建議 - 結論與建議 - 預力鋼梁與鋼筋混凝土柱自行復位接頭之耐震行為研究

第五章結論與建議

5.2 建議

預力鋼梁與鋼筋混凝土柱接合可避免鋼梁與鋼筋混凝土柱接合的複雜性，同時此系統也會因鋼梁預力的關係而具有自行復位的能力，減少地震後結構物修復的成本，由於國內外並無相關的設計規範提供參考，仍須進行研究確保其在地震下的反應行為，依據本研究可提如下若干建議：

1. 鋼腱為提供結構自行復位的構件，須確保在最大的層間側位移角下仍保持彈性，同時需避免鋼梁產生挫屈，於梁翼加勁板末端之梁中設置垂直加勁板可有效地防止挫屈發生，另外為避免不可預期之破壞行為，須在梁柱接合處加置防掉落措施，以確保結構物的安全，梁腹板與柱使用螺栓接合可達此目的，同時螺栓的存在並不會影響預力梁柱接頭自行復位的能力。

2. 預力梁柱接合系統之行為特性為梁柱介面會在外力作用下產生分離，此一行為會因傳統固接的樓版系統而不易分離，因此需對樓版的效應加以評估。另外本研究僅針對預力接頭進行反覆載重測試，對含預力接頭構架的行為仍需進一步地驗證，確保構架自行復位的能力。

參考文獻

1. AISC. (2002). Seismic provisions for structural steel buildings. AISC, Chicago. IL.

2. ACI. (2002). Building Code and Commentary. ACI 318M-02/318RM-02.

3. Cheok, G. and Lew, H. (1993). “Model precast cncrete beam-to-column connections subject to cyclic loading.” PCI J., 38 (4), 80-92.

4. Cheok, G. and Stone, W. (1994). “Performance of 1/3 scale model precast concrete beam-column connections subjected to cyclic inelastic loads−Report No. 4,” Rep. No.

NISTIR 5436, National Institute of Standards and Technology, NIST, Gaithersburg, Md.

5. Chou, C. C. and Uang, C. M. (2002). “Cyclic performance of a type of steel beam to steel-encased reinforced concrete column moment connection.” J. Constructional Steel Research, 58, 637-663.

6. Christopoulos, C., Filiatrault, A., Uang, C. M., and Folz, B. (2002). “Posttensioned energy dissipating connections for moment-resisting steel frames.” J. Struct. Eng., ASCE, 128(9), 1111–1120.

7. Christopoulos, C., Filiatrault, A., and Folz, B. (2002). “Seismic response of self-centring hysteretic SDOF systems.” Earthquake Eng. Struct. Dyn., 31, 1131–1150.

8. Chou, C. C., Chen, J. H., Chen, Y. C., (2004) “Performance evaluation of posttensioned steel connections for moment-resisting frames” 6th Korea-Japan-Taiwan Joint Seminar on Earthquake Engineering for Building Structures, Taiwan.

9. Chou, C. C. and Chen, Y. H. (2005). ”Cyclic tests of post-tensioned precast CFT segmental bridge columns with unbonded strands.” Earthguake Eng. Struct. Dyn. (Accepted)

10. Chou, C. C., Chen, J. H., Chen, Y. C., and Tsai, K. C. (2005). “Experimental and Analytical Studies of Self-Centering Steel Connections.” US-Taiwan Workshop on Self-Centering Structural Systems, NCREE Report No:05-004, Taipei, Taiwan.

11.Chou, C. C., Tsai, K. C., Chen, J. H., Chen, Y. C., and Chuang, S. C. (2005) “Cyclic Behavior of Post-tensioned Steel Connections with Reduced Flange Plate and Slab.” 1st International Conference on Advances in Experimental Structural Engineering, Nagoya, Japan.

12.Deierlein, G. G. and Noguchi, H. (2004). “Overview of U.S.-Tapan Research on the Seismic Design of Composite Reinforced Concrete and Steel moment frame Structures.“ J.

Struct. Eng. ASCE, 130(2), 361-367.

13.Englekirk, R. E. (1996). “An innovative design solution for precast prestressed concrete buildings in high seismic zones.” PCI J., 41(4), 44–53.

14.Englekirk, R. E. (2002). “Design-construction of the paramount – a 39-story precast prestressed concrete apartment building.” PCI J., 47(4), 56–71.

15.Garlock, M., Ricles, J. M., Sause, R. (2005). “Experimental studies of full-scale posttensioned steel connections.” J. Struct. Eng., 131(3), 448–448.

16.Hews J. T. and Priestley, M. T. N. (2002). ”Seismic design and performance of precast concrete segmental bridge columns.” Rep. NO. SSRP 2001/25, University of California, San Diego, La Jella. CA.

17.Nakaki, S. D., Stanton, J. F., and Sritharan, S. (1999). “An overview of the PRESSS five-story precast test building.” PCI J., 44(2), 26–39.

18.Nishiyama, M., Watanabe, F., and Muaguruma, H. (1991). “Seismic performance of prestressed concrete beam-column joint assemblages.” Pacific Conference on Earthquake Engineering, New Zealand, 217–228.

19.Park, R., and Thompson, K. J. (1977). “Cyclic load tests on prestressed and partially prestressed beam-column joints.” PCI J., 22(5), 84–100.

20.Pampanin, S., Priestley, M. J. N., and Sritharan, S. (1999). “Frame direction modeling of the five-story PRESSS precast test building.” Rep. No. SSRP 99/20, University of California, San Diego, La Jolla, CA.

21.Priestley, M. J. N., and Tao, J. R. (1993). “Seismic response of precast prestressed concrete frames with partially debonded tendons.” PCI J., 38(1), 58–66.

22.Priestley, M. J. N., and MacRae, G. A. (1996). “Seismic tests of precast beam-to-column joint subassemblages with unbonded tendons.” PCI J., 41(1), 64–81.

23.Priestley, M. J. N. (1996). “The PRESSS program-current status and proposed plans for phase III.” PCI J., 41(2), 22–40.

24.Ricles, J. M., Sause, R., Garlock, M. M., and Zhao, C. (2001). ‘‘Posttensioned seismic-resistant connections for steel frames.’’ J. Struct. Eng., ASCE, 127(2), 113–121.

25.Ricles, J. M., Sause, R., Peng, S. W., and Lu, L. W. (2002). “Experimental evaluation of

850–859.

26.Rojas, P., Ricles, J. M., Sause, R. (2005). ‘‘Seismic performance of post-tensioned steel moment resisting frames with friction devices.’’ J. Struct. Eng., ASCE, 131(4), 529–540.

27.Uang, C. M. and Bonded, D. (1996). ”Static Cyclic Testing of Pre-Northridge and haunch repaired Steel moment Connections.” SSRP 96/102, University of California, Sau Diego, CA.

28.Watanabe, F., Okamoto, S., Hiraishi, H. (2000). ”Development of the Structual design and construction guideline for high-rise PC buildings Japanese PC project.” 12WCEE.

表 2.1 試體接頭區特性

表2.3 各組試體在不同步驟下的勁度

Specimen No. 1 2 3 4 5

K

c (kN-m) ₇₄₈₇₂₅ ₇₄₈₇₂₅ ₇₄₈₇₂₅ ₇₄₈₇₂₅ ₇₄₈₇₂₅

K

PZ (kN-m) ₃₈₅₇₁₁ ₃₈₅₇₁₁ ₈₀₀₇₄₉ ₆₃₄₇₃₇ ₆₃₄₇₃₇

K

b (kN-m) ₁₁₅₈₀₅ ₁₁₅₈₀₅ ₁₁₅₈₀₅ ₁₁₅₈₀₅ ₁₁₅₈₀₅

K

ST,t (kN-m) ₄₂₅₃ ₄₁₅₈ ₄₂₅₃ ₄₁₅₈ ₄₂₅₃

K

ST (kN-m) ₄₁₀₂ ₄₀₁₄ ₄₁₀₂ ₄₀₁₄ ₄₁₀₂

K

ER (kN-m) ₃₉₃₇₄ ₃₂₄₂₅ ₄₀₅₃₂ ₃₄₇₄₂ ₃₇₀₅₈

K

PR1 (kN-m) ₂₂₂₅ ₁₇₃₆ ₂₂₂₅ ₂₀₅₁ ₂₀₅₁

K

PR2 (kN-m) ₁₄₈₇ ₁₆₇₈ ₁₄₈₇ ₁₅₆₁ ₁₅₆₁

K

1 (kN-m) ₉₆₄₁₀ ₉₃₆₈₁ ₁₁₁₃₄₈ ₁₀₄₆₇₃ ₁₀₅₇₈₈

K

2= K5 (kN-m) ₃₇₁₃₄ ₃₁₈₇₆ ₄₀₀₁₈ ₃₄₈₂₆ ₃₆₇₅₆

K

₃= K₆(kN-m) ₆₁₇₄ ₅₆₂₃ ₆₂₂₅ ₅₉₅₉ ₆₀₄₅

K

₄= K₇(kN-m) ₅₄₆₉ ₅₅₆₇ ₅₅₁₀ ₅₄₈₆ ₅₅₇₂

表2.4 剛體旋轉角與層間位移角關係

Specimen θc (rad) θbe (rad) θPZ (rad) θg (rad) θt (rad)

1 0.0007 0.0047 0.0014 0.01 0.0168

2 0.0005 0.0033 0.0010 0.01 0.0148

3 0.0008 0.0052 0.0007 0.02 0.0267

4 0.0007 0.0042 0.0008 0.03 0.0357

5 0.0007 0.0045 0.0008 0.03 0.0360

表2.5 鋼材材料性質 Beam

Item

Web Flange FRP Jacket RFP Grade A572 A572 A572 A36 A36

Thickness (mm) 10 16 9 6 10 8 12

F

_y (MPa) 400 393 418 310 290 324 290

F

u(MPa) 517 496 545 431 428 441 434

ε

_y(%) 0.202 0.197 0.209 0.155 0.144 0.163 0.146

ε

_u(%) 18.9 18.1 19.2 21.8 20.7 22.3 21.5

表2.6 鋼筋材料性質

No.

