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Effect of anchorage and prestress to reduce lateral drift in suspended high-rise structures
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Effect of anchorage and prestress to reduce lateral drift in suspended high-rise structures
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EFFECT OF ANCHORAGE AND PRESTRESS TO REDUCE LATERAL DRIFT IN SUSPENDED HIGH-RISE STRUCTURES by Ping-hiing Kuo A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE August 199.0 Copyright 1990 Ping-hung Kuo UMI Number: EP41420 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI' "" Qtesartstbn PjWftUng UMI EP41420 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 UNIVERSITY OF SOUTHERN CALIFORNIA T H E G R A D U A T E S C H O O L U N IV E R S IT Y P A R K LO S A N G E L E S , C A L IF O R N IA 9 0 0 0 7 This thesis, written by T i N £ H U N & .m e ? . ..... under the direction of hl*£. Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of jUastei- d$ Bui H W Science Dean D ate.A ^LLJ.PM . THESIS COMMITTEE / Chairm an_ K . S L & ACKNOWLEDGMENTS Throughout the course of this thesis no one has helped me more than my chief advisor, Prof. G. G. Schierle, who carefully read my first writing, gave me advice, and improved the organization. I really learned a lot about structures by doing this thesis research with him. He even allowed" me to use his programs for structural analysis and design. Prof. J. Ambrose and Prof. D. Vergun, who are both my thesis advisors, are always there for my questions. I am deeply grateful to their comments and suggestions. Reading their books really helped a lot to picture basic structural behaviors and advanced my knowledge on structure. I owe a substantial debt to a number of my friends. I am happy to single out Mr. Hung, who was my roommate during university, and Mr. Wu, who is my classmate while I studied in USC. Mr. Hung helped me with model testing without hesitation whenever I needed his assistance. Mr. Wu has kindly shared his ideas with me while I wanted to discuss my thoughts. We both worked on something relating to Portal Method, on which he wrote a program for his degree and by which I calculated my high-rise structures. We had many joyful discussions during our work together. In the end, my friend, Uen-fang Yehdeserves the most thanks. AII~of the work would be impossible without her help and personal encouragement. She assisted in much of model testing and typing. At the last stage of my thesis, she even changed her schedule to organize the chapters for me. I owe her a lot, and I can hardly describe it in one word. Ping-hung Kuo Los Angeles, CA May, 1990 ---------------------------------------- CONTENTS--------------------------------------- CHAPTER PAGE ACKNOWLEDGEMENTS ABSTRACT 1. INTRODUCTION 1 2. GENERAL BACKGROUND OF SUSPENDED HIGH-RISE STRUCTURES 2-1 Suspended structures 3 2-2 Urban design consideration 4 2-3 Architecture consideration 7 2-4 Structure consideration 10 3. CASE STUDIES 3-1 Classification of high-rise structures 13 3-2 Classification of suspended structures 16 3-3 Case studies 19 4. PRESTRESS AND HIGH-RISE STRUCTURES 4-1 Consideration of lateral force effects 41 4-2 Sources of lateral loads and their effects 42 4-3 Concepts of high-rises analysis 44 4-4 Principle of reinforced concrete and 45 prestressed concrete 4-5 Prestressed cable systems 47 4-6 Suspended structures and prestress \ 48 5. PROTOTYPES TESTED 5-1 Considered prototypes 51 5-2 Selected structures for testing 54 iv . CORRELATIONS OF MODEL AND ORIGINAL STRUCTURE 6-1 Derivation of model and original correlations 56 6-2 Numerical data 59 . MODEL BUILDING AND TESTING 7-1 Model building 63 7-2 Test procedure 64 TEST RESULTS AND ANALYSIS 8-1 Numeric test results 68 8-2 Graphic test results 69 8-3 Test results and summary 70 . CONCLUSIONS AND RECOMMENDATIONS 9-1 Conclusions 72 9-2 Recommendations for future research 74 0. ARCHITECTURAL APPLICATIONS 76 REFERENCES 82 APPENDIX A: SDG 85 APPENDIX B: CAFA 86 APPENDIX C: 1. Frame analysis by 88 Portal Method 2. Hanger analysis APPENDIX D: Force scale calculations 97 APPENDIX E: Location of lateral forces 100 on model APPENDIX F: Glossary 101 v LIST OF FIGURES Fig. 2-1 Federal Reserve Bank, Minne. 6 Fig. 2-2 Suspended structures using air rights over freeway. 6 Fig. 2-3 Freedom of floor arrangement. 6 Fig. 2-4 Future addition of Federal Reserve Bank. 8 Fig. 2-5 Future addition of Hong Kong Bank. 8 Fig. 2-6 Allowable stress for concentrically loaded columns 12 per AISC specifications. (Popov, 1968) Fig. 2-7 Comparing height-to-width ratio for rigid frames 12 and suspended structures. Fig. 3-1 Lateral resisting systems 14 Fig. 3-2 Tubular systems 15 Fig. 3-3 Suspended systems: Tower and stack options 17 Fig. 3-4 Suspended systems: Anchorage and prestress options 18 Fig. 4-1 Wind pressure diagram on buildings. 43 Fig. 4-2 Seismic force diagram. 43 Fig. 4-3 Structural behavior of cantilever beams. 44 Fig. 4-4 Structural behavior of high-rise buildings. 44 Fig. 4-5 Prestressed simple beams. 