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University of Southern California Dissertations and Theses

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Seismic retrofitting with cost effectiveness

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Seismic retrofitting with cost effectiveness

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SEISMIC RETROFITTING WITH COST EFFECTIVENESS: STEEL BRACED FRAME, STEEL
MOMENT FRAME, CONCRETE SHEAR WALL, CONCRETE MOMENT FRAME

by

Han Sang Kim

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 Han Sang Kim
ii

Acknowledgements
I would like to give my warmest thanks to Professor Anders Carlson. As my committee
chair, he has unfailingly attended to my questions and concerns throughout my whole
thesis process. Though having so much on his plate, he has continued to share and shed
light in improving and revising my thesis. I was blessed to have an opportunity to work
with Professor Carlson.

I would like to deeply thank Professor Mohsen Kargahi who has helped me greatly as my
committee member. It all started following a Thursday night steel design course when I
had asked of his guidance in my thesis, and what a great help he has been. Professor,
thank you for your generous help even whilst your work and even opening up your
home during your precious weeknights. My thesis would not be where it is without your
concerns and guidance.

My thanks and gratitude extends to Professor Marc Schiler, our thesis studio instructor.
Professor Schiler, you have so lovingly encouraged our class each week with discipline
ultimately out of a genuine concern for us to finish. Not only were you a professor I
respected but a man of character I look up to and hope to follow. Without your initial
approval during my application process into the MBS program, I would not have had this
chance to study in the first place.

iii

My family holds a special place in my heart, and I cannot express enough thanks to my
parents who have never once discouraged me in my studies and in life. My brother,
Hyun Sang, is my role model and will forever strive together.

Lastly, I would like to give my highest regards to God, who I devote this thesis and my
life to. I contribute where I am in life all to Him, and I hope my work and my life glorifies
God. Lord, thank you for holding me and guiding me in all facets of my life and through
this strenuous yearlong process in completing this thesis.

All glory to God.
iv

Table of Contents
Acknowledgements ..............................................................................................................ii
List of Tables ..................................................................................................................... viii
List of Figures .................................................................................................................... xiii
Abstract ............................................................................................................................ xvii
Chapter 1: Introduction
1.1 Background ................................................................................................................ 1
1.1.1 Recent Earthquakes ............................................................................................ 1
1.1.2 Nature of Earthquakes........................................................................................ 4
1.1.3 Parameters of Seismic Design ............................................................................ 5
1.2 Research Statement .................................................................................................. 7
1.3 Goals/Objective ......................................................................................................... 8
1.3.1 Building Codes .................................................................................................... 9
1.3.2 Structural Systems ............................................................................................ 10
1.3.3 Structural Retrofits ........................................................................................... 10
1.3.4 Cost Implications .............................................................................................. 11
1.4 Structure and Method ............................................................................................. 12
1.4.1 Structural System Analyses .............................................................................. 13
1.4.2 Rehabilitation of Existing Buildings .................................................................. 14
1.4.3 Cost Analysis ..................................................................................................... 14
Summary ....................................................................................................................... 15

Chapter 2: Seismic Design
2.1 Goals and Provisions ................................................................................................... 16
2.2 Building Codes and Guidelines ................................................................................ 17
2.2.1 County of Los Angeles Building Laws 1971 and California Building Code 201017
2.2.2 ASCE 41 ............................................................................................................. 18
2.3 Effects and Dynamic Behavior ................................................................................. 23
Analysis Procedures ................................................................................................... 25
2.4 Structural Systems ................................................................................................... 25
2.4.1 Steel Moment Frame ........................................................................................ 26
2.4.2 Steel Braced Frame ........................................................................................... 27
2.4.3 Concrete Shear Wall System ............................................................................ 28
2.4.4 Concrete Moment Frame ................................................................................. 29
2.5 Seismic Retrofitting ................................................................................................. 30
2.5.1 Steel Moment Frame Retrofits ......................................................................... 32
v

2.5.2 Steel Braced Frame Retrofits ............................................................................ 32
2.5.3 Concrete Shear Wall Retrofits .......................................................................... 33
2.5.4 Concrete Moment Frame Retrofits .................................................................. 34
Summary ....................................................................................................................... 35

Chapter 3: Research Procedures
3.1 Design of Existing Buildings ........................................................................................ 36
3.1.1 Steel Braced Frame ........................................................................................... 37
3.1.2 Steel Moment Frame ........................................................................................ 41
3.1.3 Concrete Shear Wall Core ................................................................................. 44
3.1.4 Concrete Moment Frame ................................................................................. 46
3.2 Analyze Existing Structure: Case Studies................................................................. 48
3.2.1 Waite Phillips Hall (WPH) ................................................................................. 49
3.2.2 Webb Tower (WTO) .......................................................................................... 51
3.3 Implement Retrofits ................................................................................................ 52
3.3.1 Evaluation ......................................................................................................... 52
3.3.2 Implementation ................................................................................................ 53
3.3.3 Validity of Table ................................................................................................ 53
Summary ....................................................................................................................... 54

Chapter 4: Steel Structure Design and Retrofit
4.1 Design of Steel Braced Frame Structure ..................................................................... 55
4.1.1 Design Using 1971 Los Angeles Building Code ................................................. 55
4.1.2 Braced Frame Details ........................................................................................ 58
4.1.3 Design of Framing Members ............................................................................ 58
4.1.4 Framing Details ................................................................................................. 62
4.1.5 Existing Building Weights ................................................................................. 64
4.2 Design of Steel Moment Frame Structure .............................................................. 66
4.2.1 Design using 1971 Los Angeles Building Code .................................................. 66
4.2.2 Moment Frame Details ..................................................................................... 67
4.2.3 Design of Framing Members ............................................................................ 68
4.2.4 Framing Details ................................................................................................. 70
4.2.5 Existing Building Weights ................................................................................. 71
4.3 Retrofit Design of Steel Braced Frame Structure .................................................... 73
4.3.1 Implementation of Different Retrofit Solutions ............................................... 73
4.3.2 SBF Retrofit 1: Additional Bracing .................................................................... 74
4.3.3 SBF Retrofit 2: Addition of Shear Walls ............................................................ 77
4.3.4 SBF Retrofit 3: Additional Plates ....................................................................... 81
4.4 Retrofit Design of Steel Moment Frame Structure ................................................. 83
4.4.1 Implementation of Retrofit Solutions .............................................................. 83
4.4.2 SMF Retrofit 1: Additional Bracing ................................................................... 85
vi

4.4.3 SMF Retrofit 2: Shear Walls .............................................................................. 87
4.4.4 SMF Retrofit 3: Additional Plates ..................................................................... 90
4.5 Comparisons between Retrofit Implementations .................................................. 92
4.5.1 Cost Considerations .......................................................................................... 93
4.5.2 Architectural Considerations ............................................................................ 96
4.5.3 Constructability Concerns ................................................................................ 97
Summary ....................................................................................................................... 98

Chapter 5: Concrete Structure Design and Retrofit
5.1 Design of Concrete Shear Wall Core Structure ........................................................... 99
5.1.1 Design using 1971 Los Angeles Building Code .................................................. 99
5.1.2 Framing Details ............................................................................................... 101
5.1.3 Design of Framing Members .......................................................................... 102
5.1.4 Framing Details ............................................................................................... 104
5.1.5 Existing Building Weight ................................................................................. 106
5.2 Design of Concrete Moment Frame Structure ...................................................... 109
5.2.1 Design using 1971 Los Angeles Building Code ................................................ 109
5.2.2 Framing Details ............................................................................................... 111
5.2.3 Design of Framing Members .......................................................................... 112
5.2.4 Size of Framing Members ............................................................................... 113
5.2.5 Existing Building Weight ................................................................................. 115
5.3 Retrofit Design of Concrete Shear Wall Core Structure ........................................ 118
5.3.1 Implementation of Retrofit Solutions ............................................................ 118
5.3.2 CSW Retrofit 1: Additional Bracing ................................................................. 119
5.3.3 CSW Retrofit 2: Addition of Shear Walls ........................................................ 122
5.4 Retrofit Design of Concrete Moment Frame Structure ........................................ 125
5.4.1 Implementation of Retrofit Solutions ............................................................ 125
5.4.2 CMF Retrofit 1: Additional Bracing ................................................................. 127
5.4.3 CMF Retrofit 2: Addition of Shear Walls ........................................................ 129
5.5 Comparisons of Retrofits ....................................................................................... 132
5.5.1 Cost Considerations ........................................................................................ 132
5.5.2 Architectural Considerations .......................................................................... 135
5.5.3 Constructability Concerns .............................................................................. 136
Summary ..................................................................................................................... 136

Chapter 6: Case Studies – Waite Phillips Hall and Webb Tower
6.1 Analysis of Waite Phillips Hall ................................................................................... 138
6.1.1 Existing Building Information ......................................................................... 138
6.1.2 Performance under 2010 California Building Code ........................................ 146
6.1.3 WPH Retrofit 1: Additional Bracing ................................................................ 147
6.1.4 WPH Retrofit 2: Additional Shear Walls ......................................................... 149
vii

6.2 Analysis of Webb Tower ........................................................................................ 153
6.2.1 Existing Building Information ......................................................................... 153
6.2.2 Performance under 2010 California Building Code ........................................ 162
6.2.3 WTO Retrofit 1: Additional Bracing (Existing Retrofit) ................................... 163
6.2.4 WTO Retrofit 2: Additional Shear Walls ......................................................... 166
6.3 Comparison of Retrofit Implementations ............................................................. 169
6.5.1 Cost Considerations ........................................................................................ 169
6.5.2 Architectural Considerations .......................................................................... 172
6.5.3 Constructability Concerns .............................................................................. 173
Summary ..................................................................................................................... 174

Chapter 7: Summary and Conclusions
7.1 Summary ............................................................................................................... 176
7.2 Conclusions ............................................................................................................ 177
7.2.1 Performance Comparisons ............................................................................. 177
7.2.2 Cost Comparisons ........................................................................................... 178
7.2.3 Architectural/Constructability Concerns ........................................................ 180
7.2.4 Matrix of Tabulated Information .................................................................... 183
7.3 Experiences ........................................................................................................... 183
7.3.1 SAP 2000 Software ......................................................................................... 183
7.3.2 Addition of Diaphragms in Model Study ........................................................ 184
7.3.3 Seismic Design Criteria ................................................................................... 184
7.4 Recommendations for Further Research .............................................................. 185
7.4.1 Choice of Computer Software ........................................................................ 185
7.4.2 Simplified Structural Models and Analysis ..................................................... 186
7.4.3 Framing Detailing and Connections ............................................................... 186
7.4.4 Additional Retrofit Implementations ............................................................. 187
7.4.5 Comparison of Construction Time .................................................................. 187

Bibliography .................................................................................................................... 188

Appendix: Structural Design Excel Spreadsheet ............................................................. 190

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List of Tables

TABLE 1: TOTAL DEAD LOAD (SBF) .................................................................................... 56
TABLE 2: TOTAL BASE SHEAR (SBF) ................................................................................... 56
TABLE 3: DISTRIBUTION OF LATERAL FORCES .................................................................. 57
TABLE 4: LIST OF COLUMNS (SBF) ..................................................................................... 62
TABLE 5: LIST OF BEAMS (SBF) .......................................................................................... 63
TABLE 6: LIST OF GIRDERS (SBF) ....................................................................................... 63
TABLE 7: LIST OF BRACES (SBF) ......................................................................................... 63
TABLE 8: BEAM WEIGHTS (SBF) ........................................................................................ 64
TABLE 9: GIRDER WEIGHTS (SBF) ...................................................................................... 64
TABLE 10: BRACE WEIGHTS (SBF) ..................................................................................... 64
TABLE 11: COLUMN WEIGHTS (SBF) ................................................................................. 65
TABLE 12: LOADING VALUES (SMF) .................................................................................. 66
TABLE 13: TOTAL BASE SHEAR (SMF) ................................................................................ 66
TABLE 14: DISTRIBUTION OF BASE SHEAR (SMF) ............................................................. 67
TABLE 15: LIST OF BEAMS AND GIRDERS (SMF) ............................................................... 70
TABLE 16: LIST OF COLUMNS (SMF) ................................................................................. 70
TABLE 17: BEAM/GIRDER WEIGHTS (SMF) ....................................................................... 71
TABLE 18: COLUMN WEIGHTS (SMF) ................................................................................ 72
TABLE 19: BASE SHEAR COMPARISON (SBF) ..................................................................... 73
TABLE 20: LIST OF BRACES (SBF RETROFIT 1) ................................................................... 76
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TABLE 21: LIST OF COLUMNS (SBF RETROFIT 1) ............................................................... 76
TABLE 22: COST ANALYSIS (SBF RETROFIT 1) .................................................................... 77
TABLE 23: INCREASED LOADING VALUES ......................................................................... 78
TABLE 24: DESIGN OF SHEAR WALLS (SBF RETROFIT 2) ................................................... 80
TABLE 25: COST ANALYSIS (SBF RETROFIT 2) .................................................................... 80
TABLE 26: LIST OF COLUMNS/BRACES (SBF RETROFIT 1) ................................................. 82
TABLE 27: COST ANALYSIS (SBF RETROFIT 3) .................................................................... 83
TABLE 28: BASE SHEAR COMPARISON (SMF) ................................................................... 84
TABLE 29: LIST OF BRACES (SMF RETROFIT 1) .................................................................. 86
TABLE 30: COST ANALYSIS (SMF RETROFIT 1) ................................................................... 87
TABLE 31: INCREASED LOADING VALUES (SMF RETROFIT 2) ........................................... 88
TABLE 32: DESIGN OF SHEAR WALLS (SMF RETROFIT 2) .................................................. 89
TABLE 33: COST ANALYSIS (SMF RETROFIT 2) ................................................................... 90
TABLE 34: LIST OF COLUMNS (SMF RETROFIT 3) .............................................................. 91
TABLE 35: COST ANALYSIS (SMF RETROFIT 3) ................................................................... 92
TABLE 36: TOTAL DEAD LOAD (CSW) .............................................................................. 100
TABLE 37: TOTAL BASE SHEAR (CSW) ............................................................................. 100
TABLE 38: DISTRIBUTION OF BASE SHEAR (CSW) ........................................................... 101
TABLE 39: LIST OF COLUMNS (CSW) ............................................................................... 104
TABLE 40: LIST OF BEAMS AND GIRDERS (CSW) ............................................................. 105
TABLE 41: WEIGHT OF BEAMS (CSW) ............................................................................. 106
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TABLE 42: WEIGHT OF GIRDERS (CSW) ........................................................................... 107
TABLE 43: WEIGHT OF SHEAR WALL (CSW) .................................................................... 107
TABLE 44: WEIGHT OF COLUMNS (CSW) ........................................................................ 108
TABLE 45: TOTAL DEAD LOAD (CMF) .............................................................................. 110
TABLE 46: TOTAL BASE SHEAR (CMF) ............................................................................. 110
TABLE 47: DISTRIBUTION OF BASE SHEAR (CMF) ........................................................... 111
TABLE 48: LIST OF COLUMNS (CMF) ............................................................................... 114
TABLE 49: LIST OF BEAMS AND GIRDERS (CMF) ............................................................. 115
TABLE 50: WEIGHT OF BEAMS AND GIRDERS (CMF) ...................................................... 116
TABLE 51: WEIGHT OF COLUMNS (CMF) ........................................................................ 117
TABLE 52: BASE SHEAR COMPARISONS (CSW) ............................................................... 118
TABLE 53: LIST OF BRACES (CSW RETROFIT 1) ................................................................ 121
TABLE 54: COST ANALYSIS (CSW RETROFIT 1) ................................................................ 122
TABLE 55: INCREASED BASE SHEAR (CSW RETROFIT 2) .................................................. 123
TABLE 56: COST ANALYSIS (CSW RETROFIT 2) ................................................................ 125
TABLE 57: BASE SHEAR COMPARISONS (CMF) ............................................................... 126
TABLE 58: LIST OF BRACES (CMF RETROFIT 1) ................................................................ 128
TABLE 59: COST ANALYSIS (CMF RETROFIT 1) ................................................................ 129
TABLE 60: INCREASED DEAD LOAD VALUES (CMF RETROFIT 2) ..................................... 130
TABLE 61: INCREASED BASE SHEAR (CMF RETROFIT 2) .................................................. 130
TABLE 62: SHEAR WALL DESIGN (CMF RETOFIT 2) ......................................................... 131
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TABLE 63: COST ANALYSIS (CMF RETROFIT 2) ................................................................ 132
TABLE 64: TOTAL DEAD LOAD (WPH) ............................................................................. 140
TABLE 65: TOTAL BASE SHEAR (WPH) ............................................................................. 141
TABLE 66: DISTRIBUTION OF BASE SHEAR (WPH) .......................................................... 141
TABLE 67: LIST OF COLUMNS (WPH) .............................................................................. 142
TABLE 68: LIST OF BEAMS (WPH) .................................................................................... 143
TABLE 69: WEIGHT OF BEAMS (WPH) ............................................................................. 144
TABLE 70: WEIGHT OF SHEAR WALLS (WPH) .................................................................. 144
TABLE 71: WEIGHT OF COLUMNS (WPH) ....................................................................... 145
TABLE 72: BASE SHEAR COMPARISONS (WPH) ............................................................... 146
TABLE 73: LIST OF BRACES (WPH RETROFIT 1) ............................................................... 148
TABLE 74: COST ANALYSIS (WPH RETROFIT 1) ................................................................ 149
TABLE 75: INCREASED LOADING ..................................................................................... 151
TABLE 76: SHEAR WALL DESIGN (WPH RETROFIT 2) ...................................................... 152
TABLE 77: COST ANALYSIS (WPH RETROFIT 2) ................................................................ 153
TABLE 78: TOTAL DEAD LOAD (WTO) ............................................................................. 156
TABLE 79: TOTAL BASE SHEAR (WTO) ............................................................................. 157
TABLE 80: DISTRIBUTION OF BASE SHEAR (WTO) .......................................................... 157
TABLE 81: LIST OF COLUMNS (WTO) .............................................................................. 158
TABLE 82: LIST OF BEAMS (WTO) .................................................................................... 159
TABLE 83: WEIGHTS OF BEAMS (WTO) ........................................................................... 160
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TABLE 84: WEIGHT OF COLUMNS 1 (WTO) .................................................................... 160
TABLE 85: WEIGHT OF COLUMNS 2 (WTO) .................................................................... 161
TABLE 86: BASE SHEAR COMPARISON (WTO) ................................................................ 162
TABLE 87: LIST OF BRACES (WPH RETROFIT 1) ............................................................... 165
TABLE 88: COST ANALYSIS (WTO RETROFIT 1) ............................................................... 165
TABLE 89: INCREASED LOADING (WTO RETROFIT 2) ...................................................... 167
TABLE 90: SHEAR WALL DESIGN (WTO RETROFIT 2) ...................................................... 168
TABLE 91: COST ANALYSIS (WTO RETROFIT 2) ............................................................... 168
TABLE 92: COST INCREASE COMPARISONS..................................................................... 171
TABLE 93: COST COMPARISON CHART ........................................................................... 180
TABLE 94:BEAM DESIGN (SMF) ....................................................................................... 190
TABLE 95: GIRDER DESIGN (SMF).................................................................................... 190
TABLE 96: NON‐MOMENT FRAME DESIGN (SMF) .......................................................... 191
TABLE 97: MOMENT FRAME DESIGN (SMF) ................................................................... 191
TABLE 98: BEAM DESIGN (SBF) ....................................................................................... 192
TABLE 99: GIRDER DESIGN (SBF) ..................................................................................... 192
TABLE 100: EDGE GIRDER DESIGN (SBF) ......................................................................... 193
TABLE 101: EDGE BEAM DESIGN (SBF) ........................................................................... 193

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List of Figures

FIGURE 1: CHRISTCHURCH EARTHQUAKE ........................................................................... 1
FIGURE 2: 2011 TOHOKU EARTHQUAKE ............................................................................. 2
FIGURE 3: SAN ANDREAS FAULT LINE ................................................................................. 5
FIGURE 4: STEEL BRACED FRAME PLAN ............................................................................ 39
FIGURE 5: STEEL MOMENT FRAME PLAN ......................................................................... 42
FIGURE 6: CONCRETE SHEAR WALL CORE PLAN ............................................................... 45
FIGURE 7: CONCRETE MOMENT FRAME PLAN ................................................................. 47
FIGURE 8: WAITE PHILLIPS HALL ELEVATION AND PLAN VIEWS ...................................... 50
FIGURE 10: ELEVATION AND PLAN VIEWS OF WEBB TOWER .......................................... 51
FIGURE 11: LATERAL LOAD APPLICATION ......................................................................... 57
FIGURE 12: STEEL BRACED FRAME SAP 2000 MODEL ...................................................... 58
FIGURE 13: BEAM LAYOUT IN SAP 2000 ........................................................................... 59
FIGURE 14: COLUMN FRAMING PLAN (SBF) ..................................................................... 63
FIGURE 15: BEAM FRAMING PLAN (SBF) .......................................................................... 63
FIGURE 16: BRACED FRAMING PLAN (SBF) ....................................................................... 63
FIGURE 17: STEEL MOMENT FRAME PLAN ....................................................................... 68
FIGURE 18: BEAM FRAMING PLAN (SMF) ......................................................................... 70
FIGURE 19: COLUMN FRAMING PLAN (SMF) .................................................................... 71
FIGURE 20: SBF PERFORMANCE PRIOR TO RETROFITS ..................................................... 74
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FIGURE 21: SBF RETROFIT 1 ELEVATION ........................................................................... 75
FIGURE 22: SBF RETROFIT 1 PERFORMANCE .................................................................... 76
FIGURE 23: BOX COLUMN SECTION .................................................................................. 77
FIGURE 24: SBF RETROFIT 2: PLAN AND ELEVATION ........................................................ 78
FIGURE 25: SBF RETROFIT 2 PERFORMANCES .................................................................. 79
FIGURE 26: PERFORMANCE (SBF RETROFIT 3) .................................................................. 81
FIGURE 27: PERFORMANCE PRIOR TO RETROFITS (SMF) ................................................. 84
FIGURE 28: ELEVATION VIEW (SMF RETROFIT 1).............................................................. 85
FIGURE 29: PERFORMANCE (SMF RETROFIT 1) ................................................................ 86
FIGURE 30: PLAN AND ELEVATION VIEWS (SMF RETROFIT 2) .......................................... 87
FIGURE 31: PERFORMANCE (SMF RETROFIT 2) ................................................................ 88
FIGURE 32: SHEAR WALL ELEVATION ............................................................................... 89
FIGURE 33: PERFORMANCE (SMF RETROFIT 3) ................................................................ 91
FIGURE 34: COST ANALYSIS (SBF) ..................................................................................... 95
FIGURE 35: COST ANALYSIS (SMF) .................................................................................... 95
FIGURE 36: LATERAL LOAD APPLICATION ....................................................................... 101
FIGURE 37: PLAN AND ELEVATION VIEW (CSW) ............................................................. 101
FIGURE 39: COLUMN FRAMING PLAN (CSW) ................................................................. 104
FIGURE 40: BEAM AND GIRDER FRAMING PLAN ............................................................ 105
FIGURE 41: LATERAL LOAD APPLICATION ....................................................................... 111
FIGURE 42: ELEVATION AND PLAN VIEWS (CMF) ........................................................... 112
xv

FIGURE 43: COLUMN FRAMING PLAN (CMF) ................................................................. 114
FIGURE 44: PERFORMANCE PRIOR TO RETROFITS (CSW)............................................... 119
FIGURE 45: PLAN AND ELEVATION VIEW (CSW RETROFIT 1) ......................................... 120
FIGURE 46: PERFORMANCE (CSW RETROFIT 1) .............................................................. 120
FIGURE 47: PLAN AND ELEVATION VIEWS (CSW RETROFIT 2) ....................................... 122
FIGURE 48: INCREASED DEAD LOAD (CSW RETROFIT 2) ................................................. 123
FIGURE 49: PERFORMANCE (CSW RETROFIT 2) .............................................................. 124
FIGURE 50: DESIGN OF SHEAR WALLS (CSW RETROFIT 2) .............................................. 124
FIGURE 51: PERFORMANCE PRIOR TO RETROFITS (CMF) ............................................... 126
FIGURE 52: PLAN AND ELEVATION VIEW (CMF RETROFIT 1) ......................................... 127
FIGURE 53: PERFORMANCE (CMF RETROFIT 1) .............................................................. 128
FIGURE 54: PLAN AND ELEVATION VIEW (CMF RETROFIT 2) ......................................... 129
FIGURE 55: PERFORMANCE (CMF RETROFIT 2) .............................................................. 131
FIGURE 56: COST ANALYSIS (CSW) .................................................................................. 134
FIGURE 57: COST ANALYSIS (CMF) .................................................................................. 135
FIGURE 58: PLAN VIEW (WPH) ........................................................................................ 139
FIGURE 59: ELEVATION VIEWS (WPH) ............................................................................ 139
FIGURE 60: COLUMN FRAMING PLAN (WPH) ................................................................. 142
FIGURE 61: BEAM FRAMING PLAN (WPH) ...................................................................... 143
FIGURE 62: PERFORMANCE PRIOR TO RETROFITS (WPH) .............................................. 147
FIGURE 63: ELEVATION VIEWS (WPH RETROFIT 1) ......................................................... 148
xvi

FIGURE 64: PERFORMANCE (WPH RETROFIT 1) ............................................................. 148
FIGURE 65: PLAN AND ELEVATION VIEWS (WPH RETROFIT 2) ....................................... 150
FIGURE 66: PERFORMANCE (WPH RETROFIT 2) ............................................................. 152
FIGURE 67: PLAN VIEW (WTO) ........................................................................................ 154
FIGURE 68: ELEVATION VIEWS (WTO) ............................................................................ 154
FIGURE 69: PLAN AND ELEVATION VIEW PRIOR TO RETROFITS (WTO) ......................... 155
FIGURE 70: COLUMN FRAMING PLANS (WTO) ............................................................... 159
FIGURE 71: BEAM FRAMING PLAN (WTO) ...................................................................... 159
FIGURE 72: PERFORMANCE PRIOR TO RETROFITS (WTO) .............................................. 163
FIGURE 73: PLAN VIEW (WPH RETROFIT 1) .................................................................... 164
FIGURE 74: ELEVATION VIEW (WPH RETROFIT 1) .......................................................... 164
FIGURE 75: PERFORMANCE (WTO RETROFIT 1) ............................................................. 165
FIGURE 76: PLAN AND ELEVATION VIEW (WTO RETROFIT 2) ......................................... 166
FIGURE 77: PERFORMANCE (WTO RETROFIT 2) ............................................................. 167
FIGURE 78: COST ANALYSIS (WPH) ................................................................................. 171
FIGURE 79: COST ANALYSIS (WTO) ................................................................................. 172
FIGURE 80: MATRIX OF RETROFIT IMPLEMENTATIONS ................................................. 183

xvii

Abstract
Located in the heart of Los Angeles, USC is considered an earthquake prone zone, and
there is a vital imperative to ensure the safety of all students and faculties during such
an event. In order to prevent casualties, buildings must be checked and assured to
perform under design loads.

