑟𝑔 ≥ 4𝐴𝑏;

(e)normal-weight concrete;

(f) minimum clear cover of 2𝑑𝑏

(g)minimum clear spacing of 3𝑑𝑏 between bars.

Conditions

Exterior Beam-column Joints

under Cyclic Loading

Specimen Design and Details𝑓𝑐′ = 70 𝑀𝑃𝑎𝑓𝑦 = 734 𝑀𝑃𝑎 (𝑆𝐷690) 𝑓𝑦𝑡 = 843 𝑀𝑃𝑎 (𝑆𝐷790)

Varying shear demands and Ash,ratio

ℓ𝑎ℓ𝑑𝑡

≈ 1.0

2𝑑𝑏 𝑐𝑙𝑒𝑎𝑟 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

Global and Local Response @ 4% drift

𝑉𝑒𝑥𝑝

𝑉𝑛,𝐴𝐶𝐼= 0.85

𝐴𝑠ℎ𝐴𝑠ℎ,𝐴𝐶𝐼

= 1.00 (1.20)

𝑤𝑖𝑡ℎ 𝑓𝑦𝑡 = 690 (843)𝑀𝑃𝑎

Beam Yielding

Global and Local Response @ 6% drift

𝑉𝑒𝑥𝑝


𝐴𝑠ℎ𝐴𝑠ℎ,𝐴𝐶𝐼

= 1.00 (1.20)

𝑤𝑖𝑡ℎ 𝑓𝑦𝑡 = 690 (843)𝑀𝑃𝑎

Followed by Joint Shear Failure

𝑉𝑒𝑥𝑝


BJ failure

J failure

𝑉𝑒𝑥𝑝


ℓ𝑎ℓ𝑑𝑡

≈ 1.0



𝑉𝑒𝑥𝑝


ℓ𝑎ℓ𝑑𝑡

= 1.6

B failure


𝑓𝑐′ = 119 𝑀𝑃𝑎

𝑓𝑦 = 744 𝑀𝑃𝑎

𝑉𝑒𝑥𝑝

𝑉𝑛,𝐴𝐶𝐼= 0.63 BJa failure

ℓ𝑎ℓ𝑑𝑡

= 0.63

𝑓𝑐′ = 44.4 𝑀𝑃𝑎

𝑓𝑦 = 707 𝑀𝑃𝑎 (𝑆𝐷685)

Anchorage Failure!

Locations of the heads (or hooks)(ACI 352R-02, 4.5.3.2)



• Confinement





設計公式修訂建議(黃世建等人)

• 橫箍柱 (ACI 318-14)

47

MPaf yt 800≤其中

cg fAP ′3.0>當

或 MPafc 70>′

0 09

max 0 3 1

0.2

c

yt

gsh c

c yt ch

gcf n p

yt ch

f.

f

AA f.

sb f A

Afk k k

f A

放寬使用90°-180°彎鉤並交錯配置，但須提高圍束箍筋量

Required

ACI 352R-02 Design Example

• 韌性抗彎構架接頭區亦須負責傳遞柱軸力，故需要配置柱箍筋圍束柱核心混凝土。

• 細則比照柱端部(耐震彎鉤、間隔、換端)

• 除非梁構材貫穿接頭且梁寬最少為柱寬度之3/4，視為具有圍束作用時，則在該梁構材構入範圍內，平行該梁構材方向可配置較少之繫筋，每組橫向鋼筋之總斷面積得為柱規定值之半 (Ash,ratio > 0.50)

• 箍筋間距仍不得超過 6𝑑𝑏及15 cm。

接頭箍筋

Effect of Ash,ratio on

Joint StrengthJ failure

BJ failure

C3

C5

Joint Shear Strength Degradation

Degradation of joint

shear capacity

B-type

BJ-type

Joint shear demand

(proportional to beam flexure capacity)

Jo

int

sh

ea

r fo

rce

Deformation or Drift

2

3

1J-type

Diagonal strut

mechanism

3

Bond deterioration

Concrete softening

2Truss mechanism

1cc

Yield

penertration

Low Ash,ratio

Degradation ofjoint shear capacity

Deformation or Drift

Jo

int

sh

ea

r c

ap

ac

ity

High

Ash,ratio

Yield

penertration

Effect of Ash,ratio on

Drift Capacity

B3

B5



• Confinement





ACI Code 接頭剪力設計

un VV

接頭標稱剪力強度𝑉𝑛 = 𝛾 𝑓𝑐′𝐴𝑗

接頭配置 𝑉𝑛 for 𝑓𝑐′

in psi

𝑉𝑛 for 𝑓𝑐′ in

MPa

𝑉𝑛 for 𝑓𝑐′ in

Τ𝑘𝑔𝑓 𝑐𝑚2

接頭四面皆受梁圍束

20 𝑓𝑐′𝐴𝑗 1.67 𝑓𝑐

′𝐴𝑗 5.3 𝑓𝑐′𝐴𝑗

接頭三面或一雙對面受梁圍束

15 𝑓𝑐′𝐴𝑗 1.25 𝑓𝑐


其他 12 𝑓𝑐′𝐴𝑗 1.00 𝑓𝑐


(b) 接頭三面或兩對面有梁束制(a) 接頭四面有梁束制 (c) 其他束制條件者



𝑉𝑛 = 0.083𝛾 𝑓𝑐′𝐴𝑗


xbhbbj 2

b

x

x

h

bj

Joint effective area

(psi)

(MPa)

(kgf/cm2) ACI 318

Case study, bj and -value per ACI 318

• Beam width bb= 24 in.• Increasing square column section from 24x24 in. to 48x48 in.

Plan view of connectionBeyond 𝑏𝑐xℎ𝑐 = 32x32,𝑏𝑏

𝑏𝑗< 0.75，both 𝛾 values drop to 12

Trans. beam

Trans. beam

bb=24"24"x24"Column

48"x48"

32"x32"

Loading beam

Loading beam

bb=24"

24"x24"Column

48"x48"

32"x32"

Loading beam

Loading beam

Frame subjected to Lateral Loading

Interior joint Exterior joint

Tee joint Knee joint

Interior joint

Exterior joint

Code Change Proposal

接頭標稱剪力強度𝑉𝑛 = 𝛾 𝑓𝑐′𝐴𝑗



(psi)

(MPa)

(kgf/cm2)

柱連續性梁連續性橫向梁圍束示意圖 𝛾值

連續

連續

兩側皆有 20

任一側無 15

不連續

兩側皆有 15

任一側無 12

垂直剪力方向構入接頭兩側面之橫向梁覆蓋接頭面寬度寬度達3/4以上，則該接頭視為具有橫向梁圍束作用

Case study, proposed -value

• Beam width bb= 24 in.• Increasing square column section from 24x24 in. to 48x48 in.

𝑏𝑏,𝑡𝑟

ℎ𝑐< 0.75，𝛾 value drop down one category Plan view of connection

Trans. beam

Trans. beam

bb=24"24"x24"Column

48"x48"

32"x32"

Loading beam

Loading beam

bb=24"

24"x24"Column

48"x48"

32"x32"

Loading beam

Loading beam

b

x2

x1

hj=hcol

bj


jjj hbA

(a)梁主筋貫穿梁柱接頭, hj=hcol (b)梁主筋錨定於接頭內, hj=ldt

b

x2

x1

hj=ldt

bj


𝑏𝑗 = 𝑏 + 𝑥1 + 𝑥2 ≤ 𝑏𝑐𝑜𝑙

其中𝑥1及𝑥2分別為梁兩邊至柱邊之距離(圖6.3)，代入上式計算時，𝑥1或𝑥2值不得超過 Τℎ𝑐𝑜𝑙 4。[黃世建等人(2014)]

Effective Joint Area

除非梁主筋之錨定長度皆超過3/4柱深度以上，接頭有效深度ℎ𝑗得為柱深度ℎ𝑐𝑜𝑙

(設計手冊)

