A Study on Performance of Existing Building Using Ordinary Moment Resisting Frame in Seismic Zone2A
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YANGON TECHNOLOGICAL UNIVERSITY DEPARTMENT OF CIVIL ENGINEERING
A STUDY ON PERFORMANCE OF EXISTING BUILDING USING ORDINARY MOMENT-RESISTING FRAME IN SEISMIC ZONE 2A
BY
MAUNG THIHA KYAW H.C. 3 (APRIL 2005)
(M.E. THESIS)
JANUARY 2007 YANGON
YANGON TECHNOLOGICAL UNIVERSITY DEPARTMENT OF CIVIL ENGINEERING
A STUDY ON PERFORMANCE OF EXISTING BUILDING USING ORDINARY MOMENT-RESISTING FRAME IN SEISMIC ZONE 2A
MAUNG THIHA KYAW H.C. 3 (APRIL 2005)
A THESIS SUBMITTED TO THE DEPARTMENT OF CIVIL ENGINEERING IN PARTIAL FULFILMENT OF THE REQUIERMENTS FOR THE DEGREE OF MASTER OF ENGINEERING (CIVIL)
JANUARY 2007 YANGON
YANGON TECHNOLOGICAL UNIVERSITY DEPARTMENT OF CIVIL ENGINEERING
We certify that we have examined, and recommend to the University Steering Committee for Post Graduate Studies for acceptance the thesis entitled "A STUDY ON PERFORMANCE OF EXISTING BUILDING USING ORDINARY MOMENT-RESISTING FRAME IN SEISMIC ZONE 2A" submitted by Maung Thiha Kyaw, Roll No. H.C. 3 (April 2005) in partial fulfilment of the requirements for the degree of Master of Engineering.
Board of Examiners:
1. Dr. Khin Than Yu Professor and Head
……………………….
Department of Civil Engineering, Y.T.U.
(Chairman/Supervisor)
2. U Aung Than Win Lecturer Department of Civil Engineering, W.Y.T.U.
………………………. (Co-Supervisor)
3. U Myo Min Hlaing Lecturer and Head Department of Civil Engineering, W.Y.T.U.
……………………….. (Member)
4. U Toe Toe Win Lecturer Department of Civil Engineering, Y.T.U.
……………………….. (Member)
5. U Saw Htwe Zaw Director ACECOMS, Satellite Centre
……………………….. (External Examiner)
i
ACKNOWLEDGEMENTS Firstly, the author would like to express his grateful thanks to his honourable supervisor, Dr. Khin Than Yu, Professor and Head of Department of Civil Engineering, Yangon Technological University, for her guidance and invaluable suggestions throughout the preparation of this study. The author also would like to express grateful thanks to his co-supervisor, U Aung Than Win, Lecturer, Department of Civil Engineering, Yangon Technological University, for his invaluable helps, indispensable guidance, patient and constructive suggestions. The author is sincerely thankful to Daw Cho Cho, Associate Professor and Deputy Head of Department of Civil Engineering, Yangon Technological University, for her kind invaluable guidance, suggestions and kind help. The author would like to express his heartfelt gratitude to the board of examiners of this thesis. Special thanks are also due to all his teachers of Civil Engineering Department of Yangon Technological University for their invaluable teaching and careful guidance. The author would like to express his deepest gratitude to his parents for their noble support, encouragement and their unique loving kindness to attain his destination without any trouble. Finally, thanks to all who helped him with necessary assistance for this study.
ii
ABSTRACT Within previous decades, the seismic effects had not been considered when designed and constructed the buildings. But now, due to the development of technology and knowledge, the seismic effects had been taken into consideration in design and construction of the structures. This study deals with the building which was not considered the seismic effects and is reviewed with subjected to moderate seismic forces to know the performance of the building. In this study, twelve-storey reinforced concrete building (ordinary moment-resisting frame) was considered to investigate the effects of moderate earthquake but substructure analysis was not considered. First, the three dimensional model was analysed and designed under gravity load and wind load. And then, the same model was reanalysed with the effects of moderate seismic forces (zone 2A). Repeated analyses for this structure were considered for seismic forces (zone 2A) in both factored and unfactored load conditions. For analysis and design of without seismic effect, ten load combinations were considered and then twenty-six load combinations with seismic effects. Finally, analysis results in main structural components such as axial force and bending moments for columns, shear, torsion and bending moments for beams were compared for the performance of ordinary moment-resisting frame under three different types of analytical conditions described in above. Moreover, storey drifts, storey displacement and storey shear were also compared in this study. Structural analysis was carried out by using Extended Three Dimensional Analysis of Building Systems (ETABS) version 8.4.8 software. Load assumptions and combinations were considered according to the provisions of Uniform Building Code – UBC (1997) and American Concrete Institute -ACI 318-99 respectively.
iii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS
i
ABSTRACT
ii
TABLE OF CONTENTS
iii
LIST OF FIGURES
viii
LIST OF TABLES
xv
LIST OF SYMBOLS
xvi
CHAPTER
1
2
TITLE
INTRODUCTION
1
1.1.
General
1
1.2.
Objectives of the Study
1
1.3.
Scope of the Study
2
1.4.
Data of Case Study
2
1.5.
Outline of Thesis
2
LITERATURE REVIEW
3
2.1.
General
3
2.2.
Seismic Damage
3
2.3.
Correlation of Intensity, Magnitude and Acceleration
4
2.3.1.
Peak Ground Acceleration
4
2.3.2.
Richter Magnitude Scale
4
2.3.3.
Intensity Scale
4
2.4.
Seismic Risk Zone
5
2.5.
Tall Building Behaviour During Earthquakes
6
2.6.
Types of Structural Systems
7
2.7.
Moment-Resisting Frame
7
2.8.
Types of Moment-Resisting Frames
8
2.8.1.
Special Moment-Resisting Frame
8
2.8.2.
Intermediate Moment-Resisting Frame
8
2.8.3.
Ordinary Moment-Resisting Frame
9
2.9.
Reinforced Concrete Beam Behaviour
2.10. Columns
9 10
iv 2.10.1. Axial Compression
3
2.11. Static Analysis Procedure
11
2.12. Building Drift Caused by Lateral Forces
12
2.13. Overview of ETABS Software
13
PREPARATION FOR STRUCTURAL ANALYSIS AND DESIGN
14
3.1.
Design Parameters and Assumptions for Calculation
14
3.2.
Loading
14
3.2.1. Gravity Loads
14
3.2.1.1.
Dead load
15
3.2.1.2.
Live load
15
3.2.2.
Lateral Loads
15
3.2.2.1. Wind load
15
3.2.2.2. Earthquake load
17
Load Combinations
20
3.3.
Grouping of Structural Components
21
3.4.
Analysing
22
3.5.
Analysis Output
22
3.5.1.
Analysis Results for Columns
22
3.5.2.
Analysis Results for Beams
22
3.5.3.
Analysis Results for Storey Drifts, Storey
3.2.3
Displacement and Storey Shear 3.6. 4
10
Concrete Frame Design
22 22
COMPARISON OF ANALYSIS RESULTS
23
4.1.
General
23
4.2.
Comparison of Storey Drifts
23
4.3.
Comparison of Storey Displacements
25
4.4.
Comparison of Storey Shear
26
4.5.
Comparison of Critical Forces in Columns
27
4.5.1. Comparison of Axial Force for Columns
28
4.5.1.1.
Comparison of axial force for corner columns
4.5.1.2.
28
Comparison of axial force for end columns
29
v 4.5.1.3.
Comparison of axial force for interior columns
30
4.5.2. Comparison of Bending Moment in X Direction for Columns 4.5.2.1.
34
Comparison of bending moment in x direction for corner columns
4.5.2.2.
Comparison of bending moment in x direction for end columns
4.5.2.3.
34
36
Comparison of bending moment in x direction for interior columns
37
4.5.3. Comparison of Bending Moment in Y Direction for Columns 4.5.3.1.
41
Comparison of bending moment in y direction for corner columns
4.5.3.2.
Comparison of bending moment in y direction for end columns
4.5.3.3.
42
Comparison of bending moment in y direction for interior columns
4.6.
41
43
Comparison of Critical Forces in Beams
47
4.6.1. Comparison of Shear Force for Beams
47
4.6.1.1.
Comparison of shear force for edge beams
4.6.1.2.
Comparison of shear force for cantilever beams
4.6.1.3.
50
Comparison of shear force for interior beams
4.6.2. Comparison of Torsion for Beams 4.6.2.1.
Comparison of torsion for edge beams
4.6.2.2.
Comparison of torsion for cantilever beams
4.6.2.3.
47
52 56 56
58
Comparison of torsion for interior beams
60
4.6.3. Comparison of Bending Moment at Support for Beams
65
vi 4.6.3.1.
Comparison of bending moment at support for edge beams
4.6.3.2.
Comparison of bending moment at support for cantilever beams
4.6.3.3.
65
67
Comparison of bending moment at support for interior beams
69
4.6.4. Comparison of Bending Moment at Midspan for Beams 4.6.4.1.
73 Comparison of bending moment at midspan for edge beams
4.6.4.2.
Comparison of bending moment at midspan for cantilever beams
4.6.4.3.
73
75
Comparison of bending moment at midspan for interior beams
76
4.7. Comparison of Critical Forces for One Panel Continuous Beam-Column Frame
81
4.7.1. Comparison of Critical Forces Differences for Columns
81
4.7.2. Comparison of Critical Forces Differences for
4.8.
Beams
82
Discussions on Comparisons
92
4.8.1. Comparison of Storey Drifts
92
4.8.2. Comparison of Storey Displacements
92
4.8.3. Comparison of Storey Shear
92
4.8.4. Comparison of Columns
92
4.8.4.1.
Axial force
92
4.8.4.2.
Bending moment in x direction
93
4.8.4.3.
Bending moment in y direction
93
4.8.5. Comparison of Beams
94
4.8.5.1.
Shear force
94
4.8.5.2.
Torsion
94
4.8.5.3.
Bending moment at support
95
4.8.5.4.
Bending moment at midspan
95
vii 4.8.6. Comparison of Critical Forces for One Panel Continuous Beam-Column Frame 4.8.7. Summarised Discussions on Comparisons 5
96 96
DISCUSSIONS, CONCLUSIONS AND RECOMMENDATIONS
98
5.1.
Discussions and Conclusions
98
5.2.
Recommendations
099
REFERENCE LIST
100
APPENDICES
101
viii
LIST OF FIGURES
Figure
Page
2.1.
Moment-Resisting Frame
2.2.
Behaviour of Reinforced Concrete Beam under Increasing Load
10
3.1.
Vertical Distribution of Design Base Shear
19
4.1.
Comparison of Storey Drift in X-Direction
24
4.2.
Comparison of Storey Drift in Y-Direction
24
4.3.
Comparison of Storey Displacement - Ux
25
4.4.
Comparison of Storey Displacement - Uy
26
4.5.
Comparison of Storey Shear -Vx
27
4.6.
Comparison of Storey Shear -Vy
27
4.7.
Comparison of Axial Force for Corner Column, C70
28
4.8.
Comparison of Axial Force for Corner Column, C41
28
4.9.
Comparison of Axial Force for Corner Column, C58
29
4.10.
Comparison of Axial Force for End Column, C55
29
15
4.11.
Comparison of Axial Force for End Column, C69
30
15
4.12.
Comparison of Axial Force for Interior Column, C42
30
4.13.
Comparison of Axial Force for Interior Column, C44
31
4.14.
Comparison of Axial Force for Interior Column, C45
31
4.15.
Comparison of Axial Force for Interior Column, C46
32
4.16.
Comparison of Axial Force for Interior Column, C53
32
4.17.
Comparison of Axial Force for Interior Column, C54
33
4.18.
Comparison of Axial Force for Interior Column, C59
33
4.19.
Comparison of Axial Force for Interior Column, C60
34
4.20.
Comparison of Bending Moment in X Direction for Corner Column, C70
4.21.
8
34
Comparison of Bending Moment in X Direction for Corner Column, C41
35
ix 4.22.
Comparison of Bending Moment in X Direction for Corner Column, C58
4.23.
Comparison of Bending Moment in X Direction for End Column, C55
4.24.
42
Comparison of Bending Moment in Y Direction for End Column, C69
4.38.
42
Comparison of Bending Moment in Y Direction for End Column, C55
4.37.
41
Comparison of Bending Moment in Y Direction for Corner Column, C58
4.36.
41
Comparison of Bending Moment in Y Direction for Corner Column, C41
4.35.
40
Comparison of Bending Moment in Y Direction for Corner Column, C70
4.34.
40
Comparison of Bending Moment in X Direction for Interior Column, C60
4.33.
39
Comparison of Bending Moment in X Direction for Interior Column, C59
4.32.
39
Comparison of Bending Moment in X Direction for Interior Column, C54
4.31.
38
Comparison of Bending Moment in X Direction for Interior Column, C53
4.30.
38
Comparison of Bending Moment in X Direction for Interior Column, C46
4.29.
37
Comparison of Bending Moment in X Direction for Interior Column, C45
4.28.
37
Comparison of Bending Moment in X Direction for Interior Column, C44
4.27.
36
Comparison of Bending Moment in X Direction for Interior Column, C42
4.26.
36
Comparison of Bending Moment in X Direction for End Column, C69
4.25.
35
43
Comparison of Bending Moment in Y Direction for Interior Column, C42
43
x 4.39.
Comparison of Bending Moment in Y Direction for Interior Column, C44
4.40.
Comparison of Bending Moment in Y Direction for Interior Column, C45
4.41.
46
Comparison of Bending Moment in Y Direction for Interior Column, C59
4.45.
45
Comparison of Bending Moment in Y Direction for Interior Column, C54
4.44.
45
Comparison of Bending Moment in Y Direction for Interior Column, C53
4.43.
44
Comparison of Bending Moment in Y Direction for Interior Column, C46
4.42.
44
46
Comparison of Bending Moment in Y Direction for Interior Column, C60
47
4.46.
Comparison of Shear Force for Edge Beam - B10
48
4.47.
Comparison of Shear Force for Edge Beam - B77
48
4.48.
Comparison of Shear Force for Edge Beam - B472
49
4.49.
Comparison of Shear Force for Edge Beam - B16
49
4.50.
Comparison of Shear Force for Cantilever Beam - B270
50
4.51.
Comparison of Shear Force for Cantilever Beam - B273
50
4.52.
Comparison of Shear Force for Cantilever Edge Beam - B169
51
4.53.
Comparison of Shear Force for Cantilever Edge Beam - B166
51
4.54.
Comparison of Shear Force for Interior Beam - B12
52
4.55.
Comparison of Shear Force for Interior Beam - B11
52
4.56.