46 Fig. 4-6 Prestressed cantilever beams. 46 Fig. 4-7 Effect of prestress on strain. 47 Fig. 4-8 Gravity transmission of rigid frames and 50 suspended structures. Fig. 4-9 Suspended structures and prestress. 50 Fig. 4-10 Strain differences between columns and hangers. 50 vi Fig. 5-1 Selected structures for testing. 54 Fig. 5-2 Prototypes considered but not tested. 55 Fig. 5-3 Dimensions of the central core of test cases. 55 Fig. 6-1 Original cross-section. 62 Fig. 7-1 Test preparation. 67 Fig. 7-2 Model details. 67 vii LIST OF TABLES Table 5-1 Selected structures for testing Table 5-2 Prototypes considered but not tested Table 6-1 Scales for various cases. Table 6-2 Element sizes in model and original Table 6-3 Lateral forces simulated on model. Table 6-4 Hanger prestress on model Table 8-1 Test model drifts Table 8-2 Graphic test results "ABSTRACT Assuming that lateral drift can be reduced by prestress or other methods, suspended structures are investigated to compare the effectiveness of reducing lateral drift, by the following methods (Fig.5-1): 1. CSS: Conventional Suspended Structure 2. TASS: Truss Anchored Suspended Structure 3. TASS+PS: Truss Anchored Suspended Structure w/ Prestress 4. GASS: Ground Anchored Suspended Structure 5. GASS+PS: Ground Anchored Suspended Structure w/ Prestress A static model of a typical suspended structure was built and tested for heights of 10, 20, and 30 stories to compare the effect of prestressing and hanger anchorage for various heights. Test results reveal in Table 8-1 that GASS+PS exhibits the best overall drift reduction of 49% for 30 stories, and the best drift reduction due to prestress of 32 % for 20 stories. In general, among the same test cases, the effectiveness increases with the height. ix 1. INTRODUCTION The high-rise building, no doubt, is one of the landmarks in our cities, and the most remarkable architectural achievement in this century. With better opportunities of employment and education, cities attract more and more people to move in and stay in order to seek a better life style. Because of the limitation of land and the increasing population, high-density development in cities is necessary. It appears that increasing the building's height is one of the most economic and feasible resolutions. After the discovery of the elevator, high-rise buildings started to grow rapidly in cities. As the urbanization continues and population grows, the height and number of high-rise buildings increase. With increasing height of buildings wind and seismic forces play a dominant role in structural design. Lateral drift of high-rises must be carefully considered in structural design for safety and stability. The comfort of occupants living on the top floor is also a concern for architects and engineers. Service facilities, such as piping and elevators, may be damaged due to over drift. In addition, glass breakage and furniture damage will be caused by excessive drift. Therefore, lateral drift must be carefully dealt with in structural design. 1 Prestressing generates permanent stresses in a structure in order to improve its behavior and strength under various service conditions. Prestressed concrete is weil-known by engineers today. When it was first used in the U.S. in the late 1940’s, most U.S. engineers were not completely familiar with this mode of construction and it was not taught in the universities. However, as the theories advanced, new construction methods and materials developed, more and more prestressed concrete has been used in building construction domestically and internationally. At present prestressed concrete is no longer a strange term in building construction. A high-rise structure can be considered as a vertical cantilever beam because of similar structural behavior. If prestress can be introduced to a simple beam to reduce deflection, can it possibly be applied on high-rise structures to reduce the lateral drift? The application of prestress presented in this thesis is a new attempt to reduce lateral drift in high-rise buildings. Is it feasible? How is the efficiency? This thesis compares the effect of five design cases to observe the effect of height, prestress, and anchorage, on lateral drift. 2. GENERAL BACKGROUND OF SUSPENDED HIGH-RISE STRUCTURES 2-1 Suspended structures With highly effective use in materials, suspended systems are very attractive. In suspended systems, ail loads are transmitted through the central core, which may be constructed in steel, or in concrete. The loads from the free ends of the floor beams are supported by hangers suspended from either girders or trusses projecting from the core, which transmits the loads to the foundations. The ground level around the core are thus free of supports. The hangers, which carry loads in tension, are thus very slender. Suspended systems have several advantages with respect to urban, architectural and structural engineering considerations. 