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Design proposal and analysis of curved brace system to reduce drift in moment frame structures

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DESIGN PROPOSAL AND ANALYSIS OF CURVED BRACE SYSTEM TO REDUCE
DRIFT IN MOMENT FRAME STRUCTURES

by
Aishwarya Balagopal

A Thesis Presented to the
FACULTY OF THE USC SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF BUILDING SCIENCE

August 2012

Copyright 2012 Aishwarya Balagopal

ii

ACKNOWLEDGEMENTS
I would like to take this opportunity to sincerely thank everybody who has
directly or indirectly helped me complete this thesis .
I would like to extend my gratitude to my committee member who have helped
me throughout the process . Prof.G.Schierle. Prof.A.Carlson. Mr.M.Murat and
Mr.E.Losche. I am extremely grateful to all of them for their time and technical support
throughout the thesis. I thank them for the timely help and support in exploring structural
systems and software's. It would have been nearly impossible for me to complete my
research without their support and their background in their respective field of expertise.
Secondly I would like to thank my family. A special thanks to my parents for the
trust they bestowed on me and for being my guardians at every step of my life. Without
their presence in my life none of this would have been possible. I thank them for giving
me the opportunity to do my further studies in the United States and building the
confidence in me to achieve my goals and tackle my hurdles in the right manner.
I would like to thank Saurabh for being extremely patient with me and bearing the
brunt of my frustration in the process of my thesis research. He has been a pillar of
support and encouragement for me at every step of this thesis research.
I would like to thank all my friends who have been with me, especially Sukreet, Wonhee,
Yi Lun, William, Priyanka and Morgan for all the support given to me at the most crucial
stages in the period of this thesis. My sincere thanks to Han Kim for his help with
SAP2000. I thank everyone who has been of help to me in every small way.

iii

TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................................................................................. ii
LIST OF TABLES …………………………………………………………………...…vii
LIST OF FIGURES …………………………………………………………….…….....xi
ABS T RA CT….. ................................................................................................................xv
CHAPTER 1 INTRODUCTION ......................................................................................1
1.1 OVERVIEW.............................................................................................................. 1
1.2 EARTHQUAKES : .................................................................................................. 3
1.3 BEHAVIOR OF BUILDINGS STRUCTURESUNDER EATRTHQUAKE
LOADING:...................................................................................................................... 4
CHAPTER MOMENT FRAME .....................................................................................8
2.1 MOMENT FRAMES ............................................................................................... 8
2.1.1 TYPES OF MOMENT FRAMES: ..................................................................... 9
2.2 DESIGN OF MOMENT FRAMES ....................................................................... 10
CHAPTER 3 EARTHQUAKE RESISTANT SYSTEMS ............................................15
3.1 COMMON EARTHQUAKE RESISTANT SYSTEMS: PASSIVE SYSTEMS .. 15
3.1.1 MOMENT RESISTING FRAMES : .............................................................. 15
3.1.2 BRACED FRAME.......................................................................................... 16
3.1.3 FRAMED TUBE STRUCTURES: ................................................................. 17
3.1.4 BELT TRUSS AND OUTRIGGER : ............................................................. 17
3.1.5 BUNDLED TUBE STRUCTURE:................................................................. 18
3.2 COMMON EARTHQUAKE RESISTANT SYSTEMS : ACTIVE SYSTEMS .. 19
3.2.1 BASE ISOLATOR.......................................................................................... 19
3.2.2 TYPES OF BASE ISOLATOR : .................................................................... 21
3.3 TUNED MASS DAMPERS (TMD) ...................................................................... 23
3.3.1 WORKING ....................................................................................................... 23
3.3.2 TYPES OF MASS DAMPERS ........................................................................ 24
3.4 VISCO ELEASTIC DAMPER .............................................................................. 26
CHAPTER 4 ANALYSIS OF 21 STORIED 90ft X 90ft STRUCTURE ....................27
4.1 DESIGN PAPRAMETERS : .................................................................................. 27

iv

4.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE: ............................. 28
4.2 LOAD CASES ....................................................................................................... 31
4.2.1 DEAD LOAD : ................................................................................................. 32
4.2.2 LIVE LOAD: .................................................................................................... 32
4.2.2 SEISMIC LOAD.( ALONG X & Y AXIS) ..................................................... 33
4.2.3 WIND LOAD ................................................................................................... 34
4.3 ANALYSIS : .......................................................................................................... 38
4.4 SYSTEMS ANALYZED ....................................................................................... 40
4.5 BASE SHEAR ........................................................................................................ 41
4.6 ANALYSIS FOR DRIFT ....................................................................................... 43
4.6.1 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS ..................... 45
4.6.2 DRIFT DUE TO SEISMIC LOADING ALONG THE Y AXIS ..................... 54
4.6.3 DRIFT DUE TO WIND LOADING ALONG THE X AXIS .......................... 61
4.6.4 CASE 1 COMPARISON OF EXISITNG SYSTEMS ..................................... 61
4.6.5 DRIFT DUE TO WIND LOADING ALONG THE Y AXIS .......................... 68
4.7 CONCLUSION ...................................................................................................... 75
CHAPTER 5 ANALYSIS OF 21 STORIED 150ft X 90ft STRUCTURE ..................76
5.1 DESIGN PAPRAMETERS : .................................................................................. 76
5.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE: ............................. 77
5.1.2 CONCRETE SLAB DESIGN OF MOMENT FRAME STRUCTURE: ......... 79
5.2 LOAD CASES ....................................................................................................... 81
5.2.1 DEAD LOAD .................................................................................................. 81
5.2.2 LIVE LOAD ..................................................................................................... 82
5.2.3 SEISMIC LOAD.( ALONG X & Y AXIS) ..................................................... 83
5.2.4 WIND LOAD ................................................................................................... 84
5.3 ANALYSIS: ........................................................................................................... 89
5.4 SYSTEMS ANALYZED ....................................................................................... 91
5.4.1 BASE SHEAR .................................................................................................. 92
5.4.2 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS ..................... 98
5.4.3 DRIFT DUE TO SEISMIC LOADING ALONG THE Y AXIS ................... 106
5.4.4 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED
JOINT ...................................................................................................................... 112
5.4.5 DRIFT DUE TO WIND LOADING ALONG THE X AXIS ........................ 116
5.4.6 DRIFT DUE TO WIND LOADING ALONG THE Y AXIS ........................ 124
5.5 CONCLUSION .................................................................................................... 129

v

CHAPTER 6 ANALYSIS OF 50 STORIED 150 ft X 150 ft STRUCTURE ............130
6.1 DESIGN PAPRAMETERS : ................................................................................ 130
6.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE: ........................... 131
6.1.2 CONCRETE SLAB DESIGN OF MOMENT FRAME STRUCTURE: ....... 133
6.2 LOAD CASES ..................................................................................................... 135
6.2.1 DEAD LOAD : ............................................................................................... 136
6.2.2 LIVE LOAD: .................................................................................................. 136
6.2.3 SEISMIC LOAD ............................................................................................ 137
6.2.4 WIND LOAD ................................................................................................. 137
6.3 ANALYSIS: ......................................................................................................... 142
6.3.1 BASE SHEAR ................................................................................................ 145
6.3.2 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS ................... 147
6.3.3 DRIFT DUE TO WIND LOADING ALONG THE X AXIS ........................ 150
6.4 CONCLUSION: ................................................................................................... 153
CHAPTER 7 CONCLUSION .......................................................................................154
7.1 CONCLUSION FROM THE ANALYSIS : ........................................................ 155
7.1.1 DEFLECTION ............................................................................................... 155
7.1.2 ECONOMIC FACTOR .................................................................................. 156
7.2 FUTURE STUDY : .............................................................................................. 158
7.2.1 COMPARISON WITH OTHER SYSTEMS. ................................................ 158
7.2.2 SITE STUDY ................................................................................................. 158
7.2.3 SOFTWARE .................................................................................................. 158
BIBLIOGRAPHY ..........................................................................................................160
APPENDIX – A - MODELLING AND ANALYZING IN SAP 2000 V15 ..............161
APPENDIX B - MODAL ANALYSIS ........................................................................174
APPENDIX C - ADDITIONAL MATERIAL DATA - STEEL SECTIONS ...........188

vi

LIST OF TABLES

Table 1 Material Properties 02 - Basic Mechanical Properties..........................................28
Table 2 Material Properties 03a - Steel Data .....................................................................29
Table 3: Material Properties 03e - Rebar Data .................................................................29
Table 4 Material Properties 03b - Concrete Data ..............................................................30
Table 5 Area Section Properties, Part 1 of 3 ......................................................................30
Table 6 Area Section Properties, Part 2 of 3 ......................................................................30
Table 7 Area Section Properties, Part 3 of 3 ......................................................................31
Table 8 Case - Static 1 - Load Assignments ......................................................................31
Table 9 Load Pattern Definitions .......................................................................................32
Table 10 Auto Wind - ASCE7-05, Part 1 of 2 ...................................................................35
Table 11 Auto Wind - ASCE7-05, Part 2 of 2 ...................................................................35
Table 12 Load Combination Definitions ...........................................................................36
Table 13 Base shear of Existing Systems along the X axis ...............................................41
Table 14 Base Shear of Existing Systems along the Y axis ..............................................41
Table 15 Base Shear of Diagonal Curved Brace - Fixed at each end – Along the X
axis. .............................................................................................................................42
Table 16 Base Shear of Diagonal Curved Brace - Fixed at each end – Along the Y
axis ..............................................................................................................................43
Table 17 Deflection (in ft) in the X axis due to Seismic loading along the X axis ...........45
Table 18 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces fixed at both ends. .................................................................48
Table 19 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces pinned at both ends. ..............................................................50

vii

Table 20 Deflection (in ft) due to Seismic loading along the Y axis .................................54
Table 21 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. .................................................................56
Table 22 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces pinned at both ends. ..............................................................58
Table 23 Deflection (in ft) due to Seismic loading along the X axis .................................61
Table 24 Deflection (in ft) due to Wind loading along the X axis by different
diagonal curved braces fixed at both ends. .................................................................63
Table 25 Deflection (in ft) due to Wind load along the X axis by different diagonal
curved braces pinned at both ends. .............................................................................65
Table 26 Deflection (in ft) due to Wind loading along the X axis ....................................68
Table 27 Deflection (in ft) due to Wind loading along the X axis by different
diagonal curved braces fixed at both ends. .................................................................70
Table 28 Deflection (in ft) due to Wind load along the X axis by different diagonal
curved braces pinned at both ends. .............................................................................72
Table 29 Material Properties 02 - Basic Mechanical Properties........................................77
Table 30 Material Properties 03a - Steel Data ...................................................................78
Table 31 Material Properties 03e - Rebar Data .................................................................78
Table 32 Material Properties 03b - Concrete Data ............................................................79
Table 33 Area Section Properties, .....................................................................................79
Table 34 Case - Static 1 - Load Assignments ....................................................................81
Table 35 Load Pattern Definitions .....................................................................................82
Table 36 Auto Wind - ASCE7-05, Part 1 of 2 ...................................................................85
Table 37 Auto Wind - ASCE7-05, Part 2 of 2 ...................................................................85
Table 38 Combination Definitions.....................................................................................86
Table 39 Base Shear of Existing Systems along the X axis ..............................................92

viii

Table 40 base Shear of Existing Systems along the Y axis ...............................................92
Table 41 Base Shear of Diagonal Curved Brace- Fixed at both ends- along the X
axis ..............................................................................................................................93
Table 42 Base Shear of Diagonal Curved Braces- Fixed at both end - Along the Y
axis ..............................................................................................................................94
Table 43 Base Shear of Diagonal Curved Brace- Pinned at both ends- along the X
axis ..............................................................................................................................95
Table 44 Base Shear of Diagonal Curved Brace- Pinned at both ends- along the Y
axis ..............................................................................................................................96
Table 45 Deflection (in ft) in the X axis due to Seismic loading along the X axis ...........98
Table 46 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces fixed at both ends. ...............................................................101
Table 47 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces pinned at both ends .............................................................103
Table 48 Deflection (in ft) due to Seismic loading along the Y axis ...............................106
Table 49 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. ...............................................................109
Table 50 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces pinned at both ends. ............................................................112
Table 51 Deflection (in ft) due to Wind loading along the X axis ..................................116
Table 52 Deflection (in ft) due to Wind loading along the X axis by different
diagonal curved braces fixed at both ends. ...............................................................118
Table 53 Deflection (in ft) due to Wind loading along the X axis by different
diagonal curved braces pinned at both ends. ............................................................120
Table 54 Deflection (in ft) due to Wind loading along the X axis ..................................124
Table 55 Deflection (in ft) due to Wind loading along the Y axis by different
diagonal curved braces fixed at both ends. ...............................................................126
Table 56 Material Properties 02 - Basic Mechanical Properties......................................131
Table 57 Material Properties 02 - Basic Mechanical Properties......................................132

ix

Table 58 Material Properties 03e - Rebar Data ...............................................................132
Table 59 Material Properties 03b - Concrete Data ..........................................................133
Table 60 Area Section Properties, Part 1 of 3 ..................................................................133
Table 61 Area Section Properties, Part 2 of 3 ..................................................................134
Table 62 Area Section Properties, Part 3 of 3 ..................................................................134
Table 63 Case - Static 1 - Load Assignments ..................................................................135
Table 64 Load Pattern Definitions ...................................................................................136
Table 65 Auto Wind - ASCE7-05, Part 1 of 2 .................................................................138
Table 66 Auto Wind - ASCE7-05, Part 2 of 2 .................................................................138
Table 67 Combination Definitions Table ........................................................................139
Table 68 Base shear along the X axis ..............................................................................145
Table 69 Base Shear along the Y axis .............................................................................146
Table 70 Deflection (in ft) due to Seismic loading along the X axis ...............................147
Table 71 Drift due to Wind loading along th X Axis ......................................................150
Table 72 Modal Analysis : Moment Frame .....................................................................174
Table 73 Modal Analysis : Central Bay Braced Frame ( Core Brace ) ...........................175
Table 74 Modal Analysis : Peripheral Braced Frame System .........................................176
Table 75 Modal Analysis : Straight Diagoonal Brace System ........................................177
Table 76 Modal Analaysis : Curved Diagonal Brace System - Curve 2 ........................178
Table 77 Modal Analysis : Moment Frame Structure .....................................................179
Table 78 Modal Analysis : Central Bay Braced Frame ( Core Brace ) ...........................180
Table 79 Modal Analysis : Peripheral Braced Frame System ........................................181
Table 80 Modal Analysis Straight Diagonal Brace System.............................................182
Table 81 Modal Analysis : Curved Diagonal Brace System - Curve 2 ...........................183

x

Table 82 Modal Analysis Double Straight Brace System ..............................................184
Table 83 Modal Analysis : Double Curved Brace System ..............................................185
Table 84 Modal Analysis : Multiple Straight brace ( Every 10 floors) ..........................186
Table 85 Modal Analysis : Multiple curved Brace ( Every 10 Floors ) ..........................187
Table 86 Frame Section PropertiGes 01 - General, Part 1 of 4 .......................................188
Table 87 Frame Section Properties 01 - General, Part 2 of 4 ..........................................190
Table 88 Frame Section Properties 01 - General, Part 3 of 4 ..........................................191
Table 89 Frame Section Properties 01 - General, Part 4 of 4 ..........................................192
Table 90 Frame Section Properties 02 - General, Part 1 of 4 ..........................................193
Table 91 Frame Section Properties 01 - General, Part 2 of 4 ..........................................195
Table 92 Frame Section Properties 01 - General, Part 3 of 4 ..........................................197
Table 93 Frame Section Properties 01 - General, Part 4 of 4 ..........................................199
Table 94 Frame Section Properties 01 - General, Part 1 of 4 ..........................................201
Table 95 Frame Section Properties 01 - General, Part 2 of 4 ..........................................203
Table 96 Frame Section Properties 01 - General, Part 3 of 4 ..........................................205
Table 97 Frame Section Properties 01 - General, Part 4 of 4 ..........................................207

xi

LIST OF FIGURES
Figure 1 Structural systems compared in the research .........................................................2
Figure 2 Friction caused by the movement of plates. ..........................................................3
Figure 3 Structural Damage caused during the 1989 in San Fransisco Earthquake
.Photograph Courtesy : J.K. Nakata, , U.S. Geological Survey ...................................4
Figure 4 Moment frame connection
(http://www.fageneng.com/eng_services/structural.htm).............................................8
Figure 5 ConXtech prefabricated moment frame system, with shop welded collars
that the beams slid into. http://dcm-designs.com/steel-prefabricated-moment-
frame/ ..........................................................................................................................10
Figure 6 Fracture of a column flange and web at a moment connection due to the
Northridge earthquake ................................................................................................13
Figure 7 Seismic braced rfame system. http://www.aisc.org .............................................16
Figure 8 Belt Truss And Outrigger ....................................................................................17
Figure 9 Design of Outrigger and Belt truss system ..........................................................18
Figure 10 Lembaga Tabung Haji Building - Kula Lumpur with the section drawing
showing the inner tube form. http://theconstructor.org/structural-engg/high-
rise-structures/5/ .........................................................................................................18
Figure 11 A base isolator with rubber bearings used in the foundation of a building .......20
Figure 12 Largest tuned mass damper made of steel has been used in Taipei 101 to
counteract the drift induced in the building by lateral loading. ..................................23
Figure 13 Visco elastic dampers placed in the steel trusses in the WTC ..........................26
Figure 14 Building Section– G+ 20 Storeys – ...................................................................27
Figure 15 Floor Plan - (L) 90 ft x (B) 90ft – 3 Bay Layout ..............................................27
Figure 16 Curved braces with 3 different radii used to analyze the system ......................38
Figure 17 Gavity steel versus wind premium check ..........................................................39
Figure 18 Different Systems Analyzed for a Layout of 90X 90X 252 FT ........................40

xii

Figure 19 Deflection (in ft) due to Seismic loading along the X axis ...............................46
Figure 20 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces fixed at both ends. .................................................................49
Figure 21 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces pinned at both ends. ..............................................................52
Figure 22 Deflection (in ft) in the X axis due to Seismic loading along the X axis ..........53
Figure 23 Deflection (in ft) due to Seismic loading along the y axis ................................55
Figure 24 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. .................................................................57
Figure 25 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. .................................................................59
Figure 26 Deflection (in ft) due to Seismic loading along the Y axis ...............................60
Figure 27 Deflection (in ft) in the X axis due to Wind load along the X axis ...................62
Figure 28 Deflection (in ft) due to Windload along the X axis by different diagonal
curved braces fixed at both ends. ................................................................................64
Figure 29 Deflection (in ft) due to Wind load along the X axis by different diagonal
curved braces pinned at both ends. .............................................................................66
Figure 30 Deflection (in ft) due to Wind loading along the X axis ..................................67
Figure 31 Deflection (in ft) due to Wind loading along the Y axis: ..................................69
Figure 32 Deflection (in ft) in the X axis due to Seismic loading along the X axis by
different diagonal curved braces fixed at both ends. ..................................................71
Figure 33 Deflection (in ft) due to Wind load along the Y axis by different diagonal
curved braces pinned at both ends. ............................................................................73
Figure 34 Deflection (in ft) due to Wind load along the y axis ........................................74
Figure 35 The diagonal straight brace and curved brace with different radii ....................89
Figure 36 Gavity steel versus wind premium check ..........................................................90
Figure 37 Different Systems Analyzed for a Building of 90 X 150 X 252 ft ....................91

xiii

Figure 38 Deflection (in ft) due to Seismic loading along the X axis .............................100
Figure 39 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces fixed at both ends. ...............................................................102
Figure 40 Deflection (in ft) due to Seismic loading along the X axis by different
diagonal curved braces pinned at both ends. ............................................................104
Figure 41 Deflection (in ft) in the X axis due to Seismic loading along the X axis ........105
Figure 42 Deflection (in ft) due to Seismic loading along the y axis ..............................108
Figure 43 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. ...............................................................111
Figure 44 Deflection (in ft) due to Seismic loading along the Y axis by different
diagonal curved braces fixed at both ends. ...............................................................114
Figure 45 Deflection (in ft) due to Seismic loading along the Y axis .............................115
Figure 46 Deflection (in ft) due to Wind load along the X axis ......................................117
Figure 47 Deflection (in ft) due to Wind loading along the X axis by different
diagonal curved braces fixed at both ends. ...............................................................119
Figure 48 Deflection (in ft) in the X axis due to Wind load along the X axis by
different diagonal curved braces pinned at both ends. .............................................122
Figure 49 Deflection (in ft) in due to Wind loading along the X axis ............................123
Figure 50 Deflection (in ft) due to Wind loading along the Y axis .................................125
Figure 51 Deflection (in ft) due to Wind load along the Y axis by different diagonal
curved braces ............................................................................................................127
Figure 52 Deflection (in ft) due to Wind load along the Y axis .....................................128
Figure 53 John Hancock center at Chicago uses a single diagonal brace every 10
stories http://www.chicagoarchitecture.info/Building/1006/The-John-Hancock-
Center.php.................................................................................................................142
Figure 54 Different brace systems analyzed for drift in 50 storied structure ..................143
Figure 55 Gavity steel versus wind premium check ........................................................143
Figure 56 Steel design check for stress in steel members ................................................144

xiv

Figure 57 Lateral drift produced by seismic load in the different brace systems. ...........149
Figure 58 Lateral drift produced by wind load in the different brace systems. ...............152
Figure 59 Zoomed Elevation Of Bracing at a Single floor ..............................................156
Figure 60 Model in SAP 2000 showing the released joints in beams –( the red
indicates concrete panels and blue steel sections) ....................................................165
Figure 61 Defining mass source in SAP .........................................................................165
Figure 62 Design Coefficients and factors for Seismic Force resisting systems
determined from Table 12.2-1 from ASCE 7-05 ......................................................166
Figure 63 Seismic Load data in SAP ...............................................................................166
Figure 64 Defining Wind Load in SAP ...........................................................................167
Figure 65 Steel frame Design overwrites (ASCE 7-05) .................................................168
Figure 66 Steel design check for the base moment frame structure ................................169
Figure 67 Error windows indicating errors witnessed during the process .......................169
Figure 68 Error window 1 indicating errors witnessed during the process .....................170
Figure 69 Error window 2 indicating errors witnessed during the process .....................170
Figure 70 Final structure derived with the column and beam sizes derived after
analyzing in SAP 2000 .............................................................................................171
Figure 71 The figure shows the single member as a brace across the building and
the brace as a member every floor to floor height ....................................................172
Figure 72 Manually constructing the diagonal curved braced ........................................172

xv

ABSTRACT

Wind and seismic loads cause buildings to shift from their vertical axis of inertia
resulting in lateral displacement, also termed as drift. It is extremely crucial to stabilize
tall buildings in the event of large lateral load that cause buildings to flex beyond their
limit of elasticity, resulting in structural damage that can prove to be fatal. This thesis
proposes to study the efficiency of a diagonal curved brace system as an alternate to
retrofit existing steel moment frame structures. The study was conducted with a moment
frame structure as a base case and how retrofitting the structure with the proposed
diagonal curved brace induced better performance in the structure as compared to the
performance of the structure when retrofitted with different forms of straight brace
systems. Analyses of the proposed system was performed in SAP2000- a finite element
analysis software, the mass of steel in the structure has been constant for all retrofit
structures in the study. The idea of using a parabolic brace form was obtained from the
catenary form used in the design of suspension bridges and the parabolic form used in the
design of the Eiffel tower.

1
CHAPTER 1 INTRODUCTION
1.1 OVERVIEW
When a structural member such as a beam supported at both end is subjected to loading
(dead / live load) it begins to bend / curve. This parabolic form caused due to self weight of the
member is known as the catenary form. The behavior of catenary forms was initially researched
by Robert Hooke in 1670 and the equations were later derived by Leibniz, Huygens and Johann
Bernoulli in 1691.The study of catenary form plays a crucial role in the design of bridges and
arches in architecture. The parametric equations for the catenary are given by : (Weisstein,Eric )
i

where t = 0 corresponds to the vertex and a is a parameter that determines how quickly the
catenary "opens up." Catenaries for values of a ranging from 0.05 to 1.00 by steps of 0.05 are
illustrated above.
The arc length, curvature, and tangential angle for t>0 are given by

The sslope is proportional to the arc length as measured
from the center of symmetry.

2
Most structures make use of a straight framed brace frame system to provide additional
strength and stiffness to moment frame structures in resisting lateral load. This thesis analyzes
the use of a diagonally supported parabolic frame inspired from the catenary form in comparison
to a straight brace frame system. This curved brace system was analyzed to check its efficiency
in resisting drift in structures under lateral loading due to seismic and wind loading. In order to
research the efficiency of a curved brace system various models were studied in SAP 2000 a
finite element analysis computer tool widely used in the field of structural engineering. To check
the efficiency a moment frame structure was retrofitted with a diagonal straight brace frame ,
peripheral bracing and core brace frame system. The deflection caused by each of the system was
then compared to arrive at a conclusion. The initial study was carried out on a 21 story building
with a 3 bay square layout. Based on the conclusions of the 1
st
model, the system was tested in
SAP for a building with a rectangular layout and a 50 storied structure to study how form and
height affects the efficiency of this system.

Figure 1 Structural systems compared in the research
Moment Frame
Structure
Core BracedFrame
Structure
Peripheral Braced
Frame Structure
Diagonal Straight
Braceframe
Diagonal Curved
Braceframe

3
Figure 2 Friction caused by the movement
of plates.
http://earthsci.org/processes/struct/equake
2/EQHazardsRisks.html

1.2 EARTHQUAKES :

CAUSE OF AN EARTHQUAKE:
The earth is made up of 3 main layers:
1. Central core
2. Asthenosphere
3. Outermost Lithosphere
The hard lithosphere is not a single
smooth layer but instead made of various plates
that are not interlocked but rest against each
other. The lithosphere rests on the soft
asthenosphere which acts as a liquid base to the solid plates allowing movement of these plates.
These plates move at the rate of about 0-100 mm per year. (Earthquake Engineering)
During their movement the tectonic plates tend to cause friction among them. This friction is
what is experienced as an earthquake. When rock beds experience a mutual slip on a certain
plane it results in the formation of faults.
Faults can cause earthquakes in the following ways:
1. Strain that can be accumulated in the fault for a long period of time reaches its limit.
2. Slip occurs at the fault and causes a rebound.
3. Occurrences of a push pullforce at the fault.
4. Faults cause radial wave propagation as an effect of an earthquake.

4
When designing structures it is very
important to conduct site analysis and attain
geotechnical information regarding the site and
its surrounding area. Buildings must always be
built within a safe distance from fault lines to
prevent them from collapse or experiencing
structural deformation in the event of an
earthquake. (Wakabayashi, 1986)

1.3 BEHAVIOR OF BUILDINGS STRUCTURESUNDER EARTHQUAKE LOADING:
Performance of a building is affected by the dynamic response of the structure along with
various other factors. A crucial characteristic of buildings in response to seismic loads is the
ductility of the structure. Structures with high ductile strength perform well under earthquake
load due to higher energy dissipation capacity. However structures with low ductility tend to
have poor resistance against earthquakes. Strength of such buildings deteriorates after lateral
displacement causes to exceed the maximum strength of the structure. As loading on the
structure continues, the structure tends to weaken finally resulting in structural collapse.
If the total strain of the component material to its breaking limit is sufficiently large the
structure is considered to possess good ductility. Ductility also requires that the ratio of the yield
stress (Fy) to ultimate stress (Fu) is close to unity Brittle structures such as masonry structures
tend to fail easily under seismic load if they are not reinforced, Or if the seismic demand exceeds
the strength to which they were designed. On the other hand steel structures perform well due to
their characteristic of plastic deformity that gives them high ductility. Composite structures have
Figure 3 Structural Damage caused during
the 1989 in San Fransisco Earthquake
.Photograph Courtesy : J.K. Nakata, , U.S.
Geological Survey

5
good resistance to seismic loading since the presence of steel reinforcement provides ductility to
the structure which can also have high strength.
Some of the common causes of structural failure in reinforced concrete structures are as follows
(Wakabayashi, 1986)
1. Inadequate story shear strength caused by insufficient columns and walls
2. Brittle shear failure of columns or beams, or walls.
3. Brittle shear failure of columns which have been shortened by the supporting effect of
nonstructural elements
4. Slip of anchored bars or shear failure of the joint block in beam to column
connections.
5. Brittle failure of single or coupled shear walls, particularly shear walls with opening.
6. Torsion caused by the non-coincidence on the floor plan center of gravity and center
of stiffness
7. Concentration of damage at a specific story due to unequal distribution of the
stiffness along the height.
8. Separation of secondary members such as exterior walls because of poor connections.
9. Failure due to overturning moments.
10. Shear failure/ sliding shear failure
11. Buckling of columns
During an earthquake the friction caused by plate movement causes tectonic plates to
move in both directions resulting in heavy vibration termed as earthquakes. Building structures
have their foundations deeply rooted within the outer lithosphere. The ground acceleration
produced during an earthquake is transmitted to the structure through its foundation.

6
Structural damage of any form can prove dangerous to the future existence of a building.
When designing buildings the first factor of concern to designers and engineers, is the ability of
the structure to withstand lateral and gravity load . (Bungale, 1988)
Applying Newton’s law of motion:
“Every object in a state of uniform motion tends to remain in that state of motion unless
an external force is applied to it.”
The building inertia is set into motion due to the ground acceleration. Since each
structure has a period of resonance characteristic to the structure, as a result of the seismically
induced vibrations buildings tend to oscillate like a pendulum during an earthquake causing
elastic behavior in them. An example to explain the behavior of tall buildings would be a diving
board. The diving board is fixed at one end and free at the pool end. When a diver jumps of the
board he applies a point load to the board. Once the diver jumps off the board, the board tends to
oscillate at the free end until the strain energy imparted to the board by the diver dissipates.
The period of resonance of the building is about 0.1 times the number of stories measured
in seconds .Thus as the building is designed for more no of story’s the frequency of resonance of
the structures decreases making the structure less vulnerable to structural damage. Several
characteristics affect the behavior of buildings during lateral loading such as: shape, size, height,
mass, stiffness factor, width to height ratio, materials, elasticity, connections, dampers, etc. All
the above mentioned factors play a crucial role in determining the structural stability of the
structure and must be considered when designing buildings in seismic zones. An important
design element for structural stability is to design the structure to have a sturdier base and reduce
mass gradually towards the top .One of the many rules of thumb for structural design is, the

7
height to width ratio of buildings should be <= 6. This makes the structures stable under heavy
lateral displacement load like an earthquake or wind pressure. (Arbabian, 2000)

8
Figure 4 Moment frame connection
(http://www.fageneng.com/eng_services/st
ructural.htm)
CHAPTER 2 MOMENT FRAME
2.1 MOMENT FRAMES

Moment frame structures were developed in the 19
th
century due to limitation of masonry
structures to build taller structures and resist lateral loads in the desired manner. Moment frames
consist of column beam steel skeletal structural system which make it possible to construct taller
structures with good resistance to lateral loads. Moment frame structures date back to the era
when construction of steel structures commenced. Typical buildings where constructed from “H”
sections by welding plates to “L” And “Z” section.
Some of the common moment frame joinery
systems included welding and bolting with the help
of gusset plates. The main characteristic feature of
moment frames is their ability to transfer moments
from beam to column and reverse. Special moment
frames achieve ductility through yielding beams and
columns. Seismic loading may induce several cycles
of inelastic rotation in the structure. Moment frame
connections should be designed of withstanding such
inelastic rotation.This characteristic of moment
frames make them the most desired system in tall
buildings especially in seismic zones. They are designed to resist lateral loads arising from wind
and seismic activities as well as vertical gravity load. Moment frame structures are built to be
rigid under vertical loading but must possess ductility to resist lateral loads. The term ‘Moment
Frame’ is defined by the capacity to transfer moments between beam and column.
(Scott & Hamburger)

9
2.1.1 TYPES OF MOMENT FRAMES:
Moment frames are of three types:
1. Ordinary Moment Frame (OMF)
2. Intermediate Moment Frame (IMF)
3. Special Moment Frame (SMF)
2.1.1.1 ORDINARY MOMENT FRAME :

Ordinary moment frames are used in the construction of buildings in low seismic areas .
OMF does not have high rigidity value to resist large deformations but possess large elastic
coefficient so as to retain its original form under lateral loading such as wind.Ordinary moment
frames are not very good in withstanding inter-story drift and rotational force reactions. This
system is recommended in structures that have high ceilings.
2.1.1.2 INTERMEDIATE MOMENT FRAME:

Intermediate Moment Frames are designed in structures located in areas ranging from
low seismic to mid seismic zones. These structures have lower elastic coefficient than ordinary
moment frames and are designed to be more rigid under seismic lateral loading. Intermediate
Moment Frames are designed to undergo certain amount of deformation to resist seismic loads.
They can also withstand certain amount of inter story drift.
2.1.1.3 SPECIAL MOMENT FRAME
Special Moment Frames are designed for buildings constructed in high seismic zones.
These frames are designed to bear inter story drift. When buildings are subjected to seismic loads
of high intensity it is very crucial for the system to dissipate the energy transferred.

10
Figure 5 ConXtech prefabricated
moment frame system, with shop
welded collars that the beams slid into.
http://dcm-designs.com/steel-
prefabricated-moment-frame/
2.2 DESIGN OF MOMENT FRAMES
Moment frame system was first applied in Chicago.“Typically, steel framing was
completely encased by masonry, concrete, or a
combination of these, to provide fire resistance.
Anecdotal evidence suggests that designers of these
early moment frame structures neglected the
structural contributions of concrete and masonry
encasement and further assumed that framing
connections had sufficient flexibility to be treated as
“pinned” connections for gravity loading and
“fixed” connections for lateral loading. Despite
these assumptions, the steel framing in these
structures was substantially stiffened and
strengthened by composite behavior with their
encasements and exhibited significant fixity at
framing connections for both lateral and gravity
loadings.
Soon connections where designed to use angles and split tees to connect the top and
bottom beam flanges to columns instead of large gusset plates to incorporate large glass panels
spanning from one column to the other. The next design improvement introduced was the
process of welding flanges and then riveted to beam flanges. An advantage of this system was
that the elements could be prepared in shops to desired lengths brought to site and then riveted.
Since riveting proved to be a costly process it was replaced by bolting.

11
A structure is said to behave in a ductile manner if it is capable of withstanding large
inelastic deformations without significant degradation in strength, and without the development
of instability and collapse. Steel moment frames achieve their ductility through yielding
developed in the beam column junction. The system is assumed to be capable of having
extensive yielding and plastic deformation without loss of strength. They are also responsible for
the dissipation of seismic energy during an earthquake. The plastic deformation includes plastic
rotation occurring in a beam. Many engineers believed that steel moment-frame buildings were
essentially invulnerable to earthquake-induced structural damage and thought that should such
damage occur, it would be limited to ductile yielding of members and connections. Earthquake-
induced collapse was not believed possible. Partly as a result of this belief, many large industrial,
commercial and institutional structures employing steel moment-frame systems were
constructed.
Almost from their inception as a means of building construction, engineers began to
observe that steel moment-frames seemed to exhibit superior performance in earthquakes. More
than 20 such structures were subjected to and survived the great 1906 San Francisco earthquake
and the fires that followed it, while few other buildings in the central commercial district of San
Francisco remained standing. Many of these steel frame buildings are still in service today. For
nearly 90 years, engineers continued to observe apparent superior performance of these
structures, building the reputation that they had superior earthquake-resisting capability. It is
worth noting that much of the seismic and fire resistance possessed by these structures was a
result of the composite interaction of the steel framing with the encasing masonry and concrete.
Modern steel structures typically do not have the benefit of these features.

12
As a result of the apparent superior performance of these structures, building codes of the
1960s adopted preferential design criteria for steel moment frames. Under these codes, buildings
having complete vertical load-carrying space frames as their lateral force resisting system could
be designed for two thirds of the seismic forces specified for braced frames and half the forces
specified for bearing wall structures. Further, these codes required such frames in buildings
exceeding 240 feet in height.
In the 1960s and 1970s, researchers began to perform cyclic laboratory testing of steel
moment framing. The researchers determined that some control on the proportioning and
detailing of these structures was necessary to obtain superior inelastic behavior in strong
earthquakes. Slowly, throughout the 1970s and 1980s, the building codes began to adopt the
recommendations of these researchers and require special design, configuration, and detailing of
steel moment frames used for seismic resistance in regions of high seismic risk. Frames
conforming to these design criteria were first designated as Ductile Moment Resisting Space
Frames, and then finally, in 1988, as Special Moment-Resisting Space Frames. The term
"special" was adopted, both because special criteria applied to the design of these structures and
also because special, superior behavior was anticipated of them in strong earthquakes.
Initially, the special design criteria were limited to a requirement that connections be
capable of developing the strength of the connected members, with the WUF-B connection
identified as a deemed-to-comply standard. Later, requirements were introduced to provide for
strong-column/weak-beam behavior, balance of the shear strength of panel zones with beam
flexural capacity, and addition of section compactness and lateral bracing criteria. Building codes
of this era required the use of ductile moment-resisting space frames in all structures exceeding
240 feet in height in zones of high risk of experiencing strong ground motion. As a result, nearly

13
Figure 6 Fracture of a column flange and web
at a moment connection due to the Northridge
earthquake
http://www.propertyrisk.com/refcentr/steel.ht
m
every tall building constructed in the western U.S. in this era was of steel moment-frame
construction. Such structures designed in the 1960s and 1970s tended to employ moment-
resisting connections at every beam-column joint, providing great redundancy and distribution of
lateral force resistance. However, by the 1980s engineers had begun to economize their designs
and minimize expensive field welding by using fewer bays of moment-resisting framing that
employed heavier beams and columns, resulting in less redundant structures with more
concentrated lateral force resistance. In extreme cases, some tall structures were provided with
only a single bay of moment-resisting framing on each side of the building.
Following the 1994 Northridge
earthquake, engineers were surprised to
discover that a number of modern special
moment-resisting frame structures had
experienced unanticipated brittle fracturing
of their welded beam-column connections.
Similar damage occurred one year later, in
the 1995 Kobe, Japan earthquake.
Following these discoveries, a consortium
of professional associations and researchers,
known as the SAC Joint Venture, engaged in a federally funded, multi-year program of research
and development to determine the causes of this unanticipated behavior and to develop
recommendations for more robust moment frame construction. Conducted at a cost of $12
million over eight years, the SAC research determined the fractures were a result of the basic
connection geometry, lack of control of base material properties, the use of weld filler metals

14
with inherent low toughness, uncontrolled deposition rates, inadequate quality control and other
factors. The resulting research is the basis for the current steel special moment frame code design
requirements.

15
CHAPTER 3 EARTHQUAKE RESISTANT SYSTEMS

Each structure needs to be designed to different levels of resistance. Certain buildings
like hospitals, power plants, dams and nuclear reactors have to be designed to resist extreme
earthquakes. These buildings must not only not collapse but also be operational after an
earthquake. Such buildings should be designed to resist earthquakes of the highest magnitude.
Lateral load on a building is extremely variable unlike vertical load It increases with the height
of the building. Lateral systems do the role of transferring wind and earthquake load and also to
resist the effects due to secondary moment arising in columns due to the P-delta effect. The
Lateral load resisting systems also must limit inter-story drift.
Over the period of time research has developed a variety of systems that help build
structures that are economical and effective in resisting lateral load. Some of the already existing
systems used for earthquake and wind resistant design have been outlined in this chapter.
3.1 COMMON EARTHQUAKE RESISTANT SYSTEMS: PASSIVE SYSTEMS
Some of the common structural systems used are : (Schierle)
3.1.1 MOMENT RESISTING FRAMES :

Moment resisting frames were one of the first systems developed to help buildings resist
seismic load. The ductility provided by this type of framing provides elasticity to structures
sufficient enough to create repairable damage and prevent buildings from collapse. They can be
constructed of composite materials.

16
Figure 7 Seismic braced rfame system.
http://www.aisc.org
3.1.2 BRACED FRAME

As the name suggests, this system braces the building frame with triangular braces
providing more lateral resistance than moment frames – thus more stiffness but less ductility.
Braced frames are essentially of two types.
 Concentric braced frame
 Eccentric braced frame
Most braced frame systems are
designed as concentric brace system. In
concentric brace system the centroid of every
member must pass through the same point.
Eccentric braced frame structures utilize axis
offsets to deliberately introduce flexure and
shear into beams. They are more ductile than
concentric braced frames but more stiff than
moment frames. They are designed particularly to accommodate eccentricity on connections.
During a severe earthquake the eccentric beams yields either in shear or in bending, dissipating
energy. Braced frames can be configured to various forms. The most effective type is the fully
triangulated vertical truss.
While concentric braced frames consist of triangles, eccentric braced frames form
trapezoids. The brace offset from the post provides ductility.

17
3.1.3 FRAMED TUBE STRUCTURES:

This system was invented by Fazlur Khan among several other systems. In this system
the structural system of the building is placed on the exterior façade thus wrapping the space
within and making use of this external periphery to resist lateral loads. By placing the lateral
resistance system on the exterior tall buildings are able to achieve greater stability. However the
system is a very cost consuming proposal because of the numerous moment resistant joints
between beams and closely spaced columns. The system represents a hollow tube thus deriving
its name. Unlike a bundled tube it is subjected to shear lag since shear is transferred only at
outside walls, while bundled tubes transfer shear also at inner walls. The lateral resistance is
increased in corner columns and decreased at inner columns.

Figure 8 Belt Truss And Outrigger
3.1.4 BELT TRUSS AND OUTRIGGER :

The belt truss system consists of trusses that transfer shear from the tension posts to
compression posts to reduce drift. They also connect the core to the outer columns at certain
locations to resist drift under lateral load. The main core may consist of braced core or shear wall

18
core with outriggers extending on both sides. When subjected to lateral load due to wind or
earthquake the outriggers reduce drift by transferring shear from the tension side to to the
compression side. Belt trusses are usually located at the mechanical floors. Belt trusses are very
effective for braced frames but ineffective for moment frame structures.
3.1.5 BUNDLED TUBE STRUCTURE:

Similar to a Framed tube structure, a bundled tube structure consists of 2 or more tubes
framed by closely spaced columns, interconnected to form a multi-cell tube. In this system shear
is resisted by frames in the lateral load direction. This system help overcome the shear lag
experienced in conventional frame tube structures by transferring shear not only at peripheral
frames but also by the frames separating the tubes. It is also possible to design a braced bundle
tube similar to the bundled framed tube. Braced bundled tubes provide greater stiffness but
disrupt spatial flow because of its triangulated bracing.

Figure 10 Lembaga Tabung Haji Building - Kula Lumpur with the section drawing showing the
inner tube form. http://theconstructor.org/structural-engg/high-rise-structures/5/
Figure 9 design of Outrigger and Belt truss system
http://www.fgg.uni-lj.si/kmk/esdep/master/wg14/l1500.htm

19
3.2 COMMON EARTHQUAKE RESISTANT SYSTEMS : ACTIVE SYSTEMS
3.2.1 BASE ISOLATOR
Definition: (civil engineering) “Components placed within a building (not always at the
base) which are relatively flexible in the lateral direction, yet can sustain the vertical load. When
an earthquake causes ground motions, base isolators allow the structure to respond much more
slowly than it would without them, resulting in lower seismic demand on the structure. Isolators
may be laminated steel with high-quality rubber pads, sometimes incorporating lead or other
energy-absorbing materials.” (Cheng, Hongping, & Lou, 2008)
Going beyond conventional solutions with the help of science and technology structural
engineers have developed new passive solutions to help buildings resist earthquake. Base
isolators are an ingenious but costly seismic isolation system. Although the idea of resting
structures on rollers was proposed many times the idea was always considered nonviable.
Base isolators where invented by Dr. Bill Robinson of Auckland New Zealand. (William
Robinson )Base isolators are one of the most successful but costly systems and also the most 7.
The system reduces oscillation by decoupling the structure from the horizontal ground motion by
interposing a layer to allow some horizontal movement of the structure and reduce the building
frequency. This system does not absorb the energy from ground motion but deflects it through
the dynamic system.

20
Figure 11 A base isolator with rubber bearings used in the foundation of a building
http://www.seismicisolation.com/
Working:
General practice of construction for building structures consist of building columns that
are anchored into the earth by the foundation system. The foundation is constructed on the hard
strata of earth. When implementing base isolators into a building the foundation system is
different. Two thick slab of concrete are constructed on the hard strata. Sandwiched between
them are the rollers or lead rubber bearings .Systems using lead rubber bearings are commonly
used in construction. Lead bearings have a central solid plug and the periphery is made up of
layers of rubber sandwiched together with layers of steel. These steel plates act as reinforcement
to the system. When an earthquake occurs the force of inertia causes the building to be displaced.
Base isolators act as a spacer, isolating the building from the ground.Thus there is no direct
contact between the earth and the structure, thus reducing the seismic impact on the building.

21
3.2.2 TYPES OF BASE ISOLATOR :
There are two types of base isolation systems:
 Elastomeric bearing system
 Sliding system
Of the two existing system the most commonly used system is the elastomeric bearing
system. Since rubber bearings are relatively easy to manufacture, have no moving parts, and are
resistant to environmental degradation it is a more durable option.
3.2.2.1 ELASTOMERIC BEARING SYSTEM :
This system is typified by the use of elastomeric bearings, the elastomer made of either
natural rubber or neoprene. In this system, the building or structure is decoupled from the
horizontal components of the earthquake ground motion by interposing a layer with low
horizontal stiffness between the structure and the foundation. This layer gives the structure a
fundamental frequency that is lower than its fixed-base frequency and also lower than the
predominant frequencies of the ground motion. The first dynamic mode of the isolated structure
involves deformation only in the isolation system, the structure above being relatively rigid. The
higher modes that will produce deformation in the structure are orthogonal to the first mode and
consequently also to the ground motion. These higher modes do not participate in the motion, so
that if there is high energy in the ground motion at these higher frequencies, this energy cannot
be transmitted into the structure. The isolation system does not absorb the earthquake energy, but
rather deflects it through the dynamics of the system. This type of isolation works when the

22
systemacts linear when un-dampened.Damping is beneficial to suppress any possible resonance
between building and ground frequency.
3.2.2.2 SLIDING SYSTEM
This works by limiting the transfer of shear across the isolation interface. Many
sliding systems have been proposed and some have been used. In China there are at least three
buildings on sliding systems that use a specially selected sand at the sliding interface. A type of
isolation containing a lead-bronze plate sliding on stainless steel with an elastomeric bearing has
been used for a nuclear power plant in South Africa. The friction-pendulum system is a sliding
system using a special interfacial material sliding on stainless steel and has been used for several
projects in the United States, for both new and retrofit construction.

23
Figure 12 Largest tuned mass damper made of steel has been used in Taipei 101 to
counteract the drift induced in the building by lateral loading.
http://blog.wolfram.com/2011/03/18/built-to-last-understanding-earthquake-
engineering/
3.3 TUNED MASS DAMPERS (TMD)
The TMDsystem was developed to reduce the amplitude of resonance that occurs in the
structure due to wind or seismic ground motion.
(Soong & Constantinou, 1994)

3.3.1 WORKING
The TMD system works on the principle of restricting the amplitude of drift in the
structure by counteracting the direction of force with the help of a heavy mass. This system was
initially invented in 1909 by H.Frahm a German physicist in order to reduce the continuous
rocking effect caused in a ship and also reduce vibrations in the hull. This system was only used
for ships until Jacob Pieter Den Hartog published this concept in a book on mechanical
vibrations however his proposed system was only applicable to bodies that oscillate along a
single axis, also known as single degree of freedom.

24
3.3.2 TYPES OF MASS DAMPERS
Tuned mass dampers are now used to reduce lateral drift due to wind load.They help in
tall buildings to resist multidirectional oscillation which thus helped structures counter lateral
loading due to heavy wind .The TMD system was first usedat the Sydney Tower 1970 at the time
the tallest structure in Sydney. The first office building with TMD was the City Corp tower New
York, built 1977. The TMD system has proved to be very successful ever since then and
continues to do so even today with very minor changes in the design proposal.
TMD are of the following types:
 Passive dampers
 Active dampers
 Semi Active dampers
3.3.2.1 PASSIVE DAMPERS
This is one of the oldest systems that is still in practical use. It is also considered to be the
most efficient and sustainable system. The passive system consists of three main components –
mass, damper and spring. This system helps dissipate the energy induced in the structure due to
wind or ground motion. The force induced in the damper is obtained from the kinetic energy of
the mass. In order to obtain the required dampness to counteract forces on tall buildings passive
damper system requires enormously large mass. Taipei 101 has one of the largest passive
dampers. Passive systems require large masses which occupy a lot of area and can prove to be
difficult in construction and assembly.