Comparison of Shear Force for Interior Beam - B14
53
4.57.
Comparison of Shear Force for Interior Beam - B51
53
4.58.
Comparison of Shear Force for Interior Beam - B61
54
4.59.
Comparison of Shear Force for Interior Beam - B97
54
4.60.
Comparison of Shear Force for Interior Beam - B140
55
4.61.
Comparison of Shear Force for Interior Beam - B130
55
4.62.
Comparison of Shear Force for Interior Beam - B60
56
4.63.
Comparison of Torsion for Edge Beam - B10
56
4.64.
Comparison of Torsion for Edge Beam - B77
57
4.65.
Comparison of Torsion for Edge Beam - B472
57
xi 4.66.
Comparison of Torsion for Edge Beam - B16
58
4.67.
Comparison of Torsion for Cantilever Beam - B270
58
4.68.
Comparison of Torsion for Cantilever Beam - B273
59
4.69.
Comparison of Torsion for Cantilever Edge Beam - B169
59
4.70.
Comparison of Torsion for Cantilever Edge Beam - B166
60
4.71.
Comparison of Torsion for Interior Beam - B12
60
4.72.
Comparison of Torsion for Interior Beam - B11
61
4.73.
Comparison of Torsion for Interior Beam - B14
61
4.74.
Comparison of Torsion for Interior Beam - B51
62
4.75.
Comparison of Torsion for Interior Beam - B61
62
4.76.
Comparison of Torsion for Interior Beam - B97
63
4.77.
Comparison of Torsion for Interior Beam - B140
63
4.78.
Comparison of Torsion for Interior Beam - B130
64
4.79.
Comparison of Torsion for Interior Beam - B60
64
4.80.
Comparison of Bending Moment at Support for Edge Beam - B10
65
4.81.
Comparison of Bending Moment at Support for Edge Beam - B77
65
4.82.
Comparison of Bending Moment at Support for Edge Beam - B472
66
4.83.
Comparison of Bending Moment at Support for Edge Beam - B16
66
4.84.
Comparison of Bending Moment at Support for Cantilever Beam B270
4.85.
Comparison of Bending Moment at Support for Cantilever Beam B273
4.86.
67
Comparison of Bending Moment at Support for Cantilever Edge Beam - B169
4.87.
67
68
Comparison of Bending Moment at Support for Cantilever Edge Beam - B166
68
4.88.
Comparison of Bending Moment at Support for Interior Beam - B12
69
4.89.
Comparison of Bending Moment at Support for Interior Beam - B11
69
4.90.
Comparison of Bending Moment at Support for Interior Beam - B14
70
4.91.
Comparison of Bending Moment at Support for Interior Beam - B51
70
4.92.
Comparison of Bending Moment at Support for Interior Beam - B61
71
4.93.
Comparison of Bending Moment at Support for Interior Beam - B97
71
4.94.
Comparison of Bending Moment at Support for Interior Beam - B140
72
4.95.
Comparison of Bending Moment at Support for Interior Beam - B130
72
xii 4.96.
Comparison of Bending Moment at Support for Interior Beam - B60
73
4.97.
Comparison of Bending Moment at Midspan for Edge Beam - B10
73
4.98.
Comparison of Bending Moment at Midspan for Edge Beam - B77
74
4.99.
Comparison of Bending Moment at Midspan for Edge Beam - B472
74
4.100.
Comparison of Bending Moment at Midspan for Edge Beam - B16
75
4.101.
Comparison of Bending Moment at Midspan for Cantilever Edge Beam - B169
4.102.
75
Comparison of Bending Moment at Midspan for Cantilever Edge Beam - B166
76
4.103.
Comparison of Bending Moment at Midspan for Interior Beam - B12
76
4.104.
Comparison of Bending Moment at Midspan for Interior Beam - B11
77
4.105.
Comparison of Bending Moment at Midspan for Interior Beam - B14
77
4.106.
Comparison of Bending Moment at Midspan for Interior Beam - B51
78
4.107.
Comparison of Bending Moment at Midspan for Interior Beam - B61
78
4.108.
Comparison of Bending Moment at Midspan for Interior Beam - B97
79
4.109.
Comparison of Bending Moment at Midspan for Interior Beam - B140
79
4.110.
Comparison of Bending Moment at Midspan for Interior Beam - B130
80
4.111.
Comparison of Bending Moment at Midspan for Interior Beam - B60
80
4.112.
Comparison of Axial Force Differences for Columns from One Panel Continuous Beam - Column Frame
4.113.
Comparison of Bending Moment in X Direction Differences for Columns from One Panel Continuous Beam - Column Frame
4.114.
83
Comparison of Bending Moment at Support Differences for Beams from One Panel Continuous Beam - Column Frame
4.118.
82
Comparison of Torsion Differences for Beams from One Panel Continuous Beam - Column Frame
4.117.
82
Comparison of Shear Force Differences for Beams from One Panel Continuous Beam - Column Frame
4.116.
81
Comparison of Bending Moment in Y Direction Differences for Columns from One Panel Continuous Beam - Column Frame
4.115.
81
83
Comparison of Bending Moment at Midspan Differences for Beams from One Panel Continuous Beam - Column Frame
84
A.1.
Three Dimensional View of Case Study Building
101
A.2.
First Floor Level Beams and Columns Structure Key Plan
102
55
xiii A.3.
Second Floor Level Beams and Columns Structure Key Plan
A.4.
Typical Floor (third to tenth floor) Level Beams and Columns Structure Key Plan
103
000
104
000 55
A.5.
Eleventh Floor Level Beams and Columns Structure Key Plan View
105
A.6.
Roof Level One Beams and Columns Structure Key Plan View
106
A.7.
Concrete Design Sections of Ground Floor Plan View
107
A.8.
Concrete Design Sections of First Floor Plan View
108
A.9.
Concrete Design Sections of Second Floor Plan View
109
A.10.
Concrete Design Sections of Third Floor to Eleventh Floor Plan View
110
A.11.
Concrete Design Sections of Roof Level One Plan View
111
A.12.
Concrete Design Sections of Elevation View-1 and Elevation View-9
112
A.13.
Concrete Design Sections of Elevation View-2 and Elevation View-8
113
A.14.
Concrete Design Sections of Elevation View-3
114
A.15.
Concrete Design Sections of Elevation View-4
115
A.16.
Concrete Design Sections of Elevation View-5
116
A.17.
Concrete Design Sections of Elevation View-6
117
A.18.
Concrete Design Sections of Elevation View-7
118
A.19.
Frame Span Loads (WALL) of Elevation View-3
119
A.20.
Frame Span Loads (WALL) of Elevation View-7
120
A.21.
Frame Span Loads (WALL) of Elevation View-I
121
A.22.
Frame Span Loads (WALL) of Elevation View-J
122
A.23.
Uniform Loads GRAVITY (SUPERDL) of First Floor Plan View
123
A.24.
Uniform Loads GRAVITY (SUPERDL) of Third Floor Plan View
124
A.25.
Uniform Loads GRAVITY (LIVE) of First Floor Plan View
125
A.26.
Uniform Loads GRAVITY (LIVE) of Third Floor Plan View
126
A.27.
Axial Force Diagram (COMB2) of Elevation View-E
127
A.28.
Axial Force Diagram (COMB2) of Elevation View-7
128
A.29.
Bending Moment in X Direction Diagram (COMB3) of Elevation View-E
A.30.
000
130
555
131
555
Bending Moment in X Direction Diagram (COMB16) of Elevation View-E
A.31.
129
Bending Moment in X Direction Diagram (COMB3) of Elevation View-7
55
xiv A.32.
Bending Moment in X Direction Diagram (COMB15) of Elevation View-7
A.33.
555
134
Bending Moment in Y Direction Diagram (COMB10) of Elevation View-7
A.36.
133
Bending Moment in Y Direction Diagram (COMB18) of Elevation View-E
A.35.
555
Bending Moment in Y Direction Diagram (COMB9) of Elevation View-E
A.34.
132
135
Bending Moment in Y Direction Diagram (COMB17) of Elevation View-7
136
A.37.
Shear Force Diagram (COMB2) of First Floor Plan View
137
A.38.
Shear Force Diagram (COMB20) of First Floor Plan View
138
A.39.
Shear Force Diagram (COMB2) of Fifth Floor Plan View
139
A.40.
Shear Force Diagram (COMB20) of Fifth Floor Plan View
140
A.41.
Torsion Diagram (COMB5) of First Floor Plan View
141
A.42.
Torsion Diagram (COMB22) of First Floor Plan View
142
A.43.
Torsion Diagram (COMB5) of Fifth Floor Plan View
143
A.44.
Torsion Diagram (COMB22) of Fifth Floor Plan View
144
A.45.
Bending Moment Diagram (COMB4) of First Floor Plan View
145
A.46.
Bending Moment Diagram (COMB19) of First Floor Plan View
146
A.47.
Bending Moment Diagram (COMB4) of Fifth Floor Plan View
147
A.48.
Bending Moment Diagram (COMB19) of Fifth Floor Plan View
148
A.49.
Plan View of Beam and Column Labels
149
B.1.
Front Elevation
150
B.2.
Side Elevation
151
B.3.
Ground Floor and First Floor Plan
152
B.4.
Typical Floor (Third Floor to Tenth Floor) Plan
153
B.5.
Eleventh Floor Plan
154
B.6.
Roof Level One Plan
155
xv
LIST OF TABLES
Table
2.1.
Page
Approximate Approximate Relationship between Mercalli Intensity and Peak Ground Acceleration
5
2.2.
Approximate Code Maximum Zone Acceleration and Magnitude
6
2.3.
Effects of an Earthquake by Zone
6
2.4.
UBC-1997 Storey Drift Limitations
4.1.
Comparison of Storey Drifts without Earthquake and with Earthquake
4.2.
87
Comparison of Critical Forces for Beams (One Panel) - Shear Force
4.8.
Comparison of Critical Forces for Beams (One Panel) - Torsion
4.9.
Comparison of Critical Forces for Beams (One Panel) - Bending Moment at Support
4.10.
86
Comparison of Critical Forces for Columns (One Panel) - Bending Moment in Y Direction
4.7.
85
Comparison of Critical Forces for Columns (One Panel) - Bending Moment in X Direction
4.6.
26
Comparison of Critical Forces for Columns (One Panel) - Axial Force
4.5.
25
Comparison of Storey Shear without Earthquake and with Earthquake
4.4.
23
Comparison of Storey Displacements without Earthquake and with Earthquake
4.3.
13
88 89
90
Comparison of Critical Forces for Beams (One Panel) - Bending Moment at Midspan
91
xvi
LIST OF SYMBOLS a
acceleration
A
amplitude
Ast
longitudinal steel area
Ag
gross cross sectional area
Ce
a factor that combines the effects of height, exposure and gust factor
Cq
pressure coefficient which takes into consideration
Ca
seismic response coefficient for Na
Cv
seismic response coefficient for Nv
D.L
dead load
E
modulus of elasticity
f’c
compressive strength of concrete, cylinder
Ft
concentrated force at the top of the structure
fy
yield strength of reinforcing steel
g
acceleration of gravity
h
storey height
hi
height above base to level i
hn
height above base to level n
hx
height above base to level x
I
seismic important factor depending on occupancy category
Iw
wind important factor
L.L
live load
M
moment
M
Ritcher magnitude
MM
modified Mercalli scale
Na,Nv
near-source factor
P
design wind pressure
PGA
peak ground acceleration
qs
wind stagnation pressure at a standard height of 33 ft corresponding to the 50 years
xvii R
response modification factor or overstrength factor
T
fundamental period of vibration
V
total design lateral force or shear at the base
W
total weight of the structure, total seismic dead load
W.L
wind load
wi, wx
portion of W located at or assigned to level i or x respectively
Δm
maximum inelastic response displacement
Δs
storey drift
CHAPTER 1 INTRODUCTION
1.1. General In Myanmar, according to political, social and economical demands, bridges, dams, hydropower plants, high-rise buildings etc., are designed and constructed nowadays. With the growth of population, high-density living is increasingly adopted as a solution to a problem of shelter. That is why most of the cities in Myanmar need various types of high-rise building with safety, serviceability and servicing. In Yangon area, many high-rise buildings are needed due to the rapid growth of population. Within previous decades, the seismic effects had not been considered when the buildings were designed and constructed. But now due to the availability of referenced books and computer software, it is considered the earthquake effects on the analysis and design of buildings. In this study, building which was not considered seismic forces when designed is reviewed with earthquake effects. To get a reliable analysis and design for high-rise building, computer aided analysis may be fast and economical method. In this study, 12-storey residential reinforced concrete building is solved by using ETABS (Extended Three dimensional Analysis on Building Systems) nonlinear version 8.4.8 software.
1.2. Objectives of the Study The objectives of the study are as follows: 1. To gain knowledge in analysis and design of moment-resisting frames. 2. To have better knowledge in effects of earthquake on building structures. 3. To study the behaviour of structural members in Ordinary Moment-Resisting Frame. 4. To know the performance of Ordinary Moment-Resisting Frame when subjected to moderate seismic forces.
2 1.3. Scope of the Study The scopes of the study to achieve the objectives are as follows: 1. Analysis and design of framing system will be carried out by using ETABS nonlinear version 8.4.8. 2. Equivalent static loading is used for lateral loads (wind and earthquake effects). 3. Equivalent static earthquake and wind loads are based on Uniform Building Code (UBC) 1997. 4. Structural elements are designed according to ACI 318-99. 5. Structural analysis is considered only for linear elastic analysis and the study was not extended to cases of inelastic material behaviour. 6. Comparison of forces in main structural components: Column
:
Axial force and Bending Moment in two directions.
Beam
:
Shear Force, Torsion and Bending Moment at support and midspan..
7. Comparison of storey drifts, storey displacements and storey shear.
1.4. Data of Case Study In this study, 12-storey residential reinforced concrete building (ordinary moment-resisting frame) is considered as a hypothetical model. This building is located in seismic zone 2A. Maximum length and width of building are 136 feet and 126 feet respectively. Height of building is 140 feet above natural ground level.
1.5. Outlines of Thesis There are five chapters in this thesis. Chapter one is introduction about this study. In Chapter two, it explains about the literature review of moment resisting frame and seismic design. Chapter three represents preparation of data for analysis and design using ETABS software. In Chapter four, structural analysis, design results and comparison of member forces are presented. Discussions, conclusions and recommendations for further purposes are presented in the last Chapter. Books and articles that were cited in this study are listed in references.
