第五章 結論與討論
5.1 結論
1. 依據應變諧和之假設與 Modified Kent-Park 模式曲線，可以合理 地模擬鋼骨鋼筋混凝土構材其參數變化 (箍筋間距、鋼骨型式、
軸力比、偏心距與正負彎矩)，並準確地預測其極限彎矩強度與 剩餘強度的行為。
2. 本研究所定義高圍束區域混凝土之圍束範圍與應力-應變關係，
由於高圍束區域位於中性軸與形心軸附近，對於整體的強度影響 較小，故在計算斷面的強度時，應可採用本研究所提之簡化圍束 方式較佳。
3. 對於鋼骨鋼筋混凝土梁柱構材而言，分析結果顯示箍筋間距較密 者具有較佳之圍束能力，與前人實驗結果相吻合。
4. 在相同鋼骨含量條件下，不同鋼骨型式之 SRC 斷面構材承受軸 力與彎矩作用時，對其極限彎矩強度與剩餘強度的影響，以內含 T 字型鋼骨構材之高圍束區域效果較十字型鋼骨佳；內含十字型 鋼骨斷面之構材其高圍束區域貢獻較 H 型鋼骨斷面佳。
5. 對於承受不同軸力比之非對稱斷面鋼骨鋼筋混凝土梁柱構材，其 極限彎矩強度依彎矩作用方向而有所不同，在高軸力作用下，鋼
骨多集中於受壓側之構材，其極限彎矩強度較低軸力作用之構材 高；鋼骨多集中於受拉側之構材，其極限彎矩強度較低軸力作用 之構材低。SRC 梁柱構材在承受較高軸力作用下，不論構材承受 正彎矩或負彎矩作用，其韌性表現皆不如承受較低軸力作用的試 體。
6. T 字型鋼骨斷面 SRC 構材受鋼骨偏心的影響，鋼骨偏向拉力側 則擁有較高之極限彎矩強度，但構材之韌性表現則較鋼骨偏向壓 力側差。
5.2 建議
就一般工程界較為熟悉之規範，建議採用 ACI-318 規範與 AISC-LRFD (2005) 所提議之塑性應力分佈法，其皆能準確的預 測出構材的軸力與極限彎矩強度。
參考文獻
ACI, (2002), “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary-ACI 318R-02,” American Concrete
Institute.
AIJ, (1991), “AIJ Standards for Structural Calculation of Steel Reinforced Concrete Structures,” Architectural Institute of Japan.
AISC, (1999), “Load and Resistance Factor Design Specification for Structural Steel,” American Institute of Steel Construction.
AISC, (2005), “Load and Resistance Factor Design Specification for Structural Steel,” American Institute of Steel Construction.
Chen, C. C. and Lin, N. J., (2006) “Analytical Model for Predicting Axial Capacity and Behavior of Concrete Encased Steel Composite Stub Columns,” Journal of Constructional Steel Research, Vol. 62, No. 5, pp. 424-433.
El-Tawil, S., Sanz-Picon, C. F., and Deierlein, G. G., (1995), “Evaluation of ACI 318 and AISC (LRFD) Strength Provision for Composite Beam-Columns,” Journal of Constructional Steel Research, Vol. 34, pp. 103-123.
Furlong, R. W., (1976) “AISC Columns Design Logic Makes Sense for Composite Columns, Too,” Engineering Journal, AISC, pp. 1-7.
Mirza, S. A., (1989) “Parametric study of composite column strength variability,” Journal of Constructional Steel Research, Vol. 14, No. 2, pp. 121-137.
Mirza, S. A. and Skrabek, B. W., (1991) “Reliability of short composite
beam-column strength interaction,” Journal of Structural Engineering, ASCE, Vol. 117, No. 8, pp. 2320-2339.
Mirza, S. A. and Skrabek, B. W., (1992) “Statistical analysis of slender composite beam-column strength,” Journal of Structural Engineering, ASCE, Vol. 118, No. 5, pp. 1312-1332.
Park, R., Priestley, M.J.N., and Gill, W.D., (1982) “Ductility of square-confined concrete columns,”J. Struct. Div., ASCE, Vol. 108, No. 4, pp. 929-950.