25
3.3.2.2 ACTIVE DAMPERS
This system unlike the passive system makes use of electrical power. Active damper
systems, unlike passive systems,require much smaller mass. To achieve the force required to be
induced in the damper active system require electrical power. This further enhances the force
induced into the mass. This system is not a very reliable system since during most natural
calamities electrical powers tend to be shut down rendering the system useless. Thus active
systems require a standby power generator.
3.3.2.3 SEMI ACTIVE DAMPERS
As the name suggests the semi active damper is similar to the active system but instead
of electrical power this system makes use of energy obtained from battery power. This system is
a much more sustainable system than the active system and also overcomes the shortcomings of
an active damper but has its own shortcomings

26
Figure 13 Visco elastic dampers placed in the steel trusses in the WTC
http://www.designcommunity.com/discussion/7551.html
3.4 VISCO ELEASTIC DAMPER
Another approach for controlling seismic damage in buildings and improving their
seismic performance is by installing Seismic Dampers such as diagonal braces.

WORKING
(Poalacci, Ciampi, & De Angelis)

These dampers act like the hydraulic shock absorbers in cars – much of the sudden jerks
are absorbed in the hydraulic fluids and only little is transmitted above to the chassis of the car.
When seismic energy is transmitted through them, dampers absorb part of it, and thus damp the
motion of the building.
One of the unique characteristics of viscoelastic materials is that their properties are
influenced by many parameters. They can include: frequency, temperature, dynamic strain rate,
static pre-load, time effects such as creep and relaxation, aging, and other irreversible effects. In
working with this class of materials, we strive to define the materials complex modulus (stiffness
and damping properties) as a function of these parameters. Most important of these include
temperature and frequency effects.

27
CHAPTER 4 ANALYSIS OF 21 STORIED 90ft X 90ft
STRUCTURE

4.1 DESIGN PAPRAMETERS :

The initial design parameters for the structure such as the column beam dimensions have
been calculated by hand .
The proposal has been tested on a 3 x 3 bay Moment frame structure.
1. Span (L) ………………………………………………………………………...…90 ft
2. Width (B)………………………………………………………………………….90 ft
3. Floor to Floor height (h)…………………………………………………………. 12 ft
4. Total height (H)……………………………………………………………….…..252 ft
5. No of storey (N) ………………………………………………………………21 ( G+20)

Figure 15 Floor Plan - (L) 90 ft x (B) 90ft –
3 Bay Layout

Figure 14 Building Section– G+ 20
Storey’s –
(floor to Floor height 12ft )

28
Table 1Material Properties 02 - Basic Mechanical Properties
Material UnitWeight UnitMass E1 G12 U12 A1
Kip/ft3 Kip-s2/ft4 Kip/ft2 Kip/ft2 1/F
4000Psi 1.5000E-01 4.6621E-03 519119.50 216299.79 0.200000 5.5000E-06
A615Gr60 4.9000E-01 1.5230E-02 4176000.00 6.5000E-06
A992Fy50 4.9000E-01 1.5230E-02 4176000.00 1606153.85 0.300000 6.5000E-06
4.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE:

External frame:
1. Column for 16-21 stories ……………………………………………………...W 14 x 370
2. Beam for 16-21 stories ………………………………………………………...W 21 X 68
3. Column for 11-15 stories ……………………………………………………...W 14 x 398
4. Beam for 11-15 stories ………………………………………………………..W 21 X 73
5. Column for 6-10 stories ………………………………………………………W 14 x 426
6. Beam for 6-10 stories ………………………………………………………....W 21 X 93
7. Column for 1- 5 stories ……………………………………………………….W 14 x 500
8. Beam for 1-5 stories ………………………………………………………….W 21 X 111
Internal structure:
9. Column for 16-21 stories …………………………………………………..W 14 x 370
10. Beam for 16-21 stories……………………………………………………..W 18 X 86
11. Column for 11-15 stories …………………………………………………..W 14 x 398
12. Beam for 11-15 stories…………………………………………………… W 18 X 97
13. Column for 6-10 stories …………………………………………………….W 14 x 426

29
14. Beam for 6-10 stories……………………………………………………….W 18X 106
15. Column for 1- 5 stories …………………………………………………….W 14 x 500
16. Beam for 1-5 stories………………………………………………………..W 18 X 119
Corner columns : …………………………………………….Built up box section of W 14 x 342
Brace section for SMF: ………………………………………………………………W14 x 109
Un-braced beam length (minor & LTB): ……………………………………………………0.2
Table 2Material Properties 03a - Steel Data
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A992Fy50 7200.00 9360.00 -0.100000

Table 3: Material Properties 03e - Rebar Data
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A615Gr60 8640.00 12960.00 -0.100000

CONCRETE SLAB DESIGN OF MOMENT FRAME STRUCTURE:
1. Concrete :………………………………………………………………….4000psi
2. Section : ………………………………………………………………30 ft x 30 ft
3. Thickness: …………………………………………………………………6 inch.

30
4. Rebar layout : …………………………………………………………….Default.
5. Total no of sections …………………………………………………………..180
Table 4 Material Properties 03b - Concrete Data
Material Fc FinalSlope
Kip/ft2
4000Psi 576.00 -0.100000

Table 5Area Section Properties, Part 1 of 3
Section Material AreaType Type DrillDOF Thickness BendThick F11Mod
ft ft
6" THK
SLAB
4000Psi Shell Shell-
Thick
Yes 0.50000 0.50000 1.000000

Table 6 Area Section Properties, Part 2 of 3
Section F22Mod F12Mod M11Mod M22Mod M12Mod V13Mod V23Mod MMod

6" THK
SLAB
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

31
Table 7 Area Section Properties, Part 3 of 3
Section WMod

6" THK SLAB 1.000000

4.2 LOAD CASES

4.2.1. DEAD LOAD
4.2.2. LIVE LOAD
4.2.3. SEISMIC ( X & Y AXIS )
4.2.4. WIND ( X & Y AXIS)
Table 8 Case - Static 1 - Load Assignments
Case LoadType LoadName LoadSF

DEAD Load pattern DEAD 1.000000
LIVE Load pattern LIVE 1.000000
SEISMIC X Load pattern SEISMIC X 1.000000
SEISMIC Y Load pattern SEISMIC Y 1.000000
WIND Load pattern WIND 1.000000
WIND- 90 Load pattern WIND- 90 1.000000

32
4.2.1 DEAD LOAD :

1. Total Self-weight of steel : ………………………………………………3390.5 kips
2. Total Self-weight of concrete:……………………………………………12757 kips
3. a. Façade ……………………………………………………………………….7 psf
b. MEP & ceiling ……………………………………………………………..10 psf
c. Partitions& Finishes …………………………………………………………15 psf
d. Secondary Beams……………………………………………………………..5 psf
e. Deck …………………………………………………………………………..3psf
TOTAL MISCELLANEOUS DEAD LOAD: ………………………………..40 psf.
4.2.2 LIVE LOAD: ……………………………………………………………………………….100 psf.
Table 9 Load Pattern Definitions
LoadPat DesignType SelfWtMult AutoLoad

SEISMIC X QUAKE 0.000000 IBC2006
SEISMIC Y QUAKE 0.000000 IBC2006
WIND WIND 0.000000 ASCE7-05
WIND- 90 WIND 0.000000 ASCE7-05

33
4.2.2 SEISMIC LOAD.( ALONG X & Y AXIS)
4.2.2.1 ORDINARY MOMENT FRAME:

1. Location :( USC) Los Angeles - 90089
2. Site Class: D
3. Site Coefficient, Fa………………………………………………..………………….1
4. Site Coefficient, Fv…………………………………………………………………1.5
5. SDS ……………………………………………………………………………….1.23
6. SD1………………………………………………………………………………0.641
7. Response Modification (R) ......................................................................................3.5
8. System Over strength Ω -..…………………………………………………………...3
9. Deflection Amplification, Cd –………………………………………………………3
4.2.2.2 SPECIAL MOMENT FRAME : (SMF)
1. Location: USC 90089
2. Site Class ………………………………………………………………………….…D
3. Site Coefficient, Fa………………………………………………..…………………1
4. Site Coefficient, Fv………………………………………………………………...1.5
5. SDS ………………………………………………………………………………1.23
6. SD1……………………………………………………………………………....0.641

34
7. Response Modification (R) .........................................................................................8
8. System Over strength, Ω - ..………………………………………………………….3
9. Deflection Amplification, Cd –……………………………………………………,,5.5
4.2.2.3 SPECIAL CONCENTRIC BRACED FRAME: (SCBF)

1. Location: USC 90089
2. Site Class: ……………………………………………………………………………..D
3. Site Coefficient, Fa…………………………………………………………….……....1
4. Site Coefficient, Fv……………………………………………………………………………1.5
5. SDS …………………………………………………………………………………1.23
6. SD1………………………………………………………………………...………0.641
7. Response Modification (R) .........................................................................................7.5
8. System Over strength , Ω - ..…………………………………………………………2.5
9. Deflection Amplification, Cd –………………………………………………………5.5
4.2.3 WIND LOAD

1. Wind Direction ………………………………………………………………..0 & 90
2. Windward Coefficient (Cp)………………………………………………………..0.8
3. Leeward Coefficient (Cp) …………………………………………………………0.5

35
4. Wind Speed ……………………………………………………………………85mph
5. Exposure type ……………………………………………………………………… C
6. Gust Factor………………………………………………………………………..0.85
7. Directionality Factor, Kd………………………………… ……………………… 0.85
Table 10 Auto Wind - ASCE7-05, Part 1 of 2
LoadPat Angle WindwardCp LeewardCp ASCECase E1 E2 Wind
Speed
Exposure
Degree mph
WIND 0.000 0.80000 0.50000 1 0.000 0.000 85.00 C
WIND-
90
90.000 0.80000 0.50000 1 0.1500 0.150 85.00 C
Table 11 Auto Wind - ASCE7-05, Part 2 of 2
LoadPat
I Kzt GustFactor Kd

WIND 1 1 0.85 0.85
WIND- 90 1 1 0.85 0.85

36
Table 12 Load Combination Definitions
ComboName ComboType CaseName ScaleFactor
DSTL1 Linear Add DEAD 1.4
DSTL2 Linear Add DEAD 1.2
DSTL2 LIVE 1.6
DSTL3 Linear Add DEAD 1.2
DSTL3 LIVE 1
DSTL3 WIND 1.6
DSTL4 Linear Add DEAD 1.2
DSTL4 LIVE 1
DSTL4 WIND -1.6
DSTL5 Linear Add DEAD 1.2
DSTL5 LIVE 1
DSTL5 WIND- 90 1.6
DSTL6 Linear Add DEAD 1.2
DSTL6 LIVE 1
DSTL6 WIND- 90 -1.6
DSTL7 Linear Add DEAD 0.9
DSTL7 WIND 1.6

37
DSTL8 Linear Add DEAD 0.9
DSTL8 WIND -1.6
DSTL9 Linear Add DEAD 0.9
DSTL9 WIND- 90 1.6
DSTL10 Linear Add DEAD 0.9
DSTL10 WIND- 90 -1.6
DSTL11 Linear Add DEAD 1.3
DSTL11 LIVE 1
DSTL11 SEISMIC X 1
DSTL12 Linear Add DEAD 1.3
DSTL12 LIVE 1
DSTL12 SEISMIC X -1
DSTL13 Linear Add DEAD 1.3
DSTL13 LIVE 1
DSTL13 SEISMIC Y 1

Table : 12 Continued

38
Figure 16 Curved braces with 3
different radii used to analyze the
system
4.3 ANALYSIS :

With the model data set as per IBC 2006 and ASCE 705 for seismic and wind loading
respectively the model was calibrated in SAP2000 to check for steel design. The aim of the
analysis was to check the reduction in drift on introducing a diagonal curved brace in existing
Moment frame structures and to compare if the use of curved braces were economically
beneficial as compared to one of the common –most efficient seismic solution for structures –
braced frame structural system. The moment frame was then retrofitted to reduce drift in the
following ways :
1. Peripheral bracing
2. Bracing along the core axis
3. A diagonal straight brace along the façade
4. A curved diagonal brace along the façade.
The curved brace system was further analyzed for 3
types of curved brace each having different radii as shown in
the figure. The curved braces were also analyzed for both fixed
joints and hinged joints.
Each model was analyzed in SAP to check for the
following issues before analyzing the system for the drift
induced.
1. Steel design check for Overstress on beams and
columns due to shear /Axial forces/ Bending moment.

39
2. The mass of the structure after retrofitting the moment frame structure was kept constant
for all retrofit models.
 Mass of concrete = 12757 kips.
 Mass of steel = 3585 kips (+ or – 3kips)
Gravity steel versus wind premium check = 3585000/90 x 90x 21 = 21.07 ( OK)

Figure 17 Gavity steel versus wind premium check

3. All sections were Seismically compact
4. Column to beam ratio was maintained.
5. All loads on the structure were as per calculations.
The deflection data obtained due to seismic and wind loading along both aces was extracted
from the analysis run on SAP and the different results were compared as follows.

40
4.4 SYSTEMS ANALYZED

Figure 18 Different Systems Analyzed for a Layout of 90X 90X 252 FT

Moment
Frame
Structure
Core
BracedFrame
Structure
Peripheral
Braced Frame
Structure
Diagonal
Straight
Braceframe
Diagonal
Curved
Braceframe

41
4.5 BASE SHEAR
Table 13 Base shear of Existing Systems along the X axis
GLOBAL Fx
MOMENT CORE
BRACE
FRAME
PERIPHERAL
BRACE
FRAME
DIAGONAL STRAIGHT
BRACEFRAME

SEISMIC X -874 -884 -880 -885
SEISMIC Y 0 0 0 0
WIND X -533 -533 -533 -533
WIND Y 0 0 0 0

Table 14 Base Shear of Existing Systems along the Y axis
GLOBAL Fy
MOMENT CORE
BRACE
FRAME
PERIPHERAL
BRACE FRAME
DIAGONAL
STRAIGHT
BRACEFRAME

SEISMIC X 0 0 0 0
SEISMIC Y -874 -884 -880 -885
WIND X 0 0 0 0
WIND Y -533 -533 -533 -533

42
Table 15 Base Shear of Diagonal Curved Brace - Fixed at each end – Along the X axis.
GLOBAL
Fx

DIAGONAL
CONCAVE
CURVED BRACE--
1FIXED JOINTS
DIAGONAL
CONCAVE
CURVED
BRACE—2
FIXED
JOINTS
DIAGONAL
CONCAVE
CURVED
BRACE—3
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—1
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—2
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—3
FIXED
JOINTS

SEISMIC X -885 -885 -885 -885 -885 -885
SEISMIC Y 0 0 0 0 0 0
WIND X -533 -533 -533 -533 -533 -533
WIND Y 0 0 0 0 0 0

43
Table 16 Base Shear of Diagonal Curved Brace - Fixed at each end – Along the Y axis
GLOBAL Fy
DIAGONAL
CONCAVE
CURVED
BRACE--
1FIXED
JOINTS
DIAGONAL
CONCAVE
CURVED
BRACE—2
FIXED
JOINTS
DIAGONAL
CONCAVE
CURVED
BRACE—3
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—1
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—2
FIXED
JOINTS
DIAGONAL
CONVEX
CURVED
BRACE—3
FIXED
JOINTS

SEISMIC X 0 0 0 0 0 0
SEISMIC Y -885 -885 -885 -885 -885 -885
WIND X 0 0 0 0 0 0
WIND Y -533 -533 -533 -533 -533 -533

4.6 ANALYSIS FOR DRIFT

From the data extracted from the analysis in SAP , the deflection obtained due to seismic
and wind loading were compared in the following stages to check efficiency of the various
systems in progression .

Case 1. The first step was to compare the reduction in drift (U1) to the moment frame
structure when retrofitted by bracing the periphery, the core axial bracing and a straight
diagonal brace.

44
Case 2. The 3 different curved braces were analyzed both as a concave brace to the
structure and a convex brace as shown in the figure. All brace members were designed to
be fixed at both ends to the structure.

Case 3. The 3 different curved braces were analyzed both as a concave brace to the
structure and a convex brace and all brace members were designed to be pinned at both
ends to the structure.

Case 4. The curved brace system reducing deflection to the minimal was then compared
with the systems in the first comparison to conclude which system induced least
deflection on retrofitting the moment frame.

45
4.6.1 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS
4.6.1.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 17 Deflection (in ft) in the X axis due to Seismic loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 1.567 0.253 0.462 0.013
20 1.542 0.247 0.446 0.013
19 1.508 0.240 0.426 0.013
18 1.462 0.231 0.404 0.013
17 1.405 0.221 0.380 0.012
16 1.339 0.209 0.354 0.012
15 1.264 0.197 0.327 0.011
14 1.182 0.185 0.299 0.010
13 1.094 0.172 0.270 0.010
12 1.002 0.158 0.243 0.009
11 0.908 0.143 0.216 0.008
10 0.814 0.128 0.189 0.008
9 0.719 0.114 0.163 0.007
8 0.624 0.101 0.140 0.006
7 0.530 0.088 0.119 0.005
6 0.440 0.076 0.098 0.005
5 0.351 0.064 0.079 0.004
4 0.263 0.051 0.061 0.003
3 0.178 0.039 0.044 0.002
2 0.098 0.027 0.029 0.001
1 0.032 0.014 0.014 0.001
GRND 0.000 0.000 0.000 0.000

46

Figure 19 Deflection (in ft) due to Seismic loading along the X axis

Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably from 1.6 to 0.4-0.5 feet . Of the
mentioned systems the peripheral brace minimizes deflection caused due to seismic loading as
compared to deflection caused by using a diagonal braced frame system. Going further from this
conclusion the next comparison was conducted to study a diagonal curved brace system.

0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
PERIPHERAL BRACE
CORE BRACE
DIAGONAL STRAIGHT

47
4.6.1.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

It was evident in the previous chart a peripheral braced system functioned much more
efficient than a diagonal straight brace system. The next study was conducted to study the effect
of a curved diagonal brace system in comparison to straight brace frame system. The brace
members vary in form and radii. The curves are distinguished by 3 different radii and each radius
has been tested for a concave and convex form generating 6 different brace for analysis. Each of
the brace has a fixed joint at both end.

48
Table 18 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX -
BRACE 3 -
FIXED
21 0.49 0.39 0.44 0.45 0.40 0.44
20 0.47 0.38 0.43 0.45 0.41 0.44
19 0.44 0.36 0.42 0.45 0.41 0.44
18 0.41 0.34 0.40 0.45 0.40 0.43
17 0.39 0.33 0.39 0.43 0.39 0.42
16 0.36 0.31 0.37 0.41 0.37 0.40
15 0.33 0.29 0.35 0.39 0.36 0.39
14 0.30 0.26 0.32 0.37 0.34 0.38
13 0.27 0.24 0.29 0.35 0.33 0.36
12 0.24 0.21 0.26 0.33 0.31 0.35
11 0.21 0.19 0.22 0.31 0.29 0.33
10 0.18 0.16 0.19 0.28 0.27 0.30
9 0.15 0.13 0.16 0.25 0.24 0.28
8 0.12 0.11 0.14 0.22 0.21 0.26
7 0.10 0.09 0.12 0.19 0.19 0.23
6 0.09 0.08 0.10 0.16 0.17 0.21
5 0.07 0.06 0.08 0.14 0.14 0.18
4 0.05 0.04 0.06 0.11 0.12 0.15
3 0.03 0.03 0.04 0.08 0.09 0.11
2 0.02 0.02 0.02 0.05 0.05 0.06
1 0.01 0.01 0.01 0.02 0.02 0.02
GRND 0.00 0.00 0.00 0.00 0.00 0.00

49
0
0.1
0.2
0.3
0.4
0.5
0.6
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CONCAVE -BRACE 1 -FIXED
CONCAVE -BRACE 2 -FIXED
CONCAVE -BRACE 3 -FIXED
CONVEX -BRACE 1 -FIXED
CONVEX -BRACE 2 -FIXED
CONVEX -BRACE 3 -FIXED

Figure 20 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces fixed at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the concave brace -2 with fixed ends achieves least
deflection. Thus concluding the concave brace with the intermediate radii to be the most efficient
of the curved braces analyzed, that are fixed at both ends.

50
4.6.1.3 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

The previous case studied the efficiency of curved frames with fixed joints at both ends.
Thus the next step was to analyze which of the six curved brace system performed better if both
ends of the brace was pinned.
Table 19 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces pinned at both ends.
CONCAVE
-BRACE 1
-PINNED
CONCAVE -
BRACE 2 -
PINNED
CONCAVE
-BRACE 3
-PINNED
CONVEX -
BRACE 1 -
PINNED
CONVEX -
BRACE 2 -
PINNED
CONVEX -
BRACE 3 -
PINNED
21 0.54 0.51 0.48 0.43 0.46 0.57
20 0.52 0.49 0.48 0.43 0.46 0.57
19 0.50 0.48 0.47 0.43 0.46 0.57
18 0.47 0.46 0.45 0.42 0.45 0.56
17 0.44 0.43 0.43 0.41 0.44 0.54
16 0.41 0.40 0.41 0.39 0.42 0.53
15 0.37 0.37 0.38 0.37 0.41 0.52
14 0.33 0.34 0.34 0.36 0.39 0.50
13 0.29 0.30 0.31 0.34 0.37 0.48
12 0.26 0.26 0.27 0.32 0.36 0.46
11 0.22 0.23 0.23 0.30 0.34 0.43
10 0.19 0.20 0.20 0.28 0.31 0.41
9 0.16 0.17 0.18 0.25 0.28 0.38

51
8 0.13 0.14 0.15 0.22 0.26 0.34
7 0.11 0.12 0.13 0.20 0.23 0.31
6 0.09 0.10 0.11 0.17 0.20 0.27
5 0.07 0.08 0.09 0.14 0.17 0.23
4 0.05 0.06 0.06 0.11 0.13 0.18
3 0.04 0.04 0.04 0.08 0.10 0.13
2 0.02 0.02 0.02 0.05 0.06 0.07
1 0.01 0.01 0.01 0.02 0.02 0.03
GRND 0.00 0.00 0.00 0.00 0.00 0.00

Continued…
Table : 19 Continued

52
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CONCAVE -BRACE 1 -PINNED
CONCAVE -BRACE 2 -PINNED
CONCAVE -BRACE 3 -PINNED
CONVEX -BRACE 1 -PINNED
CONVEX -BRACE 2 -PINNED
CONVEX -BRACE 3 -PINNED

Figure 21 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces pinned at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the convex pinned system decreases the deflection on
the upper stories while concave pinned system reduces deflection in the upper stories but
increases deflection in lower stories.

53
4.6.1.4 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

Figure 22 Deflection (in ft) in the X axis due to Seismic loading along the X axis

Conclusion:
Comparative study of the existing braced frame systems with the diagonal straight frame
and curved brace system indicates that a concave curved brace system reduces drift more
efficiently than the other systems.

0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MOMENT
MOMENT FRAME (same mass)
PERIPHERAL BRACE
CORE BRACE
DIAGONAL STRAIGHT
CONCAVE -BRACE 2 -FIXED

54
4.6.2 DRIFT DUE TO SEISMIC LOADING ALONG THE Y AXIS

4.6.2.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 20 Deflection (in ft) due to Seismic loading along the Y axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 1.70 0.47 0.40 0.41
20 1.68 0.45 0.39 0.42
19 1.64 0.43 0.38 0.42
18 1.59 0.41 0.37 0.41
17 1.53 0.38 0.36 0.40
16 1.46 0.36 0.34 0.38
15 1.38 0.33 0.33 0.36
14 1.29 0.31 0.31 0.33
13 1.19 0.28 0.29 0.30
12 1.09 0.25 0.27 0.27
11 0.99 0.23 0.25 0.25
10 0.89 0.20 0.23 0.23
9 0.79 0.18 0.21 0.21
8 0.69 0.15 0.18 0.18
7 0.59 0.13 0.16 0.15
6 0.49 0.11 0.14 0.12
5 0.40 0.09 0.12 0.10
4 0.30 0.07 0.09 0.08
3 0.21 0.05 0.07 0.06
2 0.12 0.04 0.05 0.04
1 0.04 0.02 0.02 0.01
GRND 0.00 0.00 0.00 0.00

55

Figure 23Deflection (in ft) due to Seismic loading along the y axis

Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably. In comparison to the efficiency of the
systems with respect to reduction in drift a peripheral brace frame structure performs better than
a diagonal straight brace frame system.