第六章梁柱接頭相關規定

本章建議鋼筋混凝土梁柱構架接頭設計及細部配置之相關規定，係以符合韌性抗彎構架接頭之強度及韌性要求來撰寫。除非另有規定，本章之相關規定僅適用於梁柱接頭• 常重混凝土𝑓𝑐

′ ≤100 MPa (1000 kgf/cm2)• 縱向鋼筋 𝑓𝑦 ≤690 MPa (7000 kgf/cm

2 )

• 橫向鋼筋 𝑓𝑦𝑡 ≤790 MPa (8000 kgf/cm2 )

6.1 剪力強度

6.2 接頭箍筋

6.3 接頭鋼筋伸展及錨定

𝑉𝑛 = 𝛾 𝑓𝑐′𝐴𝑗

𝐴𝑠ℎ

20) and 6

max( cp

yos

b

c

f

fα

d

h

a

a

(SI unit)ℓ𝑑𝑡 ≥ 0.192𝑓𝑦𝑑𝑏

𝑓𝑐′

𝑀𝑖𝑛𝑖𝑚𝑢𝑚 2𝑑𝑏 𝑐𝑙𝑒𝑎𝑟 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

(SI unit)

References

李宏仁、張又仁、張家榮、黃世建，(2014) 「高強度鋼筋混凝土梁柱接頭剪力強度測試」，國家地震工程研究中心報告，NCREE-14-008。

李宏仁、徐富威、陳盈璋、黃世建(2016)，高強度鋼筋混凝土五螺箍柱及預鑄梁柱接頭耐震性能測試，國家地震工程研究中心報告， NCREE-16-002。

李宏仁、柳文皓、陳惠雅、黃世建(2016)，具橫向梁及版之RC梁柱接頭耐震性能研究及資料庫建構，國家地震工程研究中心報告， NCREE-16-010。

李宏仁、黃柏嘉、黃世建(2016)，具橫向梁及版之新高強度鋼筋混凝土外部接頭耐震性能測試，國家地震工程研究中心報告， NCREE-16-012。

• Brooke, N. J.; and Ingham, J. M., "Seismic Design Criteria for Reinforcement Anchorages at

Interior RC Beam-Column Joints," Journal of Structural Engineering, V. 139, No. 11. 2013,

pp. 1895-1905.

• Kang, T. H. K.; Shin, M.; Mitra, N.; and Bonacci, J. F., "Seismic Design of Reinforced

Concrete Beam-Column Joints with Headed Bars," ACI Structural Journal, V. 106, No. 6,

Nov-Dec. 2009, pp. 868-877.

• Lee, H.-J.; and Hwang, S.-J., "High-strength concrete and reinforcing steel in beam-column

connections," Structures Congress 2013, Pittsburgh, PA, 2013, pp. 1606-1615.

• Watanabe, K.; Kiyohara, T.; Tasai, A.; and Hasegawa, Y., "Deformation Capacity of High

Strength RC Exterior Beam Column Joint with Beam Main Bars Anchored Mechanically,"

Proceedings of the Japan Concrete Institute, V. 26, No. 2. 2004, pp. 481-486.

李宏仁等人 (NCREE-16-002)62

ACE JOINT

續接器

Be a m unit Be a m unit

Column unit

Groute d Coupling S le e ve

Ca s t-in-pla ce concre teGrout

Lb = 6 m

Lc = 3.2 m

TOPS JOINT

預鑄柱頭續接

20 ~ 22

17 ~ 19

17 20

18 21

19 22

S

N

W E W E

柱續接鋼筋之應變

• 接頭上下端柱筋皆可達到降伏• 上柱續接器端無明顯損壞

S

S

W E S N

E

E 23 ~ 28

23 24 25 26 27 28

梁續接鋼筋之應變

• 梁柱交接面鋼筋可達降伏強度• 接頭區應變梯度明顯• 能充分續接鋼筋貫穿接頭區

67BOLTOPS 在預鑄梁之應用

預鑄柱 + 預鑄梁下半部及接頭 BOLTOPS套管續接避開梁塑鉸區

bond requirements of straight beam bars passing through ... · 美國混凝土學會(aci) 352...

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