西村 繁、齋藤 文孝、上原 廣、西村 泰志、南 宏一 (1991)，「Flexural Behavior of Composite Columns with Eccentricity of H-Shaped Steel (Part 1 )」，日本建築學會大會學術演講梗概集，東北，編號 21642，
pp. 1697-1698。
齋藤 文孝、加藤 博之、上原 廣、西村 泰志、南 宏一 (1992)，
「Flexural Behavior of SRC Columns with Unsymmetrical Steel Section」，日本建築學會大會學術演講梗概集，北陸，編號 21783，
pp. 1739-1740。
李健銘 (2000)，「含T 字型鋼骨斷面之包覆型鋼骨鋼筋混凝土梁柱構 材之耐震行為」，國立交通大學土木工程學系碩士論文，陳誠直指 導。
林義閔 (1999)，「非對稱斷面鋼骨鋼筋混凝土 (SRC) 梁柱構材極限 強度之研究」，國立交通大學土木工程學系碩士論文，陳誠直指導。
林俊昌 (1996)，「鋼骨鋼筋混凝土 (SRC) 構造耐震設計之研究」，國 立交通大學土木工程學系碩士論文，翁正強指導。
徐中道 (1996)，「鋼骨鋼筋混凝土柱耐震行為研究」，國立交通大學 土木工程學系碩士論文，陳誠直指導。
陳誠直、葉士青 (1996)，「鋼骨鋼筋混凝土柱極限強度和耐震行為研 究 (Ⅰ)」，國科會專題計劃 (NSC84-2211-E009-013)。
陳建中 (1999)，「鋼骨鋼筋混凝土梁撓曲試驗行為」，國立台灣科技 大學營建工程學系碩士論文，陳正誠指導。
連陽 (1995)，「鋼骨鋼筋混凝土柱軸向載重研究」，國立台灣大學土 木工程學系碩士論文，蔡克銓指導。
翁正強、陳村林 (1990)，「SRC 梁柱極限設計之探討-簡單強度疊加 法」，結構工程，第五卷，第四期。
翁正強、顏聖益、管啟旭 (1994)，「結合AISC 與 ACI 規範的 SRC 梁 柱設計新方法」，第二屆結構工程研討會論文集 (一)。
翁正強、廖慧明、張荻薇、陳誠直 (2004)，「鋼骨鋼筋混凝土構造 (SRC) 設計規範與解說」，內政部建築研究所。
表3.1 收斂性分析
BH-TE 試體中性軸距斷面上緣 150 mm
纖維元素厚度 (mm) -P n (kN) -M n (kN-m) +P n (kN) +M n (kN-m)
60 600 -237 1645 232
30 481 -231 1609 225
10 495 -231 1584 225
5 493 -231 1584 225
1 493 -231 1584 225
表 3.2 陳建中 (1999) 之 SRC 梁柱斷面尺寸及斷面配置
Structural steel Longitudinal bar Specimen
Cross section
(mm)
Length (mm)
Shape Size Top Bottom
Lateral tie spacing
(mm)
Concrete strength
f ′
c(MPa)
Yield strength of
steel F
ys(MPa)
Yield
strength of
rebar F
yr表 3.3 徐中道 (1996) 之 SRC 梁柱斷面尺寸及斷面配置
Structural steel Longitudinal bar
Specimen
Cross section
(mm)
Length (mm)
Shape Size Top Bottom
Lateral tie spacing
(mm)
Concrete strength
f ′
c(MPa)
Yield strength of
steel F
ys(MPa)
Yield strength of rebar F
yr(MPa) SRC1 300×300 2390 十 H175×90×5×8 + H175×90×5×8 4-#6+2-#6 4-#6+2-#6 70 37.4 326 490 SRC2 300×300 2390 十 H175×90×5×8 + H175×90×5×8 4-#6+2-#6 4-#6+2-#6 100 37.4 326 490 SRC3 300×300 2390 十 H175×90×5×8 + H175×90×5×8 4-#6+2-#6 4-#6+2-#6 150 37.4 326 490 SRC4 300×300 2390 H H150×150×7×10 4-#6+2-#6 4-#6+2-#6 70 37.4 320 490 SRC5 300×300 2390 H H150×150×7×10 4-#6+2-#6 4-#6+2-#6 100 37.4 320 490
54
表 3.4 林義閔 (1999) 之 SRC 梁柱斷面尺寸及斷面配置
Structural steel Longitudinal bar Specimen
Cross section
(mm)
Length (mm)
Shape Size Top Bottom
Lateral tie spacing
(mm)
Concrete strength
f ′
c(MPa)
Yield strength of
steel F
ys(MPa)
Yield strength of
rebar F
yr表 3.5 林義閔 (1999) 之 SRC 短柱斷面尺寸及斷面配置
Structural steel Longitudinal bar Specimen
Cross section
(mm)
Length (mm)
Shape Size Top Bottom
Lateral tie spacing
(mm)
Concrete strength
f ′
c(MPa)
Yield strength of