0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE

56
4.6.2.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 21 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
-FIXED
21 0.48 0.38 0.43 0.45 0.40 0.44
20 0.46 0.37 0.42 0.45 0.41 0.44
19 0.44 0.35 0.41 0.45 0.41 0.44
18 0.41 0.33 0.39 0.44 0.40 0.43
17 0.38 0.31 0.38 0.43 0.39 0.42
16 0.35 0.30 0.36 0.41 0.37 0.41
15 0.32 0.28 0.34 0.39 0.36 0.40
14 0.29 0.25 0.31 0.37 0.34 0.38
13 0.26 0.23 0.28 0.35 0.33 0.37
12 0.23 0.21 0.25 0.33 0.31 0.36
11 0.21 0.18 0.21 0.31 0.29 0.33
10 0.18 0.15 0.18 0.28 0.27 0.31
9 0.14 0.12 0.16 0.25 0.24 0.29
8 0.12 0.10 0.14 0.22 0.22 0.27
7 0.10 0.09 0.12 0.19 0.20 0.25
6 0.08 0.07 0.10 0.17 0.18 0.22
5 0.07 0.06 0.08 0.14 0.15 0.20
4 0.05 0.04 0.05 0.12 0.13 0.16
3 0.03 0.03 0.04 0.09 0.10 0.12
2 0.02 0.01 0.02 0.06 0.06 0.08
1 0.01 0.01 0.01 0.02 0.02 0.03
GRND 0.00 0.00 0.00 0.00 0.00 0.00

57
0
0.1
0.2
0.3
0.4
0.5
0.6
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED

Figure 24 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the concave brace -2 with fixed ends achieves least
deflection. Thus concluding the concave brace with the intermediate radii to be the most efficient
of the curved braces analyzed, that are fixed at both ends.

58
4.6.2.3 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 22 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces pinned at both ends.
CONCAVE -
BRACE 1 -
PINNED
CONCAVE -
BRACE 2 -
PINNED
CONCAVE -
BRACE 3 -
PINNED
CONVEX -
BRACE 1 -
PINNED
CONVEX -
BRACE 2 -
PINNED
CONVEX -
BRACE 3 -
PINNED
21 0.54 0.50 0.49 0.42 0.45 0.50
20 0.52 0.48 0.48 0.43 0.46 0.50
19 0.50 0.47 0.47 0.43 0.46 0.50
18 0.47 0.45 0.46 0.42 0.45 0.49
17 0.43 0.42 0.44 0.41 0.44 0.48
16 0.40 0.39 0.41 0.39 0.42 0.46
15 0.36 0.36 0.38 0.37 0.41 0.45
14 0.32 0.33 0.35 0.35 0.39 0.44
13 0.28 0.29 0.31 0.33 0.38 0.43
12 0.25 0.26 0.27 0.32 0.36 0.41
11 0.21 0.22 0.24 0.30 0.34 0.39
10 0.18 0.19 0.21 0.28 0.32 0.37
9 0.15 0.16 0.18 0.25 0.29 0.35
8 0.12 0.13 0.15 0.22 0.27 0.32
7 0.10 0.11 0.13 0.20 0.24 0.29
6 0.09 0.10 0.10 0.17 0.21 0.26
5 0.07 0.08 0.08 0.15 0.18 0.22
4 0.05 0.06 0.06 0.12 0.15 0.18
3 0.03 0.04 0.04 0.09 0.11 0.13
2 0.02 0.02 0.02 0.05 0.07 0.08
1 0.01 0.01 0.01 0.02 0.02 0.03
GRND 0.00 0.00 0.00 0.00 0.00 0.00

59
0
0.05
0.1
0.15
0.2
0.25
CURVED CONCAVE BRACE 1-
PINNED
CURVED CONCAVE BRACE 2-
PINNED
CURVED CONCAVE BRACE 3-
PINNED
CURVED CONVEX BRACE 1-
PINNED
CURVED CONCVEX BRACE 2-
PINNED
CURVED CONVEX BRACE 3-
PINNED

Figure 25 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the convex pinned system decreases the deflection on
the upper stories while concave pinned system reduces deflection in the upper stories but
increases deflection in lower stories. Thus use of a convex brace system may not be efficient due
to the extremities in deflection caused in the upper n lower stories.

60
4.6.2.4 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

OVERALL COMPARISON :

Figure 26 Deflection (in ft) due to Seismic loading along the Y axis

Conclusion:
Comparative study of the existing braced frame systems with the diagonal straight frame
and curved brace system indicates that a concave curved brace system with fixed ends reduces
drift more efficiently than the other systems.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MOMENT
MOMENT (Same Mass)
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 2-
FIXED

61
4.6.3 DRIFT DUE TO WIND LOADING ALONG THE X AXIS
4.6.4 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 23 Deflection (in ft) due to Seismic loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 0.62 0.11 0.19 0.17
20 0.62 0.11 0.18 0.17
19 0.61 0.11 0.17 0.17
18 0.60 0.10 0.17 0.17
17 0.58 0.10 0.16 0.17
16 0.56 0.10 0.15 0.16
15 0.54 0.09 0.14 0.15
14 0.52 0.09 0.13 0.14
13 0.49 0.08 0.12 0.14
12 0.46 0.08 0.11 0.13
11 0.42 0.07 0.10 0.12
10 0.39 0.07 0.09 0.11
9 0.35 0.06 0.08 0.10
8 0.31 0.05 0.07 0.09
7 0.27 0.05 0.06 0.08
6 0.23 0.04 0.05 0.07
5 0.19 0.04 0.04 0.05
4 0.14 0.03 0.03 0.04
3 0.10 0.02 0.03 0.03
2 0.06 0.02 0.02 0.02
1 0.02 0.01 0.01 0.01
GRND 0.00 0.00 0.00 0.00

62

Figure 27 Deflection (in ft) in the X axis due to Wind load along the X axis

Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably from 1.6 to 0.1-0.2 feet. Of the
mentioned systems the peripheral brace minimizes deflection caused due to seismic loading as
compared to deflection caused by using a diagonal braced frame system. Going further from this
conclusion the next comparison was conducted to study a diagonal curved brace system.

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE

63
4.6.4.1 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 24 Deflection (in ft) due to Wind loading along the X axis by different diagonal curved
braces fixed at both ends.

CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
–FIXED
21 0.17 0.14 0.16 0.19 0.17 0.19
20 0.17 0.14 0.16 0.19 0.17 0.19
19 0.16 0.14 0.16 0.19 0.17 0.19
18 0.16 0.13 0.16 0.19 0.17 0.19
17 0.15 0.13 0.15 0.18 0.17 0.18
16 0.14 0.12 0.15 0.18 0.16 0.18
15 0.13 0.12 0.14 0.17 0.16 0.18
14 0.13 0.11 0.14 0.16 0.15 0.17
13 0.12 0.10 0.13 0.16 0.15 0.17
12 0.11 0.10 0.11 0.15 0.15 0.17
11 0.10 0.08 0.10 0.14 0.14 0.16
10 0.09 0.07 0.09 0.14 0.13 0.15
9 0.07 0.06 0.08 0.12 0.12 0.14
8 0.06 0.05 0.07 0.11 0.11 0.13
7 0.05 0.05 0.06 0.10 0.10 0.13
6 0.04 0.04 0.05 0.09 0.09 0.11
5 0.04 0.03 0.04 0.08 0.08 0.10
4 0.03 0.02 0.03 0.06 0.07 0.08
3 0.02 0.02 0.02 0.05 0.05 0.06
2 0.01 0.01 0.01 0.03 0.03 0.04
1 0.00 0.00 0.00 0.01 0.01 0.01
GRND 0.00 0.00 0.00 0.00 0.00 0.00

64
0
0.05
0.1
0.15
0.2
0.25
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
0.196229816
0.144534937
0.166500104
0.196229816
0.183158035
0.205454439

Figure 28Deflection (in ft) due to Windload along the X axis by different diagonal curved braces
fixed at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the concave brace -2 with fixed ends achieves least
deflection. Thus concluding the concave brace with the intermediate radii to be the most efficient
of the curved braces analyzed, that are fixed at both ends.

65
4.6.4.2 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 25 Deflection (in ft) due to Wind load along the X axis by different diagonal curved braces
pinned at both ends.
CONCAVE
-BRACE 1
-PINNED
CONCAVE
-BRACE 2
-PINNED
CONCAVE
-BRACE 3
-PINNED
CONVEX -
BRACE 1 -
PINNED
CONVEX -
BRACE 2 -
PINNED
CONVEX -
BRACE 3 -
PINNED
21 0.19 0.18 0.18 0.18 0.19 0.21
20 0.18 0.18 0.18 0.18 0.20 0.22
19 0.18 0.18 0.18 0.18 0.20 0.22
18 0.17 0.17 0.17 0.18 0.19 0.21
17 0.17 0.17 0.17 0.17 0.19 0.21
16 0.16 0.16 0.16 0.17 0.18 0.21
15 0.15 0.15 0.15 0.16 0.18 0.20
14 0.14 0.14 0.14 0.16 0.18 0.20
13 0.13 0.13 0.13 0.15 0.17 0.20
12 0.11 0.12 0.12 0.15 0.17 0.19
11 0.10 0.10 0.11 0.14 0.16 0.18
10 0.09 0.09 0.10 0.13 0.15 0.18
9 0.08 0.08 0.08 0.12 0.14 0.17
8 0.06 0.07 0.07 0.11 0.14 0.16
7 0.06 0.06 0.07 0.10 0.12 0.15
6 0.05 0.05 0.06 0.09 0.11 0.13
5 0.04 0.04 0.05 0.08 0.10 0.11
4 0.03 0.03 0.03 0.06 0.08 0.09
3 0.02 0.02 0.02 0.05 0.06 0.07
2 0.01 0.01 0.01 0.03 0.03 0.04
1 0.00 0.00 0.00 0.01 0.01 0.01
GRND 0.00 0.00 0.00 0.00 0.00 0.00

66
0
0.05
0.1
0.15
0.2
0.25
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
PINNED
CURVED CONCAVE BRACE 2-
PINNED
CURVED CONCAVE BRACE 3-
PINNED
CURVED CONVEX BRACE 1-
PINNED
CURVED CONCVEX BRACE 2-
PINNED
CURVED CONVEX BRACE 3-
PINNED

Figure 29 Deflection (in ft) due to Wind load along the X axis by different diagonal curved
braces pinned at both ends.

Conclusion:
It can be concluded from the above graph the concave pinned system works much more
efficient than the convex system when the bracing members have been pinned at both ends.

67
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
PINNED
4.6.4.3 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

Figure 30 Deflection (in ft) due to Wind loading along the X axis

Conclusion:
In the case of wind loading deflection caused must not be greater than height of the
building/500 .Thus considering a 21 storied building with a height of 252 feet the maximum
allowable deflection is 0.5 feet. The graph indicates that the intermediate curved concave braced
system minimizes the deflection to well below the maximum allowable limit and achieves the
least deflection as compared to the other systems.

68
4.6.5 DRIFT DUE TO WIND LOADING ALONG THE Y AXIS
4.6.5.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 26 Deflection (in ft) due to Wind loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 0.70 0.19 0.17 0.17
20 0.70 0.19 0.17 0.18
19 0.69 0.18 0.17 0.18
18 0.68 0.17 0.17 0.18
17 0.66 0.16 0.16 0.17
16 0.64 0.16 0.16 0.17
15 0.61 0.15 0.15 0.16
14 0.59 0.14 0.15 0.15
13 0.55 0.13 0.14 0.14
12 0.52 0.12 0.13 0.13
11 0.48 0.11 0.13 0.12
10 0.44 0.10 0.12 0.12
9 0.40 0.09 0.11 0.11
8 0.36 0.08 0.10 0.10
7 0.31 0.07 0.09 0.08
6 0.27 0.06 0.08 0.07
5 0.22 0.05 0.07 0.06
4 0.17 0.04 0.05 0.05
3 0.12 0.03 0.04 0.04
2 0.07 0.02 0.03 0.02
1 0.02 0.01 0.02 0.01
GRND 0.00 0.00 0.00 0.00

69
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE

Figure 31Deflection (in ft) due to Wind loading along the Y axis:

Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably from 1.6 to 0.1-0.2 feet. Of the
mentioned systems the peripheral brace minimizes deflection caused due to seismic loading as
compared to deflection caused by using a diagonal braced frame system. Going further from this
conclusion the next comparison was conducted to study a diagonal curved brace system.

70
4.6.5.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 27 Deflection (in ft) due to Wind loading along the X axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
-FIXED
21 0.20 0.14 0.17 0.20 0.18 0.21
20 0.20 0.14 0.17 0.20 0.18 0.21
19 0.20 0.14 0.16 0.20 0.18 0.21
18 0.20 0.14 0.16 0.20 0.18 0.20
17 0.19 0.13 0.16 0.19 0.18 0.20
16 0.19 0.13 0.16 0.19 0.17 0.20
15 0.18 0.12 0.15 0.18 0.17 0.19
14 0.17 0.12 0.14 0.17 0.17 0.19
13 0.17 0.11 0.13 0.17 0.16 0.19
12 0.16 0.10 0.12 0.16 0.16 0.18
11 0.16 0.09 0.10 0.16 0.15 0.17
10 0.15 0.07 0.09 0.15 0.14 0.17
9 0.13 0.06 0.08 0.13 0.13 0.16
8 0.12 0.06 0.07 0.12 0.12 0.15
7 0.11 0.05 0.06 0.11 0.12 0.14
6 0.10 0.04 0.05 0.10 0.11 0.13
5 0.09 0.03 0.04 0.09 0.09 0.12
4 0.07 0.03 0.03 0.07 0.08 0.10
3 0.06 0.02 0.02 0.06 0.06 0.07
2 0.04 0.01 0.01 0.04 0.04 0.05
1 0.01 0.00 0.01 0.01 0.02 0.02
GRND 0.00 0.00 0.00 0.00 0.00 0.00

71
0
0.05
0.1
0.15
0.2
0.25
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED

Figure 32Deflection (in ft) in the X axis due to Seismic loading along the X axis by different
diagonal curved braces fixed at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted with the concave brace -2 with fixed ends achieves
least deflection. Thus concluding the concave brace with the intermediate radii to be the most
efficient of the curved braces analyzed, that are fixed at both ends.

72
4.6.5.3 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 28 Deflection (in ft) due to Wind load along the X axis by different diagonal curved
braces pinned at both ends.
CONCAVE
-BRACE 1
-PINNED
CONCAVE
-BRACE 2 -
PINNED
CONCAVE
-BRACE 3 -
PINNED
CONVEX
-BRACE 1
-PINNED
CONVEX
-BRACE 2
-PINNED
CONVEX
-BRACE 3
-PINNED
21 0.19 0.19 0.19 0.20 0.21 0.23
20 0.19 0.18 0.19 0.20 0.21 0.23
19 0.19 0.18 0.19 0.20 0.21 0.23
18 0.19 0.18 0.18 0.20 0.21 0.23
17 0.19 0.17 0.18 0.19 0.20 0.23
16 0.18 0.17 0.17 0.19 0.20 0.22
15 0.17 0.16 0.17 0.18 0.20 0.22
14 0.17 0.15 0.15 0.17 0.19 0.22
13 0.16 0.13 0.14 0.17 0.19 0.22
12 0.16 0.12 0.13 0.16 0.18 0.21
11 0.15 0.11 0.11 0.16 0.18 0.20
10 0.14 0.09 0.10 0.15 0.17 0.20
9 0.13 0.08 0.09 0.13 0.16 0.19
8 0.12 0.07 0.08 0.12 0.15 0.18
7 0.11 0.06 0.07 0.11 0.14 0.17
6 0.10 0.05 0.06 0.10 0.13 0.15
5 0.09 0.04 0.05 0.09 0.11 0.13
4 0.07 0.03 0.04 0.07 0.09 0.11
3 0.06 0.02 0.03 0.06 0.07 0.08
2 0.03 0.01 0.02 0.04 0.04 0.05
1 0.01 0.00 0.01 0.01 0.02 0.02
GRND 0.00 0.00 0.00 0.00 0.00 0.00

73
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CONCAVE -BRACE 1 -PINNED
CONCAVE -BRACE 2 -PINNED
CONCAVE -BRACE 3 -PINNED
CONVEX -BRACE 1 -PINNED
CONVEX -BRACE 2 -PINNED
CONVEX -BRACE 3 -PINNED

Figure 33 Deflection (in ft) due to Wind load along the Y axis by different diagonal curved
braces pinned at both ends.

Conclusion:
From the above graph it can be concluded of the 6 different types of curved braces that
the moment frame structure was retrofitted the convex pinned system decreases the deflection on
the upper stories while concave pinned system reduces deflection in the upper stories but
increases deflection in lower stories.

74
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 2-
PINNED
4.6.5.4 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

Figure 34Deflection (in ft) due to Wind load along the y axis

Conclusion:
The above graph clearly shows that the curved brace system with a particular radii
produces lesser drift as compared to the other braced frame systems.

75
4.7 CONCLUSION

Deflection:
The above study has made it evident that although any general curved braced system does
not produce the lesser deflection- a curved brace system with a particular radii does produce
lesser deflection as compared to a peripheral or core brace frame system. The difference in
deflection is evident under both seismic and wind load .The drift produced by the curved system
is well within the code requirement.

Thus the proposed curved brace system does function with maximum efficiency in
reducing the drift caused by lateral loads in a structure with a square layout and 21 storied.
Testing this system further the next step is to analyze the system on a moment frame structure
with a rectangular layout to study if building form affects the efficiency of this system.

76
CHAPTER 5 ANALYSIS OF 21 STORIED 150ft X 90ft
STRUCTURE
5.1 DESIGN PAPRAMETERS :

The proposal has been tested on a 5 x 3 bay Moment frame structure.
1. Span (L) ………………………………………………………………………….. 15 0 ft
2. Width (B)……………………………………………………………………………90 ft
a. Floor to Floor height (h)…………………………………………………………….12 ft
b. Total height (H)……………………………………………………………………252 ft
c. No of storey (N) ……………………………………………………………..21 ( G+20)
Fig : 4.2 BUILDING PLAN – 150 FT X 90FT ( 30FT
X 30FT BAY)
Fig : 4.2 BUILDING SECTION – G+ 20 Storeys – (floor to Floor height 12ft )

77
Table 29 Material Properties 02 - Basic Mechanical Properties
Material UnitWeight UnitMass E1 G12 U12 A1
Kip/ft3 Kip-s2/ft4 Kip/ft2 Kip/ft2 1/F
4000Psi 1.5000E-01 4.6621E-03 519119.50 216299.79 0.200000 5.5000E-06
A615Gr60 4.9000E-01 1.5230E-02 4176000.00 6.5000E-06
A992Fy50 4.9000E-01 1.5230E-02 4176000.00 1606153.85 0.300000 6.5000E-06

5.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE:

External frame:
17. Column for 13-21 stories ……………………………………………………...W 14 x 426
18. Column for 7-12 stories ………………………………………………………W 14 x 500
19. Column for 1- 6 stories ………………………………………………………W 14 x 605
20. Beam for 18-21 stories ………………………………………………………. W 24 X 76
21. Beam for 18-21 stories ……………………………………………………… W 24X 84
22. Beam for 13-17 stories ……………………………………………………… W 24 X 73
23. Beam for 7-12 stories ………………………………………………………..W 24 X 94
24. Beam for 1-6 stories …………………………………………………………W 24 X 103
Internal structure
25. Column for 16-21 stories ……………………………………………………W 14 x 211
26. Beam for 16-21 stories……………………………………………………….W 18 X 86
27. Column for 11-15 stories ……………………………………………………W 14 x 311
28. Beam for 11-15 stories………………………………………………………W 18 X 97

78
29. Column for 6-10 stories …………………………………………………….W 14 x 426
30. Beam for 6-10 stories…………………………………………………………W 18X 119
31. Column for 1- 5 stories ………………………………………………………W 14 x 550
32. Beam for 1-5 stories………………………………………………………….W 18 X 130
Corner columns : ………………………………………………Built up box section of W 14 x 342
Brace section for SCBF (150 bay): …………………………………………………… W27x 102
Brace section for SCBF (90 bay): …..…………………………………………………W27x 146
Unbraced beam length (minor & LTB): ………………………………………………………0.2
Table 30 Material Properties 03a - Steel Data
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A992Fy50 7200.00 9360.00 -0.100000

Table 31 Material Properties 03e - Rebar Data
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A615Gr60 8640.00 12960.00 -0.100000

79
5.1.2 CONCRETE SLAB DESIGN OF MOMENT FRAME STRUCTURE:

6. Concrete :………………………………………………………………… 4000psi
7. Section : ………………………………………………………………30 ft x 30 ft
8. Thickness: ………………………………….………………………………6 inch.
9. Rebar layout : ……………………………………………………………..Default.
10. Total no of sections ………………………….………………………………. 300
Table 32 Material Properties 03b - Concrete Data
Material Fc FinalSlope
Kip/ft2
4000Psi 576.00 -0.100000

Table 33 Area Section Properties,
Section Material AreaType Type DrillDOF Thickness BendThick F11Mod
ft ft
6" THK
SLAB
4000Psi Shell Shell-
Thick
Yes 0.50000 0.50000 1.000000

80
Table 33: Continued

Section F22Mod F12Mod M11Mod M22Mod M12Mod V13Mod V23Mod WMod

6" THK
SLAB
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.000000

Table 33 : Continued

Section WMod

6" THK SLAB 1.000000

81
5.2 LOAD CASES

5.2.1 DEAD LOAD
5.2.2. LIVE LOAD
5.2.3. SEISMIC ( X & Y AXIS )
5.2.4. WIND ( X & Y AXIS)
Table 34 Case - Static 1 - Load Assignments

Case LoadType LoadName LoadSF

DEAD Load pattern DEAD 1.000000
LIVE Load pattern LIVE 1.000000
SEISMIC X Load pattern SEISMIC X 1.000000
SEISMIC Y Load pattern SEISMIC Y 1.000000
WIND Load pattern WIND 1.000000
WIND- 90 Load pattern WIND- 90 1.000000

5.2.1 DEAD LOAD:

1. Total Self-weight of steel (BRACED SYSTEM ) :………………………..5645 kips
2. Total Self-weight of concrete:……………………………………………21262 kips

82
3. a. Façade ……………………………………………………………………………..7 psf
b. MEP & ceiling …………………………………………………………..…...10 psf
c. Partitions & Finishes …………………………………………………………15 psf
d. Secondary Beams…………………………………………………….………..5 psf
e. Deck …………………………………...…………………………………..……3psf
TOTAL MISCELLANEOUS DEAD LOAD : ………………………………... 40 psf.
5.2.2 LIVE LOAD
LIVE LOAD………………………………………………….……………………100psf
Table 35 Load Pattern Definitions

LoadPat DesignType SelfWtMult AutoLoad

SEISMIC X QUAKE 0.000000 IBC2006
SEISMIC Y QUAKE 0.000000 IBC2006
WIND WIND 0.000000 ASCE7-05
WIND- 90 WIND 0.000000 ASCE7-05

83
5.2.3 SEISMIC LOAD.( ALONG X & Y AXIS)

5.2.3.1 ORDINARY MOMENT FRAME :
1. Location: (USC) Los Angeles - 90089
2. Site Class: D
3. Site Coefficient, Fa………………………………………………………………….…1
4. Site Coefficient, Fv……………………….………………………………………….1.5
5. SDS ………….……………………………………………………………………..1.23
6. SD1………………………………………………………………………………...0.641
7. Response Modification (R) .........................................................................................3.5
8. System Over strength, Ω - ..………………………………….………………………..3
9. Deflection Amplification, Cd –………………………………………………………. 3
5.2.3.2 SPECIAL MOMENT FRAME: (SMF)