CHAPTER 2 LITERATURE REVIEW
2.1. General Earthquakes result from the sudden movement of tectonic plates in the earth's crust. The movement takes place at fault lines, and the energy released is transmitted through the earth in the form of waves that causes ground motion many miles from the epicenter. Regions adjacent to active fault lines are the most prone to experience earthquake. As the ground moves, inertia tends to keep structure in place, resulting in the imposition of displacements and forces that can have catastrophic results. The purpose of the seismic design is to proportion structures so that they can withstand the displacements and the forces induced by the ground motion. Seismic design has emphasised the effects of horizontal ground motion, because the horizontal components of an earthquake usually exceed the vertical component and because structures are usually much stiffer and stronger in response to vertical loads than they are in response to horizontal loads.
2.2. Seismic Damage Structural damage due to an earthquake is not solely a function of the earthquake ground motion. The primary factors affecting the extent of damage are: 1. Earthquake characteristics such as peak ground acceleration, duration of strong shaking, frequency content and length of fault rupture. 2. Site characteristics such as distance between the epicenter and structure, geology between the epicenter and structure, soil conditions at the site, and natural period of the site. 3. Structural characteristics such as natural period and damping of the structure, age and construction method of the structure and seismic provisions (i.e., detailing)
included
in
the
design
(Lindeburg
and
Baradar
2001).
4 2.3. Correlation of Intensity, Magnitude and Acceleration with Damage Correlation of earthquake intensity, magnitude and acceleration with damage are possible since many factors contribute to seismic behaviour and structural performance.
2.3.1. Peak Ground Acceleration The peak ground acceleration, PGA, is easily measured by a seismometer or accelerometer and is one of the most important characteristics of an earthquake. The PGA can be given in various units, including ft/sec2, in/sec2, or m/s2. However, it is most common to specify the PGA in “g’s” (i.e, as a fraction or percent of gravitational acceleration) (Lindeburg and Baradar 2001).
PGA =
a ft / sec2 32.2
PGA =
ain / sec 2
PGA =
am / s2
386 9.81
× 100%
[U.S.]
Equation 2.1
× 100%
[U.S.]
Equation 2.2
[SI]
Equation 2.3
× 100%
2.3.2. Richter Magnitude Scale The magnitude, M, of an earthquake is determined from the logarithm to base ten of the amplitude recorded by a seismometer. The Richter magnitude, M, is calculated from the maximum amplitude, A, of the seismometer trace. A0 is the seismometer reading produced by an earthquake of standard size (i.e, a calibration earthquake). Generally, A0 is 0.94 x 10-5 in (0.001 mm).
⎛ A ⎞ ⎟⎟ M = log10 ⎜⎜ ⎝ A0 ⎠
Equation 2.4
Richter magnitude is expressed in whole numbers and decimal fractions. The magnitude of an earthquake depends on the length and breadth of the fault slip, as well as on the amount of slip (Lindeburg and Baradar 2001).
2.3.3. Intensity Scale The intensity of an earthquake is based on the damage and other observed effects on people, buildings, and other features. Intensity varies from place to place
5 within the disturbed region. The Modified Mercalli scale consists of 12 increasing levels of intensity (expressed as Roman numerals the initials MM) that range from imperceptible shaking to catastrophic destruction. The lower numbers of the intensity scale generally are based on the manner in which the earthquake is felt by people. The higher numbers are based on observed structural damage. The numerals do not have a mathematical basis and therefore are more meaningful to non-technical people than to those in technical fields. Although there are some empirical relationships, no exact correlations of intensity, magnitude, and acceleration with damage are possible since many factors contribute to seismic behaviour and structural performance. However, within a geographical region with constituent design and construction methods, fairly good correlation exists between structural performance and ground acceleration, because the Mercalli intensity scale is based specially on observed damage. Approximate relationship between modified Mercalli intensity and peak ground acceleration are shown in Table 2.1 (Lindeburg and Baradar 2001).
Table 2.1. Approximate Relationship between Mercalli Intensity and Peak Ground Acceleration Modified Mercalli Intensity
Peak Ground Acceleration (g)
IV
0.03 and below
V
0.03 ~ 0.08
VI
0.08 ~ 0.15
VII
0.15 ~ 0.25
VIII
0.25 ~ 0.45
IX
0.45 ~ 0.60
X
0.60 ~ 0.80
XI
0.80 ~ 0.90
XII
0.90 and above
Source: Lindeburg and Baradar (2001)
2.4. Seismic Risk Zone There are several methods of evaluating the significance of the seismic risk zones. One method is to correlate the zones with the approximate accelerations and
6 magnitudes, as shown in Table 2.2.
Table 2.2. Approximate Code Maximum Zone Acceleration and Magnitude Zone
Maximum Acceleration
Maximum Magnitude
0
0.04g
4.3
1
0.075g
4.7
2A
0.15g
5.5
2B
0.20g
5.9
3
0.30g
6.6
4
0.40g
7.2
Source: Lindeburg and Baradar (2001)
Another interpretation of the significance of the zones is to correlate them to the effects of an earthquake and the Modified Mercalli intensity as shown in Table 2.3. Table 2.3. Effects of an Earthquake by Zone Zone
Effect
0
No damage
1
Minor damage corresponding to MM intensities V and VI; distant earthquake may damage structures with fundamental periods greater than 1.0 sec
2
Moderate damage corresponding to MM intensity VII
3
Major damage corresponding to MM intensity VIII
4
Major damage corresponding to MM intensity VIII and higher
Source: Lindeburg and Baradar (2001)
2.5. Tall Building Behaviour During Earthquakes The behaviour of tall building during an earthquake is a vibration problem. The seismic motions of the ground do not damage a building by impact as does a weaker’s ball, or by externally applied pressure such as wind, but rather by internally generated internal forces caused by vibration of the building mass. An increase in the mass has two undesirable affects on the earthquake design. First, it results in an increase in the force, and second, it can cause buckling of vertical elements such as
7 columns and walls when the mass pushing down exerts its force on the member bent or moved out of the plump by the lateral forces (Taranath 1998).
2.6. Types of Structural Systems The Uniform Building Code (UBC)-1997 recognises seven major types of structural systems capable of resisting lateral forces. These systems are as follows: 1. Bearing wall system 2. Building frame system 3. Moment-resisting frames 4. Dual systems 5. Cantilever column building systems 6. Shear wall frame interaction system 7. Undefined system (Lindeburg and Baradar 2001).
2.7. Moment-Resisting Frame Moment-resisting frames resist forces in members and joints primarily by flexure and rely on a frame to carry both vertical and lateral loads. Lateral loads are carried primarily by flexure on the members and joints. Theoretically, joints are completely rigid. Moment-resisting frames counteract the horizontal forces of earthquake through the bending strengths of the beams and columns connected rigidly at their junctions with one another; of course, this bending is accompanied by shear forces. Moment-resisting frames can be constructed of concrete, masonry or steel. From an architectural standpoint, moment-resisting frames have positive and negative implication. 1. Positive They allow greater flexibility than shear walls and braced frames in the functional planning of the building. 2. Negative They exhibit greater deflections than shear walls and braced frames, so that the detailing of non-structural elements becomes more problematic.
8
Figure 2.1. Moment-Resisting Frame System Source: Structures and Codes Institute 2.8. Types of Moment-Resisting Frames Moment-resisting frames are subdivided on the basis of seismic zones. There are five types of moment-resisting frames: 1. Steel and concrete special moment-resisting frame (SMRF), 2. Masonry moment-resisting wall frame (MMRWF), 3. Concrete intermediate moment-resisting frame (IMRF), 4. Steel or concrete ordinary moment-resisting frame (OMRF), and 5. Special steel truss moment-resisting frame (STMRF). These systems provide a sufficient degree of redundancy and have excellent inelastic response capacities (Lindeburg and Baradar 2001).
2.8.1. Special Moment-Resisting Frame A moment frame in which members and joints are capable of resisting forces by flexure as well as along the axis of the members. Special moment-resisting frame is specially detailed to provide ductile behaviour. The special moment-resisting frame is appropriate in high seismic risk areas, especially seismic zone 3 and 4 (Lindeburg and Baradar 2001).
2.8.2. Intermediate Moment-Resisting Frame A moment frame in which members and joints are capable of resisting forces by flexure as well as along the axis of the members. Intermediate moment-resisting frame is designed in accordance with section 1921.8 of UBC 1997.
9 The intermediate moment-resisting frame is appropriate in moderate seismic risk areas, especially seismic zone 2 (Lindeburg and Baradar 2001).
2.8.3. Ordinary Moment-Resisting Frame A moment frame in which members and joints are capable of resisting forces by flexure as well as along the axis of the members. Ordinary moment-resisting frame is not met special detailing requirements for ductile behaviour. The ordinary moment-resisting frame is appropriate in minimal seismic risk areas, especially seismic zone 0 and 1 (Lindeburg and Baradar 2001).
2.9. Reinforced Concrete Beam Behaviour Plain concrete beams are insufficient as flexural members because the tension strength in bending is a small fraction of the compression bending. In consequence, such beams fail on the tension side at low loads long before the strength of the concrete on the compression side has been fully utilized. For this reason steel reinforcing bars are placed on the tension side as close to the extreme tension fibre as is compatible with proper fire and corrosion protection of the steel. In such a reinforced concrete beam the tension caused by the bending moments is chiefly resisted by the steel reinforcement, while the concrete alone is usually capable of resisting the corresponding compression. When the load on such a beam is gradually increased from zero to the magnitude that will cause the beam to fail, several different stages of behaviour can be clearly distinguished. At low loads, as long as the maximum tension stress in the concrete is smaller than the modulus of rupture, the entire concrete is effective in resisting stress, in compression on one side and in tension on the other side of the neutral axis. In addition, the reinforcement, deforming the same amount as the adjacent concrete, is also subject to tension stresses. The distribution of strains and stresses in concrete and steel over the depth of the section is as shown in Figure 2.2(c). When the load is further increased, the tension strength of the concrete is soon reached, and tension cracks develop. The general shape and distribution of these cracks is also small that they are not objectionable from the viewpoint of either corrosion protection or appearance. Evidently, in a cracked section that is in a cross section located at a crack such as a-a in Figure 2.2(d), the concrete does not transmit any tension stresses. The distribution of strains and stresses at or near a cracked
10 section is that shown in Figure 2.2(e). Figure 2.2(f) shows the distribution of stains and stresses close to the ultimate load. Eventually the carrying capacity of the beam is reached (Nilson 1997).
Figure 2.2. Behaviour of Reinforced Concrete Beam under Increasing Load Source: Nilson (1997) 2.10. Column Columns are defined as members that carry loads chiefly in compression. Usually columns carrying bending moments as well, about one or both axes of the cross section, and bending action may produce tensile forces over a part of the cross section (Nilson 1997).
2.10.1. Axial Compression Three types of reinforced concrete compression members in use are as follows: 1. Members reinforced with longitudinal bars and lateral ties. 2. Members reinforced with longitudinal bars and continuous spirals. 3. Composite compression members reinforced longitudinally with structural
11 steel shapes, pipe, or tubing, with or without additional bars, and various types of lateral reinforcement. The main reinforcement in columns is longitudinal, parallel to the direction of the load, and consists of bars arranged in a square, rectangular, or circular pattern. The ratio of longitudinal steel area Ast to gross cross section Ag is in the range from 0.01 to 0.08 according to ACI Code. The lower limit is necessary to ensure resistance to bending moment not accounted for in the analysis and to reduce the effects of creep and shrinkage of the concrete under sustained compression. Ratios higher than 0.08 not only economical, but also would cause difficulty owing to congestion of the reinforcement, particularly where the steel must be spliced. Generally, the larger diameter bars are used to reduce placement costs and to avoid unnecessary congestion. Columns may be divided into two broad categories: short columns, for which the strength is governed by the materials and the geometry of the cross section, and slender columns, for which the strength may be significantly reduced by lateral directions. Effective lateral bracing, which prevents relative lateral movement of the two ends of a column, is commonly provided by shear walls, elevator and stair shafts, diagonal bracing, or a combination of these. Although slender columns are more common now because of the wider use of high strength materials and improved methods of dimensioning members, it is still true that most columns in ordinary practice can be considered short columns (Nilson 1997).
2.11. Static Analysis Procedure There are two different approaches in seismic design. They are static analysis and dynamic analysis procedures. Both of which are correct in their own ways. Static deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity. The static force procedure is also referred to as the equivalent static lateral-force procedure. The UBC-97 provides the provisions for determining base shear by the static lateral-force procedure. The structures considered for this procedure are mainly regular structures. The static method may be used for the buildings with the following characteristics. 1. All structures, regular or irregular, in seismic zone 1 and occupancy categories 4 and 5 in seismic zone 2.
12 2. Regular structures under 240 feet in height with lateral force resistance provided by systems listed in section 2.2 of this thesis. 3. Irregular structures not more than five stories or 65 feet in height 4. Structures with flexible upper portions supported on a rigid lower portion.
2.12. Building Drift Caused by Lateral Forces A horizontal force applied to an object tends to push it sideways. If it is unrestrained at its base, it slides in the direction of the applied force. With buildings, sliding is counteracted by the frictional sliding resistance between the bottom of the foundation and the soil and by the lateral bearing resistance of the soil against the vertical faces of the foundation and the piles. Lateral forces acting above the foundation push the superstructure sideways until the resistance of the structure reaches an equilibrium with that force. The amount of horizontal displacement that occurred is called drift. Drift causes stress in structural seismic elements and nonstructural elements because it forces them into deformed shapes. Storey drift is the lateral displacement of one level of a structure relative to the level above or below. In the UBC-1997, drift requirements are based on the strength design method to conform with newly developed seismic base shear forces. Storey drifts should be determined using the maximum inelastic response displacement, Δm, which is defined as the maximum total drift or total stroey drift caused by the design level earthquake. Displacement includes both elastic and inelastic contributions to the deformation. The UBC-1997 requires computation of seismic building drifts based on the response that occurs during the design earthquake. Displacements Δs are computed from elastic static analysis using the design seismic forces of the UBC-1997.
where
Δm
= 0.7RΔs
Δm
= maximum inelastic response displacement
Δs
= design level response displacement
R
= response modification factor
Equation 2.5
There are two main reasons to control drift. First, excessive movement in upper storeys has strong adverse psychological and physical effects on occupants. Second, it is difficult to ensure structural and architectural integrity with large amount
13 of drift. Excessive drift can be accompanied by large secondary bending moments and inelastic behaviour. Three components of drift are: 1. column and girder bending and shear 2. joint rotation 3. frame bending
Table 2.4. UBC-1997 Storey Drift Limitations Structure's Normal Period Calculated Storey Drift Using Δm T < 0.7 sec Δm ≤ 0.25h (short period structures) (2.5 % of storey height) T ≥ 0.7 sec Δm ≤ 0.2h (long period structures) (2.0 % of storey height) Source: International Conference of Building Officials (1997)
2.13. Overview of ETABS Software ETABS (Extended Three Dimensional Analysis of Building Systems) is a special purpose computer program developed specially for building systems. ETABS is a versatile and powerful program with many functions. It can share data with other software such as SAFE, SAP2000 and AutoCAD. For buildings, ETABS provides automation and specialised options to make the process of model creation, analyse and design fast and convenient. It provides tools for laying out floor framing, columns, frames and walls, in either concrete or steel, as well as technologies for generating automatically gravity and lateral loads, seismic and wind loads according to the requirements of the selected building code. It can also design steel frame, concrete frame, composite frame and so on. Moreover, ETABS provides many analysis results such as bending moments, torsional moment, shear force, axial force, support reactions and displacements of the structural members.
CHAPTER 3 PREPARATION FOR STRUCTURAL ANALYSIS AND DESIGN 3.1. Design Parameters and Assumptions for Calculation Design parameters and assumptions for analysis and design of case study reinforced concrete building are as follows: 1. Analysis property data Unit weight of concrete
= 150 pcf
Modulus of elasticity of concrete
= 2850 x103 psi
Poisson's ratio
= 0.2
Coefficient of thermal expansion
= 5.5 x 10–6
2. Design property data Compressive strength of concrete, f'c
= 2500 psi
Yield strength of reinforcement, fy
= 40000 psi
Shear strength of shear reinforcement, fys = 40000 psi
3.2. Loading Loading on tall buildings differ from loading on low-rise building in its accumulation into much larger structural forces, in the increased significance of wind loading, and in the greater importance of dynamic effects. There are three types of load considered in this structural analysis and design. They are gravity loads that include dead load and live load, wind and earthquake loads.
3.2.1. Gravity Loads Dead loads are defined as gravity loads that will be accelerated laterally with the structural frame under earthquake motion. Live loads are defined as gravity loads that do not accelerate laterally at the same rate as the structural frame when the structure undergoes earthquake motion.
15 3.2.1.1. Dead load Data for dead load which are used in structural analysis are as follows: Unit weight of concrete
= 150 pcf
4½ inches thick brick wall weight
= 50 psf
9 inches thick brick wall weight
= 100 psf
Weight of glass area
= 20 psf
Superimposed dead load
= 20 psf
Elevator weight
= 2 tons
3.2.1.2. Live load Data for live load which are used in structural analysis are as follows: Live load on residential area
= 40 psf
Live load on office area
= 50 psf
Live load on commercial area
= 100 psf
Live load on lobby area
= 100 psf
Live load on stair
= 100 psf
Live load on car parking
= 60 psf
Live load on drive way
= 250 psf
Live load on roof
= 20 psf
3.2.2. Lateral Loads There are certain loads that are almost always applied horizontally, and these must often be considered in structural analysis and design. Such loads are called lateral loads. Some kinds of lateral loads that are important for structures are wind load and earthquake load. . 3.2.2.1. Wind load In designing for wind, the UBC-97 suggested that 1. Wind shall be assumed to come from any horizontal direction. 2. No reduction in wind pressure shall be taken for the shielding effect of adjacent structures. 3. Structures sensitive to dynamic effects, such as building with a height to width ratio greater than five, structures sensitive to wind excited oscillations, such as vortex shedding or icing, and buildings over 400 feet in height, shall be, and
16 any structure may be, designed in accordance with approved national standards. The forces exerted by winds on buildings increase dramatically with the increased in building heights. For building of up to about 10 stories and of typical proportion, the design is rarely affected by wind load. Above this height, however, the increase in size of structural member to account for wind loading, incurs a cost premium that increase progressively with height. In designing for wind, three types of exposure are considered and the characteristics of these are as follows: 1. Exposure B has terrain with buildings, forest or surface irregularities, covering at least 20 percent of the ground level area extending 1 mile or more form the site. 2. Exposure C has terrain that is flat and generally open, extending ½ mile or more from the site in any full quadrant. 3. Exposure D represents the most severe exposure in areas with basic wind speed of 80 miles per hour (mph) or greater and has terrain that is flat and unobstructed facing large bodies of water over 1 mile or more in width relative to any quadrant of building site. Exposure D extends inland from the shoreline ¼ mile or 10 times the building height whichever is greater. Required data used for calculation of wind loads are: Exposure type
=B
Effective height for wind load
= 140 feet
Basic wind velocity
= 80 mph
The design wind pressure of building for any height is obtained from the formula that is considered in UBC-97. P = CeCqqsIw where,
Equation 3.1
P = design wind pressure Ce = combined height, exposure and gust factor coefficient Cq = pressure coefficient for the structure or portion of structure under consideration Iw = importance factor
17 3.2.2.2. Earthquake load Earthquake load consists of the inertial forces of the building mass that results from the shaking of its foundation by a seismic disturbance. Other severe earthquake forces may exist, such as those due to land sliding, subsidence, active faulting below the foundation, or liquefaction of the local subgrade as a result of vibration. Whereas earthquakes occur, their intensity is relative inversely proportion to their frequency of occurrence; severe earthquakes are rare, moderate ones more often, and minor ones are relatively frequent. To estimate the seismic loading two general approaches are used; which take into account the property of the structure and the past records of earthquake in the region. The first approach, termed the equivalent lateral force procedure and the second is modal analysis procedure. The later is more complex and longer than the first. In the first approach, two steps are included: 1. Determination of design base shear The UBC (1997) states that structure shall be design to resist a minimum total lateral seismic load V, which shall be assumed to act no concurrently in orthogonal directions parallel to the main axes of the structure, where V is computed from the formula, V=
CvI W RT
Equation 3.2
The total design base shear need not exceeding the following. V = 2 .5
CaI W R
Equation 3.3
The total design base shear shall not be less than the following.
V = 0.11CaIW where,
Equation 3.4
V = total design lateral force or shear as at the base W = total seismic dead load Cv = seismic response coefficient represents acceleration response at 1.0 sec. period Ca = seismic response coefficient represents effective peak acceleration at grade
18 I = important factor depends on occupancy categories According to UBC (1997), for all buildings, the value of T may be computed from the following:
T = Ct (hn ) ¾ where,
Equation 3.5
T = elastic fundamental period of vibration, in seconds, of the structures in the direction under consideration hn = height of structure in feet above base level Ct = 0.035 for steel moment resisting-frames Ct = 0.030 for reinforced concrete moment resisting-frames and eccentrically braced frames Ct = 0.020 for all other buildings
2. Distribution of total base shear UBC (1997) In deciding on an appropriate distribution for the horizontal load, the following factors are considered. (a) the effective load at a floor level is equal to the product of the mass assigned to that floor and the horizontal acceleration at that level. (b) the maximum acceleration at any level of the structure in the fundamental mode is proportional to its horizontal displacement in that mode. (c) the fundamental mode for regular structure, consisting of shear walls and frames, is approximately linear from the base. The total design base shear, V, is distributed over the height of the structure in conformance with Equations 3.6, 3.7, 3.8 and distributed according to Figure 3.1. V = Ft +
n
∑F
Equation 3.6
i
i =1
where,
Ft = concentrated force applied at the top of the structure Ft = 0.7 TV ≤ 0.25 V for
T > 0.7 sec
Ft = 0
T ≤ 0.7 sec
for
Equation 3.7
The remaining portion of the base shear is distributed over the height of the structure, including top level, n, according to the expression Fx =
(V-Ft) wx hx n
∑wh
i i
i =1
Equation 3.8
19 where,
wi, wx hi, hx
= portion of W located at or assigned to level i or x respectively = height above the base to level i or x respectively
The storey shear, Vx, at any storey, is the sum of the top force, Ft, and the forces Fx, above that storey. Vx = Ft +
n
∑F
Equation 3.9
x
i=x
where,
Vx = design storey shear in storey x Ft = top force Fx = design seismic force applied to level x
Figure 3.1. Vertical Distribution of Design Base Shear Source: Structures and Codes Institute
Data for earthquake loading are as follows: Seismic Zone
= 2A
Zone Factor, Z
= 0.15
Structural System
= Ordinary Moment-Resisting Frame
Soil Type
= SD
Importance Factor, I
=1
Response Modification Factor, R
= 3.5
Ct (Reinforced Concrete Frame)
= 0.030
Seismic Coefficient, Ca
= 0.22
Seismic Coefficient, Cv
= 0.32
20 3.2.3. Load Combinations According to ACI 318-99, the 26 design load combinations, which used in this study, are as follows: 1. COMB1
1.4 D.L
2. COMB2
1.4 D.L + 1.7 L.L
3. COMB3
1.05 D.L + 1.275 L.L + 1.275 WINX
4. COMB4
1.05 D.L + 1.275 L.L - 1.275 WINX
5. COMB5
1.05 D.L + 1.275 L.L + 1.275 WINY
6. COMB6
1.05 D.L + 1.275 L.L - 1.275 WINY
7. COMB7
0.9 D.L + 1.3 WINX
8. COMB8
0.9 D.L - 1.3 WINX
9. COMB9
0.9 D.L + 1.3 WINY
10. COMB10
0.9 D.L - 1.3 WINY
11. COMB11
1.05 D.L + 1.28 L.L + EQX
12. COMB12
1.05 D.L + 1.28 L.L - EQX
13. COMB13
1.05 D.L + 1.28 L.L + EQY
14. COMB14
1.05 D.L + 1.28 L.L - EQY
15. COMB15
0.9 D.L + 1.02 EQX
16. COMB16
0.9 D.L - 1.02 EQX
17. COMB17
0.9 D.L + 1.02 EQY
18. COMB18
0.9 D.L - 1.02 EQY
19. COMB19
1.16 D.L + 1.28 L.L + EQX
20. COMB20
1.16 D.L + 1.28 L.L - EQX
21. COMB21
1.16 D.L + 1.28 L.L + EQY
22. COMB22
1.16 D.L + 1.28 L.L - EQY
23. COMB23
0.79 D.L + 1.02 EQX
24. COMB24
0.79 D.L - 1.02 EQX
25. COMB25
0.79 D.L + 1.02 EQY
26. COMB26
0.79 D.L - 1.02 EQY
To know the performance of the ordinary moment-resisting frame, 18 unfactored load combinations were also considered. 1. UCOMB1
D.L
2. UCOMB2
D.L + L.L
21 3. UCOMB3
D.L + L.L + WINX
4. UCOMB4
D.L + L.L - WINX
5. UCOMB5
D.L + L.L + WINY
6. UCOMB6
D.L + L.L - WINY
7. UCOMB7
D.L + WINX
8. UCOMB8
D.L - WINX
9. UCOMB9
D.L + WINY
10. UCOMB10
D.L - WINY
11. UCOMB11
D.L + L.L + EQX
12. UCOMB12
D.L + L.L - EQX
13. UCOMB13
D.L + L.L + EQY
14. UCOMB14
D.L + L.L - EQY
15. UCOMB15
D.L + EQX
16. UCOMB16
D.L - EQX
17. UCOMB17
D.L + EQY
18. UCOMB18
D.L - EQY
where, D.L
= dead load
L.L
= live load
WINX
= wind load in x direction
WINY
= wind load in y direction
EQX
= earthquake load in x direction
EQY
= earthquake load in y direction
In this study, 10 load combinations (COMB1 to COMB 10) were considered for without seismic effect. With seismic effect, 26 load combinations (COMB1 to COMB 26) were considered.
3.3. Grouping of Structural Components For analysis and design purposes, members were divided into groups of similar behaviour. For columns, there were three groups; corner, end and interior in each storey. For beams, there were also three groups, edge, cantilever and interior.
22 3.4. Analysing After applying loads on structure, models were ready to analyse. Linear static analysis was performed in this study.
3.5. Analysis Output 3.5.1. Analysis Results for Columns When analysis was finished, the frame forces for each column specified in modeling mode were obtained. The column forces are axial force, bending moment in x-direction and y-direction. These results were collected to excel spreadsheets and extracted maximum values. With these results the graphs were drawn. Moreover, compare the results for the ordinary moment-resisting frame without and with seismic effects.
3.5.2. Analysis Results for Beams Same as columns, the beam forces were obtained in analysis output mode. These results were collected to excel and compared the maximum value at the critical sections of the beams.
3.5.3. Analysis Results for Storey Displacements, Storey Drifts and Storey Shear Displacements, storey drifts and storey shear were obtained from ETABS software and collected to excel and then made the comparison of results.
3.6. Concrete Frame Design In the design of concrete frame, in general, the program calculates and reports the required areas of steel for flexure and shear based on the axial force, bending moments, shear, load combination factors and other criteria.
CHAPTER 4 COMPARISON OF RESULTS 4.1. General Effects of earthquake loads on ordinary moment-resisting frame were compared using the results of analysis and design. First of all, the analysis results were compared. The items that are considered in the comparison are column and beam forces, storey displacement, storey drifts and storey shear. The axial force, bending moments for x-direction and y-direction are considered for columns. Also for beams, bending moments, shear and torsional moment are considered.
4.2. Comparison of Storey Drifts Comparison of storey drifts were considered the points at which the junction of beam and column. Among these points, the maximum drifts occurred were compared in this study. Comparison of storey drifts without seismic and with seismic are shown in Table 4.1, Figure 4.1 and Figure 4.2. Discussions on comparison are presented in section 4.8 of this study.
Table 4.1. Comparison of Storey Drifts without Earthquake and with Earthquake Drift X Height Storey Without Difference (ft.) EQX EQ (%) Roof 11 0.0924 1.2230 1224 11F 11 0.1428 1.5158 961 10F 11 0.2038 1.9708 867 9F 11 0.2281 2.0977 820 8F 11 0.2494 2.2111 787 7F 11 0.2712 2.3211 756 6F 11 0.2989 2.4637 724 5F 11 0.3212 2.5360 690 5F 11 0.3212 2.5360 690
Without EQ 0.1735 0.1896 0.2264 0.2313 0.2430 0.2626 0.2766 0.2911 0.2911
Drift Y Difference EQY (%) 0.9883 470 1.4666 673 2.0200 792 2.1482 829 2.2631 831 2.4196 821 2.5088 807 2.5980 793 2.5980 793
Drift Limit (0.02h) 2.6400 2.6400 2.6400 2.6400 2.6400 2.6400 2.6400 2.6400 2.6400
24 Table 4.1. - Continued Storey 4F 3F 2F 1F GF Base
Drift X Height (ft.) Without EQX Difference EQ (%) 11 0.3342 2.5164 653 11 0.3312 2.3807 619 14 0.4141 2.8565 590 14 0.3330 2.2393 573 10 0.0995 0.6622 566 0 0.0000 0.0000 0
Without EQ 0.3006 0.2996 0.3761 0.3011 0.0897 0.0000
Drift Y Difference EQY (%) 2.6455 780 2.6112 771 3.2536 765 2.5872 759 0.7678 756 0.0000 0
Drift Limit (0.02h) 2.6400 2.6400 3.3600 3.3600 2.4000 0.0000
Storey Drift -X Comparison
Drift X (in.)
4.0 3.0 2.0 1.0
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
Base
0.0
without EQ with EQ Drift Limit
Floor
Figure 4.1. Comparison of Storey Drift in X Direction without Earthquake and with Earthquake
Storey Drift-Y Comparison
Drift Y (in.)
4.0 3.0 2.0 1.0
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
Base
0.0
without EQ with EQ Drift Limit
Figure 4.2. Comparison of Storey Drift in Y Direction without Earthquake and with Earthquake
25 4.3. Comparison of Storey Displacements Comparison of storey displacements was considered the points at which the maximum the displacement occurred. Comparison of storey displacements without seismic and with seismic are shown in Table 4.2, Figure 4.3 and Figure 4.4. Discussions on comparison are presented in section 4.8 of this study. Table 4.2. Comparison of Storey Displacements without Earthquake and with Earthquake Storey
Height (ft.)
Roof 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF Base
11 11 11 11 11 11 11 11 11 11 14 14 10 0
Displacement, Ux Without EQ 1.3550 1.3173 1.2590 1.1758 1.0827 0.9809 0.8702 0.7482 0.6171 0.4807 0.3455 0.1765 0.0406 0.0000
EQX 11.0181 10.5189 9.9002 9.0958 8.2396 7.3371 6.3897 5.3841 4.3490 3.3219 2.3502 1.1843 0.2703 0.0000
Displacement, Uy
Difference (%) 713 699 686 674 661 648 634 620 605 591 580 571 566 0
Without EQ 1.3311 1.2603 1.1829 1.0905 0.9961 0.8969 0.7897 0.6768 0.5580 0.4353 0.3130 0.1595 0.0366 0.0000
EQY 11.5420 11.1386 10.5400 9.7155 8.8387 7.9150 6.9274 5.9034 4.8430 3.7632 2.6974 1.3694 0.3134 0.0000
Difference (%) 767 784 791 791 787 782 777 772 768 765 762 759 756 0
Storey Displacement, Ux Comparison 12.0
Ux (in.)
10.0 8.0 6.0 4.0 2.0
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
Base
0.0
without EQ with EQ
Figure 4.3. Comparison of Storey Displacement - Ux without Earthquake and with Earthquake
26
Storey Displacement,Uy Comparison 12.0
Uy (in.)
10.0 8.0 6.0 4.0 2.0 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
Base
0.0
without EQ with EQ
Floor
Figure 4.4. Comparison of Storey Displacement - Uy without Earthquake and with Earthquake
4.4. Comparison of Storey Shear Comparison of storey shear without seismic and with seismic for each storey are shown in Table 4.3, Figure 4.5 and Figure 4.6. Discussions on comparison are presented in section 4.8 of this study. Table 4.3. Comparison of Storey Shear without Earthquake and with Earthquake Vx (kips)
Vy (kips)
Storey
Without EQ
EQX
Difference (%)
Without EQ
EQY
Difference (%)
RF 11.F 10.F 9.F 8.F 7.F 6.F 5.F 4.F 3.F 2.F 1.F G.F
34 62.8 94.7 126.6 157.5 188.3 217.8 247.2 275.3 301.7 334.9 372.5 391.3
326.6 602.3 890.9 1156.9 1400.6 1622.0 1820.5 1995.2 2145.1 2269.2 2392.6 2468.2 2485.7
861 859 841 814 789 761 736 707 679 652 614 563 535
37.4 67.1 95.4 123.7 151.1 178.4 204.5 230.7 255.6 279 309.2 344 361.5
326.6 602.3 890.9 1156.9 1400.6 1622.0 1820.5 1995.2 2145.1 2269.2 2392.6 2468.2 2485.7
773 798 834 835 827 809 790 765 739 713 674 618 588
27
Storey Shear Vx Comparison 2500
Vx (kips)
2000 1500 1000
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
500
without EQ
Floor
with EQ
Figure 4.5. Comparison of Storey Shear - Vx without Earthquake and with Earthquake
Storey Shear Vy Comparison 2500
Vy (kips)
2000 1500 1000 500
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ
Figure 4.6. Comparison of Storey Shear -Vy without Earthquake and with Earthquake
4.5. Comparison of Critical Forces in Columns Comparison of critical forces in columns includes axial force and bending moments in two directions without seismic and with seismic effects for three groups of column. Discussions on comparison are presented in section 4.8 of this study.
28 4.5.1. Comparison of Axial Force for Columns Comparison axial force for column includes corner, end and interior columns.
4.5.1.1. Comparison of axial force for corner column Comparisons of axial forces for corner columns are shown in Figure 4.7 to Figure 4.9.
Axial Force Comparison for Corner Column - C70 Axial Force (kips)
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.7. Comparison of Axial Force for Corner Column, C70, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Axial Force Comparison for Corner Column - C41
Axial Force (kips)
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.8. Comparison of Axial Force for Corner Column, C41, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
29
Axial Force Comparison for Corner Column - C58
Axial Force (kips)
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.9. Comparison of Axial Force for Corner Column, C58, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.5.1.2. Comparison of axial force for end column Comparisons of axial forces for end columns are shown in Figure 4.10 to Figure 4.11.
Axial Force Comparison for End Column - C55
Axial Force (kips)
1200 1000 800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored) with EQ (unfactored)
Figure 4.10. Comparison of Axial Force for End Column, C55, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
30
Axial Force Comparison for End Column - C69
Axial Force (kips
1200 1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.11. Comparison of Axial Force for End Column, C69, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.5.1.3. Comparison of axial force for interior column Comparisons of axial forces for end columns are shown in Figure 4.12 to Figure 4.19.
Axial Force Comparison for Interior Column - C42
Axial Force (kips
1200 1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.12. Comparison of Axial Force for Interior Column, C42, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
31
Axial Force Comparison for Interior Column - C44 1200
Axial Force (kips
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored) with EQ (unfacto red)
Floor
Figure 4.13. Comparison of Axial Force for Interior Column, C44, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Axial Force Comparison for Interior Column - C45
Axial Force (kips
1500 1200 900 600 300
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.14. Comparison of Axial Force for Interior Column, C45, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
32
Axial Force Comparison for Interior Column - C46
Axial Force (kips
1600
1200
800
400
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.15. Comparison of Axial Force for Interior Column, C46, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Axial Force Comparison for Interior Column - C53
Axial Force (kips
1500 1200 900 600 300
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (facto red) with EQ (unfactored)
Figure 4.16. Comparison of Axial Force for Interior Column, C53, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
33
Axial Force Comparison for Interior Column - C54
Axial Force (kips
1500 1200 900 600 300
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.17. Comparison of Axial Force for Interior Column, C54, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Axial Force Comparison for Interior Column - C59
Axial Force (kips
1500 1200 900 600
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
300
wo EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.18. Comparison of Axial Force for Interior Column, C59, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
34 Axial Force Comparison for Interior Column - C60
Axial Force (k ips)
1500 1200 900 600 300
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.19. Comparison of Axial Force for Interior Column, C60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.5.2. Comparison of Bending Moment in X Direction for Columns Comparison bending moments for column includes corner, end and interior columns.
4.5.2.1. Comparison of bending moments in x direction for corner column Comparisons of bending moments in x direction for corner columns are shown in Figure 4.20 to Figure 4.22.
M3 Comparison for Corner Column - C70
M3 (kips-ft)
1000 800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored) with EQ (unfactored)
Figure 4.20. Comparison of Bending Moment in X Direction for Corner Column, C70, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
35
M3 Comparison for Corner Column - C41 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.21. Comparison of Bending Moment in X Direction for Corner Column, C41, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for Corner Column - C58 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.22. Comparison of Bending Moment in X Direction for Corner Column, C58, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
36 4.5.2.2. Comparison of bending moments in x direction for end column Comparisons of bending moments in x direction for end columns are shown in Figure 4.23 to Figure 4.24.
M3 Comparison for End Column - C55 1000
M3 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.23. Comparison of Bending Moment in X Direction for End Column,C55, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for End Column - C69 1000
M3 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.24. Comparison of Bending Moment in X Direction for End Column,C69, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
37 4.5.2.3. Comparison of bending moments in x direction for interior column Comparisons of bending moments in x direction for interior columns are shown in Figure 4.25 to Figure 4.32.
M3 Comparison for Interior Column - C42
M3 (kips-ft)
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.25. Comparison of Bending Moment in X Direction for Interior Column, C42, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for Interior Column - C44 1000
M3 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.26. Comparison of Bending Moment in X Direction for Interior Column, C44, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
38
M3 Comparison for Interior Column - C45 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.27. Comparison of Bending Moment in X Direction for Interior Column, C45, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for Interior Column - C46 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.28. Comparison of Bending Moment in X Direction for Interior Column, C46, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
39
M3 Comparison for Interior Column - C53 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.29. Comparison of Bending Moment in X Direction for Interior Column, C53, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for Interior Column - C54 1000
M3 (kips-ft)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red) with EQ (unfacto red)
Figure 4.30. Comparison of Bending Moment in X Direction for Interior Column, C54, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
40
M3 Comparison for Interior Column - C59 1000
M3 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.31. Comparison of Bending Moment in X Direction for Interior Column, C59, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M3 Comparison for Interior Column - C60 1000
M3 (kips-ft)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Figure 4.32. Comparison of Bending Moment in X Direction for Interior Column, C60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
41 4.5.3. Comparison of Bending Moment in Y Direction for Columns Comparison bending moments for column includes corner, end and interior columns. 4.5.3.1. Comparison of bending moments in y direction for corner column Comparisons of bending moments in y direction for corner columns are shown in Figure 4.33 to Figure 4.35.
M2 Comparison for Corner Column - C70
M2 (kips-ft)
1000 800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red) with EQ (unfactored)
Floor
Figure 4.33. Comparison of Bending Moment in Y Direction for Corner Column, C70, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M2 Comparison for Corner Column - C41
M2 (kips-ft)
1000 800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red) with EQ (unfacto red)
Figure 4.34. Comparison of Bending Moment in Y Direction for Corner Column, C41, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
42
M2 Comparison for Corner Column - C58 1000
M2 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored) with EQ (unfacto red)
Floor
Figure 4.35. Comparison of Bending Moment in Y Direction for Corner Column, C58, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.5.3.2. Comparison of bending moments in y direction for end column Comparisons of bending moments in y direction for end columns are shown in Figure 4.36 to Figure 4.37.
M2 Comparison for End Column - C55 1000
M2 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.36. Comparison of Bending Moment in Y Direction for End Column, C55, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
43
M2 Comparison for End Column - C69 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.37. Comparison of Bending Moment in Y Direction for End Column,C69, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.5.3.3. Comparison of bending moments in y direction for interior column Comparisons of bending moments in y direction for end columns are shown in Figure 4.38 to Figure 4.45.
M2 Comparison for Interior Column - C42 1000
M2 (kips-ft)
800 600 400 200 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.38. Comparison of Bending Moment in Y Direction for Interior Column, C42, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
44
M2 Comparison for Interior Column - C44 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.39. Comparison of Bending Moment in Y Direction for Interior Column, C44, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M2 Comparison for Interior Column - C45 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.40. Comparison of Bending Moment in Y Direction for Interior Column, C45, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
45
M2 Comparison for Interior Column - C46 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.41. Comparison of Bending Moment in Y Direction for Interior Column, C46, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M2 Comparison for Interior Column - C53 1000
M2 (kips-ft)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red) with EQ (unfacto red)
Figure 4.42. Comparison of Bending Moment in Y Direction for Interior Column, C53, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
46
M2 Comparison for Interior Column - C54 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.43. Comparison of Bending Moment in Y Direction for Interior Column, C54, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
M2 Comparison for Interior Column - C59 1000
M2 (kips-ft)
800 600 400 200
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
wo EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.44. Comparison of Bending Moment in Y Direction for Interior Column, C59, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
47
M2 Comparison for Interior Column - C60 1000
M2 (kips-ft)
800
600 400
200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Figure 4.45. Comparison of Bending Moment in Y Direction for Interior Column, C60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.6. Comparison of Critical Forces in Beams Comparison of critical forces in beams includes shear force, torsion and bending moments in at support and mid span without seismic and with seismic effects for three groups of beams. Discussions on comparison are presented in section 4.8 of this study.
4.6.1. Comparison of Shear Force for Beams Comparison shear force for beams includes edge, cantilever and interior beams.
4.6.1.1. Comparison of shear force for edge beams Comparisons of shear force for edge beams are shown in Figure 4.46 to Figure 4.49.
48
Shear Force Comparison for Edge Beam - B10
Shear Force (kips)
100
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.46. Comparison of Shear Force for Edge Beam - B10, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Edge Beam - B77
Shear Force (kips)
100
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.47. Comparison of Shear Force for Edge Beam – B77, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
49
Shear Force Comparison for Edge Beam - B472
Shear Force (kips)
100
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.48. Comparison of Shear Force for Edge Beam – B472, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Edge Beam - B16
Shear Force (kips)
100
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.49. Comparison of Shear Force for Edge Beam – B16, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
50 4.6.1.2. Comparison of shear force for cantilever beams Comparisons of shear force for cantilever beams are shown in Figure 4.50 to Figure 4.53.
Shear Force Comparison for Cantilever Beam - B270
Shear Force (kips)
20 15 10 5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.50. Comparison of Shear Force for Cantilever Beam B270, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Cantilever Beam - B273
Shear Force (kips)
20 15 10 5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
Figure 4.51. Comparison of Shear Force for Cantilever Beam
with EQ (factored) with EQ (unfacto red)
B273, between
without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
51
Shear Force Comparison for Cantilever Edge Beam - B169
Shear Force (kips)
20
15
10
5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.52. Comparison of Shear Force for Cantilever Edge Beam B169, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Cantilever Edge Beam - B166
Shear Force (kips)
20
15
10
5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.53. Comparison of Shear Force for Cantilever Edge Beam B166, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
52 4.6.1.3. Comparison of shear force for interior beams Comparisons of shear force for interior beams are shown in Figure 4.54 to Figure 4.62.
Shear Force Comparison for Interior Beam - B12
Shear Force (kips)
100 80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.54. Comparison of Shear Force for Interior Beam B12, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Interior Beam - B11
Shear Force (kips)
100 80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.55. Comparison of Shear Force for Interior Beam B11, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
53
Shear Force Comparison for Interior Beam - B14 100
Shear Force (kips)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Floor
Figure 4.56. Comparison of Shear Force for Interior Beam B14, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Interior Beam - B51 100
Shear Force (kips)
80 60
40 20
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Figure 4.57. Comparison of Shear Force for Interior Beam B51, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
54
Shear Force Comparison for Interior Beam - B61 100
Shear Force (kips)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.58. Comparison of Shear Force for Interior Beam B61, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Interior Beam - B97 100
Shear Force (kips)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.59. Comparison of Shear Force for Interior Beam B97, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
55
Shear Force Comparison for Interior Beam - B140 100
Shear Force (kips)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.60. Comparison of Shear Force for Interior Beam B140, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Shear Force Comparison for Interior Beam - B130 100
Shear Force (kips)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.61. Comparison of Shear Force for Interior Beam B130, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
56
Shear Force Comparison for Interior Beam - B60
Shear Force (kip s)
100 80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Floor
Figure 4.62. Comparison of Shear Force for Interior Beam B60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.6.2. Comparison of Torsion for Beams Comparison of torsion for beams includes edge, cantilever and interior beams.
4.6.2.1. Comparison of torsion for edge beams Comparisons of torsion for edge beams are shown in Figure 4.63 to Figure 4.66.
Torsion Comparison for Edge Beam - B10
Torsion (kips-ft)
100 75 50 25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
Figure 4.63. Comparison of Torsion for Edge Beam
with EQ (factored) with EQ (unfacto red)
B10, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
57
Torsion Comparison for Edge Beam - B77
75
50
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
0
1st
25
Ground
Torsion (kips-ft)
100
without EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.64. Comparison of Torsion for Edge Beam
B77, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Edge Beam - B472
Torsion (kips-ft)
100
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
Figure 4.65. Comparison of Torsion for Edge Beam
with EQ (factored) with EQ (unfacto red)
B472, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
58
Torsion Comparison for Edge Beam - B16
Torsion (kips-ft)
100 75 50 25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.66. Comparison of Torsion for Edge Beam
B472, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.6.2.2. Comparison of torsion for cantilever beams Comparisons of torsion for cantilever beams are shown in Figure 4.67 to Figure 4.70.
Torsion Comparison for Cantilever Beam - B270
Torsion (kips-ft
50 40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.67. Comparison of Torsion for Cantilever Beam B270, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
59
Torsion Comparison for Cantilever Beam - B273 50
Torsion (kips-ft
40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.68. Comparison of Torsion for Cantilever Beam B273, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Cantilever Edge Beam - B169 50
Torsion (kips-ft
40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ
Floor
Figure 4.69. Comparison of Torsion for Cantilever Edge Beam
with EQ (factored) with EQ (unfactored)
B169, between
without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
60 Torsion Comparison for Cantilever Edge Beam - B166
Torsion (kips-ft
50 40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.70. Comparison of Torsion for Cantilever Edge Beam
B166, between
without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.6.2.3. Comparison of torsion for interior beams Comparisons of torsion for interior beams are shown in Figure 4.71 to Figure 4.79.
Torsion Comparison for Interior Beam - B12
Torsion (kips-ft)
100 80 60 40 20
Floor
Figure 4.71. Comparison of Torsion for Interior Beam
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
B12, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
61
Torsion Comparison for Interior Beam - B11 100
Torsion (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.72. Comparison of Torsion for Interior Beam
B11, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Interior Beam - B14 100
Torsion (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
Figure 4.73. Comparison of Torsion for Interior Beam
with EQ (factored) with EQ (unfacto red)
B14, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
62
Torsion Comparison for Interior Beam - B51 100
Torsion (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.74. Comparison of Torsion for Interior Beam
B51, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Interior Beam - B61 100
Torsion (kips-ft)
80 60 40
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
20
without EQ with EQ (facto red)
Floor
Figure 4.75. Comparison of Torsion for Interior Beam
with EQ (unfacto red)
B61, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
63
Torsion Comparison for Interior Beam - B97 100
Torsion (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red) with EQ (unfactored)
Floor
Figure 4.76. Comparison of Torsion for Interior Beam
B97, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Interior Beam - B140 100
Torsion (kips-ft)
80 60 40 20
Floor
Figure 4.77. Comparison of Torsion for Interior Beam
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfactored)
B140, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
64
Torsion Comparison for Interior Beam - B130 100
Torsion (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.78. Comparison of Torsion for Interior Beam
B130, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Torsion Comparison for Interior Beam - B60 100
Torsion (kips-ft)
80 60 40 20
Floor
Figure 4.79. Comparison of Torsion for Interior Beam
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfactored)
B60, between without
Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
65 4.6.3. Comparison of Bending Moment at Support for Beams Comparison Bending Moment at Support for beams includes edge, cantilever and interior beams. 4.6.3.1. Comparison of bending moment at support for edge beams Comparisons of bending moment at support for edge beams are shown in Figure 4.80 to Figure 4.83.
Bending Moment at Support Comparison for Edge Beam - B10 300
M3 (kips-ft)
250 200 150 100 50 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.80. Comparison of Bending Moment at Support for Edge Beam B10, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Edge Beam - B77 300
M3 (kips-ft)
250 200 150 100 50 Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.81. Comparison of Bending Moment at Support for Edge Beam
B77,
between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
66
Bending Moment at Support Comparison for Edge Beam - B472 300
M3 (kips-ft)
250 200 150 100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
50
without EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.82. Comparison of Bending Moment at Support for Edge Beam B472, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Edge Beam - B16 300
M3 (kips-ft)
250 200 150 100 50
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.83. Comparison of Bending Moment at Support for Edge Beam
B16,
between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
67 4.6.3.2. Comparison of bending moment at support for cantilever beams Comparisons of bending moment at support for cantilever beams are shown in Figure 4.84 to Figure 4.87.
Bending Moment at Support Comparison for Cantilever Beam - B270 50
M3 (kips-ft)
40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.84. Comparison of Bending Moment at Support for Cantilever Beam B270, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Cantilever Beam - B273 50
M3 (kips-ft)
40 30 20 10
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.85. Comparison of Bending Moment at Support for Cantilever Beam B273, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
68
Bending Moment at Support Comparison for Cantilever Edge Beam B169 50
M3 (kips-ft)
40 30 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
10
witho ut EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.86. Comparison of Bending Moment at Support for Cantilever Edge Beam B169, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Cantilever Edge Beam B166 50
M3 (kips-ft)
40 30 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
10
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.87. Comparison of Bending Moment at Support for Cantilever Edge Beam B166, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
69 4.6.3.3. Comparison of bending moment at support for interior beams Comparisons of bending moment at support for interior beams are shown in Figure 4.88 to Figure 4.96.
Bending Moment at Support Comparison for Interior Beam - B12 500
M3 (kips-ft)
400 300 200 100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.88. Comparison of Bending Moment at Support for Interior Beam B12, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Interior Beam - B11 500
M3 (kips-ft)
400 300 200 100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.89. Comparison of Bending Moment at Support for Interior Beam B11, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
70
Bending Moment at Support Comparison for Interior Beam - B14 500
M3 (kips-ft)
400
300
200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.90. Comparison of Bending Moment at Support for Interior Beam B14, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Interior Beam - B51 500
M3 (kips-ft)
400
300 200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.91. Comparison of Bending Moment at Support for Interior Beam B51, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
71
Bending Moment at Support Comparison for Interior Beam - B61 500
M3 (kips-ft)
400
300
200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (facto red)
Floor
with EQ (unfacto red)
Figure 4.92. Comparison of Bending Moment at Support for Interior Beam B61, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Interior Beam - B97 500
M3 (kips-ft)
400
300
200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.93. Comparison of Bending Moment at Support for Interior Beam B97, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
72
Bending Moment at Support Comparison for Interior Beam - B140 500
M3 (kips-ft)
400
300
200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.94. Comparison of Bending Moment at Support for Interior Beam B140, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Support Comparison for Interior Beam - B130 500
M3 (kips-ft)
400
300
200
100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.95. Comparison of Bending Moment at Support for Interior Beam B130, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
73
Bending Moment at Support Comparison for Interior Beam - B60 500
M3 (kips-ft)
400 300 200 100
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.96. Comparison of Bending Moment at Support for Interior Beam B60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load) 4.6.4. Comparison of Bending Moment at Midspan for Beams Comparison Bending Moment at midspan for beams includes edge, cantilever and interior beams.
4.6.4.1. Comparison of bending moment at midspan for edge beams Comparisons of bending moment at midspan for edge beams are shown in Figure 4.97 to Figure 4.100.
Bending Moment at Midspan Comparison for Edge Beam - B10
M3 (kips-ft)
100 75 50 25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.97. Comparison of Bending Moment at Midspan for Edge Beam B10, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
74
Bending Moment at Midspan Comparison for Edge Beam - B77 100
M3 (kips-ft)
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfactored)
Figure 4.98. Comparison of Bending Moment at Midspan for Edge Beam B77, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Midspan Comparison for Edge Beam - B472 100
M3 (kips-ft)
75
50
25
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfactored)
Figure 4.99. Comparison of Bending Moment at Midspan for Edge Beam B472, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
75
Bending Moment at Midspan Comparison for Edge Beam - B16 100
M3 (kips-ft)
75
50
25
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored) with EQ (unfacto red)
Floor
Figure 4.100. Comparison of Bending Moment at Midspan for Edge Beam B16, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.6.4.2. Comparison of bending moment at midspan for cantilever edge beams Comparisons of bending moment at midspan for cantilever edge beams are shown in Figure 4.101 to Figure 4.102.
Bending Moment at Midspan Comparison for Cantilever Edge Beam B169
M3 (kips-ft)
20 15 10 5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ
Floor
with EQ (facto red) with EQ (unfacto red)
Figure 4.101. Comparison of Bending Moment at Midspan for Cantilever Edge Beam B169, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
76
Bending Moment at Midspan Comparison for Cantilever Edge Beam B166
M3 (kips-ft)
20 15 10 5
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.102. Comparison of Bending Moment at Midspan for Cantilever Edge Beam B166, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
4.6.4.3. Comparison of bending moment at midspan for interior beams Comparisons of bending moment at midspan for interior beams are shown in Figure 4.103 to Figure 4.111.
Bending Moment at Midspan Comparison for Interior Beam - B12 100
M3 (kips-ft)
80 60 40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.103. Comparison of Bending Moment at Midspan for Interior Beam B12, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
77
Bending Moment at Midspan Comparison for Interior Beam - B11 100
M3 (kips-ft)
80
60
40
20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.104. Comparison of Bending Moment at Midspan for Interior Beam B11, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Midspan Comparison for Interior Beam - B14 100
M3 (kips-ft)
80
60
40
20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.105. Comparison of Bending Moment at Midspan for Interior Beam B14, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
78
Bending Moment at Midspan Comparison for Interior Beam - B51 100
M3 (kips-ft)
80
60
40
20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ with EQ (factored)
Floor
with EQ (unfacto red)
Figure 4.106. Comparison of Bending Moment at Midspan for Interior Beam B51, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Midspan Comparison for Interior Beam - B61 100
M3 (kips-ft)
80
60
40
20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (facto red) with EQ (unfactored)
Figure 4.107. Comparison of Bending Moment at Midspan for Interior Beam B61, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
79
Bending Moment at Midspan Comparison for Interior Beam - B97 100
M3 (kips-ft)
80
60
40
20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
witho ut EQ with EQ (facto red) with EQ (unfactored)
Floor
Figure 4.108. Comparison of Bending Moment at Midspan for Interior Beam B97, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Midspan Comparison for Interior Beam - B140 100
M3 (kips-ft)
80 60 40
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
20
without EQ
Floor
with EQ (factored) with EQ (unfactored)
Figure 4.109. Comparison of Bending Moment at Midspan for Interior Beam B140, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
80 Bending Moment at Midspan Comparison for Interior Beam - B130 100
M3 (kips-ft)
80 60 40
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
0
Ground
20
without EQ with EQ (facto red)
Floor
with EQ (unfactored)
Figure 4.110. Comparison of Bending Moment at Midspan for Interior Beam B130, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
Bending Moment at Midspan Comparison for Interior Beam - B60 100
M3 (kips-ft)
80 60
40 20
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
without EQ
Floor
with EQ (factored) with EQ (unfacto red)
Figure 4.111. Comparison of Bending Moment at Midspan for Interior Beam B60, between without Earthquake, with Earthquake (factored load) and with Earthquake (unfactored load)
81 4.7. Comparison of Critical Forces for One Panel Continuous Beam-Column Frame Comparisons of critical forces for columns and beams, which are continuous frame in choosing one panel, are shown in the following Figure 4.112 to Figure 4.118 and Table 4.4 to Table 4.10. Discussions on comparison are presented in section 4.8 of this study.
4.7.1. Comparison of Critical Force Differences for Column Comparison of critical force differences for columns from one panel continuous beam-column frame are shown in Figure 4.112 to Figure 4.114.
Compariosn of Axial Force Differences for Columns 50
Differences (%)
40 30 20 10
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
C54
C41
C55
C42
Figure 4.112. Comparison of Axial Force Differences for Columns from One Panel Continuous Beam-Column Frame
Compariosn of Bending Moment in X Direction Differences for Columns 1000
Differences (%)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
C54
C41
C55
C42
Figure 4.113. Comparison of Bending Moment in X Direction Differences for Columns from One Panel Continuous Beam-Column Frame
82
Compariosn of Bending Moment in Y Direction Differences for Columns 1000
Differences (%)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
C54
C41
C55
C42
Figure 4.114. Comparison of Bending Moment in Y Direction Differences for Columns from One Panel Continuous Beam-Column Frame
4.7.2. Comparison of Critical Force Differences for Beams Comparison of critical force differences for beams from one panel continuous beam-column frame are shown in Figure 4.115 to Figure 4.118.
Comparison of Torsion Differences for Beams 1200 1000
Differences (%)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
B11
B60
B51
B10
Figure 4.115. Comparison of Shear Force Differences for Beams from One Panel Continuous Beam-Column Frame
83
Comparison of Torsion Differences for Beams 1200 1000
Differences (%)
800 600 400 200
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
B11
B60
B51
B10
Figure 4.116. Comparison of Torsion Differences for Beams from One Panel Continuous Beam-Column Frame
Comparison of Bending Moment at Support Differences for Beams 500
Differences (%)
400 300 200 100
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
B11
B60
B51
B10
Figure 4.117. Comparison of Bending Moment at Support Differences for Beams from One Panel Continuous Beam-Column Frame
84
Comparison of Bending Moment at Midspan Differences for Beams 500 400
Differences (%)
300 200 100
Floor
Roof
11th
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
Ground
0
B11
B60
B51
B10
Figure 4.118. Comparison of Bending Moment at Midspan Differences for Beams from One Panel Continuous Beam-Column Frame
85 Table 4.4.
86 Table 4.5.
87 Table 4.6.
88 Table 4.7.
89 Table 4.8.
90 Table 4.9.
91 Table 4.10.
92 4.8. Discussions on Comparisons The comparisons of responses and critical forces of structure are shown in above articles by graphically without and with seismic effects for factored and unfactored load conditions. Detailed discussions are described in below with referred to those above comparison graphs.
4.8.1. Comparison of Storey Drifts It is inevitable that tall buildings subjected to earthquake are more or less prone to sway which is technically defined as drift. This drift tends to create failure of member and deteriorate comfort of the occupants. From the comparison of results, storey drifts due to without seismic effect is increased to minimum of 470 percent and maximum of 1224 percent when considered with seismic effect. Although the storey drifts in the case study building are increased due to earthquake loads, most of them are still below the allowable limits. But only one floor, 4th floor (52 feet above ground level), exceeds the allowable limit about 0.21 percent.
4.8.2. Comparison of Storey Displacements From Table 4.2, Figure 4.3 and Figure 4.4, comparative study for the differences of storey displacements is as follow: Storey displacement due to without seismic force is increased to minimum of 566 percent and maximum of 791 percent when considered with seismic effects.
4.8.3. Comparison of Storey Shear From Table 4.3, Figure 4.5 and Figure 4.6, the storey shear due to without seismic force is increased to minimum of 535 percent and maximum of 861 percent when considered with seismic effects.
4.8.4. Comparison of Columns Comparison of columns includes axial force, bending moment in x and y directions without seismic and with seismic effects for three groups of column.
4.8.4.1. Axial force For corner columns, axial forces due to seismic effect under zone 2A are
93 increased to minimum one percent and maximum 28 percent for factored load conditions. Axial force increments are high at the middle floors. For end columns, axial force due to seismic forces is minimum one percent and maximum eight percent higher than that of without seismic forces for factored load conditions. For unfactored load conditions, axial force is not increased in these columns. For interior columns, axial forces without and with seismic effects are not different for factored load conditions.
4.8.4.2. Bending moment in x direction For corner columns, bending moment in x direction without seismic effects is increased to minimum nine percent and maximum 671 percent when considered with seismic effects under zone 2A for factored load conditions. For these columns, increment is high at the bottom storeys. For end columns, bending moment in x direction without seismic effects is increased to minimum 32 percent and maximum 603 percent when considered with seismic effects under zone 2A for factored load conditions. For interior columns, bending moment in x direction without seismic effects is increased to minimum 153 percent and maximum 565 percent when considered with seismic effects under zone 2A for factored load conditions. From the comparison graphs, the shapes of moment increment curves are similar for both factored and unfactored load conditions.
4.8.4.3. Bending moment in y direction For corner columns, bending moment in y direction without seismic effects is increased to minimum 40 percent and maximum 574 percent when considered with seismic effects under zone 2A for factored load conditions. For these columns, increment is high at the bottom storeys. For end columns, bending moment in y direction without seismic effects is increased to minimum 134 percent and maximum 627 percent when considered with seismic effects under zone 2A for factored load conditions. For interior columns, bending moment in y direction without seismic effects is increased to minimum 132 percent and maximum 619 percent when considered with seismic effects under zone 2A for factored load conditions.
94 From the comparison graphs, the shapes of moment increment curves are similar for both factored and unfactored load conditions.
4.8.5. Comparison of Beams Comparison of beams includes shear force, torsional moment, bending at support and midspan without seismic and with seismic effects for three groups of beams. . 4.8.5.1. Shear force For edge beams, shear force without seismic effects is increased to minimum one percent and maximum 403 percent when considered the seismic effects for factored load conditions. For these beams, increased percentage is high at the middle storeys and low at the top storeys. For cantilever beams, shear force without seismic effects is increased to minimum one percent and maximum seven percent when considered the seismic effects. Also for cantilever edge beams, shear force increased to minimum three percent and maximum 69 percent when considered the seismic effects. For interior beams, shear force without seismic effects is increased to minimum one percent and maximum 226 percent when considered the seismic effects for factored load conditions. For these beams, shear increment percent is high at the middle storeys.
4.8.5.2. Torsion For edge beams, torsion without seismic effects is increased to minimum 14 percent and maximum 445 percent when considered the seismic effects under zone 2A for factored load conditions. For cantilever beams, torsion without seismic effects is increased to minimum 74 percent and maximum 492 percent when considered the seismic effects. For these beams, torsion increment is high at the middle storeys. From the comparison graph, torsion curve is gradually decreased to top storeys. Also for cantilever edge beams, torsion increased to minimum 18 percent and maximum 375 percent when considered the seismic effects. For these beams, increment percentage is high, but the magnitude of torsion without and with seismic are not so large. For interior beams, torsion without seismic effects is increased to minimum 16
95 percent and maximum 686 percent when considered the seismic effects for factored load conditions. For these beams, torsion increment percentage is high at the middle storeys. From the comparison graph, torsion with seismic effects for unfactored load conditions curve lied close to the factored load conditions for all of the beams mentioned above.
4.8.5.3. Bending moment at support For edge beams, negative bending moment at support without seismic effects is increased to minimum 25 percent at the top storeys and maximum 509 percent at the middle storeys when considered the seismic effects under zone 2A for factored load conditions. Positive bending moment at support without seismic effects is increased mostly at the middle storeys and increased percentage is high in these storeys. For cantilever beams, negative bending moments at support without seismic effects are not different when considered the seismic effects for factored load conditions. Also for cantilever edge beams, negative bending moment at support is increased to minimum 22 percent and maximum 245 percent when considered the seismic effects. For interior beams, negative bending moment at support without seismic effects is increased to minimum 17 percent and maximum 365 percent when considered the seismic effects under zone 2A for factored load conditions. From comparison graph, negative bending moment at support increment percentage is high at the middle storeys. Positive bending moment at support without seismic effects is increased mostly at the middle storeys and percent increment is high in these storeys.
4.8.5.4. Bending moment at midspan For edge beams, positive bending moment at midspan without seismic effects is not different when considered the seismic effects under zone 2A for factored load conditions except for ground floor beams. For cantilever edge beams, positive bending moments at midspan without seismic effects is increased to minimum two percent and maximum 30 percent when considered the seismic effects under zone 2A for factored load conditions. For interior beams, positive bending moments at midspan without and with
96 seismic effects under zone 2A are nor different for factored load conditions except for ground floor beams. For ground floor beams, bending moment at midspan increased to minimum 177 percent and maximum 350 percent when considered seismic for factored load conditions.
4.8.6. Comparison of Critical Forces for One Panel Continuous Beam-Column Frame Comparison of critical forces for four columns and four beams in one panel are important for determining force increments and changing deformation when subjected to moderate seismic forces. Axial forces of column are found to increase to maximum 22 percent at the corner column and also increased to maximum five percent in end column. But axial forces of interior column are not increased in this one panel continuous beam-column frame. Bending moments in x direction of columns are increased to minimum 174 percent and maximum 485 percent. Bending moment in y-direction of interior and end columns are increased to minimum 464 percent and maximum 663 percent at the lower and middle storeys. Also bending moment in y-direction of corner column increased to minimum 210 percent and maximum 559 percent at the lower and middle stories. Bending moment at support of beams increased to maximum 460 percent at the middle stories. Bending moments at midspan of beams are not increased except at the ground floor beams which increased to maximum 270 percent. Torsion had increased to maximum 441 percent at the middle stories. Shear force also increased to maximum 200 percent except the ground floor beams. At ground floor beam, shear force increased about 250 percent.
4.8.7. Summarised Discussions on Comparisons From the comparative study for the existing building which was designed without consideration for seismic effects and then subjected to moderate seismic forces in zone 2A, it was found that the followings: 1. Force increments in the columns are greater than that of in the beams. 2. The most critical force for column is bending moment in this study. 3. The most critical force for beams is bending moment in this study. 4.
Most critical forces are found at middle storeys for beams and bottom storeys for columns.
97 5. Storey drift increments are large but most of the drifts are within the allowable limit and only one floor exceeds the allowable limit about 0.21 percent. It is found that the force and force increments are large mostly at the bottom and middle storeys. Thus initial damage will be begun at the middle and bottom storeys.
Table 4.4. Comparison of Critical Force for Columns (One Panel) – Axial Force (kips) Storey
Interior Column, C54 Corner Column, C41 End Column, C55 Without Without Without Diff: With EQ Diff: (%) With EQ Diff: (%) With EQ EQ EQ EQ (%)
Interior Column, C42 Without With EQ Diff: (%) EQ
Roof
90.8
90.6
0
32.9
33.4
2
60.8
59.7
-2
55.5
55.5
0
11th Floor
197.7
197.4
0
97.8
98.5
1
149.5
148
-1
141.5
141.6
0
10th Floor
302.9
302.6
0
160.6
161.1
0
233.8
232.6
-1
226.1
226.1
0
9th Floor
409.3
409
0
224.3
228.1
2
317.5
316.4
0
310.9
310.9
0
8th Floor
517
516.6
0
287.7
303.4
5
402.4
401.4
0
396.5
396.5
0
7th Floor
625.9
625.6
0
352
384.1
9
488.8
487.9
0
482.2
482.1
0
6th Floor
736.4
736
0
417.6
470.8
13
576.6
578.8
0
568.9
568.8
0
5th Floor
848.3
848
0
482.9
561.5
16
666.5
680.2
2
655.8
655.7
0
4th Floor
961.7
961.4
0
549.5
656.9
20
756.4
782.6
3
744.9
744.8
0
3rd Floor
1074.6
1074.3
0
617.5
753.6
22
848.6
887.7
5
835.9
835.8
0
2nd Floor
1193.5
1193.1
0
709.5
828.9
17
949.3
975.7
3
938.8
938.8
0
1st Floor
1304.3
1303.9
0
811.4
909.5
12
1047.9
1054.3
1
1033.1
1033.1
0
G Floor
1327.4
1327.1
0
830.1
925.6
12
1067.5
1072.1
0
1053
1052.9
0
Table 4.5. Comparison of Critical Force for Columns (One Panel) – Bending Moment in X Direction (kips-ft) Storey
Interior Column, C54 Corner Column, C41 End Column, C55 Without Without Without Diff: With EQ Diff: (%) With EQ Diff: (%) With EQ EQ EQ EQ (%)
Interior Column, C42 Without With EQ Diff: (%) EQ
Roof
13.8
53.9
291
23
31.7
38
39.4
51.9
32
17.7
54.2
206
11th Floor
23.5
98.1
317
37.7
68.9
83
32.1
74.3
131
32.4
102.2
215
10th Floor
32.1
142.2
343
30
79.0
163
38
105.4
177
32.3
120.2
272
9th Floor
39.2
186.0
374
39.4
108.0
174
34.2
103.3
202
42.9
157.9
268
8th Floor
43.5
207.1
376
35.8
108.6
203
38.3
118.4
209
53.2
208.8
292
7th Floor
50.1
247.3
394
39.5
121.8
208
41.9
138.3
230
59
232.3
294
6th Floor
54.7
291.7
433
45
138.6
208
43.8
147.8
237
69
272.8
295
5th Floor
60.8
291.7
380
43.8
146.3
234
50
174.9
250
68
279.4
311
4th Floor
70.2
345.5
392
42.5
146.8
245
44.8
157.7
252
73.3
311.4
325
3rd Floor
71.7
340.4
375
84
282.8
237
82.8
296.0
257
94.2
350.0
272
2nd Floor
74.6
390.5
423
69.2
287.8
316
75.8
333.3
340
98.4
366.7
273
1st Floor
97.7
564.9
478
71.2
376.9
429
82.7
454.3
449
90.9
470.5
418
G Floor
138.6
808.2
483
87.9
496.9
465
112.6
627.4
457
111.9
654.3
485
Table 4.6. Comparison of Critical Force for Columns (One Panel) – Bending Moment in Y Direction (kips-ft) Storey
Interior Column, C54 Corner Column, C41 End Column, C55 Without Without Without Diff: With EQ Diff: (%) With EQ Diff: (%) With EQ EQ EQ EQ (%)
Interior Column, C42 Without With EQ Diff: (%) EQ
Roof
6.6
54.6
727
17.9
26.3
47
12
48.5
304
10.7
50.8
375
11th Floor
9.1
81.1
791
28.4
58.0
104
16.3
72.3
344
11.9
78.6
561
10th Floor
18.3
141.3
672
23.6
61.2
159
25.2
139.6
454
15.7
91.5
483
9th Floor
25.8
177.3
587
32.7
101.5
210
24.7
147.3
496
23.2
135.3
483
8th Floor
30.9
212.8
589
30.3
100.0
230
29.5
192.7
553
29.3
170.8
483
7th Floor
33.9
231.1
582
34.9
120.7
246
34.7
225.1
549
33.6
195.3
481
6th Floor
38.8
296.0
663
41.6
149.9
260
37
240.4
550
42.1
246.0
484
5th Floor
48.2
296.0
514
39.9
151.0
278
48.5
313.0
545
41.9
242.6
479
4th Floor
54.3
354.4
553
47.6
199.2
318
57.3
364.0
535
49.2
272.1
453
3rd Floor
52.1
318.5
511
60.8
336.6
454
57.7
400.8
595
50.7
303.1
498
2nd Floor
76
428.3
464
40.4
266.1
559
44.5
318.2
615
58.6
332.3
467
1st Floor
101.6
577.9
469
68.1
340.9
401
80.6
401.9
399
84
478.7
470
G Floor
148.4
839.6
466
103.5
456.7
341
137.4
602.3
338
114
647.6
468
Table 4.7. Comparison of Critical Force for Beams (One Panel) – Shear Force (kips) Interior Beam, B11 Storey
Interior Beam, B60
Without Diff: With EQ EQ (%)
Without EQ
Interior Beam, B51
With EQ Diff: (%)
Without EQ
Edge Beam, B10
With EQ Diff: (%)
Without EQ
With EQ Diff: (%)
Roof
22.5
22.4
0
11.6
12.7
9
7.9
10.2
29
10.3
10.4
1
11th Floor
30.2
31.9
6
20.3
26.6
31
17.3
22.6
31
24.5
26.4
8
10th Floor
31.3
36.8
18
18.4
27.9
52
14.9
25.3
70
24.9
30.2
21
9th Floor
31
41
32
18.3
32.4
77
14.9
29.8
100
24.7
33.3
35
8th Floor
30.9
44.3
43
18.3
37.7
106
14.9
33.2
123
24.6
37
50
7th Floor
31
47.8
54
18.1
41.6
130
14.8
37.7
155
24.6
39.9
62
6th Floor
31
50.9
64
18
45.2
151
15.3
41.9
174
24.4
42.4
74
5th Floor
31
53
71
18.3
47.8
161
15.8
46
191
24.5
44.4
81
4th Floor
31
54.3
75
18.9
49.2
160
16.3
48.9
200
24.4
45.9
88
3rd Floor
29.9
54.6
83
19.2
49.3
157
16.3
48.7
199
24.3
46.8
93
2nd Floor
30.8
52.6
71
19.1
47.9
151
16.2
42.8
164
30.1
52.4
74
1st Floor
25.2
44
75
16.9
42.5
151
16.8
37.4
123
26.1
44.3
70
G Floor
4.5
16
256
4.5
19.2
327
4.7
16.8
257
4.6
16.2
252
Table 4.8. Comparison of Critical Force for Beams (One Panel) – Torsion (kips-ft) Storey
Interior Beam, B11 Without Diff: With EQ EQ (%)
Interior Beam, B60 Without With EQ Diff: (%) EQ
Interior Beam, B51 Edge Beam, B10 Without Without With EQ Diff: (%) With EQ Diff: (%) EQ EQ
Roof
7.2
11.2
56
1.2
2.5
108
1.7
3.1
82
8.4
9.6
14
11th Floor
2.9
11.2
286
7.7
13.5
75
4
7.1
78
12.9
18.3
42
10th Floor
6.7
23.5
251
6.5
16.1
148
3.8
9.5
150
12.6
23.6
87
9th Floor
6.8
29.5
334
6.8
21.1
210
3.7
10
170
12.5
29
132
8th Floor
7.2
35.9
399
8
24.3
204
3.9
11.3
190
12.7
32.8
158
7th Floor
8.3
43.6
425
9
28.7
219
4.4
13.4
205
13.4
37.7
181
6th Floor
9.4
50.1
433
9.8
32.2
229
4.5
14.5
222
14.2
42
196
5th Floor
10.5
56.8
441
10.3
34.5
235
4.8
15.3
219
14.7
44.5
203
4th Floor
11.3
61.1
441
10.9
36.5
235
4.8
15.3
219
15.3
46.1
201
3rd Floor
11.5
60.2
423
11.4
37.8
232
4.8
15.3
219
15.8
47
197
2nd Floor
11.3
53
369
11
36.3
230
7.2
26.9
274
11.9
50.5
324
1st Floor
6.7
37.6
461
5
23.5
370
5.2
24.1
363
7.2
37
414
G Floor
0.2
1.3
550
0.1
0.2
100
0
0.1
0.1
1.3
1200
Table 4.9. Comparison of Critical Force for Beams (One Panel) – Bending Moment at Support (kips-ft) Interior Beam, B11 Storey
Interior Beam, B60
Without Diff: With EQ EQ (%)
Without EQ
Interior Beam, B51
With EQ Diff: (%)
Without EQ
Edge Beam, B10
With EQ Diff: (%)
Without EQ
With EQ Diff: (%)
Roof
86.6
86.2
0
28.1
42.6
52
23.9
33.0
38
32.4
47.2
46
11th Floor
94
129.2
37
52.6
112.1
113
49.6
85.2
72
69.7
117.9
69
10th Floor
99.8
184.5
85
45.9
120.5
163
51.8
114.0
120
76.6
156.8
105
9th Floor
99.5
208.7
110
48.1
146.2
204
54.6
142.1
160
75.7
183.9
143
8th Floor
98.2
229.2
133
51.7
172.6
234
55.1
163.0
196
78.3
208.3
166
7th Floor
99.7
255.1
156
54.2
194.1
258
52.9
181.1
242
81
228.1
182
6th Floor
102.9
274.0
166
56.5
212
275
50.1
203.6
306
85.1
248.4
192
5th Floor
104.9
285.9
173
59.2
225.3
281
46.5
222.4
378
88.4
264.0
199
4th Floor
107.1
293.7
174
61
230.3
278
44.3
236.2
433
89.8
273.0
204
3rd Floor
108
295.8
174
61.8
229.8
272
41.7
233.7
460
91.5
278.6
204
2nd Floor
102.9
280.8
173
62
225
263
39.7
196.2
394
99.2
272.8
175
1st Floor
86.6
244.1
182
54.9
197.6
260
36.8
171.2
365
90.1
244.8
172
G Floor
27
127.1
371
22.3
115.8
419
22.6
101.7
350
27.6
130.9
374
Table 4.10. Comparison of Critical Force for Beams (One Panel) – Bending Moment at Midspan (kips-ft) Interior Beam, B11
Storey
Interior Beam, B228 Without Without EQ With EQ Diff: (%) With EQ Diff: (%) EQ
Interior Beam, B224 Edge Beam, B10 Without Without With EQ Diff: (%) With EQ Diff: (%) EQ EQ
Roof
50.8
50.3
-1
21.9
21.9
0
19.9
20.1
1
22.8
22.8
0
11th Floor
78.4
78.1
0
38.3
38.3
0
32.5
32.5
0
67.4
67.4
0
10th Floor
77.5
77.5
0
35.1
35.1
0
28.6
28.6
0
65.2
65.2
0
9th Floor
75.9
75.9
0
34.9
34.9
0
28
29.7
6
63.5
63.5
0
8th Floor
74.6
74.6
0
34.6
34.6
0
27.3
28.9
6
61.2
61.2
0
7th Floor
73.4
73.4
0
34.4
34.4
0
26.7
26.7
0
59.8
59.8
0
6th Floor
72.7
72.7
0
34.2
34.2
0
25.9
26.1
1
58
58.0
0
5th Floor
72.3
72.3
0
34.2
34.2
0
25.7
25.7
0
57.5
57.5
0
4th Floor
71.9
71.9
0
34.2
34.2
0
25.5
25.5
0
57.1
57.1
0
3rd Floor
71.6
71.6
0
34.2
34.2
0
25.2
25.9
3
56
56.0
0
2nd Floor
71.4
71.4
0
33.5
33.5
0
25.3
25.3
0
69.4
69.4
0
1st Floor
60
60.0
0
31.3
31.3
0
31.3
31.3
0
62.8
62.8
0
G Floor
6.1
16.9
177
4.7
17.4
270
4.9
15.6
218
6
18.1
202
CHAPTER 5 DISCUSSIONS, CONCLUSIONS AND RECOMMENDATIONS
5.1. Discussions and Conclusions In this study of performance of ordinary moment-resisting frame in seismic zone 2A, structural analysis and design are carried out by using ETABS software. In making structural analysis, it is necessary to know at the outset the cross-sectional dimensions of the members. At first, preliminary member sizes are assumed and then analysed as ordinary moment-resisting frame with gravity and wind loads. If necessary, the assumed cross-sections are modified and repeated the analysis until getting the adequate member sizes. Finally, the ordinary moment-resisting frame was reanalysed with seismic loads under UBC zone 2A for both factored and unfactored load conditions. But the ordinary moment-resisting frame was not redesigned. Storey drift increments are large for both cases but most of the drifts are within the allowable limit and only one floor exceeds the allowable limit about 0.21 percent. For columns, axial force increases largely at the corner columns, but there is only a little increase in end columns and there is not increase at the interior columns. For beams, increase percent for torsion is high but the magnitudes are not so large. Torsional moment increases largely in cantilever beams but shear force is not increase in those beams. Secondly, shear force increase percent is high at the ground floor beams. Positive bending moment at midspan for beams is not increase in beams but that is only increases in ground floor beams. From the comparative study for Ordinary Moment-Resisting Frame without and with seismic effects, the most critical force for columns is bending moment. Also for beams, the most critical force is bending moment in interior beams. Between these of column and beam, more critical force is found in column at the bottom storeys. It is found that the force and force increments are large mostly at the middle and bottom storeys. Thus from this study, it may be stated that damage will be initiated at those
99 storeys. Although percent increments for critical forces are large, the magnitudes of forces are negligible for some cases. Moreover, the problem may become the less serious owing to selection practice of to be constructable design. Only linear elastic responses and equivalent static linear analysis are considered in this study. If further study will be conducted by using nonlinear elastic analysis, it may get more suitable solutions.
5.2. Recommendations On the basis of this study, the following recommendations are done. 1. Further research should be conducted for better understanding about the behaviour of the building (ordinary moment-resisting frame) under higher and lower earthquake intensities. 2. Further study should be conducted by using nonlinear elastic analysis and P-delta effect using the cracked transformed sections. 3. Further study should be conducted by using pushover analysis to know the failure sequence. 4. Series of research should be conducted for resulting the complete picture of the problem.
REFERENCE LIST
Fanella, D.A., Mushi, J.A., and Rabbat, B.G. 1999. Notes on ACI-318-99 Building Code Requirements for Structural Concrete. 7th ed. U.S.A.: Portland Cement Association.
Fanella, D.A., and Mushi, J.A. Design of Concrete Buildings for Earthquake and Wind Forces. U.S.A.: Portland Cement Association.
International Conference of Building Officials. 1997. "Structural Engineering Provisions." Uniform Building Code UBC (1997). U.S.A.: International Conference of Building Officials. Lindeburg, M.R., and Baradar, M. 2001. Seismic Design of Building Structures. 8th ed. U.S.A.: Professional Publications, Inc. Nilson, A.H. 1997. Design of Concrete Structures. 12th ed. Singapore. McGraw Hill Co. Inc.
Structures and Codes Institute. No Date. Code Master. December 2006
Taranath, B.S. 1998. Structural Analysis and Design of Tall Buildings. McGraw Hill Book Company-Singapore
APPENDICES
APPENDIX A STRUCTURAL KEY PLAN, DESIGN SECTIONS AND RESULTS FROM ETABS
Figure A.1. Three Dimensional View of Case Study Building
102
Figure A.2. First Floor Level Beams and Columns Structure Key Plan
103
Figure A.3. Second Floor Level Beams and Columns Structure Key Plan
104
Figure A.4. Typical Floor (third to tenth floor) Level Beams and Columns Structure Key Plan
105
Figure A.5. Eleventh Floor Level Beams and Columns Structure Key Plan View
106
Figure A.6. Roof Level One Beams and Columns Structure Key Plan View
107
Figure A.7. Concrete Design Sections of Ground Floor Plan View
108
Figure A.8. Concrete Design Sections of First Floor Plan View
109 .
Figure A.9. Concrete Design Sections of Second Floor Plan View
110
Figure A.10. Concrete Design Sections of Third Floor to Eleventh Floor Plan View
111
Figure A.11. Concrete Design Sections of Roof Level One Plan View
112
Figure A.12. Concrete Design Sections of Elevation View-1 and Elevation View-9
113
Figure A.13. Concrete Design Sections of Elevation View-2 and Elevation View-8
114
Figure A.14. Concrete Design Sections of Elevation View-3
115
Figure A.15. Concrete Design Sections of Elevation View-4
116
Figure A.16. Concrete Design Sections of Elevation View-5
117
Figure A.17. Concrete Design Sections of Elevation View-6
118
Figure A.18. Concrete Design Sections of Elevation View-7
119
Figure A.19. Frame Span Loads (WALL) of Elevation View-3 (lb-ft Units)
120
Figure A.20. Frame Span Loads (WALL) of Elevation View-7 (lb-ft Units)
121
Figure A.21. Frame Span Loads (WALL) of Elevation View-I (lb-ft Units)
122
Figure A.22. Frame Span Loads (WALL) of Elevation View-J (lb-ft Units)
123
Figure A.23. Uniform Loads GRAVITY (SUPERDL) of First Floor Plan View (lb-ft Units)
124
Figure A.24. Uniform Loads GRAVITY (SUPERDL) of Third Floor Plan View (lb-ft Units)
125
Figure A.25. Uniform Loads GRAVITY (LIVE) of First Floor Plan View (lb-ft Units)
126
Figure A.26. Uniform Loads GRAVITY (LIVE) of Third Floor Plan View (lb-ft Units)
127
Figure A.27. Axial Force Diagram (COMB2) of Elevation View-E (kip-ft Units)
128
Figure A.28. Axial Force Diagram (COMB2) of Elevation View-7
(kip-ft Units)
129
Figure A.29. Bending Moment in X Direction Diagram (COMB3) of Elevation View-E (kip-ft Units)
130
Figure A.30. Bending Moment in X Direction Diagram (COMB16) of Elevation View-E (kip-ft Units)
131
Figure A.31. Bending Moment in X Direction Diagram (COMB3) of Elevation View-7 (kip-ft Units)
132
Figure A.32. Bending Moment in X Direction Diagram (COMB15) of Elevation View-7 (kip-ft Units)
133
Figure A.33. Bending Moment in Y Direction Diagram (COMB9) of Elevation View-E (kip-ft Units)
134
Figure A.34. Bending Moment in Y Direction Diagram (COMB18) of Elevation View-E (kip-ft Units)
135
Figure A.35. Bending Moment in Y Direction Diagram (COMB10) of Elevation View-7 (kip-ft Units)
136
Figure A.36. Bending Moment in Y Direction Diagram (COMB17) of Elevation View-7 (kip-ft Units)
137
Figure A.37. Shear Force Diagram (COMB2) of First Floor Plan View (kip-ft Units)
138
Figure A.38. Shear Force Diagram (COMB20) of First Floor Plan View (kip-ft Units)
139
Figure A.39. Shear Force Diagram (COMB2) of Fifth Floor Plan View(kip-ft Units)
140
Figure A.40. Shear Force Diagram (COMB20) of Fifth Floor Plan View (kip-ft Units)
141
Figure A.41. Torsion Diagram (COMB5) of First Floor Plan View (kip-ft Units)
142
Figure A.42. Torsion Diagram (COMB22) of First Floor Plan View (kip-ft Units)
143
Figure A.43. Torsion Diagram (COMB5) of Fifth Floor Plan View (kip-ft Units)
144
Figure A.44. Torsion Diagram (COMB22) of Fifth Floor Plan View (kip-ft Units)
145
Figure A.45. Bending Moment Diagram (COMB4) of First Floor Plan View (kip-ft Units)
146
Figure A.46. Bending Moment Diagram (COMB19) of First Floor Plan View (kip-ft Units)
147
Figure A.47. Bending Moment Diagram (COMB4) of Fifth Floor Plan View (kip-ft Units)
148
Figure A.48. Bending Moment Diagram (COMB19) of Fifth Floor Plan View (kip-ft Units)
149
Figure A.49. Plan View of Beam and Column Labels
APPENDIX B ARCHITECTURAL DRAWINGS
Figure B.1. Front Elevation
151
Figure B.2. Side Elevation
152
Figure B.3. Ground Floor and First Floor Plan
153
Figure B.4. Typical Floor (Third Floor to Tenth Floor) Plan
154
Figure B.5. Eleventh Floor Plan
155
Figure B.6. Roof Level One Plan
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