Under the current California Building Code (CBC), engineers must design all structural
members for new buildings to meet CBC 2010 standards. However, designing to simply
meet the standards cannot ensure the safety of the building and its occupants as seismic
loads in earthquakes cannot be predicted and can exceed building code expectations.
When retro‐fitting of existing buildings (designed under earlier, less stringent codes) is
considered, the CBC 2010 standards may be applied with the same caveat.

This study considers structural retrofit systems for existing buildings, taking into account
economic as well as structural factors. Two USC buildings, Waite Phillips Hall (WPH), a
12‐story classroom/office building, and Webb Tower (WTO), a 14‐story residential
building, were chosen as case‐studies to represent mid‐size buildings constructed in the
Los Angeles area. Four hypothetical structural systems for retrofit were studied: steel
braced frame, steel moment frame, concrete shear wall core, and concrete moment
frame systems. In accordance to design earthquake loads, the different systems’
xviii

differences in framing element size, weight, and cost were detailed and recorded. This
study will help future architects, engineers and contractors to understand the value
issues in trade‐offs of material and structural choices.

The thesis conducted a study of these structural systems in these steps: first, differing
levels of design loads were implemented to each system, and framing elements had
been selected accordingly. Simplified hand calculations were used to calculate design
loads, and an excel spreadsheet with design formulae was used to select the framing
elements. A three‐dimensional modeler, SAP 2000, was used to assign all members and
evaluate each structural system. Second, through SAP 2000’s feature, “steel/concrete
design check of structure”, all members proved viable in accordance to current code.
Data from the building was then extruded onto an Excel spreadsheet in order to analyze
cost for each system and retrofit.

Through this study, a guideline for choosing the most cost‐efficient structural system
was created for an earthquake zone such as Los Angeles. Though these structural
systems cannot represent all building types in Los Angeles, the present study outlines a
system for typological study for working professionals in design of structures. This study
hopes to assist designers and contractors in the reality of building for safety rather than
cost.
1

Chapter 1: Introduction
1.1 Background

Figure 1: Christchurch Earthquake
1

1.1.1 Recent Earthquakes
In 2010 alone, there have been many headlines of various earthquakes globally which
devastated many lives of people and homes. In March 2010, the earthquake in Japan
devastated many citizens in the city of Sendai as well as creating large tidal waves that
led to a nuclear meltdown in the Fukushima power plants. The recorded magnitude on
the Richter scale was at an astonishing 9.0, and researchers believe Japan will have

1
“Christchurch Earthquake”
2

spent $300 billion and a full 3‐5 years for full recovery. Numerous aftershocks following
the initial earthquake brought further fear in Japan (Tohoku).
2

Figure 2: 2011 Tohoku Earthquake
3

Earlier in February 2011, the earthquake in Christchurch, New Zealand, its second
largest city with a population of 390,000, killed 181 lives and took a toll on the buildings
as many were concrete block and unreinforced masonry construction.
4
The downtown
core is still closed to the public seven months later. The nation of Haiti is still recovering
from its earthquake in 2009 as unreinforced masonry structures showed how vulnerable

2
“2011 Tohoku Earthquake”
3
“2011 Tohoku Earthquake”
4
“2011 Christchurch Earthquake – Wikipedia, the free encyclopedia”
3

they were against a 7.0 magnitude earthquake.
5
Though designers and builders in the
profession may not be able to stop the occurrence of earthquakes, what can they do to
provide safer societies for communities?

Californians aren’t exempt from the fear of earthquakes or the possible damage they
can bring. There have been many talks with regards to the next big earthquake in
California, and researchers claim that the “big earthquake” on the San Andreas Fault has
been overdue for about 100 years.
6
In preparation for such an event, do engineers and
architects have a part in constructing safer structures? In the last decade alone,
Southern California suffered from its most devastating earthquake in 60 years, the 6.7
Richter scale 1994 Northridge Earthquake, where more than 50 people died, 5000
injured, 10,000 buildings red or yellow tagged, and more than 25,000 houses vacated.
7

Past research in design seemed to prove our structures, under the earthquake codes
that were current in 1994, were safe and reliable. However, following the seismic event,
researchers were kept busy trying to understand why, for instance, a steel moment
frame building failed in unexpected ways and why soft‐story construction suffered so
much damage. To better understand how earthquakes affect the design of structure, we
will touch upon the nature of earthquakes.

5
“2010 Haiti Earthquake – Wikipedia, the free encyclopedia”
6
“San Andreas Fault Line – Wikipedia, the free encyclopedia”
7
“1994 Northridge earthquake – Wikipedia, the free encyclopedia”
4

1.1.2 Nature of Earthquakes
To better understand the design of structures in response to seismic activity, we will
first study the rationale behind an earthquake. An earthquake occurs through a
dislocation in the crust, man‐made explosion, or volcano, seismic waves or vibrations
which propagate beginning from the point of origin.
8
This dislocation can cause the
adjacent rock to carry the propagation of energy to the next. If the amount of released
energy is small, the seismic waves will dissipate unnoticeable. However, if the energy is
considerably large, the affect it has on the inhabitants and structures in areas of strong
shaking will be chaotic.

Underneath our surface are plates which are in constant movement at the rate of a
millimeter a week. There are roughly about 12 large plates with many smaller plates,
and when these plates try to move past each other, friction builds up and locks them in
place. Once a slippage occurs, the released energy translates into a strike‐slip type of
earthquake. The San Andreas Fault which is located in California is the border between
two very significant plates: the Pacific and the North American plates. Therefore, one
can imagine how devastating the after‐effects of the San Andreas Earthquake will be to
the many buildings and people living in California.
9


8
Ambrose and Vergun, Design for Lateral Forces
9
Ibid.
5

Figure 3: San Andreas Fault Line
10

1.1.3 Parameters of Seismic Design
In order to predict and design for a particular earthquake, it is necessary to study three
parameters in seismic design: magnitude, acceleration, and location. Magnitudes are
studied and assessed through a Richter scale, which Professor Richter had normalized as
a scale to measure the amount of energy released by an earthquake.
11
Through a
moment magnitude scale, one can measure the amount of energy released through the
formula, where E is the energy released in Ergs and M is the magnitude:
Log E = 11.4 + 1.5M

10
“San Andreas Fault Line”
11
Ambrose and Vergun, Design for Lateral Forces.
6

As the magnitude is given in logarithmic scale, each unit of magnitude increased by a
factor of 31.6.
12
Therefore, a 7.0 scale earthquake is 31.6 times stronger than a 6.0 scale
quake. Additionally, the magnitude of an earthquake is easy to record as it does not vary
by location.

An accelerograph record provides the time‐history of ground shaking, and it provides a
good scale for the intensity of an earthquake, which is the numeric record of a quake’s
effect as experienced at a particular location.
13
The acceleration of a quake is recorded
in a factor of g, the acceleration due to gravity of 32ft/s
2
.

The magnitude or frequency of the occurrence of earthquakes cannot be predicted,
however, over time and through studies, it is possible to use good judgment in
estimating the ground shaking while designing structures for seismic efforts. For
preliminary designs, seismic maps are available from the USGS, United States Geological
Survey: “The U.S. Geological Survey (USGS) National Seismic Hazard Maps display
earthquake ground motions for various probability levels across the United States and
are applied in seismic provisions of building codes, insurance rate structures, risk
assessments, and other public policy. This update of the maps incorporates new findings
on earthquake ground shaking, faults, seismicity, and geodesy. The resulting maps are

12
Ibid.
13
Ibid.
7

derived from seismic hazard curves calculated on a grid of sites across the United States
that describe the frequency of exceeding a set of ground motions.”
14
For an accurate
estimate of seismic forces, a site‐specific seismic evaluation tool such as Java Ground
Motion Parameter Calculator, provided by USGS, can be used to design.

1.2 Research Statement
Structural retrofits mainly concern strengthening and improving the capacities of
buildings which may not meet current code standards as well as its importance level.
Buildings built earlier may be built using obsolete techniques or may not be considered
safe according to current building code. For instance, the welding or connection details
may not be up to standard design and construction which may jeopardize the safety of
the structure under seismic activities.

There have been many studies done with regards to seismic design, however, there
aren’t many guidelines regarding the implementation of structural retrofits on past
buildings. This thesis looks to help architects and engineers reach a preliminary idea
regarding how a particular retrofit solution will benefit in both cost and efficiency. For
instance, this study investigates how a diagonal bracing creates stiffness and improve
the strength of the particular structure.

14
“Hazard Mapping Images and Data”
8

Not only is the design of structural members in a retrofit important but cost can become
the primary factor behind an owner’s decision whether to implement a retrofit. First,
the necessity of structural retrofit will be studied, and if yes, the study will then focus on
how much retrofit is needed as well as the cost for each level of retrofit.

Through this study, a guideline will be created for designers in the profession to
consider for structural retrofits. They will learn the vast array of available retrofits for
particular situations and how each retrofit helps to benefit the building. Through a cost‐
analysis, the contractor in the profession will also be able to assess how important the
retrofit will be and analyze whether the implementation is plausible. Though this study
primarily focuses on mid‐rise buildings built in Los Angeles, the different retrofit
solutions will be applicable to buildings built in other earthquake prone locations.

1.3 Goals/Objective
In designing a building, the architectural layout and mechanical plans may be important,
but a building maintains its main objective as providing safety for its occupants. In early
times, the safety may have been against marauders or enemies looking to overtake their
portion of land. In contemporary society, it is vital to build safe structures against
impending earthquakes especially in a seismic zone such as Los Angeles. So what is
considered a safe structure and where do we draw the line? To answer this question,
the thesis looks to provide a guideline for preliminary design of structure in seismic
9

areas with the following topics in concern through a parametric study of cost and
structural retrofits. The following elaborates more on what this thesis looks to uncover.

1.3.1 Building Codes
Building codes serve as the standard for designing structures in order to protect public
health, safety and general welfare as they relate to the construction and occupancy of
buildings and structures.
15
In the United States, the Uniform Building Code (UBC)
headed by the International Council of Building Officials primarily held jurisdiction over
the design of buildings until its final version of the code, UBC 1997.
16
Now, buildings are
designed under the International Building Code (IBC) headed by the International Code
Council (ICC) starting from 2000.
17
Despite many discrepancies, the International
Building Code (IBC) is now adopted at the state or local level in 50 states plus
Washington, D.C.
18
This thesis will study how past codes and today’s code differ in
stringent design and how each design behaves under a certain given load.


15
“Building code – Wikipedia, the free encyclopedia”
16
“Uniform building code – Wikipedia, the free encyclopedia”
17
“International Building Code – Wikipedia, the free encyclopedia”
18
Ibid.
10

1.3.2 Structural Systems
As technology and research improves there are a number of structural systems a
designer can implement. Not only do these systems have a structural aspect in adding
load capacity to the structure, but these systems have their pros and cons in
architectural design as well. In this thesis, the four systems in study are steel moment‐
resistive frames, steel braced frames, concrete shear wall core, and concrete moment‐
resistive frames. These four systems behave differently under seismic loading and have
their advantages over each other. Additionally, these systems use a different amount of
material during design considerations as well as providing architectural and
constructability considerations.

1.3.3 Structural Retrofits
Many different types of retrofits can be implemented on structures with regards to a
particular problem an existing building has. The goal of this thesis is to find and analyze
the implementation of various retrofits and examine the difference in strength capacity.
The various implications in implementation will also consider architectural concerns,
ease of implementation, and engineering rationale. For instance, it would be better
suited for a connection plate to increase its net area (A
n
) by increasing the number of
bolts rather than having to change the size of the plate.
19
A solution which eliminates a
local problem is best suited for this situation.

19
Segui, Steel Design, 45
11

1.3.4 Cost Implications
It sure is important to strengthen existing buildings through retrofits to prevent major
damage during an earthquake. However, the flip side of the argument is also valid: is a
residential building with expensive retrofits which can withstand a 9.0 magnitude
earthquake which occurs every 300 years worth it?

Through a study, FEMA attempted to gather data for seismic rehabilitating buildings in
FEMA 156: Typical Costs for Seismic Rehabilitation of Existing Buildings. According to the
study, these five points of research were primarily focused: “a clear definition of costs, a
rigorous data collection procedure, a written data collection protocol, intensive follow‐
up efforts to verify the data, and a stringent quality control process.”
20
As for its sample
data, FEMA has studied more than 2000 seismic retrofits prior to the year 1993. The
data separates different building types, such as unreinforced masonry, wood framing,
steel moment frame, steel braced frame, concrete shear wall, etc, as well as
categorizing seismicity into four levels: low, moderate, high and very high.
21

From these samples of data, one can see the variance in costs amongst the building
types. Retrofits for a moment frame building in a low seismic zone differed from a

20
FEMA 156, Typical Costs for Seismic Rehabilitation of Existing Buildings
21
Ibid.
12

braced frame in a low seismic zone in costs. As proved in this study, the cost in the
retrofit of various systems will differ, and each difference will be examined.

1.4 Structure and Method
In creating a guideline for structural retrofitting of existing buildings, a set of
hypothetical mid‐rise buildings were created. The buildings are 12 stories high with 75’ x
75’ floor areas. Four predominant structural systems amongst mid‐rise buildings were
studied: steel moment frame, steel braced frame, reinforced concrete shear wall, and
reinforced concrete moment frame. These four systems were analyzed and designed
per 1971 Los Angeles building code as existing buildings. Then, these buildings were
analyzed under today’s current code as per 2010 California Building Code. Various
retrofit ideas were implemented and an optimized design was recommended. Each
implementation of retrofit system was tabulated into a matrix which shows the increase
in strength in comparison to design loads and the cost of implementing the system by
increased amount in material.

Given two buildings in Los Angeles, Waite Phillips Hall (WPH) and Webb Tower (WTO),
this study implemented an analysis of various structural retrofits and their related costs.
Waite Phillips Hall (WPH) and Webb Tower (WTO) were chosen as case‐studies to
represent mid‐rise buildings constructed in the Los Angeles area. The guidelines made
13

from the study helped with preliminary decisions with regards to the knowledge of
which type of systems work and which do not.

For the architect, the study on the array of structural retrofits will give them ideas as to
which systems are best combined and which are most design‐friendly. Though they may
not have the engineering expertise, this study can help them understand in tangible
terms as the study is based on a real building built in Los Angeles. For the engineer, the
cost analysis will help them view from the contractor’s perspective in valuing finances.
In comparing the value and effectiveness of systems with cost, the engineer can have a
better pool to decide from. In analyzing the relationship between retrofits and cost, the
research has been divided by: structural system analyses, structural retrofit
implementations, and cost analyses.

1.4.1 Structural System Analyses
The four structural systems along with the two case‐study buildings were analyzed using
their architectural and structural plans. By taking into account the buildings’ heights and
structural system, hand calculations based on code were used to calculate seismic
design loads. A three‐dimensional model in SAP 2000 was created by inputting column
spacing and all other dimensions. Through an analysis in SAP 2000, each framing
members’ moment, shear, and axial values were recorded. From these values, framing
member sizes were selected, and an excel spreadsheet calculated the required values.
14

1.4.2 Rehabilitation of Existing Buildings
Following the previous analysis, each structure was given several retrofit ideas. Different
structural systems were placed into consideration: rigid framing and braced framing.
Along with these two different framing, it was necessary to combine these framing with
various retrofits of their own. For example, an existing braced frame was retrofitted
with additional bracings added to exterior bays while an alternative was to add moment
connections to the existing braced frame. Through the analysis run in SAP 2000, these
various combinations produced varying behaviors under seismic activity.

1.4.3 Cost Analysis
Naturally, in designing for a greater earthquake force, there is an increase in the size
and weight of framing elements. This increase in weight of material is how the study
determined the increase in cost. Though there are many other factors involved with cost
in seismic retrofitting, this simplified approach showed useful comparative data by
detailing the difference in amounts of material used between different structural
systems. After gathering these values, a cost per amount of material provided by a
reliable cost estimate source gave numbers easily used in a comparative analysis.


15

Summary
The next big earthquake in California is no longer a mystery but is widely expected.
What can be done to help prepare future building designs and currently built
structures? This thesis explores the importance in maintaining the safety of occupants in
buildings by properly analyzing structures with sound engineering. Additionally, with
structures which are designed for an outdated, less stringent building code, the study
explores options for different retrofit ideas while assessing cost with each
implementation.

The methodology described reveals easy‐to‐follow rationale behind engineering to help
not only the trained engineers but also the architects who do not have such familiarity
with structural engineering. The case‐study analysis hopes to bring into light the safety
and construction of WPH and WTO, while various retrofits and systems help in providing
a guideline for preliminary design of structures.

In the following chapters, the details and further elaboration of various methodologies
are described.

16

Chapter 2: Seismic Design
2.1 Goals and Provisions
In order to design a building permitted by the city, the building must abide under the
requirements or code as provided by the respective jurisdiction’s building code. For
instance, areas of high seismicity would enforce stricter building code guidelines when
compared to areas of low seismicity. Despite the differences among jurisdictions, the
building code has a common goal: provide the safety of occupants. Bungale S. Taranath
Ph.D. writes most seismic codes are written with these goals in mind: “1) minimize the
hazard of life for all structures; 2) increase the expected performance of structures
having a substantial public hazard due to occupancy or use; and 3) improve the
capability of essential facilities to function after an earthquake.”
22
Earthquake forces can
cause serious damage to the framing of a structure as seismic loading is cyclical. Most
building codes expect some structural damage “when the building experiences design
ground motions because almost all building codes allow inelastic energy dissipation in
structural systems.”
23
Certain building types such as nuclear facilities are not allowed to
be designed in the inelastic range, but many structures used for commercial or
residential purposes allow the design of certain members to yielding with prior
considerations in making sure the elements which support the gravity load are intact.

22
Taranath, Wind and Earthquake Resistant Buildings, 502
23
Ibid, 501.
17

Designing all structures for the elastic range, though it may be safe, would be highly
uneconomical. However, the number of lost lives and damage to buildings from
earthquakes continue to show the imperative for improvements needed in the building
code.
24

2.2 Building Codes and Guidelines
An insight into the philosophy behind the building codes and guidelines is described
below in hope of understanding what today’s standards call safe and having met
requirements. The 1971 County of Los Angeles Building Code and the 2010 California
Building Code were building design requirements enforced in the respective years. ASCE
41 is a guideline specifically published for the seismic rehabilitation of existing buildings
by the American Society of Civil Engineers.
25

2.2.1 County of Los Angeles Building Laws 1971 and California Building Code 2010
The seismic design of structures in this thesis will be maintained within two building
codes: 1971 County of Los Angeles Building Laws and the 2010 California Building Code.
The 1971 County of Los Angeles Building Laws contains four documents: the County of
Los Angeles Building Code, the Plumbing Code, the Mechanical Code, and the Electrical

24
Ibid, 501.
25
ASCE 41, Seismic Rehabilitation of Existing Buildings
18

Code. Behind these four documents lie various adaptations.
26
The Mechanical Code
adopts the 1970 Uniform Mechanical Code from the International Association of
Plumbing and Mechanical Officials and the International Conference of Building
Officials. The code shows requirements for heating, ventilation, air conditioning/comfort
cooling and refrigeration. The Building Code adopts the 1970 Uniform Building Code,
and the Plumbing Code adopts the 1970 Uniform Plumbing Code. From these codes
come the fundamental purposes in protecting the public health, safety and welfare
within minimum code standards by building design, construction, and administrative
procedures.

The 2010 California Building Code has significantly grown not only in content but in
detail from its 40 year old predecessor. The 2010 CBC addresses building standards from
architecture, structural, to mechanical and electrical. Through numerous research and
studies, the formulas for calculations have developed, and these charts and values hope
to create safer structures while being mindful of cost.

2.2.2 ASCE 41
ASCE 41: Seismic Rehabilitation of Existing Buildings serves to provide a standard for
nationally applicable provisions in the seismic rehabilitation of existing buildings, while
the 2010 California Building Code primarily refers to the design of new construction. In

26
County of Los Angeles Uniform Building Laws
19

this section, the four main different analyses options will be discussed as well as the
standard’s approach in dealing with seismic retrofits in existing buildings.
27

Scope/Goal
The ASCE 41 standard deals with seismically upgrading structures through three steps.
First, the existing building must be evaluated through an approved process or
methodology in defining the deficiencies in the building. Second, a rehabilitation
objective must be selected in which the designer plans to undertake. Rehabilitation
objectives refer to goals targeting certain building performance levels in the midst of
certain earthquake levels. These objectives will be given further detail in the following
section. Third, the appropriate processes to achieve the selected objectives must be
implemented.
28

ASCE 41 recognizes that there are still uncertainties in designing seismically as the
standard does not guarantee the structure will meet the rehabilitation objectives
despite compliance. New research and the understanding of behaviors of buildings
under earthquakes continue to improve existing codes.



27
ASCE 41, Seismic Rehabilitation of Existing Buildings
28
Ibid.
20

Seismic Rehabilitation Process
Prior to implementing seismic retrofits to a building, the ASCE 41 standard advises a
methodology to cover details in design. First, an initial evaluation of the existing building
must be performed to check the structure’s deficiencies. If interest is found to upgrade
the building’s seismic capabilities, several considerations can be studied: “structural
characteristics, site seismic hazards, results from prior seismic evaluations, historic
status, economic considerations, and societal issues.”
29
Gathering this information is to
simplify and ensure the process of rehabilitation as the process takes off from its initial
stages. Historical and societal issues can be concerns for buildings that are of historical
value or other issues this thesis will not touch upon. Economic considerations prove to
be a vital leverage for whether a retrofit goes through from planning to implementation.
If an upgrade is not a necessity but proves to be too costly, it is more likely the upgrade
will not occur.

Secondly, a rehabilitation objective will be chosen for a given building. Concerns with
regards to deciding on an objective include whether the rehabilitation project is
voluntary or mandated. In a voluntary project, the building owner can simply choose to
his liking what the objective should be. However, in a mandated project, the objective
must abide by the local code and advice of the code official.


29
Ibid.
21

Third, a rehabilitation method must be chosen: either simplified or systematic. A
simplified rehabilitation method only applies to buildings which are applicable to Table
10‐1 in ASCE 41. These buildings must not have irregularities or the retrofit must project
the elimination of irregularities. Therefore, the simplified approach agrees that the
given building is small, regular that do not require advanced analysis as well as achieving
the Life Safety Performance Level for the BSE‐1 Earthquake Hazard Level. However, this
thesis will force the systematic rehabilitation method as maximum stories represented
in Table 10‐1 are six. The systematic rehabilitation method includes the analysis
procedures: linear static procedure, linear dynamic procedure, nonlinear static
procedure, and nonlinear dynamic procedure.
30

Fourth, rehabilitation designs will be performed by developing a mathematical model,
from which then force and deformation responses will be evaluated. Fifth, the
rehabilitation design will be reviewed with compliance to code as well as how it fits
economically.
31

Rehabilitation Objectives
Rehabilitation objectives rely on meeting a particular building performance level target
for a design earthquake hazard level. ASCE 41 divides target building performance levels

30
Ibid.
31
Ibid.
22

into four: operational performance level, immediate occupancy level, life safety
performance level, and collapse prevention level. Operational performance level (1‐A)
ensures the overall damage to be very light and generally, the structure maintains its
strength and stiffness with no permanent drift. All operations functions as normal in this
level. Immediate occupancy level (1‐B) is inflicted with light damage with elevators
having to restart and some nonstructural components failing. However, there is no
permanent drift or loss of strength of stiffness in the overall structure. Life safety level
(3‐C) takes moderate damage, and gravity load resistant members still stand. Damage
may be beyond economic repair, but the members still retain some strength. Collapse
prevention level (5‐E) takes severe damage, and the building is near collapse with
extensive damage done to the structure. However, columns and walls still function
though with large permanent drifts.
32

The earthquake hazard levels are also divided into four probabilities: 50%/50 year,
20%/50 year, 10%/50 year, and 2%/50 year. The percentage refers to the probability of
a particular earthquake occurring in a 50 year span. For instance, the 50%/50 year
earthquake would refer to a seismic event which may occur with a 50% chance within a
50 year period. On the other hand, the 2%/50 year earthquake is one that doesn’t occur
as often but is the most deadly. The decrease in percentage in these levels shows the

32
Ibid.
23

increase in severity of the seismic event. The mean return period in years is shown as 72
years, 225 years, 474 years, and 2475 years respectively.
33

The target building performance levels and earthquake hazard levels intersect to create
three different objectives: basic safety objective, enhanced rehabilitation objective, and
limited objectives. Basic safety objectives ensure that life safety performance and an
earthquake with 474 years of return can be reached along with collapse prevention level
with an earthquake with 2475 years of return. Today’s building code meet the basic
safety objective, and if the designer intends to meet a higher objective, enhanced
rehabilitation objectives can met through structural retrofits.
34
It should be understood
that seismic retrofit strategies typically improve the existing structural behavior but don
not satisfy current code requirements for new designs.

2.3 Effects and Dynamic Behavior
The inability to predict the nature of earthquakes creates an array of possibilities for the
performance of a particular building designed with a particular load as per code. We will
discuss six potential areas of concern in designing a building for seismic loads as
discussed by James Ambrose and Dmitry Vergun: maximum direct force, harmonic

33
Ibid.
34
Ibid.
24

effects, progressive failures, three‐dimensional movement, effects of deformation, and
energy absorption.
35
Maximum direct force is the largest lateral force applied to the
structure which will produce stresses, deformations, and create destabilizing effects.
Harmonic effects refer to the elastic spring behavior of a building during rapid
movement or deformation along with the harmonic nature of earthquakes. Progressive
failures are the concerns as to the weakening of structural elements exposed to
repeated seismic loads overtime. Three‐dimensional movement can occur during
repeated shaking, and structural elements may be exposed to forces in directions they
weren’t designed for. For instance, a tension member may be called to sustain
compressive loads in the midst of a seismic event. The effects of deformation refer to
the danger of displacement in connections, P‐delta effects in columns, or non‐structural
elements. Lastly, energy absorption is a structure’s “most significant strength in terms of
seismic response” and this can be fully realized in a dynamic analysis.
36

In describing the behavior of a building undergoing an earthquake, the base of the
building will begin to translate suddenly while the upper portion of the building will
exhibit a lag due to the flexibility of the structure and inertial resistance.
37
The

35
Ambrose and Vergun, Design for Lateral Forces
36
Ibid.
37
Ibid.
25

complexities of the three‐dimensional earthquake ground motion translate into three‐
dimensional deformation.

Analysis Procedures
The four different analysis procedures as described in ASCE 41 are linear static
procedure, linear dynamic procedure, nonlinear static procedure, and nonlinear
dynamic procedure. The linear analyses maintain the linear stress‐strain relationship
with amplification factors to account for the nonlinear earthquake behavior. Linear
analyses’ results are more conservative than the nonlinear analyses; therefore, extra
money and material can be saved using nonlinear analyses. As we will see in future
chapters, the linear static procedure is implemented to simplify the steps toward
analysis.
38

2.4 Structural Systems
In choosing a structural system for a particular building, there are many considerations
which determine the decision of one system over another. For instance, it may make
sense for a column free floor plan in an office type of building, while shear walls may be
considered for residential apartments. Since the behavior of systems during an
earthquake differs by parameters such as of material, connection details, and framing
plan, suitable systems must be selected in respect to building dimensions and height.

38
ASCE 41, Seismic Rehabilitation of Existing Buildings
26

Commonly in mid‐rise construction, steel and reinforced concrete buildings are most
often used, and these four structural systems’ behavior and characteristics will be
detailed below: steel moment frame, steel braced frame, reinforced concrete shear wall
system, and reinforced concrete moment frame.

2.4.1 Steel Moment Frame
Moment‐resistive frames can also be described as a rigid frame, and rigid frames insure
that the connection between a column and beam resist moment so both the column
and beam are inflicted with bending or flexural loading. In the history of steel design,
moment‐resistive frames were considered in the 20
th
century with the demand for taller
buildings. The different techniques for welding and bolting improved which allowed
skyscrapers such as the Empire State Building in New York to give rise. These moment
frame elements are designed for the inelastic region under severe earthquake loads,
however the connections of these frames must be able to remain intact through several
cycles of inelastic rotation due to seismic loading.

This was not the case during the 1994
Northridge Earthquake in Southern California, as many welded flange connections failed
at low levels of plastic deformation and did not perform as expected.
39

Another consideration with steel moment frames is its serviceability in drift or
deformation. Larger member sizes account for the necessary deflection requirements

39
Naeim, The Seismic Design Handbook, 261
27

with it being its primary reason. There are two main deflection characteristics, due to
bending or shear. Usually in the design of drift in prismatic beams, the overall
deflection is governed by bending, and deflection from shear can be neglected.
However, in the design of rigid framing, beam shear deflection can constitute nearly
80% of total deflection whilst the remaining 20% can attribute to bending deflection.
40

2.4.2 Steel Braced Frame
Steel braced frame systems are an alternative to tall building designs. While rigid frame
elements take bending in columns and beams, braced frame columns have minimal
bending. Instead, axial members such as diagonal bracing primarily absorb the
horizontal shear and they carry “lateral shear predominantly by the horizontal
component of axial action allowing for nearly a pure cantilever behavior.”
41
With axial
stiffness in columns and web elements, the braced frame system resists lateral loads:
columns resist overturning moment and diagonals work to resist horizontal shear. In
braced framing, it is the flexural deformation which governs over shear deformation.
42


40
Ambrose and Vergun, Design for Lateral Forces, 92
41
Ibid, 82.
42
Naeim, The Seismic Design Handbook, 252
28

2.4.3 Concrete Shear Wall System
The use of shear walls in concrete buildings to resist lateral forces is implemented
throughout many existing structures. There are many different options in using shear
walls as described by Dr. Bungale S. Taranath: flat slab‐frame with shear walls, coupled
shear walls, shear wall core supported, and shear wall‐frame interaction systems.
43
All
these systems exist and operate with specific design intents in mind. For instance, the
flat slab‐frame with shear wall system is intended primarily for buildings with heights of
10 or less stories and is designed for regions with low seismicity as the slab’s capacity for
large rotations or moments is weak and thus can lead to punching stress demands.
44

The coupled shear wall system is a “system of interconnected shear walls [exhibiting] a
stiffness that far exceeds the summation of the individual wall stiffness,” and the
interconnecting members allow the system to work as a composite unit which allows up
to 40 stories in height.
45
Shear wall‐frame interaction systems use the interaction
between shear walls and moment frames to increase the stiffness of the building, and
this system can be used for mid to high‐rise building heights.
46
Lastly, the shear wall
core system is another efficient system which uses the location of elevators, stairs, and
duct spaces by surrounding these elements with shear walls from the foundation to the

43
Taranath, Steel, Concrete, and Composite Design of Tall Buildings
44
Ibid.
45
Ibid.
46
Ibid.
29

roof of a structure. The framing of the structure can be determined in a number of
different methods: cast‐in‐place concrete, precast concrete or structural steel.
47

2.4.4 Concrete Moment Frame
Similar to a steel moment frame system, the beams and columns of a concrete moment
frame system are rigid at their joints, and the system is characterized as flexible.
However, cast‐in‐place concrete buildings have an advantage in continuity at joints.
When compared to shear wall structures, “rigid frames are not as stiff as shear wall
construction and are considered more ductile and less susceptible to catastrophic
earthquake failures.”
48
Horizontal seismic ties with small spacing could help prevent
diagonal cracking and promote ductile behavior. Generally, interior rigid framing is
inefficient due to the number of columns which interrupt the circulation, and the beam
depths require larger floor to floor heights. Therefore, implementing exterior moment
frames is recommended to create more freedom in architectural design.
49



47
Ibid.
48
Ibid.
49
Schierle, Structure and Design
30

2.5 Seismic Retrofitting
Structures are designed under the jurisdiction of local or international building codes as
studied in the previous chapter. However, as the guidelines for design continue to
evolve with new studies and research, can buildings built in the past be trusted to
withstand an earthquake when clearly current guidelines aren’t met? Additionally,
buildings designed per modern codes are expected to “resist low‐level earthquakes
without damage, resist moderate‐level of earthquakes without structural damage, and
resist high‐level earthquakes of intensity equal to the strongest experienced or forecast
for the building site without collapse.”
50
But how are these claims proven and what can
justify the collapse of buildings during past earthquakes? In understanding the answers
to these questions, it is evident to ensure the safety of buildings built in the past
through seismic retrofits.

Difficulties
Seismic retrofitting existing buildings is more difficult than new construction, and
designers can dispute over whether a seismic retrofit is necessary in a given building.
One may point out the lack of ductility in the existing system, while the other may refute
the former’s claim through code justification. These uncertainties were answered to a
certain extent, and designers were given a general consensus with the publication of

50
Taranath, Wind and Earthquake Resistant Buildings, 501
31

FEMA 356: Prestandard and Commentary on the Seismic Rehabilitation of Buildings in
2002. This code has now developed into ASCE 41: Seismic Rehabilitation of Existing
Buildings in 2007 and provides improvements over the FEMA standard.
51
Using these
standards, it is crucial for designers to conduct an assessment and understanding of the
“existing construction, its limiting strength and deformation characteristics, qualification
of the owner’s economic and performance objectives, and selection of an appropriate
design criterion to meet these objectives.”
52

Deficiencies
There are a number of common deficiencies which require seismic retrofits of existing
buildings in upgrading lateral load resisting elements. Some common situations are but
not limited to: irregular building configurations, soft story construction, large stiffness
differential, unreinforced masonry walls, diaphragms without ties, insufficient lengths of
bar anchorage and splices, flat slab framing systems, etc.
53
These problems have several
upgrade possibilities, but having prior knowledge of the structural system in an existing
building can tremendously help optimize retrofitting. In the following, common
upgrades and retrofit ideas will be listed for the following structural systems: steel
moment frame, steel braced frame, concrete shear wall, and concrete moment frame.

51
Ibid, 503.
52
ASCE 41, Seismic Rehabilitation of Existing Buildings
53
Taranath, Wind and Earthquake Resistant Buildings, 505
32

2.5.1 Steel Moment Frame Retrofits
There are several measures which prove to be effective in improving the seismic
capacity of steel moment frame structures. First, the moment frame structure can be
stiffened through retrofits, and the several applications of this effect are described.
Concentric or eccentric bracing can be added at particular bays in the building to
increase the stiffness of the system with proper placement to avoid increased torsion.
Infill walls and ductile concrete shear walls can be added to the system to increase
stiffness; however, they must be placed properly to avoid increased torsion. The framing
can be welded with steel member sizes to increase stiffness. Furthermore, new steel
frames can be erected to the exterior of structures to redistribute stiffness and load
paths. However, these exterior additions change the architecture of the building.
Secondly, steel moment frame connections can be reassessed to ensure the forming of
plastic hinges to be away from the column to beam connection. This is to prevent major
damage in the connection as explored by reduced beam section beams.
54

2.5.2 Steel Braced Frame Retrofits
According to Dr. Taranath’s chapter on “Seismic Rehabilitation of Existing Buildings,” the
reinforcing of existing steel braced buildings is relatively simpler than that of the steel
moment frame system. There are a few suggestions that are made to strengthen and
refresh the connections built previously. Cover plates, angles, and other structural

54
Ibid, 522.
33

tension members can be added to the existing structure to create new and additional
bracings in the exterior facades of the building. These manners of retrofitting will not
necessarily require the occupants from the building to evacuate during construction.
Additionally, bolted connections can be replaced by welded connections and fasteners
can be replaced to reinforce the frame.
55

2.5.3 Concrete Shear Wall Retrofits
The biggest problems which arise with the deficiencies in concrete shear wall structures
are due to irregular configurations of buildings such as stiffness differentials, soft
stories, unreinforced masonry walls, and etc. In order to improve these buildings there
are several methods to tackle these problems: increase wall thickness, increase shear
wall strength, adding new walls, and increasing column capacities.
56

Increasing the wall thickness will help create more stiffness and seismic capacities of the
walls. Both the exterior and interior shear walls can be strengthened by applying
reinforced shotcrete to the wall surfaces. “Shotcrete, a mixture of aggregate, cement,
and water sprayed by a pneumatic gun at high velocity, is widely used for strengthening
walls because it bonds well with concrete.”
57
There are a number of detailed

55
Ibid, 520.
56
Ibid, 513.
57
Ibid, 514.
34

instructions which follow the strengthening of these walls, which must be followed per
code. Increasing the shear strength in walls can be implemented by either bonding new
concrete with horizontal and vertical reinforcement to existing walls or using composite
fiber sheets epoxied to the existing shear walls.

The concrete columns can be reinforced through an addition of composite fiber,
concrete, or steel jackets around the existing columns to add strength. The addition of
shear walls or even steel braced frames can help a concrete shear wall structure if the
new addition does not interfere heavily with the existing building layout or circulation.
58

2.5.4 Concrete Moment Frame Retrofits
Concrete moment frame damages from earthquakes included failures in beam‐column
joints, buckling of column bars, and broken up concrete. To help, beam column joints
can be encased using steel or high‐strength fiber jackets which can be bolted on to the
beams at the ends and filled with grout in between. Epoxy can be injected to frame
joints as well. Additional jackets in steel, concrete, high‐strength fiber can be added to
beams, columns, or joints but with acknowledgement in which new materials should act
compositely with the existing materials.
59



58
Ibid, 513.
59
Ibid, 521.
35

Summary
In this chapter, the various structural systems and their retrofit options were studied.
These four systems will now be created and analyzed in a hypothetical setting, Los
Angeles, CA. With the several venues in analysis procedure developed in ASCE 41, the
thesis will evaluate the structures and study what various deficiencies lie in the designs
using the earlier, 1971 building code.

36

Chapter 3: Research Procedures
3.1 Design of Existing Buildings
Before implementing retrofits, it is necessary to create the design of hypothetical
existing buildings. As described earlier in chapter 2, four mid‐rise buildings with the
same height will be studied with four different structural systems: steel braced frame,
steel moment frame, concrete shear wall core, and concrete moment frame. These
buildings will be designed for Los Angeles, and they will be designed under 1971 Los
Angeles Building Code provisions to replicate buildings built in the 1970s. Within each
structural system, the dimensions of the buildings will be the same; however, the
structural plans will differ according to an optimized design of the systems. Though
architectural, mechanical, electrical elements can be important to account for, the
buildings will be designed purely with the structural systems in place lacking elements
such as elevators or stairwells. However, the weight of these non‐structural elements
will be accounted for in the calculations of various loadings.

The four structures will be equally dimensioned as followed. The total height of the
structure is 147 feet, with 12’ story heights along with one 15’ height for the first floor
lobby. The structure adopts a square plan with bays spanning 75’ on its width and
length. The building is considered a mid‐rise with its 12 stories.

37

The structures are designed and assessed for a Los Angeles site, more specifically on the
campus of the University of Southern California: zip‐code 90089. This location was
chosen to create an accurate resemblance of buildings built in Los Angeles as well as to
draw comparisons with the two case study buildings which will be later studied: Webb
Tower and Waite Phillips Hall, which are both USC campus buildings. As for soil/site
classification, the structures will be designed for site class D: due to the lack of
information provided. Described further below are the specifications about each
structural system and methods.

3.1.1 Steel Braced Frame
The steel braced frame design creates a system which is less ductile than the steel
moment frame structure.
60
The stiffness in the building can be a major positive in an
earthquake event. Below, the baseline condition for the steel braced frame is discussed
along with detailed specifications tied with images to better explain the hypothetical
building.

Static Linear Procedure (Hand Calculations)
Weight plays a large role in determining the base shear applied to a building, which is
the equivalent horizontal force of that of an earthquake in static linear analysis. As for
the weight of the braced frame, it is necessary to make several assumptions to estimate

60
Ambrose and Vergun, Design for Lateral Forces, 82.
38

the dead load and live load per square feet in the structure. It is necessary to look at the
loading values for live load required by code to estimate the pounds per square feet
needed to be applied to the building and the portion of live load that the code considers
to be part of the seismic building weight. Several factors for dead load include: flooring,
ceiling, mechanical systems, electrical equipments, partitions, steel, and floor slab. Thus,
the weight of steel in a braced frame would differ vastly with the weight of concrete in a
concrete shear wall system. Therefore, an educated estimate is required to provide the
proper loading values in order to calculate the base shear which is determined by 1971
Los Angeles Building Code as V = ZKCW, where V is base shear, Z is a numerical
coefficient equal to one in Los Angeles, K is a numerical coefficient as set forth in a table
in determining lateral system ductility, C is related to the fundamental period of
vibration of the structure, and W is the total dead load. Following the determination of
the base shear, this sum of forces must be distributed floor by floor according to code.
39

Figure 4: Steel Braced Frame Plan
With these assumptions made, it is now time to design the columns and beams of the
structure. Using ASD design procedures, beams must be designed to pass flexure, shear,
and deflection checks. Beams which span longer lengths tend to be critical in flexure. In
the same manner, columns can be designed by checking their slenderness ratio and
effective length. The bracing elements must be checked for yielding, fracture, and block
shear failures. These framing elements are listed in the AISC Steel Manual with design
charts to help the user find the necessary numbers quickly and efficiently.

Static Linear Analysis (Computer Model – SAP 2000)
After calculating the base shear, a three‐dimensional frame was created using SAP 2000.
SAP 2000 is a powerful tool for structural analyses and various analytical procedures can
40

be implemented using SAP 2000. SAP 2000 offers three‐dimensional modeling with
capabilities in various analyses: buckling analysis, time‐history analysis, tension and
compression only springs, p‐delta analysis, pushover analysis, target force analysis,
response spectrum analysis, eigen and ritz analysis, and more.
61
This powerful engine
not only implements the intricate analysis, but SAP 2000’s library also can generate
seismic loads based on various codes such as: UBC 97, IBC 2006, NBCC 2010, and
more.
62
However, earthquake design loads were manually assigned to the model to
follow 1971 Los Angeles code guidelines. The model then was assigned with appropriate
framing sizes and analyzed. Through analysis, SAP 2000 checked the design of the
structure to make sure elements do not fail due to overstress, lateral torsional buckling,
weak column to beam ratio, etc. Through a trial and error method, optimum framing
members were selected to lighten the structure.

Cost Analysis
To create a cost efficient system, the steel braced frame employed optimum framing
members by finding the lightest sections which resist design loads. Following the design
of the steel braced system, all framing elements’ weights were added. This number
serves to show the amount of material used in the structure, thus cost. In the initial
design of the structure, $0.50/pound rate was used for steel to represent the cost

61
“SAP 2000 Analysis.”
62
“SAP 2000 Loading.”
41

needed in new construction. Additionally, $0.02/pound was used for concrete to
represent new construction. With retrofits, a rate of $3.50/pound for steel was used
with considerations for breaking and detachments of existing facades. A rate of $400
per cubic yard was used for concrete in retrofitting.

3.1.2 Steel Moment Frame
The steel moment frame is a less stiff and more ductile system than the steel braced
frame system. Therefore, the moment frame system induces more drift than a stiffer
system. However, a steel moment frame system’s ductility may allow the structure to
dissipate seismic forces in more modes and more overall.
63

Static Linear Procedure (Hand Calculations)
Similar steps as described above in section 3.1.1 will be taken to calculate the base
shear of the steel moment frame system. When calculating the dead load, the weight of
steel along with other structural components must be concluded with an educated
guess. As for the K value, we must find the correct value for a steel moment frame
structure in the tables provided in the 1971 Los Angeles Building Code. As mentioned
before, the K value represents the lateral system ductility.
64


63
Ambrose and Vergun, Design for Lateral Forces, 92.
64
County of Los Angeles Uniform Building Laws, 114.
42

When designing the layout of the structure, the placement of moment frames as lateral
force resistors is vital. Since a corner column with moment connections on two axes
takes both east‐west and north‐south lateral forces, the column essentially must be
designed with heavy sections to resist greater loads. Therefore as shown in this design,
it is advisable to place moment frames in one direction to avoid biaxial bending in
corner columns.

Figure 5: Steel Moment Frame Plan
Looking at the structural plan shown here, the moment frames exist on the exteriors of
the building at all sides. These moment resisting frames will take a 100% of all seismic
force, and they will be designed as beam‐columns. Beam‐columns are elements which
are under both axial and moment forces to create both flexure and compression. In a
43

moment connection, the flexure or bending from the beams are transferred to the
column.

Static Linear Analysis (Computer Model – SAP 2000)

In creating the model in SAP 2000, it is vital to differentiate the beam to column
connections between the moment frames and the interior framing. The beams and
columns in the interior of the structure are only designed for gravity loads, while the
moment frames act to resist both gravity and lateral loads. All framing elements were
assigned with appropriate sections as designed per preliminary design. Following the
analysis of the model, SAP 2000 checked the structure for any design failures. The
sections which failed were corrected through a trial and error process.

Cost Analysis
To create a cost efficient system, the steel moment frame employed optimum framing
members by finding the lightest sections which resist design loads. Following the design
of the steel moment system, all framing elements’ weights were added. This number
serves to show the amount of material used in the structure, thus cost. In the initial
design of the structure, $0.50/pound rate was used for steel to represent the cost
needed in new construction. Additionally, $0.02/pound was used for concrete to
represent new construction. With retrofits, a rate of $3.50/pound for steel was used
44

with considerations for breaking and detachments of existing facades. A rate of $550
per cubic yard was used for concrete in retrofitting.

3.1.3 Concrete Shear Wall Core
A concrete shear wall core system utilizes the vertical distribution system’s central
location to create a punched‐wall core that separates the vertical distribution from the
occupied spaces beyond. This core along with the beams and columns resist lateral
forces applied to the structure.
65

Static Linear Procedure (Hand Calculations)
Concrete buildings tend to be heavier than steel buildings; therefore, the weight of the
shear wall core system may be greater than the systems previous. Similarly, the K value
in the formula to calculate base shear will also be different as the system behaves
differently than past systems.

65
Taranath, Wind and Earthquake Resistant Buildings, 354
45

Figure 6: Concrete Shear Wall Core Plan

Static Linear Analysis (Computer Modeling – SAP 2000)

Using SAP 2000, this new frame was created with new materials assigned to beams and
columns: concrete. Using preliminary designed beams, columns and shear wall
thicknesses, all elements were assigned to the model. Following the analysis, the check
of concrete design showed areas of overstress and failures. Appropriate sections
replaced the structure to pass the design check.

Cost Analysis
To create a cost efficient system, the concrete shear wall core system employed
optimum framing members by finding the lightest sections of concrete which resist
46

design loads. Following the design of the concrete shear wall core system, all framing
elements’ weights were added. This number serves to show the amount of material
used in the structure, thus cost. In the initial design of the structure, $0.50/pound rate
was used for steel to represent the cost needed in new construction. Additionally,
$0.02/pound was used for concrete to represent new construction. With retrofits, a rate
of $3.50/pound for steel was used with considerations for breaking and detachments of
existing facades. A rate of $550 per cubic yard was used for concrete in retrofitting.

3.1.4 Concrete Moment Frame
The concrete moment frame system acts similar to a steel moment frame system in its
connections and behavior. The columns will act as beam‐columns, resisting both axial
and bending forces. However, the concrete system will have more stiffness than the
steel system, possibly creating an optimum solution for a mid‐rise building built for Los
Angeles.
66

Static Linear Procedure (Hand Calculations)
Similar to that of the steel moment frame system, this structure has a similar K value
from the 1971 Los Angeles Building Code. The material of concrete is heavier, however,
so there is an increase of the overall dead load in the system, raising the base shear.
Different from the steel moment frame structure in section 3.1.2, the concrete moment

66
Taranath, Wind and Earthquake Resistant Buildings, 352.
47

frame system employs moment connected frames in all joints. With the design of the
concrete moment frame structure, the corner columns subjected to biaxial forces
cannot be avoided. Following the base shear calculations, the appropriate distribution
of lateral forces is employed per floor.

Figure 7: Concrete Moment Frame Plan
Static Linear Analysis (Computer Modeling – SAP 2000)
The three dimensional model was properly assigned its lateral forces per floor, and all
framing elements were assigned. Through analysis in SAP 2000, the concrete design was
checked for overstress, lateral torsional buckling, weak column to beam ratio, etc.
Optimum sections were selected to decrease weight while meeting load capacities.


48

Cost Analysis
To create a cost efficient system, the concrete moment frame system employed
optimum framing members by finding the lightest sections of concrete which resist
design loads. Following the design of the concrete moment frame system, all framing
elements’ weights were added. This number serves to show the amount of material
used in the structure, thus cost. In the initial design of the structure, $0.50/pound rate
was used for steel to represent the cost needed in new construction. Additionally,
$0.02/pound was used for concrete to represent new construction. With retrofits, a rate
of $3.50/pound for steel was used with considerations for breaking and detachments of
existing facades. A rate of $550 per cubic yard was used for concrete in retrofitting.

3.2 Analyze Existing Structure: Case Studies
Following the design and analysis of the previous four hypothetical structures, two
existing buildings from the USC campus have been selected as case‐studies: Waite
Phillips Hall and Webb Tower. Both structures were built in the mid 20
th
century and are
roughly 13 stories tall. These two case studies will be analyzed under both the 1971 Los
Angeles building code as well as today’s 2010 California Building Code. Retrofits which
were implemented in the upgrade of the hypothetical structures will be studied with
these two case study buildings. The study of these two structures verifies the
implementation of retrofits necessary for existing buildings in Los Angeles.
49

3.2.1 Waite Phillips Hall (WPH)
Waite Phillips Hall currently serves as an office/lecture building at the USC main campus.
It was completed in 1966 and is currently one of the tallest buildings at USC with 12
stories and 156’ tall.
67
WPH exhibits a shear wall core system in the middle of its
structural plan with shear walls resisting lateral loads.

Linear Static Procedure (Hand Calculations)
Given the structural drawings with beam and column schedules, it was easier to attain
an accurate measurement of weight of the structure. Following the distribution of
forces on the structure, the members that exist for the current structure was checked
with the design loads. The base shear as per 1971 Los Angeles building code was
calculated.

67
“Buildings on the University of Southern California Campus.”
50

Figure 8: Waite Phillips Hall Elevation and Plan Views
Linear Static Analysis (Computer Modeling – SAP 2000)
By developing a simplified three dimensional model of WPH in SAP 2000, the computer
model was assigned with the existing framing sections. The model under 1971 code was
then analyzed and checked for concrete and steel design to make sure all elements are
satisfied under code. Following the analysis under 1971 loads, the model was then
applied with today’s 2010 CBC codes. With the existing framing elements, SAP 2000
analyzed the model and checked the structure to reveal any failures within the
structure.


51

Cost Analysis
With the same philosophy implemented in previous cost analyses, the weights of all
framing sections were added. However since WPH is an existing building, the framing
elements’ weights were listed with accuracy.

3.2.2 Webb Tower (WTO)
Webb Tower currently serves on the USC main campus as a residence hall for students.
WTO has been retrofitted in 2005 with bracing elements to create further stiffness in
the system in resisting seismic loads. This study hopes to uncover the building’s capacity
prior to the implementation of retrofits. The building is a concrete moment frame
system with 14 stories.
68

Figure 9: Elevation and Plan Views of Webb Tower


68
“Buildings on the University of Southern California.”
52

Linear Static Procedure (Hand Calculations)
Unfortunately, I did not have access to the beams and column schedules for Webb
Tower despite receiving many structural plans. For this study, member sizing was
hypothetically created using similar methods as that of the four hypothetical structural
systems.

Linear Static Analysis (Computer Modeling – SAP 2000)
By developing a simplified three dimensional model of WTO in SAP 2000, the computer
model was assigned with the existing framing sections. The model under 1971 code was
then analyzed and checked for concrete and steel design to make sure all elements are
satisfied under code. Following the analysis under 1971 loads, the model was then
applied with today’s 2010 CBC codes. With the existing framing elements, SAP 2000
analyzed the model and checked the structure to reveal any failures within the
structure.

3.3 Implement Retrofits
3.3.1 Evaluation
SAP 2000 is the tool which allows this study to see whether the building designed for
1971 design loads is sufficient enough for today’s 2009 IBC standards. Following the
analysis under the 1971 code, each of the four hypothetical buildings along with the two
case studies were placed with new loads under the 2010 CBC. With the new loads
53

assigned, the new analysis pointed out several failure points throughout each structure,
which requires structural retrofitting. After evaluating each structure’s needs and weak
points, realistic retrofit ideas were implemented.

3.3.2 Implementation
Following the evidence in need for structural retrofits, the various structural systems
were enhanced with new elements in order to stiffen or add capacity to existing
members. Using the recommendations for retrofits on hand, the four structural systems
underwent the recommended procedures and a new model reflecting the
implementations was analyzed to see changes. Throughout these implementations, the
addition of material was taken into account to see the rise in cost as well as the increase
in capacity of the structure on a relative scale. In a table format, each different type of
structural system was bundled with its set of possible retrofits. Each retrofit idea has its
own pros and cons.

3.3.3 Validity of Table
With each retrofit’s performance recorded on the table, the two case study buildings
were retrofitted using the “best” design, which was most cost‐effective. For example,
Webb Tower, prior to its bracing retrofit, was implemented with a design recommended
from the table. This proposal was put in comparison to its current bracing addition to
analyze which scheme is more efficient.
54

Summary
As described above, four structural systems were selected for study: steel braced frame,
steel moment frame, concrete shear wall core, and concrete moment frame. These
structures were hypothetically designed to resemble a mid‐rise building in Los Angeles.
Each of these buildings was designed per 1971 Los Angeles building code’s seismic
design guidelines. Through an analysis in SAP 2000, optimum framing sections, which
are light yet efficient, were selected.

Moving onto the retrofitting phase, these same structures were placed under the more
stringent 2010 CBC seismic design guidelines. The newly added loads pointed out weak
points and stress failures in the systems which required retrofitting. From the analysis of
several implementations, a table recording the pros and cons of each retrofit was
created. This table validates efficient structural retrofit schemes which can be
implemented in the two case study buildings. From the research approach and steps
pointed out in this chapter, we will look in the following chapters and see actual results
and data accumulated from calculations and analyses. Chapter 4 focuses on the two
steel structures and chapter 5 details the two concrete structures.
55

Chapter 4: Steel Structure Design and Retrofit
4.1 Design of Steel Braced Frame Structure
In the evaluation of the steel braced frame structure, the structure will first be designed
as given by the dimensions mentioned in Chapter 3. Hence, in this thesis, a mid‐rise
building will be represented by a 75’ by 75’ area with 12 floors. Earthquake loads were
added to the structure as per the 1971 Los Angeles Building Code. Through a linear
static analysis in SAP 2000, framing element sizes were selected which adequately meet
code.

4.1.1 Design Using 1971 Los Angeles Building Code
Total Lateral Force, V
The total lateral force which every structure must be designed to withstand is given by
the formula, V = ZKCW. Z is given as the numerical coefficient of one. K is a horizontal
force factor for structures specified by a table within the 1971 building code. This
particular structure is classified under “all building framing systems except as
hereinafter classified” with a K value of one. C is a numerical coefficient which can be
calculated by the formula,
.

. T is the fundamental period of vibration of the
structure in seconds and can be calculated by the formula,
. n
√
where h
n
is the
total height of the structure and D is the dimension of the building in feet in a direction
56

parallel to the applied forces. W is the total dead load of the structure, and the
estimated dead load values are listed below.
69

Flooring 5.0 PSF
T‐bar Ceiling 5.0 PSF
Mech & Electrical 5.0 PSF
Partitions 15.0 PSF
Steel 25.0 PSF
3.25” Slab + 3” Deck 45.0 PSF
Total Dead Load 100.0 PSF

Table 1: Total Dead Load (SBF)

As shown above, the total dead load in pounds per square feet is 100. Therefore, the
total W value for all twelve floors is 6750 kips (

). Below is a table
which shows the evaluation of the total lateral force.
hn 147’
D 75’
T 0.848
C 0.0523
W(dead) 6750 kips
K 1
V 356.46 kips

Table 2: Total Base Shear (SBF)

Distribution of Lateral Force
The total lateral force, V, is distributed from the 2
nd
to the Roof level using the formula,
x
x x
∑ i i

. F
x
denotes the force distribution at a particular floor; w
x
refers to the
height at a particular floor, and h
x
refers to the height at a particular floor from the base
of the building. The values F
x
values in the chart below are in kips.

69
County of Los Angeles Building Laws, 107.
57

Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 356.5 562.5 147 82687.5 53.9
12th 356.5 562.5 135 75937.5 49.5
11th 356.5 562.5 123 69187.5 45.1
10th 356.5 562.5 111 62437.5 40.7
9th 356.5 562.5 99 55687.5 36.3
8th 356.5 562.5 87 48937.5 31.9
7th 356.5 562.5 75 42187.5 27.5
6th 356.5 562.5 63 35437.5 23.1
5th 356.5 562.5 51 28687.5 18.7
4th 356.5 562.5 39 21937.5 14.3
3rd 356.5 562.5 27 15187.5 9.9
2nd 356.5 562.5 15 8437.5 5.5

Table 3: Distribution of Lateral Forces

Now these F
x
values are divided into two to apply the loads parallel to two frame lines of
action. The same loading is applied in two orthogonal directions as shown below.

Figure 10: Lateral Load Application

58

4.1.2 Braced Frame Details

Figure 11: Steel Braced Frame SAP 2000 Model
At each floor, diagonal bracing is implemented in the two middle bays on all four
exterior facades of the structure. As shown in the rightmost figure above, the bracing
and beams are pin connections as denoted by the discontinued lines with green dots at
their ends. All interior beams and girders are also pin‐connected throughout the
structure.

4.1.3 Design of Framing Members
In order to adequately assign adequate framing elements in the steel braced frame
structure, the model must first be analyzed in SAP 2000 under design loads. After
assigning all gravity and lateral loads to the computer model, an analysis was run with
the following four ASD load combinations: 1) D, 2) D+L+L
r
, 3) D+E
x
+L, 4) D+E
y
+L (D, dead
load; L, live load; L
r
, roof live load; E
x
, earthquake load in the x‐direction; E
y
, earthquake
59

load in the y‐direction).
70
Following the analysis, each framing element’s required
moment (M
u
), shear (V
u
), and axial values (P
u
) were recorded by looking at each
maximum value.

Beam Design

Figure 12: Beam Layout in SAP 2000
The elements in red as shown above are interior beams within the structure. The beams
rest on either columns or girders. It is 18.75’ in length and is continuously laterally
supported and is kept in place by the concrete slab. Each of the beams’ tributary widths
are also 18.75’. By recording values from the results, an adequate section can be
selected from the AISC Steel Manual. For instance, below we see the required moment
to be 71.3 kips‐ft for the 2
nd
floor level. Typically for beams, the moment values tend to
govern as opposed to the shear values. By looking at the “Available Moment vs.
Unbraced Length” chart for W shapes, the W10x30 size with a moment capacity of 84

70
Segui, Steel Design, 23.
60

kip‐ft was selected.
71
The same procedure follows for the other beams. The interior
girders support the interior beams described above, and the same procedure follows for
each typical interior girder.

Column Design

Within the space, there are three different types of columns we must design for:
interior, edge, and corner columns. The interior columns are responsible for resisting
gravity loads from any floors above. Each of these interior columns has tributary areas
of 351.6 ft
2
or 18.75’ by 18.75’.

The edge columns are located along the exterior faces of the building and are also
connected to the bracing elements. The corner columns are located on the four corners
of the structure.

Brace Design
The braces are placed in the two middle bays on each façade to resist lateral loads.
Wide flanges sections are used as bracing throughout the structure. They act to resist
both compression and tension forces. A preliminary design calculation was made by
following steel design procedures before needing to be calibrated with seismic codes.


71
AISC, Steel Construction Manual
61

SAP 2000 Calibration
Following the results from the Excel spreadsheet; the sections were re‐applied to the
SAP 2000 model. The model was tested using ASD design philosophy as allowable stress
design was used at the time of 1971 LA code. The “steel design check of structure”
results notified various errors in the model which included lateral torsional buckling,
seismically compact sections, beam to column ratios, and stress failure.

Lateral torsional buckling occurred due to the lack of mid‐span supports along the
beams. This issue was resolved after overwriting SAP 2000 to ensure the beams were
continually supported along its length. In addition, sections used in seismic design must
be seismically compact. In order for a section to be ruled seismically compact, elements
of the member’s cross section must be thick enough to withstand local buckling. It must
follow this formula provided by seismic design provisions
f
0.3
. Using steel (E =
29,000 ksi) and grade 50 steel (Fy = 50 ksi), the section’s
f
value must be less than 7.22.
Beam to column ratios must be satisfied to ensure the strong column, weak beam
design philosophy. This approach forces the beams to fail before the columns to localize
damage. If columns failed before beams, it could result in progressive or total building
collapse. Lastly, each member must be sufficient for all code load combinations to
ensure their demand/capacity ratios are less than one.

62

Through calibration, many framing sections were modified from the hand calculations.
Noticeably, columns had to be significantly increased in size to meet the beam to
column ratios.

4.1.4 Framing Details
Listed below are details of each framing element.
Columns
Level C1 C2 C3 C4
12 W14x48 W14x48 W14x48 W14x48
11 W14x48 W14x48 W14x48 W14x48
10 W14x48 W14x48 W14x48 W14x48
9 W14x48 W14x48 W14x48 W14x48
8 W14x48 W14x68 W14x48 W14x48
7 W14x48 W14x68 W14x48 W14x48
6 W14x48 W14x82 W14x48 W14x68
5 W14x48 W14x82 W14x48 W14x68
4 W14x48 W14x82 W14x48 W14x68
3 W14x48 W14x82 W14x48 W14x82
2 W14x48 W14x132 W14x48 W14x82
1 W14x48 W14x132 W14x48 W14x132
Table 4: List of Columns (SBF)
63

Figure 13: Column Framing Plan (SBF)
Beams

Level B1 B2
3~R W12x26 W10x19
2 W14x26 W10x19
Table 5: List of Beams (SBF)
Girders
Level G1 G2
3~R W16x40 W12x26
2 W16x45 W10x39
Table 6: List of Girders (SBF)

Table 7: List of Braces (SBF)
Braces
Level BF1
5~12 W10x19
1~4 W10x26
Figure 14: Beam Framing Plan (SBF)
Figure 15: Braced Framing Plan
(SBF)
64

4.1.5 Existing Building Weights
By identifying the number of each respective framing section, which includes the beams,
columns, and braces, the total weight of framing elements is described below.
B1
Level 3~R 2
Weight (plf) 26 26
Length 18.75 18.75
Weight (lbs) 487.5 487.5
Quantity 308 28
TOTAL (kip) 150.2 13.7
163.8
B2
Level 3~R 2
Weight (plf) 19 19
Length 18.75 18.75
Weight (lbs) 356.3 356.3
Quantity 88 8
TOTAL (kip) 31.4 2.9
34.2
Table 8: Beam Weights (SBF)
G1
Level 3~R 2
Weight (plf) 40 45
Length 18.75 18.75
Weight (lbs) 750 843.8
Quantity 132 12
TOTAL (kip) 99 10.1
109.1
G2
Level 3~R 2
Weight (plf) 26 39
Length 18.75 18.75
Weight (lbs) 487.5 731.3
Quantity 88 8
TOTAL (kip) 42.9 5.9
48.8
Table 9: Girder Weights (SBF)

BF1
Level 1~4 5~12
Weight (plf) 26 19
Length 22 22
Weight (lbs) 572 418
Quantity 32 64
TOTAL (kip) 18.3 26.8
45.1
Table 10: Brace Weights (SBF)

65

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 48 48 48 48 48 48 48 48 48 48 48 48
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 576 576 576 576 576 576 576 576 576 576 576 576
Quantity 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL (kip) 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6
55.3
C2
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 132 132 82 82 82 82 68 68 48 48 48 48
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 1584 1584 984 984 984 984 816 816 576 576 576 576
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL (kip) 6.3 6.3 3.9 3.9 3.9 3.9 3.3 3.3 2.3 2.3 2.3 2.3
44.2
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 48 48 48 48 48 48 48 48 48 48 48 48
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 576 576 576 576 576 576 576 576 576 576 576 576
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL (kip) 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3
27.6
C4
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 132 82 82 68 68 68 48 48 48 48 48 48
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 1584 984 984 816 816 816 576 576 576 576 576 576
Quantity 9 9 9 9 9 9 9 9 9 9 9 9
TOTAL (kip) 14.3 8.9 8.9 7.3 7.3 7.3 5.2 5.2 5.2 5.2 5.2 5.2
85.1
Table 11: Column Weights (SBF)
Therefore, the total weight of the steel braced frame structure is 613.1 kips.
66

4.2 Design of Steel Moment Frame Structure
In low to mid‐rise buildings, moment frame systems are highly effective in resisting
lateral loads as its flexibility allows earthquake energies to dissipate, and it reduces the
influence of higher frequency energies. However, in order to resist both axial and
bending forces, moment connected frames require heavier steel sections. Below, we
will design a mid‐rise steel moment frame structure as per 1971 Los Angeles Building
Code.

4.2.1 Design using 1971 Los Angeles Building Code
The same formula as in section 4.1.1 is applied here to calculate the base shear, V =
ZKCW. The significant difference between the braced frame values is the coefficient K.
Flooring 5.0 PSF
T‐bar Ceiling 5.0 PSF
Mech & Electrical 5.0 PSF
Partitions 15.0 PSF
Steel 25.0 PSF
3.25” Slab + 3” Deck 45.0 PSF
Total Dead Load 100.0 PSF
Table 12: Loading Values (SMF)
hn 147
D 75
T 0.849
C 0.053
W(dead) 6750
K 0.67
V 238.8
Table 13: Total Base Shear (SMF)
67

From the base shear value above, the new distribution of base shear amongst the floors
are as below.
Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 238.8 562.5 147 82687.5 36.1
12th 238.8 562.5 135 75937.5 33.2
11th 238.8 562.5 123 69187.5 30.2
10th 238.8 562.5 111 62437.5 27.3
9th 238.8 562.5 99 55687.5 24.3
8th 238.8 562.5 87 48937.5 21.4
7th 238.8 562.5 75 42187.5 18.4
6th 238.8 562.5 63 35437.5 15.5
5th 238.8 562.5 51 28687.5 12.5
4th 238.8 562.5 39 21937.5 9.6
3rd 238.8 562.5 27 15187.5 6.6
2nd 238.8 562.5 15 8437.5 3.7
Table 14: Distribution of Base Shear (SMF)

4.2.2 Moment Frame Details
All interior columns and beams are pin connected and resist only gravity loads.
However, moment frames are placed around the building’s perimeter to resist gravity
and lateral loads. To prevent biaxial bending, the corner columns are moment
connected in only one direction.
68

Figure 16: Steel Moment Frame Plan
4.2.3 Design of Framing Members
In order to assign adequate framing elements in the steel moment frame structure, the
model must first be analyzed in SAP 2000 under design loads. After assigning all gravity
and lateral loads to the computer model, an analysis was run with the following four
ASD load combinations: 1) D, 2) D+L+L
r
, 3) D+E
x
+L, 4) D+E
y
+L (D, dead load; L, live load;
L
r
, roof live load; E
x
, earthquake load in the x‐direction; E
y
, earthquake load in the y‐
direction).
72
Following the analysis, each framing element’s required moment (M
u
),
shear (V
u
), and axial values (P
u
) were recorded by looking at each maximum value.

Beams
There are four types of beam we want to design for: interior beam, interior girder, edge
beam, and moment frame beam. Aside from the moment frame beam, the other three

72
Segui, Steel Design, 23.
69

beam types are only designed to resist gravity loads. In designing for the moment frame
beam, interaction formulas as specified by AISC Steel Construction manual must be met
to perform at design loads. Following the hand calculated preliminary design; the
members are then applied to the SAP 2000 model to be checked.

Columns
There are three types of columns we must design: interior columns, corner moment
frame columns, edge moment frame columns. The interior columns resist only gravity
loads. The corner and edge moment frame columns resist both gravity and 100% of all
lateral loads. These columns resist big moment and axial forces. Following the hand
calculated preliminary design; the members are then applied to the SAP 2000 model to
be checked.

SAP 2000 Calibration
Following the results from the Excel spreadsheet, the sections were re‐applied to the
SAP 2000 model. The model was tested with ASD design as per 1971 code. The “check of
structure” results notified various errors in the model which involved lateral torsional
buckling, seismically compact sections, beam to column ratios, and stress failure. As
described previous in Section 4.1.3, sections must be seismically compact, and designed
with demand/capacity ratios below one.

70

4.2.4 Framing Details
Listed below are sizes of framing members used in the steel moment frame structure.
Beams/Girders
Level B/G
2~R W10x19
Table 15: List of Beams and Girders (SMF)

Figure 17: Beam Framing Plan (SMF)
Columns
Level C1 C2 C3 C4
12 W14x38 W14x38 W14x38 W14x38
11 W14x38 W14x38 W14x38 W14x38
10 W14x48 W14x48 W14x38 W14x38
9 W14x48 W14x48 W14x38 W14x38
8 W14x48 W14x48 W14x38 W14x74
7 W14x48 W14x48 W14x38 W14x74
6 W14x68 W14x68 W14x38 W14x74
5 W14x68 W14x68 W14x38 W14x74
4 W14x68 W14x68 W14x38 W14x74
3 W14x68 W14x68 W14x38 W14x74
2 W14x68 W14x68 W14x38 W14x82
1 W14x68 W14x68 W14x48 W14x82
Table 16: List of Columns (SMF)
71

Figure 18: Column Framing Plan (SMF)

4.2.5 Existing Building Weights
Following the design of all framing elements, all the weight of all elements built in the
SAP 2000 model have been quantified. The weight of the moment frame structure is a
slightly heavier than that of the previously designed braced frame structure. The
gathered data is shown below.
B/G
Level 2~R
Weight (plf) 19
Length 18.75
Weight (lbs) 356.3
Quantity 672
TOTAL (kip) 239.4
239.4
Table 17: Beam/Girder Weights (SMF)
72

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 68 68 68 68 68 68 48 48 48 48 38 38
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 816 816 816 816 816 816 576 576 576 576 456 456
Quantity 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL (kip) 6.5 6.5 6.5 6.5 6.5 6.5 4.6 4.6 4.6 4.6 3.6 3.6
64.9
C2
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 68 68 68 68 68 68 48 48 48 48 38 38
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 816 816 816 816 816 816 576 576 576 576 456 456
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL (kip) 3.3 3.3 3.3 3.3 3.3 3.3 2.3 2.3 2.3 2.3 1.8 1.8
32.4
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 48 38 38 38 38 38 38 38 38 38 38 38
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 576 456 456 456 456 456 456 456 456 456 456 456
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL (kip) 2.3 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
22.4
C4
Level 1 2 3 4 5 6 7 8 9 10 11 12
Weight (plf) 82 82 74 74 74 74 74 74 38 38 38 38
Length 12 12 12 12 12 12 12 12 12 12 12 12
Weight (lbs) 984 984 888 888 888 888 888 888 456 456 456 456
Quantity 9 9 9 9 9 9 9 9 9 9 9 9
TOTAL (kip) 8.9 8.9 8.0 8.0 8.0 8.0 8.0 8.0 4.1 4.1 4.1 4.1
82.1
Table 18: Column Weights (SMF)
The total weight of the steel moment frame structure is 441.2 kips.
73

4.3 Retrofit Design of Steel Braced Frame Structure
4.3.1 Implementation of Different Retrofit Solutions
Following the design of the steel braced frame structure based on lateral loads
described by the 1971 Los Angeles Building Code, this same structure will now undergo
loads specified by the current CBC 2010 code. Below is a chart comparing the two base
shear values. However, when comparing these two values, it is important to multiply the
1971 value by 1.4 to make a fair comparison between the ASD and LRFD design values.
Thus, the LRFD equivalent 1971 base shear value is shown in red.
1971 LA
CBC
2010
Roof 53.9 129.1
12th 49.5 118.6
11th 45.1 108.1
10th 40.7 97.5
9th 36.3 87
8th 31.9 76.4
7th 27.5 65.9
6th 23.1 55.3
5th 18.7 44.8
4th 14.3 34.3
3rd 9.9 23.7
2nd 5.5 13.2
Total Base Shear 356.4 853.9
498.9
Table 19: Base Shear Comparison (SBF)
After re‐assigning new lateral loads on the model, the elements shown in red are
members which do not meet code. As the red shows, the exterior bracing must be
reinforced to be able to resist axial compression from the lateral loads. Additionally, the
74

columns which are connected to the braces must be reinforced to resist higher axial
loads. Most of the members fail due to overstress.

Figure 19: SBF Performance prior to Retrofits

4.3.2 SBF Retrofit 1: Additional Bracing
As you can see from images above, the framing elements highlighted in red signify
failure of the members. As mentioned previously, these failures were mostly due to
higher demand than capacity. In order to help support the braces along with the
columns supporting the braces, the first venue for seismic retrofitting began with adding
more bracing elements on the exterior faces of the structure. This configuration is
intended to distribute the lateral force more evenly throughout the structure. The
triangulation of the outer framing bays should help to dissipate earthquake forces from
the overstressed inner bays and have the building perform more efficiently overall.
75

Figure 20: SBF Retrofit 1 Elevation
Performance of Retrofit
With the addition of the new bracing elements on all four exterior sides of the structure,
all framing elements are able to resist the higher current code loads successfully.
However, some of the corner columns had to be reinforced with steel plates to resist
higher loads introduced by spreading the lateral system across the entire building face.
(Note: The members in red in Figure 22 meet the current code, but SAP 2000’s inability
to check the design of customized sections for seismic compactness results in red
members.)
76

Figure 21: SBF Retrofit 1 Performance
Framing Details
Appropriate steel members were used as bracing elements in the designated positions.
The corner column section of W14x48 needed two plates of 0.25” thickness to be
welded on the sides of the column to increase its capacity to resist axial loads. The new
designed section can now resist considerably larger axial loads than its original. Below
are details of the new additions.
Diagonal Bracing
Level BF2
1~8 W10x19
Table 20: List of Braces (SBF Retrofit 1)

Corner Column
Level C3
1~2 W14x48 PL
Table 21: List of Columns (SBF Retrofit 1)

77

Figure 22: Box Column Section

Cost Analysis
With the addition of the bracing element as well as the needed plate additions, the new
weight of the structure is assessed below, and the cost of the newly implement retrofits
are tabulated below ($3.50/pound of steel).The total weight of the steel braced frame
structure is now increased from 613.1 kips to 640.5 kips. SBF Retrofit 1: Additional
Bracing cost a total of $95,807 in necessary seismic retrofits.
BF2 Additional Plates W14x48 PL
Level 1~8 Thickness (ft) 0.021
Weight (plf) 19 Weight (pcf) 490
Length 18.75 Length (ft) 12
Weight (lbs) 356.3 Height (ft) 1.17
Quantity 64 Quantity 32
Total (kip) 22.8 Total (kip) 4.6
Cost ($) $79,800 Cost ($) $16,007
Table 22: Cost Analysis (SBF Retrofit 1)

4.3.3 SBF Retrofit 2: Addition of Shear Walls
In this retrofit, shear walls are added to the braced frame structure to help stiffen the
structure to increase the building’s ability to resist earthquake forces. The shear walls
are configured inside the structure and have been designed accordingly. All shear wall
78

components have been designed with a 6’ wide by 8’ tall entry path to ensure access
throughout the space.

Figure 23: SBF Retrofit 2: Plan and Elevation
With the addition of shear walls, the structure increased in weight, increasing the dead
load from 100 PSF to 125 PSF. This change in weight has also increased the base shear
from 853 kips to 1067 kips and the lateral force applied to each floor.
DL Loading Distribution of Base Shear Fx
Flooring 5 Roof 161.4
Ceiling 5 12th 148.2
Mechanical/Electrical 5 11th 135.1
Partitions 15 10th 121.9
Steel 30 9th 108.7
Concrete Shear Wall 20 8th 95.5
Deck 45 7th 82.4
125 6th 69.2
5th 56.0
LL Loading 4th 42.8
First Floor 100 3rd 29.6
2nd Floor and Up 50 2nd 16.5
Table 23: Increased Loading Values
79

Performance of Retrofit

The shear walls helped reduce loads on the exterior braced framing by transferring
some of the seismic load to the interior bays with walls. With the increased stress on the
columns supporting the shear walls, first story interior columns failed due to overstress.
In order to help resist stress in these columns, first story shear walls were designed to
resist stresses in the column as well.

Figure 24: SBF Retrofit 2 Performances
Framing Details
The shear walls used are 20”, 10”, and 8” thick and have an opening of 6’x8’ to allow
pathway for circulation per floor. Following the addition of the shear walls in the
structure, some of the columns supporting the shear walls needed reinforcement. The
first story interior columns which failed due to overstress were relieved by designing the
first floor shear walls to resist stresses in the columns. In designing the shear walls, walls
were checked for shear, axial and moment load capacities.

80

CHECK FOR SHEAR Level Vc Pc Mc Thickness
Vu = phi*10*(f'c^0.5)*b*d 1 257 1922 3990 20"
phi 0.75 2 163 1256 935 10"
f'c 5000 3 135 1078 671 10"
b 72 4 127 919 615 8"
d 8 5 121 744 525 8"
Vu 305.5 6 112 581 425 8"
7 96 453 346 8"
8 77 320 228 8"
9 61 206 129 8"
10 0.6 114 1.2 8"
Table 24: Design of Shear Walls (SBF Retrofit 2)
Cost Analysis
With the addition of new concrete material and the addition of steel plates, below is
listed the details in the change of weight of material. The additional weight of concrete
is 850 kips and steel is 2.3 kips. The rate of $3.50/pound is used for the cost of steel, and
a rate of $550/cubic yard is used for the cost of concrete for retrofits. SBF Retrofit 2:
Additional Shear Walls cost $123,429 with these additional retrofits.

Additional Plates W14x132PL
Concrete Shear
Wall 1 2~3 4~10
Thickness (ft) 0.042 Thickness (ft) 1.67 0.83 0.67
Weight (pcf) 490 Weight (pcf) 150 150 150
Length (ft) 12 Length (ft) 18.75 18.75 18.75
Height (ft) 1.17 Height (ft) 12 12 12
Quantity 8 Opening (ft
2
) 48 48 48
Total (kip) 2.3 Quantity 4 8 28
Cost ($) $8,003 Total (kip) 177.3 177 495.6
Cost ($) $24,085 $24,037 $67,304
Table 25: Cost Analysis (SBF Retrofit 2)

81

4.3.4 SBF Retrofit 3: Additional Plates
Lastly, the steel braced frame will be modified by simply reinforcing the columns and
beams with extra plates welded to the sides or bottom of the steel sections. This
implementation intends to solve localized overstressed members.

Performance of Retrofit
With the new lateral loads assigned to the structure, we can notice from section 4.3.1
how the braced frames, along with the columns which support it, require retrofit. The
newly added loads require greater steel section areas and other alternatives to support
greater axial forces. However, with the addition of steel plates to existing steel
members, the overall structure can be safely occupied as per code. (Note: The members
in red in Figure 27 meet the current code, but SAP 2000’s inability to check the design of
customized sections for seismic compactness results in red members.)