1. Location: USC 90089
2. Site Class …………………………………………………………………………… D
3. Site Coefficient, Fa………………………………………………………………….…1
4. Site Coefficient, Fv……………………………………….………………………….1.5
5. SDS……………………………………………….………………………………..1.23
6. SD1…………………………………………………....…………………………...0.641

84
7. Response Modification (R) ...........................................................................................8
8. System Over strength, Ω -..……………………….…………………………………..3
9. Deflection Amplification, Cd –……………………………………………………. 5.5

5.2.3.3 SPECIAL CONCENTRIC BRACED FRAME : (SCBF)
1. Location: USC 90089
2. Site Class: ……………………………………………………………………………. D
3. Site Coefficient, Fa…………………………..…………………….……………….…1
4. Site Coefficient, Fv………………………………………………………………….1.5
5. SDS ………………………………………………………………………………..1.23
6. SD1………………………………………………………………………………...0.641
7. Response Modification (R) ......................................................................................7.5
8. System Over strength, Ω - ..……………………………… ………………………..2.5
9. Deflection Amplification, Cd –……………………………………………………. 5.5
5.2.4 4.2.4 WIND LOAD
1. Wind Direction ………………………………..………………………………..0 & 90
2. Windward Coefficient (Cp)…………………………………….. ………………….0.8
3. Leeward Coefficient (Cp) ………………………………………………………..…0.5
4. Wind Speed ……………………………………………………..………………85mph

85
5. Exposure type …………………………………………..…………………………… C
6. Gust Factor……………………………………..……………………………..…… 0.85
7. Directionality Factor, Kd………………………………………………………….. 0.85
Table 36 Auto Wind - ASCE7-05, Part 1 of 2

LoadPat Angle WindwardCp LeewardCp ASCECase E1 E2 Wind
Speed
Exposure
Degree mph
WIND 0.000 0.80000 0.50000 1 0.000 0.000 85.00 C
WIND-
90
90.000 0.80000 0.50000 1 0.1500 0.150 85.00 C

Table 37 Auto Wind - ASCE7-05, Part 2 of 2

LoadPat I Kzt GustFactor Kd SolidRatio

WIND 1.000000 1.000000 0.850000 0.850000
WIND- 90 1.000000 1.000000 0.850000 0.850000

86

Table 38 Combination Definitions

ComboName ComboType CaseName ScaleFactor

DSTL1 Linear Add DEAD 1.400000
DSTL2 Linear Add DEAD 1.200000
DSTL2 LIVE 1.600000
DSTL3 Linear Add DEAD 1.200000
DSTL3 LIVE 1.000000
DSTL3 WIND 1.600000
DSTL4 Linear Add DEAD 1.200000
DSTL4 LIVE 1.000000
DSTL4 WIND -1.600000
DSTL5 Linear Add DEAD 1.200000
DSTL5 LIVE 1.000000
DSTL5 WIND- 90 1.600000
DSTL6 Linear Add DEAD 1.200000
DSTL6 LIVE 1.000000
DSTL6 WIND- 90 -1.600000
DSTL7 Linear Add DEAD 0.900000
DSTL7 WIND 1.600000

87

ComboName ComboType CaseName ScaleFactor

DSTL8 Linear Add DEAD 0.900000
DSTL8 WIND -1.600000
DSTL9 Linear Add DEAD 0.900000
DSTL9 WIND- 90 1.600000
DSTL10 Linear Add DEAD 0.900000
DSTL10 WIND- 90 -1.600000
DSTL11 Linear Add DEAD 1.300000
DSTL11 LIVE 1.000000
DSTL11 SEISMIC X 1.000000
DSTL12 Linear Add DEAD 1.300000
DSTL12 LIVE 1.000000
DSTL12 SEISMIC X -1.000000
DSTL13 Linear Add DEAD 1.300000
DSTL13 LIVE 1.000000
DSTL13 SEISMIC Y 1.000000
DSTL14 Linear Add DEAD 1.300000
DSTL14 LIVE 1.000000
DSTL14 SEISMIC Y -1.000000
Table 38 : Continued

88

ComboName ComboType CaseName ScaleFactor

DSTL15 Linear Add DEAD 0.800000
DSTL15 SEISMIC X 1.000000
DSTL16 Linear Add DEAD 0.800000
DSTL16 SEISMIC X -1.000000
DSTL17 Linear Add DEAD 0.800000
DSTL17 SEISMIC Y 1.000000
DSTL18 Linear Add DEAD 0.800000
DSTL18 SEISMIC Y -1.000000
DSTL19 Linear Add DEAD 1.000000
DSTL20 Linear Add DEAD 1.000000
DSTL20 LIVE 1.000000

Table 38 : Continued

89
5.3 ANALYSIS:

The analysis run in the previous chapter proved the success of a curved brace of a
particular radius in producing the least deflection as compared to the other systems. In an attempt
to further study the efficiency of the system similar analysis were undergone on a 150 x 90 ft
structure to study the effect of the building form on the system.
4. Peripheral bracing
5. Bracing along the core axis
6. A diagonal straight brace along the façade
7. A curved diagonal brace along the façade.
The curved brace system was further analyzed for 3
types of curved brace each having a different radius as shown
in the figure. The curved braces were also analyzed for both
fixed joints and hinged joints.
Each model was analyzed in SAP to check for the following
issues before analyzing the system for the drift induced.
8. Steel design check for Overstress on beams and
columns due to shear /Axial forces/ Bending moment.
The mass of the structure after retrofitting the moment
frame structure was kept constant for all retrofit
models.

Figure 35 The diagonal straight brace
and curved brace with different radii

90
 Mass of concrete = 21262.5 kips.
 Mass of steel = 5645 kips (+ or – 3kips)
Gavity steel versus wind premium check = 5645000/150 x 90x 21) = 19.91 ( OK)
Figure 36 Gavity steel versus wind premium check
9. All sections were Seismically compact
10. Column to beam ratio was maintained.
11. All loads on the structure were as per calculations.
The deflection data obtained due to seismic and wind loading along both aces was extracted
from the analysis run on SAP and the different results were compared as follows.

91
5.4 SYSTEMS ANALYZED

Figure 37 Different Systems Analyzed for a Building of 90 X 150 X 252 ft

Moment
Frame
Structure
Core
BracedFrame
Structure
Peripheral
Braced Frame
Structure
Diagonal
Straight
Braceframe
Diagonal
Curved
Braceframe

92
5.4.1 BASE SHEAR
(kips)

Table 39 Base Shear of Existing Systems along the X axis
GLOBAL Fx
MOMENT CORE
BRACE
FRAME
PERIPHERAL
BRACE FRAME
DIAGONAL
STRAIGHT
BRACEFRAME
SEISMIC X -2055 -885 -2072 -2071
SEISMIC Y 0 0 0 0
WIND X -533 -533 -533 533
WIND Y 0 0 0 0

Table 40 base Shear of Existing Systems along the Y axis
MOMENT CORE
BRACE
FRAME
PERIPHERAL
BRACE FRAME
DIAGONAL
STRAIGHT
BRACEFRAME
SEISMIC X 0 0 0 0
SEISMIC Y -2055 -885 -2072 -2071
WIND X 0 0 0 0
WIND Y -533 -533 -533 533

93
Table 41 Base Shear of Diagonal Curved Brace- Fixed at both ends- along the X axis

GLOBAL Fy
Diagonal
Concave
Curved
Brace -1
Pinned
Joints
Diagonal
Concave
Curved
Brace -2
Pinned
Joints
Diagonal
Concave
Curved
Brace - 3
Pinned
Joints
Diagonal
Convex
Curved
Brace -1
Pinned
Joints
Diagonal
Convex
Curved
Brace -2
Pinned
Joints
Diagonal
Convex
Curved
Brace - 3
Pinned
Joints

SEISMIC X -2071 -2071 -2071 -2071 -2071 -2071
SEISMIC Y 0 0 0 0 0 0
WIND X -533 -533 -533 -533 -533 -533
WIND Y 0 0 0 0 0 0

94
Table 42 Base Shear of Diagonal Curved Braces- Fixed at both end - Along the Y axis

GLOBAL Fy
Diagonal
Concave
Curved
Brace -1
Pinned
Joints
Diagonal
Concave
Curved
Brace -2
Pinned
Joints
Diagonal
Concave
Curved
Brace - 3
Pinned
Joints
Diagonal
Convex
Curved
Brace -1
Pinned
Joints
Diagonal
Convex
Curved
Brace -2
Pinned
Joints
Diagonal
Convex
Curved
Brace - 3
Pinned
Joints

SEISMIC X 0 0 0 0 0 0
SEISMIC Y -2071 -2071 -2071 -2071 -2071 -2071
WIND X 0 0 0 0 0 0
WIND Y -533 -533 -533 -533 -533 -533

95
Table 43 Base Shear of Diagonal Curved Brace- Pinned at both ends- along the X axis

GLOBAL Fx
Diagonal
Concave
Curved
Brace -1
Pinned
Joints
Diagonal
Concave
Curved
Brace -2
Pinned
Joints
Diagonal
Concave
Curved
Brace - 3
Pinned
Joints
Diagonal
Convex
Curved
Brace -1
Pinned
Joints
Diagonal
Convex
Curved
Brace -2
Pinned
Joints
Diagonal
Convex
Curved
Brace - 3
Pinned
Joints

SEISMIC X -2071 -2071 -2071 -2071 -2071 -2071
SEISMIC Y 0 0 0 0 0 0
WIND X -533 -533 -533 -533 -533 -533
WIND Y 0 0 0 0 0 0

96
Table 44 Base Shear of Diagonal Curved Brace- Pinned at both ends- along the Y axis

GLOBAL Fy
Diagonal
Concave
Curved
Brace -1
Pinned
Joints
Diagonal
Concave
Curved
Brace -2
Pinned
Joints
Diagonal
Concave
Curved
Brace - 3
Pinned
Joints
Diagonal
Convex
Curved
Brace -1
Pinned
Joints
Diagonal
Convex
Curved
Brace -2
Pinned
Joints
Diagonal
Convex
Curved
Brace - 3
Pinned
Joints

SEISMIC X 0 0 0 0 0 0
SEISMIC Y -2071 -2071 -2071 -2071 -2071 -2071
WIND X 0 0 0 0 0 0
WIND Y -888 -888 -888 -888 -888 -888

97
Conclusion
From the data extracted from the analysis in SAP , the deflection obtained due to seismic
and wind loading were compared in the following stages to check efficiency of the various
systems in progression .

Case 1. The first step was to compare the reduction in drift to the moment frame structure when
retrofitted by bracing the periphery, the core axial bracing and a straight diagonal brace.

Case 2. All curved brace systems were analyzed. The curved brace system consisted of braces
with 3 varied radii in both concave and convex form. The braces were tested for both fixed
and pinned joints. The convex system was tested only for fixed joints since it was evident
the use of convex forms was not very efficient.

Case 3. The curved system with the least deflection is then compared with the other systems to
compare the deflections obtained by the different systems under the mentioned lateral
loading.

98
5.4.2 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS
5.4.2.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 45 Deflection (in ft) in the X axis due to Seismic loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 1.94 0.74 0.31 0.44
20 1.91 0.72 0.30 0.44
19 1.87 0.68 0.30 0.44
18 1.82 0.64 0.29 0.43
17 1.75 0.60 0.28 0.41
16 1.67 0.56 0.27 0.39
15 1.58 0.51 0.25 0.37
14 1.49 0.47 0.24 0.35
13 1.38 0.42 0.23 0.33
12 1.27 0.38 0.21 0.30
11 1.16 0.33 0.20 0.27
10 1.05 0.29 0.18 0.25
9 0.93 0.25 0.16 0.23
8 0.81 0.21 0.14 0.20
7 0.69 0.18 0.13 0.17
6 0.57 0.15 0.11 0.15
5 0.46 0.12 0.09 0.12
4 0.34 0.09 0.07 0.09

99
3 0.23 0.06 0.06 0.06
2 0.13 0.04 0.04 0.04
1 0.04 0.02 0.02 0.01
GRND 0.00 0.00 0.00 0.00

Table 45 : Continued

100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
CORE BRACE
BRACE PERIPHERY
STRAIGHT BRACE
Figure 38 Deflection (in ft) due to Seismic loading along the X axis
Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably. In comparison to the efficiency of the
systems with respect to reduction in drift a peripheral brace frame structure performs better than
a diagonal straight brace frame system.

101
5.4.2.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 46 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX -
BRACE 3 -
FIXED
21
0.48 0.39 0.37 0.45 0.46 0.41
20
0.48 0.38 0.37 0.45 0.47 0.41
19
0.47 0.38 0.37 0.45 0.46 0.40
18
0.45 0.37 0.36 0.43 0.45 0.39
17
0.43 0.35 0.34 0.42 0.44 0.39
16
0.40 0.33 0.32 0.40 0.42 0.37
15
0.37 0.30 0.30 0.38 0.40 0.36
14
0.33 0.27 0.28 0.36 0.38 0.34
13
0.29 0.25 0.26 0.34 0.36 0.33
12
0.26 0.23 0.24 0.31 0.34 0.31
11
0.24 0.21 0.21 0.29 0.31 0.29
10
0.21 0.18 0.19 0.26 0.29 0.27
9
0.19 0.16 0.17 0.24 0.26 0.25
8
0.16 0.14 0.15 0.21 0.24 0.23
7
0.14 0.12 0.13 0.18 0.21 0.20
6
0.11 0.10 0.10 0.16 0.18 0.17
5
0.09 0.08 0.08 0.13 0.14 0.14

102
4
0.07 0.06 0.07 0.10 0.11 0.11
3
0.05 0.04 0.05 0.07 0.08 0.08
2
0.03 0.02 0.03 0.04 0.04 0.05
1
0.01 0.01 0.01 0.01 0.02 0.02
GRND
0.00 0.00 0.00 0.00 0.00 0.00

Figure 39 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces fixed at both ends.

0
0.1
0.2
0.3
0.4
0.5
0.6
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED
Table 46 : Continued

103
5.4.2.3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 47 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces pinned at both ends

CONCAVE -BRACE 1
-PINNED
CONCAVE -BRACE 2 -
PINNED
ONCAVE -BRACE 3 -
PINNED
21 0.51 0.40 0.39
20 0.50 0.40 0.39
19 0.49 0.40 0.39
18 0.47 0.38 0.37
17 0.45 0.36 0.35
16 0.41 0.34 0.33
15 0.38 0.31 0.31
14 0.34 0.28 0.29
13 0.30 0.26 0.27
12 0.27 0.24 0.24
11 0.24 0.21 0.22
10 0.22 0.19 0.20
9 0.19 0.16 0.17
8 0.16 0.14 0.15
7 0.14 0.12 0.13
6 0.12 0.10 0.11
5 0.09 0.08 0.09
4 0.07 0.06 0.07
3 0.05 0.05 0.05
2 0.03 0.03 0.03
1 0.01 0.01 0.01
GRND 0.00 0.00 0.00

104

Figure 40 Deflection (in ft) due to Seismic loading along the X axis by different diagonal curved
braces pinned at both ends.

5.4.2.4 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS
0
0.1
0.2
0.3
0.4
0.5
0.6
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
PINNED
CURVED CONCAVE BRACE 2-
PINNED
CURVED CONCAVE BRACE 3-
PINNED

105
0
0.5
1
1.5
2
2.5
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 3-
FIXED

Figure 41 Deflection (in ft) in the X axis due to Seismic loading along the X axis

Conclusion:
Comparative study Of the systems show that a peripheral brace frame system helps
in the reduction of drift to a larger extend . The curved system does perform better than a core
braced system or a single diagonal straight brace frame system.

106
5.4.3 DRIFT DUE TO SEISMIC LOADING ALONG THE Y AXIS

5.4.3.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 48 Deflection (in ft) due to Seismic loading along the Y axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 2.75 0.63 0.53 0.66
20 2.71 0.60 0.52 0.66
19 2.65 0.57 0.50 0.66
18 2.57 0.53 0.49 0.65
17 2.47 0.49 0.47 0.63
16 2.36 0.46 0.45 0.60
15 2.24 0.42 0.42 0.56
14 2.10 0.38 0.40 0.51
13 1.96 0.35 0.37 0.46
12 1.80 0.31 0.35 0.43
11 1.65 0.27 0.32 0.39
10 1.49 0.24 0.29 0.36
9 1.33 0.20 0.26 0.32
8 1.16 0.18 0.23 0.28
7 1.00 0.15 0.21 0.23
6 0.83 0.12 0.18 0.19
5 0.67 0.10 0.15 0.15

107
4 0.51 0.08 0.12 0.11
3 0.35 0.06 0.09 0.08
2 0.20 0.05 0.07 0.05
1 0.07 0.03 0.04 0.02
GRND 0.00 0.00 0.00 0.00

Continued…
Table 48 : Continued

108
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
CORE BRACE
BRACE PERIPHERY
STRAIGHT BRACE

Figure 42Deflection (in ft) due to Seismic loading along the y axis

Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably . In comparison to the efficiency of the
systems with respect to reduction in drift a peripheral brace frame structure performs better than
a diagonal straight brace frame system.

109
5.4.3.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 49 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
-FIXED
21 0.79 0.63 0.60 0.70 0.70 0.70
20 0.76 0.61 0.58 0.71 0.71 0.70
19 0.71 0.58 0.56 0.71 0.71 0.70
18 0.66 0.55 0.54 0.70 0.70 0.68
17 0.61 0.52 0.52 0.67 0.67 0.66
16 0.56 0.48 0.49 0.64 0.64 0.64
15 0.51 0.45 0.46 0.60 0.60 0.62
14 0.46 0.41 0.42 0.58 0.57 0.60
13 0.42 0.37 0.38 0.54 0.54 0.59
12 0.37 0.33 0.33 0.51 0.51 0.56
11 0.32 0.28 0.28 0.48 0.48 0.53
10 0.28 0.23 0.24 0.45 0.44 0.49
9 0.22 0.19 0.20 0.40 0.40 0.46
8 0.18 0.16 0.18 0.35 0.35 0.43
7 0.15 0.14 0.15 0.30 0.30 0.40
6 0.13 0.11 0.12 0.26 0.26 0.36

110
5 0.10 0.09 0.10 0.22 0.22 0.31
4 0.08 0.06 0.07 0.18 0.18 0.26
3 0.05 0.04 0.04 0.14 0.14 0.19
2 0.02 0.02 0.02 0.09 0.09 0.12
1 0.01 0.01 0.01 0.03 0.03 0.04
GRND 0.00 0.00 0.00 0.00 0.00 0.00

Continued…
Table 49 : Continued

111
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED

Conclusion:
On comparing the different curved brace systems it is evident that the curved system with
a greater radii produces lower deflection than the other curved brace systems. When seismic load
acts along the Y axis..

Figure 43 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.

112
5.4.4 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 50 Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces pinned at both ends.
CONCAVE -
BRACE 1 -PINNED
CONCAVE -BRACE 2 -
PINNED
CONCAVE -BRACE
3 -PINNED
21 0.87 0.70 0.65
20 0.84 0.68 0.64
19 0.80 0.65 0.62
18 0.74 0.62 0.60
17 0.69 0.58 0.57
16 0.63 0.54 0.53
15 0.57 0.49 0.49
14 0.51 0.44 0.44
13 0.44 0.39 0.39
12 0.38 0.34 0.34
11 0.33 0.29 0.29
10 0.28 0.24 0.25
9 0.23 0.20 0.22
8 0.19 0.17 0.18
7 0.16 0.14 0.16
6 0.13 0.12 0.13

113
5 0.11 0.09 0.10
4 0.08 0.07 0.07
3 0.05 0.04 0.05
2 0.03 0.02 0.02
1 0.01 0.01 0.01
GRND 0.00 0.00 0.00

Table 50 : Continued

114

Figure 44Deflection (in ft) due to Seismic loading along the Y axis by different diagonal curved
braces fixed at both ends.
Conclusion:
On comparing the different curved brace systems it is evident that the curved system with
a greater radii produces lower deflection than the other curved brace systems. When seismic load
acts along the Y axis..

0
0.05
0.1
0.15
0.2
0.25
21 19 17 15 13 11 9 7 5 3 1
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED
CURVED CONCAVE BRACE 1-
PINNED
CURVED CONCAVE BRACE 2-
PINNED

115
0
0.5
1
1.5
2
2.5
3
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 3-
FIXED
5.4.4.1 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

Figure 45 Deflection (in ft) due to Seismic loading along the Y axis

Conclusion:
Comparitive study Of the systems show that a peripheral brace frame system helps
in the reduction of drift to a larger extend in the upper stories while the curved brace system
helps reduce drift more at the lower stories. It can be noted that the efficiency of the curved brace
is similar to that of the core braced frame system.

116
5.4.5 DRIFT DUE TO WIND LOADING ALONG THE X AXIS
5.4.5.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 51 Deflection (in ft) due to Wind loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 0.62 0.18 0.16 0.17
20 0.62 0.18 0.16 0.17
19 0.61 0.17 0.16 0.17
18 0.60 0.16 0.16 0.17
17 0.58 0.16 0.15 0.17
16 0.56 0.15 0.15 0.16
15 0.54 0.14 0.14 0.15
14 0.52 0.13 0.14 0.14
13 0.49 0.12 0.13 0.14
12 0.46 0.11 0.13 0.13
11 0.42 0.10 0.12 0.12
10 0.39 0.09 0.11 0.11
9 0.35 0.08 0.10 0.10
8 0.31 0.07 0.09 0.09
7 0.27 0.06 0.08 0.08
6 0.23 0.05 0.07 0.07

117
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
5 0.19 0.04 0.06 0.05
4 0.14 0.03 0.05 0.04
3 0.10 0.03 0.04 0.03
2 0.06 0.02 0.02 0.02
1 0.02 0.01 0.01 0.01
GRND 0.00 0.00 0.00 0.00

Figure 46 Deflection (in ft) due to Wind load along the X axis
Conclusion:
It is evident from the above chart that retrofitting the moment frame with any of the
mentioned system decreases the deflection considerably from 1.6 to 0.1-0.2 feet . Of the
mentioned systems the peripheral brace minimizes deflection caused due to seismic loading as
Table 51 : Continued

118
compared to deflection caused by using a diagonal braced frame system. Going further from this
conclusion the next comparison was conducted to study a diagonal curved brace system.
5.4.5.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 52 Deflection (in ft) due to Wind loading along the X axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
-FIXED
21 0.08 0.06 0.06 0.08 0.08 0.07
20 0.08 0.06 0.06 0.08 0.08 0.07
19 0.08 0.06 0.06 0.08 0.08 0.07
18 0.07 0.06 0.06 0.08 0.08 0.07
17 0.07 0.06 0.06 0.07 0.08 0.07
16 0.07 0.06 0.06 0.07 0.08 0.07
15 0.07 0.05 0.05 0.07 0.08 0.07
14 0.06 0.05 0.05 0.07 0.07 0.07
13 0.06 0.05 0.05 0.06 0.07 0.06
12 0.05 0.05 0.05 0.06 0.07 0.06
11 0.05 0.04 0.04 0.06 0.06 0.06
10 0.04 0.04 0.04 0.05 0.06 0.06
9 0.04 0.03 0.04 0.05 0.06 0.05
8 0.03 0.03 0.03 0.05 0.05 0.05

119
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED
7 0.03 0.03 0.03 0.04 0.05 0.04
6 0.03 0.02 0.02 0.04 0.04 0.04
5 0.02 0.02 0.02 0.03 0.03 0.03
4 0.02 0.01 0.02 0.02 0.03 0.03
3 0.01 0.01 0.01 0.02 0.02 0.02
2 0.01 0.01 0.01 0.01 0.01 0.01
1 0.00 0.00 0.00 0.00 0.00 0.00
GRND 0.00 0.00 0.00 0.00 0.00 0.00

Figure 47 Deflection (in ft) due to Wind loading along the X axis by different diagonal
curved braces fixed at both ends.
Table 52 : Continued

120
5.4.5.3 CASE 3 COMPARISON OF CURVED BRACE SYSTEM WITH HINGED JOINT

Table 53 Deflection (in ft) due to Wind loading along the X axis by different diagonal curved
braces pinned at both ends.
CONCAVE -
BRACE 1 -PINNED
CONCAVE -BRACE 2
-PINNED
CONCAVE -BRACE
3 -PINNED
21 0.22 0.18 0.17
20 0.22 0.18 0.17
19 0.21 0.18 0.17
18 0.20 0.17 0.17
17 0.19 0.17 0.17
16 0.18 0.16 0.16
15 0.17 0.15 0.15
14 0.16 0.14 0.14
13 0.15 0.13 0.13
12 0.13 0.11 0.12
11 0.12 0.10 0.10
10 0.10 0.09 0.09
9 0.09 0.08 0.08
8 0.07 0.07 0.07
7 0.06 0.06 0.06
6 0.05 0.05 0.05

121
5 0.04 0.04 0.04
4 0.03 0.03 0.03
3 0.02 0.02 0.02
2 0.01 0.01 0.01
1 0.00 0.00 0.01
GRND 0.00 0.00 0.00

Table 53 : Continued

122

Figure 48 Deflection (in ft) in the X axis due to Wind load along the X axis by different diagonal
curved braces pinned at both ends.

Conclusion:
It can be concluded from the above graph the concave pinned system works much more
efficient than the convex system when the bracing members have been pinned at both ends.

0.00
0.05
0.10
0.15
0.20
0.25
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
PINNED
CURVED CONCAVE BRACE 2-
PINNED
CURVED CONCAVE BRACE 3-
PINNED

123
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
MOMENT
BRACE 1
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 2-
FIXED
5.4.5.4 CASE 4 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS
Figure 49 Deflection (in ft) in due to Wind loading along the X axis
Conclusion:
It can be concluded from the above graph the brace frame system along the periphery of
the structure provides the least deflection than the other tested systems. The curved brace system
is not as efficient as a peripheral brace system but performs better than a diagonal straight brace
or core brace system under wind load along the X axis.

124
5.4.6 DRIFT DUE TO WIND LOADING ALONG THE Y AXIS
5.4.6.1 CASE 1 COMPARISON OF EXISITNG SYSTEMS

Table 54 Deflection (in ft) due to Wind loading along the X axis
MOMENT PERIPHERAL
BRACE
CORE BRACE DIAGONAL
STRAIGHT
21 0.82 0.18 0.16 0.20
20 0.81 0.17 0.16 0.20
19 0.80 0.17 0.16 0.20
18 0.79 0.16 0.15 0.20
17 0.77 0.15 0.15 0.20
16 0.75 0.14 0.15 0.19
15 0.72 0.13 0.14 0.18
14 0.69 0.12 0.14 0.17
13 0.66 0.11 0.13 0.16
12 0.62 0.10 0.12 0.15
11 0.58 0.09 0.11 0.14
10 0.53 0.08 0.11 0.13
9 0.49 0.07 0.10 0.12
8 0.44 0.06 0.09 0.11
7 0.38 0.06 0.08 0.09
6 0.32 0.05 0.07 0.08
5 0.27 0.04 0.06 0.07
4 0.21 0.03 0.05 0.05
Table 54 : Continued

125
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
CORE BRACE
BRACE PERIPHERY
STRAIGHT BRACE
3 0.15 0.03 0.04 0.04
2 0.08 0.02 0.03 0.03
1 0.03 0.02 0.02 0.01
GRND 0 0 0 0

Figure 50 Deflection (in ft) due to Wind loading along the Y axis
Conclusion:
The comparison shows under wind load the core brace system performs much better in
reducing the deflection of the building. However the diagonal straight brace system performs
with least efficiency of the 3 brace systems tested.

126
5.4.6.2 CASE 2 COMPARISON OF CURVED BRACE SYSTEM WITH FIXED JOINT

Table 55 Deflection (in ft) due to Wind loading along the Y axis by different diagonal curved
braces fixed at both ends.
CONCAVE
-BRACE 1 -
FIXED
CONCAVE
-BRACE 2
-FIXED
CONCAVE
-BRACE 3
-FIXED
CONVEX -
BRACE 1 -
FIXED
CONVEX -
BRACE 2 -
FIXED
CONVEX
-BRACE 3
-FIXED
21 0.20 0.17 0.16 0.22 0.22 0.23
20 0.20 0.16 0.16 0.22 0.22 0.24
19 0.19 0.16 0.16 0.23 0.22 0.23
18 0.18 0.16 0.16 0.22 0.22 0.23
17 0.18 0.15 0.15 0.22 0.22 0.23
16 0.17 0.15 0.15 0.21 0.21 0.22
15 0.16 0.14 0.14 0.20 0.20 0.22
14 0.15 0.13 0.13 0.20 0.20 0.22
13 0.14 0.12 0.12 0.19 0.19 0.21
12 0.13 0.11 0.11 0.18 0.18 0.21
11 0.11 0.10 0.10 0.18 0.18 0.20
10 0.10 0.08 0.09 0.17 0.17 0.19
9 0.08 0.07 0.08 0.15 0.15 0.19
8 0.07 0.06 0.07 0.14 0.14 0.18
7 0.06 0.05 0.06 0.13 0.13 0.17
6 0.05 0.05 0.05 0.11 0.11 0.15

127
5 0.04 0.04 0.04 0.10 0.10 0.13
4 0.03 0.03 0.03 0.08 0.08 0.11
3 0.02 0.02 0.02 0.06 0.06 0.09
2 0.01 0.01 0.01 0.04 0.04 0.05
1 0.00 0.00 0.01 0.02 0.02 0.02
GRND 0.00 0.00 0.00 0.00 0.00 0.00

Figure 51 Deflection (in ft) due to Wind load along the Y axis by different diagonal curved
braces
Conclusion:
From the above graph it can be concluded of the different braced systems tested the
curved concave with fixed end and the largest radii gives the least deflection than any other
curved system.
0
0.05
0.1
0.15
0.2
0.25
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
CURVED CONCAVE BRACE 1-
FIXED
CURVED CONCAVE BRACE 2-
FIXED
CURVED CONCAVE BRACE 3-
FIXED
CURVED CONVEX BRACE 1-
FIXED
CURVED CONVEX BRACE 2-
FIXED
CURVED CONVEX BRACE 3-
FIXED
CURVED CONCAVE BRACE 1-
PINNED
Table 55 : Continued

128
5.4.6.3 CASE 3 COMPARISON OF THE EFFICIENT CURVED BRACE WITH
EXISITING SYSTEMS

Figure 52 Deflection (in ft) due to Wind load along the Y axis

Conclusion:
Thus it can be concluded that the curved concave brace does perform better than the other
tested braced frame systems under lateral load due to wind in the Y direction.

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
GRND
MOMENT
CORE BRACE
BRACE PERIPHERY
STRAIGHT BRACE
CURVED CONCAVE BRACE 3-
FIXED

129
5.5 CONCLUSION

Deflection:
Comparing the results obtained with the results from the previous chapter we can see a
notable difference in the performance of the curved brace system. The peripheral braced frame
system produces lower deflection under seismic load in the X and Y and wind in the X axis. The
curved brace system however produces lower deflection when subjected to wind load in the Y
direction. It can be noted that between the curved brace system and peripheral brace system the
curved brace system produces lower deflection in the lower stories and greater deflection in the
upper stories as compared to the latter

Thus the proposed curved brace system does not function with maximum efficiency in
reducing the drift caused by lateral loads in a structure with a rectangular layout and 21 storied.
Testing this system further the next step is to analyze the system on a 50 storied structure to study
the behavior of the system in taller buildings.

130
CHAPTER 6 ANALYSIS OF 50 STORIED 150 ft X 150 ft
STRUCTURE

6.1 DESIGN PAPRAMETERS :

The proposal has been tested on a 5 x 5 bay structure.
d. Span (L) ……………………………………………………………………………150 ft
e. Width (B)…………………………………………….…………………………….150 ft
f. Floor to Floor height (h)… ……………………………………………...…………12 ft
g. Total height (H)……………………………………………………………………..600 ft
h. No of storey (N) …………………………………..………………………….50 ( G+49)

Fig : 4.2 BUILDING PLAN – 150 FT X 90FT ( 30FT
X 30FT BAY)

131
Table 56 Material Properties 02 - Basic Mechanical Properties

Material UnitWeight UnitMass E1 G12 U12 A1
Kip/ft3 Kip-s2/ft4 Kip/ft2 Kip/ft2 1/F
4000Psi 1.5000 4.662 519119 216299 0.20 5.50
A615Gr60 4.900 1.523 4176000 6.50
A992Fy50 4.900 1.523 4176000 1606153 0.30 6.50

6.1.1 STEEL DESIGN OF MOMENT FRAME STRUCTURE:
External frame:
1. Column for 13-21 stories ………….……………………………...………W 14 x 426
2. Column for 7-12 stories ………………………………………….………W 14 x 500
3. Column for 1- 6 stories ………………………..…………………………W 14 x 605
4. Beam for 18-21 stories ………………………………..…….…………… W 24 X 76
5. Beam for 18-21 stories ……………………………..……….…….……… W 24X 84
6. Beam for 13-17 stories ……………………………………...…………… W 24 X 73
7. Beam for 7-12 stories ……….…………………………………………… W 24 X 94
8. Beam for 1-6 stories …………………………………..…………...….… W 24 X 103
Internal structure
1. Column for 16-21 stories ………………………………………….………W 14 x 211
2. Beam for 16-21 stories…………………………………………………… W 18 X 86
3. Column for 11-15 stories …………………………………………………W 14 x 311

132
4. Beam for 11-15 stories…………………………………………………………W 18 X 97
5. Column for 6-10 stories …………………………………….…………………W 14 x 426
6. Beam for 6-10 stories………………………………………………………… W 18X 119
7. Column for 1- 5 stories …………………….…………………………………W 14 x 550
8. Beam for 1-5 stories………………………………………………………… .W 18 X 130
Corner columns : …………………………………………….Built up box section of W 14 x 342
Brace section for SCBF (150 bay) : .………………………………………………… W27x 102
Brace section for SCBF (90 bay) : .…..……………………………………………… W27x 146
Unbraced beam length (minor & LTB) : ………………………….…………………………0.2
Table 57 Material Properties 02 - Basic Mechanical Properties
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A992Fy50 7200.00 9360.00 -0.100000

Table 58 Material Properties 03e - Rebar Data
Material Fy Fu FinalSlope
Kip/ft2 Kip/ft2
A615Gr60 8640.00 12960.00 -0.100000

133
6.1.2 CONCRETE SLAB DESIGN OF MOMENT FRAME STRUCTURE:

1. Concrete :……………………………………….…….…………………………. 4000psi
2. Section : ………………………...…………………….………………………30 ft x 30 ft
3. Thickness: …………………………………………………………………………6 inch.
4. Rebar layout : ………………………………………………...…………………..Default.
5.Total no of sections ……………………………………………………………………. 300
Table 59 Material Properties 03b - Concrete Data
Material Fc FinalSlope
Kip/ft2
4000Psi 576.00 -0.100000

Table 60 Area Section Properties, Part 1 of 3
Section Material AreaType Type DrillDOF Thickness BendThick F11Mod
ft ft
6" THK
SLAB
4000Psi Shell Shell-
Thick
Yes 0.50000 0.50000 1.000000

134
Table 61 Area Section Properties, Part 2 of 3
Section F22Mod F12Mod M11Mod M22Mod M12Mod V13Mod V23Mod MMod

6" THK
SLAB
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Table 62 Area Section Properties, Part 3 of 3
Section WMod

6" THK SLAB 1.000000

135
6.2 LOAD CASES

6.2.1 DEAD LOAD
6.2.2. LIVE LOAD
6.2.3. SEISMIC ( X & Y AXIS )
6.2.4. WIND ( X & Y AXIS)
Table 63 Case - Static 1 - Load Assignments
Case LoadType LoadName LoadSF

DEAD Load pattern DEAD 1.000000
LIVE Load pattern LIVE 1.000000
SEISMIC X Load pattern SEISMIC X 1.000000
SEISMIC Y Load pattern SEISMIC Y 1.000000
WIND Load pattern WIND 1.000000
WIND- 90 Load pattern WIND- 90 1.000000

136
6.2.1 DEAD LOAD :

12. Total Self-weight of steel (BRACED SYSTEM ) :……...………………..……..5645 kips
13. Total Self-weight of concrete:.......……………………………………………..21262 kips
14. a. Façade ……………………………………………………………………………..7 psf
b. MEP & ceiling ………………………………………………………………..10 psf
c. Partitions & Finishes …………………………………………………………15 psf
d. Secondary Beams………………….…………………………….……………..5 psf
e. Deck ……………………………………………………………….……………3psf
TOTAL MISCELLANEOUS DEAD LOAD : ……………………….……… 40 psf.
6.2.2 LIVE LOAD:
LIVE LOAD …………………………………………………………………….100 psf

Table 64 Load Pattern Definitions
LoadPat DesignType SelfWtMult AutoLoad

SEISMIC X QUAKE 0.000000 IBC2006
SEISMIC Y QUAKE 0.000000 IBC2006
WIND WIND 0.000000 ASCE7-05
WIND- 90 WIND 0.000000 ASCE7-05

137
6.2.3 SEISMIC LOAD
6.2.3.1 SPECIAL CONCENTRIC BRACED FRAME : (SCBF)

1. Location: USC 90089
2. Site Class: ………………………………………………..…………………..………………. D
3. Site Coefficient, Fa………………………………………………..…….………………….…1
4. Site Coefficient, Fv………………………………………………………………………….1.5
5. SDS …………………………….…………………………………………………..1.23
6. SD1………………………………………………………………………………...0.641
7. Response Modification (R) ......................................................................................7.5
8. System Over strength , Ω - ..………………………………………………………..2.5
9. Deflection Amplification, Cd –……………………………………………………. 5.5
6.2.4 WIND LOAD

1. Wind Direction …………………………………………………………………..0 & 90
2. Windward Coefficient (Cp)……………………………….………………………….0.8
3. Leeward Coefficient (Cp) ……………………………………………………………0.5
4. Wind Speed ………………………………………………………………………85mph
5. Exposure type ………………………………………..……………………………… C
6. Gust Factor………………………………………………………………………… 0.85

138
7. Directionality Factor, Kd……………….………………………………………….. 0.85
Table 65 Auto Wind - ASCE7-05, Part 1 of 2
LoadPat Angle Windward
Cp
Leeward
Cp
ASCECase E1 E2 Wind
Speed
Exposure
Degrees mph
WIND 0.000 0.80000 0.500 1 0.000 0.0000 85.00 C
WIND-
90
90.000 0.80000 0.500 1 0.150 0.150 85.00 C

Table 66 Auto Wind - ASCE7-05, Part 2 of 2
LoadPat I Kzt GustFactor Kd SolidRatio

WIND 1.000000 1.000000 0.850000 0.850000
WIND- 90 1.000000 1.000000 0.850000 0.850000

139
Table 67 Combination Definitions Table

ComboName ComboType CaseName ScaleFactor

DSTL1 Linear Add DEAD 1.400000
DSTL2 Linear Add DEAD 1.200000
DSTL2 LIVE 1.600000
DSTL3 Linear Add DEAD 1.200000
DSTL3 LIVE 1.000000
DSTL3 WIND 1.600000
DSTL4 Linear Add DEAD 1.200000
DSTL4 LIVE 1.000000
DSTL4 WIND -1.600000
DSTL5 Linear Add DEAD 1.200000
DSTL5 LIVE 1.000000
DSTL5 WIND- 90 1.600000
DSTL6 Linear Add DEAD 1.200000
DSTL6 LIVE 1.000000
DSTL6 WIND- 90 -1.600000
DSTL7 Linear Add DEAD 0.900000
DSTL7 WIND 1.600000
DSTL8 Linear Add DEAD 0.900000

140

ComboName ComboType CaseName ScaleFactor

DSTL8 WIND -1.600000
DSTL9 Linear Add DEAD 0.900000
DSTL9 WIND- 90 1.600000
DSTL10 Linear Add DEAD 0.900000
DSTL10 WIND- 90 -1.600000
DSTL11 Linear Add DEAD 1.300000
DSTL11 LIVE 1.000000
DSTL11 SEISMIC X 1.000000
DSTL12 Linear Add DEAD 1.300000
DSTL12 LIVE 1.000000
DSTL12 SEISMIC X -1.000000
DSTL13 Linear Add DEAD 1.300000
DSTL13 LIVE 1.000000
DSTL13 SEISMIC Y 1.000000
DSTL14 Linear Add DEAD 1.300000
DSTL14 LIVE 1.000000
DSTL14 SEISMIC Y -1.000000
DSTL15 Linear Add DEAD 0.800000
Table 69 : Continued

Table 67 : Continued

141

ComboName ComboType CaseName ScaleFactor

DSTL15 SEISMIC X 1.000000
DSTL16 Linear Add DEAD 0.800000
DSTL16 SEISMIC X -1.000000
DSTL17 Linear Add DEAD 0.800000
DSTL17 SEISMIC Y 1.000000
DSTL18 Linear Add DEAD 0.800000
DSTL18 SEISMIC Y -1.000000
DSTL19 Linear Add DEAD 1.000000
DSTL20 Linear Add DEAD 1.000000
DSTL20 LIVE 1.000000

Table 67 : Continued

142
Figure 53John Hancock center at
Chicago uses a single diagonal
brace every 10 stories
http://www.chicagoarchitecture.inf
o/Building/1006/The-John-
Hancock-Center.php
6.3 ANALYSIS:

In the previous cases the buildings were 21 storied which made it possible to retrofit a
moment frame structure with the proposed systems for comparison . Moment frame structure has
a limitation with the number of stories for which it can be designed. As buildings are built higher
the use of Moment frame systems is usually avoided. For taller buildings using moment frame
system means decreasing the span between columns and an increase in the number of columns.
Since this is highly undesirable from an architectural space planning point of view, Tall
buildings do not usually make use of moment frame systems
in recent times. The most common system used for taller
buildings is a belt truss system or a braced system that is a
diagonal brace every 5- 10 floors. An example of this system
is the John Hancock building in Chicago.
To analyze the diagonal curved brace efficiency in a
50 storied building it has been compared to a diagonal straight
brace system located every 10 stories. Since the Building has
a Square layout (150 x 150 ft) the lateral load along the X and
Y Are symmetrical Concluded from the analysis run in chapter
4) and so only Seismic force along the X axis and Wind load
along the X axis have been taken into consideration for this set
of analysis.

143

Figure 54 Different brace systems analyzed for drift in 50 storied structure
All of the above models were designed to have a constant mass of 28800 kips .As per the
Gravity steel versus wind premium check 28800000/150 x 150 x 50 = 25.6 = OK
Each of the above models were checked for stress and analyzed for bending moment and shear.
Single straight
diagonal brace
Single curved
diagonal brace
Multiple
straight
diagonal
brace
Multiple
curved
diagonal brace
Double straight
diagonal brace
Double curved
diagonal brace
Figure 55 Gavity steel versus wind premium check

144
Figure 56 Steel design check for
stress in steel members
The initial step consisted of designing the single diagonal straight and curved brace system .
The mass of steel had been kept at a constant at 28800 kips . Seen below is the steel design
check conducted in SAP to check stress levels in steel members. It can be seen that a large
portion of the brace in the lower levels is highlighted in red
indicating stress ratio greater than the allowable limit. It
was found that using a single diagonal for such large spans
of brace increases the axial forces acting on the lower
structural members. These stresses could be avoided by
increasing the size of the column at the lower half since
decreasing the upper brace sizes caused the upper brace
members to be overstressed. Increasing the sections meant
greater the amount of steel required in construction. The
overstressed section produced a deflection of 3.5 feet under
seismic loading and a model with all members within the
stress ratio limit produced a deflection of 2 feet however the
mass of steel in the structure was increased to 29600 kips.
Since the other systems produced lower deflection with
lower mass of steel the analysis of a single brace frame was
eliminated for comparing the drift induced due to seismic
and wind load.

145
6.3.1 BASE SHEAR

Table 68 Base shear along the X axis
GLOBAL
Fx

DOUBLE
STRAIGHT
BRACE
DOUBLE CURVED
BRACE BRACE
MULTIPLE
STRAIGHT
BRACE
MULTIPLE
CURVED
BRACE
SEISMIC
X
-8542 -8543 -8543 -8543
SEISMIC
Y
0 0 0 0
WIND X -2561 -2561 -2561 -2561
WIND Y 0 0 0 0

146

Table 69 Base Shear along the Y axis
GLOBAL
Fy

DOUBLE
STRAIGHT
BRACE
DOUBLE CURVED
BRACE BRACE
MULTIPLE
STRAIGHT
BRACE
MULTIPLE
CURVED
BRACE
SEISMIC
X
0 0 0 0
SEISMIC
Y
-8542 -8543 -8543 -8543
WIND X 0 0 0 0
WIND Y -2561 -2561 -2561 -2561

147
6.3.2 DRIFT DUE TO SEISMIX LOADING ALONG THE X AXIS

Table 70 Deflection (in ft) due to Seismic loading along the X axis
MULTIPLE
STRAIGHT
BRACE 1 (5)
MULTIPLE
CURVED BRACE
1 (5)
DOUBLE
STRAIGHT
BRACE
DOUBLE
CURVED
BRACE
50 1.03 1.64 1.77 1.57
49 1.02 1.62 1.77 1.57
48 1.00 1.60 1.77 1.56
47 0.98 1.57 1.75 1.55
46 0.96 1.54 1.73 1.53
45 0.95 1.51 1.70 1.51
44 0.93 1.49 1.67 1.47
43 0.91 1.46 1.64 1.44
42 0.89 1.43 1.60 1.41
41 0.87 1.40 1.56 1.37
40 0.85 1.36 1.51 1.33
39 0.82 1.32 1.47 1.29
38 0.80 1.28 1.43 1.25
37 0.78 1.24 1.40 1.21
36 0.76 1.20 1.36 1.18
35 0.74 1.17 1.32 1.14
34 0.72 1.14 1.29 1.11

148
33 0.70 1.11 1.26 1.08
32 0.67 1.07 1.22 1.05
31 0.65 1.03 1.19 1.02
30 0.62 0.99 1.14 0.99
29 0.59 0.94 1.10 0.96
28 0.56 0.89 1.05 0.92
27 0.54 0.85 1.01 0.88
26 0.52 0.81 0.95 0.84
25 0.50 0.77 0.90 0.79
24 0.48 0.74 0.84 0.74
23 0.46 0.71 0.79 0.69
22 0.43 0.68 0.74 0.64
21 0.41 0.64 0.69 0.59
20 0.38 0.59 0.64 0.54
19 0.35 0.54 0.59 0.49
18 0.32 0.49 0.55 0.45
17 0.30 0.45 0.52 0.41
16 0.28 0.41 0.48 0.38
15 0.26 0.38 0.44 0.35
14 0.24 0.35 0.40 0.32
13 0.22 0.32 0.37 0.28
12 0.21 0.29 0.34 0.26
11 0.18 0.26 0.30 0.23
Table 70 : Continued

149
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
50
47
44
41
38
35
32
29
26
23
20
17
14
11
8
5
2
MULTIPLE STRAIGHT BRACE 1
(5)
MULTIPLE CURVED BRACE 1 (5)
DOUBLE STRAIGHT BRACE
DOUBLE CURVED BRACE
10 0.16 0.22 0.27 0.20
9 0.14 0.19 0.24 0.17
8 0.11 0.15 0.21 0.15
7 0.09 0.12 0.18 0.13
6 0.08 0.10 0.15 0.10
5 0.06 0.08 0.12 0.08
4 0.05 0.06 0.08 0.06
3 0.03 0.04 0.05 0.04
2 0.02 0.03 0.03 0.02
1 0.01 0.01 0.01 0.01
GRND 0.00 0.00 0.00 0.00

Figure 57 Lateral drift produced by seismic load in the different brace systems.
Table 70 : Continued

150
6.3.3 DRIFT DUE TO WIND LOADING ALONG THE X AXIS

Table 71 Drift due to Wind loading along th X Axis
MULTIPLE
STRAIGHT
BRACE 1 (5)
MULTIPLE
CURVED
BRACE 1 (5)
DOUBLE
STRAIGHT
BRACE
DOUBLE CURVED
BRACE
50 0.29 0.33 0.36 0.31
49 0.29 0.33 0.36 0.31
48 0.29 0.32 0.36 0.31
47 0.28 0.32 0.36 0.31
46 0.28 0.31 0.35 0.31
45 0.27 0.31 0.35 0.30
44 0.27 0.30 0.34 0.30
43 0.27 0.30 0.34 0.29
42 0.26 0.29 0.33 0.29
41 0.26 0.29 0.33 0.28
40 0.25 0.28 0.32 0.28
39 0.24 0.28 0.31 0.27
38 0.24 0.27 0.31 0.26
37 0.23 0.26 0.30 0.26
36 0.23 0.26 0.30 0.25
35 0.22 0.25 0.29 0.25
34 0.22 0.25 0.29 0.24

151
33 0.21 0.24 0.28 0.24
32 0.21 0.23 0.27 0.23
31 0.20 0.23 0.27 0.23
30 0.19 0.22 0.26 0.22
29 0.19 0.21 0.25 0.21
28 0.18 0.20 0.24 0.21
27 0.17 0.19 0.23 0.20
26 0.17 0.19 0.22 0.19
25 0.16 0.18 0.21 0.18
24 0.16 0.17 0.20 0.17
23 0.15 0.17 0.19 0.16
22 0.15 0.16 0.18 0.15
21 0.14 0.15 0.17 0.15
20 0.13 0.14 0.16 0.14
19 0.12 0.13 0.15 0.13
18 0.11 0.12 0.15 0.12
17 0.11 0.11 0.14 0.11
16 0.10 0.11 0.13 0.10
15 0.10 0.10 0.12 0.10
14 0.09 0.09 0.11 0.09
13 0.08 0.08 0.10 0.08
12 0.08 0.08 0.10 0.07
11 0.07 0.07 0.09 0.07
Table 71 : Continued

152
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
50
47
44
41
38
35
32
29
26
23
20
17
14
11
8
5
2
MULTIPLE STRAIGHT BRACE 1
(5)
MULTIPLE CURVED BRACE 1 (5)
DOUBLE STRAIGHT BRACE
DOUBLE CURVED BRACE
10 0.06 0.06 0.08 0.06
9 0.05 0.05 0.07 0.05
8 0.05 0.04 0.06 0.05
7 0.04 0.04 0.06 0.04
6 0.03 0.03 0.05 0.03
5 0.03 0.02 0.04 0.03
4 0.02 0.02 0.03 0.02
3 0.02 0.01 0.02 0.01
2 0.01 0.01 0.01 0.01
1 0.00 0.00 0.00 0.00
GRND 0.00 0.00 0.00 0.00
Figure 58 Lateral drift produced by wind load in the different brace systems.
Table 71 : Continued

153
6.4 CONCLUSION:

It can be concluded from the study above , the single diagonal curved brace system
induces compressive forces In the lower section causing the lower brace and lower columns to be
overstressed.. Thus the single diagonal curved system in a 50 storied structure is not as efficient
as the use of the system in a 21 storied structure.
Deflection :
A comparative study of the deflection obtained from the 4 bracing form tested concludes
that the least deflection is obtained by using multiple straight diagonal braces every 10 storey’s
than having a single or double brace system or a curved system.
Ecenomic:

Since both systems double and multiple brace have used the same amount of steel and have the
same amount of members every floor they have the same value from the economic market point
of view.

154
CHAPTER 7 CONCLUSION

SUMMARY:

The study began with the intention of studying the effect of a diagonal curved
brace which derives its form from the catenary shape of the brace member on the drift
induced in a structure when subjected to lateral load. The study was conducted on a
moment frame system so as to keep the mass of the base structure constant. This helps to
study the use of the curved brace system as an independent system and a retrofit to
existing moment frame structure. In order to study the behavior of the system based on
the form of the building 3 cases were developed. Thus studying the behavior of the
system for 2 different building layouts – a square and a rectangular plan and buildings
with different building height – 21 stories and 50 stories.

155
7.1 CONCLUSION FROM THE ANALYSIS :
7.1.1 DEFLECTION

CASE 1 : 90 x 90 ft x 21 storey’s
The curved brace system was compared to the efficiency of a diagonal straight brace , a
peripheral braced frame and a core brace frame system. The analysis showed the curved brace
system produces the least deflection under seismic and wind load in both X and Y axes

CASE 2 : 150 x 90 ft x 21 storey’s.
Unlike the results obtained from the case 1 the peripheral brace system produces lower
deflection in a rectangular layout than a curved brace system. However when subjected to wind
load along the Y axis the curved brace produces lower deflection.

CASE 3 : 150 x 150 ft x 50 storey’s :
This analysis proved that the curved brace system is not as efficient in reducing drift as a
multiple straight brace system in every 10 floors. Using a single diagonal brace for all 50 stories
induces larger stress levels in the brace and lower column sections thus requiring larger sections
for construction. Which makes the system undesirable.

Thus it can be concluded the diagonal curved brace form works efficiently in producing
minimal drift in buildings as tall as 21 stories with a square layout, but not in taller buildings or
buildings with a rectangular layout.

156
7.1.2 ECONOMIC FACTOR
The difference in deflection obtained from the different systems for a particular building
varies between 0.05 to 0.1 feet. For a 21 storied building having a height of 252 feet a difference
in deflection from 0.35 feet to 0.4 feet produced by the peripheral brace system and curved brace
system is insignificant.
Since the mass of steel has been kept constant for all the models compared there is no
gain or loss in the expense of material from the economic point of view. However the number of
members in a peripheral braced system or core braced system are much more than the number of
members used in a curved brace system. Thus the number of joints in the structure that need to
be welded and bolted are much more in the traditional brace frame systems.

12 X 4 = 48 WELD POINTS.(per floor) 4 X 4 = 16 WELD POINTS(per floor)
PERIPHERAL BRACE SYSTEM DIAGONAL CURVED BRACE SYSTEM
Figure 59 Zoomed Elevation Of Bracing at a Single floor
FACTORS THAT AFFECT THE COST OF WELDING:

1. Time — the Biggest Cost
2. Costs associated with any required stress relief.
3. Cost of electrodes.
4. Cost of shielding materials.

157
5. Cost of electric power.
6. Cost of fuel gas for pre-heat (when required).

Cost of welding is determined as
 Cost per unit. OR
 Cost per length.

Fewer members could save expenses on labor charges and miscellaneous expenses such
as welding and bolting. In buildings as tall as 21 stories or having long spans this could save a
large amount of money in construction and thus prove beneficial from the building economy
point of view.
Some of the common retrofitting systems for moment frame structures include
reinforcing the existing columns by adding additional steel plates or adding a braced frame
system. This requires contractors to pull apart the building at each column beam junction, weld
the additional member and then reseal and refinish the junctions. With the curved braced system
minimizing the percentage of the building that needs to be demolished and refinished. Similarly
installing shear walls also means changing the circulation layout of the layout. The construction
stage could mean leaving the space dysfunctional during that period of time.

Thus a huge amount of money can be saved by the owner in retrofitting moment frame
structures with the curved braced system and achieve minimal deflection.

158
7.2 FUTURE STUDY :
The current thesis analyzed the curved brace system based on 3 specific arc forms with
progressive radii that were chosen at random. On analyzing the different curves in both concave
and convex form it was seen that the deflections obtained varies with each of the form. Thus it is
very important to specify the exact form that produces the least deflection. As mentioned one of
the ways to derive this form is using the equation to find the catenary form of the brace.
There is a need to develop an equation to derive the exact form of the brace to obtain the
least deflection in the building.
7.2.1 COMPARISON WITH OTHER SYSTEMS.
The research was limited to comparing the deflections obtained from the curved brace
system to peripheral brace system and core braced frame system. To define the true efficiency
of the diagonal curved system it is very crucial that the system be compared to the deflections
obtained from different systems.
7.2.2 SITE STUDY
For this study the location considered was USC with a site class D. Thus it is important
that the system be analyzed for different soil conditions, earthquake magnitude and wind load to
determine the efficiency of the system under different site conditions.
7.2.3 SOFTWARE
The initial analysis was carried out in Multiframe. The software helped in the initial study
of the system. The latter research was completely carried out in SAP2000. Since the software
was being used for the first time it was learnt in tandem with the thesis progress. As the output of
the analysis was dependent on the software it is important that the results be verified by doing

159
the similar analysis in different software. This will also help us learn how reliable software’s are
in the overall output of the conclusion.

160
BIBLIOGRAPHY

Arbabian, H. (2000). The role of Architects in seismic design. International Conference on seismic
Performance of traditional buildings. (p. 8). Istanbul Turkey: School Of Architecture -IUST University ,
Tehran , Iran.
Bungale, T. S. (1988). Structural Analysis & Design of Tall buildings.
Cheng, F. Y., Hongping, J., & Lou, K. (2008). Smart Structures- Innovative Systems for Seismic Response
Control. CRC Press.
Earthquake Engineering. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Earthquake_engineering
Eatherton, M. R., & Hajjar, J. F. (2010). Residual Drifts of Self centering Systems Including Affect of
Ambient Building Resistance.
Eric Weisstein. (n.d.). Wolfram Math World. Retrieved from
http://mathworld.wolfram.com/Catenary.html
Hamburger, R. O. (Nov.2000). FEMA 354 - A policy Guide to Steel Moment Frame Construction.
McEntee, P. (Feb. 2009). Steel Moment frames - History and Evolution. Structural Engineer Magazine.
Poalacci, F., Ciampi, V., & De Angelis, M. Optimal design of viscoelastic bracing systems for earthquake
protection of buildings. Angelis University of Rome ‘La Sapienza’.
Quimby, B. T. (2008). A Beginner’s Guide to the Steel Construction Manual- An introduction to
designing steel structures using the AISC Steel - Construction Manual, 13th edition.
Schierle, G. Structure and design.
Scott, A. M., & Hamburger, R. O. (n.d.). Steel Special Moment Frames :A historic Perspective. Retrieved
from Structuremag- A Joint Publication of NCSEA | CASE | SEI:
http://www.structuremag.org/Archives/2010-6/C-StructPerf-Adan-June10.pdf
Soong, T. T., & Constantinou, M. C. (1994). Passive and Active Structural Vibration Control in Civil
Engineering.
Wakabayashi, M. (1986). Design of earthquake resistant buildings. Mcgraw-Hill.
Weisstein,Eric . (n.d.). Wolfram Math World. Retrieved from
http://mathworld.wolfram.com/Catenary.html
William Robinson . (n.d.). Retrieved from [http://en.wikipedia.org/wiki/William_Robinson_(scientist)].

161
APPENDIX – A
MODELLING AND ANALYZING IN SAP 2000 V15

One of the biggest challenges faced in this thesis was modeling the structural modules in
SAP2000 V15. It was very crucial to ensure that all structures modeled in SAP were accurate.
The following steps were performed to arrive at the results obtained:
Step 1 : Ensure the right member sizes.
The initial step was to do hand calculations to obtain approximate beam and column size.
The calculations were as done below:
[Prof.Schierle. 2011 – Moment Frame ]

LOADING:

DEAD LOAD CALCULATION:
Self Weight / Gravity Load : 20 psf
Miscellaneous Loads : 20 psf
Slab Metal Decking load : 60 psf
Total Dead Load : 100 psf
TOTAL DEAD LOAD OF STRUCTURE : 100 X 90 X 90 X21 / 1000
= 17010 lbs
LIVE LOAD CALCULATION:
1. Live Load ( Commercial structures ) : 100 psf
Total Live Load : 100 psf
TOTAL LIVE LOAD OF STRUCTURE: 100 X 90 X90 X21 / 1000
= 17010 lbs

162
WIND LOAD CALCULATION:
1. Average Wind Pressure (P) : 30 psf
ASCE 7 & IBC Requirements: LIVE LOAD REDUCTION FOR TRIBUTARY AREA > 600
Sq.ft
1. 50 % for members supporting one level
2. 40% for member supporting two or more levels
TOTAL LOAD ON BEAMS:
1. DEAD LOAD : 100 psf
2. LIVE LOAD : 100 x 0.5 = 50 psf
TOTAL LOAD: =150 psf
TOTAL LOAD ON COLUMNS:
1. DEAD LOAD 100 psf
2. LIVE LOAD 100 x 0.4 psf
= 40 psf
TOTAL LOAD : 140 psf

COLUMN DESIGN PARAMETERS.
4.1.2.1 COLUMN FOR G + 5 STOREYS :
Uniform Beam Load : D.L x ( L/3) / 1000
W = 125 x 30’/100 0 = 3.75 klf
Uniform Column Load:
W = 120 x 30/1000 = 3.6 klf

163
BASE SHEAR

V : P x (L/3) [n (no of storey’s supported by column )+0.5 ] x h/ 1000
V= 30 psf x 30 ‘ x 20.5 x 12/ 1000 = 147.6 k
Overturn Moments:
M = P x (L/3) x ) [n (no of storey’s supported by column )+0.5 ]
2
/2/1000
Moment at Ground Floor
M
g
= 30 x 30 x (20.5 x 12)
2
/2000

= 27232.2 k
Moment on 1
st
Floor
M
1
= 30 x 30 x (19.5 x 12 )
2
/2000 = 24640.2 k
Column Shear:
V
c
= L
trib
V/B
End Columns: 15 x 147.6 / 90 = 24.6 k
Mid Columns: 30 x 147.6 / 90 = 49.2 k
Column Bending:
M
Lateral
= V
c
x h/2
End Columns: 24.6 x 12/2 = 147.6 k
Mid Columns: 49.2 x 12/2 = 295.2 k
M
Gravity
= wL
2
/ 24
End Columns: 3.6 x 30
2
/24 = 135 k
Mid Columns: = (0)
Total Column Bending:
End Column: M
Lat
+ M
Grav
= 282.6 k
Mid Column: M
Lat
= 295.2 k

164
COLUMN AXIAL FORCE:
P
Lateral
= M
G
/B
End Column: 27232.2 / 90 = 302.58 k
Mid Column : = (0)
P
Gravity
= n WL
Tributary

End Column: 21 x 3.6 x 15 = 1134 k
Mid Column: 21 x 3.6 x 30 = 2268 k

Total Axial Force :
End Column: P
Lateral
+ P
Gravity
= 1436.5 K
Mid Column : P
Lateral
+ P
Gravity
= 2268 k
In reference to AISC steel manual a base column and beams sizes were derived. The
structure with the base beam n column sizes was modeled.

165
MODELLING IN SAP

 The 1
st
step was to design in a 3d template defining a 3 x 3 – 30 ft bay structure.
 The column n beam sizes were allotted as per the calculations.
 Base columns were assigned Joint restrains and the inner beams were released to
create a moment joint.
 6” thick concrete slabs were designed within each bay.
Figure 60 Model in SAP 2000 showing the released joints in beams –( the red indicates concrete
panels and blue steel sections)
 Local Axes for each of the members was checked.
 Miscellaneous Dead Load was calculated at
40psf and Live load at 100 psf. Both loads were
assigned to the structure as area loads - uniform
to frame (shell)
 Mass source was defined from loads
Figure 61 Defining mass source in SAP

166
The following load conditions were defined under load combinations :
1. Live Load ( Self Load multiplier - 1)
2. Dead Load (Self Load multiplier – 0 )
3. Seismic ( Along X & Y axes) - As per IBC 2006

Figure 63 Seismic Load data in SAP
Figure 62 Design Coefficients and factors for Seismic Force resisting systems determined
from Table 12.2-1 from ASCE 7-05

167
4. Wind (Along X & Y axes) - As per ASCE 7- 05

Figure 64 Defining Wind Load in SAP

168
5. All steel members were selected and in steel design overwrite the unbraced length ratio
(Minor & LTB ) were manually determined as 0.2. The framing type selected was Special
Moment frame and Special Concentric braced frame system for the braced systems.
Figure 65 Steel frame Design overwrites (ASCE 7-05)

169
RUNNING THE ANALYSIS IN SAP :

 With the model completed the analysis was run in SAP 2000
 The first step after the computer analysis was to run was to
check the structure for a design check to ensure none of the
members were overstressed.
The color graph indicates the ratio of different stress levels
in the structural members. All members indicated in red
exhibit stress levels above the acceptable limit.
This diagram indicates that the columns determined by hand
calculations were not precise ( Since an older method was
used for hand calculations and not as per the IBC 2006
codes).
 Some of the common errors witnessed in the procedure were as follows:

Figure 67 Error windows indicating errors witnessed during the process
Figure 66 Steel design
check for the base
moment frame structure

170
Figure 68 Error window 1 indicating errors witnessed during the process
Figure 69 Error window 2 indicating errors witnessed during the process

171
 The above shown errors were rectified to define the right section members. Apart from the
above mentioned factors the members also had to be checked for :
- Mass of steel
- Period of the structure given by T = 0.035 ( ht of structure in feet )
3/4

- `` Wind drift to be maintained within ht/ 500

Figure 70 Final structure derived with the column and beam sizes derived after analyzing
in SAP 2000

172
MODELLING DIFFERENT BRACE SYSTEMS:

 Since the thesis looked into retrofitting
the bracings were added to the moment
frame structure built in SAP.
 For the diagonal straight brace a single
member was constructed across the
diagonal of the building as the first step.
 The members on the façade were then
selected and divided by SAP at
intersection with another member. Thus
developing the brace as an independent single member at
every individual floor rather than a single member across
the façade.
 For the Curved system the diagonal brace was designed
as a as single curved member . Similar to the straight
brace system the members in the façade were selected
and divided at the intersection of the steel members.
However SAP does not divide the curved member like a
straight brace member.
 Thus after defining the curved member – manually the
Figure 71 The figure shows the single
member as a brace across the building and
the brace as a member every floor to floor
height
Figure 72 Manually
constructing the diagonal
curved braced

173
curve was drafted as a series of straight member over single curved brace member.
 After manually drafting the members in the façade were divided and then the diagonal
braces were deleted.
 Now that the beams were divided at joints they
 Intersected with the series of straight members that formed the curved, the diagonal
members were re- constructed as straight members (similar to connect the dot using the
divisions in the beams as reference points) as a single member at every floor.
 With this done the models were now ready for running the structural analysis in SAP
2000 as mentioned in the previous step.

174
APPENDIX B -
MODAL ANALYSIS

CASE 1 : 90 X 90 X 252 ft
MOMENT FRAME
Table 72 Modal Analysis : Moment Frame
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 4.4 0.2 1.4 2.0
MODAL Mode 2 4.2 0.2 1.5 2.3
MODAL Mode 3 1.7 0.6 3.7 14.0
MODAL Mode 4 1.5 0.7 4.1 16.8
MODAL Mode 5 1.4 0.7 4.4 19.5
MODAL Mode 6 0.9 1.1 7.1 50.0
MODAL Mode 7 0.8 1.2 7.7 59.3
MODAL Mode 8 0.6 1.6 10.3 105.9
MODAL Mode 9 0.6 1.7 10.9 117.8
MODAL Mode 10 0.6 1.8 11.4 129.9
MODAL Mode 11 0.5 2.2 13.9 194.0
MODAL Mode 12 0.4 2.5 15.7 247.5

175
CENTRAL BAY BRACED FRAME ( CORE BRACE)

Table 73 : Modal Analysis : Central Bay Braced Frame ( Core Brace )
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.2 0.4 2.8 8.0
MODAL Mode 2 2.2 0.5 2.9 8.3
MODAL Mode 3 1.2 0.8 5.3 28.1
MODAL Mode 4 0.7 1.4 8.7 75.3
MODAL Mode 5 0.7 1.4 9.1 82.1
MODAL Mode 6 0.4 2.4 15.2 230.8
MODAL Mode 7 0.4 2.5 15.9 252.3
MODAL Mode 8 0.4 2.6 16.6 276.7
MODAL Mode 9 0.3 3.6 22.7 515.8
MODAL Mode 10 0.3 3.8 23.8 567.6
MODAL Mode 11 0.2 4.0 25.3 638.0
MODAL Mode 12 0.2 4.3 26.8 720.9

176
PERIPHERAL BRACED FRAME SYSTEM
Table 74 Modal Analysis : Peripheral Braced Frame System
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.3 0.4 2.8 7.7
MODAL Mode 2 2.2 0.5 2.8 8.0
MODAL Mode 3 1.2 0.8 5.3 27.8
MODAL Mode 4 0.8 1.2 7.5 56.2
MODAL Mode 5 0.8 1.2 7.7 60.0
MODAL Mode 6 0.6 1.8 11.3 128.2
MODAL Mode 7 0.5 1.9 11.9 140.7
MODAL Mode 8 0.4 2.3 14.3 204.1
MODAL Mode 9 0.4 2.4 14.9 223.4
MODAL Mode 10 0.4 2.4 15.2 230.3
MODAL Mode 11 0.4 2.8 17.7 314.3
MODAL Mode 12 0.3 3.0 19.1 364.9

177
STRAIGHT DIAGONAL BRACE SYSTEM
Table 75 Modal Analysis : Straight Diagoonal Brace System
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.3 0.4 2.8 7.7
MODAL Mode 2 2.2 0.5 2.8 8.0
MODAL Mode 3 1.2 0.8 5.3 27.8
MODAL Mode 4 0.8 1.2 7.5 56.2
MODAL Mode 5 0.8 1.2 7.7 60.0
MODAL Mode 6 0.6 1.8 11.3 128.2
MODAL Mode 7 0.5 1.9 11.9 140.7
MODAL Mode 8 0.4 2.3 14.3 204.1
MODAL Mode 9 0.4 2.4 14.9 223.4
MODAL Mode 10 0.4 2.4 15.2 230.3
MODAL Mode 11 0.4 2.8 17.7 314.3
MODAL Mode 12 0.3 3.0 19.1 364.9

178
CURVED DIAGONAL BRACE SYSTEM – CURVE 2
Table 76 Modal Analaysis : Curved Diagonal Brace System - Curve 2
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.4 0.4 2.7 7.1
MODAL Mode 2 2.3 0.4 2.8 7.7
MODAL Mode 3 1.2 0.8 5.1 25.8
MODAL Mode 4 0.9 1.1 7.2 51.4
MODAL Mode 5 0.8 1.2 7.5 56.0
MODAL Mode 6 0.5 1.9 12.2 147.7
MODAL Mode 7 0.5 2.0 12.7 161.3
MODAL Mode 8 0.4 2.4 15.0 226.0
MODAL Mode 9 0.4 2.7 16.7 278.6
MODAL Mode 10 0.4 2.8 17.6 308.4
MODAL Mode 11 0.3 3.2 20.2 407.9
MODAL Mode 12 0.3 3.5 21.8 476.2

179
CASE 2 : 90X 150 X 252 FT
MOMENT FRAME STRUCTURE

Table 77 Modal Analysis : Moment Frame Structure
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 5.7 0.2 1.1 1.2
MODAL Mode 2 4.7 0.2 1.3 1.8
MODAL Mode 3 2.3 0.4 2.8 7.7
MODAL Mode 4 2.0 0.5 3.2 10.4
MODAL Mode 5 1.6 0.6 3.9 15.6
MODAL Mode 6 1.1 0.9 5.5 30.4
MODAL Mode 7 0.9 1.1 6.8 46.4
MODAL Mode 8 0.8 1.3 7.9 63.1
MODAL Mode 9 0.8 1.3 8.0 63.8
MODAL Mode 10 0.6 1.6 9.9 98.9
MODAL Mode 11 0.6 1.7 10.7 114.5
MODAL Mode 12 0.5 2.1 13.4 180.3

180
CENTRAL BAY BRACED FRAME ( CORE BRACE)

Table 78 Modal Analysis : Central Bay Braced Frame ( Core Brace )
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.7 0.4 2.4 5.6
MODAL Mode 2 2.5 0.4 2.5 6.1
MODAL Mode 3 1.5 0.7 4.2 17.4
MODAL Mode 4 0.8 1.2 7.5 56.9
MODAL Mode 5 0.8 1.2 7.7 59.5
MODAL Mode 6 0.5 1.9 11.8 139.8
MODAL Mode 7 0.5 2.2 13.6 185.3
MODAL Mode 8 0.4 2.3 14.2 202.3
MODAL Mode 9 0.3 3.2 20.0 400.0
MODAL Mode 10 0.3 3.2 20.2 409.0
MODAL Mode 11 0.3 3.3 20.7 427.3
MODAL Mode 12 0.3 3.4 21.6 466.1