F

_y (MPa)

F

_u (MPa)

Ε

_y(%)

ε

_u(%)

4 372 448 0.186 20.2

11 398 487 0.199 19.2

表 2.7 混凝土抗壓強度

Cylinder NO. 1 2 3 Average 28 Day (MPa) 39 39 38 39

Specimen 1 D.O.T (MPa) 34 35 38 36 Specimen 2 D.O.T (MPa) 38 29 33 32 Specimen 3 D.O.T (MPa) 34 35 39 36 Specimen 4 D.O.T (MPa) 34 34 40 36 Specimen 5 D.O.T (MPa) 37 38 32 36

表3.1 實驗反應

表3.3 各組試體彎矩簡化計算結果比較

表4.1 削切鋼板分析模型參數變化 Specimen bR(mm) R(mm) tR(mm) Elastic Stiffness

(kN/mm) y R yt

P P _,

u R u

P P_,

y R yc

P P _,

BR50R60T5 50 60 5 468 1.12 1.14 1.13

BR50R127T5 50 120 5 379 1.08 1.06 1.09

BR50R180T5 50 180 5 342 1.07 1.03 1.08

BR120R60T5 120 60 5 690 1.13 1.14 1.14

BR120R127T5 120 120 5 618 1.09 1.06 1.10

BR120R180T5 120 180 5 573 1.07 1.02 1.08

BR150R60tT 150 60 5 794 1.11 1.16 1.12

BR150R127T5 150 120 5 729 1.07 1.10 1.08

BR150R180T5 150 180 5 717 1.05 1.07 1.06

BR50R60T8 50 60 8 590 1.11 1.16 1.12

BR50R127T8 50 120 8 569 1.07 1.09 1.08

BR50R180T8 50 180 8 513 1.05 1.07 1.06

BR120R60T8 120 60 8 1062 1.13 1.13 1.14

BR120R127T8 120 120 8 927 1.09 1.05 1.10

BR120R180T8 120 180 8 860 1.07 1.02 1.08

BR150R60T8 150 60 8 1191 1.12 1.14 1.13

BR150R127T8 150 120 8 1093 1.08 1.06 1.09

BR150R180T8 150 180 8 1075 1.07 1.03 1.08

表4.2 分析結果

Name bR

(mm) R (mm)

(mm) Tin

(kN)

Md,R

(kN-m)

MR,0.03

(kN-m) ^b

FRP

d L

BR50R60T5P975 50 60 5 975 37 542 0.43

BR50R127T5P975 50 127 5 975 30 536 0.38

BR150R127T5P975 150 127 5 975 27 559 0.58 BR150R127T8P975 150 127 8 975 54 597 0.89 BR150R180T8P975 150 180 8 975 49 588 0.82 BR150R127T8P1300 150 127 8 1300 95 673 1.8 BR150R127T12P1300 150 127 12 1300 142 813 2.4

圖 1.1 鋼梁挫屈 (Courtesy：Chou & Uang 2002)

圖 1.2 RCS 接合細節 (Courtesy: Deierlein and Noguchi 2004)

(a) Welded RFP

(b) Embeded RFP

圖 1.3 預力梁柱接頭區形式

RFP

Beam

FRP

Strands Jacket

RFP Beam

FRP

Strands

Column

RFP Beam

FRP

Strands Column

Column

M

θ g 1 2 3

6 5 4

7 o M

_d,ST

(a) Strands

1 θg

2 3 4

6 5 7

M

_d,R

M

_c,R

o

K

_R,2

K

_R,3

K

_R,4

K

_R,5

K

_R,6

K

_R,7

(b) Reduced Flange Plates (RFPs)

1 M

2 3

4 6 5 7

My Md

o θg

(c) Strands + RFPs

圖2.1 預力梁柱接頭彎矩與旋轉角關係

l,in

(a) Post-tensioning State

x T

^u,in

(b) Before Decompression

θ

Strain, ε

St re ss , σ

(σ

, ε

)

(σ

, ε

)

Bi-linear

Approximation E

1 E

1

(a) Stress-Strain Relationship

o b(x)

60° R=127 mm

B (810 mm)

x

∆ x

a b c -c

b R (220 mm) b

L

_R (b) RFP

Deformation, ∆

Force, P (∆

, P

)

(∆

, P

)

Bi-linear

Approximation K

_ae

1 K

_ap

1 7 K ₁

K ₂ K ₃

K ₄

K ₅ K ₆

θ M

K ₇ 1

2 3

4 6 5

o

圖 2.4 梁柱接頭勁度分析示意圖

L

H c d

V

_PZ

L

圖2.5 梁柱接頭試體自由體圖

0 0.01 0.02 0.03 0.04 Gap Opening Angle, θ_g (rad)

0 200 400

Ne ut ral Ax is Po si tion (mm)

0.015

圖2.6 中性軸沿梁身變化

Distance from Column Face, L/d_b

Mo m en t

M_c (Moment Capacity)

M_dm (Moment Demand)

B A

∆M₁

∆M₂

圖 2.7 加勁板長度決定方式

#4 #11

650 650

(a) Column Details and Input Data

0 40 80 120 160

Curvature (rad/km) 0

400 800 1200 1600

Momen t ( kN- m)

(b) Moment-curature Relationship 圖2.8 柱尺寸及強度

Beam 500×200×10×16

Flange Reinforcing Plate

(a) Elevation

RFP 12 mm

Beam 500×200×10×16

Flange Reinforcing Plate 9 mm

28 mm ψ Bolt 16 mm ψ Bolt

Strands 750 650 750

#4 @ 100 mm

295 220 120

32 mm Hole

Column 650×650

Flange Reinforcing Plate Strands

Strands 630 650

Cover Plate

Jacket 10 mm

Flange Reinforcing Plate A

16 mmψSlot Hole

Jacket 10 mm

圖 2.11 試體 3 梁柱接合細節

CL

Strands

Flange Reinforcing Plate Jacket 6 mm

Column 650×650

Flange Reinforcing Plate 9 mm RFP 8 mm

205 400 205

Strands 750 650

Cover Plate

16 mmψSlot Hole

Jacket 6 mm

C L

Shear Tab B

Beam 500×200×10×16

B A

Flange Reinforcing Plate Jacket 6 mm

Strands

Strands 1000 650

Cover Plate

Jacket 6 mm 16 mmψSlot Hole

ψ

-0.04 -0.02 0 0.02 0.04 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800 Gap Opening Angle, θ_g(rad) -800

0 1000 2000 3000 Distance from Column Face (mm) 0

0 1000 2000 3000

Distance from Column Face (mm) 0

0 1000 2000 3000

Distance from Column Face (mm) 0

0 1000 2000 3000

Distance from Column Face (mm) 0

0 1000 2000 3000

Distance from Column Face (mm) 0

0 0.05 0.1 0.15 0.2 0.25

0 0.005 0.01 0.015 0.02 0.025 0.03 Strain

E

_ST=1965,00 MPa

E

_ST

f

_{l p}

f

_pu

ε_lp=0.0086

圖 2.17 理想化鋼腱應力-應變關係圖

Beam 1

1520

Strands

3000

2501740

3400 3400

3000

1740

RC Column 650 × 650

Beam 2

500×200 ×10 16× H

圖2.18 試體測試構架

0 10 20 30 40 50

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

In te rst or y D ri ft ( % )

0.375

0.5

0.75 1 1.5 2

3 4 5

Cycle Number 圖2.19 反覆載重歷時

Beam 2 L8

L3 (Top), L4 (Bottom) L5

Beam 1

(a) Top View

L4 L3 520 L8

410

130

130 L6

Beam 1 L9 Beam 2

438

L7 L1 L2

438

(b) Elevation

6585 6585 100

350 310 210

870

85 6585 65 S19

S20S21

圖2.20 試體 1 量測儀器規劃圖

Beam 2 Beam 1

520 L8 L5

L3 (Top), L4 (Bottom)

(a) Top View

Beam 1 L9 Beam 2

L8 520

130

130 L5

120

438

L2 L4 L1

L7 L3

438

(b) Elevation

S27 S21S20S19 B

6585 6585 100

RFP 350 310 210 240

730

圖 2.21 試體 2 量測儀器規劃圖

Beam 1

L3 (Top), L4 (Bottom) L8

Beam 2

(a) Top View

Beam 1 L6

130

130 L5

120

L8 520

438

L1 L2

438

Beam 2

(b) Elevation

200

10085 6585 65 S19

S20S21

圖 2.22 試體 3 量測儀器規劃圖

Beam 2 L8

L3 (Top), L4 (Bottom) L5

Beam 1

(a) Top View

L4 L3 520 L8

410

130

130 L6

Beam 1 L9 Beam 2

438

L7 L2

438

(b) Elevation

240 520

350

240 870

10085 6585 65 165165

View C-C

350 520 240

4@150

圖 2.23 試體 4 量測儀器規劃圖

Beam 1

L3 (Top), L4 (Bottom) L8

Beam 2

(a) Top View

Beam 1 L6

130

130 L5

120

L8 520

438

L1 L2

438

Beam 2

(b) Elevation

520

S13 S14 S15

S16 S17 S18

350 520 250

S30

d^c L^b

δ^total

Η b

a δ¹ δ²

δ³ δ⁴

圖 2.25 柱及梁柱接合區變形量測位置

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-1000

Interstory Drift (%)

(a) Beam 1

-150 -100 -50 0 50 100 150

Beam Deflection (mm) -1000

Interstory Drift (%)

(b) Beam 2

圖3.1 試體 1 梁端彎矩與梁端變形關係

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-800 -400 0 400 800

Mo me nt ( kN-m)

-1 -0.5 0 0.5 1

M/ M

-4 -2 0 2 4

Interstory Drift, θ (%)

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5

圖 3.2 各組試體彎矩與梁端位移之包絡線

-400 -200 0 200 400

Actuator Force (kN) 800

1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.3 0.4 0.5 0.6

No rmalize d Fo rce

Beam Yielding

圖 3.3 試體 1 千斤頂力量與鋼腱預力關係

0.75 1 2 3 4 Interstory Drift, θ (%)

0 100 200 300 400 500

De co m pr es si on M om ent (kN -m )

0 0.2 0.4 0.6

M/ M

Specimen 1 Specimen 3 Specimen 5 Specimen 2 Specimen 4

圖3.4 各組試體分離彎矩與層間側位移角關係

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) 800

1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.3 0.4 0.5 0.6

No rmalize d Fo rce

Test

Simplified Analysis Iterative Analysis

圖3.5 試體 1 層間側位移角與鋼腱力量關係

-0.004 -0.002 0 0.002 0.004 Shear Strain, γ (rad)

-1000

(a) Moment-Shear Strain Relationship

-0.004 -0.002 0 0.002 0.004 Column Rotation, θ_c(rad)

-1000 (b) Moment-Column Rotation Relationship

圖3.6 試體 1 柱及梁柱接合區變形量與彎矩關係

0.75 1 2 3 4 Interstory Drift, θ (%)

0 40 80 120

De flect io n ( m m )

Panal Zone

Column Beam

Rigid Rotation

(a) Deflection Component

0.75 1 2 3 4

Interstory Drift, θ (%) 0

0.25 0.5 0.75 1 1.25

D ef le ctio n R ati o

Panal Zone Beam

Column Rigid Rotation

(b) Deflection Ratio

圖3.7 各組試體梁端變位分量關係

0 0.01 0.02 0.03 0.04 Gap Opening Angle, θ_g (rad)

0 200 400

Dis tan ce f ro m Beam Bo tt om F ac e ( m m )

Test

Iterative Analysis

圖3.8 試體 1 中性軸位置關係

0.75 1 2 3 4

Interstory Drift, θ(%) 0

0.01 0.02 0.03 0.04

G ap O pe ni ng A ngl e , θ

(r ad )

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5

圖3.9 試體 1 剛體旋轉角與層間位移角關係

-0.04 -0.02 0 0.02 0.04 θ_g (rad) based on Displacement Tranducer

-0.04 -0.02 0 0.02 0.04

θ

(r ad ) B as ed o n E q. (3 .2 )

Test

圖3.10 試體 1 分離轉角比較圖

0.75 1 2 3 4 5

Interstory Drift, θ (%) 0

0.4 0.8 1.2

St ran d Fo rc e R atio

Specimen 1 Specimen 3 Specimen 5 Specimen 2 Specimen 4

圖3.11 各組試體預力損失比值

22.5 30 60 90 120 Beam Deflection (mm)

0 20 40 60

Re si dua l D ef or m atio n ( m m )

0.75 1 2 3 4

Interstory Drift (%)

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5

圖3.12 殘留變形圖

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) -5

0 5 10 15 20

Dis pla ce m en t ( mm)

Test

Simplified Analysis Iterative Analysis

圖 3.13 試體 1 削切鋼板伸長變形與剛體旋轉角關係

0.75 1 2 3 4 Interstory Drift, θ (%)

0 200 400 600 800 1000

Mo m en t ( kN -m )

M_ST M_R

圖3.14 試體 1 彎矩簡化計算比較

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

S14 S15 S13

S11

S16 S17 S18

(a) Strain Gauge Location (Top Flange) (b) Strain Gauge Location (Bottom Flange)

0 400 800 1200 Distance from Column Face (mm)

-0.3

S13 S14 S15

S11

(a) Top Flange

0 400 800 1200

Distance from Column Face (mm) -0.3

S16 S17 S18

(b) Bottom Flange

圖3.17 試體 1 梁翼板內側應變沿梁身分佈關係

0 1000 2000 3000 Distance from Column Face (mm)

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-1000

Interstory Drift (%)

(a) Beam 1

-150 -100 -50 0 50 100 150

Beam Deflection (mm) -1000

Interstory Drift (%)

(b) Beam 2

圖3.20 試體 2 彎矩與梁端位移關係

-400 -200 0 200 400 Actuator Force (kN)

1000 1250 1500 1750

S tr an d Fo rce ( kN)

0.4 0.5 0.6 0.7

No rma li ze d Fo rce

Beam Yielding

圖3.21 試體 2 千斤頂側向力與鋼腱力量關係

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) 800

1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.4 0.5 0.6 0.7

No rma li ze d Fo rce

Test

Simplified Analysis Iterative Analysis

圖3.22 試體 2 層間位移角與鋼腱力量關係

-0.004 -0.002 0 0.002 0.004 Shear Strain ,γ (rad)

-1000 -750 -500 -250 0 250 500 750 1000

Mo m en t ( kN -m )

-1 -0.5 0 0.5 1

M/ M

(a) Moment-Shear Strain Relationship

-0.004 -0.002 0 0.002 0.004 Column Rotation ,θ_c(rad)

-1000 -750 -500 -250 0 250 500 750 1000

Mo m en t ( kN -m )

-1 -0.5 0 0.5 1

M/ M

(b) Moment-Column Rotation Relationship

圖3.23 試體 2 柱及梁柱接合區變形量與彎矩關係

0 0.01 0.02 0.03 0.04 Gap Opening Angle, θ_g (rad)

0 200 400

Dis tan ce f ro m Beam Bo tt om F ac e ( m m )

Test

Iterative Analysis

圖3.24 試體 2 中性軸位置關係圖

-0.04 -0.02 0 0.02 0.04

θ_g (rad) based on Displacement Tranducer -0.04

-0.02 0 0.02 0.04

θ

(ra d) B as ed o n E q. (3 .2 )

Test

圖3.25 試體 2 梁柱分離轉角比較圖

-0.04 -0.02 0 0.02 0.04 Gap Opening Angle, θ_g (rad)

-5 0 5 10 15 20

Di sp la ce m ent (m m )

Test

Simplified Analysis Iterative Analysis

圖3.26 試體 2 削切鋼板變形與剛體旋轉角關係

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5

S14

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5-1

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5-1

Moment (×1000 kN-m) -3 -2 -1 0 1 2 3Normalized Strain -1.5-1

0 400 800 1200 Distance from Column Face (mm)

-0.2

S13 S14 S15

S11

(a) Top Flange

0 200 400 600 800 1000

Distance from Column Face (mm) -0.2

S16 S17 S18

(b) Bottom Flange

圖3.29 試體 2 梁翼板內側應變沿梁身分佈關係

0 1000 2000 3000 Distance from Column Face (mm)

Mo m en t ( ×10 00 kN -m )

-1

Interstory Drift (%)

S23

db/4

0 - 0.5 % 0.75 - 5 %

圖3.31 試體 2 梁彎矩與梁翼加勁板外側之梁翼板應變關係

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-1000

Interstory Drift (%)

1st Test 2nd Test

(a) Beam 1

-150 -100 -50 0 50 100 150

Beam Deflection (mm) -1000

Interstory Drift (%)

1st Test 2nd Test

(b) Beam 2

圖3.32 試體 3 梁彎矩與位移關係

-400 -200 0 200 400 Actuator Force (kN)

800 1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.3 0.4 0.5 0.6

No rma li ze d Fo rce

Beam Yielding 1st Test 2nd Test

圖3.33 試體 3 千斤頂力量與鋼腱力量關係

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) 800

1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.3 0.4 0.5 0.6

No rmalize d Fo rce

Test

Simplified Analysis Iterative Analysis

圖3.34 試體 3 層間位移角與鋼腱力量關係

0 0.01 0.02 0.03 0.04 Gap Opening Angle, θ_g (rad)

0 200 400

Dis tan ce f ro m Beam Bo tt om F ac e ( m m )

1st Test 2nd Test

Iterative Analysis

圖3.35 試體 3 中性軸位置關係

-0.04 -0.02 0 0.02 0.04

θ_g (rad) based on Displacement Tranducer -0.04

-0.02 0 0.02 0.04

θ

(r ad ) B as ed o n E q. (3 .2 )

Test

圖3.36 試體 3 梁柱分離轉角比較圖

-0.04 -0.02 0 0.02 0.04 Gap Opening Angle, θ_g (rad)

-5 0 5 10 15 20

Displacement (mm)

Test

Simplified Analysis Iterative Analysis

圖3.37 試體 3 削切鋼板變形量與剛體旋轉角關係

Distance from Column Centerline (mm) -0.16

-0.12 -0.08 -0.04 0

Shear Strain (×0.01 rad)

-0.6 -0.4 -0.2 0

Normalized Shear Strain

0.5 %

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m)

-1.5

S14 S15 S13

S11

S16 S17 S18

(a) Strain Gauge Location (Top Flange) (b) Strain Gauge Location (Bottom Flange)

0 400 800 1200 Distance from Column Face (mm)

-0.3

S13 S14 S15

S11

(a) Top Flange

0 400 800 1200

Distance from Column Face (mm) -0.3

(b) Bottom Flange

圖3.40 試體 3 梁翼板內側應變沿梁身分佈關係

0 1000 2000 3000 Beam Deflection (mm)

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-1000

Interstory Drift (%)

(a) Beam 1

-150 -100 -50 0 50 100 150

Beam Deflection (mm) -1000

Interstory Drift (%)

(b) Beam 2

圖3.43 試體 4 梁端彎矩與梁端位移關係圖

-400 -200 0 200 400 Actuator Force (kN)

800 1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.4 0.5 0.6 0.7

No rma li ze d Fo rce

Beam Yielding

圖3.44 試體 4 千斤頂力量與鋼腱力量關係圖

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) 800

1000 1200 1400 1600 1800

S tr an d Fo rce (k N)

0.4 0.5 0.6 0.7

No rma li ze d Fo rce

Test

Simplified Analysis Iterative Analysis

圖3.45 試體 4 層間側位移角與鋼腱力量關係

-0.004 -0.002 0 0.002 0.004 Column Rotation,θ_c (rad)

-800 -400 0 400 800

M ome nt (k N -m)

-1 -0.5 0 0.5 1

M/ M

圖3.46 試體 4 彎矩與柱轉角關係

0 0.01 0.02 0.03 0.04

Gap Opening Angle, θ_g (rad) 0

200 400

Dis tan ce f ro m Beam Bo tt om F ac e ( m m )

Test

Iterative Analysis

圖3.47 試體 4 中性軸與剛體旋轉角關係

-0.04 -0.02 0 0.02 0.04 θ_g (rad) based on Displacement Tranducer

-0.04 -0.02 0 0.02 0.04

θ

(r ad ) B as ed o n E q. (3 .2 )

Test

圖3.48 試體 4 梁柱分離轉角比較圖

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) -5

0 5 10 15 20

Di sp la ce m ent (m m )

Test

Simplified Analysis Iterative Analysis

圖3.49 試體 4 削切鋼變形與剛體旋轉角關係

Distance from Column Centerline (mm) -0.2

-0.15 -0.1 -0.05 0

Shear Strain (×0.01 rad)

-0.6 -0.4 -0.2 0

Normalized Shear Strain

0.5 %

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5-1

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5-1

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m)

-1.5

S14 S15

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain

-1.5

0 400 800 1200 Distance from Column Face (mm)

-0.3

S13 S14 S15

S11

(a) Top Flange

0 400 800 1200

Distance from Column Face (mm) -0.3

(b) Bottom Flange

圖3.52 試體 4 梁翼板內側應變沿梁身分佈關係

0 1000 2000 3000 Distance from Column Face (mm)

0 400 800 1200 1600

Mo m en t ( kN- m )

0 1 2

M/ M

0 2 4 6

L/L_b

M_dm M_c

圖3.53 試體 4 彎矩強度與需求關係(θ_g = 0.03 rad)

-0.4 -0.2 0 0.2 0.4

Strain (%) -800

-400 0 400 800

M ome nt (k N -m)

-1.5 -1 -0.5 0 0.5 1 1.5

M/ M

-2 -1 0 1 2

Normalized Strain

0-3 % 4-5 %

S1 8

db/4

3.54 試體 4 梁彎矩與梁翼加勁板外側之梁翼板應變關係

-150 -100 -50 0 50 100 150 Beam Deflection (mm)

-1000

Interstory Drift (%)

1st Test 2nd Test

(a) Beam 1

-150 -100 -50 0 50 100 150

Beam Deflection (mm) -1000

Interstory Drift (%)

1st Test 2nd Test

(b) Beam 2

圖3.55 試體 5 梁端彎矩與梁端變形關係圖

-400 -200 0 200 400 Actuator Force (kN)

800 1000 1200 1400 1600 1800

S tr an d Fo rce ( kN)

0.3 0.4 0.5 0.6

No rma li ze d Fo rce

Beam Yielding 1st Test 2nd Test

圖3.56 試體 5 千斤頂力量與鋼腱力量關係圖

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) 800

1000 1200 1400 1600 1800

S tr an d Fo rce ( kN)

0.3 0.4 0.5 0.6

No rma lize d Fo rce

Test

Simplified Analysis Iterative Analysis

圖3.57 試體 5 層間側位移角與鋼腱力量關係

-0.008 -0.004 0 0.004 0.008 Column Rotation, θ_c(rad)

-1000 -750 -500 -250 0 250 500 750 1000

Mo m en t ( kN -m )

-1 -0.5 0 0.5 1

M/ M

圖3.58 試體 5 彎矩與柱轉角關係

0 0.01 0.02 0.03 0.04

Gap Opening Angle, θ_g (rad) 0

200 400

Dis tan ce f ro m Beam Bo tt om F ace ( m m )

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5

圖3.59 五組試體中性軸與剛體旋轉角關係

-0.04 -0.02 0 0.02 0.04 θ_g (rad) based on Displacement Tranducer

-0.04 -0.02 0 0.02 0.04

θ

(ra d) B as ed o n E q. (3 .2 )

Test

圖3.60 試體 5 梁柱分離轉角比較圖

-0.04 -0.02 0 0.02 0.04

Gap Opening Angle, θ_g (rad) -5

0 5 10 15 20

D is pl acem en t ( m m )

Test

Simplified Analysis Iterative Analysis

圖3.61 試體 5 削切鋼板變形量與剛體旋轉角關係

Distance from Column Centerline (mm) -0.2

-0.15 -0.1 -0.05 0

Shear Strain (×0.01 rad)

-0.6 -0.4 -0.2 0

Normalized Shear Strain

0.5 %

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5-1

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m) -1 -0.5 0 0.5 1Normalized Shear Strain

-1.5-1

Shear Strain (×0.01 rad) -1 Normalized Shear Strain

-1.5

Shear Strain (×0.01 rad) -1

-0.5 0 0.5 1

Moment (×1000 kN-m)

-1.5

S14 S15 S13

S11 S16 S17 S18

(a) Strain Gauge Location (Top Flange) (b) Strain Gauge Location (Bottom Flange)

Moment (×1000 kN-m) -2 -1 0 1 2Normalized Strain -1.5-1

0 400 800 1200 Distance from Column Face (mm)

-0.3

S13 S14 S15

S11

(a) Top Flange

0 400 800 1200

Distance from Column Face (mm) -0.3

S16 S17 S18

(b) Bottom Flange

圖3.64 試體 5 梁翼板內側應變沿梁身分佈關係

0 1000 2000 3000 Distance from Column Face (mm)

0 400 800 1200 1600

Mo m en t ( kN- m )

0 1 2

M/ M

0 2 4 6

L/L_b

M_dm M_c

圖3.65 試體 5 彎矩強度與需求關係(θ_g = 0.03 rad)

630 80

810 220

bm=120

L_R= 450 o

圖4.1 試體 4 削切鋼板尺寸

圖4.2 試體 4 削切鋼板結構模型網格

0 0.1 0.2 0.3 Strain

0 100 200 300 400 500

St res s ( M P a)

(a) RFP 8 mm

0 0.1 0.2 0.3

Strain 0

100 200 300 400 500

St res s ( M P a)

(b) RFP 12 mm

圖4.3 鋼材應力–應變曲線

-20 -10 0 10 20 Displacement (mm)

-600 -400 -200 0 200 400

Fo rce ( kN)

ABAQUS Model Computation (∆_y , P_y) (∆_u , P_u)

圖4.4 試體 4 削切鋼板之力量–位移曲線比較

圖4.5 試體 4 削切鋼板在降伏點前之 Mises 應力分佈情形

(a) Von Mises Stress

(b) Von Mises Stress Contour

圖4.6 試體 4 削切鋼板在降伏點時之 Mises 應力分佈情形

(a) S11 Stress

(b) S11 Stress Contour

圖4.7 試體 4 削切鋼板在降伏點時之軸向應力

圖4.8 試體 4 削切鋼板圓弧形削切在降伏點時之主軸應力方向

120 120 220

220 50 50 220

240 80 630

180 180 180

BR150R180T5

810 810 810 150 220

213 810 810 810 810 810

810

圖 4.9 削切鋼板形狀變化示意圖

0 40 80 120 160 200 Radius

1 1.04 1.08 1.12 1.16 1.2

α

b_R = 50 mm t_R = 5 mm b_R = 127 mm t_R = 8 mm b_R = 150 mm

(a) α Versus Radius

0 40 80 120 160 200

Radius 1

1.04 1.08 1.12 1.16 1.2

β

b_R = 50 mm t_R = 5 mm b_R = 127 mm t_R = 8 mm b_R = 150 mm

(b) β Versus Radius

圖4.10 降伏強度及極限強度與削切半徑關係

-20 -10 0 10 20

-150 -100 -50 0 50 100 150 Beam Delection (mm)

-1000

Interstory Drift (%)

TestNo Correction α , β Included

圖4.12 試體 1 梁端彎矩–位移關係

-150 -100 -50 0 50 100 150 Beam Delection (mm)

-1000

Interstory Drift (%)

TestNo Correction α , β Included

圖4.13 試體 2 梁端彎矩–位移關係

-150 -100 -50 0 50 100 150 Beam Delection (mm)

-800 -400 0 400 800

M ome nt (k N -m)

-1 -0.5 0 0.5 1

M/ M

-4 -2 0 2 4

Interstory Drift (%)

TestNo Correction α , β Included

圖4.14 試體 3 梁端彎矩–位移關係

-150 -100 -50 0 50 100 150 Beam Delection (mm)

-800 -400 0 400 800

M ome nt (k N -m)

-1 -0.5 0 0.5 1

M/ M

-4 -2 0 2 4

Interstory Drift (%)

Test

No Correction α , β Included

圖4.15 試體 4 梁端彎矩–位移關係

-150 -100 -50 0 50 100 150 Beam Delection (mm)

-800

Interstory Drift (%)

TestNo Correction α , β Included

圖4.18 試體 4 結構模型網格

(a) Post-tension State

(b) 4% Drift

圖4.19 梁柱接頭應力變化

在文檔中預力鋼梁與鋼筋混凝土柱自行復位接頭之耐震行為研究 (頁 64-167)

建議

第五章 結論與建議

5.2 建議

參考文獻

K

K

K

K

K

K

K

K

K

K

K

K

F

F

ε

ε

F

F

Ε

ε

RFP

Beam

FRP

Strands Jacket

RFP Beam

FRP

Strands

Column

RFP Beam

FRP

Strands Column

Column

M

θ g 1 2 3

6 5 4

7 o M

1 θg

2 3 4

6 5 7

M

M

o

K

K

K

K

K

K

1 M

2 3

4

6 5 7

My Md

o θg

x T

θ

Strain, ε

St re ss , σ

(σ

, ε

)

(σ

, ε

)

Bi-linear

Approximation E

1

E

1

o b(x)

60° R=127 mm

B (810 mm)

x

∆ x

a b c -c

b R (220 mm) b

第五章結論與建議

7 K ₁

K ₂ K ₃

K ₄

K ₅ K ₆

K ₇ 1