Figure 25: Performance (SBF Retrofit 3)

82

Framing Details
The columns which required additional plates were formed into a box shape as two
steel plates at varying thickness were attached to the sides of the wide flange. The
columns which required additional plates are listed below. The braces which needed
retrofitting were reinforced in the same manner as the columns.
Level C1 C2 C3 C4 BF1
12 W14x48 W14x48 W14x48 W14x48 W10x19
11 W14x48 W14x48 W14x48 W14x48 W10x19
10 W14x48 W14x48 W14x48 W14x48 W10x19
9 W14x48 W14x48 W14x48 W14x48 W10x19
8 W14x48 W14x68 PL W14x48 W14x48 W10x19
7 W14x48 W14x68 PL W14x48 W14x48 W10x19 PL
6 W14x48 W14x82 PL W14x48 W14x68 W10x19 PL
5 W14x48 W14x82 PL W14x48 W14x68 W10x19 PL
4 W14x48 W14x82 PL W14x48 W14x68 W10x26
3 W14x48 W14x82 PL W14x48 W14x82 W10x26 PL
2 W14x48 W14x132 PL W14x48 W14x82 W10x26
1 W14x48 W14x132 PL W14x48 W14x132 W10x26 PL
Table 26: List of Columns/Braces (SBF Retrofit 1)

Cost Analysis

The new plate additions to numerous columns and braces in the structure resulted in an
increase of 39.6 kips to the existing braced frame structure. Below are listed the varying
thicknesses of plates which were used and the number of plates used in the new
retrofit. The weight of the structure has now increased from 613.1 kips to 652.7 kips.
The additional weight of steel was assessed using the rate of $3.50/pound of steel. SBF
Retrofit 3: Additional Plates cost $138,741 with these additional retrofits.

83

Additional Plates W14x132 PL W14x82 PL W14x68 PL W10x26 PL W10x19 PL
Thickness (ft) 0.031 0.021 0.021 0.021 0.021
Weight (pcf) 490 490 490 490 490
Length (ft) 12 12 22.261 22.261 22.261
Height (ft) 1.17 1.17 1.17 0.83 0.83
Quantity 32 64 32 32 48
Weight (kip) 6.9 9.1 8.5 6.1 9.1
Total (kip) 39.6
Cost ($) $138,741
Table 27: Cost Analysis (SBF Retrofit 3)

4.4 Retrofit Design of Steel Moment Frame Structure
4.4.1 Implementation of Retrofit Solutions
Following the design of the steel moment frame structure based on lateral loads
described by the 1971 Los Angeles Building Code, this same structure will now undergo
loads specified by the current CBC 2010 code. When comparing these two values, it is
important to multiply the 1971 value by 1.4 to make a fair comparison between the ASD
and LRFD design values. Thus, the LRFD equivalent 1971 base shear value is shown in
red.

84

1971 LA
CBC
2010
Roof 36.1 53.9
12th 33.2 49.5
11th 30.2 45.1
10th 27.2 40.7
9th 24.3 36.3
8th 21.3 31.9
7th 18.4 27.5
6th 15.5 23.1
5th 12.5 18.7
4th 9.6 14.3
3rd 6.6 9.9
2nd 3.7 5.5
Total Base Shear 238.8 356.4
334.3
Table 28: Base Shear Comparison (SMF)
After re‐assigning new lateral loads on the model, the elements shown in red are
members which do not meet code. As the red shows, the moment frame beams need
additional reinforcing to resist the increased moment. Most of the columns throughout
the structure remain as operable. All interior columns and beams are designed per code.

Figure 26: Performance prior to Retrofits (SMF)
85

4.4.2 SMF Retrofit 1: Additional Bracing
In order to help the moment frame structure with the increased lateral loads, the first
retrofit of adding bracings intends to add stiffness to the overall structure. X‐bracings
were chosen to reinforce the moment frame and have been placed in the two middle
bays of each exterior façade.

Figure 27: Elevation View (SMF Retrofit 1)

Performance of Retrofit
The newly added bracings helped ease the load off from the other members by helping
resist lateral forces. The previously overstressed moment frame beams are now
designed for new loads, and the overstressed columns are now operable.
86

Figure 28: Performance (SMF Retrofit 1)
Framing Details
W14 steel members were assigned as bracings for the first four levels on each façade to
help resist loads. The axial load capacities required larger steel members, and these
members also had to obey the seismic compactness required by code. Therefore, listed
below are the bracing elements used in this retrofit. Along with the addition of braces,
several beams within the structure needed additional plates to help resist loads.
Level BF1
4 W14x48
3 W14x48
2 W14x48
1 W14x68
Table 29: List of Braces (SMF Retrofit 1)

Cost Analysis
After the bracing retrofits, the weight of the structure increased from 441.2 kips to
467.7 kips. The new addition accounts for 6% of the total weight of the existing
87

structure. The rate of $3.50/pound of steel is used for assessing new retrofits. SMF
Retrofit 1: Additional Bracing costs $92,591.
BF1 Additional Plates
Level
1 2~4
Thickness (ft) 0.031
Weight (plf)
68 48
Weight (pcf) 490
Length
24 22.3
Length (ft) 18.75
Weight (lbs)
1632 1070.4
Height (ft) 0.83
Quantity
8 24
Quantity 56
Weight (kip)
13.1 25.7
Weight (kip) 13.4
Total (kip) 13.1 Cost ($) $46,895
Cost ($) $45,696
Table 30: Cost Analysis (SMF Retrofit 1)

4.4.3 SMF Retrofit 2: Shear Walls
With this second retrofit for the steel moment frame structure, interior shear walls were
added to add stiffness to the building. Similar to the SBF Retrofit 2 in section 4.3.3, the
shear walls have a 6’x8’ opening on each floor to allow access.

Figure 29: Plan and Elevation Views (SMF Retrofit 2)
88

With the addition of shear walls, the structure increased in weight, increasing the dead
load from 100 PSF to 125 PSF. This change in weight has also increased the base shear
from 356 kips to 445 kips and lateral force applied to each floor.
DL Loading
Distribution
of Base Shear Fx
Flooring 5 Roof 67.4
Ceiling 5 12th 61.9
Mechanical/Electrical 5 11th 56.4
Partitions 15 10th 50.9
Steel 30 9th 45.4
Concrete 20 8th 39.9
Deck 45 7th 34.4
125 6th 28.9
5th 23.4
LL 4th 17.9
First Floor 100 3rd 12.4
2nd Floor and Up 50 2nd 6.9
Table 31: Increased Loading Values (SMF Retrofit 2)
Performance of the Retrofit
With the addition of the shear walls, the structure’s moment frame sections are shown
to be sufficient. The shear walls help to resist lateral loads. However, there are a few
beams supporting the shear wall which are overstressed. These beams were reinforced
with additional plates.

Figure 30: Performance (SMF Retrofit 2)
89

Framing Details
As described earlier, 8” concrete shear walls were added to the structure with its
elevation shown below. Some beams needed reinforcing due to the additional shear
stresses from the shear wall. These beams were reinforced by adding two steel plates
on its wide flanges to make a box section. In designing the shear walls, walls were
checked for shear, axial and moment load capacities.

Figure 31: Shear Wall Elevation
CHECK FOR SHEAR Level Vc Pc Mc Thickness
Vu = phi*10*(f'c^0.5)*b*d 1 131 859 685 8"
phi 0.75 2 86 833 416 8"
f'c 5000 3 83 695 366 8"
b 72 4 79 552 276 8"
d 8 5 8 402 147 8"
Vu 305.5
Table 32: Design of Shear Walls (SMF Retrofit 2)

Cost Analysis

The addition of the concrete shear walls have increased the weight of the entire
structure significantly as typical concrete weighs approximately 150 pounds per cubic
foot. The concrete shear walls and steel plates constitute a 354 kip increase in weight.
While assessing the cost of retrofits, these rates are used: $3.50/pound for steel and
$550/cubic yard for concrete. SMF Retrofit 2: Additional Shear Walls costs $94,969.
90

Concrete Shear Wall Additional Plates
Thickness (ft) 0.67 Thickness (ft) 0.031
Weight (pcf) 150 Weight (pcf) 490
Length (ft) 18.75 Length (ft) 18.75
Height (ft) 12 Height (ft) 0.83
Opening (ft
2
) 48 Quantity 56
Quantity 20 Weight (kip) 13.4
Weight (kip) 354 Cost ($) $46,895
Cost ($) $48,074
Table 33: Cost Analysis (SMF Retrofit 2)

4.4.4 SMF Retrofit 3: Additional Plates
Lastly, the steel moment frame will be modified by simply reinforcing the columns and
beams with extra plates welded to the sides or bottom of the steel sections.

Performance of Retrofit
With the new lateral loads assigned to the structure, we can notice from section 4.4.1
how the moment frame beams require retrofit. The newly added loads require greater
steel section areas and other alternatives to support increased moment. However, with
the addition of steel plates to existing steel members, the overall structure can be safely
occupied as per code. (Note: The members in red in Figure 33 meet the current code,
but SAP 2000’s inability to check the design of customized sections for seismic
compactness results in red members.)
91

Figure 32: Performance (SMF Retrofit 3)

Framing Details
The columns which required additional plates were formed into a box shape as two
steel plates at varying thickness were attached to the sides of the wide flange. The
columns which required additional plates are listed below.
Columns
Level C1 C2 C3 C4
12 W14x38 W14x38 W14x38 W14x38
11 W14x38 W14x38 W14x38 W14x38
10 W14x48 W14x48 W14x38 W14x38
9 W14x48 W14x48 W14x38 W14x38
8 W14x48 W14x48 W14x38 W14x74
7 W14x48 W14x48 W14x38 W14x74
6 W14x68 W14x68 W14x38 W14x74
5 W14x68 W14x68 W14x38 W14x74
4 W14x68 W14x68 W14x38 W14x74 PL
3 W14x68 W14x68 W14x38 W14x74 PL
2 W14x68 PL W14x68 PL W14x38 W14x82 PL
1 W14x68 PL W14x68 PL W14x48 PL W14x82 PL
Table 34: List of Columns (SMF Retrofit 3)

92

Cost Analysis
The new plate additions to numerous columns and beams in the structure resulted in an
increase of 38.8 kips to the existing braced frame structure. Below are listed the varying
thicknesses of plates which were used and the number of plates used in the new
retrofit. The weight of the structure has now increased from 441.2 kips to 479.8 kips.
While assessing retrofits, rates of $3.50/pound of steel is used. SMF Retrofit 3:
Additional Plates costs $135,920.
Additional Plates 0.375" PL Col. 0.25" PL Col. 0.375" PL Beams
Thickness (ft) 0.031 0.021 0.031
Weight (pcf) 490 490 490
Length (ft) 12 12 18.75
Height (ft) 1.17 1.17 0.83
Quantity 60 32 56
Weight (kip) 12.9 4.6 13.4
Total (kip) 38.8
Cost ($) $135,920
Table 35: Cost Analysis (SMF Retrofit 3)

4.5 Comparisons between Retrofit Implementations
In this section, the three retrofit implementations used in the steel braced frame and
steel moment frame will be compared and analyzed under three considerations: cost,
architectural, and constructability. Retrofit 1 refers to additional bracing, retrofit 2
refers to additional shear walls, and retrofit 3 refers to additional plates.

93

4.5.1 Cost Considerations
In considering the cost of each retrofit, chapter four studied the rehabilitation of the
steel braced frame and steel moment frame systems using three different retrofit
options. From the study, the estimated needed cost for each option was calculated by
quantifying the amount of steel and concrete used in the system and using a rate of
cost: $3.50/pound for steel and $550/cubic yard for concrete. The two cost analysis
figures below show similar trends: in both systems, the cheapest option was retrofit 1:
bracing.

When looking at each SAP 2000 model, the bracing retrofit proved more effective than
that of the shear wall addition. For instance, the steel moment frame structure required
four stories worth of X‐bracing for retrofit 1, however, five stories worth of concrete
shear walls were needed for retrofit 2. As for the steel braced frame structure, eight
stories of diagonal bracings were added to the exterior facades, while retrofit 2 required
ten stories of shear walls. A possible rationale behind this may be because the
earthquake loads were assigned to exterior frames of the structure; hence no lateral
forces were directly placed on interior frames. Therefore, the shear walls which were
added to the interior core of the building may have been less effective than that of the
steel bracing which were placed on the exterior frames. Accordingly, the steel bracing
retrofit proved less expensive despite the difference in unit cost of steel and concrete.
One story’s worth of W10x19 X‐bracing costs $2965, while one story’s worth of 8”
94

concrete shear wall costs $2404. SBF retrofit 2 resulted in a 28.8% cost increase when
compared to SBF retrofit 1. SMF retrofit 2 resulted in a 2.6% cost increase when
compared to SMF retrofit 1. However, it is important to note that since SMF retrofit 1 is
cheaper that SMF retrofit 2 by merely $2000, the overall margin of error allows a ±10%
variance in cost.

The third retrofit, additional steel plates, was most expensive for both the steel braced
frame and the steel moment frame. These plates were used to reinforce only elements
which failed to satisfy the current code. These steel sections were reinforced by adding
two steel plates to the columns to form a box shape. In order to maintain seismic
compactness, steel plates’ thicknesses started from 0.25”. Certainly some sections may
have merely needed 0.05” worth of extra steel, but a section so thin would suffer under
local buckling issues. Therefore, SBF retrofit 3 resulted in a 44.8% cost increase when
compared to SBF retrofit 1. SMF retrofit 3 resulted in a 46.8% cost increase when
compared to SMF retrofit 1.

95

Figure 33: Cost Analysis (SBF)

Figure 34: Cost Analysis (SMF)
$95,807
$123,429
$138,741
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (SBF)
R1: Bracing R2: Shear Wall R3: Additional Plates
$92,591
$94,969
$135,920
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (SMF)
R1: Bracing R2: Shear Wall R3: Additional Plates
96

4.5.2 Architectural Considerations
The three retrofit implementations impact the original architecture in different ways
and are described below. Retrofit 1, additional bracing, modifies the existing building’s
façade as steel members are placed on the exterior sides of the building. Certain views
from inside the building are hindered due to the erection of new steel members. The
exterior design of buildings is an important feature. Some function to reveal the building
type or intentions behind the architect and his design philosophies. On the other hand,
certain architects or engineers may approve the addition of exterior steel frames
because it expresses the structure of the building and maintains honesty of structure.
Retrofit 2, additional shear walls, does not modify the exterior facades of the existing
structure as these walls are placed inside the space. Therefore, this retrofit can be an
option for buildings which employ trademark exterior designs. However, these walls
modify and limit the existing building’s circulation with the placement of permanent
walls acting as structural elements. As shear walls, these walls typically cannot have
openings or holes unless they are designed beforehand. Typically, office buildings tend
to prefer free‐plan layouts without shear walls while residential buildings prefer shear
walls which helps act as partitions between housing units. Retrofit 3, additional plates,
does not hinder the architecture of the existing building if much at all. Due to the
increase in size of members with additional plates, certain walls may be modified to
accommodate the change in size. However, unlike retrofits 1 or 2, adding plates will not
make any major changes to the original architecture.
97

4.5.3 Constructability Concerns
Various issues involving these three retrofits during construction are described below.
The addition of steel braces as in retrofit 1 is relatively straightforward as it involves the
welding and addition of new steel members, and this procedure can be often done
without disrupting the use of a building. Adding shear walls as in retrofit 2, though cost‐
effective, is a big procedure and will hinder operation in a building during construction.
It can become a more difficult procedure if immovable pieces hinder the placing of
shear walls. The shear walls can be cast‐on‐site, which can take many weeks to cure and
erect. Otherwise, precast concrete elements can be used to build the shear walls;
however, moving the pieces indoors may be problematic depending on the size of entry
paths. As for retrofit 3, adding steel plates, constructability issues differ by
circumstances. For instance, if many columns and beams located on the lobby floor
require retrofitting, it will require major impedance to operations within the building.
However, if the overstressed members are located away from traffic‐heavy zones,
operation within the building may not be affected as much. Additionally, dry walls,
insulation, or any other material encasing the columns or beams may be removed and
replaced during and after implementing the retrofit, unless the original steel members
are exposed.
98

Summary
In the chapter, two steel structural systems were discussed: the steel braced frame and
the steel moment frame. The process toward designing and the rationale behind
choosing these systems were described elaborately. Following the procedures given in
the initial design of these two structures as per the 1971 Los Angeles Building Code,
these structures were placed under the current building code to evaluate. Naturally,
these buildings designed using older code showed signs of deficiency around certain
elements.

For each structural system, three retrofit implementations were assessed: addition of
braced frame, addition of shear walls, and addition of steel plates. These new additions
proved useful to each system, however, they differed in cost and each implementation
had its pros and cons.

In the next chapter, two additional structural systems will be discussed: the concrete
shear wall core and the concrete moment frame system. The same design philosophy
will be implemented with the two concrete systems.
99

Chapter 5: Concrete Structure Design and Retrofit
5.1 Design of Concrete Shear Wall Core Structure
In the evaluation of the concrete shear wall core structure, the model will first be
designed as given by the dimensions mentioned in Chapter 3. Hence, in this thesis, a
building with a 75’ by 75’ area with 12 floors will be representing a typical mid‐rise in
Los Angeles. Earthquake loads were added to the structure as per the 1971 Los Angeles
Building Code. Through a linear static analysis in SAP 2000, framing element sizes were
selected which meet the current code.

5.1.1 Design using 1971 Los Angeles Building Code
The total lateral force which every structure must be designed to withstand is given by
the formula, V = ZKCW. Z is given as the numerical coefficient of one. K is a horizontal
force factor for structures specified by a table within the 1971 building code. This
particular structure is classified under buildings with shear walls resisting lateral loads
with a K value of 0.8. C is a numerical coefficient which can be calculated by the formula,

.

. T is the fundamental period of vibration of the structure in seconds and can be
calculated by the formula,
. n
√
where h
n
is the total height of the structure and D
is the dimension of the building in feet in a direction parallel to the applied forces. W is
the total dead load of the structure, and the estimated dead load values are listed
below.
100

DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Deck 45
Shear Wall 20
Total Dead Load 295
Table 36: Total Dead Load (CSW)
As shown above, the total dead load in pounds per square feet is 295. Therefore, the
total W value for all four floors is 19912.5 kips (

). Below is a table
which shows the evaluation of the total lateral force.
hn 147
D 75
T 0.8
C 0.1
W(dead) 19912.5
K 0.8
V 841.3
Table 37: Total Base Shear (CSW)
Distribution of Lateral Force
The total lateral force, V, is distributed from the 2
nd
to the Roof level using the formula,
x
x x
∑ i i

. F
x
denotes the force distribution at a particular floor; w
x
refers to the
height at a particular floor, and h
x
refers to the height at a particular floor from the base
of the building. The values F
x
values in the chart below are in kips.

101

Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 841.3 1659.4 147 243928.1 127.2
12th 841.3 1659.4 135 224015.6 116.8
11th 841.3 1659.4 123 204103.1 106.5
10th 841.3 1659.4 111 184190.6 96.1
9th 841.3 1659.4 99 164278.1 85.7
8th 841.3 1659.4 87 144365.6 75.3
7th 841.3 1659.4 75 124453.1 64.9
6th 841.3 1659.4 63 104540.6 54.5
5th 841.3 1659.4 51 84628.1 44.1
4th 841.3 1659.4 39 64715.6 33.8
3rd 841.3 1659.4 27 44803.1 23.4
2nd 841.3 1659.4 15 24890.6 13.0
Table 38: Distribution of Base Shear (CSW)
Now these F
x
values are divided into two as each half is applied in two directions.

Figure 35: Lateral Load Application

5.1.2 Framing Details

Figure 36: Plan and Elevation View (CSW)
102

With the concrete shear wall core structure, an interior core of 37.5’ by 18.75’ is
designed to resist lateral loads. Elevator shafts and mechanical equipment will be stored
within the core. All other beams and columns are reinforced concrete.

5.1.3 Design of Framing Members
In order to adequately assign adequate framing elements in the concrete shear wall
core structure, the model must first be analyzed in SAP 2000 under design loads. After
assigning all gravity and lateral loads to the computer model, an analysis was run with
the following four strength design load combinations: 1) 1.4D, 2) 1.2D+1.6L, 3)
1.2D+1.0E
x
+1.6L, 4) 1.2D+1.0E
y
+1.6L (D, dead load; L, live load; L
r
, roof live load; E
x
,
earthquake load in the x‐direction; E
y
, earthquake load in the y‐direction). Following the
analysis, each framing element’s required moment (M
u
), shear (V
u
), and axial values (P
u
)
were recorded by looking at each maximum value.

SAP 2000 Calibration
From an initial preliminary design of concrete, the calculated sections were re‐applied to
the SAP 2000 model. The “concrete design check of structure” results notified various
errors in the model which involved lateral torsional buckling, overstressed reinforcing,
beam to column ratios, and stress failure.

103

Lateral torsional buckling occurred due to the lack of mid‐span supports along the
beams. This issue was resolved after overwriting SAP 2000 to ensure the beams were
continually supported along its length. Beam to column ratios must be satisfied to
ensure the strong column, weak beam design philosophy. In designing for the beams to
fail before the columns, the building will not buckle by column failure which would be
disastrous. Lastly, each member must be sufficient under given loads with less than one
ratios of demand/capacity.

Through calibration, many framing sections were modified from the hand calculations.
Noticeably, columns had to be significantly increased in size to satisfying reinforcing
ratios.

104

5.1.4 Framing Details
Listed below are details of each framing element.
Columns
Level C1 C2 C3 C4
12 14x14 14x14 14x14 14x14
11 14x14 14x14 14x14 16x16
10 14x14 14x14 14x14 16x16
9 16x16 16x16 14x14 16x16
8 16x16 16x16 14x14 16x16
7 16x16 16x16 14x14 18x18
6 18x18 18x18 14x14 18x18
5 20x20 20x20 14x14 20x20
4 20x20 20x20 16x16 24x24
3 24x24 24x24 16x16 24x24
2 24x24 24x24 16x16 28x28
1 24x24 24x24 16x16 28x28
Table 39: List of Columns (CSW)

Figure 37: Column Framing Plan (CSW)

105

Beams Girders
Level B1 B2 Level G1 G2 G3
R 12x26 10x14 R 16x32 16x32 10x14
12 12x26 10x14 12 16x32 16x32 10x14
11 12x26 10x14 11 16x32 16x32 10x14
10 12x26 10x14 10 16x32 16x32 10x14
9 12x26 10x14 9 16x32 16x32 10x14
8 12x26 10x14 8 16x32 16x32 12x18
7 12x26 10x14 7 16x32 16x32 12x18
6 12x26 10x14 6 16x32 16x32 12x18
5 12x26 10x14 5 16x32 16x32 12x18
4 12x26 12x18 4 16x32 16x32 12x18
3 12x26 12x18 3 16x32 16x32 12x18
2 12x26 12x18 2 16x32 16x32 12x18
Table 40: List of Beams and Girders (CSW)

Figure 38: Beam and Girder Framing Plan
106

For reference, beams refer to all framing elements which run horizontal per plan above.
Girders are framing elements which run vertically. B1 refers to all interior beams, and B2
refers to all exterior beams. G1 refers to all girders which are part of the shear walls. G2
refers to all interior girders which aren’t connected to shear walls. G3 refers to all
exterior girders.

5.1.5 Existing Building Weight
Using a simplified approach, cost of this system is represented by the weight of material
used in the system, more specifically the weight of the framing elements. By identifying
the number of each respective framing section, which includes the beams, columns, and
shear walls, the total weight of framing elements is described below.
B1 B2
Level R~2 Level R~5 4~2
Width (ft) 1 Width (ft) 0.83 1.00
Depth (ft) 2.17 Depth (ft) 1.17 1.50
Length (ft) 18.75 Length (ft) 18.75 18.75
Density (pcf) 150 Density (pcf) 150 150
Quantity 336 Quantity 72 24
TOTAL (kip) 2047.5 TOTAL (kip) 196.9 101.3
2047.5 298.1
Table 41: Weight of Beams (CSW)

107

G1 G2 G3
Level R~2 Level R~2 Level R~9 8~2
Width (ft) 1.33 Width (ft) 1.33 Width (ft) 0.83 1.00
Depth (ft) 2.67 Depth (ft) 2.67 Depth (ft) 1.17 1.50
Length (ft) 18.75 Length (ft) 18.75 Length (ft) 18.75 18.75
Density
(pcf) 150
Density
(pcf) 150
Density
(pcf) 150 150
Quantity 72 Quantity 72 Quantity 40 56
TOTAL (kip) 720.0 TOTAL (kip) 720.0 TOTAL (kip) 109.4 236.3
1440.0 720.0 357.6
Table 42: Weight of Girders (CSW)

Shear Wall SW1 SW2
Thickness (ft) 0.67 0.67
Weight (pcf) 150 150
Length (ft) 18.75 18.75
Height (ft) 12 12
Opening (ft
2
) 0 48
Quantity 36 48
Weight (kip) 810 849.6
1659.6
Table 43: Weight of Shear Wall (CSW)

108

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.00 2.00 2.00 1.67 1.67 1.50 1.33 1.33 1.33 1.17 1.17 1.17
Depth (ft) 2.00 2.00 2.00 1.67 1.67 1.50 1.33 1.33 1.33 1.17 1.17 1.17
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL
(kip) 57.6 57.6 57.6 40 40 32.4 25.6 25.6 25.6 19.6 19.6 19.6
420.8
C2
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.00 2.00 2.00 1.67 1.67 1.50 1.33 1.33 1.33 1.17 1.17 1.17
Depth (ft) 2.00 2.00 2.00 1.67 1.67 1.50 1.33 1.33 1.33 1.17 1.17 1.17
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 28.8 28.8 28.8 20 20 16.2 12.8 12.8 12.8 9.8 9.8 9.8
210.4
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 1.33 1.33 1.33 1.33 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.17
Depth (ft) 1.33 1.33 1.33 1.33 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.17
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 12.8 12.8 12.8 12.8 9.8 9.8 9.8 9.8 9.8 9.8 9.8 9.8
129.6
C4
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.33 2.33 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33 1.33 1.17
Depth (ft) 2.33 2.33 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33 1.33 1.17
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 9 9 9 9 9 9 9 9 9 9 9 9
TOTAL
(kip) 88.2 88.2 64.8 64.8 45.0 36.5 36.5 28.8 28.8 28.8 28.8 22.1
561.2
Table 44: Weight of Columns (CSW)
Therefore, the total weight of concrete in this system is 7112.8 kips.

109

5.2 Design of Concrete Moment Frame Structure
In the evaluation of the concrete moment frame structure, the model will first be
designed as given by the dimensions mentioned in chapter 3. Hence, in this thesis, a
building with a 75’ by 75’ area with 12 floors will be representing a typical mid‐rise in
Los Angeles. Earthquake loads were added to the structure as per the 1971 Los Angeles
Building Code. Through a linear static analysis in SAP 2000, framing element sizes were
selected which meet the current code.

5.2.1 Design using 1971 Los Angeles Building Code
The total lateral force which every structure must be designed to withstand is given by
the formula, V = ZKCW. Z is given as the numerical coefficient of one. K is a horizontal
force factor for structures specified by a table within the 1971 building code. This
particular structure is classified under buildings with moment frames resisting lateral
loads with a K value of 0.67. C is a numerical coefficient which can be calculated by the
formula,
.

. T is the fundamental period of vibration of the structure in seconds
and can be calculated by the formula,
. n
√
where h
n
is the total height of the
structure and D is the dimension of the building in feet in a direction parallel to the
applied forces. W is the total dead load of the structure, and the estimated dead load
values are listed below.

110

DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Deck 45
Total Dead Load 275
Table 45: Total Dead Load (CMF)
As shown above, the total dead load in pounds per square feet is 275. Therefore, the
total W value for all four floors is 18562 kips (

). Below is a table
which shows the evaluation of the total lateral force.
hn 147
D 75
T 0.85
C 0.053
W(dead) 18562
K 0.67
V 656.8
Table 46: Total Base Shear (CMF)
Distribution of Lateral Force
The total lateral force, V, is distributed from the 2
nd
to the Roof level using the formula,
x
x x
∑ i i

. F
x
denotes the force distribution at a particular floor; w
x
refers to the
height at a particular floor, and h
x
refers to the height at a particular floor from the base
of the building. The values F
x
values in the chart below are in kips.

111

Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 656.8 1546.9 147 227390.6 99.3
12th 656.8 1546.9 135 208828.1 91.2
11th 656.8 1546.9 123 190265.6 83.1
10th 656.8 1546.9 111 171703.1 75.0
9th 656.8 1546.9 99 153140.6 66.9
8th 656.8 1546.9 87 134578.1 58.8
7th 656.8 1546.9 75 116015.6 50.7
6th 656.8 1546.9 63 97453.1 42.6
5th 656.8 1546.9 51 78890.6 34.5
4th 656.8 1546.9 39 60328.1 26.4
3rd 656.8 1546.9 27 41765.6 18.2
2nd 656.8 1546.9 15 23203.1 10.1
Table 47: Distribution of Base Shear (CMF)
Now these F
x
values are divided into two as each half is applied in two directions.

Figure 39: Lateral Load Application

5.2.2 Framing Details
The concrete moment frame structure is designed with fixed or moment connections
throughout the structure which hopes to dissipate earthquake forces by reacting with
flexibility. Below are illustrations to describe the structure.
112

Figure 40: Elevation and Plan Views (CMF)

5.2.3 Design of Framing Members
In order to adequately assign adequate framing elements in the concrete moment
frame structure, the model must first be analyzed in SAP 2000 under design loads. After
assigning all gravity and lateral loads to the computer model, an analysis was run with
the following four strength design load combinations: 1) 1.4D, 2) 1.2D+1.6L, 3)
1.2D+1.0E
x
+1.6L, 4) 1.2D+1.0E
y
+1.6L (D, dead load; L, live load; L
r
, roof live load; E
x
,
earthquake load in the x‐direction; E
y
, earthquake load in the y‐direction). Following the
analysis, each framing element’s required moment (M
u
), shear (V
u
), and axial values (P
u
)
were recorded by looking at each maximum value.
SAP 2000 Calibration
113

From an initial preliminary design of concrete, the calculated sections were re‐applied to
the SAP 2000 model. The “concrete design check of structure” results notified various
errors in the model which involved lateral torsional buckling, overstressed reinforcing,
beam to column ratios, and stress failure.

Lateral torsional buckling occurred due to the lack of mid‐span supports along the
beams. This issue was resolved after overwriting SAP 2000 to ensure the beams were
continually supported along its length. Beam to column ratios must be satisfied to
ensure the strong column, weak beam design philosophy. In designing for the beams to
fail before the columns, the building will not buckle by column failure which would be
disastrous. Lastly, each member must be sufficient under given loads with less than one
ratios of demand/capacity.

Through calibration, many framing sections were modified from the hand calculations.
Noticeably, columns had to be significantly increased in size to satisfy reinforcing ratios.

5.2.4 Size of Framing Members
Following the evaluation run through SAP 2000, listed below is the framing sizes used in
the concrete moment frame structure.

114

Columns
Level C1 C2 C3 C4
12 16x16 16x16 14x14 14x14
11 16x16 16x16 14x14 14x14
10 16x16 16x16 14x14 16x16
9 18x18 18x18 14x14 18x18
8 18x18 18x18 16x16 20x20
7 20x20 20x20 16x16 20x20
6 24x24 24x24 16x16 24x24
5 24x24 24x24 16x16 24x24
4 24x24 24x24 18x18 28x28
3 24x24 24x24 18x18 28x28
2 24x24 24x24 18x18 28x28
1 28x28 28x28 24x24 30x30
Table 48: List of Columns (CMF)

Figure 41: Column Framing Plan (CMF)

115

Beams Girders
Level B1 B2 Level G1 G2
R 12x20 10x14 R 12x16 10x14
12 12x24 10x14 12 12x20 10x14
11 12x24 10x14 11 12x20 10x14
10 12x24 10x14 10 12x24 10x14
9 16x32 12x18 9 12x28 12x18
8 16x32 12x18 8 12x28 14x28
7 16x32 12x20 7 16x32 14x28
6 16x32 12x20 6 16x32 14x28
5 16x32 12x20 5 16x32 14x28
4 16x32 12x24 4 16x32 16x32
3 16x34 12x24 3 16x32 16x32
2 16x34 16x34 2 16x38 16x38
Table 49: List of Beams and Girders (CMF)
For reference, beams refer to all framing elements which run horizontal per plan above.
Girders are framing elements which run vertically. B1 refers to all interior beams, and B2
refers to all exterior beams. G1 refers to all interior girders, and G2 refers to all exterior
girders.

5.2.5 Existing Building Weight
Using a simplified approach, cost of this system is represented by the weight of material
used in the system, more specifically the weight of the framing elements. By identifying
the number of each respective framing section, which includes the beams and columns,
the total weight of framing elements is described below.

116

B1
Level R 12~10 9~4 3~2
Width (ft) 1 1 1.3 1.3
Depth (ft) 1.67 2.00 2.67 2.83
Length (ft) 18.75 18.75 18.75 18.75
Density (pcf) 150 150 150 150
Quantity 28 84 168 56
TOTAL (kip) 131.3 472.5 1680 595
2878.8
B2
Level R~10 9~8 7~5 4~3 2
Width (ft) 0.83 1 1 1 1.33
Depth (ft) 1.17 1.50 1.67 2.00 2.83
Length (ft) 18.75 18.75 18.75 18.75 18.75
Density (pcf) 150 150 150 150 150
Quantity 32 16 24 16 8
TOTAL (kip) 87.5 67.5 112.5 90 85
442.5
G1
Level R 12~11 10 9~8 7~3 2
Width (ft) 1.00 1.00 1.00 1.00 1.33 1.33
Depth (ft) 1.33 1.67 2.00 2.33 2.67 3.17
Length (ft) 18.75 18.75 18.75 18.75 18.75 18.75
Density (pcf) 150 150 150 150 150 150
Quantity 12 24 12 24 60 12
TOTAL (kip) 45.0 112.5 67.5 157.5 600.0 142.5
1125.0
G2
Level R~10 9 8~5 4~3 2
Width (ft) 0.83 1.00 1.17 1.33 1.33
Depth (ft) 1.17 1.50 2.33 2.67 3.17
Length (ft) 18.75 18.75 18.75 18.75 18.75
Density (pcf) 150 150 150 150 150
Quantity 32 8 32 16 8
TOTAL (kip) 87.5 33.8 245.0 160.0 95.0
621.3
Table 50: Weight of Beams and Girders (CMF)

117

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.33 2.00 2.00 2.00 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33
Depth (ft) 2.33 2.00 2.00 2.00 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL
(kip) 78.4 57.6 57.6 57.6 57.6 57.6 40 32.4 32.4 25.6 25.6 25.6
548
C2
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.33 2.00 2.00 2.00 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33
Depth (ft) 2.33 2.00 2.00 2.00 2.00 2.00 1.67 1.50 1.50 1.33 1.33 1.33
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 39.2 28.8 28.8 28.8 28.8 28.8 20 16.2 16.2 12.8 12.8 12.8
274
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.00 1.50 1.50 1.50 1.33 1.33 1.33 1.33 1.17 1.17 1.17 1.17
Depth (ft) 2.00 1.50 1.50 1.50 1.33 1.33 1.33 1.33 1.17 1.17 1.17 1.17
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 28.8 16.2 16.2 16.2 12.8 12.8 12.8 12.8 9.8 9.8 9.8 9.8
167.8
C4
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width
(ft) 2.50 2.33 2.33 2.33 2.00 2.00 1.67 1.67 1.50 1.33 1.17 1.17
Depth
(ft) 2.50 2.33 2.33 2.33 2.00 2.00 1.67 1.67 1.50 1.33 1.17 1.17
Length
(ft) 12 12 12 12 12 12 12 12 12 12 12 12
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 9 9 9 9 9 9 9 9 9 9 9 9
TOTAL
(kip) 101.25 88.2 88.2 88.2 64.8 64.8 45 45 36.45 28.8 22.05 22.05
694.8
Table 51: Weight of Columns (CMF)
Therefore, the total weight of the concrete moment frame system is 6752.1 kips.

118

5.3 Retrofit Design of Concrete Shear Wall Core Structure
5.3.1 Implementation of Retrofit Solutions
Following the design of the concrete shear wall core structure based on lateral loads
described by the 1971 Los Angeles Building Code, this same structure will now undergo
loads specified by the current 2010 California Building Code. Below is a chart comparing
the two base shear values, however in order to make fair comparisons, the value in red
is the 1971 LA base shear value multiplied by 1.4 to represent the LRFD equivalent.
1971 LA
CBC
2010
Roof 117.9 379.4
12th 108.3 348.5
11th 98.7 317.5
10th 89.1 286.5
9th 79.4 255.5
8th 69.8 224.6
7th 60.2 193.6
6th 50.6 162.6
5th 40.9 131.6
4th 31.3 100.7
3rd 21.7 69.7
2nd 12 38.7
Total Base Shear 770 2508
1078
Table 52: Base Shear Comparisons (CSW)
After re‐assigning new lateral loads on the model, the elements shown in red are
members which do not meet code. As the red shows, the exterior bracing must be
reinforced to be able to resist axial compression from the lateral loads. Additionally, the
119

columns which are connected to the braces must be reinforced to resist higher axial
loads. Most of the members fail due to overstress.

Figure 42: Performance prior to Retrofits (CSW)

5.3.2 CSW Retrofit 1: Additional Bracing
As you can see from images above, the framing elements highlighted in red signify
failure of the members. As mentioned previously, these failures were mostly due to
higher demand than capacity. In order to help support the overstressed columns and
beams, seismic retrofitting began with adding more bracing elements on the exterior
faces of the structure. This configuration hopes to distribute the lateral force more
evenly throughout the structure and stiffen the structure. The X‐bracing along the N‐S
and E‐W facades hopes to dissipate earthquake forces and allow the structure to
perform more efficiently.
120

Figure 43: Plan and Elevation View (CSW Retrofit 1)
Performance of Retrofit
With the addition of the new bracing elements on all four exterior sides of the structure,
all framing elements are able to resist new loads successfully.

Figure 44: Performance (CSW Retrofit 1)
121

Framing Details

The following sections were used to create the braced frames.
Level BF1
12 W10x19
11 W10x19
10 W10x19
9 W10x19
8 W10x19
7 W10x19
6 W10x19
5 W10x19
4 W10x19
3 W10x19
2 W10x19
1 W10x19
Table 53: List of Braces (CSW Retrofit 1)
Cost Analysis
The new framing has increased the weight of the structure as shown below. The weight
of concrete in the concrete shear wall core structure remains the same at 7112 kips.
However, the weight of steel has now increased by 40.9 kips. While assessing costs for
new retrofits, these values are used for steel and concrete materials: $3.50/pound for
steel and $550/cubic yard for concrete. CSW Retrofit 1: Additional Bracing costs
$143,268.

122

BF1
Level
1 2~12
Weight (plf)
19 19
Length
24 22.3
Weight (lbs)
456 423.7
Quantity
8 88
Weight (kip)
3.6 37.3
Total (kip) 40.9
Cost ($) $143,268
Table 54: Cost Analysis (CSW Retrofit 1)

5.3.3 CSW Retrofit 2: Addition of Shear Walls
In this retrofit, shear walls are added to the concrete shear wall core structure to stiffen
the building to better resist earthquake forces. Since, the original building already
employs a shear wall interior core, the new added shear walls are placed on the exterior
facades of the structure. The shear walls placed alongside the exterior framing to help
resist the stresses concentrated on the core.

Figure 45: Plan and Elevation Views (CSW Retrofit 2)
123

By adding concrete shear walls, the weight of the structure changes significantly,
therefore the increased dead load is shown in the figure below. The increased weight
thus attracts more lateral forces, hence Newton’s F=ma. The base shear has now
increased from 2509 kips to 2679 kips.
DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Deck 45
Shear Wall 40
315
Figure 46: Increased Dead Load (CSW Retrofit 2)
Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 2679 1771.9 147 260465.6 405.2
12th 2679 1771.9 135 239203.1 372.1
11th 2679 1771.9 123 217940.6 339.0
10th 2679 1771.9 111 196678.1 305.9
9th 2679 1771.9 99 175415.6 272.9
8th 2679 1771.9 87 154153.1 239.8
7th 2679 1771.9 75 132890.6 206.7
6th 2679 1771.9 63 111628.1 173.6
5th 2679 1771.9 51 90365.6 140.6
4th 2679 1771.9 39 69103.1 107.5
3rd 2679 1771.9 27 47840.6 74.4
2nd 2679 1771.9 15 26578.1 41.3
Table 55: Increased Base Shear (CSW Retrofit 2)
Performance of Retrofit
The exterior shear walls helped reduce loads on the interior shear wall core by being
designed to take lateral forces alongside the exterior frame.
124

Figure 47: Performance (CSW Retrofit 2)
Framing Details
In order to design the shear walls, each wall was designed to resist its respective shear,
axial, and moment forces. The additional shear walls were designed as 8” thick and are
placed on all four exterior facades of the structure. For column designations please
refer to section 5.1.4.
18.75 FEET/WALL
CHECK FOR SHEAR Vc Pc Mc Thickness
Vu = phi*10*(f'c^0.5)*b*d 1 601.9 1304 10479 8"
phi 0.75 2 384.8 1197 5976 8"
f'c 5000 3 289.9 1111 4216 8"
b 225 4 226.7 1140 3327 8"
d 8 5 187.2 1032 2320 8"
Vu 954.6 6 160.8 972 1631 8"
7 135.3 888 964 8"
8 111.4 745 389 8"
9 82.8 601 106 8"
10 52.9 474 522 8"
11 25 315 711 8"
12 36 155 613 8"
Figure 48: Design of Shear Walls (CSW Retrofit 2)

125

Cost Analysis
With the addition of new concrete material, below is listed the details in the increase in
total weight. The weight of concrete increased from 7112.8 kips to 8192.8 kips. While
assessing costs for new retrofits, these values are used for steel and concrete materials:
$3.50/pound for steel and $550/cubic yard for concrete. CSW Retrofit 1: Additional
Bracing costs $146,667.
Concrete Shear Wall 1~12
Thickness (ft) 0.67
Weight (pcf) 150
Length (ft) 18.75
Height (ft) 12
Opening (ft
2
) 0
Quantity 48
Total (kip) 1080
Cost ($) $146,667
Table 56: Cost Analysis (CSW Retrofit 2)

5.4 Retrofit Design of Concrete Moment Frame Structure
5.4.1 Implementation of Retrofit Solutions
Following the design of the concrete moment frame structure based on lateral loads
described by the 1971 Los Angeles Building Code, this same structure will now undergo
loads specified by the current 2010 California Building Code. Below is a chart comparing
the two base shear values, and in order to make a fair comparison, the 1971 LA base
shear was multiplied by 1.4 to create a LRFD equivalent, signified in red.

126

1971 LA
CBC
2010
Roof 79.5 157.5
12th 73.0 144.6
11th 66.5 131.8
10th 60.0 118.9
9th 53.5 106.1
8th 47.0 93.2
7th 40.5 80.4
6th 34.1 67.5
5th 27.6 54.6
4th 21.1 41.8
3rd 14.6 28.9
2nd 8.1 16.1
Total Base Shear 525.4 1041.5
735.5
Table 57: Base Shear Comparisons (CMF)
After re‐assigning new lateral loads on the model, the elements shown in red are
members which do not meet code. As the red shows, the columns must be reinforced to
be able to resist increased axial loads. Additionally, the moment frame beams require
retrofits to help resist larger moment. Most of the members fail due to overstress.

Figure 49: Performance prior to Retrofits (CMF)
127

5.4.2 CMF Retrofit 1: Additional Bracing
As you can see from images above, the framing elements highlighted in red signify
failure of the members. As mentioned previously, these failures were mostly due to
higher demand than capacity. In order to help support the overstressed columns and
beams, the first venue for seismic retrofitting began with adding more bracing elements
on the exterior faces of the structure. This configuration hopes to distribute the lateral
force more evenly throughout the structure and also by stiffening the structure. X
braces are used on each façade of the structure.

Figure 50: Plan and Elevation View (CMF Retrofit 1)
Performance of Retrofit
With the addition of the new bracing elements on all four exterior sides of the structure,
all framing elements except two interior columns are able to resist new loads
successfully.
128

Figure 51: Performance (CMF Retrofit 1)
Framing Details
The following sections were used to create the braced frames.
Level BF1
12 W10x19
11 W10x19
10 W10x19
9 W10x19
8 W10x19
7 W10x19
6 W10x19
5 W10x19
4 W10x19
3 W10x19
2 W10x19
1 W10x19
Table 58: List of Braces (CMF Retrofit 1)

Cost Analysis
The new framing has increased the weight of the structure as shown below. The weight
of concrete in the concrete moment frame structure remains the same at 6752 kips. The
addition of steel members contributes to 40.9 kips of steel. While assessing costs for
129

new retrofits, these values are used for steel and concrete materials: $3.50/pound for
steel and $550/cubic yard for concrete. CMF Retrofit 1: Additional Bracing costs
$143,268.
BF1
Level
1 2~12
Weight (plf)
19 19
Length
24 22.3
Weight (lbs)
456 423.7
Quantity
8 88
Weight (kip)
3.6 37.3
Total (kip) 40.9
Cost ($) $143,268
Table 59: Cost Analysis (CMF Retrofit 1)

5.4.3 CMF Retrofit 2: Addition of Shear Walls
In this retrofit, shear walls are added to the moment frame structure to further stiffen
the structure. The shear walls are configured in the interior core of the structure. The
shear walls placed alongside the interior frames to help resist the increased lateral
forces.

Figure 52: Plan and Elevation View (CMF Retrofit 2)
130

By adding concrete shear walls, the weight of the structure changes significantly,
therefore the increased dead load is shown in the figure below. The increased weight
thus attracts more lateral forces, hence Newton’s F=ma. The base shear has now
increased from 1041 kips to 1117 kips.
DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Shear Wall 20
Deck 45
Total Dead Load 295
Table 60: Increased Dead Load Values (CMF Retrofit 2)
Distribution of Base
Shear V w(x) h(x) w(x)*h(x) Fx
Roof 1117.3 1659.4 147 243928.1 169.0
12th 1117.3 1659.4 135 224015.6 155.2
11th 1117.3 1659.4 123 204103.1 141.4
10th 1117.3 1659.4 111 184190.6 127.6
9th 1117.3 1659.4 99 164278.1 113.8
8th 1117.3 1659.4 87 144365.6 100.0
7th 1117.3 1659.4 75 124453.1 86.2
6th 1117.3 1659.4 63 104540.6 72.4
5th 1117.3 1659.4 51 84628.1 58.6
4th 1117.3 1659.4 39 64715.6 44.8
3rd 1117.3 1659.4 27 44803.1 31.0
2nd 1117.3 1659.4 15 24890.6 17.2
Table 61: Increased Base Shear (CMF Retrofit 2)
Performance of Retrofit
The interior shear walls along with the braced frame helped reduce loads on the
moment frame structure by being designed to take lateral forces.
131

Figure 53: Performance (CMF Retrofit 2)

Framing Details
The additional shear walls are 10” thick for the first two levels and 8” for the other
floors, and shear walls are placed on all four interior bays of the structure as shown
above. The shear walls have been designed to resist the shear, axial, and moment forces
applied to each wall. The first two story shear walls are designed to resist the first story
columns as well.
CHECK FOR SHEAR Vc Pc Mc Thickness
Vu = phi*10*(f'c^0.5)*b*d 1 268.3 1183.8 1273.9 10"
phi 0.75 2 142.9 1194.2 571.4 10"
f'c 5000 3 123.3 1056.2 458.9 8"
b 72 4 118.6 929.2 390 8"
d 8 5 114.8 899.1 434.8 8"
Vu 305.5 6 89.5 798.3 284.5 8"
7 98.2 748.2 385.9 8"
8 80.6 617.2 246.9 8"
9 71.6 499.4 220.5 8"
10 53.8 372.8 141 8"
11 20.8 241.2 0.6 8"
12 30.8 117.9 134.7 8"
Table 62: Shear Wall Design (CMF Retofit 2)

132

Cost Analysis
With the addition of new concrete shear wall alongside the steel braces, below is listed
the details in the increase in total weight. The weight of concrete increased from 6752
kips to 7673 kips. While assessing costs for new retrofits, these values are used for steel
and concrete materials: $3.50/pound for steel and $550/cubic yard for concrete. CMF
Retrofit 2: Additional Shear Walls costs $120,185.
Concrete Shear Wall 1~2 3~12
Thickness (ft) 0.83 0.67
Weight (pcf) 150 150
Length (ft) 18.75 18.75
Height (ft) 12 12
Opening (ft
2
) 48 48
Quantity 8 40
Total (kip) 177 708
Cost ($) $24,037 $96,148
Table 63: Cost Analysis (CMF Retrofit 2)

5.5 Comparisons of Retrofits
In this section, the two retrofit implementations used in the concrete shear wall core
and concrete moment frame is compared and analyzed under three considerations:
cost, architectural, and constructability. Retrofit 1 refers to additional bracing, and
retrofit 2 refers to additional shear walls.

5.5.1 Cost Considerations
In considering the cost of each retrofit, chapter five studied the rehabilitation of the
concrete shear wall and concrete moment frame system using two different retrofit
133

options. From the study, the estimated needed cost for each option was calculated by
quantifying the amount of steel and concrete used in the system and by using a rate of
cost: $3.50/pound for steel and $550/cubic yard for concrete. The two cost analysis
figures below show different trends: for the concrete shear wall core system, the
cheaper option was retrofit 1: bracing; on the other hand, for the concrete moment
frame, the cheaper option was retrofit 2: shear wall. However, it should be noted that
the difference in cost between the two retrofits in the concrete shear wall core system
is roughly only $3000. As said earlier, the overall margin of error allows a ±10% variance
in cost.

In both the concrete shear wall core building and the concrete moment frame system,
retrofit 1 required X‐bracing in all 12 stories, and retrofit 2 employed shear walls in all
12 stories. Therefore, it is difficult to assess which retrofit best accompanies a particular
structural system. However, from observations in Section 4.5.1, bracing elements
proved more efficient than shear walls possibly because bracing was placed along the
exterior frame, where the lateral loads were applied. With the concrete shear wall core
system, the newly added shear walls were placed along the exterior frame unlike the
other systems because the original building employed a shear wall interior core.

Apart from an engineering perspective in cost, there are other cost considerations
during construction and erection of these retrofit systems. For instance, the operability
134

of the building may be hampered during construction while implementing the retrofits,
which equals more cost. Adding shear walls for instance may cause a large hindrance to
operability of a building because the construction will be occurring inside the building.
On the other hand, adding steel braces along the exterior frame may not have a major
impact to operation. This issue is discussed more in detail below.

CSW Retrofit 2 resulted in a 2.4% increase when compared to CSW Retrofit 1, and CMF
Retrofit 1 resulted in a 19.2% increase when compared to CMF Retrofit 2.

Figure 54: Cost Analysis (CSW)
$143,268
$146,667
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (CSW)
R1: Bracing R2: Shear Wall
135

Figure 55: Cost Analysis (CMF)

5.5.2 Architectural Considerations
The two retrofit implementations impact the original architecture in different ways and
are described below. Retrofit 1, additional bracing, modifies the existing building’s
façade as steel members are placed on the exterior sides of the building. Certain views
from inside the building are hindered due to the erection of new steel members.
Retrofit 2, additional shear walls, does not modify the exterior facades of the existing
structure as these walls are placed inside the space for the concrete moment frame
system. However, for the concrete shear wall core system, the shear walls were added
on the exterior facades of the building due to the existing core system. These walls
completely hindered all views from the inside along that particular bay. These walls also
modify and limit the existing building’s circulation with the placement of these
$143,268
$120,185
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (CMF)
Retrofit 1: Bracing Retrofit 2: Shear Wall
136

permanent walls acting as structural elements. Typically, office buildings tend to prefer
free‐plan layouts without shear walls while residential buildings prefer shear walls which
helps act as partitions between housing units.

5.5.3 Constructability Concerns
Various issues involving these three retrofits during construction are described below.
The addition of steel braces as in retrofit 1 is relatively straightforward as it involves the
welding and addition of new steel members, and this procedure can be often done
without disrupting the use of a building. Adding shear walls as in retrofit 2, though cost‐
effective, is a big procedure and will hinder operation in a building during construction.
It can become a more difficult procedure if immovable pieces hinder the placing of
shear walls. The shear walls can be cast‐on‐site, which can take many weeks to cure and
erect. Otherwise, precast concrete elements can be used to build the shear walls;
however, moving the pieces indoors may be problematic depending on the size of entry
paths.

Summary
In the chapter, two concrete structural systems were discussed: the concrete shear wall
core system and the concrete moment frame. The process toward designing and the
rationale behind choosing these systems were described elaborately. Following the
137

procedures given in the initial design of these two structures as per the 1971 Los
Angeles Building Code, these structures were placed under the current building code to
evaluate. Naturally, the buildings designed using older code showed signs of deficiency
around certain elements.

For each structural system, two retrofit implementations were assessed: addition of
braced frame and the addition of shear walls. These new additions proved useful to
each system, however, they differed in cost and each implementation had its pros and
cons.

In the next chapter, two case studies will be examined with the previous two chapters in
mind. The same design philosophy will be implemented with the evaluation of the two
case study buildings in the following chapter.

138

Chapter 6: Case Studies – Waite Phillips Hall and Webb Tower
6.1 Analysis of Waite Phillips Hall
As previously described in Section 3.5, Waite Phillips Hall currently serves as an
office/lecture building at the USC main campus. It was completed in 1966 and is
currently one of the tallest buildings at USC with 12 stories and 156’ tall. WPH exhibits a
shear wall core system in the middle of its structural plan with shear walls resisting
lateral loads.

6.1.1 Existing Building Information
In order to simplify the layout of WPH, only structural framing elements from the
architectural plan were used in the SAP 2000 model. The building employs three bays on
both the N‐S and E‐W façade. The bay widths differ slightly in order to employ the inner
concrete core. Within the inner core lies mechanical and elevator shafts, however, the
simplified model does not include them.
139

Figure 56: Plan View (WPH)

Figure 57: Elevation Views (WPH)

140

Analyze Existing Building
As used in the previous two chapters, the same philosophy in calculating base shear will
be described here. The total lateral force which every structure must be designed to
withstand is given by the formula, V = ZKCW.
73
Z is given as the numerical coefficient of
one. K is a horizontal force factor for structures specified by a table within the 1971
building code. This particular structure is classified under buildings with shear walls
resisting lateral loads with a K value of 0.8. C is a numerical coefficient which can be
calculated by the formula,
.

. T is the fundamental period of vibration of the
structure in seconds and can be calculated by the formula,
. n
√
where h
n
is the
total height of the structure and D is the dimension of the building in feet in a direction
parallel to the applied forces. W is the total dead load of the structure, and the
estimated dead load values are listed below.
DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Deck 45
Shear Wall 20
Total Dead Load 295
Table 64: Total Dead Load (WPH)

73
County of Los Angeles Uniform Building Laws, 107.
141

As shown above, the total dead load in pounds per square feet is 295. Therefore, the
total W value for all four floors is 19913 kips (

). Below is a table
which shows the evaluation of the total lateral force.
hn 156
D 75
T 0.90
C 0.05
W(dead) 19913
K 0.8
V 824.8
Table 65: Total Base Shear (WPH)
Distribution of Lateral Force
The total lateral force, V, is distributed from the 2
nd
to the Roof level using the formula,
x
x x
∑ i i

. F
x
denotes the force distribution at a particular floor; w
x
refers to the
height at a particular floor, and h
x
refers to the height at a particular floor from the base
of the building. The values F
x
values in the chart below are in kips.
Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 824.8 1659.4 156 258862.5 135.7
12th 824.8 1659.4 132 219037.5 114.8
11th 824.8 1659.4 120 199125 104.4
10th 824.8 1659.4 108 179212.5 94.0
9th 824.8 1659.4 96 159300 83.5
8th 824.8 1659.4 84 139387.5 73.1
7th 824.8 1659.4 72 119475 62.6
6th 824.8 1659.4 60 99562.5 52.2
5th 824.8 1659.4 48 79650 41.8
4th 824.8 1659.4 36 59737.5 31.3
3rd 824.8 1659.4 24 39825 20.9
2nd 824.8 1659.4 12 19912.5 10.4
Table 66: Distribution of Base Shear (WPH)
142

Now these F
x
values are divided into two as each half is applied in two directions.
Framing Details
Listed below are details of each framing element.
Columns
Level C1 C2 C3
12 24x16 24x24 24x24
11 24x16 24x24 24x24
10 24x16 24x24 24x24
9 24x16 24x24 24x24 W14x145
8 24x18 24x24 24x24 W14x145
7 24x18 24x24 24x24 W14x193
6 24x20 24x24 24x24 W14x193
5 24x20 24x24 24x24 W14x257
4 24x22 24x24 24x24 W14x257
3 24x22 24x24 24x24 W14x257
2 24x24 24x24 24x24 W14x257
1 24x24 24x24 24x24 W14x257
Table 67: List of Columns (WPH)

Figure 58: Column Framing Plan (WPH)
143

Beams
Level B1 B2 B3
R~2 30x30 30x30 30x30
Table 68: List of Beams (WPH)

Figure 59: Beam Framing Plan (WPH)
For reference, B1 refers to all exterior beams. B3 refers to all beam members which run
within the inner core. B2 refers to all interior beams aside from B3.

Existing Building Weights
Using a similar approach as in the previous chapters, the weights of concrete and steel
used in this building are listed below.

144

B1
B1 (L=32) B1 (L=24) B1 (L=20)
Width (ft) 2.5 2.5 2.5
Depth (ft) 2.5 2.5 2.5
Length (ft) 32 24 20
Density (pcf) 150 150 150
Quantity 24 72 48
TOTAL (kip) 720.0 1620.0 900.0
3240.0
B2 B3
B2 (L=32) B2 (L=24) B3 (L=24) B3 (L=20)
Width (ft) 2.5 2.5 Width (ft) 2.5 2.5
Depth (ft) 2.5 2.5 Depth (ft) 2.5 2.5
Length (ft) 32 24 Length (ft) 24 20
Density (pcf) 150 150 Density (pcf) 150 150
Quantity 24 60 Quantity 48 48
TOTAL (kip) 720.0 1350.0 TOTAL (kip) 1080.0 900.0
2070.0 1980.0
Table 69: Weight of Beams (WPH)

SW1 SW2
H=12 H=24 H=12 H=24
Thickness (ft) 0.67 0.67 Thickness (ft) 0.67 0.67
Weight (pcf) 150 150 Weight (pcf) 150 150
Length (ft) 32 32 Length (ft) 24 24
Height (ft) 12 24 Height (ft) 12 24
Opening (ft
2
) 64 64 Opening (ft
2
) 0 0
Quantity 22 2 Quantity 22 2
Weight (kip) 844.8 140.8 Weight (kip) 633.6 115.2
985.6 748.8
Table 70: Weight of Shear Walls (WPH)

145

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Depth (ft) 2.00 2.00 1.83 1.83 1.67 1.67 1.50 1.50 1.33 1.33 1.33 1.33
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 24
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL
(kip) 57.6 57.6 52.7 52.7 48.1 48.1 43.2 43.2 38.3 38.4 38.4 76.8
595.1
C2
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Depth (ft) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Length (ft) 12 12 12 12 12 12 12 12 12 12 12 24
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 57.6
374.4
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12
Width (ft)
see
chart
see
chart
see
chart
see
chart
see
chart
see
chart
see
chart
see
chart
see
chart 2.00 2.00 2.00
Depth (ft) 2.00 2.00 2.00
Length (ft) 12 12 24
Density
(pcf) 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 24 24 24 35 35 25.9 25.9 26.6 26.6 28.8 28.8 57.6
362.2
C3
Level 1 2 3 4 5 6 7 8 9
Cross‐section
area (ft2) 3.33 3.33 3.33 3.48 3.48 3.60 3.60 3.70 3.70
Length (ft) 12 12 12 12 12 12 12 12 12
Density (pcf) 150 150 150 150 150 150 150 150 150
Weight (plf) 257 257 257 257 257 193 193 145 145
Length (ft) 12 12 12 12 12 12 12 12 12
Quantity 4 4 4 4 4 4 4 4 4
Total (kip)
Concrete 24.0 24.0 24.0 25.0 25.0 25.9 25.9 26.6 26.6
Total (kip)
Steel 12.3 12.3 12.3 12.3 12.3 9.3 9.3 7.0 7.0
Table 71: Weight of Columns (WPH)
146

Therefore, the total weight of concrete is 10,356.1 kips. The total weight of steel is 94.1
kips.

6.1.2 Performance under 2010 California Building Code
Following the performance of WPH based on lateral loads described by the 1971 Los
Angeles Building Code, this same structure will now undergo loads specified by the
current 2010 California Building Code. Below is a chart comparing the two base shear
values, however to make fair comparisons, the 1971 LA base shear value is multiplied by
1.4 to convert it to a LRFD equivalent value, shown in red.
1971 LA CBC 2010
Roof 135.7 412.7
12th 114.8 349.2
11th 104.4 317.5
10th 94.0 285.7
9th 83.5 254.0
8th 73.1 222.2
7th 62.6 190.5
6th 52.2 158.7
5th 41.8 127.0
4th 31.3 95.2
3rd 20.9 63.5
2nd 10.4 31.7
V 824.8 2508
1154.72
Table 72: Base Shear Comparisons (WPH)
After re‐assigning the new loading values, WPH structure remains to have most of its
framing members able to withstand new forces. In the next section, various
implementations of seismic retrofitting discussed for a concrete shear core system will
be employed to strengthen elements within the structure.
147


Figure 60: Performance prior to Retrofits (WPH)

6.1.3 WPH Retrofit 1: Additional Bracing
This retrofit implementation of additional bracing was proposed to strengthen certain
members within the building. From the analysis and experimentation in section 5.3.2,
adding bracing elements tremendously helped a concrete shear wall structure by
reducing stress on members supporting the shear wall core. With this retrofit, X‐braces
were added to floors 1 through 11, while a bigger X‐brace is required for the 12
th

mechanical floor. All other members remain the same as the existing structure.
148

Figure 61: Elevation Views (WPH Retrofit 1)
Performance of the Retrofit
Following the retrofit, the previously stressed columns have been strengthened by the
W10x19 steel braces used throughout all facades.
Level BF1
R~2 W10x19
Table 73: List of Braces (WPH Retrofit 1)

Figure 62: Performance (WPH Retrofit 1)

149

Cost Analysis
Following the renditions with these additional steel bracing members, the following is
the new weight of steel used in the project. The total weight of concrete remains at
10356.1 kips. The new weight of steel used in the structure has increased from 94.1 to
142.2 kips. While assessing retrofits, rates of $3.50/pound of steel is used. WPH Retrofit
1: Additional Bracing costs $168,325.
BF1

L = 40 L = 33.9 L=27 L=24 L=20 L = 16.9
Weight (plf)
19 19 19 19 19 19
Length
40 33.9 27 24 20 16.9
Weight (lbs)
760 644.1 513 456 380 321.1
Quantity
4 4 12 12 44 44
Weight (kip)
3.0 2.6 6.2 5.5 16.7 14.1
Total (kip) 48.1
Cost ($) $168,325
Table 74: Cost Analysis (WPH Retrofit 1)

6.1.4 WPH Retrofit 2: Additional Shear Walls
This retrofit implementation of additional shear walls was proposed to strengthen
certain members within the building. From the analysis and experimentation in section
5.3.3, adding shear wall elements tremendously helped the shear wall core relieve its
capacity to resist all lateral loads; however there was a large increase in weight of
concrete. All other members remain the same as the existing structure.
150

Figure 63: Plan and Elevation Views (WPH Retrofit 2)

By adding concrete shear walls, the weight of the structure changes significantly,
therefore the increased dead load is shown in the figure below. The increased weight
thus attracts more lateral forces, hence Newton’s F=ma. The base shear has now
increased from 2508 kips to 2679 kips.

151

DL Loading
Distribution of Base
Shear V w(x) h(x) w(x)*h(x) Fx
Flooring 5 Roof 2679 1771.9 156 276412.5 440.8
Ceiling 5 12th 2679 1771.9 132 233887.5 373.0
Mechanical/Electrical 5 11th 2679 1771.9 120 212625 339.1
Partitions 15 10th 2679 1771.9 108 191362.5 305.2
Concrete 200 9th 2679 1771.9 96 170100 271.3
Deck 45 8th 2679 1771.9 84 148837.5 237.4
Shear Wall 40 7th 2679 1771.9 72 127575 203.5
315 6th 2679 1771.9 60 106312.5 169.6
5th 2679 1771.9 48 85050 135.6
LL 4th 2679 1771.9 36 63787.5 101.7
First Floor 100 3rd 2679 1771.9 24 42525 67.8
2nd Floor and Up 50 2nd 2679 1771.9 12 21262.5 33.9
Table 75: Increased Loading

Performance of the Retrofit
Following the retrofit, the previously stressed columns have been strengthened by the
8” thick concrete shear walls placed on the perimeter of the structure. The shear walls
were designed to resist shear, axial, and moment forces acting along the length of the
wall.

152

CHECK FOR SHEAR Level Vc Pc Mc Thickness
Vu = phi*10*(f'c^0.5)*b*d 1 571 1918 16663 8"
phi 0.75 2 480 1754 12971 8"
f'c 5000 3 403 1630 10224 8"
b 288 4 337 1472 7727 8"
d 8 5 287 1338 5931 8"
Vu 1221.9 6 251 1174 4325 8"
7 222 1029 3076 8"
8 189 859 1913 8"
9 148 680 981 8"
10 105 511 313 8"
Table 76: Shear Wall Design (WPH Retrofit 2)

Figure 64: Performance (WPH Retrofit 2)
Cost Analysis
Following the renditions with these additional concrete shear walls, the following is the
new weight of concrete used in the project. The total weight of concrete increased from
10356.1 to 11700 kips. The new weight of steel used in the structure has remained at
94.1 kips. While assessing costs for new retrofits, these values are used for steel and
concrete materials: $3.50/pound for steel and $550/cubic yard for concrete. WPH
Retrofit 2: Additional Shear Walls costs $182,519.
153

Concrete Shear Wall
1~10 (X‐
Axis)
1~10 (Y‐
Axis)
Thickness (ft) 0.67 0.67
Weight (pcf) 150 150
Length (ft) 32 24
Height (ft) 12 12
Opening (ft
2
) 0 0
Quantity 20 20
Weight (kip) 768 576
Total (kip) 1344
Cost ($) $182,519
Table 77: Cost Analysis (WPH Retrofit 2)

6.2 Analysis of Webb Tower
As previously described in section 3.6, Webb Tower (WTO) serves as a residential
building which houses students at USC and is located on the USC main campus. It was
recently seismically retrofitted with bracing elements and is 14 stories and 128’ tall.
WTO is a concrete moment frame structure which over time needed seismic retrofitting
to fulfill the current building code. Unfortunately, structural drawings with
beam/column sizes weren’t available, so the following framing member sizes designed
for the 1971 Los Angeles Building Code.

6.2.1 Existing Building Information
In order to simplify the layout of WTO, only structural framing elements from the
architectural plan were used in the SAP 2000 model. The building employs three bays on
the N‐S façade and four bays on the E‐W façade. Below is the plan view of the simplified
154

SAP 2000 model, and the plan denotes bracing elements which are currently employed
on WTO. The currently existing building has steel bracing on one bay per façade from
the first level to the roof level, which was only added in early 2000. Prior to the seismic
retrofit, the building was simply a concrete moment frame without braces to help resist
lateral forces.

Figure 65: Plan View (WTO)

Figure 66: Elevation Views (WTO)
155

However, this section will first analyze WTO prior to the seismic retrofits (i.e. bracing)
with 1971 Los Angeles building code loads then assess how the building behaves under
the current 2010 California Building Code standards. In addition to the bracing retrofit, a
shear wall retrofit will also be studied with 2010 CBC loads. Below is a plan and
elevations of WTO prior to the bracing elements.

Figure 67: Plan and Elevation View prior to Retrofits (WTO)
156

Analyze Existing Building
As used in the previous two chapters, the same philosophy in calculating base shear will
be described here. The total lateral force which every structure must be designed to
withstand is given by the formula, V = ZKCW.
74
Z is given as the numerical coefficient of
one. K is a horizontal force factor for structures specified by a table within the 1971
building code. This particular structure is classified under buildings with moment frames
resisting lateral loads with a K value of 0.67. C is a numerical coefficient which can be
calculated by the formula,
.

. T is the fundamental period of vibration of the
structure in seconds and can be calculated by the formula,
. n
√
where h
n
is the
total height of the structure and D is the dimension of the building in feet in a direction
parallel to the applied forces. W is the total dead load of the structure, and the
estimated dead load values are listed below.
DL Loading
Flooring 5
Ceiling 5
Mechanical/Electrical 5
Partitions 15
Concrete 200
Deck 45
275
Table 78: Total Dead Load (WTO)


74
County of Los Angeles Uniform Building Laws, 107.
157

As shown above, the total dead load in pounds per square feet is 275. Therefore, the
total W value for all fourteen floors is 30430 kips (

). Below is a
table which shows the evaluation of the total lateral force.
hn 128.4
D 104
T 0.63
C 0.06
W(dead) 30430
K 0.67
V 1189.5
Table 79: Total Base Shear (WTO)
Distribution of Lateral Force
The total lateral force, V, is distributed from the 2
nd
to the Roof level using the formula,
x
x x
∑ i i

. F
x
denotes the force distribution at a particular floor; w
x
refers to the
height at a particular floor, and h
x
refers to the height at a particular floor from the base
of the building. The values F
x
values in the chart below are in kips.
Distribution of Base Shear V w(x) h(x) w(x)*h(x) Fx
Roof 1189.5 2173.6 128.4 279090.2 152.5
14th 1189.5 2173.6 119.65 260071.2 142.1
13th 1189.5 2173.6 110.9 241052.2 131.7
12th 1189.5 2173.6 102.15 222033.2 121.3
11th 1189.5 2173.6 93.4 203014.2 110.9
10th 1189.5 2173.6 84.65 183995.2 100.6
9th 1189.5 2173.6 75.9 164976.2 90.2
8th 1189.5 2173.6 67.15 145957.2 79.8
7th 1189.5 2173.6 58.4 126938.2 69.4
6th 1189.5 2173.6 49.65 107919.2 59.0
5th 1189.5 2173.6 40.9 88900.2 48.6
4th 1189.5 2173.6 32.15 69881.2 38.2
3rd 1189.5 2173.6 23.4 50862.2 27.8
2nd 1189.5 2173.6 14.65 31843.2 17.4
Table 80: Distribution of Base Shear (WTO)
Now these F
x
values are divided into two as each half is applied in two directions.
158

Framing Details
Unfortunately, due to the lack of information regarding WTO’s beam and column
sections, these sections were selected through SAP2000’s analysis while checking the
structure’s capacity. These sections proved sufficient under 1971 Los Angeles Building
Code.
Columns
Level C1 C2 C3
14 24x24 24x24 24x24
13 24x24 24x24 24x24
12 24x24 24x24 30x30
11 24x24 24x24 30x30
10 28x28 24x24 30x30
9 28x28 24x24 34x34
8 30x30 24x24 34x34
7 30x30 24x24 40x40
6 30x30 24x24 40x40
5 34x34 24x24 40x40
4 34x34 24x24 40x40
3 34x34 24x24 W14x145 44x44
2 34x34 24x24 W14x145 44x44
1 40x40 24x24 W14x257 48x48
Table 81: List of Columns (WTO)

159

Figure 68: Column Framing Plans (WTO)
Beams
Level B1 B2
R~2 16x40 28x16
Table 82: List of Beams (WTO)

Figure 69: Beam Framing Plan (WTO)
For reference, B1 refers to all exterior beams. B2 refers to all interior beams.
160

Existing Building Weights
Using a similar approach as in the previous chapters, the weights of concrete and steel
used in this building are listed below.
B1 B2

B1
(L=26)
B1
(L=26)
B1
(L=26)
B1
(L=23)
B1
(L=23)
B1
(L=23)
B2
(L=26)
B2
(L=23)
Width
(ft) 1.67 3.33 3.67 1.67 3.33 3.67 Width (ft) 1.33 1.33
Depth
(ft) 3.33 3.33 3.67 3.33 3.33 3.67 Depth (ft) 2.33 2.33
Length
(ft) 26 26 26 23 23 23 Length (ft) 26 23
Density
(pcf) 150 150 150 150 150 150
Density
(pcf) 150 150
Quantity 144 12 12 24 2 2 Quantity 196 42
TOTAL
(kip) 3120.0 520.0 629.2 460.0 76.7 92.8 TOTAL (kip) 2378.1 450.8
4898.6 2828.9
Table 83: Weights of Beams (WTO)

C1
Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Width (ft) 3.33 2.83 2.83 2.83 2.83 2.50 2.50 2.50 2.33 2.33 2.00 2.00 2.00 2.00
Depth (ft) 3.33 2.83 2.83 2.83 2.83 2.50 2.50 2.50 2.33 2.33 2.00 2.00 2.00 2.00
Length (ft) 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 8 8 8 8 8 8 8 8 8 8 8 8 8 8
TOTAL
(kip) 116.7 84.3 84.3 84.3 84.3 65.6 65.6 65.6 57.2 57.2 42.0 42.0 42.0 42.0
933.0
Table 84: Weight of Columns 1 (WTO)

161

C2
Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Width (ft)
see
chart
see
chart
see
chart
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0 2.00
Depth (ft)
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0
2.0
0 2.00
Length (ft)
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5 8.75
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150
Quantity 4 4 4 4 4 4 4 4 4 4 4
TOTAL
(kip) 18.3 19.4 19.4 21 21 21 21 21 21 21 21 21 21 21
288.1
C2 (Add’l)
Level 1 2 3
Cross‐
section
area (ft2) 3.48 3.70 3.70
Length (ft) 8.75 8.75 8.75
Density
(pcf) 150 150 150
Weight
(plf) 257 145 145
Length (ft) 8.75 8.75 8.75
Quantity 4 4 4
Total (kip)
Concrete 18.3 19.4 19.4
Total (kip)
Steel 9.0 5.1 5.1
C3
Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Width (ft) 4.00 3.67 3.67
3.3
3
3.3
3
3.3
3
3.3
3
2.8
3
2.8
3
2.5
0
2.5
0
2.5
0
2.0
0 2.00
Depth (ft) 4.00 3.67 3.67
3.3
3
3.3
3
3.3
3
3.3
3
2.8
3
2.8
3
2.5
0
2.5
0
2.5
0
2.0
0 2.00
Length (ft) 8.75 8.75 8.75
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5
8.7
5 8.75
Density
(pcf) 150 150 150 150 150 150 150 150 150 150 150 150 150 150
Quantity 6 6 6 6 6 6 6 6 6 6 6 6 6 6
TOTAL
(kip)
126.
0
105.
9
105.
9
87.
5
87.
5
87.
5
87.
5
63.
2
63.
2
49.
2
49.
2
49.
2
31.
5 31.5
1024.8
Table 85: Weight of Columns 2 (WTO)
162

Therefore, the total weight of concrete is 9973 kips. The total weight of steel is 19.1
kips.

6.2.2 Performance under 2010 California Building Code
Following the performance of WTO based on lateral loads described by 1971 Los
Angeles Building Code, this same structure will now undergo loads specified by the
current 2010 CBC code. Below is a chart comparing the two base shear values, however
to make fair comparisons, the 1971 LA base shear value is multiplied by 1.4 to convert it
to its LRFD equivalent, shown in red.
1971 LA CBC 2010
Roof 152.5 247.3
14th 142.1 230.4
13th 131.7 213.6
12th 121.3 196.7
11th 110.9 179.9
10th 100.6 163.0
9th 90.2 146.2
8th 79.8 129.3
7th 69.4 112.5
6th 59.0 95.6
5th 48.6 78.8
4th 38.2 61.9
3rd 27.8 45.1
2nd 17.4 28.2
V 1189.5 1928.6
1665.3
Table 86: Base Shear Comparison (WTO)

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After re‐assigning the new loading values, WTO structure seems to have several framing
members overstressed. In the next sections, two retrofit implementations will be
employed to strengthen the structure under new loads.

Figure 70: Performance prior to Retrofits (WTO)

6.2.3 WTO Retrofit 1: Additional Bracing (Existing Retrofit)
Currently, Webb Tower is retrofitted with large bracing elements in the exterior
framing. This section has employed the same framing to help strengthen the original
structure under the current building code. We will see below the various elevations and
plans as to where the bracing elements are added.
164

Figure 71: Plan View (WPH Retrofit 1)

Figure 72: Elevation View (WPH Retrofit 1)


165

Performance of the Retrofit
Following the retrofit, the previously stressed columns have been strengthened by the
W10x19 steel braces used throughout all facades.
Level BF1
R~2 W10x19
Table 87: List of Braces (WPH Retrofit 1)

Figure 73: Performance (WTO Retrofit 1)
Cost Analysis
Following the renditions with these additional steel bracing members, the following is
the new weight of steel used in the project. The total weight of concrete remains at
9973.6 kips. The new weight of steel used in the structure has increased from 19.1 to
51.6 kips. While assessing retrofits, rates of $3.50/pound of steel is used. WTO Retrofit
1: Additional Bracing costs $113,901.
BF1
L = 19.6 L = 15.6 L=18.6 L = 14.4
Weight (plf)
19 19 19 19
Length
19.6 15.6 18.6 14.4
Weight (lbs)
372.4 296.4 353.4 273.6
Quantity
4 52 4 52
Weight (kip)
1.5 15.4 1.4 14.2
Total (kip) 32.5
Cost ($) $113,901
Table 88: Cost Analysis (WTO Retrofit 1)
166

6.2.4 WTO Retrofit 2: Additional Shear Walls
This retrofit implementation of additional shear walls was proposed to strengthen
certain members within the building. From the analysis and experimentation in section
5.4.3, adding shear wall elements tremendously helped the shear wall core relieve its
capacity to resist all lateral loads; however there was a large increase in weight of
concrete. All other members remain the same as the existing structure.

Figure 74: Plan and Elevation View (WTO Retrofit 2)

By adding concrete shear walls, the weight of the structure changes significantly,
therefore the increased dead load is shown in the figure below. The increased weight
thus attracts more lateral forces, hence Newton’s F=ma. The base shear has now
increased from 1928 kips to 2068 kips.

167

DL Loading Base Shear Fx
Flooring 5 Roof 265.3
Ceiling 5 14th 247.2
Mechanical/Electrical 5 13th 229.1
Partitions 15 12th 211.0
Concrete 200 11th 193.0
Deck 45 10th 174.9
Shear Wall 20 9th 156.8
295 8th 138.7
7th 120.7
6th 102.6
5th 84.5
4th 66.4
3rd 48.3
2nd 30.3
Table 89: Increased Loading (WTO Retrofit 2)
Performance of the Retrofit
Following the retrofit, the previously stressed columns have been strengthened by the
8” thick concrete shear walls placed on the interior core of the structure. The shear wall
placed along the building’s interior core was designed to resist axial, shear, and moment
forces along its wall length. Shear walls are constructed from the first level to the tenth
level.

Figure 75: Performance (WTO Retrofit 2)

168

FOR 26' of WALL
CHECK FOR SHEAR Vc Pc Mc Thickness
Vu =
phi*10*(f'c^0.5)*b*d 1 970 3195 14306 8"
phi 0.75 2 748 3160 9643 8"
f'c 5000 3 723 2911 8298 8"
b 312 4 712 2866 7711 8"
d 8 5 645 2588 6143 8"
Vu 1323.7 6 598 2314 4845 8"
7 536 2040 3644 8"
8 498 1962 3154 8"
9 424 1660 2054 8"
10 351 1451 1289 8"
Table 90: Shear Wall Design (WTO Retrofit 2)

Cost Analysis
Following the renditions with these additional concrete shear walls, the following is the
new weight of concrete used in the project. The total weight of concrete increased by
665 kips. There was no change in the weight of steel. While assessing costs for new
retrofits, these values are used for steel and concrete materials: $3.50/pound for steel
and $550/cubic yard for concrete. WPH Retrofit 2: Additional Shear Walls costs $90,377.
Concrete Shear Wall 1 2
Thickness (ft) 0.67 0.67
Weight (pcf) 150 150
Length (ft) 23 26
Height (ft) 8.75 8.75
Opening (ft
2
) 48 48
Quantity 20 20
Weight (kip) 306.5 359.0
Total (kip) 665.5
Cost ($) $90,377
Table 91: Cost Analysis (WTO Retrofit 2)
169

6.3 Comparison of Retrofit Implementations
In this section, the two retrofit implementations used in the rehabilitation of Waite
Phillips Hall and Webb Tower is compared and analyzed under three considerations:
cost, architectural, and constructability. Retrofit 1 refers to additional bracing, and
retrofit 2 refers to additional shear walls. The results from the case studies were used to
compare and solidify the data from the four hypothetical structures.

6.5.1 Cost Considerations
In considering the cost of each retrofit, chapter six studied the rehabilitation of Waite
Phillips Hall and Webb Tower using two different retrofit options. From the study, the
estimated needed cost for each option was calculated by quantifying the amount of
steel and concrete used in the system and by using a rate of cost: $3.50/pound for steel
and $550/cubic yard for concrete. The two cost analysis figures below show similar
trends as that of the two hypothetical concrete structures in Chapter 5: for Waite
Phillips Hall, similar to the concrete shear wall core system, the cheaper option was
retrofit 1: bracing; on the other hand, for Webb tower, similar to the concrete moment
frame, the cheaper option was retrofit 2: shear wall. Waite Phillips Hall employs a
concrete shear wall core structural system, while Webb Tower is a concrete moment
frame system.

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Looking at the two steel structural systems from Chapters 4, retrofit 1 seemed as the
cheaper option. This can mainly attribute to the fact that steel bracing placed along the
exterior frame was more effective than adding shear walls. However, for the two
concrete structural systems, retrofit 2 seemed a viable option for the concrete moment
frame. On the other hand, new shear walls were placed along the exterior for the
concrete shear wall core system, which may explain the reason why adding braces
resulted in saving costs. Additionally, results may seem to point toward a preference for
shear wall addition retrofits for the concrete shear wall core and concrete moment
frame structures. WPH retrofit 1 required steel bracing on three additional levels in
addition to bracing which stretches from the first level to the roof. On the other hand,
WPH retrofit 2 only required shear walls from the first level to the tenth level. The same
is true with WTO retrofits. The table below shows a comparison between retrofit 1:
bracing and retrofit 2: shear wall amongst all six buildings. The percent increase column
indicates the increase in cost in percentage using the cheaper retrofit as the base line.
Interestingly enough, the concrete shear wall structures, CSW and WPH, both show
similar results in that steel bracing just seems to edge out the shear wall retrofit within
10% increase in costs. The concrete moment frame structures, CMF and WTO, also show
similar results in that in both cases, the shear wall retrofit is more cost advantageous.
The numbers in red highlights the most cost‐effective option for the respective
structural system.

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R1: Bracing R2: Shear Wall % Increase
SBF $95,807 $123,429 28.8%
SMF $92,591 $94,969 2.6%
CSW $143,268 $146,667 2.4%
CMF $143,268 $120,185 19.2%
WPH $168,325 $182,519 8.4%
WTO $113,901 $90,377 26.0%
R3: Additional Plates R1: Bracing % Increase
SBF $138,741 $95,807 44.8%
SMF $135,920 $92,591 46.8%
Table 92: Cost Increase Comparisons

Figure 76: Cost Analysis (WPH)
$168,325
$182,519
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (WPH)
Retrofit 1: Bracing Retrofit 2: Shear Wall
172

Figure 77: Cost Analysis (WTO)

6.5.2 Architectural Considerations
As for architectural considerations, the same impact which applied to the four
hypothetical structures will apply here. Retrofit 1, additional bracing, modifies the
existing building’s façade as steel members are placed on the exterior sides of the
building. Certain views from inside the building are hindered due to the erection of new
steel members. With WTO’s currently existing retrofit, we can clearly see the architect
did not consider the steel bracing as a negative. From a building which didn’t stand out,
the added bracing has characterized Webb Tower as the “braced structure” on the
campus of USC. On the other hand, adding bracing to WPH may not be a good idea from
an architectural standpoint. Currently, WPH employs a brick veneer façade with thin
windows which makes the building seem like a framed tube structure. Rather than the
$113,901
$90,377
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
Cost Analysis (WTO)
Retrofit 1: Bracing Retrofit 2: Shear Wall
173

first retrofit, it may be best to implement retrofit 2, by adding more shear walls if
retrofits are needed. Retrofit 2, additional shear walls, does not modify the exterior
facades of the existing structure as these walls are placed inside the space. These walls
however modify and limit the existing building’s circulation with the placement of these
permanent walls acting as structural elements. However, the shear walls added in Waite
Phillips Hall are placed on the exterior facades of the building, thus hindering views from
the building. Typically, office buildings tend to prefer free‐plan layouts without shear
walls while residential buildings prefer shear walls which helps act as partitions between
housing units.

6.5.3 Constructability Concerns
The addition of steel braces as in retrofit 1 is relatively straightforward as it involves the
welding and addition of new steel members, and this procedure can be often done
without disrupting the use of a building. However, this retrofit may not be as easy as it
sounds when applied to WPH. Because of WPH’s current veneer façade on its four sides,
it is most likely that the addition of bracing would lead to the removal of the brick
veneer wall and window. Not only would it increase costs but will hamper operation on
all four facades, thus affecting all entrances and exits.

On the other hand, WTO currently employs the steel bracing retrofit along its exterior
frames. Although concrete shear walls were more cost‐efficient according to this study,
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there certainly may have been many cost trade‐offs which may have been present in the
retrofit implementation. For instance, adding shear walls to an existing building requires
demolition of existing elements as walls are placed inside a building. Additionally, it may
have not been possible for WTO to add shear walls to its interior because of its elevator
shafts. The other option would have been adding walls along the exterior façade, but
this would have led to certain rooms to have no outside view, which is crucial for
student housing.

Summary
Following the analyses of existing buildings on campus, the two case study buildings
served to validate the analysis made through hypothetical studies in the four structural
systems studied in chapters 4 and 5. The two case study buildings represented two of
the four structural systems analyzed in this thesis. Waite Phillips Hall was congruent to a
concrete shear wall core system, and Webb Tower served as an example of a concrete
moment frame structure. When both systems were applied with retrofit
implementations as done to the hypothetical study models, all models behaved in
similar fashion. Both results led to the same conclusion that the addition of shear walls
provided best cost efficiency to these two systems from a purely structural standpoint.
However, this chapter further showed how valuable other considerations can be in
choosing a type of retrofit.
175

In the following conclusion chapter, the experience from running this research process is
elaborated and further work is mentioned. The shortcomings and flaws within the
research process are also touched on to ensure a better, focused research as others
uncover different strategies in seismic retrofitting.
176

Chapter 7: Summary and Conclusions
7.1 Summary
This research was undertaken to investigate existing structures built according to
outdated building codes in light of a likely seismic event in the near future in Southern
California. Additionally, this study focused on mid‐rise buildings located in Los Angeles,
and though the term “mid‐rise” is non‐definitive, the thesis used a “mid‐rise” standard
as a building employing 12 stories with 12 feet heights along with 75 feet by 75 feet
floor areas. Through a comparative analysis under 1971 Los Angeles Building Code and
2010 California Building Code, four structural systems underwent analysis in a structural
design software, SAP2000, and showed that the current building code requirements are
more stringent than the 1971 code cause many members to be deficient for current
standards. The four structural systems studied were steel braced frame, steel moment
frame, concrete shear wall core, and concrete moment frame systems.

These four systems were then implemented with seismic retrofits including braced
frames and shear walls. Framing sizes were determined and the newly retrofitted
models were tested to perform under recent 2010 CBC. The effectiveness of each
retrofit implementation was recorded by its performance, cost, and
architectural/constructability concerns.

177

These results from these four structural systems were validated with the study of two
case study buildings: Waite Phillips Hall and Webb Tower. Both buildings are located on
the campus of the University of Southern California and are deemed to fit the “mid‐rise”
criteria given in this study. Waite Phillips Hall is a concrete shear wall core structure with
12 floors, constructed in 1966. Webb Tower is a concrete moment frame structure with
14 floors, constructed in 1972. Recently, Webb Tower had been retrofitted with braced
frames in 2005. These two buildings were analyzed with similar procedures to the four
systems, particularly the concrete shear wall core and concrete moment frame
structures.

7.2 Conclusions
From the results regarding the six studied buildings, conclusions regarding the
advantages and disadvantages amongst retrofit implementation can be made. These
advantages and disadvantages are discussed with three criteria in mind: performance,
cost, and architectural/constructability.

7.2.1 Performance Comparisons
When evaluating the performance impact of each retrofit implementation, it was quite
clear that the addition of braces served best to sufficiently help the structure resist
lateral loads. The braces helped to stiffen the building, and they were particularly
helpful in the retrofit of moment frame structures. The addition of shear walls, while
178

helpful added a significant amount of weight to the overall structure which increased
the seismic demand as well.

When looking at the effectiveness of the three different retrofit implementations to the
six different buildings, some conclusions can be drawn. In Chapter 4, the steel braced
frame and the steel moment frame structures both required less bracing elements than
the shear wall retrofit. For instance, the steel moment frame structure required four
levels of steel X‐bracing for retrofit 1: bracing, while for retrofit 2: shear wall, the steel
moment frame structure need shear walls from the first level to the fifth level.

However, the conclusions are quite the opposite when looking at the four concrete
buildings: concrete shear wall core, concrete moment frame, Waite Phillips Hall, and
Webb Tower. These buildings showed they required more steel bracing to sufficiently
retrofit each system, while requiring less shear walls to do the same. For instance, Waite
Phillips Hall required an additional three levels of steel X‐bracing elements along with
bracing from the first to the roof levels. On the other hand, Waite Phillips Hall only
required shear walls from the first to tenth level to suffice the current code.

7.2.2 Cost Comparisons
The steel braced frame underwent three different retrofit implementations: additional
bracing, additional shear walls, and additional steel plates. For all three retrofit
179

implementations, retrofit 1: bracing provided the most cost‐efficient retrofit. Using
retrofit 1 as the base line; retrofit 2: shear wall was a 28.8% cost increase, while retrofit
3: additional plates was a 44.8% cost increase.

The steel moment frame underwent three different retrofit implementations: additional
bracing, additional shear walls, and additional steel plates. For all three retrofit
implementations, retrofit 1: bracing provided the most cost‐efficient retrofit. Using
retrofit 1 as the base line; retrofit 2: shear wall was a 2.6% cost increase, while retrofit
3: additional plates was a 46.8% cost increase.

The concrete shear wall core system underwent two different retrofit implementations:
additional bracing and additional shear walls. For the two retrofit implementations,
retrofit 1: bracing provided the most cost‐efficient retrofit. Using retrofit 1 as the base
line; retrofit 2: shear wall was a 2.4% cost increase.

The concrete moment frame system underwent two different retrofit implementations:
additional bracing and additional shear walls. For the two retrofit implementations,
retrofit 2: shear wall provided the more cost‐efficient retrofit. Using retrofit 2 as the
base line; retrofit 1: bracing was a 19.2% cost increase.

180

The first case study building, WPH, underwent two different retrofit implementations:
additional bracing and additional shear walls. For the two retrofit implementations,
retrofit 1: bracing provided the most cost‐efficient retrofit. Using retrofit 1 as the base
line; retrofit 2: shear wall was a 8.4% cost increase.

The second case study building, WTO, underwent two different retrofit
implementations: additional bracing and additional shear walls. For the two retrofit
implementations, retrofit 2: shear wall provided the more cost‐efficient retrofit. Using
retrofit 2 as the base line; retrofit 1: bracing was a 26% cost increase.
R1: Bracing R2: Shear Wall % Increase
SBF $95,807 $123,429 28.8%
SMF $92,591 $94,969 2.6%
CSW $143,268 $146,667 2.4%
CMF $143,268 $120,185 19.2%
WPH $168,325 $182,519 8.4%
WTO $113,901 $90,377 26.0%
R3: Additional Plates R1: Bracing % Increase
SBF $138,741 $95,807 44.8%
SMF $135,920 $92,591 46.8%
Table 93: Cost Comparison Chart

7.2.3 Architectural/Constructability Concerns
Apart from performance and cost effectiveness of each retrofit system, it is also vital to
consider whether the particular implementation regards for the structure’s architecture
181

and whether it is easily constructible. In this regard, the three different implementations
will be discussed: addition of braces, shear walls, and plates.

First, the addition of braces to an existing building largely impacts the original design of
a building, as they are placed on the exterior facades of a building. Additionally, these
braces typically are large and placed in the middle bays of buildings which dominate
each façade. Certain views from the building can be hindered by the bracing elements,
and the original design philosophy may become tainted. However, erecting these braced
frames would be easily done, as it doesn’t involve a large renovation of the existing
structure. During construction, the building may still be operable. However, as
mentioned previously in Chapter 6, study from the two case study structures led a
possible conclusion that adding steel bracing along the exterior frame can also be very
costly. For example, Waite Phillips Hall currently has a brick veneer façade on all four
sides. In order to build a steel braced frame along the structure, it would require
demolition of the entire façade in order to properly connect the bracing to the existing
columns. Additionally, the exterior design of Waite Phillips Hall would be compromised.
The trade off in cost may be too large for WPH to implement this retrofit. On the other
hand, adding steel braces on Webb Tower made lots of sense. First off, adding shear
walls to an already existing building requires demolition of existing non‐structural
elements in the space. Constructing concrete shear walls whether by cast‐in‐place or
precast concrete is also a difficult and costly task. Therefore, the other option would
182

have been to employ shear walls along the exterior frame like its braced additions.
However, this would block outside views from certain rooms, which is vital for student
housing.

Secondly, the addition of shear walls will not largely impact the outside views of a
building, if these walls are placed in the interior acting as a core in a building. However,
the original floor plan may be changed from a flexible one to a fixed plan due to the
shear walls which remain permanent as they act as bearing walls. A floor plan for office
type buildings are typically steel framed or concrete framed because of its ability to
open the floor plan for various usages. For residential buildings, shear walls can be
efficient as they act naturally as partitions between different units. In terms of
constructability, adding shear walls to an existing building will be a tough task, and
operation within the building will be largely hindered.

Lastly, the addition of steel plates to the existing columns and beams do not impact the
building architecturally. Columns which need reinforcement typically were changed
from a wide‐flange shape to a box‐column with the addition of two steel plates on its
sides. Beams were reinforced by adding plates to the bottom of the flange. However, it
would take laborious work to reinforce each framing member especially in the removal
of dry walls or other finishes to reach each steel member. It may be effective in small
retrofit cases, where the numbers of failed beams/columns are small and localized, but
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the labor costs may also be tremendous. For a huge retrofit undertaking as shown in the
thesis, solely adding plates would not be cost efficient.

7.2.4 Matrix of Tabulated Information
Systems
Steel Braced Frame
Steel Moment
Frame
Concrete Shear Wall
Core
Concrete Moment
Frame
Retrofits
R1: Additional
Bracing
$95,807 $92,591 $143,268 $143,268
R2: Additional Shear
Walls
$123,429 $94,969 $146,667 $120,185
R3: Additional
Plates
$138,741 $135,920 ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐
Figure 78: Matrix of Retrofit Implementations
7.3 Experiences
Throughout the process of developing this thesis, there were many valuable notables
that should be mentioned. Apart from fulfilling research towards the hypothesis, this
experience had led to a better understanding of seismic design of structures. Below are
the few notables worthy of mention.

7.3.1 SAP 2000 Software
Throughout this process, SAP 2000 was the main software used to check each model’s
validity. The software’s strengths and capabilities are many to mention, and this thesis
simply scratched the surface of the capacity of this program. Throughout this research, I
had modeled each case study to reflect a building’s skeletal structure by simply creating
184

framing elements. The program could allow for a more sophisticated model, but for the
sake of the study, I had opted for a simpler model.

7.3.2 Addition of Diaphragms in Model Study
In the initial design of each model, I had designed all framing elements, such as beams
and columns, but I had left out the addition of diaphragms, such as floor slabs. Prior to
evaluating these models, I had not factored the importance of creating concrete slabs in
these models. Instead, the weights of all slabs were included within the dead load which
was applied to the beams as weight per linear foot. This approach essentially reduced
my three‐dimensional model to a two‐dimensional model. Following this first version,
the new model included the floor slabs in between the beams and girders to emulate
how a real structure would deform under gravity and lateral loads. The dead load was
then applied to each area as weight per square feet. The addition of diaphragms most
largely affected buildings with shear walls.

7.3.3 Seismic Design Criteria
When checking the design of structure in SAP 2000, the program notes certain elements
which disobey current seismic codes. For instance, the cross section of framing elements
used under seismic loading must be “seismically compact”. This additional constraint
ensures the safety in design using more stringent standards. However, after juggling
with numerous cross sectional options using section designer in SAP 2000, I have been
185

unable to accurately figure out built up section shapes which obey this criteria. I am
unsure whether the program is unable to calculate the required parameters when using
customized built up sections, or if I am unable to meet the standards given through code.

7.4 Recommendations for Further Research
Following a year‐long research of seismic retrofits, there were numerous factors which
were not covered by the scope of this thesis. However, they cannot be merely put aside
as excess information but must be considered to create a better processed research
paper. These factors and recommendations for further research regarding the topic are
discussed.

7.4.1 Choice of Computer Software
Throughout this study, one computer application was chosen to run all analysis and
information. Unfortunately, it is not advisable in any research to rely all information
from one source especially computer software which may not be able to accurately
resemble a realistic application. Though SAP 2000 is largely credible due to its usage in
academia and in the workplace, other software and their capabilities cannot be ignored.
In further research, it would be wise to use a wide variety of structural design software
to validate the results from analysis.

186

7.4.2 Simplified Structural Models and Analysis
Due to the time constraints in developing this thesis, many of the models used in
research were simplified to three‐dimensional models with basic structural framing.
Many elements such as stairwells, elevators, partitions, and mechanical equipment
were simply load values distributed over a floor area rather than being specifically
placed in the model. Additionally, all analysis this thesis covered was linear static
analysis. Rather than a dynamic approach, which would have resulted in a more
accurate reading, a static approach was chosen to move the focus away from the
specificity of lateral loads to the behavior of structures with seismic retrofits. However,
a dynamic analysis would provide the thesis with more accurate results.

7.4.3 Framing Detailing and Connections
In the study and analysis of seismic design, it is particularly important in the design of
connections and detailing of framing elements. As showcased from the 1994 Northridge
Earthquake, many moment frame buildings failed at their connections which led to
many changes within the building code. However, the scope of this research did not
consider any variance in connections. The only exception being that moment frame
connections were designed as continuous while braced frame connections were
designed as pinned. In future research, it is also advisable to focus solely in the design of
connections in seismic retrofits. Particularly, in this research, a comparison was made
between the 1971 building code with the 2010 CBC. Within the scope of this thesis, base
187

shear values were compared, however, there are many detailing considerations which
weren’t considered.

7.4.4 Additional Retrofit Implementations
One of this study’s weaknesses would be the lacking number of retrofit
implementations. In a future study, a wider variety of retrofit applications could provide
a better detailed conclusion. For instance, it would be advisable to specify a certain type
of braced frame as there are endless configurations as to how braced frames can be
placed for best effectiveness.

7.4.5 Comparison of Construction Time
Time is valuable, and the time it takes to construct or erect structures can impact the
overall cost of the project. Though not mentioned in this study, it may be valuable to
assess the differences in construction time amongst the three retrofit implementations.
For instance, it may be quicker to erect steel braces along the exterior frame of an
existing building as opposed to constructing shear walls within an existing building. The
study in the differences in construction time can help better understand the issues
surrounding cost in seismic retrofits.

188

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Appendix: Structural Design Excel Spreadsheet

Preliminary Steel Frame Design (SMF):
Beam Design 2nd 3rd~12th
DL 100 100
LL 100 50
L 18.75 18.75
tributary width 9.375 9.375
W(DL) 0.9375 0.9375
W(LL) 0.9375 0.46875
W(u) 2.625 1.875
M(u) 115.3564 82.39746
V(u) 24.60938 17.57813
Ix 245 199
deflection (live) 0.36694 0.22588
check (live) 0.625 0.625
deflection (total) 0.73388 0.67764
check (total) 0.9375 0.9375
COST ANALYSIS W14x38 W8x31
Weight (plf) 38 31
Weight (plf x length) [in lbs] 712.5 581.25
Number of Beams 28 308
Total Weight (per story) 19950 179025
Total Weight (in lbs) 198975
Table 94:Beam Design (SMF)
Girder Design 2nd 3rd~12th
L 18.75 18.75
M(u) 143.6 123
V(u) 15.5 13.2
deflection (total) 1.63 1.404
check (total) 0.9375 0.9375
COST ANALYSIS W12x40 W10x39
Weight (plf) 40 39
Weight (plf x length) [in lbs] 750 731.25
Number of Beams 12 132
Total Weight (per story) 9000 96525
Total Weight (in lbs) 105525
Table 95: Girder Design (SMF)
191

Non‐Moment Frame Beam 2nd 3rd~12th
L 18.75 18.75
M(u) 72.4 62.1
V(u) 7.8 6.7
deflection (total) 0.828 0.708
check (total) 0.9375 0.9375
COST ANALYSIS W10x30 W12x26
Weight (plf) 30 26
Weight (plf x length) [in lbs] 562.5 487.5
Number of Beams 4 44
Total Weight (per story) 2250 21450
Total Weight (in lbs) 23700
Table 96: Non‐moment Frame Design (SMF)
Moment Frame Beam 2nd 3rd~12th
L 18.75 18.75
M(u) 481.7 356.9
V(u) 53.7 27.8
deflection (total) 0.828 0.708
check (total) 0.9375 0.9375
COST ANALYSIS W18x76 W16x67
Weight (plf) 76 67
Weight (plf x length) [in lbs] 1425 1256.25
Number of Beams 12 132
Total Weight (per story) 17100 165825
Total Weight (in lbs) 182925
Table 97: Moment Frame Design (SMF)

192

Preliminary Steel Frame Design (SBF):
Beam Design 2nd 3rd~12th
DL 100 100
LL 100 50
L 18.75 18.75
tributary width 9.375 9.375
W(DL) 0.9375 0.9375
W(LL) 0.9375 0.46875
W(u) 1.622 1.387
M(u) 71.2793 60.95215
V(u) 15.20625 13.00313
Ix 291 510
deflection (live) 0.308936 0.088137
check (live) 0.625 0.625
deflection (total) 0.617871 0.264412
check (total) 0.9375 0.9375
COST ANALYSIS W10x30 W12x26
Weight (plf) 30 26
Weight (plf x length) [in lbs] 562.5 487.5
Number of Beams 28 308
Total Weight (per story) 15750 150150
Total Weight (in lbs) 165900
Table 98: Beam Design (SBF)
Girder Design 2nd 3rd~12th
L 18.75 18.75
M(u) 143.6 123
V(u) 15.5 13.2
deflection (total) 1.63 1.404
check (total) 0.9375 0.9375
COST ANALYSIS W12x40 W10x39
Weight (plf) 40 39
Weight (plf x length) [in lbs] 750 731.25
Number of Beams 12 132
Total Weight (per story) 9000 96525
Total Weight (in lbs) 105525
Table 99: Girder Design (SBF)

193

Edge Girder Design 2nd 3rd~12th
L 18.75 18.75
M(u) 72.4 62.1
V(u) 7.9 6.8
deflection (total) 1.63 1.404
check (total) 0.9375 0.9375
COST ANALYSIS W10x30 W12x26
Weight (plf) 30 26
Weight (plf x length) [in lbs] 562.5 487.5
Number of Beams 8 88
Total Weight (per story) 4500 42900
Total Weight (in lbs) 47400
Table 100: Edge Girder Design (SBF)
Edge Beam Design 2nd 3rd~12th
L 18.75 18.75
M(u) 36.3 31
V(u) 7.7 6.6
deflection (total) 1.63 1.404
check (total) 0.9375 0.9375
COST ANALYSIS W10x22 W8x21
Weight (plf) 22 21
Weight (plf x length) [in lbs] 412.5 393.75
Number of Beams 8 88
Total Weight (per story) 3300 34650
Total Weight (in lbs) 37950
Table 101: Edge Beam Design (SBF)

Abstract (if available)

Abstract Located in the heart of Los Angeles, USC is considered an earthquake prone zone, and there is a vital imperative to ensure the safety of all students and faculties during such an event. In order to prevent casualties, buildings must be checked and assured to perform under design loads. Under the current California Building Code (CBC), engineers must design all structural members for new buildings to meet CBC 2010 standards. However, designing to simply meet the standards cannot ensure the safety of the building and its occupants as seismic loads in earthquakes cannot be predicted and can exceed building code expectations. When retro‐fitting of existing buildings (designed under earlier, less stringent codes) is considered, the CBC 2010 standards may be applied with the same caveat. ❧ This study considers structural retrofit systems for existing buildings, taking into account economic as well as structural factors. Two USC buildings, Waite Phillips Hall (WPH), a 12‐story classroom/office building, and Webb Tower (WTO), a 14‐story residential building, were chosen as case‐studies to represent mid‐size buildings constructed in the Los Angeles area. Four hypothetical structural systems for retrofit were studied: steel braced frame, steel moment frame, concrete shear wall core, and concrete moment frame systems. In accordance to design earthquake loads, the different systems' differences in framing element size, weight, and cost were detailed and recorded. This study will help future architects, engineers and contractors to understand the value issues in trade‐offs of material and structural choices. ❧ The thesis conducted a study of these structural systems in these steps: first, differing levels of design loads were implemented to each system, and framing elements had been selected accordingly. Simplified hand calculations were used to calculate design loads, and an excel spreadsheet with design formulae was used to select the framing elements. A three‐dimensional modeler, SAP 2000, was used to assign all members and evaluate each structural system. Second, through SAP 2000’s feature, “steel/concrete design check of structure”, all members proved viable in accordance to current code. Data from the building was then extruded onto an Excel spreadsheet in order to analyze cost for each system and retrofit. Through this study, a guideline for choosing the most cost‐efficient structural system was created for an earthquake zone such as Los Angeles. Though these structural systems cannot represent all building types in Los Angeles, the present study outlines a system for typological study for working professionals in design of structures. This study hopes to assist designers and contractors in the reality of building for safety rather than cost.

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