181
PERIPHERAL BRACED FRAME SYSTEM

Table 79 Modal Analysis : Peripheral Braced Frame System
OutputCas
e
StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1
2.5 0.4 2.5 6.1
MODAL Mode 2
2.0 0.5 3.1 9.6
MODAL Mode 3
1.3 0.8 4.8 23.4
MODAL Mode 4
0.9 1.2 7.4 54.1
MODAL Mode 5
0.7 1.5 9.2 85.0
MODAL Mode 6
0.5 2.0 12.9 165.4
MODAL Mode 7
0.4 2.3 14.2 200.5
MODAL Mode 8
0.4 2.5 15.8 249.3
MODAL Mode 9
0.4 2.8 17.8 318.2
MODAL Mode 10
0.3 3.1 19.5 381.7
MODAL Mode 11
0.3 3.1 19.6 384.8
MODAL Mode 12
0.3 3.1 19.6 386.1

182
STRAIGHT DIAGONAL BRACE SYSTEM

Table 80 Modal Analysis Straight Diagonal Brace System
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.9 0.4 2.2 4.8
MODAL Mode 2 2.3 0.4 2.8 7.6
MODAL Mode 3 1.4 0.7 4.4 19.0
MODAL Mode 4 1.1 0.9 5.9 34.5
MODAL Mode 5 0.8 1.2 7.6 58.2
MODAL Mode 6 0.7 1.4 8.8 76.7
MODAL Mode 7 0.6 1.8 11.0 121.2
MODAL Mode 8 0.6 1.8 11.2 124.6
MODAL Mode 9 0.5 1.9 12.2 149.5
MODAL Mode 10 0.5 2.2 13.7 188.2
MODAL Mode 11 0.4 2.5 15.9 253.3
MODAL Mode 12 0.3 2.9 18.5 340.6

183
CURVED DIAGONAL BRACE SYSTEM – CURVE 2

Table 81 Modal Analysis : Curved Diagonal Brace System - Curve 2
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 2.8 0.4 2.3 5.1
MODAL Mode 2 2.2 0.4 2.8 7.8
MODAL Mode 3 1.4 0.7 4.6 21.2
MODAL Mode 4 1.2 0.8 5.1 26.3
MODAL Mode 5 0.9 1.1 6.9 48.2
MODAL Mode 6 0.7 1.4 8.5 72.0
MODAL Mode 7 0.6 1.7 10.8 117.2
MODAL Mode 8 0.6 1.8 11.3 127.1
MODAL Mode 9 0.6 1.8 11.4 129.2
MODAL Mode 10 0.5 2.1 13.4 180.0
MODAL Mode 11 0.4 2.4 15.1 226.9
MODAL Mode 12 0.4 2.8 17.8 315.7

184
CASE 3 150 X 150 X 600 FT

DOUBLE STRAIGHT BRACE SYSTEM

Table 82 Modal Analysis Double Straight Brace System
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 4.4 0.2 1.4 2.1
MODAL Mode 2 4.3 0.2 1.4 2.1
MODAL Mode 3 2.4 0.4 2.7 7.0
MODAL Mode 4 1.6 0.6 4.0 16.2
MODAL Mode 5 1.5 0.7 4.1 16.9
MODAL Mode 6 1.2 0.9 5.4 29.6
MODAL Mode 7 1.1 0.9 5.8 33.4
MODAL Mode 8 0.9 1.1 6.9 48.0
MODAL Mode 9 0.8 1.3 8.0 64.7
MODAL Mode 10 0.7 1.4 8.5 72.4
MODAL Mode 11 0.7 1.4 8.6 74.0
MODAL Mode 12 0.7 1.4 8.7 76.0

185
DOUBLE CURVED BRACE SYSTEM

Table 83 Modal Analysis : Double Curved Brace System
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 4.59 0.22 1.37 1.87
MODAL Mode 2 4.54 0.22 1.38 1.92
MODAL Mode 3 2.40 0.42 2.61 6.83
MODAL Mode 4 1.51 0.66 4.15 17.25
MODAL Mode 5 1.48 0.68 4.25 18.07
MODAL Mode 6 1.13 0.89 5.58 31.09
MODAL Mode 7 1.07 0.94 5.88 34.60
MODAL Mode 8 0.99 1.01 6.32 39.96
MODAL Mode 9 0.92 1.09 6.82 46.57
MODAL Mode 10 0.89 1.13 7.09 50.24
MODAL Mode 11 0.72 1.38 8.67 75.15
MODAL Mode 12 0.72 1.39 8.71 75.82

186
MULTIPLE STRAIGHT BRACE (EVERY 10 FLOORS)

Table 84 Modal Analysis : Multiple Straight brace ( Every 10 floors)
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 3.9 0.3 1.6 2.6
MODAL Mode 2 3.9 0.3 1.6 2.7
MODAL Mode 3 1.9 0.5 3.4 11.4
MODAL Mode 4 1.2 0.8 5.0 25.5
MODAL Mode 5 1.2 0.8 5.1 26.0
MODAL Mode 6 0.7 1.5 9.4 88.8
MODAL Mode 7 0.7 1.5 9.6 91.3
MODAL Mode 8 0.6 1.6 9.9 97.6
MODAL Mode 9 0.6 1.8 11.1 122.8
MODAL Mode 10 0.5 1.9 11.8 140.3
MODAL Mode 11 0.5 1.9 11.9 141.7
MODAL Mode 12 0.5 2.0 12.5 157.5

187
MULTIPLE CURVED BRACE (EVERY 10 FLOORS)

Table 85 Modal Analysis : Multiple curved Brace ( Every 10 Floors )
OutputCase StepType StepNum Period Frequency CircFreq Eigenvalue
Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2
MODAL Mode 1 4.1 0.2 1.5 2.3
MODAL Mode 2 4.1 0.2 1.5 2.4
MODAL Mode 3 2.0 0.5 3.2 10.0
MODAL Mode 4 1.3 0.8 4.9 23.5
MODAL Mode 5 1.3 0.8 4.9 24.0
MODAL Mode 6 0.7 1.4 8.7 75.7
MODAL Mode 7 0.7 1.4 8.8 78.1
MODAL Mode 8 0.7 1.5 9.1 83.2
MODAL Mode 9 0.6 1.8 11.1 122.7
MODAL Mode 10 0.5 1.9 11.8 139.2
MODAL Mode 11 0.5 1.9 11.9 141.1
MODAL Mode 12 0.5 1.9 12.1 146.4

188
APPENDIX C
ADDITIONAL MATERIAL DATA - STEEL SECTIONS

STEEL SECTIONS USED IN THE DESIGN OF 90 X 90 X 252 ft LAYOUT

Table 86 Frame Section PropertiGes 01 - General, Part 1 of 4

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W14X370 A992Fy50
I/Wide
Flange
1.49 1.38 0.22 0.14 1.38 0.22
W14X398 A992Fy50
I/Wide
Flange
1.53 1.38 0.24 0.15 1.38 0.24
W14X426 A992Fy50
I/Wide
Flange
1.56 1.39 0.25 0.16 1.39 0.25
W14X500 A992Fy50
I/Wide
Flange
1.63 1.42 0.29 0.18 1.42 0.29
W18X86 A992Fy50
I/Wide
Flange
1.53 0.93 0.06 0.04 0.93 0.06
W18X97 A992Fy50
I/Wide
Flange
1.55 0.93 0.07 0.04 0.93 0.07

189

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W18X106 A992Fy50
I/Wide
Flange
1.56 0.93 0.08 0.05 0.93 0.08
W18X119 A992Fy50
I/Wide
Flange
1.58 0.94 0.09 0.05 0.94 0.09
W21X68 A992Fy50
I/Wide
Flange
1.76 0.69 0.06 0.04 0.69 0.06
W21X73 A992Fy50
I/Wide
Flange
1.77 0.69 0.06 0.04 0.69 0.06
W21X93 A992Fy50
I/Wide
Flange
1.80 0.70 0.08 0.05 0.70 0.08
W21X111 A992Fy50
I/Wide
Flange
1.79 1.03 0.07 0.05 1.03 0.07
BU 14X
342
A992Fy50
SD
Section
-- -- -- -- -- --
W14X109 A992Fy50
I/Wide
Flange
1.19 1.22 0.07 0.04 1.22 0.07

Table 86 : Continued

190
Frame Section Properties 01 - General, Part 2 of 4
Table 87 Frame Section Properties 01 - General, Part 2 of 4

SectionName Area TorsConst I33 I22 AS2 AS3
ft2 ft4 ft4 ft4 ft2 ft2
W14X370 0.76 0.01 0.26 0.10 0.21 0.51
W14X398 0.81 0.01 0.29 0.10 0.22 0.55
W14X426 0.87 0.02 0.32 0.11 0.24 0.59
W14X500 1.02 0.02 0.40 0.14 0.30 0.69
W18X86 0.18 0.00 0.07 0.01 0.06 0.10
W18X97 0.20 0.00 0.08 0.01 0.07 0.11
W18X106 0.22 0.00 0.09 0.01 0.08 0.12
W18X119 0.24 0.00 0.11 0.01 0.09 0.14
W21X68 0.14 0.00 0.07 0.00 0.06 0.07
W21X73 0.15 0.00 0.08 0.00 0.07 0.07
W21X93 0.19 0.00 0.10 0.00 0.09 0.09
W21X111 0.23 0.00 0.13 0.01 0.08 0.12
BU 14X 342 1.21 0.50 0.31 0.33 0.74 0.68
W14X109 0.22 0.00 0.06 0.02 0.05 0.15

191
Frame Section Properties 01

Table 88 Frame Section Properties 01 - General, Part 3 of 4
SectionName S33 S22 Z33 Z22 R33 R22
ft3 ft3 ft3 ft3 ft ft
W14X370
0.352 0.140 0.426 0.214 0.589 0.356
W14X398
0.379 0.151 0.464 0.233 0.597 0.359
W14X426
0.408 0.164 0.503 0.251 0.606 0.362
W14X500
0.485 0.196 0.608 0.302 0.623 0.369
W18X86
0.096 0.018 0.108 0.028 0.648 0.219
W18X97
0.109 0.021 0.122 0.032 0.653 0.221
W18X106
0.118 0.023 0.133 0.035 0.653 0.222
W18X119
0.133 0.026 0.152 0.040 0.658 0.224
W21X68
0.081 0.009 0.093 0.014 0.717 0.150
W21X73
0.087 0.010 0.100 0.015 0.719 0.151
W21X93
0.111 0.013 0.128 0.020 0.726 0.154
W21X111
0.144 0.026 0.161 0.039 0.753 0.241
BU 14X 342
0.421 0.425 0.551 0.550 0.503 0.524
W14X109
0.100 0.035 0.111 0.054 0.519 0.311

192

Table 89 Frame Section Properties 01 - General, Part 4 of 4
SectionName AMod A2Mod A3Mod JMod I2Mod I3Mod MMod WMod

W14X370 1 1 1 1 1 1 1 1
W14X398 1 1 1 1 1 1 1 1
W14X426 1 1 1 1 1 1 1 1
W14X500 1 1 1 1 1 1 1 1
W18X86 1 1 1 1 1 1 1 1
W18X97 1 1 1 1 1 1 1 1
W18X106 1 1 1 1 1 1 1 1
W18X119 1 1 1 1 1 1 1 1
W21X68 1 1 1 1 1 1 1 1
W21X73 1 1 1 1 1 1 1 1
W21X93 1 1 1 1 1 1 1 1
W21X111 1 1 1 1 1 1 1 1
BU 14X 342 1 1 1 1 1 1 1 1
W14X109 1 1 1 1 1 1 1 1

193
STEEL SECTIONS USED IN THE DESIGN OF 90 X 150 X 252 FT LAYOUT

Table 90 Frame Section Properties 02 - General, Part 1 of 4

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W14X211 A992Fy50
I/Wide
Flange
1.308 1.317 0.130 0.082 1.317 0.130
W14X311 A992Fy50
I/Wide
Flange
1.425 1.350 0.188 0.117 1.350 0.188
W14X426 A992Fy50
I/Wide
Flange
1.558 1.392 0.253 0.157 1.392 0.253
W14X500 A992Fy50
I/Wide
Flange
1.633 1.417 0.292 0.183 1.417 0.292
W14X550 A992Fy50
I/Wide
Flange
1.683 1.433 0.318 0.198 1.433 0.318
W14X605 A992Fy50
I/Wide
Flange
1.742 1.450 0.347 0.217 1.450 0.347
W18X86 A992Fy50
I/Wide
Flange
1.533 0.925 0.064 0.040 0.925 0.064
W18X97 A992Fy50
I/Wide
Flange
1.550 0.925 0.073 0.045 0.925 0.073

194

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W18X119 A992Fy50
I/Wide
Flange
1.583 0.942 0.088 0.055 0.942 0.088
W18X130 A992Fy50
I/Wide
Flange
1.608 0.933 0.100 0.056 0.933 0.100
W24X76 A992Fy50
I/Wide
Flange
1.992 0.749 0.057 0.037 0.749 0.057
W24X84 A992Fy50
I/Wide
Flange

2.008

0.752 0.064 0.039 0.752 0.064
W24X94 A992Fy50
I/Wide
Flange
2.025 0.756 0.073 0.043 0.756 0.073
W24X103 A992Fy50
I/Wide
Flange
2.042 0.750 0.082 0.046 0.750 0.082
W27X102 A992Fy50
I/Wide
Flange
2.258 0.833 0.069 0.043 0.833 0.069
W27X146 A992Fy50
I/Wide
Flange
2.283 1.167 0.081 0.050 1.167 0.081

Table 90 : Continued

195
Table 91 Frame Section Properties 01 - General, Part 2 of 4
SectionName Area TorsConst I33 I22 AS2 AS3
ft2 ft4 ft4 ft4 ft2 ft2
W14X211
0.4306 0.0022 0.1283 0.0497 0.1068 0.2853
W14X311
0.6347 0.0066 0.2088 0.0776 0.1674 0.4238
W14X426
0.8681 0.0160 0.3183 0.1138 0.2441 0.5876
W14X500
1.0208 0.0248 0.3959 0.1389 0.2981 0.6887
W14X550
1.1250 0.0323 0.4548 0.1567 0.3339 0.7605
W14X605
1.2361 0.0419 0.5208 0.1775 0.3774 0.8378
W18X86
0.1757 0.0002 0.0738 0.0084 0.0613 0.0989
W18X97
0.1979 0.0003 0.0844 0.0097 0.0691 0.1118
W18X119
0.2438 0.0005 0.1056 0.0122 0.0864 0.1386
W18X130
0.2653 0.0007 0.1186 0.0134 0.0898 0.1556
W24X76
0.1556 0.0001 0.1013 0.0040 0.0730 0.0708

196

W24X84
0.1715 0.0002 0.1143 0.0046 0.0787 0.0804
W24X94
0.1924 0.0003 0.1302 0.0053 0.0869 0.0919
W24X103
0.2104 0.0003 0.1447 0.0057 0.0936 0.1021
W27X102
0.2083 0.0003 0.1746 0.0067 0.0969 0.0961
W27X146
0.2993 0.0005 0.2730 0.0214 0.1151 0.1580
Table 91 : Continued

197
Table 92 Frame Section Properties 01 - General, Part 3 of 4
SectionName S33 S22 Z33 Z22 R33 R22
ft3 ft3 ft3 ft3 ft ft
W14X211
0.20 0.08 0.23 0.11 0.55 0.34
W14X311
0.29 0.12 0.35 0.18 0.57 0.35
W14X426
0.41 0.16 0.50 0.25 0.61 0.36
W14X500
0.48 0.20 0.61 0.30 0.62 0.37
W14X550
0.54 0.22 0.68 0.34 0.64 0.37
W14X605
0.60 0.24 0.76 0.38 0.65 0.38
W18X86
0.10 0.02 0.11 0.03 0.65 0.22
W18X97
0.11 0.02 0.12 0.03 0.65 0.22
W18X119
0.13 0.03 0.15 0.04 0.66 0.22
W18X130
0.15 0.03 0.17 0.04 0.67 0.22
W24X76
0.10 0.01 0.12 0.02 0.81 0.16
W24X84
0.11 0.01 0.13 0.02 0.82 0.16
W24X94
0.13 0.01 0.15 0.02 0.82 0.17

198

W24X103
0.14 0.02 0.16 0.02 0.83 0.17
W27X102
0.15 0.02 0.18 0.03 0.92 0.18
W27X146
0.24 0.04 0.27 0.06 0.95 0.27
Table 92 : Continued

199
Table 93 Frame Section Properties 01 - General, Part 4 of 4

SectionName AMod A2Mod A3Mod JMod I2Mod I3Mod MMod WMod

W14X211 1 1 1 1 1 1 1 1
W14X311 1 1 1 1 1 1 1 1
W14X426 1 1 1 1 1 1 1 1
W14X500 1 1 1 1 1 1 1 1
W14X550 1 1 1 1 1 1 1 1
W14X605 1 1 1 1 1 1 1 1
W18X86 1 1 1 1 1 1 1 1
W18X97 1 1 1 1 1 1 1 1
W18X119 1 1 1 1 1 1 1 1
W18X130 1 1 1 1 1 1 1 1

200

SectionName AMod A2Mod A3Mod JMod I2Mod I3Mod MMod WMod

W24X76 1 1 1 1 1 1 1 1
W24X84 1 1 1 1 1 1 1 1
W24X94 1 1 1 1 1 1 1 1
W24X103 1 1 1 1 1 1 1 1
W27X102 1 1 1 1 1 1 1 1
W27X146 1 1 1 1 1 1 1 1

Table 93 : Continued

201
STEEL SECTIONS USED IN THE DESIGN OF 150 X 150 X 600 FT LAYOUT

Table 94 Frame Section Properties 01 - General, Part 1 of 4

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W14X233 A992Fy50
I/Wide
Flange
1.33 1.32 0.14 0.09 1.32 0.14
W14X370 A992Fy50
I/Wide
Flange
1.49 1.38 0.22 0.14 1.38 0.22
W14X550 A992Fy50
I/Wide
Flange
1.68 1.43 0.32 0.20 1.43 0.32
W14X605 A992Fy50
I/Wide
Flange
1.74 1.45 0.35 0.22 1.45 0.35
W14X730 A992Fy50
I/Wide
Flange
1.87 1.49 0.41 0.26 1.49 0.41
W18X76 A992Fy50
I/Wide
Flange
1.52 0.92 0.06 0.04 0.92 0.06
W18X86 A992Fy50
I/Wide
Flange
1.53 0.93 0.06 0.04 0.93 0.06
W18X97 A992Fy50
I/Wide
Flange
1.55 0.93 0.07 0.04 0.93 0.07

202

SectionName Material Shape t3 t2 tf tw t2b tfb
ft ft ft ft ft ft
W18X130 A992Fy50
I/Wide
Flange
1.61 0.93 0.10 0.06 0.93 0.10
W18X143 A992Fy50
I/Wide
Flange
1.63 0.93 0.11 0.06 0.93 0.11
W24X117 A992Fy50
I/Wide
Flange
2.02 1.07 0.07 0.05 1.07 0.07
W24X131 A992Fy50
I/Wide
Flange
2.04 1.07 0.08 0.05 1.07 0.08
W24X146 A992Fy50
I/Wide
Flange
2.06 1.07 0.09 0.05 1.07 0.09
W24X162 A992Fy50
I/Wide
Flange
2.08 1.08 0.10 0.06 1.08 0.10
W24X176 A992Fy50
I/Wide
Flange
2.10 1.07 0.11 0.06 1.07 0.11

Table 94 : Continued

203
Table 95 Frame Section Properties 01 - General, Part 2 of 4
SectionName Area TorsConst I33 I22 AS2 AS3
ft2 ft4 ft4 ft4 ft2 ft2
W14X233
0.48 0.00 0.15 0.06 0.12 0.32
W14X370
0.76 0.01 0.26 0.10 0.21 0.51
W14X550
1.13 0.03 0.45 0.16 0.33 0.76
W14X605
1.24 0.04 0.52 0.18 0.38 0.84
W14X730
1.49 0.07 0.69 0.23 0.48 1.02
W18X76
0.15 0.00 0.06 0.01 0.05 0.09
W18X86
0.18 0.00 0.07 0.01 0.06 0.10
W18X97
0.20 0.00 0.08 0.01 0.07 0.11
W18X130
0.27 0.00 0.12 0.01 0.09 0.16
W18X143
0.29 0.00 0.13 0.02 0.10 0.17
W24X117
0.24 0.00 0.17 0.01 0.09 0.13

204

W24X131
0.27 0.00 0.19 0.02 0.10 0.14
W24X146
0.30 0.00 0.22 0.02 0.11 0.16
W24X162
0.33 0.00 0.25 0.02 0.12 0.18
W24X176
0.36 0.00 0.27 0.02 0.13 0.20
Table 95 : Continued

205

SectionName S33 S22 Z33 Z22 R33 R22
ft3 ft3 ft3 ft3 ft ft
W14X233 0.22 0.08 0.25 0.13 0.55 0.34
W14X370 0.35 0.14 0.43 0.21 0.59 0.36
W14X550-
A
0.54 0.22 0.68 0.34 0.64 0.37
W14X605 0.60 0.24 0.76 0.38 0.65 0.38
W14X730 0.74 0.31 0.96 0.47 0.68 0.39
W18X76 0.08 0.02 0.09 0.02 0.64 0.22
W18X86 0.10 0.02 0.11 0.03 0.65 0.22
W18X97 0.11 0.02 0.12 0.03 0.65 0.22
Table 96 Frame Section Properties 01 - General, Part 3 of 4

206

W18X130 0.15 0.03 0.17 0.04 0.67 0.22
W18X143 0.16 0.03 0.19 0.05 0.67 0.23
W24X117 0.17 0.03 0.19 0.04 0.85 0.24
W24X131 0.19 0.03 0.21 0.05 0.85 0.25
W24X146 0.21 0.04 0.24 0.05 0.86 0.25
W24X162 0.24 0.04 0.27 0.06 0.87 0.25
W24X176 0.26 0.04 0.30 0.07 0.87 0.25
W14X233 0.22 0.08 0.25 0.13 0.55 0.34
Table 96 : Continued

207
Table 97 Frame Section Properties 01 - General, Part 4 of 4
SectionName AMod A2Mod A3Mod JMod I2Mod I3Mod MMod WMod

W14X233 1 1 1 1 1 1 1 1
W14X370 1 1 1 1 1 1 1 1
W14X550-A 1 1 1 1 1 1 1 1
W14X605 1 1 1 1 1 1 1 1
W14X730 1 1 1 1 1 1 1 1
W18X76 1 1 1 1 1 1 1 1
W18X86 1 1 1 1 1 1 1 1
W18X97 1 1 1 1 1 1 1 1
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AISHWARYA BALAGOPAL UNIVERSITY OF SOUTHERN CALIFORNIA
Table 97 : Continued

Abstract (if available)

Abstract Wind and seismic loads cause buildings to shift from their vertical axis of inertia resulting in lateral displacement, also termed as drift. It is extremely crucial to stabilize tall buildings in the event of large lateral load that cause buildings to flex beyond their limit of elasticity, resulting in structural damage that can prove to be fatal. This thesis proposes to study the efficiency of a diagonal curved brace system as an alternate to retrofit existing steel moment frame structures. The study was conducted with a moment frame structure as a base case and how retrofitting the structure with the proposed diagonal curved brace induced better performance in the structure as compared to the performance of the structure when retrofitted with different forms of straight brace systems. Analyses of the proposed system was performed in SAP2000- a finite element analysis software, the mass of steel in the structure has been constant for all retrofit structures in the study. The idea of using a parabolic brace form was obtained from the catenary form used in the design of suspension bridges and the parabolic form used in the design of the Eiffel tower.

Linked assets

University of Southern California Dissertations and Theses

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Asset Metadata

Creator Balagopal, Aishwarya (author)

Core Title Design proposal and analysis of curved brace system to reduce drift in moment frame structures

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 08/03/2012

Defense Date 08/03/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag curved brace,OAI-PMH Harvest,reduce drift,structural systems

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Shierle, Goetz (committee chair), Carlson, Anders (committee member), Losche, Edward (committee member), Murat, Melek (committee member)

Creator Email abalagop@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-86937

Unique identifier UC11289978

Identifier usctheses-c3-86937 (legacy record id)

Legacy Identifier etd-BalagopalA-1135.pdf

Dmrecord 86937

Document Type Thesis

Rights Balagopal, Aishwarya

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA