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Bracing systems for tall buildings: A comparative study

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Bracing systems for tall buildings: A comparative study

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NOTE TO USERS Page(s) not included in the original manuscript are unavailable from the author or university. The manuscript was microfilmed as received. 43-70 This reproduction is the best copy available. __ ® UMI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BRACING SYSTEMS FOR TALL BUILDINGS: A COMPARATIVE STUDY by Rosa Neidl-Comejo A Thesis Presented to the FACULTY OF THE SCHOOL OF ARCHITECTURE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE December 2004 Copyright 2004 Rosa Neidl-Comejo Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UM I Number: 1424228 UMI UMI Microform 1424228 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION This thesis is dedicated to my family: Diego, Angela, Mariangela and Federico. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I wish to express my sincere appreciation to professor Goetz Schierle, chair of my thesis committee, who offered constant feedback and helpful suggestions in the making of this manuscript He has been my mentor during my academic preparation in Building Science, in which he constantly shared his knowledge and love for structures. Now, thanks to him, I think of structures from their pure logical rationale, and hopefully, one day I will be able to use this inspiration to become a “structural artist”. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv TABLE OF CONTENTS DEDICATION ii ACKNOWLEDGEMENTS iii LIST OF TABLES vi LIST OF FIGURES vii ABSTRACT xiii INTRODUCTION 1 CHAPTER 1: THE IMPORTANCE OF TALL BUILDING BRACING SYSTEMS FOR ARCHITECTS 3 1.1 Role of bracing systems in high-rise architecture 3 1.1.1 Development of high-rise architecture 3 l.l.l.l Defining a tall building 3 1.1.1.2 Historical overview 4 1.1.2 Structural behavior and economic factors of tall buildings S 1.1.3 Aesthetic and functional challenges 12 1.2 Effectiveness of Bracing Systems in tall buildings 13 1.2.1 Basic principals of Bracing 13 1.2.2 Braced Systems for wind and earthquake resistance 15 1.3 Other lateral load resistant systems 18 CHAPTER 2: BRACING SYSTEMS: A BACKGROUND REVIEW 21 2.1 Classification of Bracing Systems 21 2.1.1 Concentric Braced Frames (CFBs) 22 2.1.1.1 Types of Concentric Braced Frames 23 2.1.2 Special Concentric Braced Frames (SCBF) 28 2.1.3 Eccentric Braced Frames (EBFs) 30 2.1.3.1 Types of Eccentric Braced Frames 35 2 .0 .2 Effect of link beam length (A study by Dr. Egor Popov) 38 2.1.4 Dual systems 43 2.2 Design and selection of a bracing system 48 2.2.1 Engineering considerations 48 22.1.1 Gravity load 49 2.2.1.2 Wind load 51 2.2.1.3 Seismic load 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V 2.2.2 Architectural considerations 58 2.2.2.1 Aesthetical and functional considerations 58 2.22.2 Location of openings 60 2.2.23 Height considerations 61 22.2.4 Cost considerations 63 CHAPTER 3: ANALYSIS 67 3.1 Importance of analysis 67 3.2 Case studies 68 3.2.1 John Hancock tower, Chicago, by Skidmore, Owings and Merrill, 1968 68 3.2.2 Citicorp Building, New York City, by Hugh Stubbins, 1798 72 3.2.3 Bank of China, Hong Kong, by I.M. Pei, 1988 76 3.2.4 Library Tower, Los Angeles, by Pei Cobb Freed and Partners, 1989 79 3.2.5 Hotel de Las Artes, Barcelona by by Skidmore, Owings and Merrill, 1992 83 3.3 Parametric Prototype Analysis 87 3.3.1 Objective of parametric analysis 87 3.3.2 Method of analysis 88 3.3.2.1 Type of analysis (Description of Multifiame 4D) 88 3.3.2.2 Building typology 89 3.3.2.3 Variables compared for the analysis 92 3.3.3 Sample analysis 99 3.3.4 Findings and evaluation of findings 124 3.3.5 Strengths and weaknesses of this specific analysis 130 CHAPTER 4: CONCLUSIONS AND RECOMMENDATIONS 132 4.1 Conclusions 132 4.2 Recommendations for future research 133 GLOSSARY 134 REFERENCES AND BIBLIOGRAPHY 136 APENDICES 142 A Calculation of wind pressure per joint for three wind velocities, for two building heights cases 142 B Column design: base shear and weight calculations 146 C Description of Multifiame 4D 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES Table 1: Description of lateral load resistant systems and their 62 maximum height Table 2: Total number of tests performed in Multiframe 4D: 99 95 tests Table 3: Wind pressure coefficient tables 103 Table 4: Wind design procedure to allocate sizes of members in 107 each wind case Table 5: Summary of results Pocket Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vii LIST OF FIGURES Figure 1.1: The town of San Gimignano 5 Figure 1.2: Empire State Building and top of Chrysler Building 7 Figure 1.3: Concept of cantilever behavior 9 Figure 1.4: Comparison of structural systems according to their 10 stiffness figure 1.5: Concept of bracing 14 figure 1.6: Graphic description of a braced frame 14 Figure 1.7: Efficient height-to-width ratio for a bracing system 15 figure 1.8: Building shear and bending resistance 16 figure 1.9: Shear wall system 19 figure 1.10: Moment resistant frame system 20 figure 2.1: Bracing configurations 22 Figure 2.2: Configuration for a diagonal brace in single direction, 24 deformation under gravity and lateral load figure 2.3: Configuration for a diagonal brace in alternate direction, 24 deformation under gravity and lateral load figure 2.4: X-Brace Frame configuration, deformation under gravity 25 and lateral load figure 2.5: V-Braced Frame configuration, deformation under 26 gravity and lateral load Figure 2.6: Chevron Braced Frame configuration, deformation under 26 gravity and lateral load Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii Figure 2.7: K-Braced Frame configuration, deformation under 27 gravity and lateral load Figure 2.8: Concept of a Mega Braced system 28 Figure 2.9: Uniform building code seismic Zone Map 29 Figure 2.10: Possible locations for the link beam in Eccentrically 31 Braced Frames Figure 2.11: Location of link-beam stiffeners to prevent buckling of 33 web members Figure 2.12: Detail of connection of link beam adjacent to column 34 Figure 2.13: A link next to a column provides little energy dissipation 35 Figure 2.14: EBF with a single diagonal configuration, deformation 36 under gravity and lateral load. Figure 2.15: Y-Eccentrically braced frame configuration 36 Figure 2.16: Knee-brace configuration, deformation under gravity and 37 lateral load. Figure 2.17: Examples of Eccentrically Braced Frame configurations 38 with two link beams Figure 2.18: e/1 ratio of stiffness 39 Figure 2.19: Variation of elastic lateral stiffness with e/L for 2 EBF 40 configurations Figure 2.20: Variation of Frame Plastic strength according to e/1 ratio 41 Figure 2.21: Regulation of the eccentricity according to building 42 height (ideal distribution of stresses) Figure 2.22: Example of a dual system frame: braced core and interior 44 frames Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix Figure 2.23: Interaction of forces: the truss is restrained by the frame 45 at the upper part of building Figure 2.24: Frame-truss interacting system 46 Figure 2.25: Gravity load path for dingle diagonal bracing, X-bracing, 50 Chevron bracing, and alternate diagonal Figure 2.26: Variation of wind velocity with height 51 Figure 2.27 Load path for horizontal shear in single diagonal brace 53 configuration Figure 2.28 Load path for horizontal shear in X-brace configuration 54 Figure 2.29 Load path for horizontal shear in a Chevron Brace 54 configuration Figure 2.30 Load path for horizontal shear in an alternate diagonal 55 brace configuration Figure 2.31 Load path for horizontal shear in V-brace 55 Figure 2.32 Load path for horizontal shear in a EBF Knee-brace 56 Figure 2.33: Braced Frame deformation under lateral load: by 57 bending, by shear, and combined deformation Figure 2.34: Possible location of wall openings for doors and windows 60 in different bracing types Figure 2.35: Possible wall openings for doors and windows in EBF 61 configurations with two link beams Figure 2.36: Steel quantities for gravity and wind systems 63 Figure 3.1: Photograph of the X-bracing on the facade of the John 68 Hancock center Figure 3.2: J. Hancock center elevation, and load path 70 Figure 3.3: Photograph of mega columns that support the 1s t floor the 72 Citicorp Building 150 f t above ground Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X Figure 3.4: Diagram of the structural system of the Citicorp building 75 Figure 3.5: Perspective of the Bank of China 77 Figure 3.6: Diagrams illustrating the Bank of China structural system 78 Figure 3.7: Photograph of the Library Tower 80 Figure 3.8a: Floor plan of the Library Tower 81 Figure 3.8b: Diagrams illustrating the Library Tower structural system 82 Figure 3.9: Photograph of the Hotel de las Artes 83 Figure 3.10: Illustration of the Hotel de las Artes showing 84 architectural - structural form Figure 3.11: Screen shot of Multiframe 4D 89 Figure 3.12: Floor plan of hypothetical building 90 Figure 3.13: Hypothetical building cross-section and perspective view 91 Figure 3.14: Bracing configuration for hypothetical building 94 Figure 3.15: US map of basic wind speeds in miles per hour 95 Figure 3.16: Exposure of hypothetical building (Schierle, 2001-02) 96 Figure 3.17: Fazlur Kahn’s graph “Premium for height” 97 Figure 3.18: Building cross-section that shows the dimensions used to 101 designate lateral load at joints Figure 3.19: Diagrams of lateral wind load applied to hypothetical 104 building for wind of 70 mph Figure 3.20: Diagrams of lateral wind load applied to hypothetical 105 building for wind of 90 mph Figure 3.21: Diagrams of lateral wind load applied to hypothetical 106 building for wind of 110 mph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.22: Figure 3.23: Figure 3.24: Figure 3.25: Figure 3.26: Figure 3.27: Figure 3.28: Figure 3.29: Figure 3.30: Figure 3.31: Figure 3.32: xi Vertical member sizes for non-optimized structure cases 109 tested at 70mph, 90pmh, and 1 lOmph wind speeds Vertical member sizes for structural optimization #1 for a 110 building of 420 feet high, at 70mpH, 90pmh, and 1 lOmph wind speeds Vertical member sizes for structural optimization #1 for a 111 building of 540 feet high, at 70mph, 90pmh, and 1 lOmph wind speeds Vertical member sizes for structural optimization #2 of 112 two building height (420’ and 540’), at 70mph, 90pmh, and 1 lOmph wind speeds Sloping members sizes for non-optimized structure, for 113 the 420 feet tall prototype, at 70mph, 90pmh, 1 lOmph wind speeds Sloping members sizes for non-optimized structure, for 114 the 540 feet tall prototype, at 70mph, 90pmh, 1 lOmph wind speeds Sloping members sizes for structural optimizations cases 115 1 and 2 structure, for the 420 feet tall prototype, at 70 mph wind speed Sloping members sizes for structural optimizations cases 116 1 and 2 structure, for the 420 feet tall prototype, at 90 mph wind speed Sloping members sizes for structural optimizations cases 117 1 and 2 structure, for the 420 feet tall prototype, at 110 mph wind speed Sloping members sizes for structural optimizations cases 118 1 and 2 structure, for the 540 feet tail prototype, at 70 mph wind speed Sloping members sizes for structural optimizations cases 119 1 and 2 structure, for the 540 feet tall prototype, at 90 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.33: Figure 3.34: Figure 3.35: Figure 3.36: Figure 3.37: Figure 3.38: Figure 3.39: xii Sloping members sizes for structural optimizations cases 120 1 and 2 structure, for the 540 feet tall prototype, at wind design of 110 mph Diagram of drift measurement at top of the structure in 122 Multiframe 4D Graph 1 of parametric analysis results showing a 125 comparison of weight and drift in each type of brace, for three optimization cases, in a 30-stoiy building Graph 2 of parametric analysis results showing a 126 comparison of weight and drift in each type of brace, for three optimization cases, in a 40-stoiy building Graph 3 of parametric analysis results showing a 127 comparison of weight and drift in two buildings of 30 and 40-stoiy high, in three optimization cases, at three wind velocities Graph 4 of parametric analysis results showing the 128 structural weight in three optimization cases for two hypothetical buildings of 30 and 40-story high, and comparing them to real parameters in a Fazlur Kahn study Graph 5 of parametric analysis results comparing the 129 structural weight of two hypothetical buildings -of 30 and 40-story high- to real building weights, from a Fazlur Kahn study Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT The emergence of the high-rise represents the furthermost architectural phenomenon of the 19th and 20th centuries, in which economics, aesthetics, and technology merged to form a fusion of structure, materials, zoning and code requirements, energy, and social and cultural aspects. And with recent technology, tall buildings can be easily adapted to climatic, geographic, and physical circumstances. Therefore, when planning a tall building the designer needs to be aware of and understand the framing possibilities available to create the most efficient building in terms of its environmental impact, urban adaptation, functional programming, aesthetical result, and most importantly of its structural performance. The principal objective of the study presented on this thesis is to investigate and compare the characteristic features of bracing systems used, documenting the factors leading to their selection in the context of lateral load design, and its architectural implications. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 INTRODUCTION Human nature has always been challenging natural and physical laws. Thousands of years ago, high-rise constructions were created to establish a closer relationship with deities. Because of a juncture of important milestones such as industrialization and the realization of physical limits for urban growth, this spiritual concept gradually translated into a civic and prestigious symbol. At present, the role of tall buildings is a combination of social, political and economic features that reflects a metropolis’s wealth and power. In this context, the relationship between engineering and architecture becomes crucial. Therefore, architects should be able to understand the properties and manage the applications of structural and non-structural materials and systems, in order to make the most appropriate selection when designing and planning a building. Aiming to develop the aforementioned ability, designers must take into account not only aesthetic considerations, but also structural efficiency. In addition, the exposure of tall buildings to natural phenomena has highlighted structural limitations. As a result, a variety of structural systems have been designed for buildings to resist lateral movement caused by wind and seismic activity. A building needs to be stiff enough to resist such forces, while maintaining a certain level of ductility to absorb and dissipate the energy. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 To help overcome the knowledge gap in the relationship between architectural design and braced frame selection, this study will document the factors that lead to the most appropriate choice of a system in the context of lateral load design, and its architectural implications. This thesis is divided in four broad sections. First, a discussion about the importance for architects to understand bracing systems; second, a background review and description of the different braced frames used in actuality; third, an analysis of five case studies, and a demonstration study evaluating under a very limited set of parameters the most popular braced systems applied to tall buildings; and the last section will address concluding remarks and recommendations. Along the entire study, engineering and architectural considerations will be portrayed with emphasis on making the best decision at the moment of choosing a bracing system. In brief words, the present work is a humble attempt to provide accessible information for architects about the basic principals, methodologies and approaches to make an accurate selection of one the most efficient types of lateral load resisting systems: steel braced frames. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 1 THE IMPORTANCE OF TALL BUILDING BRACING SYSTEMS FOR ARCHITECTS Before start talking about Bracing Systems for tall buildings, it is important to understand other issues first. This introductory chapter will explain what is a tall building and why it has such a great effects in modem societies, as well as how bracing systems developed along with the need for height. Notions such as “tall”, “bracing” or ‘lateral load”, and issues such as “the role of a tall building in society” or “the development of bracing systems”, will be discussed in order to emphasize the importance for architects in the knowledge of bracing systems. 1.1 Role of Bracing Systems In high-rise architecture 1.1.1 Development of high-rise architecture 1.1.1.1 Defining a tall building It is important to define what a tall building is, or better said, what characteristics make a building to be considered “tall”. There is not a precise definition. However, a tall building can be classified depending on the reasons that justify its selection, and not simply by its height or number of floors. Some of the factors that can help defining a tall building can be the aspect ratio (ratio of width to height of the structure), the height from the floor to the top, the way a building imposes itself compared to the buildings around it, or the consideration of how its tallness creates a dominant impact on the surrounding urban context (CTBUH 1995a, p.x). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 From a structural point of view, and for the intent of this thesis, a building can be considered tall when the effects of lateral loads are affecting the design. This could be, for example, the moment when the designer is required to understand the notion of drift when planning a building scheme. Drift which is the amount of sideway displacement at the top (controlled by the code) of the building produced by the effects of wind or seismic motions. At the end of this study, in chapter three, the parametric analysis will be based on a thirty-story hypothetical building, with the sole objective of having a more realistic example and getting comparative results. The rationale for this selection will be explained in detail in the chapter 3. 1.1.1.2 Historical overview Even if tall buildings are commonly thought to be an effect of modem industrialization, the aspiration of building skywards is as old as human civilization; this can be illustrated with some examples such as the ancient Pyramids of Giza in Egypt or the Mayan temples in Tikal (Guatemala). However, it can be said that the actual development of high-rise architecture probably began in the sixth century with the manifestation of the tower-like pagodas of Japan; or in the Middle East, where the minarets of Muslim architecture went from square towers in the Great Mosque of Damascus, to slender spires in Turkey and India (such as Kutab Minar in Dehli). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 In any of these cases, the tallness was directly related with the connection to the Gods or supreme beings omnipresence. Such religious representations continued to be present in most of the tallest towers in medieval towns; but in other cases, like in San Gimignano in Italy (1300-1400), the great number of tall towers in this small town represented defense and rivalry. San Gimignano was the best example of high- rise architecture at that time, where building taller towers was first because of defense purposes and then, it became a symbol of challenge between two families who wanted to show their power and wealthy ness, by the height of their towers. Figure 1.1: The town of San Gimignano (Schierie 2002-2004) With the passing of time, new towers and tall buildings appeared, and this time symbolizing power and civic affairs, such as the Westminster Palace towers in England (1840-1867). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 In the second half on the nineteenth century, during a period of extreme physical and economical growth in North American cities, the conception of a tall building was deeply changed in terms of its function: from a campanile tower to a tall edifice that was unimaginable few years earlier. At this moment in time, along with the introduction of cast iron as a building material and the invention of elevators, the tall building became the result of a unique combination of industrialization, business and real state. The braced frame system evolved during the beginning of high-rise construction in the early twentieth century. Just before this time, in the late 1800’s, Chicago was the ideal place where the development of innovative architectural typology and expression could happen. The Great Chicago fire of 1871 destroyed most of the city’s original wood frame structures, which meant that the reconstruction of the entire commercial district had to incorporate fire-resistant materials to the new buildings. Steel, coal and lumber industries were fundamental resources to transforming Chicago into an industrial city. The improvement of the steel framework was an economic advantage promoted by William Le Baron Jenney in his Home Insurance Building of 1890 in Chicago (Ali and Armstrong, 1995). Since then, the metropolitan economical demands also created the need for a highly developed artistic way of building. The architectural and technical achievement of the Chicago school established a new style of architecture, as well as a new typology in the shape of the steel high-rise Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 office building. As a result, most of the development for this new type of commercial edifices happened in Chicago and New York, by architects like Louis Sullivan, Daniel Bumham, and John Wellborn Root. This phenomenon became more important after World War II, when the rapid population growth and limited land forced the necessity for urbanization, urging the construction of taller buildings. -JL_££1 Figure 1.2: Empire S ate Building (left) and top of Chrysler Building (right) (Risebero 1982, p.233.237) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 This is when skyscrapers -as we know them today- were first designed and put up by modem architects such as Walter Gropius, Mies van der Rohe, and later, Skidmore, Owings and Merril. Good examples are the Empire State Building and the Chrysler Building, built in New York City in the 1930’s. Since then and until today, steel-frame construction is one of the most efficient and cost-effective construction types used for mid-rise and high-rise building structures. 1.1.2 Structural behavior and economic factors of tall buildings The ambition of building taller towers will always remain a challenge for this and the generations to come. Inspired by evolving technology, tall buildings silhouette will continue to transform and shape the skyline of many cities, reflecting their prosperity and importance. Codella McArthur (1973) remarked “Our buildings today reflect our civilization...a direct result of the importance of time and money.,,,” (As cited in Council on Tall Buildings and Urban Habitat, 7). An example to this is that today, in metropolitan cities, such as New York or Tokyo, the high costs of land ($1250/sq.fL in NY, $25,000/sq.fL in Tokyo) has been also a major factor for the growth of taller buildings. Modem buildings, designed for strength not drift, employ high-strength steel for their structural framework, which reduces the amount of steel needed, therefore lowering the cost Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 Tall buildings are the most complex built structures given that there are many requirements and complex systems to incorporate. They are tall structures - which can be conceptualized as beam that cantilever from the earth- that are constantly receiving the impact of wind and seismic forces acting on them. * Figure 1.3: Concept o f cantilever behavior With today’s structural improvements, tall buildings are becoming more and more slender, leading to the possibility of more sway. Every month new buildings are being designed and created, new projects envisioned, and new schemes employed that resist lateral load with minimal drift Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 The most effective systems for tall buildings are the ones that fully connect the vertical gravity load resisting elements with the lateral load resisting systems. There are many innovative structural systems and the principal function of each of them is to resist the lateral loads. Fazlur Khan -of Skidmore, Owings and Merrill- documented in 1965 the hierarchy of the different systems by generally classifying them with respect to their relative effectiveness to resist lateral loads for various heights as seen in figure 1.4. TYPE I SHEAR FRAMES TYPE II INTERACTING SYSTEMS TYPE III PARTIAL TUBULAR SYSTENS TYPE IV TUBULAR SYSTEMS Ir r r iH I I < » 70 m m TYPE I TYPE II TYPE m TYPE IV Figurel.4: Comparison of structural systems according to their stiffness (Kahn cited by CTBUH 1995b, p.6) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 At one end of the scale are moment resisting frames (MRF), which are efficient for buildings in the range of 20 to 30 stories; and at the other end is the group of tubular systems with high cantilever effectiveness. The other systems were placed with the idea that the use of any particular form is cost-effective only over a limited range of building heights. The lateral forces due to wind and seismic motions provoke shear and bending deformations. Therefore, a tall building must use a system able to resist these forces without breaking, overturning, or surpassing its elastic limits. The system should be able to reduce motion perception, ensure human comfort and reduce non-structural damage. Withstanding these forces with steel braced frames is a very effective option, notably to resist wind load. Bracing systems have more strength and stiffness, and are more effective to resist deformation than rigid joints; they also use less material and have simpler connections. Bracing can be used in structural compositions of many materials, such as wood, concrete and even bamboo. Nevertheless, for mid to high-rise buildings, braced frames are most often of structural steel because of its ductility in wind and seismic loading conditions, and its relative strength to lightweight proportion. Using steel as a construction material has many advantages, such as construction speed, availability in a variety of grades and shapes, adaptability to different length of spans and floor-to-floor heights, and easy acceptance to code requirements. From an economical standpoint, steel construction is simple to retrofit, modify, adapt, or suit Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 for future demands; and because of its lightweight characteristics (25 to 35% lighter than a concrete frame), it can help reducing foundation costs (Taranath 1988, p. 209). 1.1.3 Aesthetic and functional challenges Even though the typology of tall buildings was transformed with modernity, as a symbol, its aesthetic function has not changed; it has always been and will be to emphasize a focal point, to generate a dominant presence, or symbolize culture, wealth and express power. The practice of expressing structure in buildings comes from a long time ago with the Gothic cathedrals of the Middle Age and ancient oriental wood structures. However in the case of tall buildings, “structural art” can be categorized into two major stages that date from two centuries ago. One that lasted from the late eighteenth-centuiy to the late nineteenth-century; which was a straight outcome of the industrial revolution (Council on Tall Buildings and Urban Habitat, 1995, p. 191). The other one started at the end of the nineteenth-century and continues until today. The main difference between the two periods is the type of materials that were used; the first one was based around structural uses of iron, and the second one was around new applications in steel and structural concrete. Today, with the constant evolution and combination of so many systems, there is not a defined architectural tendency that rules the design of tall buildings, as it has occurred before. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 Nevertheless, what most of the designers tend to do now is to utilize the structure as form generator, as part of the architectural expression. When braces are aesthedcal expressed, they become a strong visual element, suggesting the structural behavior of the system. There are other beneficial aspects of tall buildings that affect their function and programming. Tall buildings also provide flexibility in managing the space of operational areas; they allow for a relative proximity to complementary uses and shared amenities; and, if planned wisely, they support efficient energy utilization. 1.2 Effectiveness of Bracing Systems in tall buildings 1.2.1 Basic principals of Bracing The logic behind bracing is when any rectangular area, that by it self cannot resist sideways forces, can be stabilized by means of triangulation; introducing diagonal struts (braces) that go across opposite angles (see figure 1.5). A system of braces is used to stiffen a structure and provide better resistance to lateral forces such as earthquakes and strong winds. A simple example could be the bracing of a rectangular building that is achieved by interconnecting four massive columns at each comer with gigantic diagonals. Thus, braced frames are lateral force resisting systems for tall buildings that make the frame lighter and more rigid, and can be described as vertical truss systems that resist lateral forces, as it can be seen in figure 1.6. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 perwa4ttjcfci OF-flZ/frAS t 96r\s f is 9 © * « 6 M A e i M K U | 4 ^ p : *^M 0 A & f t A C t S p e ie tf f s tte s & s 1 o CodtfreM cr U U elU C tcA te, to & stN & tu e : t t c ?**♦<£ Figure 1.5: Concept of bracing 0 0 lit Figure 1.6: Graphic description of a braced frame (Image adapted from Schierle 2002-2004) Furthermore, a braced system can also improve the efficiency of a rigid frame by reducing drift and bending in columns. In the case of braced frames without moment joints, the diagonal members are the ones that resist all lateral forces. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 The effectiveness of the bracing system is characterized by a high ratio of stiffness to material quantity, and by the principle of being a redundant structure, even if it will require greater footings. The braces are designed for the most severe cases of compression, and they are usually in every storey of the building; columns are designed to resist overturning moment. Ideally, a frame with a height-to-width ratio of 8 to 10 is considered appropriate for a reasonably efficient bracing system; however this ratio is rarely found in real cases. From a structural point of view, the design of a building must utilize structural materials to the fullest; and from an architectural point of view, the selection and design of a system must allow the best synergy with the architectural design and economical factors. 1.2.2 Braced Systems for wind and earthquake resistance The two main concerns at the moment of designing a tall building are gravity load and lateral load. Gravity loads are vertical loads, resisted by beams and columns. - L- =- g - * J f Figure 1.7: Efficient height-to-width ratio for a bracing system Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 Lateral loads such as wind and seismic loads are primarily resisted by the lateral bracing systems. Most lateral loads are live loads whose main effect is a horizontal force acting on the structure, such as wind load against a facade, an earthquake, or the earth pressure against a retaining or a basement wall. Because of laterally directed forces induced by wind and inertia forces caused by seismic movements, a tall building tends to snap (shear) and to bend, both at the same time. Therefore, a structural system must be designed to resist both shear and bending, as it can be graphically explained in figure 1.8. When resisting shear forces, the building must not deflect excessively nor break; and when resisting bending, it must not overturn, not bend extremely, or fail under tension or compression. r Figure 1.8: Building shear and bending resistance, a) it must not break under shear; b) it must not deflect excessively under shear; c) it must not overturn in bending; d) it must not fail under tension or compression; e) it must not deflect excessively in bending. (Image adapted from Taranath 1997, p.4-5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 Lateral loads differ in intensity depending on the building's geographic setting, on the selection of structural materials, on its height and shape. The dynamic effects of lateral loads are usually analyzed as an equivalent static load for most small and medium-sized buildings. For taller buildings, dynamic computer programs using iterative routines are employed for the analysis. The design for wind and earthquake loads on a building are more intricate than gravity loads, and they are described in the Uniform Building Code in detail for many regions of the United States. Furthermore, building drifts are reduced when a structure is braced against wind and seismic forces. Winds (except hurricanes and tornados) usually do not cause major structural damage to tall buildings. The major concern of wind design is reducing the lateral drift that causes wind motion problems to occupants, and to non- structural elements like partitions, and curtain-walls. Wind loads increase with the height of a building, so for very tall buildings, the main objective of wind bracing is keeping the movements in the upper stories as humanly acceptable as possible. In contrast, earthquake loads are more complex, unsure, and likely to be more damaging than wind loading; fortunately, they do not occur too often. Seismic motions create ground movements that are classified as "shakes," "rattles," and "rolls", which describe three different types of load intensities; every structure in an earthquake zone must be capable to resist all these movements with adequate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 strength, stiffness, and ductility. During an intense earthquake, a structure must provide enough ductility in order to prevent collapse. The basic principle for earthquake design on the one hand is that the vertical system needs to remain elastic during the time history of an earthquake. On the other, the horizontal system, which was initially elastic, may become plastic during the earthquake after absorbing the energy throughout the process, preventing structural collapse. In summary, in both wind and seismic design, braced frames pick up their resistance to lateral loads by the action of the diagonal braces, which induce forces in the associated beams and columns so that everything works together like a truss. However, even if wind and seismic resistant systems follow the same principle of withstanding lateral loads, there are specific types of frames that work better for one or the other, and are explained in more detail later on in chapter 2. 1 3 Other lateral load resistant systems Braced frame system is one of the four principal types of lateral load resisting elements, from which steel braced frames provide extremely efficient ways of withstanding lateral loads. The other three types are shear walls, cantilever, and moment resisting frames. In the following paragraphs they will be briefly described with the intention of promoting analytical understanding and differentiation of all systems, before this thesis focuses only on the study on bracing systems. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 • Shear wall system Shear wall systems are the most popular systems used to stabilize structures against lateral loads. They became more common with concrete technology applied for tall buildings where shear walls would be located around service cores, stairwells, or elevator shafts. One problem of locating shear walls around elevator or service shafts is the location of required openings where most of the stresses are critical. •546W M O f’S flG K .utM L ? Figure 1.9: Shear wall system (Image adapted from Schierle 2002-2004) When combined with other functional requirements, and have a sufficient length, shear walls can be designed to economically withstand lateral loads in buildings up to 30 to 40 stories. However, as shear wall carry the load efficiently in their planar direction, it is recommended to provide shear wall in the two orthogonal directions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 * Moment Resistant Frame Moment resisting frames (MRFs) are composed of horizontal and vertical members rigidly connected, which resist lateral loads thru flexural stiffness of the members. MRFs used in tall buildings provide the advantage of a flexible architectural distribution, since they can be placed anywhere in the building (around the core, exterior or interior walls). Typical deformations of MRFs are showed in figure 1.10, a point of “contraflexure” is located around the middle of the beams and columns, maintaining the 90° at each comer of the frame. The size of the members in MRFs is usually based on stiffness rather than strength, to control drift under lateral loads. Monsit- f Fig 1.10: Moment resistant frame system (Image adapted from Schierle 2002-2004) This type of framing system is not efficient for buildings taller than 20 or 30 stories, since for taller buildings there would be a lack of efficiency caused by flexure of the members. Nevertheless, MRF’s are well suited for seismic areas due to their ability to perform in the inelastic range. 90° i s M A r t r t t f c i r f C P Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 2 BRACING SYSTEMS: A BACKGROUND REVIEW As part of the objective of this thesis, the following chapter will provide valuable information and definitions on all types of steel bracing systems. The contents will be limited to architectural concerns, and basic engineering considerations, which are believed to be important for architects and designers to know at the moment of selecting a braced system configuration. 2.1 Classification of Bracing Systems Braced frames are categorized, depending on their ductility characteristics, as either Concentric Braced Frames (CBF) or Eccentric Braced Frames (EBF). On one hand, in CBFs the axes of all members intersect at a point such that forces in every member are axial. They have a great amount of stiffness but low ductility, characteristics that make this system to be a good alternative in non-seismic areas, where high ductility is not essential. On the other hand, EBFs use axis offset to assume bending and shear into beams, which reduces the stiffness-to-weight ratio but increases the ductility and reduces seismic forces. Depending on performance considerations like strength, length, necessary stiffness, space clearances required, and the type of connection, the diagonal member in structural steel can be made of double angles, channels, tees, tubes, or wide-flange shapes. Braces can take many forms as showed in the figure 2.1. Figure 2.1-a shows diagonal bracing in 2-story increments, figures 2.1-b, 2.1-c are K-Braced frames Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 (inverted K-bracing is also called Chevron bracing), and figure 2.1-d shows an example of bracing for a three-bay frame. Figures 2.1-e to 2.1-n are bracing across single bays in one-stoiy increments. H 5 1 M A N y Y ^ V / \ A n Y Y s y O A s I 3 / > X A N / N i i j/r n r DS / 1 r n r n , r m / \ r n r n A j • I N r n ,r n r n - n x \ r n 19) M <i> w 0 ) M M Figure 2.1: Bracing configurations (Taranath 1997, p.425-426) 2.1.1 Concentric Braced Frames (CBFs) Concentric braced frames are frequently used in multistory high-rise buildings, and they are one of the most effective structural systems in steel construction at withstanding lateral wind forces because they allow total truss action. Compared to Moment Resisting Frames (MRFs), braced frames are more efficient to resist sideway loads and the stiffness required to control story drifts. CBFs were originally utilized to resist wind loading, but is has also been used for earthquake resistant Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 design. Nonetheless, in the case of an earthquake, this structural framing system is not considered ductile enough, since their stiffness generates greater seismic forces. When the frame remains in the elastic range, its behavior is satisfactory; but plastic deformation may be permanent Even though the frame is called “concentric”, sometimes there may be small eccentricities between member centerlines at the joints; when this is the case, these eccentricities are usually provided for in the design. Concentric Braced Frames can take the form of a diagonal, X, K, or V. X-braces provide higher lateral stiffness-to- weight ratios in relationship but allow no door openings. However, as X-bracing absorb some part of the column load in proportion to its stiffness, it provokes changes in the column’s gravity load transfer path. Consequently, additional forces in both diagonal and horizontal members of X-bracing systems are created, which will need to be taken into account for the design. 2.1.1.1 Types of Concentric Braced Frames * Diagonal Braced Frame When the diagonals go all in the same direction, the brace is called “Pratt” bracing; in this type of bracing, the diagonal members are in compression and the beams in tension under load from one side, and when load comes from the opposite side, diagonal braces are in tension and beams under compression (shear deformation). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 Therefore, a single diagonal brace must be prepared to withstand compression and tension produced by lateral forces in both directions of the frame. Figure 2.2: Configuration for a diagonal brace in single direction, deformation under gravity and lateral load (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) However, diagonal bracing is more common in compression-tension bracing, which is alternating their direction so that not all of the braces are in tension or compression at the same time, and the beams remain mostly unstressed -as shown in figure 2.3. Figure 2.3: Configuration for a diagonal brace frame in alternate direction, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) ]X eSN 't \ J feet* lAfegM, v i tOAO I M ue# ji. I ! Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 Diagonal braces are generally the longer type of braces and are more subject to buckling. An Ordinary Concentric Braced Frame (OCBF) is a diagonally braced frame in which all members of the bracing system are subjected primarily to axial forces. • X-Braced Frame (cross-brace) An X-brace is a type of CBF or OCBF in which a pair of diagonals intersects at mid length of the braces. In this case, the braces take most of the forces while the beams resist minimal axial load, in this type of brace, one column is in tension while the other in compression. X-braces of rods or strands resist tension only, because they deform under compression. Figure 2.4: X-Brace Frame configuration, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) • V-braced frames A V-braced frame is a type of concentrically braced frame (SCBF or OCBF) in which a pair of diagonal braces is linked at mid-point within the clear beam span, which can be seen in figure 2.5. ^ ^ f , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 3 JOM TS figure 2.5: V-Braced Frame configuration, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) * Chevron braced frames A Chevron brace is a V inverted (sometimes inverted K) type of brace where half of each beam is in compression and the other half is in tension. figure 2.6: Chevron Braced Frame configuration, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) * K-braced frames A K-brace is an Ordinary Concentrically Braced Frame in which a couple of diagonal braces are located on one side of a column, and are linked to a single point within the clear column height K-bracing is frequently used to permit unobstructed openings, because this type of bracing has a potentially dangerous effect on columns, this system is not allowed in seismic zone 3 and 4. -if V 4s Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 The Uniform Building Code identified four types of seismic regions, and numbered them from 0 to 4; 4 being the zone where earthquakes are more frequent and the construction code is more astringent. Each zone has specific structural requirements; a zone map can be looked up in section 2.1.2. • Mega bracing Mega Braces are huge braced frame systems that are utilized in addition to another interior system. The way they work is that they wrap around the facades of the entire building, going in a multiple-story direction, creating a mega tube structure (see figure 2.8, below). Uf 4/ 4/ Figure 2.7: K-Braced Frame configuration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 6 . f W 4 1 V f lp o r 1*1* —> f W 7 / \ / / r / \ \ A / \ / \ M e & A BrfZACe GefcrtW * of F o o c f c s — 5T«0Ch//UU, ▼'lOO^ M etA 80ACE*u)«tfS -tti€T^iLPlK6 i r d r Figure 2.8: Concept of a Mega Braced system 2.1.2 Special Concentric Braced Frames (SCBF) During severe earthquakes, steel moment resistant frames are susceptible to large lateral movements and brittle or ductile fracture of the beam to column connections. Consequently, designers focused their attention to concentrically steel braced frame system, which represent an economic solution to withstand seismic loads (Sabelli et al. 2003, p.l). However, this type of structure provoked concerns about its ultimate deformation capacity, and design requirements for braced frames have changed considerably during the past two decades, introducing the concept of Special Braced Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 Frames. A special resistant frame is the improvement of an ordinary braced, redesigned to have a weaker brace and a stronger beam system. The connections of the braces to the columns and beams, and the columns to the beams must be proportional, so they maintain their elasticity as they withstand deformations. In a special concentric braced frame system (SCBF), the floor beams are designed for the unbalanced vertical force of braces after buckling, resulting in a strong beam - weak brace system. Special Concentrically Braced Frames employ tension and compression braces, and/or secondary framing members that attach braces together between stories. They have more ductility than Ordinary Concentrically Braced Frames, due to a reduced loss of strength when compression braces buckle. S B 2 B i 2 A ' 2 B 2A .2A JSC. Figure 2.9: Uniform building code seismic Zone Map (UBC- eqhazmaps.usgs.gov/of95- 596/fig-a5.pdf, 2004) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 A special concentric braced frame reasonably distributes the damage distributed over the height of the building. New design provisions for construction were adopted for the first time in the 1994 edition of the Uniform Building Code (UBC), which requires the use of SCBF in every seismic zone 4. (Rai and Goel, 2003, p.973). For more detail regarding seismic zones, see the UBC seismic zone map in figure 2.9. 2.13 Eccentric Braced Frames (EBFs) The other categoiy of bracing systems is the Eccentrically Braced Frame. They are high-seismic lateral framing systems designed to withstand controlled ductile deformations, and to dissipate energy as they undergo strong ground motions. As it was discussed before, Concentric Braced Frames (CBF’s) are great for their strength and stiffness, and are mostly designed for loads caused by wind, since they have very low inelastic behavior under seismic forces and assume greater seismic forces. Moment Resistant Frames (MRF’s) are very good at dissipating energy, but can be too flexible. An Eccentric Braced Frame (EBF) is more ductile than a CBF and stiffer than a MRF, being a system that optimizes the ductility potential and has a great capacity to dissipate the energy in a large seismic force. A common Eccentrically Braced Frame consists of a beam, one or two braces, and columns. It is arranged similarly to traditional braced frames with the difference that at least one end of each brace meets a beam at a point offset from the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 beam intersection with the column or with the opposite brace, as it can be seen in figure 2.10. m H0t&: 8RACH1& IS M ot- t=8 p ' s U & s tH*rf4 Figure 2.10: Possible locations for the link beam in Eccentrically Braced Frames (US Army Corps of Engineers 2003, p.7-3) This eccentric connection concentrates bending and shear forces in the short segment next to the brace. This short section of the beam between opposing braces, or between a brace and the beam-column intersection, is called the “link” beam. EBFs are usually configured so that the braces provide stiffness in an elastic range, and the links control the strength and allow more ductility. Higher ductility thru inelastic shear or bending action of the link beam makes it a good lateral system in areas of high seismic activity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 Ductility is achieved through proper connections and member design so that all means of instability, brittle failures and web buckling are avoided; for example, providing web stiffener plates at the beam-brace intersection. The structural efficiency of EBFs relies on strength and strain characteristics of the link beam; therefore, to avoid any complication on the behavior of the link beam, doublers or holes within the link are not allowed. The design of an EBF is focused on creating a frame that will remain elastic outside a well-defined ductile link. During cases of extreme loading it is expected that the link will deform inelastically with great ductility and energy dissipation. The links need to be located in the intersecting beam at least at one end of each brace, so they will prevent buckling of the braces, and won’t transfer any horizontal component coming from the braces. To take advantage of the ductility of the link, it is important that the other parts of the system such as the beam outside the link, the connections, the braces and the columns must be designed to be strong enough to force the link to yield and that they maintain their integrity as they resist the deformations and displacements. Failure of the link doesn’t cause the whole building to collapse since the structure still maintains its vertical load transfer capacity and stiffness. In addition, shear, bending, or both shear and bending at the same time can cause the yielding mechanism of link beams. Whichever governs is a matter of the proportion of the link length to the beam length; or the ratio of its bending strength to shear Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 strength. Most Eccentrically Braced Frames with link beams that yield in shear are considered to have the most stable energy dissipating characteristics. Code provisions are planned to ensure that the beams, braces, columns and their connections stay elastic and that links remain stable; however, in the case of a major earthquake, there is a possibility of permanent deformation and structural damage of the link beam. . UH& BfiMA a s * * - uej& r*u l m - i L « * > • 1 i L i ' J 4 ftW *' W*€Re 8 M t e —to-S&M CojWgstSOM T*A*feMlSS!0*iOP11CfiaeS S lfO U L P i ' O e m i U E P Ufce CPLUM*l SH fT -^teR S - Figure 2.11: Location of link-beam stiffeners to prevent buckling of web members (US Army Corps of Engineers 2003, p.7-6) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 For link beams that are not adjacent to the columns, a simpler connection is suggested; and for the ones that are next to a column, special connection detailing is given (see figure 2.12); although the use of link beam adjacent to columns is not encouraged, since it contributes veiy little to the energy dissipation process. Dr. Egor Popov suggested (1978 cited Pattratara 1991, p.9) that instead of using link beams adjacent to columns (unless necessary by architectural requirements), which provide little energy dissipation (see figure 2.13), it is cheaper to use concentric or nearly concentric connections at one end of the braces. €. Column Top & bottom flange J m M Doubler plate Spacer Gusset plate Fuse < £ . Beam Floor beam Column Eccentricity (f) Figure 2.12: Detail of connection of link beam adjacent to column (Taranath 1997. p.437) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 In the same study (1989 cited by Pattratara 1991, p. 11), professor Egor Popov noted that when the link beam is adjacent to the column, hinge #1 and #2 dissipate less energy than hinge #3, which is in this case, the link beam. HINGE #1 LINK BEAM: HINGE #3- I---- HINGE # 2 4 Figure 2.13: A link next to a column provides little energy dissipation (adapted from Popov, cited by Pattratara 1991, p. 11) 2.13.1 Types of Eccentric Braced Frames Following are some of the most common Eccentrically Braced Frames configurations; they all perform under the same concept of the link beam taking all or most of the bending and shear stresses under lateral load conditions. Therefore, the type of configuration chosen for a specific project is mainly a matter of architectural and programmatic design requirements, such as openings or circulations paths. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 * Single diagonal A Diagonal Eccentric Braced Frame is arranged similarly to a diagonal CBF, except that one end of the brace is offset from the beam-column intersection; and, as seen in figure 2,13, the short segment of the beam is the one that yields under lateral load while the other members maintain most of their integrity. i h r wr Figure 2.14: EBF with a single diagonal configuration, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004. and Taranath 1997. p.423) Alternate diagonal (Y-braced frame -YBF) TtjT Figure 2.15: Y-Eccentrically braced frame configuration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 Y-Braced frame is a type of EBF in which the stem of the Y is the link beam of the EBF system; which come out to be an alternate-diagonal eccentric braced frame. * Knee-braced frames (KBF) A Knee-braced frame is an assembly of a beam, a column, and a brace whose ends are significantly offset from the beam-column joint, and provides enough eccentricity to introduce shear and bending, as well as axial stresses in the column and the beams. In the past, this type of system was used to provide some stiffness to the beams and provide a measure of lateral stability; today they are no longer used in zones of high seismic motions, because of potential hazard in their seismic behavior. Figure 2.16: Knee-brace configuration, deformation under gravity and lateral load. (Drawing adapted from Schierle 2004, and Taranath 1997, p.423) • EBF’s with two link beams As it was previously said, an Eccentrically Braced Frame system is configured so that the amount of stiffness provided by the braces is relative to the amount of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 eccentricity provided by the link beam. Therefore, configurations that use two link beams create a more elastic system. From an architectural point of view, these bracing arrangements give the opportunity for a more flexible spatial design. ■ + f -r x- -)r x - PlAGONM'MAce BMce Figure 2.17: Examples of Eccentrically Braced Frame configurations with two link beams 2.1.3.2 Effect of link beam length (A study by Dr. Egor Popov) Dr. Egor Popov was a professor of Civil and Environmental Engineering at the University of California at Berkeley. Prof. Popov carried out research on a wide range of topics during his career, from structural mechanics, to the theory of plates and shells, to the seismic design of structural steel, reinforced concrete systems and composite systems. However, his biggest focus was his influential work on the seismic performance of structural steel. Most of the recognition he got was for his development of Eccentrically Braced Systems and its connections. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 A study by Popov (1989 cited in Becker and Ishler 1996, p.3) showed that Eccentrically Braced Frames focused on the need for a laterally rigid framing system that has significant energy dissipation capable to accommodate large seismic forces. The study demonstrated that this is related to the function of the ratio of the link to the beam length (Popov et al., 1989, p. 44), as it can be seen in figure 2.18. To better explain this concept, it is important to know that the length of the link is the clear distance between the ends of two diagonal braces or between the diagonal brace and the column face. irtr 7 7 7 T , t m r * h t : S M 4 * (a k U C B S f t M — * S f if f t e R . J f L o k lf e U M K —> 1 toeUB\Je T R A M S Figure 2.18: e/1 ratio of stiffness (Schierle 2002-2004) As the link becomes shorter, the frame becomes stiffer, approaching the stiffness of a Concentrically Braced Frame, and rotation will be greater; as the link becomes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 longer, the frame becomes more flexible approaching the stiffness of a Moment Resistant Frame. The selection of the link length is frequently controlled by architectural or other configuration restraints. If there are no restraints, the length of the link is estimated to be 15% of the total span, for a typical bracing configuration (Becker and Ishler 1996, p.4). In figures 2.19 and figure 2.20 it is clearly demonstrated how the length of the link is directly related to the stiffness of the frame, and its plastic strength. 1 0 to « ti/L -1.0 0.75 4 0.75 u. u. 0 5 0 .050 2 o _ 00 ' 02 0 4 0 8 0 . 8 04 0 8 0. 8 02 1. 0 1 . 0 00 e l L e / L Figure 2.19: Variation of elastic lateral stiffness with e/L for 2 EBF configurations (Popov 1989 cited by Pattratara 1991, p. 12) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 1 6 14 ^ / ( 2 M p/Vp)/L = .075 12 10 8 6 4 2 0 0.4 0.0 0.2 0. 6 0.8 1.0 e / L Figure 2.20: Variation of Frame Plastic strength according to e/1 ratio (Popov 1989 cited by Pattratara 1991, p. 12) Stress levels vary in each floor of the structure. It would be ideal that when planning a structure to resist seismic loads, the designer tunes the structure’s stiffness in each floor according to the amount of stress. To do this, the length of the link beam (the eccentricity) can be proportionally regulated in each floor, so that lower floors are more rigid, and the upper ones, more flexible, as seen in figure 2.21. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 In this case, the variation of deformation would be uniform all the way through the structure, in which all members resist the same level of stress, achieving a very efficient system. 1 I • • I * / t L/C L/C L/C Figure 2.21: Regulation of the eccentricity according to building height (ideal distribution of stresses) In summary, the two main types of bracing systems discussed in this chapter (Concentrically and eccentrically Braced Frames) differ in the fact that both systems have their unique ductility characteristics. Both systems perform well under their own limitations and depending on the design conditions, which the most important Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 The building’s tapered shape and the structural continuity allow the transfer of loads from bracing to columns and vice-versa. They also reduce gradually the flow of stresses for both gravity and wind loads. The braces absorb most of the wind shear and behave as inclined columns to resist some of the gravity load, emulating the behavior of a rigid tube. The distribution of gravity load permitted that all columns on each face were of equal size. The top of the tower is a two-story mechanical floor that provides a cap for the building. * Architectural facts The building’s tapered tube structure also responded to architectural objectives. The large interior spaces accommodate different uses; the deeper spaces from window to core at the lower floors were used for offices. The upper stories, with less distance from window wall to core, were used for apartments, where natural light and views are important The X-bracing, fully exposed on the facade, is the most prominent feature of the building, and in combination with the rectilinear pattern of the spandrels and columns, creates a striking geometry of appropriate scale and visual interest The John Hancock center is a good model where structural efficiency is aesthetically expressed. There is an obvious image of rigidity and stability, where all the members tie the entire structure to the ground. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 It also provides a great architectural presence in the urban surroundings. The building mass is balanced and the architectural expression is simple. This delicate balance of stability and lightness through the exposure of the structural system is what makes this tower so aesthetically unusual. (Fazlur Khan 1967, cited by CTBUH 1995a, p. 199) 3.2.2 Citicorp Building, New York City, by Hugh Stubbins, 1978 Structural engineer LeMesurier Consultants / (Hybrid system) Figure 3.3: Photograph of mega columns that support the 1st floor the Citicorp Building 150 feet above ground (Mierop 1995, p.120-121) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Citicorp’s building is a 60-story office building that rises to 915 ft (279m) in height and has an impressive appearance in mid-town Manhattan. The four comers of the 157ft (47.8m) square floor plan cantilever 76ft (23m), supported only by four exterior columns centered on each side of the building, that stand out for a height of 114ft (34.7m) at the base. The central core also supports the tower of 1.1 million ft2 (167.000m2). The site of the building is a full block of Manhattan, except for St. Peter’s Lutheran Church that is located in the comer of it • Structural facts The structural design was a consequence of an agreement that the owner made with the church, which agreed to sell its air rights, but would not allow any building column going through its amenities, so it required that a new church would be built from scratch. This made the architect elevate the 1s t floor of the building to 150ft (46m) from the street level. Citicorp building’s structure is a steel-framed braced tube with a system of columns and diagonals that are in compression, and transmit the gravity loads into four 5ft (1.5m) wide columns located at the center of each face. Thus, each facade acts like a giant triangular truss that collects about half of the gravity load and resists the entire wind load. The four facades together form a complete braced tube system. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 efficient to resist wind forces, shear and overturning moment. Below the first floor, a central concrete core is designed to resist wind shear. The main diagonals recur in 8-story modules, and there are no columns below the floor where each of these diagonals intersect, in order to reduce gravity loads in the comer columns, and allow for additional view (see figure 3.4). Horizontal tension ties restrain the compression diagonals at four-story intervals. There is a 29ft (8.8m) deep perimeter truss on top of each center column that transfers the gravity load of the first 7 floors to the columns. The core is a braced frame below the 10th floor, and a moment frames above it. However, uncomfortable lateral sway was predicted under high wind loads, and the solution was to use a tuned mass damper (TMD) near the top of the tower. The TMD includes a concrete block of 410 tons that slides in biaxial directions (north-south and east-west) regulated to counteract the oscillation of the building sway, reduce motion by the half, and act as a vibration absorber to increase the building’s energy dissipation. * Architectural facts All architectural concerns for the Citicorp Building were not as important as the structural ones, which, in this case, were the major focus due to the difficulty of the site and the restricted urban settings. This range of parameters limited the architectural design to fully develop. However, this building as become an outstanding icon of New York city’s skyline not only because of its diagonal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 roofline—slanted as if for a solar collector but not bearing one—but also because of the popular appeal of its 7-story atrium entered at street level and designed for leisurely shopping, eating, and browsing. <k to S5 L urtdtGoumtt -Me&vuss CkH O f 1 ^ ^ 1it?S ▼ feU M H e ik (£ . ^ MAPUl££ G*e 3fcfHr Conti le*e/' H O G £ > U lM M 0et? u J noo<.«uetep»Ar- & O M M S iMtet5«cr mail G D U lM M S Figure 3.4: Diagram of the structural system of the Citicorp building (adapted from Taranath 1997, p.488) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 3.2.3 Bank of China, Hong Kong, by I.M. Pei, 1988 (Braced space truss) The 77-story Bank of China is a great example of architectural geometry. The silhouette of the skyscraper is a simplified translation of the bamboo stalk, as the architect had declared. * Structural facts The building shape is generated from a cube - of 170 ft2 in plan (52m) - that rises from the ground to 1209 ft high (368 m); as the structure goes upward, the structure mass diminishes by a quadrant each time, until finally it reduces to a single triangular prism. The first quadrant is sliced at the 17th floor, the other ones at the 38th , and 51s t and 70th floors. The design provides big areas of clear glass with panoramic views to the harbor, and surrounding mountains. At the 25th floor, the center column stops and transfers load to the four columns by the space truss system, allowing for a clear span of 158 ft (48m) for the bank lobby. The structure of the tower is made of 8 vertical plane frames, four of which comprise diagonal cross bracing. From the top quadrant down, the loads are transferred out to four massive reinforced concrete comer columns. A fifth column goes from the top floor - through the center of the tower - down to the 25th floor, where it transfers the accumulated loads. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Transferring gravity loads to the corners of the building increases resistance to high winds and the interiors stay column-free. Figure 3.5: Perspective of the Bank of China Grace. 1990, p.188) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ^ 78 Lateral loads are carried down to the fourth story through the space truss and the corner columns; at this level, shear forces are transferred to interior core walls that continue to the foundation. Transverse trusses enclose the building at various levels and help convey the load to the comer columns. 4203 f t x tfo* -® j f lf io f O eU vA 3ft*- - - n * f U r V CoulM KS tX)M PoS«€ -25** floor (KvJretcaaod 5tt>PS^ uftO B i u f-fc) \ B c yffo 1 3 - 1*1 f l o o r Figure 3.6: Diagrams illustrating the Bank of China structural system (adapted from Taranath 1997, p.556) UiftiJbft Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 The diagonal, ties and columns are structural steel tubes filled with concrete. To achieve continuity, all truss members of the space frame and to act as a single unit • Architectural facts Keeping the purity of the geometry was a structural challenge; given that the primary load-resisting system - diagonal braces and comer columns - give the tower’s striking appearance. The Bank of China is an outstanding architectural example that looses all traditional connotations of fagade; it is as a pure and simple sculptural icon that grows in space. 3.2.4 Library Tower, Los Angeles, by Pei Cobb Freed and Partners, 1989 (Perimeter ductile tube with Chevron braced core) The library tower -also known as First Interstate World Center and US Bank building- is the tallest existing building in downtown Los Angeles, California, and in the entire U.S. west coast (CTBUH 1995a, p.282). Its 75 stories (1018 feet - 310 m high) allocate 1.4 million square feet of office space. It is a very tall building considering the fact that it is located near the San Andres fault, in seismic zone 4. Designing such a tall building in the most severe seismic zone represents a challenge for any architect and engineer. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Figure 3.7: Photograph of the Library Tower (AISC 2004, http://www.aisc.orgA * Structural facts The Library Tower’s structural system is a steel Dual System composed of a continuous 73 feet-10 inches (22.5m) square braced core that works together with a perimeter ductile moment resistant Frame. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 The core is a free spanning two-story Chevron brace configuration, and the perimeter frame is composed of columns placed at a radius of 15° from the center, allowing for a free 50 feet span between the core and the outer wall. This scheme concentrates the main gravity load path in the core corner columns, leaving the braces and the moment frames susceptible to all lateral loads. a. Sxtenof weiaea trame © . o C O CD CM CM < 0 C M CM Figure 3.8a: Floor plan of Library Tower (adapted from Taranath 1997, p.85) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 The dual system used in the Library Tower is a great example of the efficiency of a dual system: the core braces provide the desired stiffness to withstand wind loads, and the moment frame to provide the desired ductility able to dissipate seismic forces. ,-ti flo e ' AO* (jO fce , BtfA G L figure 3.8b: Diagrams illustrating the Library Tower structural system (adapted from Taranath 1997, p.84) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 The structure is designed to remain essentially elastic for an anticipated earthquake of 8.3 of magnitude on the Richter scale; the maximum calculated lateral deflection at the top in 100-year is 23 in. 3.2.5 Hotel de las Artes, Barcelona, by Skidmore, Owings and Merrill, 1992 (Diagonal braced tube in the form of mega portal frames) Figure 3.9: Photograph of Hotel de las Artes (http://www.structurae.net/en/photos/index.cfm7JSs4399) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 The Hotel de las Artes is the most outstanding element of a multiuse complex in Barcelona -Spain, which was completed in 1992 before the summer Olympic Games. The tower consists of luxury hotel-apartment units, commercial office space, retail, parking, and sport facilities. Figure 3.10: Illustration of the Hotel de las Artes showing architectural-structural form Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 * Structural facts The tower is 45-story tall (450 feet - 137m) and has a square footprint that is set up in a base of columns. Its most prominent characteristic is that its structural frame is pulled out 4.9 ft (1.5m) from the building and is fully exposed without any fireproofing. Lateral loads are resisted by the corners X-bracing, which are connected at three points along the height of the building to simulate a partial trussed-tube configuration that provides enough stability for this mid-height tower (Iyengar et al. 1993, cited by CTBUH 1995a, p.209). The peripheral exposed X- braced frames are arranged on a 4-story (39 feet - 12m) module, and they develop a full three-dimensional system that withstands wind and seismic lateral forces, as well as some of the building’s gravity load. The non-fire-proofed outer structure was analyzed using methods to determine the steel temperatures as well as the character and nature of a number of hypothetical design fire events. * Architectural facts The architectural form, expression and articulation of the tower come from the fundamental nature of the exposed structural steel frame showing the rough proportions of steel I-beams, columns, and built-up members, as well as bolded and welded connections and joints. The expression of all members and joints reflect appealing shadows that provoke contrasting views that transform during the day. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 From an architectural point of view, the clear articulation of the exterior structure was achieved by a simple, straightforward architectural composition that aims to express the inherent function of the structural frame. The Hotel de las Artes building represents an outstanding work merging architecture and structural engineering. The overview of these five extraordinary case studies has demonstrated the constant challenge that represents designing a building in actuality, when there is a constant urge to build skywards and technology makes it possible. The main challenge is the development of an inbuilt interaction between architectural and structural expression, which originates from the overall building from, skin, and skeleton. This blend of structural logic and architectural passion with the skin and visual imagery will always remain the essence of future tall buildings design. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 3.3 Parametric Prototype Analysis 3.3.1 Objective of parametric analysis From what has been discussed in the previous chapters, it is clear that there are many factors that are very important at the moment of selecting a braced frame configuration for a tall building, since the range of concerns vary from structural considerations to aesthetical and programmatic. However, these issues can be narrowed down to two critical variables from which a tall building’s structural performance can be measured: the amount of drift (in inches) at the top floor under the effect of lateral forces, and the weight of the structure (in pounds per square foot: psf). The goal when designing a tall building is to achieve efficient structural performance by minimizing the drift with the less amount of steel. These two considerations are valid for every tall building; other issues, like location, typology, use, or aesthetical and architectural needs, may be of different importance depending on each case. The drift has to be always controlled by code (0.5% of the height is the allowable drift at the top of the building) since movement at upper floors can cause human discomfort such as motion sickness. The weight of the structure is also a significant factor to consider since a reduction of steel weight means budget savings, being that the structural cost is around 30% of a building’s total cost, therefore, the heavier the building, the more expensive. In this chapter, a prototype building has been tested using a computer program called Multiframe 4D; and through this analysis, the drift and the weight of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 a hypothetical structure will be compared under a limited set of parameters. The objective of this analysis is to make comparative conclusions regarding the structural performance based on drift and weight of steel of one same building, tested with five different bracing types. The final intention is to find out which of the structural configurations performs better and under which circumstances. 3.3.2 Method of analysis 3.3.2.1 Type of analysis (Description of Multiframe 4D) This analysis will be performed using a computer aided structural design software called Multiframe 4D, where a hypothetical office building is tested under three different wind conditions, with 5 types of bracing configurations; the same tests are repeated with a taller building. The selection of the testing parameters will be discussed in paragraphs 3.3.2.2 and 3.3.2.3. Multiframe 4D is a fast and accurate program that allows creating structures, testing them under different load cases and examining the results. The program lets the user input almost every structural shape, and provides a library that simulates restraints, materials, member shapes, sizes, and loading conditions. Then, it models and analyses the proposed frames to determine the building’s structural response under different load scenarios. The test can be done statically (3D analysis) or dynamically (4D analysis); the difference between these two types is that 4D analysis includes the time factor. In this case, the program analyzes the structure Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 every 0.1 seconds, simulating dynamic forces and accelerations during strong winds and earthquakes; however, 4D analysis requires high computing power, inaccessible for the purpose of this thesis. The static analysis (3D) is accurate enough to perform the test of the hypothetical framed structure proposed in this research. (For more information about Multiframe 4D, see appendix C). 4~~ “1X000 20.000 2X000 30.000 3X000 C 000 -0 3 0 1 Q M O j sr y 9*00 01*0 -a 0390 -|>4* 0230 ■ 0 1 5 7 03*0 -0 0 T * 02*0 •74M 03*0 ■*p* < 3 M O -044* L 9.R0 -•39? . 0*40 •133* . 9*00 •'*94 O M O •2 9 4 0 0400 -9 'rr . 0430 •7400 . -9*40 -7 T 1 T 0440 •2300 0400 1 .1 0 * 0900 7301 9.730 * • V* 0740 -700* [t— « * l CED '6 .0 M i-" W 0. 000 0. 0 o .o o o “ o . c 0. 000 0. 0 ooocroc o : o o o o .o 0.000* 0.0 o :o o o ~ o .c o:oocfo.c M xkM xJFnqutncyl Ptriod H r I Mconds TBW------03551 3.405* 0.204 0.125 0.110 4 12.111' 0.083 5 : 15.0-18' 0.063 Figure 3.11: Screen shot o f Multi frame 4D (Daystar Software Inc. 2004) 33.2.2 Building typology The hypothetical building used for the analysis is a typical 30-stoiy, three-bay square plan office building, with a height from floor to ceiling of 14’. The reason of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 selected scheme is because a 30-story structure is considered tall enough to present critical issues under the effect of lateral loads; it is also a common height among tall buildings around the world (there are a lot more 30-story buildings than high-rises); and for Multiframe purposes, a frame that is taller than 30 stories is not manageable for 3D analysis. Member name (W flange size) — Lenght of member a * v i t a ? * r " 1 W ttaT t W IW O W 1M O Wl W ttaTS W ltalB WltaTC C > W lta T * ■ Perimeter column 90 f t a,d: outer columns b.c: inner columns Inner bay bracing Core column P A R A M E T R IC BUILDING F L O O R P L A N Figure 3.12: Floor plan of hypothetical building Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 The building’s floor plan is a square of 90’ x 90’, which is the most common dimension used in office spaces: a 30 feet span is an efficient structural bay size / column grid when planning a scheme, it is also the most profitable dimension for leasing benefits. In addition, bracing the inner bay prevents disrupting the usable office space. a d outer columns . b c r n e r columns 30 fl 3 0 tt 3011 (j Inner bay bracing Braced inner bay a.d: outer columns b.c inner columns P Lateral load applied to building m direction s h a v e d PARAMETRIC BUILDING CROSS^ECTION PARAMETRIC BUILDING PERSPECTION VIEW Figure 3.13: Hypothetical building cross-section and perspective view Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 To make additional structural conclusions based on building heights, a second hypothetical building was proposed for the analysis: a taller building (40-story) with the same floor plan configuration. 3 3 .2 3 Variables compared for the analysis In order to make an analysis that provides a quantitative number of results, and to formulate coherent conclusions, the prototype analysis in Multiframe 4D was performed with a limited number of variables. The variables chosen for the tests were as follows: - Two different heights of building (2), - Each height tested with 5 types of bracing configurations (2x5=10), - Three types of wind velocities with each bracing configuration and each building height (10x3=30), - Three instances of structural optimization for each case, (each optimization was done with the objective of getting the lightest structure possible that remained under the maximum drift required by code), (30x3=90 tests). • Building height The first prototype is a 420 ft high, 30-story building -with a floor-to-floor height of 14’-0” ; a second prototype was used only for matters of making a clear comparison of results between two different building heights. For this case -and to facilitate the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 testing procedure without having to repeat the process of inputting the structure into the software-, the floor-to-floor height from prototype #1 was increased up to 18’ to emulate the behavior of a taller building (even though this height to not commonly used in real life situations). Consequently, the second prototype is a 540 ft high, 40- story building -with a floor-to-floor height of 13’-6”. * Bracing configurations The inner bay of both prototypes is braced at each testing time with a different configuration. The purpose is to compare the structural behavior of each brace system under the same loading conditions -considering that some systems are stiffer than others. Five common bracing systems were chosen for the analysis: - A: Single diagonal concentrically braced frame (CBF), - B: Alternate diagonal CBF, - C: V-braced CBF, - D: Chevron braced frame eccentrically braced frame (EBF), - E: Single diagonal EBF (with two link beams). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 3 0 ft 3 0 ft 30ft CBF' \ / L > . CBF V-brac* 4 2 0 ft (!«£»•) o r 5 4 0 ft (2nd cm *) | ttJ* / t - r . 7 \ EBF 1 link BRACE DIMENSIONS FO R A BUILDING4 2 0 FT HIGH (LEFT). AND 540 F T HIGH (RIGHT) a.d: outer columns b.c: inner columns BRACING CONFIGURATIONS FOR INNER BAY OF PARAMETRIC BUILDING Figure 3.14: Bracing configuration for hypothetical building Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 • Wind speed Three wind speeds were selected for the study, 70 mph, 90 mph, and 110 mph, to evaluate the structural performance of the same brace configuration under different lateral load cases. These wind velocities represent three geographical areas in which the importance of the wind factor determines de design of structures required by the building code. In one side of the scope there are cities like Miami, where the wind velocity is high (110 mph), and on the other side, where wind is more moderate like in the city of Los Angeles (70 mph). US map of basic wind speeds in miles per hour kilometer equivalent: 70 90 1 1 0 mph — 113 km/h ( L o s A n g e l e s a r e a ) mph = 145 km/h ( M i n n e a p o l i s a r e a ) mph = 177 km/h ( M i a m i a r e a ) Figure 3.15: US map of basic wind speeds in miles per hour (UBC adapted by Schierle, 2002-2004) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 The stronger the wind pressure is, the stiffer the structure requires being, and for most of these cases the structure becomes heavier and more expensive. In all three case-scenarios, the building is simulated to be located in a city protected by other structures (exposure B); issue that is important at the time of calculating the wind pressure for each wind speed, as explained 3.3.3. Figure 3.16: Exposure of hypothetical building (Schierle. 2002-2004) * Structural optim ization The amount of structural steel required per floor area is an accurate way to determine the efficiency of steel structures; and, as it has been said before, the search for structural performance is one of the main goals when designing a tall building. The concept of optimization is creating the lightest structure possible that remains under the maximum allowable drift Hypothetical building exposure E x p o s u r e B Protected city building Exposed tall building Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 In the case of this thesis analysis, three structural optimizations were needed to come up with a suitable optimized structure, in which the test results were similar to real life numbers. The numbers to which the results are compared are from Fazlur Kahn graph “Premium for Height”. Fazlur Kahn was the greatest architectural engineer of the second half of the 20th century, and was mostly known by his revolutionary innovation in the design and construction of structural systems of tall buildings, such as the John Hancock Center and the Sears tower in Chicago. 70 o. c 3 for © o o c C3 w * D S f u > < 0 80 90 1 00 10 20 4 0 5 0 60 30 70 Number of stories Figure 3.17: Fazlur Kahn’s graph “Premium for height” (Ali 2001. p. 41) Kahn classifies in his graph the structural performance of tall buildings by relating the weight of the structure to its height, and to the amount of load carrying Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 (such as floor framing weight only; gravity load alone; gravity and lateral in a non optimized structure; and gravity and lateral load in an optimized one). To better explain this concept, Kahn said, “If an animal’s size is magnified several times and its bone structure is increased proportionately, it would crumble under its own weight unless the bones are stronger and harder.” (Ali 2001, p.41) Since the curves of this graphic represent an average, there are some factors that are not specified such as the design wind pressure (which affects directly on the building’s weight), or the height from floor-to-ceiling that determines the building height and the effects of lateral load. However, the information from this graphic is as real as possible to make comparative assumptions. The weight results (in pounds per square foot) from the analysis are input into this graphic to make a logical evaluation, as explained in 3.3.3. With all these variables, the resulting number of test performed in Multiframe 4D was initially 90 tests, but a supplementary optimization was necessary for the case of the taller hypothetical building under wind pressure of 110 mph; which added 5 more tests to the whole process, having at the end 95 tests executed (table 2). A complete "run" of the analysis that explains each step of the testing procedure is documented in the subsequent section. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 N u m b er o f t e s t s p e r o p tim ization W in d 7 0 m p h 4 2 0 f t 5 4 0 ft A S i n g le D ia g o n a l "8 2! A -l A-2 ft A l t e r n a t e D ia g o n a l 1 1 B -l B-2 C V -B ra c p • C U C*1 C*2 D EB F K n e e B ra c e c ; 3 O D -l 0 - 2 E EBP 2 L in k s Z O E -: E -2 f ;« r i.* / •■f«r 2 W in d 9 0 m p h ; W in d l l O m p h 4 2 0 f t 5 4 0 f t 4 2 0 f t 5 4 0 f t A -3 A-4 ✓ / A-5 A-6 B -3 B-4 / / B -5 B-6 - C -3 C*4 / C*5 C*6 r 0 - 3 D-4 / 0 - 5 0 - 6 n E -3 E -4 / E-S E -6 f 're s? 2.3) iics: 2 4,i i '2cst X.i,' (test 1 .6,' J C f « o c ✓ „ W W 7 0 m p h ; w i n d M n p l i ; W in d U O m p h 4 2 0 ft 5 4 0 ft 4 2 0 f t S 4 0 f t 4 2 0 f t 5 4 0 f t z ' A S i n g le D ia g o n a l " S « A - l .l A -2.1 / / A -3.1 A -4.1 / / A -5.1 A*6 1 < ft A l t e r n a t e D ia g o n a l 8*1.1 8*2.1 / s B -3 .1 B-4.1 8*5.1 8 - 6 1 r . C V -B ra c e c U C - l .l C -2.1 '/ C -3 .1 C -4.1 C -5.1 C -6 .1 D E B F K n e e B ra c e w 3 o .± 0 -1 .1 0 -2 .1 / 0 - 3 1 0 -4 .1 0*5.1 0 * 6 .1 - E EBF 2 L in k s o Z E - l . l 6*2.1 \ 6 -3 .1 6 -4 .1 6 -5 .1 6*6.1 ' 5 b s ? > y S 3 O to & x (test 2. S,' ffest 2.2', 'test 2.3) ,'tcs: 2 .2 ) (test 2.5) (test 2.4} W in d 7 0 m p h / / / W in d 9 0 m p h /• / W in d l l O m p h fS - 4 2 0 f t 5 4 0 f t 4 2 0 f t S 4 0 f t / / 4 2 0 f t 5 4 0 f t _ * * / / A S i n g le D ia g o n a l A -1.2 A -2.2 / s A -3 .2 A -4 .2 A -5.2 A -6.2 - f t A l t e r n a t e D io g o n a l Z i 5 8*1.2 8 -2 .2 / / B - 3 2 B -4.2 / / 8*5.2 8 * 6 .2 C V -B ra c e c Z C -1.2 C - 2 2 * C -3 .2 C -4 .2 / C -5 .2 C -6 .2 ft D E B F K n e e B ra c e 12 3 a *- 0 -1 .2 0 - 2 .2 i 0 - 3 .2 0 - 4 .2 s D -5.2 D -6 .2 r E EBF 2 L in k s O Z 6*1.2 6 * 2 .2 6*3.2 6 -4 .2 6*5.2 6 -6 .2 ft 5 / .s ✓ !> 3 5 dearbr a r s f 3 . ; ; f f r t f 3 .2 ; ( t* * s 3 3,1 fr e s f 3 2 ) i 3 5 } i'«V>C 3 4 ) i’fesf 3 * } * Table 2: Total number of tests performed in Multiframe 4D: 95 tests 3.3.3 Sample analysis The first thing done in the parametric analysis in Multiframe was to generate the geometry of the structure by assigning the number of bays and spacing, number of stories and floor-to-floor height, and number of frames. At this point, the structure is composed of columns and beams; additionally, joists can be added, as well as joints specifications and base restraints. The inner bay columns need to be rotated 90° to resist north-south load. Global distributed load of 3klf is applied to all horizontal members, number that comes from the formula below: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 Beam load: lOOpsf x 30’/1000 = 3 KLF, where: lOOpsf = 70psf of dead load + 30psf of live load (50psf at 40% of reduction factor) Braces need to be added after gravity load is allocated, to avoid load on braces; and to simulate pin joints of the braces, member releases are assigned to them. Horizontal, vertical and sloping members are specified with shapes and dimensions, according to the numerical design of beams, columns and braces (a more detailed explanation of this process will follow). Then, the structure is analyzed statically (3D analysis), and results such as moment, shear, and deflection can be plotted for the overall structure or for members alone. A complete description of these introductoiy steps of Multiframe 4D is included in appendix A. * Wind velocities and lateral loading For the first analyses (non-optimized structure for both building heights), an average wind pressure of 30 psf was used to design the ground floor of the prototypes, and to calculate the shear at the base of the structure and the overturning moment, to find out the column sizes at the base. The same wind pressure (30psf) was used to compute lateral load at all joints of one side of the frame, utilizing each joint’s tributary area, where: P (at joint) = 30psf x tributaiy area (of joint). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 ^Tributary area with 50%ofw*id .Tributary ’area with 25% of wind load D esig n g ro u n d flo o r 5 4 0 ' high 4 2 0 ' high building building IZZ| .Tributary area with 50% of wind load o CM x I f l S O t i CO O CM w |f . s c O ' ■ CO r - CM CM J ! O II V CM ; ® M X ; x IA 5 S : t o i a C O o > o 4 2 0 ' high building 5 4 0 ' high build in g D esig n 15th f lo o r 30' 30’ 14' or (18') T o r(90 15' 1 4 'or (18') 15’ T or (9') 30 ft 30 ft 30 ft a.d: outer columns b,c: inner columns ® © @ TRIBUTARY AREA OF JOINTS FOR LATERAL LOAD DESIGN Figure 3.18: Building cross-section that shows the dimensions used to designate lateral load at joints Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 As it can be seen in the figure 3.19, the outer column joints, and the top inner joints get half of the lateral load, and the top outer joints get a quarter of the load. For the rest of the analysis (optimization 1 and 2) the wind pressure (P) was calculated according to the wind speed, using the formula P = Qs x Ce x Cq x Iw, where: (see UBC coefficient tables 3) Qs= Stagnation pressure (Uniform Building Code [UBC] Table 16-F) Ce= Exposure coefficient (UBC table 16-G) Cq= Pressure coefficient (UBC table 16-H) Iw= Importance factor (1.15 for hospitals, police and fire stations; 1 for all other buildings) After the wind pressure (P) has been calculated for each wind speed, the lateral load applied to each joint was computed, using the formula: P(at joint) = 30psf x tributary area (of joint). All details and load calculations are included in the appendix section. The following building diagrams starting at page 104 show the amount of lateral load applied to each of the testing scenarios. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 WIND P R ESSU RE (P) COEFFICENT TABLES: P=Qs*Ce*Cq*l TABLE 16-F—WIND STAGNATION PRESSURE (<fc> AT STANDARD H B 6K T-O F33 FE E ^{1M 5« mm) Basic wind speed (mph)1 ( X 1.61 for km/h) / 70 \ f 90 \ 100 ( 110 \ 120 130 Pressure * (psf) (* 0.0479 for kN/m2 ) 126 f 16.4 20.8 125.6 \ 31 J O 36.9 43.3 'Wind speed 6cm Section 1615. Stagnation pressure for each wind velocity (Qs) TABLE 16-G—COMBINED HEIGHT, EXPOSURE AND GUST FACTOR COEFFICIENT (C ^)1 HEIGHT ABOVE A V E R A Q E U E V B . O F an in—w ntw otw nu— g C T C 8 U R E D i EXPO SUREC ! EXPOSURE B x 3 M .B fo rm a 0-15 139 1.06 0.62 20 1.45 1.13 037 25 130 1.19 0.72 30 134 123 | tt76 40 132 iJ n 1 a8 4 60 1.73 1.43 { 0.95 80 131 133 1 1.04 100 138 131 1.13 120 1.93 1.67 120 160 232 1.79 131 200 2.10 137 1.42 300 223 205 133 400 234 219 130 1 Vtlocs for inlernjcdisle heights above 15 feet (4572 mm) may be intcipolned. TABLE 16-H— PRESSURE COEFFICIENTS (Q,) S T R U C T U R E OR P A R T T H E R E O F P C 8 C W F H C B I Q, F A C T O R I. Primary frames and systems w Wlfxfw3t^ ^ l p Leew3fd M ethod 1 (Normal force method) W alls: W indward waH Leeward wall Roofs1 : W ind perpendicular to rxlge Leeward roof o r flat roof W indward roof less than 2*12 (16.7%) Slope 2:12 (16.7% ) to less than 9:12 (73%) Slope 9:12 (75%) to 12:12 (100%) 0 3 inward 0 3 outward 0 .7 outward 0.7 outward 0.9 outward o r 0 3 inward 0.4 inward 0.7 inward t l M ethod 2 (Projected area method) On vertical projected area Structures 40 feet (12192 mm) o r less in height Structures over 40 feet (12 192 mm) in height On horizontal projected area1 13 horizontal any direction 1.4 horizontal any direction 0.7 upward Design for wind load P = q1CeCqIw P ■ wind pressure ia psf (pounds / ft1 ) q, - Stagnation pressure (UBC Table 16-F) C# * exposure / gust factor (UBC Table 16-G) C„ factors change over building height C , - pressure coefficient (UBC Table 16-H) 1. * Imponaace factor (1.15 for hospitals, police and fire stations. I for all other buildings). UBC Table 16-G: Expos ere B: building ia cities protected by other structures. Exposare C: building la open areas exposed to wind, unprotected. Exposare D: building near ocean o r large bodies o f water. Exposure factor coefficient depending on floor height (Ce) Pressure coefficient for method 2 (on verti cal pro jected area) (Cq) UBC Table 16-H: M ethod ! shall be used for gabled structures and may be used for all other structures. Method 2 Used for stability o f structwes < 200 ft high. Table 3: Wind pressure coefficient tables (UBC adapted by Schierle. 2002-2004) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 t.-ooc-)i- - - - V i . . ~ 5 — ,: V ~ ~ a: 1 0 S O O 1 ^ IB M 0‘ ) » * « = • * ) [ • * — IO M o V - U M O") " « • T»-V - • wV - o o o o ^ j - *»T ,-U 3 V . Jmmrnmkma ‘3 *0 0 0 7 * <000^ -« . .. • o o o ^ j - .-4- sx * V --- s j o o ^ I ---- 3 J 0 C - ^ « - - - » " i ' « « * 7 — S M * V - >"4 ■ = * > » > ‘ n »3j- • :«4 • - t . . ^ _ . ^y. Inner columns Outer columns ® 4 20 ft high Inner columns Outer columns ( 2 ) 540 ft high Lateral load applied on joints in the case of a wind speed of 70 mph, in two hypothetical building of 420 ft and of 540 ft high Figure 3.19: Diagrams of lateral wind load applied to hypothetical building for wind of 70 mph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 3 3 J __3 ____ 3 3 3 Inner columns : 3 3 •-*— - x .. N ----- 3 - i r * --- - - ~ - - T - S - . * i--- u t 4 : ... / Outer columns ( T ) 420 ft high Inner columns Outer columns (2 ) 540 ft high Lateral load applied on joints in the case of a wind speed of 90 mph, in two hypothetical building of 420 ft and of 540 ft high Figure 3.20: Diagrams of lateral wind load applied to hypothetical building for wind of 90 mph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Inner columns Outer columns 420 ft high Inner columns Outer columns ( 2 ) 540 ft high Lateral load applied on joints in the case of a wind speed of 110 mph, in two hypothetical building of 420 ft and of 540 ft high Figure 3.21: Diagrams of lateral wind load applied to hypothetical building for wind of 110 mph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 * Structural members design criteria (member shapes and sizing) All testing cases use the same size of beam and joists. The beam design was as follows: M= WL2 / 8= 3KLF x (30)2 / 8 = 337.5 K’ Section Modulus: S = M / Fb = 337.5 x 12 / 30 = 135.2 in3 Use: wl8 x 76 (Sy,^,,. = 146 in.3>135.2) *Bending stress (Fb) = 60% (safety factor) of Fy =50 ksi The columns and braces were designed separately depending on each case’s wind and height conditions. Wind design (K L = 1 4 ‘) Avara9* w in d p ra s s u ra fo r 7 0 m p h : 2 3 .5 8 p sr C olum n L oad 9 0 p s f* 3 0 /1 0 0 0 = 2 .7 Klf B eam L oad lO O psf*3 0 /1 0 0 0 = 3 KIT B a s a S tta a rV a 23-5S p*f*45f*413/100< - 3 8 2 3 K OTM = 4 3 8 .6 * 2 1 3 3 = 9 3 .5 6 3 .0 2 1C U niform B ra ce L oad= 120 psf*30V 1000 3 .6 K 1 S T M f l o o r d e s ig n S a fa S h a a r V a 23.S8p*f*4Sf * 2 0 3 /1 0 0 OTH = 2 1 5 .4 * 1 0 8 .5 = B e a m d e s ig n Me W L 2 /B - 3 k tf* ( 3 0 )2 /B 3 3 7 5 K S ection m o d u lu s S = M /fa 3 3 8 x l2 V 3 0 1 3 5 .2 in 3 (ell. 1 46 in 3 J U s e : w rl8x76 1 flo o r d e s ig n = L a '. - r ': 3 C PG *cv = \W A S u m P U se = > 4ll. Vi. P K» a + d (ow tar) 0 1 2 1 5 3 2 1 5 WI4X176 1 3 2 5 > 1 2 1 5 1 4 ' b<+< (in n e r) 3 1 1 8 .7 7 2-430 5 5 4 6 .7 7 W14X730 5 6 7 7 > 5 5 4 8 1 4 ' Diag. B race 2 2 2 .9 1 1 9 3 4 1 .9 W14X99 3 5 9 > 3 4 i 33* V -Braca 2 9 9 .7 3 8 .8 3 3 8 .5 W14X82 3 7 2 > 3 3 8 20* Kh m B raca 3 2 0 . S 3 0 .6 3 5 1 .1 W14X82 3 7 2 > 3 5 1 19’ EBF 2 lin k s 2 5 S 6 4 3 1 9 W14X74 3 3 7 > 3 1 9 25* 1 5 t h flo o r d e s ig n P L a t= M /3 0 f P G 'e v = NW A S u m P U se » fill. Vi. P K - a * d (o u te r) 0 1 2 1 5 1 2 1 5 W14X176 1 3 2 5 > 1 2 1 5 14* b-4 *c (in n e r) 779.04 2 4 3 0 3 2 0 9 .0 4 W14X426 3 2 S l> 3 2 0 9 14* D iag. B race 1 0 9 .5 1 1 9 2 2 8 .5 W14X90 3 2 5 > 2 2 8 .5 33* V -Braca 1 4 7 .2 3 8 .8 1 8 6 W14K61 2 7 2 > 1 8 6 20* K nee B race 1 5 7 .4 3 0 .6 1 8 8 W14X61 2 7 2 > 1 8 3 19* EBF 2 lin k s 1 2 5 .2 6 4 1 8 9 .2 W14X61 1 9 3 > 1 8 9 .2 25* Table 4: Wind design procedure to allocate sizes of members in each wind case Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 For their selection, the ground floor and 15 floor members where first designed, and then gradually reduced eveiy certain number of floors (depending on the case). All vertical and sloping members were W14 shapes and all horizontal members were W18 shapes. One example of this procedure is showed in Table 4, for the case of the optimization 1, building height of 420’, and 70 mph wind speed (all other calculation of member sizes can be found in the appendix B). The following building sections show the sizes of all column and braces sections used for each testing case. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 a D 4 4 I W 1 4 a1 2 0 1 • W I 4.J4 2 1 W M * 1 2 0 » • W 1 4 a 3 4 2 1 W 1 *t3 0 1 • W M O C ! W 1 4T I 2 0 W 1 4 O 7 0 1 W 14rt2 0 1 * W 1 4 . 3 7 0 1 W 1 4 rt2 0 f • W M O 7 0 1 W 1 4 i1 3 2 f * W 1 4 .3 W I WlAdS [ * wt4 C«e 1 W 1 4 ri3 2 t * W 1 4 < 3 9 Q I W 1 * 1 32 r • W M M 2 6 1 W M i1 3 2 t * W 1 4 * 4 2 9 \ W M et 3 2 t ♦ W 1 4 * 4 2 9 I W 1 4 iM 5 W t 4 * 4 5 5 I W M k M S t * wi4 * < 5 5 I W 1 *rt4 5 W M M S S i W 1 4 * 1 4 5 I ' W 1 4 * 5 0 0 I W M v M S t * W 1 4 « 5 0 0 l W M * 1 4 6 \ • W 1 4 * 5 0 0 1 W 1 4 * 1 5 8 t • W I4 ^0 1 W M riS O f ♦ W 1 4 * 3 5 0 1 vm nn r • W 1 4 « 5 5 0 1 W 1 A1 5 8 t • W M * 4 0 5 1 W 1 4 * 1 5 8 W M * 9 0 S 1 W 1 4 H S 8 | * W 1 4 * 9 0 5 1 W t4rt? 8 | * W M * « « 5 1 W M rtT B f • W 1 4 * 9 «S 1 W 1 4 * 1 7 9 r • W 1 4 * 9 9 5 1 W M rfT e \ • W t4 > 7 3 0 I W 1 * 1 79 W 1 4 « 7 3 0 f * W M * 1 7 8 W 1 4 . 7 3 0 > S 5 ? d 4 a b 4 4 I W 1 * 1 2 D r w t 4 i 3 » e 1 ' * r W M * 1 2 0 \ • W 1 4 0 0 9 t W 1 4 K 1 2 0 f • 1 W 1 4 * 3 8 9 1 W 1 * 1 2 0 r • 1 W 1 4 M 2 9 I W t * 1 2 0 | • [ W 1 M » 1 W M H 2 0 f * 1 W M * 4 2 6 1 W 1 4 k 1 3 2 t • 1 W 1 4 M S 6 * t 1 W 1 4 H 3 2 f • 1 W t 4 * 4 5 5 • 1 1 W 1 * r i 3 2 r • W 1 4 * 4 5 5 1 W M r t 3 2 f * i W 1 4 * 5 0 0 • r I W M * 1 3 2 f * 1 W 1 4 * 5 0 C 1 W 1 * 1 3 2 f * W 1 4 * 5 0 0 1 W 1 4 r t 4 S t * 1 W M i S S O 1 W t t r t 4 5 r • W M i S S O 1 V l r t * r t 4 5 I W t 4 i 5 5 0 • f i W 1 4 * 1 4 6 r • I W 1 4 4 0 5 * T 1 W t f e M S r • 1 W 1 4 4 0 S 1 W t 4 r t 4 S t • 1 W 1 4 t9 0 5 • t 1 V f f t r l S B f ' 1 W 1 4 ( 9 0 5 • \ ! v m r t s o t • W M a 9 0 S 1 W W t t f • 1 W 1 4 i 6 0 5 * f I W 1 * 1 S » t * 1 W 1 * < 9 6 5 I W 1 * 1 3 0 t * W 1 4 * 9 6 5 1 W M r t S I r • i W 1 4 ( 9 9 S * f 1 W t 4 * l 7 8 r • 1 W 1 4 * 9 9 5 • T 1 W W I 7 9 J * t W 1 4 4 6 5 1 W 1 4 T 1 7 9 t • 1 W 1 4 a 9 4 5 ♦ 1 1 W 1 M 7 I 1 * 1 W M i 7 3 0 • 1 1 W 1 * 1 7 8 1 W 1 4 * 7 3 0 t * * w u r t T e W M » 7 3 0 V » > c 4 d 4 ( J ) 420 ft high 540 ft high at d : o u te r c o lu m n s b .c : in n e r c o lu m n s Vertical members sizes (outer and inner columns) for non-optimized structure testing cases, in two hypothetical buildings of 420 ft and 540 ft high Figure 3.22: Vertical member sizes for non-optimized structure cases tested at 70mph. 90pmh. and 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 a b c d a b * * * i • *1*00 f *1* 23 3 i • *1400 f ' • ! * 1 4 ( 2 0 3 I W M 0 O » • *t*233 1 W M 0 O f ■ 1 * 1 4 ( 3 1 1 * f f *1*00 « n L ’ f • 1 * 1 4 a 3 5 7 *1*3 57 1 *1400 I • *1400 t * 1 * 1 4 ( 3 1 1 t *1*34 2 I *7400 ► • 1 *14 i2t3 1 *1400 f * *1*3 43 * f 1 *1*00 t I W 1 4 C 0 3 f 1 *1440 t * 1 * 1 4 ( 3 7 0 1 *1*100 > 1 W J 4 0 1 5 1 * 1 4 ( 1 0 0 ] • 1 * 1 4 O ? 0 I * 1 4 * 1 0 0 f • *1 * 3 11 1 * 1 4 ( 1 0 0 | * I *1*30 0 1 * 1 4 * 1 0 0 w i » » • ! *1 *3 43 • I * 1 4 ( 3 4 2 t 1 * 1 4 ( 1 0 0 1 • *14000 f * * 1 4 ( 3 0 0 1 *1*429 1 W 1 * t 2 0 ♦ • 1 *140 70 • f 1 * 1 4 ( 1 3 0 f * * 1 4 ( 4 3 0 I *1 4( 12 0 t • I *14070 • r *1 *3 00 t 1 W 1 4 > 1 3 0 f ‘ 1 *1*405 1 *1*120 i • 1 * 1 4 ( 1 2 0 t * 1 *1*455 I *1*120 1 *1*305 • t 1 * 1 4 ( 1 2 0 r • *1*500 1 W 1 4 r t 3 2 ♦ 1 * 1 4 .4 2 * 1 * 1 4 ( 1 3 2 r • I *14400 1 * 1 4 * 1 3 2 » • *14 *0 0 I * 1 4 ( 1 3 2 r * * 1 4 ( 5 0 0 I * 1 4 * 1 3 2 I I *1*45 8 i * 1 4 r t 3 2 r • 1 *1*900 1 *1*132 *1*455 i * 1 4 r t 3 2 1 * 1 4 ( 5 5 0 I * 1 4 * 1 4 5 ♦ i * 1 4 ( 9 0 0 1 W 1 4 T M S t * I *14600 ‘ f W 1 4 0 0 5 * r 1 * 1 4 (1 4 0 1 * 1 4 ( 5 0 0 1 * 1 4 ( 1 4 5 r * I *1*145 1 * ! * 1 4 ( 3 9 0 • I W 1 4 ( S S 0 * t i *14045 r * 1 *1*005 * t 1 *1*145 I * 1 4 ( 1 4 5 t * 1 * 1 4 ( 0 0 5 * t t *1*190 I *140 60 1 W 1 * 1 5 0 t * 1 *1* 00 8 * f W 1 4 1 8 0 f • 1 *1*0 05 f *1*190 1 ‘ I * 1 4 ( 0 0 5 1 * 1 4 * 1 9 0 t 1 * 1 4 ( 0 0 9 f 1 * 1 4 ( 1 9 0 [ * 1 * 1 4 ( 0 0 5 1 *1*190 f 1 * 1 4 ( 0 0 5 t *14090 f * 1 W 1 4 « 0 9 5 I * 1 4 * 1 7 0 f I *1*005 I * 1 4 ( 1 7 9 r * *1*7 30 I *1*175 f * i *1 *0 05 1 * 1 4 ( 1 7 9 t * *1*730 ‘ I *1*730 ’ I *1*730 I *1*175 f ‘ *1*175 W f > i *1*7 30 *1*730 5 1 *1*179 t ‘ * 1 4ri 79 > c d 'i' a b e d 'l' ■4' '!> ' 'I' *1440 ! t W W d l 1 W M d * W M d l ! *1*1 00 i WttrlOO I WMrtOO I * 1 * 1 0 0 t *1*13 0 I *1*130 I *1*13 0 I *1*130 I *1*133 ! *1*1£ I *1*133 I *1*13 3 I *14*45 t *1*14$ I *1*145 I *1*145 I * 1 4 * 1 9 0 I *1*190 t *1*170 I *1*170 I *1*170 f * 1 4 0 4 2 * 1 4 0 4 3 I * 1 * 3 4 3 • 1 * 1 4 0 7 0 * 1 4 0 7 0 * 1 * 1 4 0 7 0 • ! * 1 4 0 * 0 I • I * 1 4 0 0 0 ‘ 1 • V 1 4 » 4 S 9 I * 1 4 * 4 3 0 I * 1 4 * 4 3 0 • ! * 1 4 * 4 5 6 • I * 1 4 * 4 5 5 • T *14*55 • I * 1 4 * 5 0 0 I *14000 W1*J90 • ! *140 50 I *14090 ’ t *14005 • 1 *14005 • I • r *14005 ■ t *1*730 ' T *1*730 I • Wind 70 mph •W in d 90 mph Wind 110 mph (D 420 ft high j Optimization #1 \ a.d: outer columns b.c: inner columns Vertical members sizes (outer and inner columns) for structural optimization #1 testing case, for three wind velocities figure 3.23: Vertical member sizes for structural optimization #1 for a building of 420 feet high, at 70mph, 90pmh, and 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill a b c d a b 4 4 4 ” 4 - » * . t i W M 4 0 t • 1 W 1 4 * 3 7 0 * T I W M M f * W M M 1 W M d O J • i W 1 4 0 M ♦ t 1 W M M | * W 1 4 C M * f 1 W M M 1 * 1 W 1 4 0 * * • T 1 W M M t * 1 W 1 4 M M * f 1 W M M I * 1 W 1 4 . 4 M 1 W 1 « M f * 1 A 1 4 m C C 1 W M M r - W 1 4 * 4 » 1 W M M r * W 1 4 M S 5 1 W M M t • 1 W 1 4 M 9 S • t I W M M r • V V 1 4 M S S 1 W M 1 0 * } ♦ 1 W 1 4 M S S ♦ 1 I W M r t O * 7 * W 1 4 4 0 0 j W M r t O * f ’ 1 W M . 4 5 6 • r 1 W M r t O * t * W 1 4 S M 1 W M r t O * t * 1 W M 4 S 0 * t 1 W M r t O * t * v V V b S S O 1 W M r t O * \ * 1 W M M * 1 1 W M r t O * 1 • W 1 4 * S 5 0 1 W M r t 2 0 1 • W 1 4 a 5 0 0 1 W M r t 2 0 f * A 1 4 * 0 5 0 1 W M r t 2 0 f * W M « Q I W M r Q O » • W 1 4 4 0 S 1 W M r t » J * I W M 4 H 1 W M 1 2 D t * W 1 4 4 0 S 1 W M r t s o f * W M M * T 1 W M r t 2 0 1 • W 1 4 * 4 0 5 1 W M r t f i 1 ‘ 1 W M M * t 1 W M r t f i f • W 1 4 4 0 S 1 W M r t f i { * 1 W M O O S * t I W M r t f i t • W 1 4 * 4 4 5 1 W M r t f i 1 • W M r t f i 1 W M 4 0 5 • r W M 4 0 S I W M r t f i 1 ' W M r t f i W 1 4 4 D W M 4 * 5 W M r t O * 1 • W M M j * W M 4 0 5 • I W M 4 0 5 * j i W M M t • W M M W 1 4 4 * 5 v V 1 4 4 4 5 WM M | * W 1 4 M S T I W M M W M M * W M r t 4 S j * l W M 4 C S I W M M W 1 4 4 0 S W M r t t t f * W M 4 * 5 f 1 W M r t S * W 1 4 4 * 5 *M 19» | * I W 1 4 M S Wtim W 1 4 4 M W M M | * W 1 4 M 9 [ 1 W M r t S W M . 7 X W M r t V 1 ‘ W M r t M | * tvi4.no r W M n o 1 ! W M r t O * r • W M r t T I wt4*no wv4.no W M r t T I | * W T 4 * 7 3 0 [ I W M r l T * W 1 4 . 7 3 0 W M r t W f ' W M r t T I W 1 4 . 7 3 0 1 W 1 4 * 7 3 0 1 W M r t T * t ' W M r t T * ww.no W 1 4 . 7 3 0 • b e d 4' 4- a b e d 4 4* 4 4- ! ' W M 0 O W M d » ! W M r i O t ! W 1 4 r t O » w u tts o t w moo i W M r 1 2 0 I W M r t 3 2 I W M r t S t W M r f 3 2 I v n « i r i WMM I w m m s I W M M I W M M ! M M r t S * * m to* [ W M r t O * I W M r t O * [ W M r t T * I w m i t * l w i* m t • i wm* 4 M 1 W 1 M S S • ? • t ww*seo ' ! W 1 4 * 5 0 0 I A M 4 50 ' i W 1 4 4 5 0 • I W 1 4 4 K I W 1 4 4 0 S ‘ t W 1 4 4 0 S • r W I M K I W 1 4 * 4 4 5 W 1 4 . 7 3 0 • r wi4.no W 1 4 » 7 X Wt4.n0 ' I wi4.no w i4 .n o I uvmtx • I wi4.no W 1 4 . 7 3 0 • i V V 1 4 . 7 3 0 • J vvi4.no • Wind 70 mph ►W ind 90 mph Wind 110 mph 540 ft high Optim ization #7 j a.d: outer columns b,c: inner columns Vertical members sizes (outer and inner columns) for structural optimization #1 testing case, for three wind velocities Figure 3.24: Vertical member sizes for structural optimization #1 for a building of 540 feet high, at 70mph, 90pmh, and 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 a b e d 4' 'I' 4' ■ 4' I ‘ ! WIM1 W M3 I WM63 I W M fi I wwt t wm t t i [ i WMi74 I W M C t W M 4 2 I I [ W M Q O I W M rtS I W M t t I W M rtS ■ I W M b 1 4 S I W ttrt4S I W M rt* I WMriTS t wwn m -> W14rtl r W14M i W 1 *N I W trt74 r W14.74 ! W 1 4 . 4 3 I WMrtT r WMrtO I W M r tO WMrtfr I WM(10» t W 14(100 ! W14a130 ! WHitM i WMtMS I W 1*M 5 1 W I 4 it« 3 I w t 4 » m l W14CS7 ! W M C97 1 W 1 « £ 4 2 t W 14043 1 WMMM t W M p 4 » I W M rttt r W M 4S0 ! W 14(730 I W 1*730 < D • W i n d 7 0 m p h • W i n d 9 0 m p h • W i n d 1 1 0 m p h 420 ft high 540 ft high i a 4- I ' wt4rto WMrtO I • • i w i4 r to w i* n o » t • • t W14rt0 WUrtOO I W14rt0 WMrt32 t W14R1S I WttrtSO i WMrtM ! W 1 4 0 1 1 ' t W M C 1 1 I VTMW b e d * 4 ' 4^ ^ WMrtO WI4rtO WMrtO I • WMrtO WMrtO I W l4rt» W14rt* I W M rt* [ • WMrtO I ' W14rt0 I WMrtO \ W 14(t00 WMi 100 f * W 14(130 1 • WMO30 W I4.1K r * W1*1K WMtMS I ' W14(tS0 W 1 4 I 3 4 2 f W 1 4 4 5 0 I W M dSO I W M M I r W M M I W M M * 1 W **730 * ? W Mrfao * I W * k 7 3 0 • W i n d 1 1 0 m p h 540 f t high O ptim ization #2 a,d: outer columns b.c: inner columns Vertical members sizes (outer and inner columns) for structural optimization #2 testing case, for three wind velocities Figure 3.25: Vertical member sizes for structural optimization #2 of two building height (420’ and 540’), at 70mph, 90pmh, and 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 A/B "““ Si WVUtt^ \ "“•S. ■ v w ’ *«si "’ " ‘ V . \ *"-«v . \ **«, . . •""•m . \ W M r t J Q ^ ; C D S S .......................... • m*6Wt«ei W tM IW M I \ ~ / ..................../ \ “ W 1 M W 1 M 1 W 1 * 0 1 V V 1 4 i « 1 ‘ x ~ / ..................../ \ “ W M C W M 0 1 W M 4 I W 1 4 4 1 ' x ~ / ° .........................../p\ “ wi««wi«0i wi*eiwi4t«i s " / 9 ..................../ \ ” W 1 4 4 W 1 4 6 1 W M I 1 W M 4 1 \ ~ S ................................................ / \ ” W 1 * 8 W t 4 r t 1 W T 4r tim « ei \ “ / ..................“/"V W M t f M T U M M 4 M W M 4 * \ “ /” ..................../ \ “ nmewMM wiMtwiygi ..................../"S" wn *6wt*aa w i 4 4 a w t 4 « M t\ “ / ; ..................../■% " W M M IM B W 1 4 4 8 m * 6 S ‘ \ ~ / ’ ..................../° \“ m «6 W M < 8 wi4 « m wi4 « m \ ” /=..................../ \ “ W 1 4 r t W M 4 t W M N W M M “ / ........................A ” W 1 « 7 W V f e 7 4 W M » 7 4 W 1 4 a ? 4 \ ” / ° ..................../%" W 1 4 1 7 W 1 4 B 7 4 W 1* 7 4* t« 74 ‘ \ “ / ’ ’ /p\ “ m*7Wt*74 W 1 4 « 7 4 W 1 * 7 4 / \ " W > 4 l 7 W 1 4 r f 4 W t 4 > 7 4 W 1 4 i 7 4 \ - '/ p ..................../ \ “ W 1 * 7 W * * 7 4 W t * 7 4 W 1 * 7 4 \ ~ f ..................../ \ ” W I * 7 W t 4 i 7 4 W 1 * ? 4 W 1 4 . 7 4 .................."/V ” t tM SW M C W M « W 1 4 « ] \ ~ /> ..................../*%" W M « W 1 4 t f 3 W 1 4 * J W M 43 ................... *1*0*1442 W 1 4 4 2 W t 4 4 2 ° \ ” S .....................................* ” / , \ “ *1*0*1442 W M 4 2 W 1 4 4 : / \ ” W 1 * S M f t * « 2 W M C W M B \ /°\" W M W 1 M 2 vn*«wnM3 < \ “ / - • • . • - • v \ - W 1 « 9 W 1 4 d O W 1 4 4 0 W 1 4 4 0 . W M M W 4« W M 4 0 W M M \ ~ / 0 ........................A ” W t 4 r f w t 4 r f 0 * 1 4 4 0 * 1 4 4 0 \ ~ / / \ " WMMm« W 1 4 4 0 W M 4 0 s* '/’ ................... *144*1440 % W 1 4 4 0 * I4 4 0 • ‘ ‘ ‘ • * • • *M9*i*90 % - .. . . ^ p . . . WMt * % * e i *M41 wi 4» ei • *° / • • • w m t W M1 • • - • WMtt W 1 4 4 » A 1' W I 4 ( B WUA . .o . . W 1 4 6 B W I 4 6 6 . . *1*74 • * • • *1*74 ’ / ” ' • *1*74 . . O . . . . . y W 1 * 7 4 ‘ A ” • ‘ *1*74 W 1 4 7 4 . . . . WMfi . .„ ^ p . . . W 1 4 4 C WI4S WW « ' ’ • wi*42 ,WU 4S W 1 4 9 0 W M 4 0 W M M W M M • • i - *1*S0 . .0 ~ . . . • Wind 70 m ph • Wind 90 m ph • Wind 110 m ph (J) 4 2 0 ft high Non-optimized structure Sloping members sizes for non optimized structure, for three wind velocities Figure 3.26: Sloping members sizes for non-optimized structure, for the 420 feet tall prototype, at 70mph, 90pmh, 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 A/B v • W 1 4 « S 0 V W M d » „ V ' w i* * , V W 1 4 r i 0 „ V WMtft. \ wi4rioe, s v. ” • wi4»ioe, W 1 4 * * J B \ ’ W t 4 « 1 0 » . V ' W 1 4 c t 2 0 . S ' W t4rt2D , S ° Wl * 12 0, V W M r t S ^ . . W 1 * 1 3 2 . V * ' . W * 4 r 1 4 S W * * 1 4 5 . V “ W 1 * t U £ \ ^v m rt < 5 . W M M 1M S ~ / W 1 4 W M 0 1 S '1 / W W M * « 1 \ * V W t 4 4 t f 1 4 « 1 \ ” V W 1 * e W 1 * < 1 \ * V S ” V S ~ / W lW flh W \ * V • S *V W M W M tt \ * V ’ \ m S W M M 1 4 M . W I * W I * 7 < • \ * V W 1 « W 1 « T 4 \ * V ' W 1 4 r i f V 1 4 r f 4 ■ \ * V W M M TU 04 S ~ / W 1 * M r t « 7 4 S'*/’ 1 S *V W 1 4 M W M f f i A ” / M T M M T M £ 2 S ” V ' wMumtt ■ ■ \*v ■ ' S ” V • \ * V • wt**mrtO ■ 1 W M M M 0 ) ’ S *V ' S ” V W t 4 t f * 1 4 4 0 W " *fr • Wind 70 m ph • Wind 90 m ph • Wind 110 m ph • V V ' W 1 M W M 4 1 ’ V S ” ' W l 4 a < W M « 6 1 / S ” ■ “ / V ■ Wt t*V1*ei . v v . w w vm ei • V S ” ' W t M IV M I . v v • V V V S ” r * M W i 4 * V S ” ■ V S ” • W t t r i W t f a Q S V S ” ■ V S ” ■ W 14ritf1*74 . v v - W 14aW M i74 ’ V S ” • W 1 « » W t 4 * 7 4 ■ V S ” • W 1 4 i W 1 4 * 7 4 ’ V S ” ‘ wt*a*t*74 • V S ” • W t 4 n W t 4 « 7 4 ’ ” / S ” ’ W M M T M C 2 . v v - . v v . W n * 4 W W 2 V S ” V S ” V S ” • W 1 4 4 W M C V S ” • W 1 M W 1 4 K V S ” V S ” • W M W M S C V S ” • w u d w m sc V S ” • W l A d W M r t C V S ” • W 1 4 d W I * K 540 ft high Non-optimized structure • v W M t l •” V W 1 « « t •“ V vm«t •“ v W 14*1 .O y j . W 1461 ” V Wt4«81 •” V W 1448 ” V tiiuun •” v W M M •” V W14rt8 ” V W t * 6 8 “ V W14*74 •” a W t* 7 4 -” V W t«(74 •” A Wt4>74 •“ V W 1 * 7 4 •v W 1 4 b 7 4 •” V W Mtt V VV1442 “ V WMfi •“ V a m : ” a A •” V W 1 4 4 0 • “ A • ” V AMO “ V W 1 * 9 0 ” V W 1 4 t f 0 “ A W M S C Sloping members sizes for non optimized structure, for three wind velocities Figure 3.27: Sloping members sizes for non-optimized structure, for the 540 feet tall prototype, at 70mph, 90pmh, 1 lOmph wind speeds Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 A/B . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . A " . „ * ~ s > : W 1 4 « W 1 « H Vttw W 1 M 7 4 • Wind 70 mph (D 420 ft high O ptim ization #7 and #2 A . c v B . c v C . e w D . w E . c v DMUMl M m M V. 1 1M 2 M l M W OM|*WI Sloping members sizes for structural optimizations 1 &2, for wind velocity of 70 mph and building height of 420ft Figure 3-28: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 420 feet tall prototype, at 70 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 A/B C \ ..................^ s- w h m w h e o \ ...............s. “ W 1 4 ^ U W I M W M H } ^ ....................< \ ~ 7 ’ W lh lW lf cC • 4 T ^ s ~ / p V T M A ^ . W I M W I M t c \ ” / ] w uA v, vnwwnwB • < T ^ .................... W 1 4 * * . W V M M T M ^ e \ ~ /* W M B i . W M d W 1 4 A ....................\ ~ S’ V K M i I C . W M A V M O s ........................< \ ~ y ’ W 1 4 . 7 4 . W 1 4 6 M T 1 4 S 3 ..................N “ 7 W M lf C , W M B W M I 1 ...............N ” / W 1 4 . 7 4 W M W M B 1 \ C V~7 W U & L wmwmbi < r - ....................^ “ y5 w t«L w w m w ^ \ ” /° W M C L . ..................S. “ 7’ < T ^ ...............\ ~ 7 vm«An4« .....................................S . ” 7 * n * 9 C L W t * 7 W * « 7 4 < T * .................... % /° W 1 4 * f i t m * 7 W M i 7 4 ^ s W H d L W » M W » M « < T ^ .....................................% ~ 7 wi4tfa^. v m i 7 M n * 7 4 .....................................<\ ~ 7 wmx. tntantta < T ^ .................... \ ~ s W i » M L »M »1*« ' < r ^ * .................... \ / O W L, W!«n*«B .................... \ ” 7 Wii«L • " • m u <T^ •••>••• s; " /> W litt " M W * ...............% Z5 w iite wiw y iwo < T ^ ....................... <\ ~ 7 ................. zyrry ...............'syxy v^iic* , muoKvm ' ‘ ' ' ' 7S ‘ • —» • D / s “7\" W 1 M 3 W 1 M 3 v v V \ “ WMMlM V V v v 7 \ ' nweww 7 \ ' V \ “ W M O N M O 7 \ 7 %. “7 \ “ ' V \ v V V /■ x *n*etm*4t v v V \ “ W 1 4 t f B W t 4 r i 0 7 \ W t 4 K 7 4 V m 4 R 7 4 V \ " W M 7 « M M i 7 4 “7 \ ” *n *74m*T4 v v V V 7 \ w i * « w i * a i 7 \ “7 \ ” W M M W M t O " A ' V V n*eowt*fl V V / • wi^et o WTMS1 O 0 !"2>. wt*» ° / • o ’"**,. W14rfB o ^ wum W 1«74 ° < ” w i* 7 4 o WM474 ° V ' W 1*74 ° V W M 4B o m * 4 C o W 1 4 M B V ■ ry. W M 0 O o / • W 1 M 0 V ° V W 1 * « 0 V ' / • ° V W U t f O ° V W M d O ° V w w o O y s~ y. • W i n d 9 0 m p h < D 420 ft high Optimization #1 and #2 Sloping members sizes for structural optimizations 1&2, for wind velocity of 90 mph and building height of 420ft Figure 3.29: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 420 feet tall prototype, at 90 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 A/B C .... ... N f W 1 4 M W M t , - * * * \ f ttiM . W T M t f M I M f i . . . • - - m-V _ ... * » * ■ » « ■ » W 1 ^ 7 4 . • • • ■ ■ • \ / «n i7i W ! « « W t M 1 ^ s > . . . . - - N ~ ^ W7.77 W W W W W r f * ^ V , . . . • - - ^ f VMMMI . . - - • % - y , W 1 * 7 W M « 7 4 \ ~ y > ... ... wuda wi*7wi«74 \ ~ / i m a « n » « M ! \ " s « WMWWMW3 .................. m w . W M 7 W 7 . H 7 v T ^ ............... W M M . WM«*M» \ ............... \ ~ s w tw . wiMwiwo .................. • M n W t M W I W W .................. W M f l O t W M W W 1 M 0 \ ~ w tw » W M W U W ^ ............... N “ W 7 W I 3 D W M W W 1 4 M ..................S ’ ”/ W M f t J f t W M W W M M ................. V V W W O l W 7 4 W W 7 4 W 6 x i z W M . 1 S 2 W M r t W M r t O C ................... W M ria W M r t W M r t f i C •-.••• \-/> W 1 W 1 4 L w w r w v M r t o t ................... W 7 4 W 4 S W M r t W T W K K ........................s W M r t t t W M r t O T M r t J C "S, . . . . . . W 1 W 1 W W I W t W M r t X 0 “ ............... «W 9». 7 W M r t W M . 1 2 t -* - • - ^ ^ - WMM W t * f t t t n % 1 3 C * ts» — * - m m f \ MW M / S ' MWM Z \ ' 4 H W M < /”V *48WW / V m m m im i 4 M 3 W 1 W 6 3 W 1 4 i S 3 W * * 5 3 W M W I W I M I “ / 5\ “ W M M W M M w i« 8 g v n * e e W 1 * 7 4 M r * « 7 4 w i * r « w n M 7 4 ” / \ “ W M C W M fi WMttWHtt W M t O W M M v \ v W M M W M M W t W M M I M S O “/p\ ” W M M W M M “/p\ “ W 1 4 M » W 1 4 M » * V \ " W M M W M M “7 \ " W t M t t N V t M I C * W i * i O W 1 4 r t O » “7,\ “ W M r t O M f M r t O B V \ “ W M r t 2 W M r t 3 0 wiMt tv mr tao W t 4 r t 2 W 1 4 r f 3 0 W M r t M f f M l f i v /” \ “ W M O W M r t S - ^ 7 - - - W M Q W M « . » ^ 7 7 . . . . 0 ^ p . - • *14*46 ° / * * ’ W M d 3 • o / . - - W M M . c W1M61 W14h61 * <3 . . . * 1M«8 . o ^ 7 . . . W14*86 W1M74 - C ^ 7 7 . * 1 * 7 4 * 1 4 * 0 - o ^ 7 . - • * 1 4 * 2 . 0 ^ 7 7 . . . * 1 4 * 2 • « > = • • • „W1 « 0 • O ^ 7 7 . . • W M M * ° ’ W14M0 • / • • ‘ W44M» w i4M e . 0 ^ 7 7 . . . W1^ » • o ^ 7 - • • W 1«M W14i«0B ° /■ • ' W M M " ' ' ‘ w i4 r to e - O ^ , . . . W M M ft W t4rt30 . o . . w>4 >iao “'/*** WM rt30 A ' W M rt20 • Wind 110 mph < D 420 ft high Optimization #1 and #2 Sloping members sizes for structural optimizations 1 &2, for wind velocity of 110 mph and building height of 420ft Figure 3.30: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 420 feet tall prototype, at 110 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 A/B --------- v • ’ * . . . . . . * * W M 6 1 . . . . ^ • • • W M 6 1 • • - 3 v * • • . . . . . . • - J W M t f l • • • J V ‘ ’ * • . . . ,« " • « , . . . * - W M « B • ' ’ V ‘ ‘ • • . . . . . . * - W M 7 4 • • ‘ * V ' * • W M i 7 4 ■ • • a V ’ ' ’ . . . . . . • * W M M • J v ■ • • W M M • V . . . . . . • - W M M ---------- . • * . . . . . . • * W M M • - W M M • ^ V • • W M M • • • * v • • • - . . . . . . * - W M n a o . . . o ^ - - . . . . . . * • W M r 1 2 0 • • V ' ' • - . . . * « " •« . . . • * W M c 1 2 0 " V W M r O O • • • " v • • • . . . . . . W M r tS • • ^ V 1 ' s W M c t t ? A . . * x * W M r tS — > • m m — » ■ \ / wm* w i 4 » o • w W M W M 4 3 . W 1 « W M > 4 S ’ \ * V ' \ “ / W M t W M M ‘ W W 1 M V 1 4 6 3 ’ W W 1 4 M V M 4 1 ’ W W M W M 4 1 ’ \ V • W 1 4 iW 1 4 m 6 1 W ' ’ W W 144V M 08 \ V w W144AH4.74 W ' wi« wm£4 \* v W14*W14>74 W W t4>W 14afi \ * V W 1 4 W 1 4 A W ' W M W M 4 2 W ' W ' W 1 4 W V 1 4 t f 3 w ' W 1 * W M « 2 W ■ M 1 4 4 A H 4 m 8 2 \ V ' W t 4 W * 1 4 « 9 0 w • W M W 1 4 W 0 w ' W 1 4 W V 1 4 M W ' W M W M M W ‘ W 1 4 l W 1 4 « M w ■ W 1 4 W t « M W • W 1 4 « W M M A ‘ r M « ----- m •• S\ •• ‘ V V ‘ W M M W M r Q ’ “A " ' W lfr Wlfcg ‘ V V ‘ W 1 4 » 4 f f 1 « 4 & V V wi*awi4£3 • v v ■ W 1 4 ^ W 1 4 < $ 3 • V V ■ W M r f W t 4 * 1 • V V • W 1 4 m 0 W 1 4 m 6 1 . ■ W W r fM I A tt • V V • wm^ wmm ■ V V ■ W 1 4 * W 1 * 6 8 ■ V V ■ W M - ; W M r f 4 • V V ' W 1 4 « M t 4 a 7 4 ’ V \ “ ' W 14M M i7 4 ’ V V ' W 1 4 r f W 1 4 r t 7 • V V ' W M 4 W 1 4 4 S . v v . W M M T M C . v v . W M * W 1 4 * C • - W14MMM . * / v - W 1 4 . S W 1 4 . 9 0 ' A ' Wind 70 mph 540 ft high O ptim ization #1 and #2 • v v ■ W 1 « W 1 4 W O ‘ “ A “ ‘ W M d W M M ‘ " A " • wiwswmm • V V ■ W M r f W M M ’ " A ” ' W 1 % S W t 4 M ' V \ “ ‘ W M 4 W 1 4 M ’ V V ' W M d W M M ’ ' A ' ' W 1 4 4 W 1 4 M ’ V V ' WMMU4» E • A ' WM( *“ S ' W 1 M 8 •“ V W M M “ S ' W M M •“ S ' W t * 0 1 •“ V wmm S ' S ' W 1 4 r f 4 S ' W M r 7 4 S ' W 1 4 . 7 4 ' l £ * “ x 0 ' W 1 4 * 2 ■ “ S ' W M « 2 S ' WUfi A W M M ■ ” S ' W M M *” S ' W M M S ' W M M S ' W M M “ S ' W M M • “ S ' W 1 « M •“ S ' S ' ■” S ' W 1 4 M ■“ S ’ W M M . .„ W M M . - f . W M M S ' W M M • v W M M * 0 n C . ear D . Sloping members sizes for structural optimizations 1&2, for wind velocity of 70 mph and building height of 540ft Figure 3.31: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 540 feet tall prototype, at 70 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 A/B w w rfi w i* ei a * W M A A ' W 1 -H 7 * A , m ^ 7 4 a c^°o W t* 8 C > A W M » „ “a . W 1 4 r K » . v m n a e , A w ^oo* w i 4 « i » . a - w « o ^ WWM5, W M M S, N - a - m «.a W M il S , A W 14«1» A W W r fT S A W M iiT e, \ / ■ \ ~ s ■ w i* ttn * o ■ %” / W M M I M t ’ \*V • %” / ‘ ■ \ “ / ‘ W t4 « lft4 d 3 • \ * V • VH4rt*ft*01 • ■ W I ^ W W I • \~ y • W 1 * O T 4 * 8 • \ ” / • w m w n x e • \* v • w t % * n * 7 4 • \ “/ • v m M n « 7 4 • \*V • • \ ~ / ‘ W M W M f i ’ \ ~ / ' W f4 tf n 4 r t0 W 1 W 1 X 0 • \ * v • • \ " / • v m w i 4 » • %“/ ‘ w m w m k i c m ■ \* v * • ‘ v m w r n n o ® • \* v ‘ w m m v m k i x ■ \* v ‘ v m w m r t a o • \ " / * W t* * tt4 r t2 0 ’ ‘ W 1«M n4>t32 • \ * V ‘ V m M T M rtS ’ \ ~ / 7 ‘ W M M M r tS ’ \ 'V ‘ ’ \ * V ‘ W 1 M N 1 4 M B ' ‘ A ‘ ‘ W M W M M ■ ' A " W 1 * 4 V 1 4 a O ■ “ A “ ' w i4 * * m 4 « o ’ “A “ 1 W 14^W 1M 8 ■ “ A " ' w i4 * w i4 a t t • w ■ W 1 4 k S M 1 4 « S 3 ‘ " A " ‘ W t« S W 1 4 {3 ■ W ■ W 14rtW 1*01 ‘ " A ” ' w i 4 ^ w i * 6 i . v v . W 1*eW 14att • “A ” ‘ W 1 * 6 ff1 * 6 8 . v v . W 4 l W 1 4 t ? 4 ’ W ■ W 14*M H4i74 ’ “ A “ ‘ W14rfW14«82 ’ “A “ ’ W 14*W 1««S ' A ' . v v . W 1 4 r f W M « 0 . v v . ’ W ‘ W 1M W 14M ' ' A ” ' W 1 4 > r W 1 4 * T 2 0 . v v . W 1 M r W 1 4 r t2 0 • W ■ W t*W M rttO ‘ “ A ” ‘ W 1 4 r tV 1 4 rt2 0 - - W 4rW V *rt20 ‘ " A “ ‘ w rt4 « % v i* t3 0 - " A ” ' W 1 4 ^ W 1 4 a tK ' “ A " ’ W lArW ttritt ‘ “ A " ‘ W 1*tttt«rl32 • “ A “ ‘ W 1 * r iW t« r 1 4 * - ~ / V - W 1 4 r tA H 4 v 1 4 S ' “ A ” ' W 1 4 * W M r » 4 6 • A Wt*43 “ a W 1 4 r f3 " A W M 4 “ A w im s •“ A WM6$ “ A W 1463 •“ A W 1 4 rtl “ A W!4*1 - f ” A wi4rt» ■ “ a W M > 7 4 W 1 4 a 7 4 A WtMS WM4S A W 1440 •” A W M S O •“ A W 1M » “ A W M M “ A W 1 « r t0 » •“ A w u r tc e •w W 1 4 T t O B “ a W t4rt20 “ A W 1 4 r t2 0 •“ a w M v ia o ' A W **132 A Wttrm “ a W 1 4 b 1 3 3 “ A W Y 4 r t4 S •“ a W 1 4 ri4 S • W i n d 9 0 m p h (2 ) 540 ft high Optim ization #1 and # 2 Sloping members sizes for structural optimizations 1&2, for wind velocity of 90 mph and building height of 540ft Figure 3.32: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 540 feet tall prototype, at 90 mph wind speed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 A/B W 1448 V. W 1 4 .T 4 ,. \ ' ^ 7 v . W 1442„ W 1 4 i< 2 \ W lM 0r W M t f O \ WMM, W 1 4 4 W \ - W 1 4 > l 0 » a \ W 14.W \ “ W 1 4 .1 2 0 W U r tT O \ “ W 14.1C WM.IS. \ “ W 1 4 .1 4 S . \ W 1 4 R 1 4 S \ W 14K 1S 0 \ " W l*19» \ W 14« T ? V W 1 * r t7 « \ wt4xm. =\ “ W A tK O \ W 1 4 C 1 1 . W H C 1 1 W 1 4 £ 1 1 \ “ W M C 33. \ / wi^wnrta \ " / W M « N 1 4 * 3 W M W M 1 ’ \ ~ / - W M W M 68 w m w m J 4 • ■ W M W M 74 ’ \ ~ / ’ W M W M 43 • \ ~ / • w m w m 4 0 • ■ W M W M 60 • \ * V ' W M W M 6 ® ' \ ~ / ' W M M M M ' \ “/ ' W M W M W ■ \ ~ / • w i* w t4 r t® • \ ~ / ■ W M W M r t2 0 ‘ ' W M W M rtS ) ’ ’ W 1 « W M r t3 2 ‘ \ * V ' W M W M rt3 2 • \ * V ‘ W M W M r t4 S ‘ \ * V • W M W M r M S ‘ ' w M W M rta ® • \ ~ / • • \ ~ / • W M W M r fT S • • w m w m v i t b • \ ~ / * W M W M rltt • \ * v • WMWMvMS ’ * W W W M 0 1 1 ’ • A ' ’ W M 2 1 M 2 1 1 ‘ ' f\~ ' W M 4 W M d 3 • ” / V • W 1 M W U .6 1 ‘ “/V ‘ w i« * w i* 6 i • ”/V • W 1 4 * W 1 4 « fi8 ’ v -\ w m w v m m • “/ V • W 1 4 .V T M .T 4 • “/V • W 1 4 .a M M .7 4 • “/V • W 1 4 4 W 1 M C • V \ W 1 4 ^ V 1 4 ^ S • “/V • W 1 4 4 W M 0 O ‘ “/^T ’ W M 4 W 1 4 W 0 • “/V • W M rfW 1*tt • “/V • W M r fW M W ‘ “/ T ” • W M > W M K 9 ‘ “ / V ” ' W 1 4 r t M 1 A r 1 Q 0 • V \ W 1 * r iA M 4 * 1 2 0 • “/V • W 1 4 » W M r t2 0 • “/V ' W 1 4 .W 1 4 .1 3 5 • “/V • W 1*W 14rt» ' V \ W 1 4 .W M .1 4 5 • “ / V • W 1 4 .1 M M r t4 S • “/V • W 1 4 rW M rt3 » • “ / V • W M r tM 1 4 r t9 ft W M » W M r 1 7 e 7 V ~ - W 1 4.W 14.t70 7 \ W IM W M rttt TV~' W 1 4 rtM 1 4 iW / \ W 1 4 ^ W M C 1 1 J/ \ 7 \ W lA O V M C ll vs vs S ' * " S ’ wi«s3 “ / ’ W 1«S 3 • “ S ' W 1 4 .1 •“ / • W 14.1 S ' S ' '“ S ' W 1*74 " W 1 4 .7 4 WMfi W 1 4«2 / ” W M 0 O “ S ' W 1 4 r tO • “ Z 7 ' W M M " z 7 ' W M M •“ S ' W M r tO ® " x0’ W M r tO ® •" W M r 1 2 0 " S ' W M k 1 2 0 “ y3 ’ W 1«t32 •M ^ 9 . W M rlS " S ' W 1 4 .1 4 S “ W M .M S • “ z 7 ' W M r t O ® W 1 4 r tS B " y 7 ’ W I M r lT O " W M r tT B ” W M rtO - y , - W M rtO Wind 110 mph (2 ) 5 4 0 ft high Optim ization #7 and #2 Sloping members sizes for structural optimizations 1&2, for wind velocity of 110 mph and building height of 540ft Figure 3.33: Sloping members sizes for structural optimizations cases 1 and 2 structure, for the 540 feet tall prototype, at wind design of 110 mph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 • Weight of structure After assigning sizes to all structural members, a total frame weight was calculated for each case, in pounds per square foot, where the total weight of steel of building is divided by the total square footage of building. All member lengths are known as well as weight of all member sizes (where for example a member named W14 x 90, weights 90 per linear foot). To better explain this, let’s use the case of optimization 1, building of 420’ height, wind 70 mph, with single diagonal bracing configuration, in which (all weight computations are included in the appendix section): • Total weight of columns: 1,942,640 pounds • Total weight of beams: 1,641,600 pounds • Total weight of joists: 720,000 pounds • Total weight of braces: 343,728 pounds • TOTAL WEIGHT: 4,647,968 pounds • Total Area of Building: (90’ x 90’) x 30 floors = 243,000 ft2 • Weight of structure in psf: 4,647,968 / 243,000 = 19.1 psf All weight results were input in Fazlur Kahn’s “Premium for height” graph to compare if the values remained under the normal levels (as shown in 3.3.4). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 * Drift at top of the building Drift results came out from the Multiframe static analysis, and were compared to the maximum allowable drift of the two prototype heights. The maximum allowable drift at the top floor for any tall building is required by code to be 0.5% of the total height, where in the case of the hypothetical prototype: For 420 ft high: 0.5% o f420 = 2.1 in For 540 ft high: 0.5% of 540 = 2.7 in Maximum allowable drift: 0.5% of total L Measurement of drift at Multiframe 4D s figure 3.34: Diagram o f drift measurement at top o f the structure in Multiframe 4D (Edited from Multiframe 4D screen shot) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 * Structural optimizations Drift results of first testing cases were very low, which is good to remain under the maximum allowable; however, the weight of the structure in psf was considerably high, (shown in table 5). The member dimensions had to be modified in additional structural optimizations, with the objective of reducing building weight, without over passing the drift limit required by code. Therefore, there is one case of non- optimized structure, and two cases of structural optimizations. In the case of structure non-optimized, all five cases (with each brace configuration) had the same dimensions for outer column, but different for inner columns, and braces, for this case the same wind pressure of 30psf was used for all cases. In the case of structural optimization 1, all five cases had the same outer column (but different sizes than for non-optimized), different inner columns, and different size of braces. Structural optimization 2 used same outer and inner columns dimensions for all five cases (not the same as non-optimized and optimization 1), and different brace sizes for each case. At this point, the values resulting of drift and weight were good enough to stop the parametric analysis and start comparing and evaluating the outcomes. All results from each of the optimizations cases are detailed in Table 5 “Summary of results” (see pocket), and are and clearly shown and demonstrated in graphs in 3.3.4. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 3.3.4 Findings and evaluation of findings The numbers of results are many as it can be seen in the summary of results table; therefore, to organize the testing outcomes in the form graphs, and be able to make a comparative analysis of the behavior of the different bracing systems, averages were used. Averages of weight and drift of three wind speeds and two building heights, for each bracing system in each optimization case, showed in graphs 1 and 2; averages of weight and drift of all bracing configurations combined, for each wind speed, each building height, and each optimization case, in graph 3; and averages of weight of three wind speed for each bracing type, building height and each optimization case for graphs 4 and 5. The following graphs represent the results of weight per square foot and the drift in inches at the top of the building of all systems under each optimization case and height of building, and they will be explained accordingly. Graph 1 and 2 show the structural performance (based on weight and drift) of the five bracing systems for buildings of 30 and 40 stories, for each of the optimization cases. An average of the weight and the drift among the three wind speeds -in all five configurations cases- was used for these graphs. The drift in all of the systems (showed in a percentage of the maximum allowable) remained under the limits; the variation of drift among the five bracing types is very small, and in all of the cases, brace type E performed better. However, there is a more apparent difference on the weight of the structure when all three optimizations are compared, and it is clear that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 in the case of optimization #2 the weight of the structure is a lot lighter (about 5 pounds from the non-optimized case). From these two graphs, it can also be stated that the weight of the building increases with height. To better explain this, the frame of 540ft height is 129% taller than the one of 420ft, and the weight of the building increases between 110 and 120%, for all cases. Structural Performance Based on Weight and Drift (% of max. allowable) Non-optimized and Optimized structures for a 30-story building Max. aJhwabfc drift ( A ) for30story bldg. (420ft): 2.1 in.=100% 2 5 .0 0 15.00 10.00 Non-Optimized .Optimized 1 Optimized 2 A.cm B.cw C . cn D .n» E w Figure 3.35: Graph 1 of parametric analysis results showing a comparison of weight and drift in each type of brace, for three optimization cases, in a 30-story building Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 Structural Performance Based on Weight and Drift (% of max. allowable) Non-optimized and Optimized structures for a 40-story building Max. allowable drift (h ) for 30 story bldg. (420ft): 2.1 in.=100% 20.00 10.00 c 3. Non-Opttmtzed b . Optimized i c . Optimized 2 B .a O .n r E.iw □ □ □ □ □ Figure 3.36: Graph 2 of parametric analysis results showing a comparison of weight and drift in each type of brace, for three optimization cases, in a 40-story building Graph 3 shows the same results of drift and weight, but organized in a different way, by the category of wind velocities. Averages of all bracing systems combined have been used to compare the variation in structural performance between wind speeds; results are also demonstrated for each building height Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 From graph 3 it can be concluded that both drift and weight increase proportionately to wind velocity. A verage w eig h t (psf) a n d av e rag e d rift (A) o f all bracing system s com bined, u n d e r d ifferen t w in d s p e e d s , a n d stru ctu ral o p tim izatio n Max. allowabledrift (&) for30 story bldg. (420ft): 2.7 in.-100% Max. allowable drift (IS) for 40*tory bldg. (540ft): 2.7 in=700% Figure 3.37: Graph 3 of parametric analysis results showing a comparison of weight and drift in two buildings of 30 and 40-story high, in three optimization cases, at three wind velocities Graphs 4 and 5 show the weight of the structure (in pounds per square foot - psf) for all bracing configurations under both building heights. The prototype analysis results are inserted in Fazlur Kahn’s “Premium for height” graph. From graph 4 it can be demonstrated that the weight results from optimization #2 (curve 2) u-siory 40-stoiy i_209% ^ 23, 3 1 2 3. 71 21 Ajoax a 2 1 , * e T 1634^ . A 33, «0 - s t o r y ’ 3 0 - s to r y J>pl> n i n d •inrod : mf a. N on-O ptim ized f b. O ptim ization 1 C. O ptim ization 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 are in the normal range for both building heights, which was not the case in optimization #1- the resulting weight for this case were too large compare to real life numbers. The weight results for non-optimization case were what it is expected for the non-optimized structure curve (4). Structural steel weight related to building height (by Fazlur Kahn) ® Weight of structural steel considering floor framing only © W eight of structural steel considering gravity load only © W eight of structural steel for total structure optimized @ Weight of structural steel for total structure not optimized A . c w a<- Cc. D.~ E .m Nw»- optimi/Ht A A A A Optimization 1 £ ", Optimization 2 ' p\t tot 40 \ftxv Ixitkltnp, in r,tch optimization A ■ J 100 100 300 A A r\ 4 I i ! I r r * I j U U cn OJ Weight of structural steel in psf (pounds per square foot) Figure 3.38: Graph 4 o f parametric analysis results showing the structural weight in three optimization cases for two hypothetical buildings of 30 and 40-story high, and comparing them to real parameters in a Fazlur Kahn study (adapted from Fazlur Kahn, cited by Schierle, 2002-2004) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 Weight of structural steel per floor area of actual buildings, and prototype builings o f 30 and 40 stories £ Actual buildings (see list below) 9 Prototype buildings (30 and 40 story high, average psf of all systems in optimization 2) § Weight of structural steel for total structure optimized Weight of structural steel for total structure not optimized CO < D O o o & 00 uo CO cu o Weight o f structural steel in psf (pounds per square foot) H Empire State building New York P First Interstate building Los A ngeles 1 Chrysler building New York Q Seagram building New York J World Trade center New York R Alcoa building Pittsburgh K Sears tower Chicago S Alcoa building San Francisco L Pan Am building New York T Bechtel building San Francisco M United Nations building New York U Burlington H ouse New York N US Steel building Pittsburgh V IDS Center Minneapolis 0 John Hangkock building Chicago w Koenig residence Los A ngeles Figure 3.39: Graph 5 of parametric analysis results comparing the structural weight of two hypothetical buildings -of 30 and 40-stoiy high- to real building weights, from a Fazlur Kahn study (adapted from Fazlur Kahn, cited by Schierle, 2002-2004) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 Graph 5 show the averaged weight (among all bracing types) for both building heights compared to existing building around the world. The results show to be under the normal range. As a summarizing conclusion from all these graphs, the "best" bracing system cannot be stated, all systems performed as expected in all cases, the variations (which exists) remains minimal among all five different configurations. A greater difference is showed when the effects of lateral forces from the three types of wind speeds results are compared, which is also expected to happen. 3.3.5 Strengths and weaknesses of this specific analysis This study was valuable to understand the relationship between weight and drift, to building height and magnitude of lateral forces. It was also to realize the importance of optimizing a structure by reducing weight of steel to maintain the lower structural cost, and controlling the drift at the same time. The software allowed identifying, in a very simple and graphical way, the overall structural behavior of a tall building as well as failure modes. Consequently, the hypothetical analysis using Multiframe 4D can be considered more like a teaching tool, which provides an accurate guidance for the design of a structure. This is because there are certain limitations that the software presents that set a limit for the study to be a demo-study only, without entering too much in detail. The biggest restriction that the software presented is that it is very hard to cope with a large number of parameters, since it doesn’t tell which Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 are the parameters that make the differentiations in each testing case. To perform the Multiframe 4D part of this thesis, a rigorous and detailed study had to be maintained, in the form of a record of input data for each testing case, and then be able to make accurate conclusions from the results. This is why this study only focused in a small set of conditions: two building heights, little number of braces, and a couple of defined physical conditions. Therefore the conclusions obtained from the Multiframe results are valid only for the cases presented in this study. Nonetheless, for the purpose of this thesis, this demos- study was enough for to create a comparative analysis of five bracing systems in a typical 30-story office building, located in a city context, under three winds velocity. The information obtained form the Multiframe study is intended to be a complement to what has been said in the previous chapters about bracing systems. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 4 CONCLUSIONS AND RECOMMENDATIONS 4.1 Conclusions The information presented in this thesis demonstrated how important is the knowledge on bracing systems at the moment of designing a tall building, which requires a clear understanding of the behavior of structural systems and the most important parameters affecting their selection. Every designer needs to know that any structural system should be able to provide enough strength to carry and resist loads, provide lateral stiffness to control drift, provide ductility to absorb seismic loads, and satisfy all design requirements. From a structural point of view, the goal is always to achieve efficiency, cost- effectiveness, simplicity of detailing and construction. From an architectural point of view, the goal is to accommodate programmatic needs and achieve aesthetical requirements. Therefore, the selection of the best system for a certain project is dependent on the creativity and sensibility of the designer and engineer of the building, who will need to work together as a team during the early stages of the design. Moreover, the strength of a building not only comes from the material’s stiffness, it also comes from the way the building is configured and how its parts are arranged, so the system works as a whole. This makes the creativity of design, or just as Fazlur Kahn once said, “the strength of a building comes from its design.” Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 4.2 Recommendations for future research There are two main recommendations important for future research on the study of bracing systems. The first one is regarding the parametric building analysis. As it was previously said in chapter 3, the structural analysis in the Multiframe 4D study offered only analytical results from static analysis, and this may not be enough for real-life situations. However, to expand this research it is recommended to follow a similar study that comprehends all types of bracing frames, using software that implements dynamic analysis. The second recommendation is to develop more in depth guidelines for the design and selection of bracing systems for architects. This thesis was a humble intent to provide accessible information regarding bracing systems from an architectural point of view, and the initial literature research noted that there is not much in bibliography available on the topic. The idea would be to create a manual that is not too technical but not too superficial either, but enough for architectural interests. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 Connection: Dead load: Drift: Ductility: Failure: Framed tube: Hybrid building frame: Joint: Load effects: Node: P-delta effect Resistance: Stability: GLOSSARY A combination of joints used to transmit forces between two or more members. Connections are categorized by the type and amount of force transferred. Actual weight of structural elements (also known as gravity load). Lateral displacement due to lateral forces. The amount of inelastic deformation before failure. In earthquake design, it is common to create ductile systems by using specially detailed regions of the structure as “crumble zones” to absorb damage and allow large inelastic deformations of the system without collapse. Condition where a limit state is reached. It may or not produce collapse of structural systems. Perimeter of structure consisting of closely spaced columns and spandrels, which makes the building act as an equivalent tube. Frame construction composed of different structural building materials, such as concrete and steel. An area where two or more ends, surfaces or edges are attached. Joints are categorized by the type of fastener or weld used, and method of force transfer. Moments, shears, and axial forces in a member due to loads or other actions. Point at which subsidiary parts originate or come together. Secondary effect of column axial loads and lateral defection on moments in members. Maximum load carrying capability as defined by a limit state. The ability of a structure or a system to maintain position and geometry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 Stiffness: The ratio of deformation to associated load level. System stiffness is measured by some characteristic deflection relative to an applied load. For example, the deflection at the top of a high-rise building under wind loads. Strength: The ability to sustain load. System strength is measured by the amount of load that a system can sustain before reaching some damage level, such as permanent deformation or complete collapse. The collapse of a system typically involves a sequence of element failures; a well-designed system may experience severe damage in many elements before while continuing to sustain higher loads. Structural An assemblage of load carrying components that are joined system: together to provide interaction or independence. Trussed tube Tubular system for tall buildings in which lateral forces are system: resisted by truss action. Tuned: Adjusted carefully. W14: Nominally 356 mm (14-in) deep steel section with wide flange or I shape. (Part of the nomenclature was adapted from CTBUH 1995b, p. 395-398) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 REFERENCES AND BIBLIOGRAPHY ABRAMSON, D, M., 2001. Skyscraper rivals: the AIG Building and the architecture of Wall Steet.. New York: Princeton ALI, M, M., 2001. Art o f the Skyscraper: the genius ofFazlur Khan. New York: Rizzoli International Publications, Inc. AMERICAN INSTITUTE OF STEEL CONSTRUCTION. 1989. Manual o f Steel Construction: Allowable Stress Design. Ninth Edition. Chicago: AISC. AMERICAN INSTITUTE OF STEEL CONSTRUCTION. 2002. Seismic Provisions o f Structural Steel Buildings. Chicago: American Institute of Steel Construction. AMERICAN INSTITUTE OF STEEL CONTRUCTION, INC. (2002). Seismic Provisions fo r Structural Steel Buildings. Chicago. American Institute of Steel Construction, Inc. APPLIED TECHNOLOGY COUNCIL, (1997). Building Safety and Earthquakes [online]. ATC/SEAOC Joint Venture. Available from: www.atcouncil.org BECKER, R., ISHLER, M., (1996). Seismic Design Practice For Eccentrically Braced Frames. Steel Tips. California/Nevada Ironworkers Union. 1-27 BECKER, R., ISHLER, M., 1996. Seismic design practice for Eccentrically Braced Frames. Steel tips, 1-5. BECKER, R., ISHLER, M., 1996. 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Multi purpose High-rise Towers and Tall Buildings: Proceedings o f the Third International Conference “ Conquest o f Vertical Space in the 21s ' Century” . London. WARREN AERIAL. (2002). Library Tower [online]. American Institute of Steel Construction. Available from: www.aisc.org [Accessed 30 July 2004]. WHITE, W. D., HAJJAR, F. J., 1997. Design of steel frames without consideration of effective length. Engineering Structures, 19 (10), 797-810. ZAKNI, I., 1998.100 o f the world’ s tallest buildings. Corte Madera, CA: Gingko Press. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 A P P E N D IC E S A Calculation of wind pressure per joint for three wind velocities, for two building heights cases W IND LOAD ON JOINTS FOR STRUCTURE 4 2 0 FEET HIGH~| W ind P re ssu re : P = Qs*Ce*Cq W ind S p eed : 70 m ph Exposure B Floor Height Ce c < ? P (csf) In n e r co ls P (k ip s) O uter cols P (kips) 1 14 12.6 0.62 1.4 10.94 4 .5 9 2 3 0 2 28 12.6 0.76 1.4 13.41 5 .63 2.82 3 42 12.6 0.84 1.4 14.82 6 .2 2 3.11 4 56 12.6 0.95 1.4 16.76 7 .0 4 3.52 5 70 12.6 1.04 1.4 18.35 7 .71 3.85 6 84 12.6 1.04 1.4 18.35 7 .71 3.85 7 98 12.6 1.13 1.4 19.93 8 3 7 4.19 8 112 12.6 1.13 1.4 19.93 8 3 7 4.19 9 126 12.6 1.2 1.4 21.17 8 .8 9 4.45 10 140 12.6 1.2 1.4 21.17 8 .89 4.45 11 154 12.6 1.2 1.4 21.17 8 .8 9 4.45 12 168 12.6 1.31 1.4 23.11 9 .7 1 4.85 13 182 12.6 1.31 1.4 23.11 9 .71 4.85 14 196 12.6 1.42 1.4 25.05 10 .5 2 5.26 15 210 12.6 1.42 1.4 25.05 10.52 5.26 16 224 12.6 1.42 1.4 25.05 1 0 3 2 5.26 17 238 12.6 1.42 1.4 25.05 10.52 5.26 18 252 12.6 1.42 1.4 25.05 10.52 5.26 19 266 12.6 1.42 1.4 25.05 1 0 3 2 5.26 20 280 12.6 1.42 1.4 25.05 10.52 5.26 21 294 12.6 1.42 1.4 25.05 1 0 .5 2 5.26 22 308 12.6 1.63 1.4 28.75 12.08 6.04 23 322 12.6 1.63 1.4 28.75 12.08 6.04 24 336 12.6 1.63 1.4 28.75 12.08 6.04 25 350 12.6 1.63 1.4 28.75 12.08 6.04 26 364 12.6 1.63 1.4 28.75 12.08 6.04 27 378 12.6 1.63 1.4 28.75 12.08 6.04 28 392 12.6 1.63 1.4 28.75 12.08 6.04 29 406 12.6 1.8 1.4 31.75 13.34 6.67 30 420 12.6 1.8 1.4 31.75 6 .6 7 3.33 Average: 2 3 .5 8 4 .9 5 2 .48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143 W ind S peed: 90 mph Floor Haight Os Ce C q P (psf) In n e r c o ls P (k ip s) O u ter cols _ P (k ip s) 1 14 20.8 0.62 1.4 18.05 7 .5 8 3.79 2 28 20.8 0.76 1.4 22.13 9 .3 0 4 .6 5 3 42 20.8 0.84 1.4 24.46 10.27 5 .14 4 56 20.8 0.95 1.4 27.66 1 1 .62 5.81 5 70 20.8 1.04 1.4 30.28 1 2 .72 6.36 6 84 20.8 1.04 1.4 30.28 1 2 .72 6 .36 7 98 20.8 1.13 1.4 32.91 1 3 .82 6.91 8 112 20.8 1.13 1.4 32.91 1 3 .82 6.91 9 126 20.8 1.2 1.4 34.94 14.68 7 .3 4 10 140 20.8 1.2 1.4 34.94 1 4 .68 7 .3 4 11 154 20.8 1.2 1.4 34.94 14.68 7.34 12 168 20.8 1.31 1.4 38.15 1 6 .0 2 8.01 13 182 20.8 1.31 1.4 38.15 1 6 .02 8.01 14 196 20.8 1.42 1.4 41.35 1 7 3 7 8 .6 8 15 210 20.8 1.42 1.4 41.35 17 .3 7 8.68 16 224 20.8 1.42 1.4 41.35 17.37 8.68 17 238 20.8 1.42 1.4 41.35 17.37 8.68 18 252 20.8 1.42 1.4 41.35 17 .3 7 8.68 19 266 20.8 1.42 1.4 41.35 17 .3 7 8.68 20 280 20.8 1.42 1.4 41.35 17.37 8 .6 8 21 294 20.8 1.42 1.4 41.35 17.37 8 .6 8 22 308 20.8 1.63 1.4 47.47 19 .9 4 9 .9 7 23 322 20.8 1.63 1.4 47.47 19 .9 4 9 .9 7 24 336 20.8 1.63 1.4 47.47 1 9 .9 4 9.97 25 350 20.8 1.63 1.4 47.47 19 .9 4 9 .9 7 26 364 20.8 1.63 1.4 47.47 19 .9 4 9 .9 7 27 378 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 28 392 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 29 406 20.8 1.8 1.4 52.42 22 .0 1 11.01 30 420 20.8 1.8 1.4 52.42 11.01 5.50 Average: 38.92 8.17 4.09 W ind S p eed : 110 mph Floor Height < ? * Ce Cg P (psf) In n e r co ls P (k ip s) O u ter cols P (k ip s) 1 14 31 0.62 1.4 26.91 11.30 5 .6 5 2 28 31 0.76 1.4 32.98 1 3 .8 5 6 .9 3 3 42 31 0.84 1.4 36.46 15.31 7.66 4 56 31 0.95 1.4 41.23 17 .3 2 8 .6 6 5 70 31 1.04 1.4 45.14 18.96 9 .4 8 6 84 31 1.04 1.4 45.14 18 .9 6 9 .4 8 7 98 31 1.13 1.4 49.04 2 0 .6 0 10.30 8 112 31 1.13 1.4 49.04 2 0 .60 10.30 9 126 31 1.2 1.4 52.08 2 1 .8 7 10.94 10 140 31 1.2 1.4 52.08 2 1 .8 7 1 0 .94 11 154 31 1.2 1.4 52.08 2 1 .8 7 10.94 12 168 31 1.31 1.4 56.85 2 3 .8 8 1 1.94 13 182 31 1.31 1.4 56.85 2 3 .8 8 11.94 14 196 31 1.42 1.4 61.63 2 5 .8 8 12.94 15 210 31 1.42 1.4 61.63 2 5 .88 1 2.94 16 224 31 1.42 1.4 61.63 2 5 .88 12.94 17 238 31 1.42 1.4 61.63 2 5 .8 8 12.94 18 252 31 1.42 1.4 61.63 2 5 .8 8 1 2.94 19 266 31 1.42 1.4 61.63 2 5 .8 8 1 2.94 20 280 31 1.42 1.4 61.63 2 5 .8 8 1 2 .94 21 294 31 1.42 1.4 61.63 2 5 .88 1 2 .94 22 308 31 1.63 1.4 70.74 2 9 .7 1 1 4.86 23 322 31 1.63 1.4 70.74 2 9 .71 14.86 24 336 31 1.63 1.4 70.74 2 9 .71 14.86 25 350 31 1.63 1.4 70.74 2 9 .71 1 4.86 26 364 31 1.63 1.4 70.74 2 9 .71 14.86 27 378 31 1.63 1.4 70.74 2 9 .71 14.86 28 392 31 1.63 1.4 70.74 2 9 .71 14.86 29 406 31 1.8 1.4 78.12 3 2 .8 1 16.41 30 420 31 1.8 1.4 78.12 16.41 8 .2 0 Average: 58.01 12.18 6.09 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 I W IND LOAD ON JOINTS FOR STRUCTURE 5 4 0 FEET HIGH I W ind P re ssu re: P = Qs*Ce*Cq W ind S p eed: 70 mph Exposure B Floor Heioht 9s Ce P (psf) In n e r co ls P (W ps) O u te r cols P (k ip s) 1 18 12.6 0.67 1.4 11.82 4.96 2.48 2 36 12.6 0.72 1.4 12.70 5.33 2.67 3 54 12.6 0.95 1.4 16.76 7.04 3.52 4 72 12.6 1.04 1.4 18.35 7.71 3.85 5 90 12.6 1.04 1.4 18.35 7.71 3.85 6 108 12.6 1.13 1.4 19.93 8.37 4.19 7 126 12.6 1.2 1.4 21.17 8.89 4.45 8 144 12.6 1.31 1.4 23.11 9.71 4.85 9 162 12.6 1.31 1.4 23.11 9.71 4.85 10 180 12.6 1.31 1.4 23.11 9.71 4.85 11 198 12.6 1.42 1.4 25.05 10.52 5.26 12 216 12.6 1.42 1.4 25.05 10.52 5.26 13 234 12.6 1.42 1.4 25.05 10.52 5.26 14 252 12.6 1.42 1.4 25.05 10.52 5.26 15 270 12.6 1.63 1.4 28.75 12.08 6.04 16 288 12.6 1.63 1.4 28.75 12.08 6.04 17 306 12.6 1.63 1.4 28.75 12.08 6.04 18 324 12.6 1.63 1.4 28.75 12.08 6.04 19 342 12.6 1.63 1.4 28.75 12.08 6.04 20 360 12.6 1.63 1.4 28.75 12.08 6.04 21 378 12.6 1.63 1.4 28.75 12.08 6.04 22 396 12.6 1.8 1.4 31.75 13.34 6.67 23 414 12.6 1.8 1.4 31.75 13.34 6.67 24 432 12.6 1.8 1.4 31.75 13.34 6.67 25 450 12.6 1.8 1.4 31.75 13.34 6.67 26 468 12.6 1.8 1.4 31.75 13.34 6.67 27 486 12.6 1.8 1.4 31.75 13.34 6.67 28 504 12.6 1.8 1.4 31.75 13.34 6.67 29 522 12.6 1.8 1.4 31.75 13.34 6.67 30 540 12.6 1.8 1.4 31.75 6.67 3.33 Average: 2S.8S S. 43 2.71 W ind S p eed: 90 mph Floor Height 9s Ce Cq P (psf) In n e r c o ls P (k ip s) O u ter co ls P (k ip s) 1 18 20.8 0.67 1.4 19.51 8 .1 9 4 .1 0 2 36 20.8 0.72 1.4 20.97 8 .8 1 4 .4 0 3 54 20.8 0.95 1.4 27.66 1 1 .6 2 5 .8 1 4 72 20.8 1.04 1.4 30.28 1 2 .7 2 6 .3 6 5 90 20.8 1.04 1.4 30.28 1 2 .7 2 6 .3 6 6 108 20.8 1.13 1.4 32.91 1 3 .8 2 6 .9 1 7 126 20.8 1.2 1.4 34.94 1 4 .6 8 7 .3 4 8 144 20.8 1.31 1.4 38.15 1 6 .0 2 8 .0 1 9 162 20.8 1.31 1.4 38.15 1 6 .0 2 8 .0 1 10 180 20.8 1.31 1.4 38.15 1 6 .0 2 8 .0 1 11 198 20.8 1.42 1.4 41.35 1 7 .3 7 8 .6 8 12 216 20.8 1.42 1.4 41.35 1 7 .3 7 8 .6 8 13 234 20.8 1.42 1.4 41.35 1 7 .3 7 8 .6 8 14 252 20.8 1.42 1.4 41.35 1 7 .3 7 8 .6 8 15 270 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 16 288 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 17 306 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 18 324 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 19 342 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 20 360 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 21 378 20.8 1.63 1.4 47.47 1 9 .9 4 9 .9 7 22 396 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .0 1 23 414 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .01 24 432 20.8 1.8 1.4 52.42 22 .0 1 11 .0 1 25 450 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .0 1 26 468 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .0 1 27 486 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .01 28 504 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .0 1 29 522 20.8 1.8 1.4 52.42 2 2 .0 1 1 1 .0 1 30 540 20.8 1.8 1.4 52.42 11 .0 1 5 .5 0 Average: 42.68 8.96 4.48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 W ind S p eed : 110 mph Floor Hciqht Os Co c9 P (psf) In n e r cols P O d p s) O u ter c o ls P (k ip s) 1 18 31 0.67 1.4 29.08 12.21 6.11 2 36 31 0.72 1.4 31.25 13 .1 2 6 .56 3 54 31 0.95 1.4 41.23 17 .3 2 8 .6 6 4 72 31 1.04 1.4 45.14 1 8 .9 6 9 .48 5 90 31 1.04 1.4 45.14 1 8 .9 6 9 .4 8 6 108 31 1.13 1.4 49.04 2 0 .6 0 10.30 7 126 31 1.2 1.4 52.08 2 1 .8 7 10.94 8 144 31 1.31 1.4 56.85 2 3 .8 8 11.94 9 162 31 1.31 1.4 56.85 2 3 .8 8 11.94 10 180 31 1.31 1.4 56.8S 2 3 .8 8 1 1 .9 4 11 198 31 1.42 1.4 61.63 2 5 .8 8 1 2 .9 4 12 216 31 1.42 1.4 61.63 2 5 .8 8 12.94 13 234 31 1.42 1.4 61.63 2 5 .8 8 12.94 14 252 31 1.42 1.4 61.63 25 .8 8 1 2 .9 4 IS 270 31 1.63 1.4 70.74 2 9 .7 1 14.86 16 288 31 1.63 1.4 70.74 29 .7 1 14.86 17 306 31 1.63 1.4 70.74 2 9 .7 1 14.86 18 324 31 1.63 1.4 70.74 2 9 .7 1 14.86 19 342 31 1.63 1.4 70.74 29 .7 1 14.86 20 360 31 1.63 1.4 70.74 2 9 .7 1 14.86 21 378 31 1.63 1.4 70.74 2 9 .7 1 14.86 22 396 31 1.8 1.4 78.12 3 2 .8 1 16.41 23 414 31 1.8 1.4 78.12 3 2 .8 1 16.41 24 432 31 1.8 1.4 78.12 3 2 .8 1 16.41 25 450 31 1.8 1.4 78.12 3 2 .8 1 16.41 26 468 31 1.8 1.4 78.12 3 2 .8 1 16.41 27 486 31 1.8 1.4 78.12 3 2 .8 1 16.41 28 504 31 1.8 1.4 78.12 3 2 .8 1 16.41 29 522 31 1.8 1.4 78.12 3 2 .8 1 16.41 30 540 31 1.8 1.4 78.12 1 6 .4 1 8.20 Average: 6 3 .6 1 23.36 6 .68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 B Column design: base shear and weight calculations W ind d esign (K L= 14‘ ) Optimization Case # 1 Wind 70 m ph Average wind pressure for 70 mph: 23.58 osf Column Load 90osf*3 0 /1 0 0 0 s 2.7 K lf Beam Load lOOosf*3 0 /1 0 0 0 = 3 K lf B ase Shear V & 2 3 .5 8 o sf* 4 5 f* 4 1 3 /1 0 0 0 = 438.23 K OTM = 4 3 8 .6 * 2 1 3 3 = 93,563.02 K * Uniform Brace Load= 1 2 0 o sf* 3 0 '/1 0 0 0 = 3.6 K 1 5 T H F l o o r d e s i g n B ase Shear V = 23.58p sf*45f*203/1000 OTM = 2 1 5 .4 * 1 0 8 3 = B e a m d e s i a n Ms W L 2/8s 3k ff*(30)2 / 8 337.5 K * Section modulus S sM /fo 338x12730 13S.2 In3 (all. 146 in3) Use: w l8 x 7 6 P Lat=M/30 P Grav=NWA Sum P Use Pali. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1325>1215 14’ b +c (inner) 3118.77 2430 5548.77 W14X730 5677>5548 14* Diag. Brace 222.9 119 341.9 W14X99 359>341 33* V-Brace 299.7 38.8 338.5 W14X82 372>338 20* Knee Brace 320.5 30.6 351.1 W14X82 372>351 19* EBF 2 links 255 64 319 W14X74 337>319 25' 1 5 t h f l o o r d e s i a n P LatsM/30 PGrav=NWA Sum P Use P all. vs. P K L a+d (outer) 0 1215 1215 W14X176 1325>12l5 14* h + c (inner) 779.04 2430 3209.04 W14X426 3251>3209 14* Diag. Brace 109.5 119 228.5 W14X90 325>228.5 33' V-Brace 147.2 38.8 186 W14X61 272>186 20' Knee Brace 157.4 30.6 188 W14X61 272>188 19* EBF 2 links 125.2 64 189.2 W14X61 193> 189.2 25* W ind desig n (KL=14') W ind 90 m ph O ptim ization Case #1 Average wind pressure for 9 0 mph: 38.9 osf Column Load 90 p sf* 3 0 /1 0 0 0 = 2.7 Klf Beam Load 1 0 0 p sf* 3 0 /1 0 0 0 = 3 Klf B ase Shear V ■ 3 8 .9 o sf* 4 5 f* 4 1 3 /1 0 0 0 ■ 722.96 K OTM = 7 2 2 .9 6 * 2 1 3 3 a 154,351.21 K * Uniform Brace Loads 1 2 0 p sf* 3 0 7 l0 0 0 = 3.6 K 1 5 T H F l o o r d e s i g n B ase Shear V ■ 38.9p sf*45f*203/1000 • OTM = 355.4*108.5 = B e a m d e s i a n M s W L2/8= 3k tf*(30)2 / 8 337.5 K * Section modulus S = M /fa 338x12730 135.2 In3 (all. 146 in3) Use: w l8 x 7 6 1 s t f l o o r d e s i a n P lat=M /30 P Grav=NWA Sum P U se Pall. vs. P KL a+d (outer) 0 1215 1215 W14X176 1325>1215 14* b +c (inner) 5145.04 2430 7575.04 W14X730 14* Diag. Brace 367.4 119 486.4 W14X109 399>486 33* V-Brace 439.9 38.8 478.7 W14X90 580>478 20* Knee Brace 528.2 30.6 558.8 W14X90 580>558 19' EBF 2 links 255 64 319 W14X90 515>319 25* 1 5 t h f l o o r d e s i a n P Lat=M/30 P Grav=NWA Sum P Use Pall. vs. P K L a+d (outer) 0 1215 1215 W14X176 132S>1215 14* b +c (inner) 1285.19 2430 3715.19 W14X500 3840>3715 14* Diag. Brace 180.6 119 299.6 W14X90 325>200 33* V-Brace 242.8 38.8 281.6 W14X68 305>281 20* Knee Brace 259.6 30.6 290.2 W14X61 310>290 19* EBF 2 links 206.5 64 270.5 W14X82 267 25* 21S.4 K 2 3 ,3 7 1 .2 6 K ’ 35S.« K 3 8 3 5 5 .6 4 K ’ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 Wind design (KL-14') Wind 90 mph Average wind pressure for 110 mph: 58 o s f Column Load 90p sf*3 0 /1 0 0 0 = 2.7 Klf Beam Load I 0 0 p sf* 3 0 /I0 0 0 = 3 K lf B ase Shear V = 5 8 p sf*45f*413/1000 = 1077.93 K OTM = 1077.93*213.5 = 230,138.06 K* Uniform Brace Loads 120 o s f* 3 0 '/1 0 0 0 s 3.6 K 1 5 T H F lo o r d e s i g n B ase Shear V = 58osf*45f*203/1000 = OTM s 529.8*108.5 = Beam desian M s W L 2/8s 3ktf*(30)2 / 8 337.5 K ’ Section modulus S sM /fo 338x12730 135.2 in3 (alt. 146 in3) Use: W18X76 1 st floor design P Lat=M/30 P Grav=NWA Sum P Use P all. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1325>1215 14* b + c (Inner) 7671.27 2430 10101.27 W14X730 14* Diag. Brace 547.5 119 666.5 W14X159 666=665 33* V-Brace 735.9 38.8 774.7 W14X120 776>774 20’ Knee Brace 787 30.6 817.6 W14X132 877>817 19’ EBF 2 links 626.1 64 690.1 W14X120 692>690 25’ 15th floor design P Ut=M/30 P Grav=NWA Sum P Use P ail. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1325> l2lS 14' b + c (inner) 1916.22 2430 4346.22 W14X605 3840>37lS 14* Diag. Brace 269.3 119 388.3 W14X99 404>388 33' V-Brace 362 38.8 400.8 W14X90 580>400 20* Knee Brace 387.1 30.6 417.7 W14X82 423 19* EBF 2 links 308 64 372 W14X90 515>372 25* W ind design (KL=18’ ) W ind 70 m ph Average wind pressure for 70 mph: 25.8 p s f Column Load 9 0 o s f 3 0 /1 0 0 0 = 2.7 Ktf Beam Load 2 0 0 o sf* 3 0 /1 0 0 0 = 3 K tf Base Shear V = 25 .8 o sf* 4 5 * 5 3 1 /1 0 0 0 = 616.49 K OTM = 616.5*274.5 s 169,226.78 K’ Uniform Brace Loads 120 psf*3 0 7 1 0 0 0 * 3.6 K 1 5 T H F l o o r d e s i g n B ase Shear V S 25.8p sf*45*261/1000 OTM s 3 0 3 *1393 = Beam design M s W L 2/8s 3ktf*(30)2 / 8 337.5 K* Section modulus S sM /fo 338x12730 135.2 in3 (all. 146 in3) Use: w l8 x 7 6 1 st floor design PLat=M/30 P Grav=NWA Sum P Use Pall. vs. P K L a + d (outer) 0 1215 1215 W14X176 1231>1215 18’ b + c (inner) 5640.89 2430 8070.89 W14X730 18’ Diag. Brace 359.3 105 464.3 W14X132 492>464 35’ V-Brace 472.2 32.5 504.7 W14X90 5l5>504 23.5' Knee Brace S29.7 28.6 558.3 W14X99 603>558 22* EBF 2 links 401.1 55 456.1 W14X99 489>456 27.6' 15th floor desian P Lat=M/30 P Grav=NWA Sum P Use p all. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1231>1215 18’ b + c (inner) 1409.05 2430 3839.05 W14X55Q 3992>3839 18’ Diag. Brace 176.8 105 281.8 W14X90 325>28l 35’ V-Brace 232.3 32.5 264.8 W14X82 267>264 23.5' Knee Brace 260.6 28.6 289.2 W14X82 318>288 22’ EBF 2 links 197.3 55 252.3 W14X90 444>252 27.6' 529.8 K 57.486.56 K ’ 303.0 K 4 2 ^ 7 1 .4 3 K* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 148 Wind design (K L-18') Wind 90 m ph A verage w ind pressure for 90 mph: 42.6 osf Column Load 90 o sf* 3 0 /1 0 0 0 = 2.7 Klf Beam Load 1 0 0 o sf* 3 0 /1 0 0 0 = 3 Klf B ase S hear V = 4 2 .6 o sf*45*531/1000 = 1017.93 K OTM = 1 0 1 8 * 2 7 4 .5 = 279,420.96 K * Uniform Brace L o a d s 120 o sf* 3 0 7 l0 0 0 = 3.6 K 15TH Floor design B ase Shear V = 42.6p sf*45*261/1000 OTM s 5 0 0 3 * 1 3 9 .5 = Beam desian M s W L 2 /8 s 3 ktf* (3 0 )2 / 8 337.5 K * Section m odulus S sM /fa 338x12730 135.2 in3 (all. 146 in3) Use: w l8 x 7 6 1 st floor desian P lat=M/30 PGrav=NWA Sum P u se p ail. vs. P K L a+d (ou ter) 0 1215 1215 W14X176 1231>12lS 18* b+c (in n er) 9314.03 2430 11744.03 W14X730 18* Diag. Brace 593.7 105 698.7 W14X176 744>698 35* V-Brace 780.4 32.5 812.9 W14X145 875>812 23.5’ Knee Brace 875.4 28.6 904 W14X145 923>904 22* EBF 2 links 640.4 55 695.4 W14X145 773>695 27.6* P Lat=M/30 P Grav=NWA Sum P Use P all. vs. P K L a+ d (ou ter) 0 1215 1215 W14X176 1231>1215 18* b + c (in n er) 2326.57 2430 4756.57 W14X665 4870>4756 18* Diag. Brace 291.9 105 396.9 W14X109 399>396 35* V-Brace 383.6 32.5 416.1 W14X90 5lS>416 23.5’ Knee Brace 430.3 28.6 458.9 W14X90 548>458 22* EBF 2 links 325.8 55 380.8 W14X90 406>380 27.6* W ind d esig n (K L= 18’ ) W ind 1 1 0 m p h Average w ind pressure for 110 mph: 63.6 osf Column Load 9 0 o sf* 3 0 /1 0 0 0 = 2.7 Klf Beam Load 100 p sf* 3 0 /1 0 0 0 = 3 Klf B ase S hear V = 6 3 .6osf*45*531/1000 = 1519.72 K OTM s 1 5 1 9 3 * 2 7 4 3 = 417,163.69 K * Uniform Brace Loads 120 p sf* 3 0 7 1 0 0 0 s 3.6 K 15TH Floor design B ase Shear V s 63 .6 o sf*45*261/1000 OTM s 74 7 * 1 3 9 .5 s Beam desian M s W L 2 /8 s 3ld f* (3 0 )2 / 8 337.5 K * Section m odulus S sM /fa 338x12730 135.2 in3 (all. 146 in3) Use: w l8 x 7 6 P Lat=M/30 1 st floor design P Grav=NWA Sum P Use Pall. vs. P K L a+ d (ou ter) 0 1215 1215 W14X176 1231>1215 18* b + c (inner) 13905.46 2430 16335.46 W14X730 18* Diag. Brace 890.6 105 995.6 W14X233 I0l5>995 35* V-Brace 1170.5 32.5 1203 W14X211 1289>1203 23.5* Knee Brace 1313 28.6 1341.6 W14X211 1356>1341 22* EBF 2 links 994.2 55 1049.2 W14X193 1046*1049 27.6* 15th floor desian P Lat=M/30 p Grav=NWA a+ d (ou ter) 0 1215 b + c (Inner) 3473.47 2430 Diag. Brace 435.7 105 V-Brace 572.6 32.5 Knee Brace 642.3 28.6 EBF 2 links 486.3 55 Sum P Use Pall. vs. P K L 1215 W14X176 1231>1215 18' 5903.47 W14X730 18* 540.7 W14X14S 541>504 35* 605.1 W14X109 626>605 23.5* 670.9 W14X120 735>670 22* 541.3 W14X109 541-541 27.6* 500.3 K 69,797.01 K ' 747.0 K 104,203.99 K* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 149 Wind design (KL— 14') A verage wind p ressu re for 70 mph: 23.58 osf Column Load 9 0 o s f* 3 0 /1 0 0 0 = 2.7 K lf Beam Load 1 0 0 o s f* 3 0 /1 0 0 0 = 3 Klf Base Shear V = 2 3 .5 8 o sf* 4 5 f* 4 1 3 /1 0 0 0 = 438.23 K OTM = 4 3 8 .6 * 2 1 3 ^ = 93,563.02 K ’ Uniform Brace L oad s 1 2 0 p sf*30’/1 0 0 0 = 3.6 K O ptim ization Case # 2 W ind 70 m ph 15TH Floor design B ase Shear V = 23.58p sf* 4 5 f* 2 0 3 /1 0 0 0 OTM a 215.4*208.5 = Beam desian Ms W L 2 /8 s 3 ld f* (3 0 )2 / 8 337.S K * Section m odulus S sM /fa 338x12730 135.2 in3 (all. 146 in3) Use: w l8 x 7 6 1 s t f l o o r d e s i a n PLat=M/30 PGrav=NWA Sum P U se Pall. vs. P K L a+d (outer) 0 1215 1215 W14X176 1325>1215 14* b +c (inner) 3118.77 2430 5548.77 W14X730 5677>S548 14* Diag. Brace 222.9 119 341.9 W14X99 359>341 33‘ V-Brace 299.7 38.8 338.5 W14X82 372>338 20* Knee Brace 320.5 30.6 351.1 W14X82 372>35l 19* EBF 2 links 255 64 319 W14X74 337>3l9 2S’ P Lat=M/30 P Grav=NWA Sum P U se Pall. vs. P K L a+d (outer) 0 1215 1215 W14X176 1325>121S 14* b+c (inner) 779.04 2430 3209.04 W14X426 3251>3209 14* Diag. Brace 109.5 119 228.5 W14X90 325>228.5 33' V-Brace 147.2 38.8 186 W14X61 272>186 20* Knee Brace 157.4 30.6 188 W14X61 272>188 19’ EBF 2 links 125.2 64 189.2 W14X61 193>189.2 25* W ind d esig n (KL— 1 4 ’ ) W ind 90 m ph O ptim ization Case # 2 Average wind p ressu re for 9 0 mph: 38.9 osf Column Load 9 O p sf* 3 0 /1 0 0 0 s 2.7 K lf Beam Load 1 0 0 p sf* 3 0 /1 0 0 0 = 3 Klf Base Shear V - 3 8 .9 p sf* 4 5 f* 4 1 3 /1 0 0 0 ■ 722.96 K OTM s 7 2 2 .9 6 * 2 1 3 3 = 154,351.21 K * Uniform Brace L o a d s 1 2 0 p sf* 3 0 * /l0 0 0 = 3.6 K 15TH Floor design Base Shear V ■ 38.9p sf* 4 5 f* 2 0 3 /1 0 0 0 « OTM s 355.4*108.5 s B eam desian Ms W L 2 /8 s 3 k tf* (3 0 )2 / 8 337.5 K ’ Section m odulus S sM /fa 338x12730 135.2 in3 (alt. 146 in3) Use: w l8 x 7 6 1 s t floor desion P Late M/30 P Grav=NWA a+ d (ou ter) 0 1215 b +c (inner) 5145.04 2430 Diag. Brace 367.4 119 V-Brace 439.9 38.8 Knee Brace 528.2 30.6 EBF 2 links 255 64 Sum P U se Pall. vs. p K L 1215 W14X176 132SM 215 14* 7575.04 W14X730 14* 486.4 W14X109 399>486 33' 478.7 W14X90 580>478 20’ 558.8 W14X90 580>558 19’ 319 W14X90 515>319 25* P Lat=M/30f P Grav» N W A Sum P u se P all. vs. P K L a+d (ou ter) 0 1215 1215 W14X176 1325>121S 14’ b +c (inner) 1285.19 2430 3715.19 W14X500 3840>3715 14’ Diag. Brace 180.6 119 299.6 W14X90 325>200 33’ V-Brace 242.8 38.8 281.6 W14X68 305>281 20* Knee Brace 259.6 30.6 290.2 W14X61 310>290 19’ EBF 2 links 206.5 64 270.5 W14X82 267 25* 215.4 K 2 3 ,3 7 1 .2 6 K ‘ 355.4 K 3 8 ,5 5 5 .6 4 K* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 150 Wind design (KL=14') Wind 110 mph Average wind pressure for 110 mph: 58 osf Column Load 90nsf*3 0 /1 0 0 0 = 2.7 K lf Beam Load 100osf*30/1000 = 3 K lf Base Shear V & 58p sf*45f*413/1000 = 1077.93 K OTM s 1077.93*213*5 = 230,138.06 K * Uniform Brace Loads 120 p sf*30'/1000= 3.6 K 1 5 T H F l o o r d e s i g n Base Shear V = S 8psf*4S f*203/l0O 0 = OTM s 529.8*108*5 = B e a m d e s i a n M s W L2/8= 3ktf*(30)2 / 8 337.5 K * Section m odulus S sM /fo 338x12730 135.2 in3 (all. 146 In3) Use: w l8 x 7 6 P Lat=M/30 P Grav=NWA Sum P Use Pall. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1325>1215 14* b + c (inner) 7671.27 2430 10101.27 W14X730 14' Diag. Brace 547.5 119 666.5 W14X159 666=665 33' V-Brace 735.9 38.8 774.7 W14X120 776>774 20' Knee Brace 787 30.6 817.6 W14X132 877>817 19* EBF 2 links 626.1 64 690.1 W14X120 692>690 25* 1 5 t h f l o o r d e s i a n P Lat=M/30 PGrav=NWA Sum P Use P ail. vs. P K L a+d (outer) 0 1215 1215 W14X176 1325>1215 14' b + c (inner) 1916.22 2430 4346.22 W14X60S 3840>371S 14' Diag. Brace 269.3 119 388.3 W14X99 404>388 33’ V-Brace 362 38.8 400.8 W14X90 580>400 20* Knee Brace 387.1 30.6 417.7 W14X82 423 19* EBF 2 links 308 64 372 W14X90 515>372 25* W ind design (KL=18') W ind 70 m ph A veraoe wind pressure for 70 mph: 25.8 osf Column Load 90osf*3 0 /1 0 0 0 = 2.7 Klf Beam Load 1 0 0 p sf* 3 0 /l0 0 0 s 3 K tf B ase Shear V s 25.8osf*45*531/1000 = 616.49 K OTM s 6 1 6 3 * 2 7 4 3 = 169,226.78 K * Uniform Braes Loads 120 p sf* 3 0 7 1 0 0 0 s 3.6 K 1 5 T H F l o o r d e s i g n Base Shear V = 2 5 3 o sf* 4 S * 2 6 1 /1 0 0 0 OTM s 3 0 3 * 1 3 9 3 = B e a m d e s i a n M s W L 2/8s 3ktf*(30)2 / 8 337.5 K * Section modulus S sM /fo 338x12730 135.2 in3 (all. 146 in3) Use: w l8 x 7 6 P Lat=M/30 1 s t floor desian P Grav=NWA Sum P Use Pall. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1231>1215 18* b + c (inner) 5640.89 2430 8070.89 W14X730 18* Diag. Brace 359.3 105 464.3 W14X132 492>464 35* V-Brace 472.2 32.5 504.7 W14X90 515>504 23.5* Knee Brace 529.7 28.6 5S8.3 W14X99 603>558 22* EBF 2 links 401.1 55 456.1 W14X99 489>456 27.6* P Lat=M/30 15th floor desian PGrav=NWA Sum P Use P all. vs. P K L a + d (outer) 0 1215 1215 W14X176 1231>121S 18' b + c (inner) 1409.05 2430 3839.05 W14X550 3992>3839 18* Diag. Brace 176.8 105 281.8 W14X90 325>281 35* V-Brace 232.3 32.5 264.8 W14X82 267>264 23.5* Knee Brace 260.6 28.6 289.2 W14X82 318>288 22* EBF 2 links 197.3 55 252.3 W14X90 444>252 27.6* 529.8 K S7.486.S6 K ' 303.0 K 4 2 J 7 1 A 2 K* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151 Wind design (K L-18') Wind 90 mph Average wind pressure for 9 0 mph: 42.6 osf Column Load 9 0 o s f* 3 0 /l0 0 0 = 2.7 K lf Beam Load 1 0 0 o sf* 3 0 /1 0 0 0 = 3 Klf B ase Shear V = 4 2 .6 p sf* 4 5 * 5 3 1 /1 0 0 0 = 1017.93 K OTM = 1 0 1 8 * 2 7 4 3 = 279,420.96 K * Uniform Brace Loads 1 20 p sf* 3 0 '/1 0 0 0 = 3.6 K 15TH Floor design B ase Shear V = 4 2 .6p sf*45*261/1000 OTM s 5 0 0 3 * 1 3 9 .5 = Beam desian M= W L 2/8s 3kJf*(30)2 / 8 337.5 K ’ Section modulus S sM /fo 338x12730 135.2 in3 (alt. 146 In3) Use: w !8 x 7 6 P Lat=M/30 1 st floor desian P Grav=NWA Sum P Use Pall. vs. P K L a + d (outer) 0 1215 1215 W14X176 1231>1215 18’ b +c (inner) 9314.03 2430 11744.03 W14X730 18' D iag. Brace 593.7 105 698.7 W14X176 744>698 35' V-Brace 780.4 32.5 812.9 W14X14S 875>812 23.5' Knee Brace 875.4 28.6 904 W14X145 923>904 22* EBF 2 links 640.4 55 695.4 W14X145 773>695 27.6* 15th floor desian P lat=M/30 P Grav=NWA Sum P Use Pall. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1231>1215 18' b + c (inner) 2326.57 2430 4756.57 W14X665 4870>4756 18* Diag. Brace 291.9 105 396.9 W14X109 399>396 35* V-Brace 383.6 32.5 416.1 W14X90 515 >416 23.5' Knee Brace 430.3 28.6 458.9 W14X90 548>458 22* EBF 2 links 325.8 55 380.8 W14X90 406>380 27.6* W ind design (K L ^1 8 f ) W ind 110 m ph Average wind pressure for 110 mph: 63.6 osf Column Load 90 o sf* 3 0 /1 0 0 0 = 2.7 Klf Beam Load 1 0 0 o sf* 3 0 /1 0 0 0 = 3 Klf Base Shear V = 6 3 .6 p sf* 4 5 * 5 3 1 /1 0 0 0 = 1519.72 K OTM - 1 5 1 9 .7 * 2 7 4 3 ■ 417,163.69 K * Uniform Brace Loads 1 2 0 p s f* 3 0 7 l0 0 0 = 3.6 K 15TH Floor design Base Shear V = 6 3 .6 p sf*45*261/1000 OTM ■ 7 4 7 * 1 3 9 3 ■ Beam desion M= W L 2 /8s 3k tf*(30)2 /S 337.5 K ’ Section m odulus S sM /fo 338x12730 135.2 In3 (all. 146 in3) Use: w l8 x 7 6 P Lat=M/30 1 st floor design P Grav=NWA Sum P Use Pall. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1231>1215 18* b+ c (inner) 13905.46 2430 16335.46 W14X730 18* Diag. Brace 890.6 105 995.6 W14X233 10l5>995 35* V-Brace 1170.5 32.5 1203 W14X211 1289>1203 23.5' Knee Brace 1313 28.6 1341.6 W14X211 13S6>1341 22* EBF 2 links 994.2 55 1049.2 W14X193 1046*1049 27.6* P Lat=M/30 P Grav=NWA Sum P Use Pall. vs. P K L a+ d (outer) 0 1215 1215 W14X176 1231>1215 18* b + c (inner) 3473.47 2430 5903.47 W14X730 18* Diag. Brace 435.7 105 540.7 W14X145 541>504 35* V-Brace 572.6 32.5 605.1 W14X109 626>605 23.5' Knee 8race 642.3 28.6 670.9 W14X120 735>670 22* EBF 2 links 486.3 55 541.3 W14X109 541*541 27.6* 500.3 K 69,797.01 K ' 747.0 K 104,203.99 K ' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 1 . W eight o f Non-Opt)mized Structure in Prototype Building o f 4 2 0 fe e t hiah T o t.t! M oor arm-. 2 4 3 0 0 0 s t n f . W e i g h t / f t - r t f . L e n g th T o ta l W e ig h t 18 ITS 176 14 672 118.27? a 48 159 159 6 7 ? 106.848 4 8 145 145 14 672 9 7 4 4 0 48 137 132 14 6 7 ? 88.704 48 170 120 6 7 ? ft 730 730 336 245.280 ?4 6 6 5 665 336 723 4 40 24 6 0 5 60S 336 203.280 74 550 550 336 184.800 ft 500 500 336 168 0 00 74 45 5 4 5 5 336 152.880 74 i 1 476 4 2 6 14 336 143 136 a 24 398 398 336 24 370 370 3 3? 124.370 a 24 colum ns W i4x 342 342 14 336 114.912 a 4 8 0 S u b t o t a l c o lu m n * 6 7 2 0 2 .1 8 5 .6 6 0 9 77Q beam * W1 R x|76 7 6 30 21600 1.641.600 a 480 lo ists W 18xlso 5 0 30 14400 720.000 a 1 2 0 0 S u b t o t a l b e a m * / to is tn 3 6 0 0 0 2 3 6 1 . 6 0 0 « 74 120 120 33 792 95.040 a 24 brace W14x 109 109 33 7 9? 74 9 9 9 9 33 792 78.408 74 brace W l4x « x > 9 0 33 792 71.280 a 24 brace W14x 82 8 2 33 792 64.944 a 129 S o b t o t a l h r.i 3 X 0 3 X . 0 0 0 9 1 7 4 0 T o t a l s t r u c t u r e w i t h d i a a o n a l b r a c e 46680 4 .9 4 3 .2 8 0 * Weight per square foot: 2 0 .3 4 p s f <9 9 9 9 0 20 9 6 0 8 6 .400 a 4 8 brace W14x 82 8 2 20 9 6 0 78.720 a 48 74 74 20 9 6 0 71.040 Hi f t f t 6 8 20 9 6 0 6 5 .780 48 brace W l4v 61 61 20 9 6 0 58.560 a p 2 4 f i___________________________s - h r ^ . ,1 4 « 0 0 3 6 0 .0 0 0 # 11 X 0 T o t a l s t r u c t u r e w i t h V » b r a c e _______________ 96 0 0 4 .9 0 7 .2 8 0 W etght p e r square toot: 2 0 .1 9 p s f Hi 90 9 0 19 912 8 2 .080 4 8 brace W l4x 8 ? 8 2 19 912 74.784 ?4 74 19 9 1 2 6 7 .488 • 4 8 brace W l4x 60 6 8 19 9 1 2 6 2 .016 a 4 8 brace W14x 61 61 19 9 1 2 55.632 a -2 .4 A ___________________________S u b to ta l b ra c e s ________________ 4 5 0 0 _ 3 4 2 .0 0 0 9 11 X 0 T o t a l s t r u c t u r e w i t h K n e e b r a e * 9 1 2 0 4 .8 8 9 .2 8 0 4 w eig h t p e r sq u are toot: 2 0 .1 2 p s f ft b race W 14x|90 9 0 25 6001 54.000 a 24 b race W 14x|62 8 2 25 6 0 0 4 9 .200 ft b race W 14x)74 74 2S 600 4 4 .4 0 0 a ft brace W l4 x j6 8 8 8 25 6 0 0 4 0 X 0 a 24 b race W 14xl6l 61 2S 600) 36.600 a -JU S______________________S u b to ta l h r a w . ________________ M O O 7 7 * 0 0 0 * 1 1 7 4 0 T o t a l S t r u c t u r e w i t h E B F 2 l i n k s _____________ 6 0 0 0 4 .7 7 2 .2 8 0 # W etght p e r sq u are foot: 1 9 .6 4 p s f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 2. Weight o f Non-Optlmlzed Structure In Prototype Building of 540 feet hloh T ot.tl flo o r .i o m : 2 4 3 0 0 0 v f W e i g h t / f t oir L e n g th e a c h ( f t) Total tenoth ( f t) W e ig h t 7 / / / / / / / / / / / S 7 / / / / / / S / / / S A / / y & s s s s / . 48 1 7 f t 176 18 864 152.064 a 1S Q 150 864 145 145 48 1 3 2 13? 18 864 114.048 48 rnliwnrK W l4x 12ft 120 18 864 103.680 74 mltimns wi4x 730 730 18 432 315.360 a 665 665 4 8 605 605 18 864 522.720 ?4 mlimmWUr 450 5 5 0 18 432 237.600 24 mo 500 18 43? 216 0 00 24 455 4 5 5 18 432 196 560 24 <?ft 4 7 6 18 432 184.032 a 24 colum ns W i4x 3 4 8 398 18 432 171.936 B 480 S u h t o t .i l col im n< 8 640 3.0S 1.216 # 720 beam s W l8 x |7 6 76 30 21600 1.641 600 a 480 tO lS tS W 18xl50 50 30 14400 720.000 a 1200 S u b t o r .t ! b r . i i w / m is ts 36000 2 3 6 1 .6 0 0 a 24 145 145 35 840 121.800 a 24 n ? 132 35 840 110 880 a 24 120 120 35 840 100.800 a 24 109 109 35 840 91 660 a 24 brace W i4x 99 9 9 35 840 63.160 a J 2 B __________________________ S u b to ta l b ra c e s ________________4 2 0 0 5 0 8 .2 0 0 9 11 7 4 0 T o t a l s t r u c t u r e w i t h d i a g o n a l h r a c e 48S«0 5 , 9 2 1 . 0 1 6 0 w e ig h t p er square foot: 2 4 . 3 7 p s f «ft brace w i4 x 90 9 0 23.S 1128 101 S70 a *ft brace W i4x 52 8 2 23.S 1128 9 2.496 a 4fl hm re W l4x 74 74 23.S 1128 8 3.472 4ft brace W l4x 5ft 6 8 23.5 1128 76.704 48 brace W i4x 61 61 23.5 1128 68.806 a -3 . 4 ft__________________________ ftuE tP tf* E f'T ™ ________________ S 6 4 0 _ _ 4 2 3 .0 0 0 » I I M P T o t a l s t r u c t u r e w i t h V - b r a c e 11280 5.835.816 t t W eight p er sq u are foot: 24.02 psf 48 brace W i4x 9ft 9 0 22 1056 9 5 .040 a 48 ft? 8 2 22 1056 86 .5 9 ? 4ft brace W i4x 74 74 22 1056 78.144 a 48 brace W14X f t 6 8 22 1056 71.808 a 48 brace W l4x 61 61 22 1056 6 4 .416 a 240 9 n h t n t .i l h r.. rt 5 2 8 0 3 9 6 .0 0 0 a I 8 6 0 T o t a l stru ctu re w i t h Knee b r a c e 10560 5.808.816 t t W eight p er square foot: 2 3.90 V 24 b race W i4x 9ft 9 0 27.6 662.4 59.616 a 24 brace W14x a ? 82 27.6 662.4 54.317 a 2« brace W14X 7 4 74 27.6 662.4 4 9 .018 a 24 brace W l4x ft 6 8 27.6 662.4 4 5 .043 * 24 brace w i4 x 61 61 27.6 662.4 4 0 .4 0 6 * |1 7 a S u M n t,> l h r . r » v T T H ? * **0-400 . . # 1 1 7 4 0 T o t a l s t r u c t u r e w i t h E B F 2 lin k s 6 624 5 .6 6 1 .2 1 6 0 W eight p er square foot: 2 3 3 0 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 3 . Optimization 1: Weight of Structure in Prototype Building of 420 feet hiah, wind 70 moh T n t.il flo o r d! r .i: 2 4 3 0 0 0 I W e ig h t/ftl Length | Total w eight I 32 columns W14x 1 7 6 - 176 1 448 78.848 £ 32 columns W l4x 1S9_ ISO 1 448 71.232 £ 32 columns W14x 145 145 1 448 64.960 £ 32 columns W14x 132 132 1 448 59.136 £ columns W14x 120 170 1 448 53.760 £ 32 columns W14X 109 109 1 448 48.832 £ columns W14x 22___ 0 0 1 4 4 8 44.352 £ 16 m iitm nsW 14x 20___ ; 9 0 1 224 20.160 £ columns W14x 730 730 1 224 163.520 £ 16 columns W14x 665__: 665 1 274 148.960 £ 24 m li mine W14x 60S i 60S 1 336 203.280 £ 24 columns W14x SSQ__1 550 1 336 184.800: £ columns W14x 500 son 1 774 112.000' £ 16 columns W14x <15 4 5 5 1 224 101.920 £ columns W l4x 47fr 4 7 6 1 274 95.4241 £ 398 1 774 89.1521 £ 170 370 1 224 82.880 £ 14? 342 1 774 7 6 608 £ columns W l4x i n 311 1 774 69.664 £ 16 columns W l4x f t ? 283 1 224 63.3921 £ 16 columns W14x 717 257 1 224 57.5681 £ 16 columns W14x 233 233 1 224 52.1921 • 4 4 0 S u b to tjl co lu m n * 672 0 1.942.640 9 720 beam s W l8x|76 76 301 2160011 1.641.6001 a 4 8 0 1O *SW 18xl50 50 301 1440011 720.0001 #1 1300 S u b to tjl b**.im * / io<sts 36000 2 3 6 1 .6 0 0 * 32 brace W l4x|99 00i 33 1056 104.544 £ 32 brace W l4xt90 90 33 1056 95.040 £ 28 brace W14x 82 87 331 974 75.768 £ 2 8 brace W 14xl74 74 331 924 68.376 9 120 SllhtOffll hr.-.• r»». 3960 343.728 # 11740 T o t a l s t r u c t u r e w i t h d i a a o n a l b r a c e 46680 4 . 6 4 7 . 9 6 8 9 W eight p e r sq u a re foot: 19.13 Pi 4 0 brace W14x 92 82 2 0 800 65.600 £ 4 0 brace W14x 74 74 2 0 800 S9.200 £ 32 brace W14x f l 68 7 0 640 4 3 570 £ 32 hrareW 14x 91 61 7 0 640 1 3 9 0*0 £ 32 brace W l4x 5? 53 2 0 640 1 33.920 £ 32 brace W14x 49 4 8 2 0 640 ' 30.720 £ 32 brace W l4x 43 4 3 2 0 640 1 27.520 4 240 S n h tn t.it htd: r r r. 48 0 0 299.520 9 11860 T o t a l s t r u c t u r e w i t h V - b r a c e 9600 4.603.760 9 W eight p e r sq u a re foot: 18.95 pi 4 0 brace W14x iff? J 8 ? 19 ' 760 62.320 £ 4 0 brace W14x 74 74 19 ' 760 56.240 £ 32 brace W l4x 99 68 19 ' 608 4 1 3 4 4 £ 32 brace W14x 9 1 61 19 608 37.088 £ 32 brace W14x L S 2 __ 53 ! 19 608 32.224 £ 32 brace W14x 42_ 4 8 1 19 608 29.184 £ 32 l brace W14x 43 4 3 1 19 608 26.144 » S iih tn la t hr.* r n * 4 5 6 0 284.544 9 [ S e p T o ta l s t r u c t u r e w i t h K n e e b r a c e 9120 4 .58 8 .7 8 4 # w eig h t p e r sq u a re foot: 18.88 p! 24 brace W14x 2*__ 74 25 600 4 4 * 0 0 £ 24 brace W14x £8___ 68 25 600 40.8 0 0 £ 24 brace W14x £1____ 61 2 5 6 00 36.600 £ 16 brace W14x S2___ S3 2 5 400 2 1 2 0 0 £ 16 brace W14x 4fi___ 4 8 25 400 1 9 2 0 0 £ 16 brace W i4x 43 43 2S 400 1 7 2 0 0 # 120 S iihtnf.il hr.* r ~ s 300 0 179.400 9 [ 1740 T o t a l s t r u c t u r e w i t h E 8 F 2 l i n k s 6 000 4.483.640 9 weight per square foot: 1 8 .4 5 p s f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 4 . Optimization 1: Weight of Structure in Prototype Building of 420 feet hiah. wind 90 moh T oM l f lo o r 2 4 3 0 0 0 • W e i g h t / f t off L e n g th e a c h ( f t) T o ta l le n e th f f t l W eig h t fo o u n d s ) / / / / / / / / / / / / / z Y //f V / / S S S / S / / / / S / / S / S / S / / S / S / / / S S S V , 3 ? 1 7 6 1 7 6 1 4 4 4 8 78.848 » 3? column* w i4 x 159 159 14 4 4 8 71.232 0 3? 145 145 14 4 4 8 64 960 f 32 132 132 14 4 4 8 59 136 32 120 120 14 448 53 760 3 ? 109 109 14 446 48.832 0 3? 99 9 9 14 448 44.352 f 16 90 90 14 224 20.160 3? 730 730 14 448 327 0 40 3? f i f t f t 665 14 4 4 8 797 9 20 74 f i f t f t 605 14 336 203.280 0 ?4 1 W 550 14 336 1 8 4 8 0 0 24 500 16 45*? 455 14 224 101.920 0 columns W i4x 42 6 426 14 224 95.424 39ft 1 ft 370 370 14 224 82.880 a 16 3 4? 1 ft 311 311 14 224 69 664 f 6 colum ns W l4x 283 283 14 112 31.696 0 4 8 0 S u h to t.it c o lu m n * € 7 3 0 2 ,1 6 0 ,6 0 4 * 770 beam s W l8 x |7 6 76 301 216001 1.641.600 a 480 W « S W 1 8 x l5 0 SO 30l 144001 720.000 0 1 2 0 0 S u b to ta l »oist» 3 0 0 0 0 ? / « 1 . g O O » n brace W l4x 109 109 33! 660 71.940 70 brace W i4x 9° 99 331 660 65.340 f 70 90 9 0 3 3 1 660 59.400 0 16 82 82 33 528 43.296 16 b race w i4 x 74 74 33) 528 39.072 16 f t f t 68 33| 528 35.904 12 brace w i4 x 61 61 331 396 24.156 0 - U f i ___________________________W " - " 1________________ 3 0 0 0 _ 3 3 0 .1 0 0 » 1 1 7 4 0 T o t a l s t r u c t u r e w i t h d i a o o n a l h r a c e 4 6 6 8 0 4,870.372 9 W eight p e r sq u are foot: 2 0 . 0 4 p s f 40 90 90 20 800 72.000 0 40 82 82 20 800 65.600 3? brace W i4x 74 74 20 640 47.360 37 brace W i4x f t f t 66 20 640 43.520 74 61 61 20 4 8 0 29.780 74 53 53 20 4 8 0 2S.440 24 brace W l4x 40 4 6 20 4 8 0 23.040 0 24 b race W l4x 43 43 20 460 20.640 0 2 4 0 5 o h to f.< l hr.> r^ < _________ « B » _ 3 S ti U » S L £ 1B 60 T o t a l s t r u c t u r o w i t h V - b r a c e 0 6 0 0 4 > 8 5 8 , 1 4 4 # weight per square foot 19.99 psf 3? 9ft 90 19 608 54 720 f 37 b race W14v ft? 82 19 608 49 .656 0 Z * brace W i4x 74 74 19 4 5 6 33.744 0 7 * brace W i4x f t f t 68 19 456 31.006 0 24 brace wi4x ftl 61 19 4 5 6 27.816 0 37 b ra e e w i4 x 5 3 S3 19 MR 32.224 0 32 brace W i4x <ft 46 19 608 29.184 0 4 0 brace W i4x 4 3 43 19 760 32.680 0 2 4 0 ___________________________S irh to tat b race*________________4 5 6 0 2 9 U 2 3 2 • l i a o o T o t a l s t r u c t u r e w i t h K n e e b r a c e 9 1 2 0 4 . 8 2 2 . 4 9 6 # w eight p e r sq u are foot: 1 9 . 8 5 p s f ft brace w i4 x 90 90 25 1400 126.000 0 20 b race W l4x 02 82 25 500 41.000 2ft 74 74 2S 4 0 0 29.600 0 2ft f t f t 68 25 400 27.200 0 12 brace W i4x 61 61 25 300 18.300 0 3J 1 4 i orace w i« x ie i i o ti j w i i p . j w i * -1 2 9 ______________________Sli&lttd1 frttCg_____________ 3 0 0 0 2 4 2 .1 0 0 8 1 1 7 4 0 T o t a l s t r u c t u r e w i t h E B F 7 l i n k s 6 0 0 0 4 . 7 7 3 . 3 6 4 # W eight p e r sq u are foot: 1 9 . 6 4 p s f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 5 . Optimization 1: Weight of Structure in Prototype Building of 420 feet hlah. wind 1X0 moh T o u l f lo o r 2 4 3 0 0 0 sf 9 W e i g h t / f t D lf L e n g th e a c h fffcl T o ta l l e n o th f f t l W e ig h t f o o u n d i ) w / / / / / / / / / / / > / / / / / / / / / / / / / / / / / / / / / / / / / > / / / / / / / / / / 3 2 1 7 6 1 7 6 4 4 8 78.848 a 3 ? 1S9 159 4 4 8 71.232 9 32 145 145 4 4 8 6 4 .960 3? 13? 132 4 4 8 5 9 .136 3? 120 120 4 4 8 5 3 .760 9 3? colum ns W i4x 109 109 4 4 8 4 8 .8 3 2 9 3 ? 99 9 9 4 4 8 4 4 .3 5 2 9 16 90 9 0 224 20.160 4 0 colum ns W14x 730 730 560 4 0 6 .8 0 0 4 0 colum ns W14* 665 665 560 372.400 4 0 eoium ns W14x (SOS «»s fifiO 338 800 550 550 4 4 8 246.400 9 34 500 500 336 168.000 9 24 455 4SS 336 1S2.880 16 426 426 774 95.424 26 colum ns W14x 398 396 224 89.152 a colum ns W l4x 370 , 370 112 . 41.440 9 4 9 0 S u b to ta l c o lu m n s 07 2 0 1 3 5 » J 7 6 f 770 b eam s Wt 8x176 76 30 21600 1 .641.600 4 8 0 10«S W 18xl50 50 30 14400 720.000 9 1 2 0 0 S u b to ta l b e a m s ' . c o s 3 6 0 0 0 2 J 6 1 . 6 0 0 9 12 1S9 159 331 396 62.964 9 12 145 14S 33l 396 5 7 .420 9 17 132 132 3 3 | 396 5 2 .272 12 120 120 3 3 | 396 4 7 .5 2 0 8 brace W l4x 109 109 3 3 1 264 2 8 .776 1? brace W i4x 9 9 9 9 331 396 39.204 f 12 brace W l4x 90 9 0 3 3 1 396 3 5 .640 1 ? brace W l4x a ? 82 33) 396 32.472 9 1 ? brace W 14X 7 4 74 33) 396 29.304 9 a 68 6 8 33) 264 17.952 8 brace W i4x 61 61 331 264 16.104 9 r 1 2 S t___________________________S u b to ta l b race*________________ 39 6 0 ______ 4 1 9 ,0 2 8 9 1 1 7 4 0 T o t a l s t r u c t u r e w i t h d i a o o n a l b r a c e 4 6 6 8 0 5 , 1 3 5 . 8 0 4 Weight per square foot: 2 1.13 p sf 3 ? brace w i4 x 179 120 20 640 76.800 9 3? 199 109 20 640 6 9 .760 f 3? brace W i4x 99 9 9 20 640 6 3 .360 9 32 brace W i4x 99 9 0 20 640 57.600 9 74 a? 8 2 20 4 8 0 39.360 24 brace W i4x 74 74 20 4 8 0 35.520 16 rw 6 8 20 320 2 1 .760 16 fti 61 20 320 19.S20 16 9 3 53 20 320 16.960 16 brace W14x 4 8 48 20 320 15.360 9 -JM fl________________________ S ufetstd tea css___________________________________ if liaeo T o t a l s t r u c t u r e w i t h V - b r a c e 9 6 0 0 S . 1 3 2 . 1 7 6 # w eig h t p e r sq u a re foot: 2 1 .1 2 psf 2« brace W l4x 13? 132 19 4 5 6 6 0 .192 * 74 170 120 19 4 5 6 54.720 24 109 109 19 4 5 6 4 9 .704 74 99 99 19 4 5 6 f 24 99 9 0 19 4 5 6 16 brace W i4x 97 82 19 304 24.928 • 19 74 74 19 304 22 .496 9 19 99 6 8 19 304 20.672 9 19 91 61 19 304 18.544 9 19 93 53 19 304 16.112 9 19 4 $ 48 19 304 14.592 9 24 brace W i4x 4 3 43 19 4 5 6 19.608 9 p r « w ______4 5 6 0 __ 3 6 7 . 7 S 2 m 1 1 9 6 0 a l s t r u c t u r e w i t h K n e e b r 9 1 2 0 5 , 1 0 3 , 9 2 8 t t W eight p e r sq u a re foot: 21.00 p sf | N 19 brace W i4x 170 120 25 4 0 0 4 8 .000 « 19 1 0 ? 109 2S 4 0 0 4 3 .600 19 ? ? 99 25 4 0 0 39.600 9 1 2 ?ft 90 25 300 27.000 12 brace W i4x a ? 82 25 300 24.600 9 a 74 74 25 200 14.800 9 a 9 a 68 7S 200 13.600 9 a 91 61 25 200 12.200 a 53 53 25 200 10.600 9 a 49 48 25 200 9 .6 0 0 9 8 brace W i4x 43 43 25 200 8 .6 0 0 9 _ t t 8 _ 11 7 4 0 S u b to ta l b race* T o t a l s t r u c t u r e w i t h E B F 2 l i n k s 3 0 0 0 2 5 2 .2 0 0 9 6 0 0 0 4 . 9 6 8 . 3 7 6 # W eight p e r sq u a re foot: 20.4 5 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 157 6. Optimization 1: Weight of Structure in Prototype Building of 540 feet htah, wind 70 moh t o t.i l f lo o r , v m : 2 4 3 0 0 0 *f W e ig h t / f t L en g th 32 colum ns W i4x _ 1 7 6 176 18 1 5761 101.376 £ 32 colum ns W i4x 159 159 18 576 91.584 * 32 colum ns W i4x 145 18 576 ft3 5?n £ 32 colum ns W i4x n ? 132 18 576 76.03? * 32 colum ns W i4x 179 120 18 576 69.120 £ 32 colum ns W i4x 199 109 18 S76 62.784 £ 32 colum ns W i4x 99 99 18 576 5 7 074 £ 16 colum ns W l4x 99 90 18 288 25.920 £ 40 colum ns W l4x 730 730 18 720 525.600 £ 40 colum ns W14v 66S 665 1ft 720 47ft Ann £ 4 0 colum ns W i4x 1 60S 605 18 I 720 435.600 £ 32 colum ns W14* sso 550 18 576 3 1 6 8 0 0 £ 24 colum ns W l4x soo SOO 18 437 216.000 * 24 colum ns W l4v _ 4 S 5 455 18 4 3 ? 196.560 £ 16 colum ns W i4x — 426 426 18 288 1?? 66ft £ 16 colum ns W l4v 398 398 1ft 288 114.624 £ 8 colum ns W i4x 370 370 18 1441 53.2801£ 4 0 0 S u b to ta l colum n* 8 8 4 0 3 .0 2 7 3 1 2 * 720 b eam s W18x 76 ! 76 301 21600 I 1.641.6001 *1 480 «M«S W lSx SO 50 301 1440011 720.0001*1 1 2 0 0 S u b to ta l bn.iim* / ioi*t« 3 6 0 0 0 2 3 6 1 . 6 0 0 » 16 brace W i4x 132 132 35 560 73.920 » 1? brace W i4x 129 120 3S 420 50.400 1? brace W i4x 199 109 35 420 45.780 * 12 brace W i4x 99 99 35 4 2 0 41.580 12 brace W i4x 99 90 35 4 2 0 37.800 • 12 brace W i4x ft2 82 35 4 2 0 34.440 1? 74 74 35 420 31.080 1? frS 68 35 4 2 0 28.560 20 brace W l4x 61 61 35 700 42.700 * 11 7 4 0 T o t a l s t r u c t u r e w i t h d i a g o n a l b r a c e 4 8 8 4 0 5 . 7 7 5 , 1 7 2 # W eight per sq u are foot: 2 3 . 7 7 p s f 64 99 90 23.5 1504 135.360 * K 82 82 23.5 1316 107.912 24 74 74 23.5 564 41.736 24 68 68 23.5 564 38.3S2 * 24 61 61 23.5 564 19 brace W i4x 93 53 23.5 376 19.928 * 16 b race W i4x 48 48 23.5 376 18.048 16 braee W l4x 43 43 23.S 376 16.168 * ________________________ s u b t i l S 640 4 ii. e o e * 11 8 6 0 T o t a l S t r u c t u r e w i t h V - b r a c e 11280 5 . 8 0 0 , 3 2 0 t t W eight per square foot: 23.87 psf w £ J3 * 1 § weight per square foot: 23.84 psf 4 8 9 9 99 22 1056 104.544 • 98 99 90 22 1056 95.040 32 82 82 22 704 57.728 24 brace W i4x 74 74 22 528 39.072 m 24 b race W i4x 68 66 22 578 35 904 18 61 61 27 352 21.472 18 b race w i4 x 53 S3 22 352 16.656 * 18 b race w i4 x 4 8 4 8 22 352 16.896 * 16 brace w i4 x 4 3 43 22 352 15.136 * -2 4 0 Subt<?tj!_bf-jC>s______________ 3200_____ 4 04.44 8 9 1 1 « 6 0 T o t a l s t r u c t u r e w i t h K n e e b r a c e ____ 10560 5 , 7 9 3 , 3 6 0 # 32 brace W i4x 99 99 27.6 8 8 3 .2 87.437 * 28 brace w u x 99 90 27.6 772.8 69.557 1 6 82 82 27.6 4 4 1 .6 36.211 * 12 brace W l4x 74 74 27.6 331.2 24.509 « ft tiff 68 27.6 220.8 15.014 * 8 61 61 27.6 220.8 13.469 * 8 S3 53 27.6 220.8 11.702 8 b race W i4x 4 8 48 27.6 2 20.8 10.598 • - 3 2 2 ____________________________________ h r . r . . ________________ r a - > f 1 1 7 4 0 T o t a l s t r u c t u r e w i t h E B F 2 l i n k s _____________ 6624 5 . 6 5 7 , 4 0 5 # W eight per square Ibot: 23.28 p sf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 7. Optimization 1: Weight of Structure in Prototype Building of 540 feet hiah, wind 90 moh T o t.il flo o r 2 4 3 0 0 0 Dtf Langth T o ta l tO Q O thttW . Watght w / T f fiM Z T ? 32 176 176 18 S76 101.376 w 32 column* W14x 159 159 18 576 91.584 8 t t column* W14v 137 132 18 576 76.032 a 32 120 120 18 576 6 9 .120 3? column* W14v 109 109 18 576 62.784 ft 32 9 9 99 18 576 57.024 a 16 9 0 90 18 288 25.920 a 1 8 colum ns W14* 730 730 18 864 630.720 a n . _ gehimns W24z f t? f t 5 18 2296 8 61 .6 4 0 a t t 60S 60S 18 576 348.480 f 24 550 550 18 432 237.600 a 16 column* w i4 x SOO SOO 18 288 144.000 1 6 4S5 455 16 column* W i4v 4 2 6 426 18 288 172.688 a 16 colum ns W i4x 398 398 18 288 114.624 a 4 0 0 S u b t o t a l c o lu m n s 8 6 4 0 3 . 1 M3 S 2 a 770 beam s W i8 x |7 6 76 30 21600 1 641.600 f 480 i o « s W i8 x l5 0 50 30 14400 720.000 a 1 2 0 0 S u b t n r .i l h e . m * / m is t* 3 6 0 0 0 2 3 6 1 . 6 0 0 9 1? brace W l4x 176 176 35 420 73.970 12 159 159 35 420 66.780 12 hm ee W 14x 115 145 35 420 60.900 f 12 13? 132 35 420 55.440 8 120 120 35 280 33.600 8 109 109 35 280 30.520 8 hm re W l4x 9 9 9 9 35 280 27.720 a 8 9 0 9 0 35 280 25.200 8 braee W i4x 87 82 35 280 22.960 8 brace W i4x 74 74 35 280 20.720 a 8 . ft 68 35 280 19.040 # 16 brace W i4x 61 61 35 S60 34.160 a ^uhfcn^i I' 4 2 0 0 479.0ft f 11 7 4 0 T o t.il s t r u c t u r e w i t h d i a g o n a l b ra c t* 48840 5 , 9 9 0 . 9 1 2 # W eight per square (Poe: 2 4 . 6 5 psf 24 braee W i4x 145 145 23.S 564 ftl .780 f ?4 brace W i4x 132 23.5 564 74.448 a 24 120 120 23.5 564 6 7 .680 24 brace W i4x 109 109 23.5 564 6 1 .476 f 1? brace W l4x 9 ? 99 23.5 376 37.224 a 16 brace W l4x 40 on 23.5 376 33.840 16 t t 82 23.5 376 30.832 a 2? brace W l4x 7« 74 23.5 376 7 7 8 2 4 a 1 6 . f t 68 23.5 376 25.568 a 61 61 23.5 376 72.936 1? brace W i4x 53 53 23.5 376 19.928 a 16 braee W14» 4ft 4 8 23.S 376 18.048 16 brace W l4x 43 43 23.5 376 16.168 a —2 4 0 ___________________________s u b to ta l h r * r « ._______________ 5 6 4 0 S 1 7 .7 S 2 9 11 8 6 0 T o t a l s t r u c t u r e w i t h V - h r a c e 11280 6 . 0 3 7 . 7 0 4 # W eight per square foot: 2 4 . 8 5 psf ?4 brace W l4x 14$ 145 22 528 76.560 a ?4 brace w i4 x 2?2 132 22 528 6 9 .696 a ?4 brace W l4x 120 120 22 528 6 3 360 f 24 109 109 22 528 5 7 552 16 braee W i4x 9 9 99 22 3S2 34.848 a 16 9 0 90 22 352 31.680 4 2? brace W l4x t t 82 22 352 28.864 a 2? brace W l4x 7« 74 22 3S2 26 0 48 a 2? brace W14x 68 68 22 3S2 73 9 36 a 16 61 61 22 352 21.472 f 2? brace W l4x S3 S3 22 352 18.656 a 2? brace W l4x f t 4 8 22 352 16.896 a 16 brace w i4 x 4 3 43 22 3S2 15.136 a 2 4 0 Si.hM tM h r j . r x 5 M 0 4 0 4 .7 0 4 4 i i 8 6 0 T o t a l s t r u c t u r e w i t h K n e fr b r a c e 10560 6 . 0 0 4 . 6 5 6 4 W eight per square foot: 2 4 . 7 1 p s f 22 brace W i4x 2 f t 145 27.6 331.2 48 .024 a 12 13? 132 27.6 331.2 4 3 .718 a 17 brace W l4x 120 120 27.6 331.2 39.744 a 12 109 109 27.6 331.2 36.101 a 8 99 99 77.6 220.8 71.859 8 90 90 27.6 220.A 19.872 a 8 t t 82 27.6 220.8 18.106 a 8 74 74 27.6 770 ft 16.339 f 0 brace W l4x f t 68 27.6 220.8 15.014 a 8 61 61 27.6 270.fi 13.469 a n brace W l4x t t S3 27.6 220.8 11.702 s 5 brace W i4x f t 4 8 27.6 220.8 10.S98 a 8 brace w i4 x 43 43 27.6 2 20.8 9 .494 a J t t P ___________________________S u b to ta l h r* rg*_______________ 3 3 1 2 3 0 4 .0 4 2 . 9 1 7 4 0 T o t a l s t r u c t u r e w i t h E B F 2 l i n k s 6624 S . 8 2 3 . 9 9 4 # W eight per square foot: 2 3 . 9 7 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 8. Optimization 1: Weight of Structure in Prototype Building of 540 feet hioh. wind 110 moh T o t.tl f lo o r o r r .i ; 2 4 3 0 0 0 -if I Weight / f t ) Length I Total | W tight | 3 ? 1 colum n* W l4x 176 176 18 576 101.376 £ 32 colum n* W l4x 119 159 18l 576 91.584 £ 3 ? 145 145 18| 576 ft3 5?0 £ 32 13? 132 1fti 576 7 6 0 3? £ 3 2 colum ns W l4x 170 120 1ft S76i 6 9 1 2 0 £ 3 ? . eolum n* W14* 109 109 1 8 | 5761 6 2 784 £ 3 2 99 99 if t| 576 5 7 024 £ 16 colum ns W l4x 90 90 1 8 288 75.920 £ 120 730 730 18} 2 160 1.576 800 £ 3? columns w i4 x 669 66S 1 8 | 576 383.040 £ 24 colum ns w i4 x 609 605 18) 432 261.360 £ 16 colum ns w i4 x 990 5S0 18l 288 1S8.400 £ 1 6 colum ns W i4x 900 S O O 18) 288 144.000 £ 16 colum ns W i4x 499 455 1 8 288 131.040 £ 16 colum ns W14X 426 426 I 8 t 288 122.688 * 4 0 0 S u b t o t a l c o lu m n * . 8 6 6 0 3.366.688 * 720 76 3 0 216001 1.641.600 a 4 8 0 loisrs w iftxl50 SO 3 0 144001 720.000 * 1 2 0 0 S u m o t.il >o.vrs 3 6 0 0 0 2 3 6 1 .6 0 0 * i? 731 ?33 35 4 2 0 12 211 211 35 420 88.620 a 12 193 193 3 5 420 81.060 a 8 179 176 3 5 280 49.280 a 159 159 3 5 280 44.570 ft 149 14S 35 280 40.600 ft 13? 132 3S 280 36.960 a 8 1?0 120 3 5 280 33.600 a ft 109 109 3 5 280 8 99 99 3 5 280 8 90 90 35 280 25.200 8 ft? 82 3 5 280 6 7* 74 3 5 280 20.720 a 4 brace W l4x 68 68 35 140 9 5 2 0 a , - U f i ____________________________________________________________ 4 2 0 0 4 0 0 .1 4 0 a 11 7 4 0 T o t a l s t r u c t u r e w i t h d i a o o n a l b r a c e 4 8 8 * 0 6 . 3 1 5 , 4 2 8 # weight per square foot: 25.99 psf 16 ?11 211 2 3 .5 376 79.336 16 191 193 2 3 .5 376 16 176 176 2 3 .5 376 66.176 1 6 159 159 2 3 .5 376 59.784 16 149 145 23.5 376 54.S70 a 16 132 132 2 3 .5 376 49.632 a 16 brace W i4x 129 120 2 3 .5 376 45.170 a 16 10? 109 2 3 .5 376 40.984 16 brace W l4x 99 99 23.5 376 37.274 16 90 90 23.S 376 3 3 8 4 0 a 16 92 82 2 3 .5 376 3 0 8 3 2 a 16 74 74 2 3 .5 376 27.824 I f brace W i4x 99 6 8 23.5 376 25.S68 a 16 61 61 2 3 .5 376 22 9 36 16 brace W l4x 2 — 53 2 3 .5 376 19.928 a 2 * 0 Subtotal brace* 56 4 0 6 4 4 2 7 2 * 11B 6 0 T o t a l s t r u c t u r e w i t h V - b r a c e 11280 6 .3 7 2 .5 6 0 * W eight per square foot: 25.22 psf 24 braee W i4x 211 211 22 528 a 16 193 193 22 352 67.936 1 6 braee W l4x 176 176 22 357 61.95? 16 199 159 22 352 16 145 145 22 3 5 ? 51.040 a 16 13? 132 22 352 16 brace W l4x 1?0 120 22 352 47.740 a 16 brace W i4x 10? 109 22 352 38.368 a I f 99 99 22 352 34.848 a 1 6 brace W i4x 90 90 22 352 31.680 a 16 ft? 82 22 3 5 ? 2ftJI64 16 74 74 22 352 76.04ft 1$ 60 68 22 352 23.936 a 1 6 brace W i4x 61 61 22 3S2 21.472 8 brace W i4x S3 S3 22 176 9.328 a S O S L __________________________ S u b to ta l_b r a e * ________________ S 2 8 0 6 5 1 .5 5 2 * 1 1 6 0 T o t a l s t r u c t u r e w i t h K n e e b r a c e ____________ 10560 6 . 3 5 7 , 8 4 0 # weight per square foot: 26.16 psf 22 b race W i4x 193 193 2 7 .6 331.2 63.922 a ft b raee W i4x 176 176 2 7 .6 220.8 38.861 a 8 15? 159 2 7 .6 2 20.8 35.107 a f t b race W i4x 1*5 145 2 7 .6 2 20.8 32.016 a ft b raee W i4x 15? 132 2 7 .6 220.8 29.146 8 b race W i4x 120 120 7 7 .6 220.8 26.496 a 8 b raee W i4x 109 109 2 7 .6 220.8 24.067 a 8 b raee W i4x 99 9 9 2 7 .6 220.8 21.859 a 8 b raee W i4x 90 9 0 2 7 .6 2 20.8 19.872 a 8 b race W l4x ft? 8 2 2 7 .6 220.8 18.106 a 8 b raee W i4x 74 74 2 7 .6 2 20.8 16.339 a A b ra e e W i4x 66 66 2 7 .6 220.8 15.014 a ft b raee W i4x 61 61 2 7 .6 220.8 13.469 a 8 b raee W i4x ff? 53 2 7 .6 220.8 11.702 a 4 b ra e e W i4x 48 4 8 2 7 .6 110.4 5,299 a 1 2 0 SuM nf.il h ra ro * 3 3 1 3 3 7 * 11 7 4 0 T o t a l s t r u c t u r e w i t h E B F 2 l i n k s 6 6 2 * 6 , 0 7 7 , 5 6 3 » weight per square foot: 25.01 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 160 9 . Optimization 2: Weight of Structure in Prototype Building o f 420 feet hiati. wind 70 mph T o ta l f lo o r 2 4 3 0 0 0 sf | w « t g h t / f t | L e n g th | T o u t I m i g h t I 16 colum ns W l4x 176 176 224 39.424 0 1ft colum ns W l4x 119 1W 224 35.616 £ 16 eolum ns W l4x 145 14S 224 32.480 £ 1ft colum ns W l4x' 13? 132 224 2 9 .568 £ 1ft colum ns W l4x 120 120 224 26.R80 £ 16 colum ns W l4x 109 109 224 2 4 .416 £ 16 colum ns W 14x 9 9 9 9 224 2 2 .176 £ 16 colum ns W l4x 9 0 90 224 7 0 160 £ 16 8 2 82 774 1ft 36ft £ 16 colum ns W l4x 74 74 224 1 6 .576 £ 16 eolum ns W l4x 6 8 6ft 224 15 2 3? £ 16 colum ns W l4x 61 61 224 13.664 £ 16 colum ns W14x S3 53 224 11-872 £ 16 colum ns W l4x 4 8 48 224 10.752 £ 16 colum ns W l4x 4 3 43 224 9 6 3 ? £ 16 c olum ns W l4x 730 730 1 224 1 6 3 ^ 2 0 £ 16 colum ns W l4x 5 5 0 550 224 123.200 £ 16 colum ns W l4x 4 2 6 476 224 9 5 .4 2 4 £ 1ft colum ns W l4x 342 34? 224 7 6 .608 £ 16 colum ns W l4x 257 257 224 5 7 .568 l £ 16 colum ns W l4x 193 193 224 4 3 .2 3 2 1 £ 16 colum ns W l4x 14S 146 224 3 2 .480 l£ 1ft colum ns W l4x 120 120 224 2 6 .880 £ 1ft colum ns W i4x 109 109 224 1 2 4 .416 £ 1ft colum ns W i4x 2 2 ___ 99 224 i 2 2 .176 £ 1ft colum ns W i4x 2 2 ___ 90 224 20 .160 1ft colum ns W i4x 32__ ' 82 224 18.368 £ 1ft eolum ns w i4 x 2±_ _ 74 224 16.576 £ 16 m lu m n s W14x £ 8 ___ 68 224 1S.232 £ 16 colum ns W l4x 61 61 2 24 13.664 # 4 3 0 S u b t o t a l c o lu m n * < 7 2 0 1 , 0 7 6 3 2 0 9 720 76 30 21600 1.641.600 4 8 0 w tses w i s v l s o 50 3 0 14400 7 2 0 .0 0 0 • 1 2 0 0 3 6 0 0 0 2 3 6 1 , 6 0 0 f 8 3? b ra c e W l4x 9 9 99 33 10561 104.544 B 8 2 2 b ra c e W i4x 9Q 90 33 1056} 9 5 .0 4 0 • 29 ft? 82 33 924} 7 5 .7 6 8 B S 28 b ra c e w i4 x 74 74 33 9241 6 8 .3 7 6 B * 1 » _________________________S i . f f t . ' 3 9 6 0 343.725 * 1 1 7 4 0 T o t a l s t r u c t u r e w i t h d i a g o n a l b r a c n 4 6 6 8 0 3 . 7 8 1 , 6 4 8 < t W eight p er s o u are foot: 1 5 . 5 6 p s f 4 0 8 2 82 20 8 0 0 6 5 .6 0 0 32 f t f t 68 2 0 6 4 0 4 3 .5 2 0 B 32 61 61 2 0 6 4 0 3 9 .040 B 32 53 53 20 6 4 0 3 3 .920 B 32 *ft 48 20 6 4 0 3 0 .720 B 32 b ra c e w i4 x 4 3 43 20 6 4 0 27 .520 B -J M fl________________________ SMhtnt.v h r..rr< _______________4 0 0 0 200 3 2 0 9 11860________T o t a l S t r u c t u r e w i t h V - b r a c e _______________ 9 6 0 0 3 .7 3 7 .4 4 0 # W eight p er s q u are foot: 1 5 . 3 8 p s f 4 0 8 2 82 19 760 6 2 .3 2 0 B 4 0 b ra c e W l4x 74 74 19 760 5 6 .240 B 32 f t f t 68 19 6 0 8 4 1 .3 4 4 B 32 61 61 19 6 0 8 3 7 .088 B 32 53 53 19 6 0 8 3 2 .224 32 4ft 48 19 6 0 8 2 9 .184 B 32 b race w i4 x 4 3 43 19 6 0 8 2 6 .144 B - 2 4 Q ___________________________ 5 u b U » « i I .r a r ^ _________________ 4 W O_____ 2 8 4 3 4 4 8 1 1 8 6 0 T o t a l s t r u c t u r e w i t h K n e e b r a c e _____________91 2 0 3 . 7 2 2 . 4 6 4 # W eight per sq u are foot: 1 5 . 3 2 p s f ?4 74 74 25 6 0 0 4 4 .4 0 0 e 24 f t f t 68 25 6 0 0 4 0 .8 0 0 B ft ftl 61 25 6 0 0 3 6 .6 0 0 f 16 b ra c e W i4x ft? 53 26 4 2 6 2 2 .0 4 8 16 b ra c e W14x 4ft 4ft 25 4 0 0 1 9 .200 16 b ra c e w i4 x 4 3 43 2 5 4 0 0 17.200 # S u h r o t.M h r .v m , 11 7 4 0 T o t a l s t r u c t u r e w i t h E 8 F 2 l i n k s 6 0 3 2 3 . 6 1 8 , 1 6 8 * W eight p e r sq u a re foot* 1 4 . 8 9 p s f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 10. Optimization 2: Weight of Structure in Prototype Building of 420 feet hkah. wind 90 moh T n t.il t lo o r 2 4 3 0 0 0 s'. I Weight / n I Length I Total | W eight I 176 176 1 224 3 9 4 24 a 16 154 159 1 224 35.616 a 16 H 5 145 1 224 32.480 # 16 n ? 132 1 224 a 16 120 120 1 224 26.880 ff 109 109 1 274 24.416 ff 16 99 99 14 224 22.176 ff 16 90 40 14 224 20.160 ff 1 6 82 82 14 224 18.366 ff 74 74 224 16.S76 ff 68 68 224 15.232 a 16 61 61 14 224 13.664 ff 1 6 53 53 224 11.872 ff 4A 48 224 10.752 a 16 41 43 14 224 9.6 3 2 ff 16 710 730 14 224 1 6 3 5 2 0 f s s o 550 224 123.200 ff 16 67ft 426 14 224 4 5 4 24 ff 16 147 342 14 224 7 6 6 08 f 16 757 257 14 224 57.568 f 143 143 224 43.2 3 2 145 145 224 32.480 a 120 120 14 224 26.880 16 109 109 14 224 2 4 4 16 ff 16 55 49 14 224 22.176 a 16 5ft 90 14 224 20.160 a 16 67 62 14 224 1 8 3 6 8 a 16 74 74 24 224 16.576 a 16 66 68 224 15 737 a 16 colum ns W14x 61 61 24 224 13.664 a 4 8 0 S u b t o t a l c o lu m n * 6 7 2 0 1 .0 7 6 .3 2 0 9 720 b eam s W l8 x |7 6 76 30 21600 1.641.600 A 4 8 0 w s ts w i8 x lS 0 SO 30 14400 720.000 *i 1 2 0 0 S u b t o ta l br*am * / 3 6 0 0 0 2 .3 6 1 .6 0 0 9 h raee W 14 x |lt)4 109 33 660 71 440 a 20 b race W l4x 99 49 33 660 6 5 .3 4 0 a 20 h ra re W 14v|4ft 40 33 660 5 4 4 0 0 ff 16 1 b race W14x 82 82 33 528 4 3 .2 4 6 a 16 i b ra c e W l4 x | 74 74 33 528 39.072 a i b ra c e W l4 x |6 8 68 33 528 3 5 4 04 0 12 b race w i4 x l6 i 61 33 396 24.1 5 6 a 1 2 0 r a* 3 0 6 0 3 3 9 .1 0 8 * 1 7 4 0 T o t a l s t r u c t u r e w i t h d i a a o n a l b r a c e 46680 3 . 7 7 7 . 0 2 8 « W eight p er sq u are foot: 1S .54 p s f 4 0 40 90 20 800 72.000 4 0 brace W l4x 82 82 20 800 65.6 0 0 a 32 74 74 20 640 4 7 .3 6 0 a 32 68 68 20 640 4 3.S 20 f f ?4 brace W14x $1 61 20 480 2 4 2 80 a 24 53 S3 20 480 25.4 4 0 f f 24 4 8 48 20 480 23.0 4 0 f f 24 brace W14x 43 43 20 480 20.6 4 0 a S u b t n r a l hr.*<-«»<. [ i 8 6 0 T o t a l s t r u c t u r e w i t h V - b r a c o 9600 3 , 7 6 4 . 8 0 0 # weight per square foot: 15.49 psf 37 50 90 19 60S| 54.720 a 3? brace W14x 97 82 14 6 0 8 1 4 9 .8 5 6 a 24 brace W l4x 74 74 19 456 33.744 a 24 brace W14x 68 68 19 4561 31.008 a 24 brace W l4x 61 61 19 4S6| 27.816 a 32 brace W14x S3 53 19 6081 32.224 a 32 brace W !4x 4 8 48 19 608] 29.184 a 4 0 brace W l4x 4 3 43 19 760l 3 2.6 8 0 a - 2 4 0 ___________________________S u h t n t.0 h n r f . ________________4 5 4 0 2 9 1 -2 3 2 9 11 8 6 0 T o t a l s t r u c t u r e w i t h K n e e b r a c e 9120 3 . 7 2 9 . 1 5 2 P W eight p e r sq u are foot: 15.35 psf S6 90 25 1400 126.000 a 20 82 25 500 41.0 0 0 f f 16 b race W l4 x |7 4 74 2S 400 29.600 f f 16 68 26 416 28.288 f f 12 b rc te w i4 x i6 l 61 2S 300 1 8 3 0 0 * . 1 2 0 __________________ 3 0 1 0 2 6 3 .1 8 8 _ # 11 7 4 0 T o t a l s t r u c t u r e w i t h E B F 2 l i n k s 603 2 3 . 6 8 1 . 1 0 8 9 w eight p e r sq u are foot: 15.15 p sf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 11. Optimization 2: Weight of Structure in Prototype Building of 420 feet hiah. wind 110 moh T u t j l f l o o r 2 4 3 0 0 0 st 3 £ i I . 1 W e i g h t / f t o ff L en g th e a c h m i T o tal le n o th m i W e ig h t ( p o u n d s ) y / / V / // / / / / / /A O Y / / / // S / A YSSSSSSSSSSSSSJ 16 176 14 224 39.424 g 16 159 14 224 3 5 .616 # 16 145 224 3 2 .480 16 132 14 224 2 9 .568 120 14 224 2 6 .8 8 0 16 109 14 224 2 4 .416 tf 16 9 9 1 4 224 2 2 .1 7 6 16 9 0 14 224 2 0 .1 6 0 g 16 8 2 14 224 1 8 .368 g 16 74 14 224 1 6 .576 6 8 14 224 15.737 16 61 14 224 13.664 g 16 53 14 224 1 1 .872 g 16 4 8 14 224 1 0 .757 g I t colum ns W l4ir|43 4 3 14 224 9 .6 3 2 g 16 eolum nsW 14x|730 730 14 224 163.520 g 16 SSO 14 224 123.2 0 0 P 16 4 2 6 224 9 5 .4 2 4 g 16 342 224 7 6 608 f 16 257 14 774 5 7 .5 6 8 16 193 14 724 4 3 .2 3 2 16 145 14 224 3 2 .4 8 0 p 16 120 14 724 2 6 .8 8 0 16 colum ns w i4 x | 109 109 14 224 2 4 .4 1 6 g 16 9 9 14 724 7 7 .1 7 6 16 colum ns W 14x|90 9 0 14 224 2 0 .160 P 16 82 224 1 8 .368 g 16 colum ns W l 4*174 74 14 774 1 6 .576 g 16 68 14 774 16 7 3? g 16 columns W l4 * l6 l 61 14 224 13.664 a 430 Subtotal folumm 6720 1.076320 * 720 76 30 216001 1 .6 4 1 .6 0 0 * 480 io « s w i 8 x l s o 50 30 144001 7 2 0 .0 0 0 * 1 2 0 0 S u b t o t a l S u m s ' to .s t s 3 6 0 0 0 2 J 6 X . 6 0 0 * 1? Brace w i4 x 15? 159 33 3961 6 2 .9 6 4 g 12 141? 145 33 396* 5 7 .4 2 0 ft 12 Brace W i4x 1?? 132 33 396 57 .272 a 2? brace W l4x i n 120 33 396 4 7 .5 2 0 a 8 Brace W i4x 20? 109 33 264 2 8 .7 7 6 a 12 99 9 9 33 396 3 9 704 p 1? hrare W 14x 90 9 0 33 396 3 S .640 a 1? hrare W 14* 8 ? 8 2 33 396 3 2 .4 7 2 f 1? hrare W 14x 74 74 33 396 2 9 .304 p f t 68 68 33 264 1 7 .952 P 8 Brace W i4x 61 61 33 264 16.104 a _ 1 » ___________________ Subtotal been*____________3960 419.623 • Il740 Total stru ctu re w ith diagonal brace 46680 3 .8 5 7 ,5 4 8 9 W eight per square fooe 1 5 .8 7 psf 37 Brace W l4x 17? 120 20 640 7 6 8 0 0 f 37 hm reW l4w 209 109 20 640 6 9 .7 6 0 37 99 99 20 6 4 0 6 3 .3 6 0 3? 90 90 70 640 5 7 .6 0 0 74 0 ? 82 70 4 8 0 3 9 .3 6 0 24 74 74 20 4 8 0 3 5 .5 2 0 16 brace W l4x 66 68 20 320 2 1 .7 6 0 • 16 61 61 20 ? ? 0 1 9 .520 a 16 brace W14* S3 53 20 320 1 6 .9 6 0 a 16 Brace w i4 x 48 4 8 20 320 1S.360 a 240 Subtotal_hrac*____________-^*77 f i I860 Total stru ctu re with V-brace___________ 9600 3 .8 5 3 .9 2 0 3 weight per square foot: 1 5 .8 6 psf 24 brace W i4x 232 132 19 4 5 6 6 0 .1 9 7 a 24 brace W l4x 220 120 19 4 5 6 54.720 a 24 brace W i4x 10? 109 19 456 4 9 .7 0 4 a 24 hraee W l4x 99 9 9 19 456 4 5 .1 4 4 a 24 brace W i4x 9 0 9 0 19 4 56 4 1 .0 4 0 a 26 brace W l4x 82 8 2 19 304 2 4 .9 2 8 a 26 brace W i4x 74 74 19 304 2 2 .4 9 6 a 26 brace W l4x 66 6 8 19 304 2 0 .672 a 26 hraee W l4x 61 61 19 304 1 8 .544 a 26 hraee W i4x n 53 19 304 16.112 f 26 hraee W l4x 46 4 8 19 304 14.S92 a 24 brace W14x 4 3 4 3 19 4 5 6 1 9 .608 a JMfl____________________Subt.-M! braces____________4560 387.752 « 1360 Total stru ctu re with Knee brace 9120 3 ,8 2 5 .6 7 2 # W eight per SQuare foot: 1 5 .7 4 psf 16 170 120 25 400 4 8 .0 0 0 16 hraee W l4x 109 109 25 400 4 3 600 a 16 99 99 25 400 3 9 .6 0 0 a 22 hraee W14x 9 0 90 2S 300 2 7 .0 0 0 a 12 brace W i4x 62 82 2S 300 2 4 .6 0 0 a 6 74 74 7S 200 1 4 .800 p 6 brace W i4x 68 68 2S 200 1 3 .600 a 6 brace W i4x 61 61 25 200 12200 a 6 brace W l4x S3 S3 2S 200 1 0 .600 a 6 brace W i4x 99 4 8 25 200 9 .6 0 0 a 8 brace W i4x 4 3 43 2S 200 8 .6 0 0 a 3000 _ 2 S 2^00 * 1X740 Total stru ctu re w ith EBF 2 links 6000 3 .6 9 0 .1 2 0 # weight per square foot: 1 5 .1 9 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 12. Optimization 2: Weight of Structure in Prototype Building of 540 feet hkjh. wind 70 molt T o i.tl f lo o r 2 4 3 0 0 0 sf ._ y W eig h t/ft Length 1 each ( f t ) 1 ► Total W eight f o o u n d a t W / 6 176 lS l 2881 SO.ftRA * 16 159 18) 288 4 S .792 1 6 1*5 18 288 16 132 18 288 38.0 1 6 1ft 120 181 288 1 4 560 16 109 18| 288 31.3 9 2 9 16 99 18j 288 2 8 .5 1 ? 16 90 18! 288 25.9 2 0 9 16 82 18! 288 23.6 1 6 9 1ft 7* 18| 288 1ft 66 is ! 288 14.5R* # 1ft 61 18) 288 17.568 ift 53 181 288 15.26* 1ft 4 8 i r | 288 13.82* 1ft 41 18 288 12.3 8 4 16 730 18| 288 21 0 .2 4 0 1ft 550 1R| 288 158.400 m 1ft 4 26 1R| 288 122.688 16 342 18 288 9 8 .4 9 6 1ft 257 18) 7RR 7 4 .0 1 6 1ft 193 18| 288 55.S 84 1ft 145 18| ?ft«i 4 1 .7 6 0 1ft 120 18) 288 34.S 60 16 109 18| 288 3 1 .3 9 ? 9 1ft 99 18) 288 28 .S 1 ? a 16 90 18) 288 2 5 .9 2 0 1ft 62 l 8 l 288 2 3.6 1 6 16 7* 18) 288 2 1 .3 1 ? 1ft 68 18! 288' 19.584 0 16 colum ns W l* v l6 l 61 181 2881 17.568 a 4 8 0 Subtotal columns 8 4 8 0 1 3 8 3 4 4 0 » 720 beemswi 8x |7 6 76 30 216001 1 .6 * 1 .6 0 0 a 48 0 lotses w is x ls o 50 30 144001 720 .0 0 0 a 1 2 0 0 Subtotal hr.im < / 3 4 0 0 0 2 J 6 1 . 6 0 0 9 16 11? 112 35 560 1 ? b race W l4x 1?ft 120 35 420 50.4 0 0 I ? 109 109 35 42 0 4 5 .7 8 0 1? 9 9 9 9 3S 4 2 0 12 b race W14* 9 0 90 35 4 2 0 37.8 0 0 a 1? b race w i* x ft? 82 3S 420 12 b race W i4x 7* 7* 35 4 20 3 1 .0 8 0 a 12 b race W i*x ft? 68 35 4 2 0 2 8.S 60 m 2 0 b ra c e W i*x 61 61 35 7 0 0 4 2 .7 0 0 9 p l2 f i________________________ Siihtnf.*! h r .r .s ______________ 4 2 0 0 3 8 4 .2 4 0 * 11740 T o ta l s t r u c t u r e w it h d ia g o n a l b ra c e ________ 4 86*0 4 . 1 3 1 . 7 0 0 # W eight p er sq u are foot: 1 7 .0 0 p sf ft* b race V ft4r 9 0 90 21.5 ISO* 135.360 5ft ft? 82 23.5 1316 1 07.91? 24 74 7* 23.S 564 * 1 .71ft 24 f t f t 68 71.5 564 3 8 .3 5 ? 24 ftl 61 23.5 564 a 1ft b race W l*x ft? 53 23.5 376 19.928 a 1ft 4ft 48 23.5 376 18.0 4 8 1 6 b race W14> 4 3 4 3 23.5 376 16.1 6 8 9 I-24S____________________ ftu tt"* * 1 h a s s s ________________ 5 4 4 0 ----------4 1 1 . 0 0 8 t 1 1 8 4 0 T o t a l s t r u c t u r e w i t h V - b r a c P 11280 4 . 1 5 7 . 3 4 8 » W eight p er sq u are foot: 1 7 . 1 1 p sf b race w i* x 9 9 99 22 1056 104.5*4 9 * 8 b race W l*x 90 90 22 1056 9 5 .0 4 0 0 3 ? b race W l*x 82 82 22 70* S 7.728 0 24 b race W l*x 74 7* 22 528 39.0 7 2 9 24 b race w i* x f t f t 68 22 S28 3 5.9 0 * 9 1ft b race W l*x ftl 61 22 3S2 2 1.4 7 2 9 1ft b race w i* x ft? S3 22 352 1 8.6 5 6 1ft b race w i4 x *ft 48 22 352 16.8 9 6 9 16 b race W i4x 4 3 4 3 22 3S2 15.1 3 6 9 2 4 0 __ ... h r ; w ______________ 5 28 0 4 0 4 .4 4 8 » 1 1 8 4 0 T o t a l s t r u c t u r e w i t h K n e o b r a c e I0 S 6 0 4 ,1 4 9 ,8 8 3 i t W eight p e r sq u are foot: 1 7 .0 8 p sf ft? 99 99 27.6 8 83.2 8 7 .4 1 7 0 2ft b race W l4x 9 0 9 0 27.6 7 72.8 6 9 .SS? a 1ft 82 82 27.6 4 4 1 .6 36.211 a 12 74 74 27.6 331.2 24.5 0 9 R f t f t 68 27.6 220.8 15.014 a f t ft1 61 27.6 220.R 13.4 6 9 9 f t b race w i* x ft? 53 27.6 2 20.8 11.7 0 2 9 8 b race W i4x 4 8 4 8 27.6 2 2 0 .8 10.5 9 6 9 r - U B ________________________ 4 nhtor„i 3 8 1 2 2 4 8 ^ 8 3 » 11 740 T o ta l s t r u c t u r e w it h EBF 2 lin k s 662* 4 . 0 1 3 . 9 3 3 P W eight p er sq u a re foot: 1 6 . 5 2 p sf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 3 . Optimization 2: W eight o f Structure in Prototype Building of 54 0 fe e t hiah. wind 90 moh 164 T o u t !1r>0f .ir.Ni: 2 4 3 0 0 0 * W e i g h t / f t o lf L en g th e a c h ( ft) T o ta l le n o th .lf tl w e i g h t { D o u n d s l V j v ///////////s s /r s //y s s s ^ ^ 1ft 176 18 288 50.68ft 1ft 159 1ft Tftft 4 5 .7 9 2 * 16 145 1A 288 4 1 .7 6 0 16 132 1ft Tftft 3 8 0 1 6 16 120 1ft 288 3 4 .5 6 0 a 1ft 109 1ft Tftft 31 .392 1$ colum ns w i4 x 9 0 99 18 288 2 8 .5 1 ? 16 90 1A 288 2 5 .9 2 0 16 82 1A 288 2 3 .6 1 6 16 74 1ft Tftft 2 1 .3 1 ? 16 68 18 288 19.5A4 16 61 18 288 1 7 .568 a 16 53 1ft 288 1 5 .264 a 16 48 1ft Tftft 13.824 16 43 18 288 1 2 3 8 4 4 16 730 1ft 288 210.2 4 0 a 16 5S0 18 288 158.400 a 1 6 co lu m n s W14x <26 <26 18 288 122.688 f 16 342 18 288 9 8 4 9 6 16 2S7 18 288 7 4 .0 1 6 a 16 193 18 288 55 .584 a 16 145 18 288 4 1 .7 6 0 16 120 1R 288 3 4 .560 16 109 18 Tftft 31 .392 a 16 99 181 288! 2 8.S 12 16 90 181 288! 2 5 .9 2 0 16 82 181 2881 2 3 .6 1 6 a 16 74 181 2881 2 1 .3 1 ? 16 co lu m n s W KwjftA 68 181 288! 19.S84 a 16 colum ns W 14xl6l 61 181 2881 1 7 .568 a 4 4 3 0 S u b t o t.it c o lu m n * 8 6 6 0 1 . 3 8 3 .3 4 0 * 7 7 Q 76 30 21600| 1.6 4 1 .6 0 0 a 4 8 0 to tsts wi8*lso 50 30 144001 720 .0 0 0 a 1 2 0 0 S u b to ta l he.M s / m ist* 3 6 0 0 0 2 3 6 1 . 6 0 0 * 1? brace w i4 x 176 176 35 420 73.9201 #1 1? b ra c e W K x 159 159 35 4 2 0 6 6 .7 8 0 ) #1 12 b race W K x 145 145 35 420 6 0.9001*) 12 b race W i4x 132 1321 35 4 2 0 55.4401 # | 9 b race W i4x 120 120! 35 280 3 3 .6 0 0 )* ) 9 b race W i4 x 199 109 35 280 30.520) » | e b race W i4x 9 9 99 35 2801 27.7 2 0 ) * | 9 b race W i4x 9 0 90 3S 280 2 S .2 0 0 |* | 9 b race W i4x 82 82 35 280 22.960) * | 6 b race W i4x 74 74 35 280 20.720) * | 8 68 68 35 1 280 16 b ra c e W l4x 61 61 35 1 560 34.1601*1 %2 Q 6iih»n»^l l>r,i co- 470Q 1 * 7 4 0 T o t a l s t r u c t u r e w i t h d i a o o n a ! b r a c e 48840 4 .2 1 6 .4 0 0 « Weight p er square foot: 1 7 .3 5 p sf 2 * b race W i4x 145 23.S 564 8 1 .7 8 0 * 24 132 132 23.S 564 7 4 .4 4 8 2 4 120 120 23.5 564 6 7 .6 8 0 • 24 109 109 23.5 564 6 1 .4 7 6 16 9 9 99 23.5 376 3 7 .224 19 b ra c e W i4x 9 0 90 23.5 376 3 3 .8 4 0 19 b race W i4x 82 82 23.5 376 3 0 .8 3 ? 1 6 74 74 23.5 376 27 .824 16 68 Aft 23.5 376 2 S .568 16 61 61 23.5 376 2 2 .9 3 6 * 16 S3 53 23.5 376 1 9 9 2 8 * 16 b ra c e W i4 x 4 8 48 23.5 376 1 8 .048 16 b race W i4x 4 3 43 23.5 376 16 .168 * , - * M ___________________ s « f i _____ 5 1 7 ^ 7 5 2 t liagQ________ T o t a l s t r u c t u r e w i t h V - b r a c e ______________11280 4 .2 6 3 .1 9 2 # Weight p e r sq u are foot: 1 7 .5 4 p s f 2 * b race W i4x 145 145 22 528 7 6 .5 6 0 * 24 b race W i4x 132 132 22 528 6 9 .6 9 6 * 2* b race W i4v 120 120 22 S28 6 3 .3 6 0 * 24 b race W i4x 109 109 22 528 5 7 .552 * 19 b race W i4x <*? 99 22 352 3 4 .8 4 8 * 1 6 brace W i4x 90 90 22 352 3 1 .6 8 0 * 1 6 82 82 22 352 2 8 .8 6 4 * 19 b race W i4x 7 4 74 22 352 2 6 .0 4 8 * 19 b race W l4x 68 68 22 352 2 3 .9 3 6 * 19 b race W i4x 61 61 22 352 2 1 .4 7 2 * 19 b ra c e W i4x 53 53 22 3S2 1 8 .6 5 6 * 19 b ra e e W i4 x 4 8 48 22 352 1 6 .896 * 16 b race W l4x 4 3 43 22 352 1 5 .136 * i 240______________ ________ S280 444.704 » I i860 T o t a l s t r u c t u r e w i t h K n e e b r a c e 10560 4 .2 3 0 ,1 4 4 # Weight p er sq u are foot: 1 7 .4 1 p s f 1 ? 145 145 27.6 331.2 4 8 .0 7 4 * 12 b race W i4x 132 132 27.6 331.2 4 3 .7 1 8 * 12 b race W i4x 120 120 27.6 331.2 3 9 .7 4 4 * 12 b ra c e W i4 x 1 0 ? 109 27.6 331.2 36.101 • 8 b ra c e W i4 x 9 9 99 27.6 220.8 2 1 .8 5 9 * 8 b race W i4 x 9 0 90 27.6 220.8 1 9 .872 * 6 b race W i4x 8 2 82 27.6 220.8 1 8 .1 0 6 * 9 b race W i4 x 7 4 74 27.6 220.8 1 6 .339 * 8 b race W i4 x 6 8 68 27.6 220.8 1S.014 • 8 61 61 77.6 220.8 1 3 .469 * 8 fft 53 27.6 220.8 1 1 .7 0 2 * 8 4 8 48 27.6 220.8 1 0 .5 9 8 * 8 b race w i4 x 4 3 43 27.6 220.8 9 .4 9 4 * -JL2fi____________________________Suh*nt». b races________________3 3 1 2 3 0 4 .0 4 2 * 11 7 4 0 T o t a l s t r u c t u r e w i t h E B F 1 l i n k s 6624 4 .0 4 9 .4 8 2 # Weight p er sq u are foot: 1 6 .6 6 p s f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 4 . Optimization 2: W eight o f Structure in Prototype Building of 540 fe e t hiah. wind 110 moh T o t.il tl'jo r 2-13000 sf 165 . * W e ig h t/ft ott Length each <ft> Total 1 Weight w/ ////> v s s s s s s s s / Y / S / S / S S / / 16 176 176 18 288 50.688 16 150 150 18 288 45.792 16 145 145 18 288 41.760 p 16 n ? 132 18 288 38.016 16 170 120 18 288 34.560 1 6 100 to o 18 288 31.392 4 56 99 9 9 18 1006 99.792 88 90 00 18 1584 142.560 # 24 cnlum nsW 14x n o 730 IB 4 3? 315.360 f 24 665 665 18 4 3? 287.280 f 16 fKff 605 18 288 174.240 « 16 590 550 18 288 158.400 16 500 500 18 288 144 000 f 16 colum ns W14x 455 4S5 18 288 131.040 p 16 399 398 18 288 114.624 9 2$ 342 342 18 288 98.496 • 16 (nlum oc W!4>r f t ? 283 18 288 81.504 9 1 6 722 211 18 78ft 60.76ft 9 16 159 159 18 288 45.792 9 16 columns W14x 23? 132 1ft 288 38.016 16 109 109 1ft 288 31.392 16 colum ns W l4x 90 99 18 286 28.512 9 •640 2.103.984 9 7 7 0 beam s WIRxl 76 76 30 216001 9 480 MMStsWlSxISO SO 30 144001 720.000 9 1 2 0 0 36000 2361.600 • 12 brace W14x 733 233 3S 420 97.860 * 12 brace W14x 711 211 35 420 ftft 620 f 12 193 193 3S 420 81.060 4 8 17fi 176 35 280 49.280 f f t 159 159 35 280 44.S20 9 A 145 145 3S 280 40.600 p f t brace W14x 137 132 35 TAO 36.960 f t 170 120 35 280 33.600 f t brace W14x 109 109 3S ?no 30.S20 f t brace W l4x 9 9 99 35 280 27.720 f brace W l4x 9 0 90 35 280 25.200 9 8 ft? 82 35 280 22.960 9 8 brace W14x 74 74 35 280 20.720 9 4 brace w i4 x 68 68 35 140 9.520 9 _12fi____________________Subtotal hr<rW____________ 4200 609.140 » 1740 Total structure w ith diaoon.il brace 48840 5,164.724 # W eight per square foot; 21.25 PSf 16 711 211 23.S 376 79.336 9 1 6 brace W l4x 193 193 23.5 376 72.S68 1 6 I 7 f 176 23.5 376 66.176 9 I f I f ? 159 23.5 376 59.784 9 16 brace W l4x 149 145 23.5 376 54.570 16 brace W14x 137 13? 23.5 376 49.632 9 I f brace W i4x 129 120 23.5 376 4S.120 9 16 109 109 23.5 376 40.984 a I f brace W14x 9 9 99 23.5 376 37.224 P 16 90 90 23.S 376 16 brace W l4x ft? ft? ? 3 5 376 30 8 3? 16 74 74 ?3.5 376 77.824 p I f f f 6 8 23.5 376 25.566 9 16 61 61 23.5 376 72.936 16 brace W i4x S3 53 23.5 376 19.928 9 _24fl_________________________________________h r , , r . . . __________________ 5640____ 666.272 9 11860 Total stru ctu re with V-brace 11280 5.221.856 # weight per square toot: 21.49 psf 24 ?11 211 22 578 1 f 19? 193 22 3 5? 67.936 1 6 I 7 f 176 22 352 61.952 * 16 brace W14x 159 159 7? 357 55.968 9 I f brace W l4x I«S 145 22 352 S i .040 9 1 6 brace W l4x 137 132 22 352 46.464 9 I f 1?Q 120 22 352 47.240 9 1 6 brace W l4x 109 109 22 352 3 8 3 6 8 9 I f brace W l4x 99 99 22 352 34.848 9 I f 90 90 22 352 31.680 9 16 ft? 8 2 22 352 78.864 9 16 74 74 22 352 76.048 9 1 f brace W l4x f f 6 8 22 352 23.936 I f f l 61 22 352 21.472 9 8 brace w i4 x 53 53 22 176 9 3 2 8 9 J M S ________________________Swhtot.li braces______________ 5280 6 5 1 3 5 2 * 1860 Total structure w ith Knee brace 10560 5.207.136 4 W eight per square foot: 21.43 psf 12 brace W l4x 193 193 27.6 331.7 63.922 9 8 17ft 176 27.6 220.8 38.861 8 lft9 159 27.6 2 2 0 .8 35.107 f 145 145 27.6 2 2 0 .8 32.016 9 8 brace W i4x 132 132 27.6 2 2 0 .8 29.146 8 brace W14x 170 120 27.6 2 2 0 .8 26.496 9 8 brace W14X 109 109 27.6 2 2 0 .8 24.067 9 8 brace W l4x 99 9 9 27.6 2 2 0 .8 2 1 3 5 9 9 8 brace W i4x 90 9 0 27.6 7 7 0 .8 19.872 9 f brace W i4x 02 82 27.6 2 2 0 .8 18.106 9 8 brace W i4x 74 74 27.6 2 2 0 .8 1 6 3 3 9 9 8 brace W l4x 68 6 8 27.6 2 2 0 .8 15.014 9 8 brace W i4x 61 61 27.6 2 2 0 .8 13.469 9 a brace W i4x S3 53 27.6 2 2 0 .8 11.702 9 4 brace W i4x 48 48 27.6 110.4 5 3 9 9 9 - 1 2 0 __________________________ f i ’f* ? ! " 1 3 3 1 2 m m * 11740 Total stru ctu re w ith EBF 2 links 6624 4.926.8S 9 # W eight per square foot: 20.28 psf Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without perm ission. VttiM | V U tll | VM«M | VI4i4t VMi4l V llifl Vt4i4l VKiM VlliSO VKiW iL— X Moment framejwith joint numbers and member names) Load diagram (uniform beam load, lateral point load) Hexagonal grid shell dome Computer aided design I analysis Advance in computer technology made structural design and analysis widely available. The theory and algorithm of structural design programs is beyond the scope of this book. However, a brief introduction clarifies their potential and use. Structure programs generate and solve a stiffness matrix of the structure. Based on the degree of freedom of joints, the output provides stress and strain. A two-dimensional truss with pin joints has two degrees of freedom and thus two unknowns per joint, X and Y-displacement. A three-d truss has three unknowns per joint. Two-d frames have four unknowns, X, Y-displacement and X, Y-rotation, while three-d frames have six unknowns per joint, X, Y, Z-displacement and X,Y, Z-rotation. The structure input is defined by joints, members connecting the joints and loads. Joints of three-d structures are defined by X, Y, Z-coordinales, joint type (pin or moment joint), and degree of freedom, regarding X, Y Z-displacemenl and X, Y, Z-rotation (joints attached to the ground are fixed with pin or moment joints). Members are defined by properties, cross section area, moment of inertia, and modulus of elasticity. Some members may have end release at one or both ends, to allow pin joints ol braces to connect to moment joints of beam to column, for example. End releases are simulated by a dummy pin adjacent to the moment joint. The geometry of a structure may be defined in the analysis program or imported as DFX file from a CAD program. Loads are defined as distributed or point load. For example gravity load is usually assigned as uniform beam load, while lateral wind or seismic load may be point loads at each level of multistory buildings. Output includes force, stress, and deformation (or members, joint displacement and rotation, as well as support reactions. Output may be in tables and I or graphic display. Graphic display provides belter intuitive understanding an d is more convenient to use. Some programs simulate non-linear material behavior and / or non-linear geometric behavior. For example, non-linear material may include plastic design of steel with non linear stress/strain relation in the plastic range. Non-linear geometric analysis is for structures with large displacements, such as cable or membrane structures. Non-linear analysis usually Involves an iterative algorithm that converges after several iterations to a desired level of accuracy. Some programs include a prestress element to provide form- finding for membranes structures. Some programs provide dynamic analysis, sometimes referred too as 4-d analysis. While programs with advanced features provide greater versatility and accuracy, they are usually more complex to use. MuUiUama-40 used for the demonstrations features 2-d and 3-d static and 4-d dynamic analysis. For static analysis Multiframe is very user friendly, intuitive, and thus good for architecture students. The 4-d dynamic feature is beyond the scope of this book. The examples presented demonstrate 2-d and 3-d design/analysis. A very convenient feature are tables of steel sections with pre-defined properties for US sections and for several other countries. The program features US and SI units. (fro m : S c h ic rlc , G . G . , 2 0 0 2 -2 0 0 4 , Structure) C Description o f M ultiframe 4D Reproduced with permission of the copyright owner. Further reproduction prohibited without perm ission. 0 » C 0 7 C _ J ____________O J J _ I S f l 3 7 l Output display Output Includes member force, stress, deformation, joint displacement and rotation, as well as support reactions, all as numeric tables and color graphs. Clicking any member or joint provides detailed information. Force and stress include axial, bending, shear, as well as combined axial and bending stress. 8ased on the output, members may be resized in proportion to stress or strain. Animation allows to visualize deformation correlated with force or stress patterns. Bending stress Axial stress Shear stress Deflection with colored stress (also available in animation mode) (from: Schierle, G .G ., 2002-2004, Siriicimv) Reproduced with permission of the copyright owner. Further reproduction prohibited without perm ission. " 1 — H F f ,r i - 1 rv.-J— f :f] ' J ■ I i - ■ j f i ....j . . . i I.. 1 , 1 i Bell truss effect CAD-analysis provides efficient means to compare framing systems. For convenience the following example was done with constant W18 beams and W14 columns, 30' beam spans, and 12. story heights. The results, comparing the effect of belt and lop trusses on a moment frame and a braced frame are very reveling: 20-sloty moment frame Gravity load w = 3 klf Wind load P = 10 k/level Frame: D rift Frame only 15.f Top truss 14.9* Belt truss 14.2* Top and belt truss 14.0’ 20-story braced frame Gravity load w = 3 klf Wind toad P= 10 k /level Frame Drift Frame only 17.6’ Top truss 11.4* Belt truss 11.1* Top and belt truss 8.6’ Note: Bell and top trusses are much more effective to reduce drift at the braced frame than at the moment frame. The combined belt and top trusses reduce drift: • 7 % at moment frame • 49 % at braced frame Interpreting the results clarifies the stark difference and fosters intuitive understanding of different deformation modes of moment and braced frames. (from : Schicrle, C i.G ., 2002-2004, Sinuiniv) m o n o m q n b > TABLE 5: SUMMARY OF RESULTS 1 . Drift and weight non optimized KL W ind 70m oh 4 2 0 I t (3 0 flo o rs) 540 f t (4 0 flo o rs) PSF D rift (In ) * o fa O . PSF D rift (In ) % e f n . W ind 90moh 4 2 0 f t (3 0 flo o rs) 540 f t (4 0 flo o rs) PSF D rift (In ) 9b of all. PSF D rift (In ) e to fa tt. W indU 4 2 0 f t (30 floors) PSF D rift (In) W ofi 420 fl540 ft A S ingle D tegonil 3 3 ' 35* 2 0 3 4 0 3 7 8 1 3 3 4 2 4 3 3 0 3 5 9 20 .7 0 2 0 3 4 0 .4 5 1 2 1 4 8 2 4 3 3 0.99 3 6 .6 7 2 0 3 4 1 1 1 8 5 3 3 B A ltern ate Ofoqonal 33* 35* 2 0 3 4 0 3 8 1 1 3 3 8 2 4 3 3 0.61 2 2 3 9 2 0 3 4 0 .4 5 5 2 1 6 7 2 4 3 3 0.995 3 6 3 5 2 0 3 4 1 3 3 8 5 4 3 C V -Brace 20* 233* 2 0 3 9 0 3 0 2 1 4 3 8 24.02 0 3 8 2 1 .4 8 2 0 3 9 0 .4 8 2 2 3 6 24.02 1.032 3 8 3 2 2 0 3 9 1 2 5 7 3 D EBF Knee Brace 19* 22* 20.12 0 3 5 6 1 2 3 9 23.9 0 3 0 4 1 8 .6 7 2 0 3 2 0 .4 1 7 1 9 3 6 23.9 0 3 9 2 3 3 .0 4 20.12 1 0 3 6 4 9 3 E EBF 2 Unfcs 25* 27.6* 1 9 .6 4 0 3 3 10.95 2 3 3 0 3 7 5 2 1 3 0 1 9 .6 4 0 .4 4 20.95 2 3 3 0.952 3 5 3 6 19.64 1 3 1 4 5 3 3 A v m t w g t p e f, d r i f t , % Ifer rff Prefer, perc 20.1 0 3 6 9 4 1283 2 3 .9 0 3 6 5 6 2085 20.2 0.4486 2 2 3 6 | 23.9 0.9722 3681 20.2 12222 5 3 3 ( te s t 2 3 ) (test 22) ( te s t 2 3 ) ( te s t 1M ) ( te s t IS) 2 . Drift and weight optimization 1 W ind 7Om0b 4 2 0 f t (3 0 flo o rs) 540 f t (4 0 flo o rs) W ind 90mph 4 2 0 f t (3 0 flo o rs) 540 f t (4 0 flo o rs) W in d U 4 2 0 f t (30 floors) KL PSF D rift (in ) fteofalL PSF D rift O n) % o f a l PSF D rift (In) 96 of ad. PSF D rift (in ) 96ofelL PSF D rift (in ) 96 o f a 420 n540 ft A S ingle D iagonal 33* 35* 1 9 3 3 0 3 9 4 14 23.77 0 3 5 4 2 0 3 2 2 0 .0 4 0 3 5 3 2 1 5 7 24.65 0.981 3 6 3 3 2 1 1 3 1 1 4 3 5 4 3 : B A ltern ate Diogonal 33* 35* 1 9 3 3 0 3 9 6 1 4 3 0 2 3 3 7 0 3 6 2 2 0 3 1 2 0 .0 4 0 3 5 7 2 1 7 6 24.65 0.988 3 6 3 9 2 1 1 3 1 1 5 5 55.01 C V -B race 20* 233 * 1 8 .9 5 0 3 0 9 1 4 3 1 2 3 3 7 0 3 8 8 2 1 3 8 19 .9 9 0 3 8 1 22.90 2 4 3 5 1.028 3 8 3 7 211 2 1 3 2 9 5 8 3 : D EBF Knee Brace 19* 22* 1ft.8ft 0 3 6 9 1 2 3 1 2 3 3 4 0 3 1 2 18 .9 6 1 9 3 5 0 3 1 8 19.90 2 4 3 1 0.893 33 .0 7 21 1 0 6 1 5 0 3 : E EBF 2 Links 25* 27.6* 1 8 4 5 0 3 9 4 14 2 3 3 8 0 3 3 6 1 9 3 5 1 9 .6 4 0 3 4 3 2110 23.97 0.952 3 5 3 6 2 0 3 5 1 1 4 2 5431 A v m n g a ptf, d r i f t , % for off frrnom p e rt 188 08924 1382 | 2 3 3 0 3 5 0 4 2089 198 0 .4 5 0 4 2 2 3 5 | 24.6 0.9684 3587 1 22 2 3 4 6 5 4 3 7 ( te s t 2.2) ( te s t 2 3 ) (test 28) (test 2.4) ( te s t 2 3 ) 3 . Drift and weight optimization 2* KL 4 2 0 f iS 4 0 f t S in g le D iagonal 33* .35* A ltern ate Oiogonal 33* 35* V -B race 20* 233* EBF Knee B race 19* 22* EBF 2 Links 25* 273* W ind 70m oh 4 2 0 f t (3 0 flo o rs) 540 f t (4 0 flo o rs) PSF D rift (in ) 96ofaR . PSF D rift (in ) 9 6 o fafl. 1 5 3 6 0 3 1 9 • 1 9 3 5 17 0 3 9 4 3 3 .U 1 5 3 6 0 3 0 9 1 9 3 8 17 0.9 2 2 3 4 3 5 1 5 3 8 0 3 5 2 1 3 3 1 7 3 1 0 3 3 8 3 4 3 4 1 5 3 2 0 3 7 9 1 8 3 5 1 7 3 8 0 3 9 3 2 9 3 7 1 4 3 9 0 3 2 4 2 0 3 9 1 6 3 2 0 .9 3 3 3 3 2 5 3 0M 162 1982 i 168 0 3 8 9 4 3 2 3 4 W ind 90moh 4 2 0 f t (3 0 flo o rs) 540 I t (4 0 flo o rs) PSF D rift (in ) 96 of all. PSF D rift (in ) 96ofaH . (test 3.1) (test 3 3 ) 1 5 3 4 0 .7 0 6 33.62 1 5 3 4 0 .6 9 7 33.19 1 5 3 9 0 .7 6 36.19 1 5 3 5 0 .6 3 8 3 0 3 8 1 5 3 4 0 .7 2 8 34.67 ISM 0.7058 33.61 ( te s t 3 3 ) 1 7 3 5 1 6 5 9 3 6 1 7 3 5 1 6 4 4 6 0 3 9 1 7 3 4 1 6 9 6 6 2 3 1 17-41 1 4 3 1 5 3 3 0 16.66 1.632 178 1 6 0 0 6 5 9 3 8 W in d U 4 2 0 f t (30 floors) PSF D rift (to ) 96 o f a 1 5 3 7 1 5 3 7 1 5 3 6 1 5 3 4 1 5 3 9 2 5 3 (test 3.4) 1 3 3 2 8734 1 3 3 8734 1 3 6 9 93.7C 1.654 78 JH 1 3 9 2 903C 18354 8 7 M (test 3 3 ) Drift an d w eight optimization 3 / only blgd. 540 f f - llO m ph Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R eproduced w ith perm ission o f the copyright ow ner. F urther reproduction prohibited w ith o u t perm ission. TABLE 5: SUMMARY OF RESULTS .■ Drift and w eight non optimized W ind 90m oh 1 f t (3 0 flo o rs) 540 f t (4 0 flo o rs) D rift (in ) ' to o f ofl. PSF D rift (In ) to o f oil. W ind llO m p h 4 2 0 f t (3 0 flo o rs ) 540 f t (4 0 flo o rs) PSF D rift (in ) to o f alU PSF D rift (h i) to o f ad. a v era g e p s f 30 flo o rs (p e r braca) av erag e ! p s f 40 flo o rs ! (p e r brace) i a v erag e d rift 3 0 flo o rs (p e r braca) to o f aB. av erag e d rift 40 flo o rs (par braca) to o f an. 0 3 5 1 2 1 3 8 2 4 3 3 0 .9 9 3 6 .6 7 2 0 3 4 V T 18 5 3 3 4 2 4 3 3 2 3 2 5 8 9 3 1 2 0 3 4 2 4 3 3 0.6 1 6 2 9 3 2 1 3 2 5 4 9 .0 6 0 3 5 5 21.67 2 4 3 3 0.995 3 6 3 5 2 0 3 4 1 3 3 8 5 4 3 9 2 4 3 3 2 3 5 6 9 0 .9 6 2 0 3 4 2 4 3 3 0.6 2 5 2 9 3 5 1 3 5 4 5 0 3 4 0 3 8 2 2 3 6 2 4 3 2 1 3 3 2 3 8 3 2 2 0 3 9 1 3 5 7 .1 4 24.02 2 3 3 9 9 4 3 4 2 0 3 9 24.02 0 .6 6 1 3 1 .4 6 1 3 8 4 5 1 3 5 0 3 1 7 1 9 3 6 2 3 .9 0 3 9 2 3 3 .0 4 2 0 3 2 1 3 3 6 4 9 3 3 23.9 2 3 9 1 8 1 3 5 20.12 23.90 0 3 7 0 2 7 3 3 1.196 4 4 3 8 0 3 4 20.95 23 3 0.9 5 2 3 5 3 6 1 9 .6 4 1 3 1 4 5 3 3 5 2 3 3 2 3 6 9 8 7 3 4 1 9 .6 4 2 3 3 0 0 3 9 5 2 8 3 2 1 3 9 9 4 8 3 0 0 . 4 4 8 6 2 1 3 6 | 2 3 . 9 0 .9 7 2 2 3 6 3 1 2 0 3 1.1212 5 3 3 9 | 2 3 .9 2 3 9 6 8 8 . 7 4 2 0 3 2 6 2 3 3 9 6 j 0 . 6 1 3 2 9 3 1 3 1 1 4 8 . 6 ( te s t 2 3 ) (testify (testify (test 1.6) 1. Drift and w eight optimization 1 W ind 90m oh I f t (3 0 flo o r* ) • 540 f t (4 0 flo o rs) D rift (in ) to o f alt. PSF D rift (in ) W o rrit 0 A 5 3 21.57 24.65 0 .4 5 7 2 1 3 6 24 .6 5 0 3 8 1 22.90 2 4 3 5 0 .4 1 8 19.90 2 4 3 1 0 3 4 3 2 1 3 0 2 3 .9 7 0 3 5 0 4 2 1 .4 5 | 2 4 . 6 ( te s t 2 3 ) 0 .9 8 1 3 6 3 3 0 .9 8 8 3 6 3 9 1 .0 2 8 3 8 3 7 0 3 9 3 3 3 3 7 0 .9 5 2 3 5 3 6 0 . 9 6 8 4 3 5 3 7 ( te s t 2 3 ) 4 2 0 f t (3 0 flo o rs ) PSF D rift (in ) to ofaO . 2 1 .1 3 1 3 4 3 2 1 3 3 1 3 5 5 2 1 .1 2 1 .2 2 9 21 1 .0 6 1 2 0 3 5 1 3 4 2 5 4 3 3 5 5 .0 0 5 8 3 2 5 0 3 2 5 4 3 8 2 1 1 3 4 6 5 4 3 7 ( te s t 2 3 ) Ph 540 f t (4 0 flo o rs) PSF D rift (in ) to o f all. a v e ra g e p s f 30 flo o rs < p e r . braca) a v erag e i p s f 4 0 | flo o rs ! <|W 1 brace) a v erag e d rift 3 0 flo o rs (p e r braca) to o fa ll. av erag e d rift 40 flo o rs (per braca) to o f an. 25.99 2 3 5 8 7 3 4 25.99 2 3 7 7 8 8 3 4 2 6 3 2 2 3 7 7 9 1 3 4 2 6 3 6 2 3 5 7 9 3 3 2 5 3 1 2 3 1 8 5 3 6 mu 2 4 3 0 2 4 3 0 24 .9 8 24.90 2 4 3 9 0.6 3 0 0.6 3 6 0.6 7 3 0 3 8 3 0 .6 2 6 3 0 .0 0 3 0 3 9 3 2 .0 5 2 7 .7 5 2 9 3 3 1 3 9 5 1 3 0 9 1 3 6 4 1 3 8 5 1 3 6 6 4 7 .9 6 4 8 .4 8 5 0 3 3 4 3 3 9 4 6 3 9 | 2 5 . 9 2 . 3 3 2 8 8 6 3 1 9 3 2 8 7 2 4 3 1 5 3 ! 0 .6 3 0 3 0 . 0 1 3 8 4 4 7 3 5 (test 2.6) ■ D rift an d weight optim ization 2* W ind 90m ph I f t (3 0 flo o rs) 540 f t (4 0 flo o rs) D rift (in ) % o f an. PSF D rift (In ) to o fa lL 0*706 3 3 .6 2 1 7 3 5 1.6 5 9 3 6 0 .6 9 7 3 3 3 9 1 7 3 5 1 .6 4 4 6 0 3 9 0 3 6 36 .1 9 1 7 3 4 1 3 9 6 6 2 3 1 0 .6 3 8 3 0 3 8 1 7 3 1 1 3 3 1 5 3 0 0 0 3 2 8 3 4 .6 7 1 6 .6 6 1 .6 3 2 5 0 ,5 4 0 3 0 5 8 3 3 . 6 1 I 1 7 3 1 . 6 0 0 6 5 9 3 8 W indU O m oh 4 2 0 f t (3 0 flo o rs ) 540 f t (4 0 flo o rs) PSF D rift (to ) to o fa tL PSF D rift (in ) to o f all. 1 5 3 7 1 5 3 7 1 5 3 6 1 5 3 4 1 5 3 9 1SJT ( te s t 3 3 ) ( te s t 3 3 ) 1 3 3 2 8 7 3 4 ♦21.55 2 3 4 1 3 3 8 7 3 4 2 1 3 5 2.68 1 .9 6 9 9 3 .7 6 2 1 3 9 2 3 1 .6 5 4 7 8 3 6 2 1 3 3 2 3 7 1 3 9 2 9 0 3 0 2 0 3 8 2.62 1 3 3 5 4 8 7 3 I 2 1 3 2.6 2 2 ( te s t 3 3 ) (te s t 3 .6 )* 9 7 3 8 9 9 3 6 1 0 0 3 0 9 1 4 8 9 7 3 4 9 7 3 1 a v e ra g e p s f 30 flo o rs ( P e r braca) av erag e j p sf 40 | flo o rs j (per brace) j a v e ra g e d rift 3 0 flo o rs (p ar brace) to o f an. av erag e d rift 40 flo o rs (par braca) to o f an. 1 5 3 6 1 5 .6 6 1 5 3 8 1 5 3 7 1 5 .0 7 I 18 .6 3 j 18.63 j 1 8 3 1 18.64 1 7 3 2 0 .9 8 6 0 3 7 9 1 3 6 0 0 3 9 0 1 3 1 5 4 6 3 4 4 6 .6 0 5 0 3 6 4 2 3 0 4 8 3 2 1 3 1 1 1.749 1.778 1 3 6 5 1 3 1 7 6 3 3 8 6 4 .7 7 6 5 3 5 5 7 3 5 6 3 .6 0 1 5 3 8 6 7 1 8 3 8 8 0 . 9 8 6 4 6 . 9 1 . 7 0 4 6 3 .2 lit optim ization 3 / only blgd. 540 f f - llO m ph 540 f t (4 0 flo o rs) j PSF D rift (In ) to o fa U .j I 1 7 3 2 4 3 1 1 4 8 3 2 \ 17.92 4 3 7 1 5 0 3 4 : 1 8 3 6 4 3 5 1 5 7 3 1 ; 1 8 3 9 3 3 8 1 3 2 3 9 { 16 .9 4 4 3 1 1 5 2 3 2 i r 1 7 3 4 . 0 0 4 1 4 8 3 \ ( te s t 3 6 )* * Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Neidl-Cornejo, Rosa (author)

Core Title Bracing systems for tall buildings: A comparative study

School School of Architecture

Degree Master of Building Science / Master in Biomedical Sciences

Degree Program Building Science

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

Tag Architecture,engineering, civil,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Schierle, G. Goetz (committee chair)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-320562

Unique identifier UC11327000

Identifier 1424228.pdf (filename),usctheses-c16-320562 (legacy record id)

Legacy Identifier 1424228.pdf

Dmrecord 320562

Document Type Thesis

Rights Neidl-Cornejo, Rosa

Type texts

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

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

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA