結論 - 三層樓鋼管混凝土柱暨挫屈束制斜撐構架行為分析

本研究進行CFT 梁柱接頭子結構與實尺寸 CFT/BRB 三層樓平面構架之非線性分析，比較分析與實驗結果，可歸納出下列幾點結論：

1. CFT 複合構件由於材料的複雜性，較不易估算其斷面性質，採用斷面收斂性分析配合斷面法計算CFT 構件斷面性質為合理之方法，可理想推估CFT 複合斷面之性質。若斷面之纖維元素數量不足，會錯估斷面之非彈性段強度。桿件收斂性影響結果甚鉅，如桿件分段不夠，會明顯低估構件非彈性段之強度與勁度。

2. 由於 CFT 柱接鋼梁之翼板貫入式接頭交會區行為複雜，以解析方式疊加鋼管與混凝土之剪力，建立交會區之剪力-剪力變形關係，分析結果於整體趨勢較接近，惟於整體強度與初始勁度較趨保守。

3. 對於全梁貫入式、雙向螺栓式以及外橫隔板式梁柱接頭子結構之模擬，分析結果之梁端力量-位移初始彈性勁度與實驗結果十分相近，

但部分子結構因實驗試體之局部破壞，使得非彈性段的強度降低，

大部分分析均可模擬試體之非彈性段勁度與強度。

4. 於梁柱交會區之模擬，將交會區所承受之剪力-剪力變形關係轉換成彎矩-旋轉角關係，並採用旋轉彈簧模擬。梁柱交會區對於整體勁度與強度有一定的影響，但因模擬的子結構試體交會區之勁度與強度足夠，對整體行為影響甚小，故於子結構與構架之梁柱交會區皆以剛性接頭模擬之。

5. 於構架模擬，考慮純鋼梁彎矩強度之初始模型進行加速度歷時分析，並與實驗結果比較，顯示出整體趨勢與實驗結果雖然接近，但

仍有差距；在各個相對最大側位移之比較上，初始模型與實驗結果相差不少，意味構架之模型可加以改進。

6. 考慮樓板對於鋼梁之正負彎矩強度之影響，進行構架模型修正。分析結果顯示修正模型之整體趨勢較初始模型更為接近實驗結果，於側位移之比較亦比初始模型更符合實驗結果。

7. DRAIN-2DX 可理想模擬構架於加速度歷時下之反應，但無法預測構架之局部破壞，亦導致模擬結果與實驗結果誤差之累積，故在 Phase I 之準確性尚稱良好，但於 Phase II 之誤差已非常明顯。

8. 側推分析結果顯示是否將交會區視為剛性接頭對於勁度影響甚小，半剛性交會區構架模型進入非彈性段強度較剛性交會區構架模型為弱，但強度降低幅度不大。惟此構架因挫屈束制為主要之消能構件，將交會區視為剛性為合理之假設。

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表4.1 構架試驗材料強度表

Type f^y

(MPa)

(MPa) Square Tube (350×350×9) 374 488 Column

Circular Pipe (400×400×9) 543 584 Flange 370 486 1F (H456×201×10×17)

Web 354 485 Flange 414 503 2F (H450×200×9×14)

Web 482 538 Flange 372 468 Beam

3F (H400×200×8×13)

web 426 493

1F 421 534

2F 397 545

BRB

3F 373 483

In tube f ′_c =31.8 MPa Concrete

Floor fc′=22.3 MPa

表 4.2 構架試驗歷時表

Excitation Hazard Level Run Time (sec) Test 1 Chi-Chi

(TCU082EW)

50% in 50 Years

(PGA=0.276g) 12.62 Test 2 Chi-Chi

(TCU082EW)

50% in 50 Years

(PGA=0.276g) 45.00 Test 3 Loma Prieta

(LP89g04NS)

10% in 50 Years

(PGA=0.426g) 40.00 Test 4 Chi-Chi

(TCU082EW)

2% in 50 Years

(PGA=0.622g) 12.56 Test 5 Chi-Chi

(TCU082EW)

2% in 50 Years

(PGA=0.622g) 45.00 Test 6 Loma Prieta

(LP89g04NS)

10% in 50 Years

(PGA=0.426g) 40.00 Phase I

Cyclic Null

Test 1 Chi-Chi (TCU082EW)

10% in 50 Years

(PGA=0.53g) 30.00 Test 2 Loma Prieta

(LP89g04NS)

2% in 50 Years

表4.4 梁柱桿件斷面參數輸入值 External

Column 300,000 0.003 681.7 681.7 8942.0 4896.7 Inner

Column 316,000 0.001 716.7 716.7 9182.6 4410.8 1F Damping Ratio

(%)

Period (sec)

表4.6 複合梁斷面參數輸入值

Steel Beam Composite Beam

(kN-m)

−

(kN-m)

−

(kN-m) 1F Beam 644.4 644.4 1038 644.4 2F Beam 658.2 658.2 1023 658.2 3F Beam 465.3 465.3 750 465.3

圖 2.1 簡單式接頭示意圖 (Schneider and Alostaz 1998)

圖 2.2 全梁貫入式接頭示意圖 (Schneider and Alostaz 1998)

圖2.3 圓形 CFT 柱與鋼板貫入式接頭立體示意圖 (羅勝宏 2002)

圖2.4 矩形 CFT 柱與鋼板貫入式接頭示意圖 (陳誠直與林南交 2003)

圖2.5 內部橫隔板式接頭示意圖 (Riches et al. 1995)

圖2.6 外部橫隔板式接頭示意圖 (Schneider and Alostaz 1998)

圖2.7 鋼管剪力釘補強式接頭示意圖 (Schneider and Alostaz 1998)

圖 2.8 剪力釘暨肋板補強式接頭示意圖 (Schneider and Alostaz 1998)

圖 2.9 複合式接頭示意圖 (Kang et al. 2001)

圖2.10 雙線性桁架元素行為示意圖 (Prakash et al. 1993)

NODE I

Plastic hinge Elastic element

NODE J

Rigid bar

Curvature Moment

Elastic element Plastic hinge

Beam-column element Rigid bar

圖2.11 梁柱元素示意圖

圖2.12 梁柱元素 P-M 關係模式示意圖 (Prakash et al. 1993)

Similary for B and D Py+

圖2.13 半剛性接頭元素型式 (Prakash et al. 1993)

圖2.14 彈性板元素示意圖 (Prakash et al. 1993)

圖2.15 彈性板元素變形圖 (Prakash et al. 1993)

圖 2.16 RBS 模型示意圖 (Shen et al. 2000)

圖2.17 蓋板式梁柱接頭模型示意圖 (Srivanich et al. 1999)

Panel Zone

圖2.18 梁柱接頭簡化模型

圖 2.20 包含線性交會區之彈性模型 (Foutch and Yun 2002)

圖2.21 非線性中心線模型 (Foutch and Yun 2002)

圖2.22 包含非線性交會區之非彈性模型 (Foutch and Yun 2002)

Specimen H4BT Detail

Specimen H4BT Section A-A Detail

A A

20 H450×200×9×14

A572 Gr.50

TYP

Tube 350x350x9 A572 Gr.50

2020

120 120

Hole φ 13

圖3.1 試體 H4BT 接合細部設計圖 (陳誠直與林南交 2003)

3000

1650 1600 1600 250 250 CFT Column

Steel Beam

圖 3.2 外柱子結構試驗構架設置圖 (陳誠直與林南交 2003)

圖3.3 雙向螺栓穿透式之梁柱接頭示意圖 (黃國倫 2003)

圖3.4 十字型子結構試驗構架設置圖 (黃國倫 2003)

圖3.5 外橫隔板配置示意圖 (Lin 2000)

Column Beam

1500 1500

2500

Cyclic Load

EAST WEST

Actuator

1200 600 Lateral

Support

圖 3.6 CL-S 試體構架架設圖 (Lin 2000)

圖3.7 CL-D 試體構架架設圖 (Lin 2000)

圖3.8 Mander 混凝土圍束理論曲線模型 (Mander et al. 1988)

f

ε

Strain

Stress

圖3.9 鋼管應力-應變關係曲線示意圖

TENSION SIDE COMPRESSION SIDE

Center line of cross section Neutral axis

σs,i

ε_x

Concrete stress

Steel stress Strain

σc,i i_th Fiber element

z y

圖 3.10 斷面分析法基本示意圖

d_c d_b

Panel zone Rigid bar

Beam

Column 0

圖3.13 子結構模型示意圖

M_bottom V_col

P_R P_R

V_R M_R

V_col M_L

V

P_L

V_PZ

V_PZ d_b

CFT Column

Panel Zone Steel Beam

VCol

圖3.15 翼板貫入式梁柱交會區受力示意圖

Vcol

Vb Vb

Mb Mb

Plastic Hinge Inflection point

Inflection point H

圖3.16 柱子結構自由體圖

Strain εs

Yield Point

Plastic Stiffness Degradation Point

Ultimate Strength Point

圖 3.17 鋼管三線性應力-應變關係圖

Yield Point

Plastic Stiffness Degradation Point

Ultimate Strength Point

圖3.18 鋼管之剪力與變形模型

Strain εc

Stress σc

σc,c

σc,u

εc,c εc,u

Ec1

Ec2

Cracking Strength Point

Ultimate Strength Point

圖 3.19 交會區混凝土雙線性應力-應變關係圖

Shear Strain γc

Shear Vc

Vc,c

Vc,u

γc,c γc,u

Gc,u

Cracking Strength Point

Ultimate Strength Point

圖3.20 鋼管之剪力與變形模型

Inner Compression Strut Zone Outer Compression Strut Zone Inner Compression Strut Zone Outer Compression

Strut Zone

圖3.21 內外壓桿示意圖

γ Vs,u

Vs,y

V_c,u

V_c,c

γ_c,c γ_s,y γ_c,u γs,u

Concrete Steel Concrete + Steel

γ_s,d Vs,d

圖 3.22 鋼管與混凝土疊加之梁柱交會區理論折線圖

0 0.004 0.008 0.012 0.016 0.02 Shear Strain (rad)

0 1000 2000 3000

Shear (kN)

H2GT Model Experiment

0 0.004 0.008 0.012 0.016 0.02 Shear Strain (rad)

0 1000 2000 3000

Shear (kN)

H3GT Model Experiment

圖 3.23 交會區剪力-剪應變實驗曲線與理論模型之比較

0 0.002 0.004 0.006 0.008 0.01 Shear Strain (rad)

0 500 1000 1500 2000 2500

Shear (kN)

Tube=350*350*9 f'c=3000 psi f'c=4000 psi f'c=5000 psi f'c=6000 psi

0 0.002 0.004 0.006 0.008 0.01 Shear Strain (rad)

0 1000 2000 3000

Shear (kN)

Tube=350*350*12 f'c=3000 psi f'c=4000 psi f'c=5000 psi f'c=6000 psi

圖3.24 參數研究之結果比較示意圖

Strain Concrete stress

Steel stress

Neutral axis

(a) Number of fiber elements = 2

Neutral axis

(b) Number of fiber elements = 4

Neutral axis

圖3.25 斷面纖維元素收斂性示意圖

0 0.04 0.08 0.12 0.16 0.2

Curvature (1/m)

0 200 400 600 800

Mome n t ( k N- m)

Number of fiber elements N=5

N=10 N=35 N=70

圖3.26 斷面收斂性分析比較圖

7 @ L / 7 P

圖 3.27 等長度桿件收斂性模型示意圖

0 50 100 150 200 250

Beam-end displacement (mm)

0 100 200 300

Beam-end force (kN)

Number of element 1 2 3 6 9

圖 3.28 等長度切段元素收斂性比較圖

3@0.1L 2@0.2L 0.3L

圖3.29 非等長度桿件收斂性模型示意圖

0 40 80 120 160 200

Beam-end displacement (mm)

0 100 200 300

Beam -e nd f orc e (k N)

Uniform length Nonuniform length

圖 3.30 等長度與非等長度桿件收斂性比較圖

L db H

Rigid bar

node

Rigid panel zone

0.15H 0.08H

0.12H 0.08H

0.05H 0.02H

0.12L 2@0.1L 0.13L 0.15L 0.25L 0.25L

圖3.31 剛接交會區之 T 型外部接頭子結構模型圖

L db H

Rigid bar

node 0.15H

0.08H

0.12H 0.08H

0.05H 0.02H

0.12L 2@0.1L 0.13L 0.15L 0.25L 0.25L Semi-rigid panel zone

db 0

圖3.32 半剛接交會區之 T 型外部接頭子結構模型圖

-8 -4 0 4 8

Beam-end drift (%)

-500 -250 0 250 500

Beam-end force (kN)

Simulation Experiment

(a) 全梁貫入式接頭 H4BT

-8 -4 0 4 8

Beam-end drift (%)

-500 -250 0 250 500

Beam-end force (kN)

Simulation Experiment

(b) 外橫隔板式接頭 CL-S-5

-10 -5 0 5 10

Beam-end drift (%)

-500 -250 0 250 500

Beam-end force (kN)

Simulation Experiment

0 100 200 300

Beam-end force (kN)

0 40 80 120 160

Beam-end displacement (mm)

Simualtion Experiment

圖3.34 全梁貫穿式接頭 H4BT 模擬結果與實驗結果之比較

0 20 40 60 80

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation Experiment

圖3.35 外橫隔板式接頭 CL-S-2 模擬與實驗結果比較

0 20 40 60 80

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation Experiment

圖3.36 外橫隔板式接頭CL-S-5 模擬與實驗結果比較

0 40 80 120 160

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation west side Experiment west side

圖 3.37 雙向螺栓式接頭 FSBE6=10=8 西側模擬與實驗結果

0 40 80 120 160

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation west side Experiment west side

圖 3.38 雙向螺栓式接頭 FSBE8≡10≡6 西側模擬與實驗結果

0 40 80 120 160

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation west side Experiment west side

圖 3.39 雙向螺栓式接頭 FSBE10=10=4 西側模擬與實驗結果

0 40 80 120 160

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation west side Experiment west side

圖 3.40 雙向螺栓式接頭 FSBW=6=8=8 西側模擬與實驗結果

0 40 80 120 160

Beam-end displacement (mm)

0 100 200 300 400

Beam-end force (kN)

Simulation west side Experiment west side

圖 3.41 雙向螺栓式接頭 FSBW8≡8≡6 西側模擬與實驗結果

0 100 200 300

Beam-end force (kN)

0 40 80 120 160

Beam-end displacement (mm)

Rigid PZ Experiment

Semi-rigid PZ by theory

圖 3.42 理論交會區強度之子結構模型與實驗之比較

0 100 200 300

Beam-end force (kN)

0 40 80 120 160

Beam-end displacement (mm)

Rigid PZ Experiment

Semi-rigid PZ by exp

圖3.43 實驗交會區強度之子結構模型與實驗之比較

-8 -4 0 4 8 Total Rotation (% rad)

-400 -200 0 200 400

Force (kN)

H4BT

-8 -4 0 4 8

Rotation (% rad) -400

-200 0 200 400

Force (kN)

H4BT Beam

-8 -4 0 4 8

Rotation (% rad) -1200

-600 0 600 1200

Moment (kN-m)

H4BT Column

-8 -4 0 4 8

Rotation (% rad) -1200

-600 0 600 1200

Moment (kN-m)

H4BT Panel Zone

圖 3.44 試體 H4BT 變形分離之遲滯迴圈圖 (陳誠直與林南交 2003)

Top View

Elevation View A=15cm²

A=25cm²

Tube350x350x9

2.15m

3@2.33m 2@3.5m 3@2.33m

b1 b1 b1 b1 b1 b1 b1 b1 b1

H400x200x8x13 H400x200x8x13

H450x200x9x14

H456x201x10x17

H450x200x9x14

H456x201x10x17 H450x200x9x14

H456x201x10x17

H400x200x8x13

A=30 cm²

3@7m

3@4m Pipe400x9 Tube350x350x9

Pipe400x9

圖 4.1 CFT/BRB 構架配置圖

圖 4.2 BRB 構造示意圖 (Tsai，2003)

圖4.3 各樓層 BRB 斷面示意圖

(a) Phase I

(b) Phase II

圖 4.4 往覆載重歷時示意圖 (蕭博謙 2004)

BRB

Rigid connection

3@4m

3@7m

0.3

Hinge

Rigid connection

BRB

圖4.5 實尺寸構架模型圖

在文檔中三層樓鋼管混凝土柱暨挫屈束制斜撐構架行為分析 (頁 71-164)