摘 要
耐震評估中常見的側推分析法以施加第一模態之側力來評估建築物。分別以三種不同高度之建築物作為分析對象，並以多振態側推分析與非線性歷時分析之結果做比較，研究結果發現上述之二種分析方法所得到的結果接近，但是對於低矮之五層樓鋼筋混凝土建築物，其第一模態即主宰其反應，而對於中高樓層結構物，最少應採用兩個模態來分析。三種建築物中，中低層結構物以多振態側推分析來處理較為適當。
ABSTRACT
Pushover analysis procedure (PA) was a very convenient tool for evaluating of seismic performance of buildings by applying the lateral for patterned as the inertia force of the first mode. The procedure has been extended to consider the pushover for multiple modes. The peak inelastic response of a 10-storey, 20-storey steel building (SB) and 5-storey reinforced concrete building (RCB) determined by the approximate MPA procedure is compared with rigorous non-linear response history analysis, it is demonstrated that MPA estimates the response of buildings responding well into the inelastic range to a acceptable accuracy. Moreover, it shows that for the low building (5-storey RCB), the first mode results is dominate while for the higher building (10-20 SB) we need at least 2 modes to converge the results to a certain acceptable errors compared with the results obtained from the RHA procedure. Finally, when comparing the errors of 3 kinds of building: low building, medium building, and high building, that the errors in the low-medium building are quite smaller than the others. Thus, the MPA procedure is a better application for low and medium buildings’ evaluation and design.
KEY WORDS: building evaluation and retrofit; modal analysis; pushover; seismic demands.
TABLE OF CONTENTS
Acknowledgement…………………………………………………………………...... i
Abstract………………………………………………………………………………... ii
Table of contents………………………………………………………………………. iii
List of figures………………………………………………………………………….. iv
List of tables…………………………………………………………………………… v
List of Notations………………………………………………………………………. vi
CHAPTER I: Introduction………………………………………………………………. 1
1.1. Overview …………………………………………………………………………. 1
1.2. Objectives of the Study…………………………………………………………… 2
1.3. Scope and Methodology…………………………………………………………... 2
1.4. Organization of the Study………………………………………………………… 3
CHAPTER II: Introduction to Multimode Pushover Analysis Method ………………… 4
2.1. Background……………………………………………………………………….. 4
2.2. Pushover Analysis Method……………………………………………………….. 5
2.2.1. Modal response history analysis…………………………………………… 5
2.2.2. Modal response spectrum analysis…………………………………………. 8
2.2.3. Modal pushover analysis…………………………………………………… 8
2.3. Multimode Pushover Analysis Method…………………………………………… 8
2.4. Supported Programs………………………………………………………………. 9
2.4.1. SAP2000 Program………………………………………………………….. 9
2.4.2. Bispec Program…………………………………………………………….. 9
CHAPTER III: Multimode Pushover Analysis Procedure………………………………. 12
3.1. SAP2000 Program – Analysis Procedure…………………………………………. 12
3.1.1. Model the Buildings and Define the Analyses……………………………... 12
3.1.1.1. 5-Storey building…………………………………………………... 12
3.1.1.2. 10-Storey building…………………………………………………. 13
3.1.1.1. 20-Storey building…………………………………………………. 13
3.1.2. Bilinear the Pushover Curves and convert to SDOF system……………….. 14
3.1.2.1. 5-Storey building…………………………………………………... 14
3.1.2.1.1. Mode1…………………………………………………... 14
3.1.2.1.2. Mode2…………………………………………………... 15
3.1.2.1.3. Mode3…………………………………………………... 15
3.1.2.1.4. Mode4…………………………………………………... 15
3.1.2.1.5. Mode5…………………………………………………... 16
3.1.2.2. 10-Storey building………………………………………………… 16
3.1.2.2.1. Mode1………………………………………………….. 16
3.1.2.2.2. Mode2………………………………………………….. 17
3.1.2.2.3. Mode3………………………………………………….. 17
3.1.2.2.4. Mode4………………………………………………….. 18
3.1.2.2.5. Mode5………………………………………………….. 18
3.1.2.3. 20-Storey building………………………………………………… 19
3.1.2.3.1. Mode1………………………………………………….. 19
3.1.2.3.2. Mode2………………………………………………….. 19
3.1.2.3.3. Mode3………………………………………………….. 19
3.1.2.3.4. Mode4………………………………………………….. 20
3.1.2.3.5. Mode5………………………………………………….. 20
3.2. Bispec Program – Analysis Procedure…………………………………………… 21
3.2.1. Model the Buildings and Define the Analyses……………………………. 21
3.2.1.1. 5-Storey building…………………………………………………. 21
3.2.1.2. 10-Storey building………………………………………………… 21
3.2.1.1. 20-Storey building………………………………………………… 21
3.2.2. Mark the Earthquake points onto the Bilinear Modal Pushover Curves…… 21
CHAPTER IV: Design building of 5, 10, and 20-Storey according to the Taiwan Building Code………………………………………………………………………….