steel F
ys(MPa)
Yield strength of rebar F
yr(MPa) CL-TE 300×300 1000 T H100×50×5×7 + H125×60×6×8 2-#6 2-#6 100 22.9 334 388 CL-TO 300×300 1000 T H100×50×5×7 + H125×60×6×8 2-#6 2-#6 100 22.9 334 388 CL-HO 300×300 1000 十 H100×50×5×7 + H125×60×6×8 2-#6 2-#6 100 22.9 330 388 CH-TE 300×300 1000 T H150×100×6×9 + H175×90×5×8 2-#6 2-#6 100 31.4 297 388 CH-TO 300×300 1000 T H150×100×6×9 + H175×90×5×8 2-#6 2-#6 100 31.4 297 388 CH-HO 300×300 1000 十 H150×100×6×9 + H175×90×5×8 2-#6 2-#6 100 31.4 295 388
56
表 3.6 陳建中 (1999) 之 SRC 梁柱實驗值與預測值的比較
M Analysis
( kN-m) M test /M ACI M test /M PSDM M test /M Analysis
M Analysis
( kN-m) M test /M ACI M test /M PSDM M test /M Analysis
表 3.8 林義閔 (1999) 之 SRC 梁柱實驗值與預測值的比較
M Analysis
( kN-m) M test /M ACI M test /M PSDM M test /M Analysis
P Analysis
( kN) P test /P ACI P test /P PSDM P test /P Analysis
表 4.1 分析模式之試體延展性係數比較表 文獻 試體編號
φ
yφ
uμ
uS1-T1
0.008 0.034 4.19
S1-T20.008 0.041 4.98
D10.011 0.119 10.90
陳建中D1-T2
0.011 0.381 34.77
SRC10.018 0.431 24.57
SRC20.017 0.268 15.74
SRC30.017 0.164 9.91
SRC40.020 0.242 11.80
徐中道SRC5
0.018 0.150 8.55
BL-TE-P2P0.015 ∞ ∞
BL-TE-P2N0.016 0.044 2.81
BL-TE-P4P0.016 0.181 11.63
BL-TE-P4N0.012 0.029 2.39
BL-TO-P2P0.017 0.051 3.10
BL-TO-P2N0.017 0.049 2.84
BL-HO-P20.017 0.051 3.08
BH-TE-P2P0.015 ∞ ∞
BH-TE-P2N0.016 0.078 4.97
BH-TE-P4P
0.013 0.126 9.36
BH-TE-P4N0.012 0.027 2.18
BH-TO-P2P0.015 0.208 14.25
BH-TO-P2N0.016 0.142 8.93
林義閔BH-HO-P2
0.017 0.059 3.51
Strain St re ss Modified Kent-Park stress-strain relations
Confined concrete Unconfined concrete
k f ' c f ' c
0.5 k f ' c
0.2 k f ' c
ε0
k
ε0 ε50u +
ε50h
圖3.1 Modified Kent-Park stress-strain relations (Park et al. 1982)
圖3.2 Mirza 之圍束混凝土區分方式 (Mirza and Skrabek 1992)
Partially confined concrete
Highly confined concrete Unconfined concrete
圖3.3 Chen and Lin 之圍束混凝土區分方式 (Chen and Lin 2006)
Highly confined concrete Partially confined concrete Unconfined concrete
型鋼 箍筋 主筋 型鋼 箍筋 主筋
型鋼 箍筋 主筋
圖3.4 SRC 構材中混凝土圍束區範圍界定
Strain
S tres s
stress-strain relations
Highly confined concrete Partially confined concrete Unconfined concrete k f ' c
f ' c
0.5 k f ' c
0.2 k f ' c
ε0
k
ε0 ε50u +
ε50h
圖 3.5 SRC 構材中混凝土之圍束與非圍束之應力-應變圖
Strain
Stress
stress-strain relations
Longitudinal bar Structural steel F yr
F ys
ε yr ε ys
圖3.6 SRC 構材中鋼筋與鋼骨之應力-應變圖
圖3.7 El-Tawil 對於纖維元素之分割方式(El-Tawil et al. 1995)
:鋼筋纖維元素 :鋼骨纖維元素
:高圍束混凝土纖維元素 :次圍束混凝土纖維元素 :非圍束混凝土纖維元素
圖 3.8 軸力與單軸彎矩分析層狀式纖維元素示意圖
START
Input Dimensions and Materials Properties
Structural Analysis
Obtain Nominal Axial Force ( ) P
nand Bending Moment ( ) M
nCalculate the Axial Force Shared by the Rebar and the Steel and the Concrete， ( ) P
n rand ( ) P
n sand ( ) P
n c：
( ) ( ) ( ) ( ) P
n= P
n r+ P
n s+ P
n cCalculate the Bending Moment Shared by the Rebar and the Steel and the Concrete， ( ) M
n rand ( ) M
n sand ( ) M
n c：
( ) ( ) ( ) ( ) M
n= M
n r+ M
n s+ M
n cCalculate the Axial Force and Bending Moment by the Rebar，
( ) ∑
See Step 1 for Details
Calculate the Axial Force and Bending Moment by the Steel，
( ) ∑
See Step 2 for Details
Calculate the Axial Force and Bending Moment by the Concrete，
( ) ∑
See Step 3 for Details
STOP
圖3.9 鋼骨鋼筋混凝土強度計算流程圖
Step 1
Calculate Stress
yr i
= F σ
Calculate Strain by the Fiber (i) of the Rebar
j
Calculate Stress Calculate Stress
yr
Calculate the Axial Force
Calculate the Bending Moment
⎟ ⎠
Assume the depth of cross section (H)；the depth of Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
CONTINOUS
圖3.10 應變諧和法之鋼筋強度計算流程圖
Step 2
Calculate Stress
ys i
= F σ
Calculate Strain by the Fiber (i) of the Steel
j
Calculate Stress Calculate Stress
ys
Calculate the Axial Force
Calculate the Bending Moment
⎟ ⎠
Assume the depth of cross section (H)；the depth of Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
CONTINOUS
圖3.11 應變諧和法之鋼骨強度計算流程圖
Step 3
CONTINOUS
NO YES
j
i
C
X ≥
Calculate Strain by the Fiber (i) of the Concrete
j
Calculate Strain by the Fiber (i) of the Concrete
i
= 0
Calculate Stress
Calculate the Axial Force
i i
i
A
P = σ ×
Calculate the Bending Moment
⎟ ⎠
Assume the depth of cross section (H)；the depth of Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
o
Calculate Stress
( ) Calculate Stress
c
Calculate Stress
圖3.12 Modified Kent-Park 混凝土強度計算流程圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t ( k N-m )
S2
rectangular confined concave confined
圖 3.13 試體 S2 之高圍束區混凝土矩形圍束與曲線圍束比較圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t (k N -m)
S3
rectangular confined concave confined
圖 3.14 試體 S3 之高圍束區混凝土矩形圍束與曲線圍束比較圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t ( k N-m )
BH-HO-P2
rectangular confined concave confined
圖3.15 試體 BH-HO-P2 高圍束區混凝土矩形圍束與曲線圍束比較圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t ( k N- m )
S2 Z m,h =0 Z m,h =Z m,p
圖3.16 試體 S2 之高圍束區混凝土剩餘強度比較圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t ( k N -m)
S3 Z m,h =0 Z m,h =Z m,p
圖3.17 試體 S3 之高圍束區混凝土剩餘強度比較圖
0 0.1 0.2 0.3
Curvature (1/m)
0 200 400 600 800 1000
Mo m e n t ( k N-m)
BH-HO-P2 Z m,h =0 Z m,h =Z m,p
圖3.18 試體 BH-HO-P2 之高圍束區混凝土剩餘強度比較圖
0.85f 'c
F
ysF
yrPlastic neutral axis
Negative bending moment
Concrete Steel
N
x-M
xx y
Rebar
圖3.19 塑性應力分佈法
Step 1
Calculate Stress
yr i
= F σ Calculate Stress
yr i
= − F σ
Calculate the Axial Force
i i
i
A
P = σ ×
Calculate the Bending Moment
⎟ ⎠
Calculate Strain by the Fiber (i) of the Rebar
j
Assume the depth of cross section (H)；the depth of
Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
CONTINOUS
圖3.20 塑性應力分佈法之鋼筋強度計算流程圖
Step 2
Calculate Stress
ys i
= F σ Calculate Stress
ys i
= − F σ
Calculate the Axial Force
i i
i
A
P = σ ×
Calculate the Bending Moment
⎟ ⎠
Calculate Strain by the Fiber (i) of the Steel
j
Assume the depth of cross section (H)；the depth of
Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
CONTINOUS
圖3.21 塑性應力分佈法之鋼骨強度計算流程圖
Step 3
CONTINOUS
NO YES of the Concrete
j
Calculate Strain by the Fiber (i) of the Concrete
i
= 0 Calculate Stress
i
= 0
σ Calculate Stress
c i
= 0 . 85 f ′ σ
Calculate the Axial Force
i i
i
A
P = σ ×
Calculate the Bending Moment
i
Available depth Available depth NO YES
Assume the depth of cross section (H)；the depth of Fiber (h)；the numbers of Fiber (n=H/h)；the neutral axle(Cj)；the location of Fiber (i) (Xi)
圖3.22 混凝土受壓應力假設以矩形應力塊之強度計算流程圖
-300 -150 0 150 300
Moment (kN-m)
0 2000 4000 6000
A x ia l F o rce ( k N)
BH-TE
PSDM (Fiber) PSDM (Traditions)
圖3.23 塑性應力分佈法之纖維元素分割法驗證
300 200 100 0
Location (mm)
-400 -200 0 200 400
Stress (MPa)
BH-TE
Longitudinal bar Structural steel Concrete
圖3.24 PSDM 之應力分佈圖
300 200 100 0
Location (mm)
-400 -200 0 200 400
Stress (MPa)
BH-TE
Longitudinal bar Structural steel Highly confined concrete Partially confined concrete Unconfined concrete
圖3.25 應變諧和纖維元素分析模式之應力分佈圖
300 200 100 0
Location (mm)
0 10 20 30 40 50
Stress (MPa)
BH-TE
Highly confined concrete Partially confined concrete Unconfined concrete
圖3.26 應變諧和纖維元素分析模式中混凝土圍束之應力分佈圖
0 0.02 0.04 0.06
Strain
0 100 200 300 400
Stress (MPa)
BH-TE
Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
圖3.27 BH-TE 斷面之分析模式中各材料應力-應變圖
350
550 100 70
a a
蓋板
H 型鋼
S7: a=178
其他 a=125320
44 0 70 60
D2
320
400 70 60
D1 及 D1-T2
S 型
Unit: mm
圖3.28 陳建中 (1999) 之 SRC 梁柱試體斷面示意圖
300
300
20
20
125
20
20
125
H175x90x5x8
H150x150x7x10
30 0
300
SRC1 SRC2 SRC3
SRC4 SRC5
Unit: mm
圖3.29 徐中道 (1996) 之 SRC 梁柱試體斷面示意圖
69
x
Unit: mm
300
300
H100x50x5x7 H125x60x6x8
16 mm dia.
Longitudinal bar (Typ.)
10 mm dia. hoop (Typ.)
CL-TE, BL-TE series
CL-TO, BL-TO series CH-TO, BH-TO series
Typ.
137 39 73
H175x90x5x8 H150x100x6x9
CL-HO, BL-HO series CH-HO, BH-HO series
H125x60x6x8
39 (Typ.)
39 (T yp .)
H100x50x5x7
H150x100x6x9 H175x90x5x8
y
+M
xCH-TE, BH-TE series
圖3.30 林義閔 (1999) 之 SRC 梁柱試體斷面示意圖
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N-m)
S1-NN test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=40.1 MPa Fys= 332 MPa Fyr= 435 MPa
圖3.31 試體 S1-NN 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N -m)
S1-NB test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=40.1 MPa Fys= 332 MPa Fyr= 435 MPa
圖 3.32 試體 S1-NB 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N- m )
S1-NS test Analysis
Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=38.8 MPa Fys= 332 MPa Fyr= 435 MPa
圖3.33 試體 S1-NS 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N-m)
S1-SS test Analysis
Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=40.1 MPa Fys= 332 MPa Fyr= 435 MPa
圖3.34 試體 S1-SS 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t (k N-m)
S1 test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=40.8 MPa Fys= 332 MPa Fyr= 435 MPa
圖 3.35 試體 S1 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N-m )
S1-T1 test Analysis
Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 200 mm Material Properties:
fc'=36.0 MPa Fys= 267 MPa Fyr= 435 MPa
圖3.36 試體 S1-T1 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N-m )
S1-T2 test Analysis
Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9 Rebar:T:2-#8 B:2-#10+2-#8 s = 100 mm Material Properties:
fc'=36.0 MPa Fys= 267 MPa Fyr= 435 MPa
圖3.37 試體 S1-T2 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N-m)
S2 test Analysis
Cross-Section Properties:
B×D=350×550 mm 2 Steel: H300×110×6.5×9 Rebar:T:2-#7 B:4-#8 s = 176 mm Material Properties:
fc'=38.4 MPa Fys= 332 MPa Fyr= 426 MPa
圖 3.38 試體 S2 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N- m )
S3 test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×60×6.5×9 Rebar:T:2-#5 B:4-#7 s = 128 mm Material Properties:
fc'=38.4 MPa Fys= 332 MPa Fyr= 424 MPa
圖 3.39 試體 S3 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N- m )
S4 test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9+2×(P105×16) Rebar:T:2-#8 B:2-#8+2-#7 s = 200 mm Material Properties:
fc'=38.4 MPa Fys= 332 MPa Fyr= 426 MPa
圖 3.40 試體 S4 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N -m)
S5 test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9+2×(P120×20) Rebar:T:2-#5 B:2-#8 s = 128 mm Material Properties:
fc'=36.0 MPa Fys= 332 MPa Fyr= 426 MPa
圖 3.41 試體 S5 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N-m)
S6 test Analysis
Cross-Section Properties:
B×D=350×550 mm
2Steel: H300×150×6.5×9+2×(P120×20) Rebar:T:2-#5 B:4-#10 s = 128 mm Material Properties:
fc'=36.8 MPa Fys= 332 MPa Fyr= 435 MPa
圖 3.42 試體 S6 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N -m)
S7 test Analysis Cross-Section Properties:
B×D=350×550 mm
2Steel: H194×150×6.5×9 Rebar:T:2-#7 B:2-#10 s = 200 mm Material Properties:
fc'=37.3 MPa Fys= 272 MPa Fyr= 435 MPa
圖 3.43 試體 S7 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t (k N -m)
D1 test Analysis Cross-Section Properties:
B×D=320×400 mm
2Steel: H300×110×6.5×9 Rebar:T:2-#6 B:2-#10 s = 152 mm Material Properties:
fc'=37.3 MPa Fys= 332 MPa Fyr= 435 MPa
圖3.44 試體 D1 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N-m )
D1-T2 test Analysis
Cross-Section Properties:
B×D=320×400 mm
2Steel: H300×110×6.5×9 Rebar:T:2-#6 B:2-#10 s = 76 mm Material Properties:
fc'=37.3 MPa Fys= 332 MPa Fyr= 435 MPa
圖3.45 試體 D1-T2 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m e n t ( k N -m)
D2 test Analysis Cross-Section Properties:
B×D=320×440 mm
2Steel: H300×110×6.5×9+2×(P90×20) Rebar:T:2-#3 B:2-#11 s = 80 mm Material Properties:
fc'=37.3 MPa Fys= 332 MPa Fyr= 468 MPa
圖3.46 試體 D2 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N-m)
BL-TE-P2P test Analysis
Cross-Section Properties:
B×D=300×300 mm
2Steel: H125×60×6×8 H100×50×5×7 Rebar:T:2-#6 B:2-#6 s = 100 mm Material Properties:
fc'=22.9 MPa Fys= 334 MPa Fyr= 388 MPa
圖 3.47 試體 BL-TE-P2P 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N -m )
BH-TE-P2P test Analysis
Cross-Section Properties:
B×D=300×300 mm
2Steel: H175×90×5×8 H150×100×6×9 Rebar:T:2-#6 B:2-#6 s = 100 mm Material Properties:
fc'=31.4 MPa Fys= 297 MPa Fyr= 388 MPa
圖3.48 試體 BH-TE-P2P 實驗與分析模式之M−
φ
曲線圖0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N -m )
BH-TO-P2P test Analysis
Cross-Section Properties:
B×D=300×300 mm
2Steel: H175×90×5×8 H150×100×6×9 Rebar:T:2-#6 B:2-#6 s = 100 mm Material Properties:
fc'=31.4 MPa Fys= 297 MPa Fyr= 388 MPa
圖3.49 試體 BH-TO-P2P 實驗與分析模式之M−
φ
曲線圖Curvature
Mo men t
M u 0.9M u M y
φ y φ u
圖4.1 曲率延展性係數之定義
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m)
S1-T1
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t (k N -m)
S1-T2
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
D1
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
D1-T2
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo m en t ( k N -m )
SRC1
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t ( k N -m )
SRC2
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
M o men t (k N -m)
SRC3
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N-m)
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
M o me n t (k N -m)
SRC4
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N -m)
SRC5
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
M o m en t (k N- m)
SRC1
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
M o men t (k N -m)
SRC4
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t ( k N -m )
SRC2
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t (k N -m)
SRC5
Composite beam-column Longitudinal bar Structural steel
Highly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0 100 200 300 400
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BL-HO-P2
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t (k N -m)
BL-TO-P2P
Composite beam-column Longitudinal bar Structural steel Highly confined concrete Partially confined concrete Unconfined concrete0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N-m)
BH-HO-P2
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BH-TO-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BL-HO-P2
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N-m)
BH-HO-P2
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m )
BL-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BL-TE-P4P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N-m)
BH-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BH-TE-P4P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t (k N -m)
BL-TE-P4N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BH-TE-P4N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t (k N -m)
BL-TO-P2P
Composite beam-column Longitudinal bar Structural steel Highly confined concrete Partially confined concrete Unconfined concrete0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m )
BL-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BH-TO-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N-m)
BH-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m )
BL-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N-m)
BH-TE-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TE-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BL-TE-P4P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t (k N -m)
BL-TE-P4N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m )
BH-TE-P4P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo m en t ( k N -m )
BH-TE-P4N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t (k N -m)
BL-TO-P2P
Composite beam-column Longitudinal bar Structural steel Highly confined concrete Partially confined concrete Unconfined concrete0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BL-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo me n t ( k N -m )
BH-TO-P2P
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
M o men t (k N -m)
BH-TO-P2N
Composite beam-column Longitudinal bar Structural steelHighly confined concrete Partially confined concrete Unconfined concrete
0 0.1 0.2 0.3
Curvature (1/m)
0
Mo men t ( k N -m )
Analysis
-400 -200 0 200 400
Moment (kN-m)
0
A x ia l F o r c e ( k N )
SRC1
ACI PSDM Analysis Test Data
Cross-Section Properties:
B×D=300×300mm
2Steel: H175×90×5×8 H175×90×5×8 Rebar:T:6-#6 B:6-#6 s=70 mm Material Properties:
fc'=37.4 MPa Fys= 326 MPa Fyr= 490 MPa
圖 4.26 試體 SRC1 分析模式與規範之P−M曲線圖
圖 4.26 試體 SRC1 分析模式與規範之P−M曲線圖