61
4.1. 5 - Storey building………………………………………………………………… 61
4.1.1. Multi-Mode Pushover Analysis - results …………………………………. 61
4.1.2. Time History Analysis - results …………………………………………... 63
4.1.3. Comparision……………………………………………………………….. 63
4.2. 10 - Storey building………………………………………………………………. 64
4.2.1. Multi-Mode Pushover Analysis - results …………………………………. 64
4.2.2. Time History Analysis - results …………………………………………... 64
4.2.3. Comparision……………………………………………………………….. 65
4.3. 20 - Storey building………………………………………………………………. 66
4.3.1. Multi-Mode Pushover Analysis - results …………………………………. 66
4.3.2. Time History Analysis - results …………………………………………... 66
4.3.3. Comparision………………………………………………………………... 66
4.4. Comparison among 5, 10, 20 - Storey building - Errors between two methods … 67
CHAPTER V: Recommendations and Conclusion……………………………………… 81
5.1. Recommendations………………………………………………………………… 81
5.3. Results and Conclusions..…….…………………………………………………... 81
References…………………………………………………………………………….. 83
LIST OF FIGURES
Figure 2.1. ATC40 and FEMA356. …………………………………………………. 11
Figure 2.2. Conceptual explanation of modal RHA of elastic MDF systems. ……… 11
Figure 3.1. Side View of 5-Storey building in X-Z Plane…………………………… 22
Figure 3.2. Plan View of 5-Storey building in X-Y Plane…………………………… 23
Figure 3.3. Side View of 5-Storey building in Y-Z Plane……………………………. 23
Figure 3.4. Side View of 10-Storey building in X-Z Plane…………………………... 24
Figure 3.5. Plan View of 10-Storey building in X-Y Plane………………………….. 24
Figure 3.6. Side View of 10-Storey building in Y-Z Plane…………………………... 25
Figure 3.7. Side View of 20-Storey building in X-Z and Y-Z Plan………………….. 26
Figure 3.8. Plan View of 20-Storey building in X-Y Plane………………………….. 27
Figure 3.9. Idealized Pushover curve M1 (5storey-building)…..…………………….. 27
Figure 3.10. Fsn/Ln - Dn Relationship - M1(5storey-building)…...…………………. 28
Figure 3.11. Idealized Pushover curve M2 (5storey-building)…….………………… 28
Figure 3.12. Fsn/Ln - Dn Relationship - M2(5storey-building)…..…………………… 28
Figure 3.13. Idealized Pushover curve M3(5storey-building)……..………………… 29
Figure 3.14. Fsn/Ln - Dn Relationship - M3(5storey-building)……………………… 29
Figure 3.15. Idealized Pushover curve M4(5storey-building)……...………………… 29
Figure 3.16. Fsn/Ln - Dn Relationship - M4(5storey-building)……...………………. 30
Figure 3.17. Idealized Pushover curve M5(5storey-building)……….………………. 30
Figure 3.18. Fsn/Ln - Dn Relationship - M5(5storey-building)……..………………. 30
Figure 3.19 Idealized Pushover curve M1(10storey-building)………………………. 31
Figure 3.20. Fsn/Ln - Dn Relationship - M1(10storey-building)……………………. 31
Figure 3.21. Idealized Pushover curve M2(10storey-building)………………………. 31
Figure 3.22. Fsn/Ln - Dn Relationship - M2(10storey-building)…….………………. 32
Figure 3.23. Idealized Pushover curve M3(10storey-building)………………………. 32
Figure 3.24. Fsn/Ln - Dn Relationship - M3(10storey-building)…….………………. 32
Figure 3.25. Idealized Pushover curve M4(10storey-building)………………………. 33
Figure 3.26. Fsn/Ln - Dn Relationship - M4(10storey-building)…………..………… 33
Figure 3.27. Idealized Pushover curve M5(10storey-building)………………………. 33
Figure 3.28. Fsn/Ln - Dn Relationship - M5(10storey-building)…….………………. 34
Figure 3.29 Idealized Pushover curve M1(20storey-building)………………………. 34
Figure 3.30. Fsn/Ln - Dn Relationship - M1(20storey-building)……………………. 34
Figure 3.31. Idealized Pushover curve M2(20storey-building)………………………. 35
Figure 3.32. Fsn/Ln - Dn Relationship - M2(20storey-building)…….………………. 35
Figure 3.33. Idealized Pushover curve M3(20storey-building)………………………. 35
Figure 3.34. Fsn/Ln - Dn Relationship - M3(20storey-building)…….………………. 36
Figure 3.35. Idealized Pushover curve M4(20storey-building)………………………. 36
Figure 3.36. Fsn/Ln - Dn Relationship - M4(20storey-building)…………..………… 36
Figure 3.37. Idealized Pushover curve M5(20storey-building)………………………. 37
Figure 3.38. Fsn/Ln - Dn Relationship - M5(20storey-building)…….………………. 37
Figure 3.39. Define Earthquake 1EL-Centro(5-Storey building)…….………………. 37
Figure 3.40. 1xEL-Centro Earthquake Data …………………...…….………………. 38
Figure 3.41. Define equivalent SDOF of (5-Storey building) mode1…………………. 38
Figure 3.42. Define equivalent SDOF of (5-Storey building) mode2…………………. 39
Figure 3.43. Define equivalent SDOF of (5-Storey building) mode3…………………. 39
Figure 3.44. Define equivalent SDOF of (5-Storey building) mode4…………………. 40
Figure 3.45. Define equivalent SDOF of (5-Storey building) mode5…………………. 40
Figure 3.46. Define equivalent SDOF of (10-Storey building) mode1………………. 41
Figure 3.47. Define equivalent SDOF of (10-Storey building) mode2………………. 41
Figure 3.48. Define equivalent SDOF of (10-Storey building) mode3………………. 42
Figure 3.49. Define equivalent SDOF of (10-Storey building) mode4………………. 42
Figure 3.50. Define equivalent SDOF of (10-Storey building) mode5………………. 43
Figure 3.51. Define equivalent SDOF of (20-Storey building) mode1………………. 43
Figure 3.52. Define equivalent SDOF of (20-Storey building) mode2………………. 44
Figure 3.53. Define equivalent SDOF of (20-Storey building) mode3………………. 44
Figure 3.54. Define equivalent SDOF of (20-Storey building) mode4………………. 45
Figure 3.55. Define equivalent SDOF of (20-Storey building) mode5………………. 45
Figure 3.56 Time History Analysis results - BISPEC (5storey building-mode1)….…. 93
Figure 3.57 Time History Analysis results - BISPEC (5storey building-mode2)….…. 93
Figure 3.58 Time History Analysis results - BISPEC (5storey building-mode3)….…. 94
Figure 3.59 Time History Analysis results - BISPEC (5storey building-mode4)….…. 94
Figure 3.60 Time History Analysis results - BISPEC (5storey building-mode5)….…. 95
Figure 3.61 Time History Analysis results - BISPEC (10storey building-mode1)…… 95
Figure 3.62 Time History Analysis results - BISPEC (10storey building-mode2)….... 96
Figure 3.63 Time History Analysis results - BISPEC (10storey building-mode3)…... 96
Figure 3.64 Time History Analysis results - BISPEC (10storey building-mode4)….... 97
Figure 3.65 Time History Analysis results - BISPEC (10Storey building-mode5)…... 97
Figure 3.66 Time History Analysis results - BISPEC (10storey building-mode1)…… 98
Figure 3.67 Time History Analysis results - BISPEC (10storey building-mode2)….…. 98
Figure 3.68 Time History Analysis results - BISPEC (10storey building-mode3)…..... 99
Figure 3.69 Time History Analysis results - BISPEC (10storey building-mode4)…….. 99
Figure 3.70 Time History Analysis results - BISPEC (10Storey building-mode5)…... 100
Figure 4.1. Define Load Application Control for Nonlinear Static Analysis ……..…... 68
Figure 4.2. Floor Displacement, Storey Drift(5storey-building)(0.25EL-Centro) (MPA)………………………………………………………………………...………...
69
Figure 4.3. Define Time History Analysis (1EL-Centro)………………….....………... 69
Figure 4.4. Floor Displacement, Storey Drift(5storey-building)(0.25EL-Centro)(RHA)…………………………………………………………………...……...
70
Figure 4.5. Floor Displacement, Storey Drift(10storey-building)(0.25EL-Centro) (MPA)………………………………………………………………………...………...
71
Figure 4.6. Floor Displacement, Storey Drift(10storey-building)(0.25EL-Centro)(RHA)…………………………………………………………………...……...
72
Figure 4.7. Floor Displacement, Storey Drift(10storey-building)(0.25EL-Centro) (MPA)………………………………………………………………………...………...
73
Figure 4.8. Floor Displacement, Storey Drift(10storey-building)(0.25EL-Centro)(RHA)…………………………………………………………………...……...
74
Figure 4.9 Floor Displacement: 0.25, 0.5, 0.75, 0.85EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…………………………...……………….....
101
Figure 4.10 Floor Displacement: 1.0, 1.5, 2.0, 3.0EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…………………………...……………….....
102
Figure 4.11 Floor Displacement: 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…………….…………………………...……………….....
103
Figure 4.12 Storey drift: 0.25, 0.5EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…………….…………………………...……………….....
103
Figure 4.13 Storey drift: 0.75, 0.85, 1.0, 1.5EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…….…………………………...……………….....
104
Figure 4.14 Storey drift: 2.0, 3.0, 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (5storey building)…………….…………………………...……………….....
105
Figure 4.15 Mean Errors between MPA-RHA (5storey building).................………..... 106
Figure 4.16 Floor Displacement: 0.25, 0.5, 0.75, 0.85EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)………………………...……………….....
108
Figure 4.17 Floor Displacement: 1.0, 1.5, 2.0, 3.0EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)………………………...……………….....
109
Figure 4.18 Floor Displacement: 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)…………….………………………...……………….....
110
Figure 4.19 Storey drift: 0.25, 0.5EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)……………………………………...……………….....
110
Figure 4.20 Storey drift: 0.75, 0.85, 1.0, 1.5EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)…….………………………...……………….....
111
Figure 4.21 Storey drift: 2.0, 3.0, 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (10storey building)………….…………………………...……………….....
112
Figure 4.22 Mean Errors between MPA-RHA (10Storey building).................……..... 113
Figure 4.23 Floor Displacement: 0.25, 0.5EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………...……………….....
115
Figure 4.24 Floor Displacement: 0.75, 0.85EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)……………………………....……………….....
116
Figure 4.25 Floor Displacement: 1.0, 1.5EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………...……………….....
117
Figure 4.26 Floor Displacement: 2.0, 3.0EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………………………….....
118
Figure 4.27 Floor Displacement: 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………………………….....
119
Figure 4.29 Storey drift: 0.25, 0.5EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………...………………….…….....
120
Figure 4.29 Storey drift: 0.75, 0.85EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)……………………………....………………….…….....
121
Figure 4.30 Storey drift: 1.0, 1.5EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………...……………….....
122
Figure 4.31 Storey drift: 2.0, 3.0EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………………………….....
123
Figure 4.32 Storey drift: 4.0, 5.0EL-Centro of 1 to 5 modes and Time history analysis. (20storey building)…………….………………………………………….....
124
Figure 4.34 Floor-Displacement, Storey Drift 1-5 modes (0.01EL-C, 5storey building)……………………………………….................................................…….....
127
LIST OF TABLES
Table 3.1. Steel Areas in Columns and the Steel bars (cm2) ( 5-Storey building) …… 46
Table 3.2. Steel Areas in Beams - Top Steel (cm2) ( 5-Storey building) …………….. 46
Table 3.3. Steel Areas in Beams - Bottom Steel (cm2) ( 5-Storey building) ………… 46
Table 3.4. Floor Mass and Distributed Mass case( 5-Storey building) ……………… 47
Table 3.5. Frame Hinge Interaction Surface(5-Storey building) ……………………. 47
Table 3.6. Frame hinge Property Data for Plastic Hinges in Beams(5-Storey building). 48
Table 3.7. Frame hinge Property Data for Plastic Hinges in Columns(5-Storey building) ……………………………………………………………………………...
49
Table 3.8. Moment Rotation Data for Plastic Hinge in Columns(5-Storey building)…. 49
Table 3.9. Sections and Types of Beams and Columns(10-Storey building)………… 50
Table 3.10. Floor Mass and Distributed Mass case(10-Storey building)……………. 50
Table 3.11. Frame Hinge Interaction Surface (10-Storey building)…………………. 51
Table 3.12. Frame hinge Property Data for Plastic Hinges in Beams(10-Storey building) ……………………………………………………………………………...
51
Table 3.13 Frame hinge Property Data for Plastic Hinges in Columns(10-Storey building) ……………………………………………………………………………..
52
Table 3.14 Moment Rotation Data for Plastic Hinge in Columns(10-Storey building).. 52
Table 3.15 Sections and Types of Beam and Column(20-Storey building)……………. 53
Table 3.16 Floor Mass and Distributed Mass case(20-Storey building) ……………… 54
Table 3.17 Frame Hinge Interaction Surface(20-Storey building) ……………………. 54
Table 3.18 Frame hinge Property Data for Plastic Hinges in Beams(20-Storey building)………………………………………………………………………………..
55
Table 3.19 Frame hinge Property Data for Plastic Hinges in Columns(20-Storey building) ……………………………………………………………………………...
56
Table 3.20 Moment Rotation Data for Plastic Hinge in Columns(20-Storey building) 56
Table 3.21 Mode shapes (5-Storey building) ………………………………………... 57
Table 3.22 Mass matrix(5-Storey building) …………………………………………. 57
Table 3.23 Mode shapes (10-Storey building) ………………………………………. 57
Table 3.24 Mass matrix(10-Storey building) ………………………………………... 57
Table 3.25 Mode shapes (20-Storey building) ………………………………………. 58
Table 3.26 Mass matrix(20-Storey building) ………………………………………... 58
Table 3.27 Time History Analysis results - BISPEC (5storey building-mode1)……... 85
Table 3.28 Time History Analysis results - BISPEC (5storey building-mode2)……... 85
Table 3.29 Time History Analysis results - BISPEC (5storey building-mode3)……... 86
Table 3.30 Time History Analysis results - BISPEC (5storey building-mode4)……... 86
Table 3.31 Time History Analysis results - BISPEC (5storey building-mode5)……... 87
Table 3.32 Time History Analysis results - BISPEC (10storey building-mode1)……... 88
Table 3.33 Time History Analysis results - BISPEC (10storey building-mode2)……... 88
Table 3.34 Time History Analysis results - BISPEC (10storey building-mode3)……... 89
Table 3.35 Time History Analysis results - BISPEC (10storey building-mode4)……... 89
Table 3.36 Time History Analysis results - BISPEC (10storey building-mode5)……... 90
Table 3.37 Time History Analysis results - BISPEC (20storey building-mode1)……... 90
Table 3.38 Time History Analysis results - BISPEC (20storey building-mode2)……. 91
Table 3.39 Time History Analysis results - BISPEC (20storey building-mode3)……... 91
Table 3.40 Time History Analysis results - BISPEC (20storey building-mode4)……... 92
Table 3.41 Time History Analysis results - BISPEC (20storey building-mode5)……... 92
Table 4.1 Floor Displacement, Storey Drift (5-Storey building)(0.25EL-Centro) (MPA)………………………………………………………………………………….
75
Table 4.2 Floor Displacement, Storey Drift (5-Storey building)(0.25EL-Centro) (RHA)………………………………………………………………………………….
75
Table 4.3 Floor Displacement, Storey Drift (10-Storey building)(0.25EL-Centro) (MPA) ………………………………………………………………………………..
76
Table 4.4 Floor Displacement, Storey Drift (10-Storey building)(0.25EL-Centro) (RHA) ………………………………………………………………………………..
77
Table 4.5 Floor Displacement, Storey Drift (20-Storey building)(0.25EL-Centro) (MPA) ………………………………………………………………………………..
77
Table 4.6 Floor Displacement, Storey Drift (20-Storey building)(0.25EL-Centro) (RHA) …………………………………………………………………………………
80
Table 4.7 Mean Errors between MPA-RHA (5storey building)…………………..…... 100
Table 4.8 Mean Errors between MPA-RHA (10storey building)…...……………….... 107
Table 4.9 Mean Errors between MPA-RHA (20storey building)……………………... 114
Table 4.10 Mean Errors between MPA-RHA (among 3 buildings)…………………... 126
Table 4.11 Mean Errors between MPA-RHA (0.01EL-C, 5storey building)..………... 128
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