2-2 Urban design consideration Architecture is a part of urban design. A well-designed architectural project as well as a successful urban design is to create a suitable environment for people to live and work. Containing a great amount of people and activities, a high-rise building must be considered as an urban project, not only as an architectural one. As part of a city, it is supposed to grow organically from its surroundings and to be enriched by it. Suspended high-rise structures have unique advantages due to their ground support. With fewer supports at ground level, suspended high-rise buildings don’t cut off the view by massy volumes. The Federal Reserve Bank in Minnesota. (Fig. 2-1) is an example of this feature. The support -free ground level allows free vision, circulation and ventilation without much interference due to a massive volume. Suspended structures can help in historical preservation. The historical preservation may be either for a building or for a plaza with historical meanings. Suspended structures can hang all floors above a historic building or the plaza, to preserve their integrity. Ancient remains can thus be preserved, and the new building can be enriched. The support-free ground level under a suspended building can provide a green park for the public. As the urbanization and population continue to grow, cities attract more and more people for better opportunities in employment and education. Cities are thus becoming more crowded than ever before. The pressure to build more floor areas in cities reduces available green land, which are gradually disappearing. By using suspended systems, the green lands can be partly preserved or evermore, the support-free areas under the building can be designed as a park, shared by the occupants and the community. The shortage of building land is one of the problems resulting from urbanization and population growth. Suspended structures can provide a possible solution to this problem. For instance, suspended structures provide a means to use air rights and build over freeways or railroad. As shown in Fig. 2-2, two service cores can be built on both sides of a freeway to support a truss, from which floors are suspended above the freeway. Thus, the land can be utilized, while at the same time creating links to re-unite artificially separated parts of the urban community. it Fig. 2-1 Federal Reserve Bank, Minne. Fig. 2-2 Suspended structures using air rights over freeway. Fig. 2-3 Freedom of floor arrangement. 6 2-3 Architecture consideration Suspended structures have several advantages with respect to architectural considerations: Suspended structures provide flexibility for various architectural functions. For instance, as mixed-used high-rise buildings are becoming popular, several activities must be contained within a single building. Various functions require different architectural layouts. The layout of residence is different from that of office. Partitions, air conditioning, and facade treatment is somehow different. In suspended systems, various functions can be grouped and contained in different stacks which are suspended together,each with an unique architectural vocabulary. Suspended structures also offer considerable freedom of floor arrangement. Because the hangers which are used to support floors are hung from above, they can stop wherever the floors stop (Fig. 2-3) Thus, allowing greater freedom to create various architectural spaces to enrich the vocabulary and spatial quality. Possible future additions are more convenient in suspended structures. The Federal Reserve Bank in Minneapolis is a good example (Hart, 1978). As shown in Fig. 2-4, “Additional stories may subsequently be added, the loads from which will be carried by a steel arch structure 7 which will surmount the lattice girders and the thrust from which will reduce the horizontal force acting in them”(Sontag, 1978). H.K. Shanghai Bank is even a better example for demonstration of future addition. It allows additional floors to be suspended between stack and atrium space without structural alterations. Open space on the ground level, provided by suspended structures, can help buildings be better recognized by people due to ground level activities. High-rise buildings with decorative tops are becoming popular in most U.S. cities. Architects want to create an interesting skyline, and developers want a distinctive image for buildings. These building crowns become identification cards of buildings in the sky, but do not relate to practical functions. However, if the open ground level under a suspended high-rise building can be designed for human use, allowing people “to meet, to hold gatherings, to hold parties, wedding receptions, and so forth,” Ackerknecht, 1986, to establish a relationship between human beings and the building, it will be better recognized by people, both visually and functionally. 9 2-4 Structure consideration Structure is the skeleton of high-rise buildings. Structural consideration is one of the most important issues about suspended systems. Buckling only happens on fewer columns, because most of the supports in suspended structures are tensile members. Columns in the central core are the only members to carry loads in compression and are likely to buckle. Replacing columns in rigid frames by hangers eliminates buckling, for better efficiency. Using high-strength steels can further improve the efficiency. For example, allowable bucking stress for steel columns with Le/r=120 is about 10 ksi (Fig. 2-6), the use of flexible tensile hangers can take advantage of high breaking strength of 210 ksi, or even higher. Steel of smaller cross-section area is capable of carrying the same load in suspended structures. So less material can be used to support a structure, and the structure can be of lighter weight. In seismic zone, decreasing the weight of buildings reduces seismic forces. Because less material is used, the construction cost for suspended structures can be reduced to a certain degree. But local cost for this kind of construction must be considered for an accurate estimation. In addition, suspension systems have the fundamental properties of steel structures; such as, “prefabrication, off-site labor, high strength/weight ratio, high stiffness, high tolerances, smaller member 10 sizes, speed of construction, reduced hoisting, reduced site labor, flexibility of alterations." (Beedle, 1988) fi While suspended structures have advantages, as described above, they have some weaknesses in certain respects. One problem is the height-to-width ratio, which indicates how effective the mass is laterally resisted. In suspended structures, the lateral forces are only resisted by the central core. Compared to a rigid frame of the same architectural layout, suspended structures have a relatively great height-to-width ratio, hence, their lateral stiffness is less than that of a conventional rigid frame (Fig. 2-7) or braced frame. This problem can be solved by extending and anchoring the hangers to the ground, to obtain the same height-to-width ratio and the same lateral stiffness. This option, which is investigated in this thesis, however reduces the openness at the ground level somehow. If the suspended hangers are prestressed, which is the other subject of this thesis, lateral stiffness can be improved, because compressive forces can be absorbed through reduction of prestress (Schierie, 1990). Thus lateral drift can be reduced. Fig. 2-6 Fig. 2-7 • Euler's hyperbola Yield strength 100 ksi 60 ksi Stress from Euler's hyperbola -r 1.92 for L}r > C ,- 42 ksi 36 ksi 1 2 0 Allowable stress for concentrically loaded columns per AISC specifications. (Popov, 1968) IX IX IX Comparing height-to-width ratio for rigid frames and suspended structures. 12 3. CASE STUDIES 3-1 Classification of high-rise structures ) { As building heights increase, the lateral drift of a building becomes so great that consideration of lateral stiffness, rather than strength of the structure, governs the design. The most common structural framing systems are classified in Fig. 3-1,3-2 (Schierle, 1990): • Shear Wall • Rigid Frame • Braced Frame • Eccentric Braced Frame • Tubular System Framed Tube Braced Tube Bundled Tube • Suspended Systems Case studies of these framing systems are introduced in the following. Specific emphasis is given to suspended systems in Chapter 3-2, since they are topics of this thesis. 13 / \ / \ / \ / s y \ / \ /N / \ / \ / \ y / / / / / / / / / / / / / / / / / x Shear wall Rigid Braced Frame Frame Fig. 3-1 Lateral resisting systems Eccentric Braced Frame 14 Framed tube Braced Tube Fig. 3-2 Tubular systems Bundled tube 15 3-2 Classification of suspended structures Based on the features of suspended structures, they are classified in Fig. 3-3 (Schierle, 1990). In general, lateral forces on suspended structures are resisted by the core, and each stack is capable of carrying about 10 floors. Therefore, the following classification is based on these two features. Single tower Double tower Multi tower CJi u cz no C D t_J r—« r o Suspended systems: Tower and stack options Fig. 3-3 17 Top anchorage Top S bottom anchorage Top S ground Top S parabolic anchorage ground anchorage 0 3 tn in O) CL O “O CD to to CD CD Fig. 3-4 Suspended systems: Anchorage and prestress options 18 3-3 Case studies 20 case studies are presented here to investigate various high-rise structures and their applications. However, more emphasis is given to suspended systems. Main structural systems and flooring structures are described as well as their lateral and vertical resisting systems. (Architectural Record, Jul. 1973 / Nov. 1973; Hart, 1978; Progressive Architecture, Sept. 1961 / Oct. 1969/Sept. 1970; Schueller, 1977) Listed below are cases selected for study: KNIGHTS OF COLUMBUS BUILDING, NEW HAVEN, CONN, ELECTRICAL ENGINEERING DEPARTMENT, DELFT LIBRARY IN PARIS, FRANCE HEAD OFFICE BUILDING FOR A STEEL COMPANY IN PITTSBURGH, USA HIGH-RISE RESIDENTIAL DEVELOPMENT AT BALORNOCK, SCOTLAND WORLD TRADE CENTER, NEW YORK, USA BANK OF CHINA, HONG KONG WESTCOAST OFFICE BUILDING. VANCOUVER, B.C., CANADA ALPINE MONTAN ADMINISTRATIVE BUILDING, LEKOBEN, AUSTRIA ADMINISTRATIVE BUILDING FOR AN ELECTRICAL ENGINEERING FIRM, SAINT DENIS, FRANCE GROUP OF EXHIBITION PAVILIONS IN TORONTO, CANADA PHILIPS ADMINISTRATIVE BUILDING, EINDHOVEN, HOLLAND BRITISH PETROLEUM LTD. STUDENTS’ HALL OF RESIDENCE, CITY UNIVERSITAIRE, PARIS OFFICE BUILDING FOR AN INSURANCE COMPANY IN LONDON 19 BMW ADMINISTRATION BUILDING, WEST GERMANY. COMPETITION PROJECT FOR UNITED NATIONS IN VIENNA HONG KONG SHANGHAI BANK, HONG KONG FEDERAL RESERVE BANK, MINNEAPOLIS, MINNESOTA COEXISTENCE, PROPOSED PROJECT 20 KNIGHTS OF COLUMBUS BUILDING Architectural design: New Haven, Conn, Kevin Roche, John Dinkello and Associates. Structural design: Built: 1970. System: Concrete shear wall / steel floors A 23-story shear core structure consists of four cylindrical concrete corner towers, connected by deep steel girders, and a central elevator core. The five hollow tubular columns support the steel floor framing concrete slab, and together with the interior core which provides resistance for lateral forces. ■ v - ' 'mi* ft;:.;:' Weathering steel girders, slung horizon tally between the towers and diagonally to connect with the central core, support floor beams and horizontal sun grilles. 21 ^ ELECTRICAL ENGINEERING DEPARTMENT, TECHNISCHE HOGE SCHOOL, DELFT Architectural design: Bruggen, Drexhage, Sterkenburg, Bodon, Rotterdam. Structural Design: Ibid. Built: 1964/1969. System: Steel rigid frame + concrete shear wall / concrete slabs The structural steel frame consists of columns and floor beams in both directions, in combination with five pairs of reinforced concrete shear walls, the latter being located at the four ends of the building and also beside the liftshaft. The building is stiffened in the longitudinal direction by the rear wall of the passenger lift shaft against lateral drift and in the transversal direction by end-shear wall. Double sfiear Mails in reinforced concrete 1 External glazing 2 Outer corridor 3 Services 4 Internal glazing 5 Induced-air ventilator 8 Concrete floor 7 Column 340 x 340 im 8 Edge beam 9 Preean concrete slab 10 Floor beam HE 300 A 11 Longitudinal beam 12 Reinforced concrete show wall Structural system: cross-section Detail of joint in transversa Arrangement of beams io a typical storey, scale 1 650 22 LIBRARY IN PARIS, FRANCE Architectural design: Lods, Depondt, Beauclair, Paris; Malizard, Boulogne-sur-Seine. Structural design: L. K. Wilenko, Paris. Built: 1966/1968. System: Steel rigid frame / concrete slabs Columns are arranged in four longitudinal and seven transverse rows, on a 7.90x7.50 m grid. Ail steel beams were prestressed by giving them a preliminary camber by means of inclined props with screw jacks, these props being removed after the slab had matured. Because of the rigid beam-to-column connections, the column also participate in the prestressing. I'-; i t r .l:-: r - r r -i ppf I 14 ■H—( ■ j i 1 i H 1 -------1 -------1 r Structural system: cross-section and longitudinal section ol rigid steel frame » t? ■ o Arrangement of beams in fourth floor Typical tippet floor, scale 1 :7SQ s r-u Wa- Method of prestTCTting the 3 {sternal column HE 300 9 floor beam g Internal column HE 600M to HE 360 8 tO Transverse beam HE 280 A I t Longitudinal beam HE 260 A 12 Edge beam U 270 13 Prestressmg props Cross-section through building 23 HEAD OFFICE BUILDING FOR A STEEL COMPANY IN PITTSBURGH, USA Architectural design: Harrison and Abramowitz and Abbe, New York. Structural design: Skilling, Helle, Christiansen, Roberson,Edwards and Hjorth, ;New York. Built: 1967/1970. System: Steel braced frame with top belt truss / metal decking with concrete The 78-story building consists of exposed exterior box columns 39 ft apart, connected by box girders on every third floor and a triangular service core. The core is braced diagonally across three floors, and hat space frame ties the exterior columns to the core at the top. The building is composed of a series of three-story buildings with every third floor - the primary floor only framing into the exterior columns. The secondary floors are supported by the core and by the primary floor framing at the exterior face. to jjk , f o H t a a S M S iS li ;»t: m e m B M m s s d Y Na/'W % ,/r \j j * i — Deflection of rhe structural system due to wind load: A Without resistance of enema! columns B With resistance of external column*, through space frame in top storey 6 Space frame her' 7 M steel a Car-Tan steel 9 Ex-Ten steel 10 A 36 steel 11 Vented storage tank 12 Upper ring main 13 Lower ring main 14 Column, 152* 152 mm (section 15 Stub 16 Air-coflditiomng duct with air diffuser 17 Lighting unit with aperture for air extraction 18 Cor-feti steel cladding for spandrel girder 19 Mullien 20 Sandwich panel. Cor-Ten steel sheet on outside 21 Steel trough decking with in-sifu concrete floor slab 22 Angle cleat Wan of typical floor. Structural system: part cross-section (above): isometric view showing primary floor beams between core and external column* (befowl 24 HIGH-RISE RESIDENTIAL DEVELOPMENT AT BALORNOCK, SCOTLAND Architectural design: S. Bunton and Associates. Structural design: W. A. Fairhurst and Partners. Built: 1966. System: Steel braced frame + shear wall / metal decking with concrete The structural steelwork for all the buildings transmits the vertical loads and also the horizontal wind forces. Internal and external columns continue unspliced in both directions by floor beams. Wind bracing by vertical lattice system in the party wall between the flats and by rigid interconnection of floor beams and columns to multi-storey portal frames in the external walls and in the internal walls near the cores. s&s s b " fiMwTPir jf a E J u n IH B S - 5 M K W * ; Vi m at r tirn point blocks •x 1 lift 2 Staircase J livjn(i.rofliiL. '■Tloggta 5 Kitchen S Room 1_ Bathroom 8 Hearing 3nd water tank 9 Portai frame !0 Wind-bracing Arrangement of beams in floor Vertical section showing the connection' between (tie cladding and the floor S - Structurel syiteat: crees-settiens through a point block 1 1 Prefabricated wall panel 14 Irvsrtu concrete floor 12 Asbestos cement sheet 19 Perimeter beam 13 Hofonb decking IS Bracket tor connection of cfadding 25 WORLD TRADE CENTER, NEW YORK, USA Architectural design: M. Yamasaki and Associates, Troy, Michigan: E. Roth and Sons, New York. Structural design: Skilling, Helle, Jackson, Seattle. Built: 1966/1973. System: Framed tube system / metal decking with concrete On each of the facades a vierendeel girder type wall is formed by 59 box-section columns ( spaced at 1.02 m centres) which are rigidly connected to spandrel panels at each floor level. At the comers of the building these walls are interconnected to transmit shear, so that, together with the floors of the building, they form a torsionally rigid framed tube which is fixed to the foundations and transmit all wind loads. ->2 Plan of typical flour, seal* 1:1300 Found tub* construction principla: loadbearing eitornal waifs stiffened by tfn floors to form s tmiosaUy ngnt tub* Assembly of the enoroal wall units {alternately staggered m one-storey heights) and floor units Vertical section through a tower blot* 1 Ancillary building 2 Plata level 3Shyiobby 4 Technical services 5 Underground ear park Constructional features of a prefabricated floor unit 26 11044918087^ D+D BANK OF CHINA, HONG KONG Architectural design: I. M. Pei and Associates. Structural design: Les Roberson. Built: 1990. System: 3-D braced space frame / metal decking with concrete The super space frame consists of 8 pieces of truss meeting at a central column. The floor of each story is made of decking and 4-inch thick concrete. The master columns are made of steel concrete. The central structural column begins to disappear from 25th storey. Gravity above the 25th storey are resisted by exterior columns between 25-51 storeys. Extra stress caused from structural transformation is used to resist lateral forces, which is also resisted by exterior cross bracing. K 5 1K S 2 A 27 WESTCOAST OFFICE BUILDING. VANCOUVER, B.C., CANADA Architectural design: Rhone, Iredale. Structural design: Bruce Bobukee Built: 1969. System: Suspended system / single tower-single stack A suspended building, square on plan, with square concrete core, which is continued upwards beyond the top floor. The suspenders are cables which pass over the top of the core and rest on saddles. Lateral forces are absorbed by the central concrete core. 28 ALPINE MONTAN ADMINISTRATIVE BUILDING, LEKOBEN, AUSTRIA Architectural design: Huth, Domenik. Structural design: Built: System: Suspended system / concrete slabs, single tower-single stack The core is square in plan, with heavy steel stanchions at the comers. Wind loads are transmitted through multi-storey rigid frames formed by the interconnection of these stanchions. Cantilevers are steel trusses. 1 2 ^ r W > T \ 29 ADMINISTRATIVE BUILDING FOR AN ELECTRICAL ENGINEERING FIRM IN SAINT DENIS,FRANCE Architectural design: B. Zehrfuss, Pahs. Structural design: J. Prouve, L. Fruitet. Built: 1969/1970. System: Suspended system / metal decking with concrete / single tower-single stack The tensile forces induced in the hanger are in turn absorbed by diagonal ties on the roof, which transmit these forces to the concrete core. Wind forces are transmitted through the solid floors to the core. Pairs of round steel bars, 45 mm dia, placed at 1.05 m in front of the facade and spaced at 4.80 m centres. 1 Main beam of weWed I -section. 700 ram deep 2 Transverse beam. I 300 3 Pressed steel edge beam 4 Secondary beam. I 140 5 Hanger, mo 4S mm die bars S Horuantal wind-bracing 7 Concrete core 8 Diagonal tie. M e 86 mm dia bar* 9 Anchor frame GROUP OF EXHIBITION PAVILIONS IN TORONTO, CANADA Architectural design: Craig, Zeidler, Strong, Toronto. Structural design: Gordon Dowdell Associates, Scarborough. Built: 1968/1971. System: Suspended system / metal decking with concrete / multi tower-single stack At the centre of each pavilion are four 762 mm dia tubular columns arranged in a square with a side length of 3.55 m. At 20.0 m above water level, four pairs of lattice girders are connected to these columns. Wind forces are transmitted through the floor slabs and through horizontal cross-bracings between the pairs of lattice girders to the four tubular columns. nnint Diagrams showing the venous functional levels 1 Exhibition area 2 Footbridge 3 Service bridge 4 Hoof promenade 6 Exhibition pavilion 6 Restaurant 7 Access bridges 8 Cinema in spheiical dome Structural system; diagonal section Connection between 1 i j lj the cable-stayed || j;| lattice girders and ; 'jr the tubular v j columns > J S Tubular columns 761 timi dia 16 Pairs of lattice girders 11 Cable stays 12 Floor beams 13 Truss ties 14 Edge beam. RH5 306 * 203 mm 21 l-section wind-bracing 16 Floor bean I-section 2S4 x 2S4 nun 17 Inclined tube 102 m dia 18 Aluminium frame 19 Square hollow section 264 <26* m m 26 Mezzanine floor 21 I-section wind-bracing 31 1 PHILIPS ADMINISTRATIVE BUILDING, EINDHOVEN, HOLLAND Architectural design: Luyt, de Jongh. Structural design: Built: System: Suspended system / single tower-single stack Core of structural steelwork with elongated shape on plan. The cantilevers are of plate girder construction. Wind loads are transmitted through multi-storey frame to the central core. i 32 BRITISH PETROLEUM LTD. Architectural design: Antwerp, Belgium, Stynen, Paul de Meyer and Reusens. Structural design: Societe Cockerill-Ougree and Bureau Constructors. Built: 1961. System: Suspended system / double tower-single stack The central core is constructed of structural-steel. All columns encased in reinforced- concrete of the lower segments of the columns are made up of structural-steel plates. Seven of the overhead trusses are supported by the steel columns; the two end trusses, however, are hung from concrete girders cantilevered from end columns in a longitudinal direction. Each hanger has a constant depth of approximately 6 in., while width varies throughout its 158 ft length. WALL AND FLOOR SECTION 33 STUDENTS’ HALL OF RESIDENCE, CITY UNIVERSITAIRE, PARIS Architectural design: C. Parent, Neuilly-sur-Seine: M. Foroughi, E. Ghiai, Teheran. Structural design: Steelwork contractors. Built: 1966/1968. System: Rigid frame + suspended system / single tower-doubl stack Three steel portal frames, spanning 12.9 m at 14.50 m centres, each with two transverse girders, placed at the top and mid-height of the building respectively. The floors of these storeys function as rigid horizontal decks, being braced by lattice girders arranged around the perimeter. The second and seventh floors of the building are connected by horizontal abutments to the portal frame columns. Lateral forces are absorbed by the rigid frame. Structural system: a -i— Typical floor errth 12 students' rooms. scale 1:400 1 Student's n 2 Corridor 3 Balcony 4 Ablutions Structural tystem for a typical upper floor Central girder between the cross girders of the portal frames: elevation, plan and cross-section ’ H i OFFICE BUILDING FOR AN INSURANCE COMPANY IN LONDON, ENGLAND Architectural design: Gollins, Melvin.Ward and Partners, London. Structural design: Scott, Wilson, Kirkpatrick and Partners, London. Built: 1964/1969. System: Suspended system / single tower-double stack In each storey, the floor beams are supported at their inner ends in pockets formed in concrete core, while their outer ends are attached to steel hangers in the facades. The horizontal forces transmitted by the cantilever frames to each side of the core balance one another, the diagonal ties being interconnected by prestressed high-tensile steel ties linking their upper points of attachment, while the struts transmit their thrust through the floor slabs within the core. Section through building — • . 1 - — t — - F " ' ' 1 iFr.iinRanE.wium vmF'riiMiiinaittH MSMIUm mFM HM I ir^tfW 'ZM H C TS S IH -«W Kr<flT-a*T ru*H IISSSIlllSSSSIlJfSH iiwiiiiiifiitiiiii niUiifiiHtiivtni iimssieiitiiisiiii’ nniKfifflfHiint ifssraiisisifiitaii IIHtlSfltllttlliTOi SISISIIillfllfflgli! Hlllf£(SiRlB1911IBi lllRillSlillVliilKiS IIIIIIiEIKRIIIIHVlr ililiiiitii ". : typical upper lioor with open- plan office apace free from interna! supports surrounding the vertical core. scale 11200 Structure! system: section through core in longitudinal direction Beam arrangement in a typical floor -= M = I 1 !" i- rH- - I— 1 35 j BMW ADMINISTRATION BUILDING, WEST GERMANY. Architectural design: Karl Schwanzer of Vienna. Structural design: i Built: 1973. I ' System: Suspended system / single tower-double stack j The building core consists of four open tubes in concrete, interlinked via beams and slabs. At the top of the cores, the four arms of a protruding crosshead beam support the total load of the suspended floors, the loads being transferred to the cores by four < suspension columns. The floor slabs are light - weight reinforced ribbed concrete. E HH-tlHlinHII M w n m iii 36 COMPETITION PROJECT FOR UNITED NATIONS IN VIENNA i Architectural design: G.G. Schierle / Marquis j Structural design: G.G. Schierle / Elsesser V n System: Suspended systems / multi tower-multi stack I This system allows future additions horizontally on the ground level vertically between j stacks. Floors are supported by hangers which extend from trusses between two circular j concrete cores. Multi- direction lateral resistance are formed by truss/core portal frames. i 22551^ HONG KONG SHANGHAI BANK, HONG KONG Architectural design: Foster and Associates. Structural design: Ove Amp and Partners. Built: 1986. System: Suspended system / multi tower-multi stack Each mast is made up of clusters of four steel columns, linked together by rectangular (launched beams at storey height intervals of 3.9 m. These links turns the mast into a vertical vierendeel structure of considerable stiffness. North South stability for the structure is provided by two storey deep x braces spanning between each suspension truss at either end of the building. Horizontal wind loads are transferred from the mast to a 1 m thick concrete diaphragm wall box basement by the ground floor concrete slab. g a s a e 38 FEDERAL RESERVE BANK, MINNEAPOLIS, MINNESOTA Architectural design: Gunnar Birkerts and Associates. Structural design: Skilling, Helle, Christiansdn, Roberson. Built: 1971. System: Suspended system / multi tower-single stack Bridge-type building with a span of 84 m. The loads from twelve storeys are transmitted through hangers to two 8.50 m deep lattice girders, assisted by two parabolic strands of l-section. The horizontal forces from the parabolic are resisted by the lattice girders. Four corner piers transmit the loads to the foundations. 39 COEXISTENCE, PROPOSED PROJECT Architectural design: Future Systems Structural design: Ove Arup and Partners System: Steel rigid frame +prestressed strands/ single tower-multi stack The tower is conceived as a series of stacked accommodation elements arranged around, and supported by, a central structural and service core. The basic structural concept is an externally stiffened tube with an inner cylindrical core in compression and a cylindrical external truss structure in tension. Lateral stiffness is provided by central shear core and exterior prestressed strands. 40 4. PRESTRESS AND HIGH-RISE STRUCTURES 4-1 Consideration of lateral force effects Drift refers to the horizontal deflection of a structure due to lateral forces. For high-rise buildings a major concern in structural design is to reduce the lateral drift through laterally resistive systems. These systems consist of some combination of horizontal elements and vertical bracing elements. The reasons to reduce lateral drift are: 1. Structural safety and stability: “Failure of any part of this system, or of connections between the parts, can result in major damage to the building, including the possibility of total collapse”. (Ambrose, 1988) 2. Lateral drift must be maintained within an acceptable range to provide occupant comfort. 3. Non-structural damage: Lateral drift may disable rigid piping, elevators, doors, and cause window glass breakage. 4. Working efficiency: People may not be able to work efficiently due to excessive lateral drift. 5. Furniture and facilities can be damaged. \ 4-2 Sources of lateral loads and their effects \ Lateral forces which cause lateral drift on buildings are : : | 1. Wind forces 2, Seismic forces A prime concern is the effect of wind and earthquake on the lateral bracing system for the building. To understand how the lateral loads of / wind and earthquake are resisted in a building it is necessary to consider the manner by which these forces are applied. Wind loads are collected by the vertical surface, transfered through horizontal floor structures, distributed to the vertical bracing system, and finally resolved by the building foundations. This is the propagation of wind forces through a structure. As shown in the wind pressure diagram (Fig. 4-1), the wind forces increase with the height of a building. The overturning moment increases sharply with the height of the building. So, in very tall buildings, wind forces often govern the structural design. "Seismic loads are actually generated by the dead weight of the building construction."(Ambrose J., 1988) In other words, it is necessary to consider all elements that are permanently attached to the structure. Take the wall of a one-story building for instance. If the seismic loads are parallel to the plane of the wall, minor load is carried by the roof due to the relative wall stiffness, and the major load is carried by the foundation. However, if the seismic loads are perpendicular to plane of wall, the roof and foundation carry 1/2 of the load respectively. As shown in Fig. 4-2, 42 in Fig. 4-2, max. force occurs at the top floor, max. shear and overturning at the bottom floor, namely, the base of a t^uilding has to resist a relatively great shear and moment due to seismic forces. Fig. 4-1 Wind pressure diagram on buildings. Force Shear Overturning Moment Fig. 4-2 Seismic force diagram. 43 4-3 Concepts of high-rises analyses High-rise buildings can be considered as vertical cantilevers for analysis, because of similar structural behaviors in Fig. 4-3, Fig. 4-4 (Schierle, 1990). The lateral drift at the top floor of high-rise buildings can be compared to the vertical deflection at the free end of cantilever beams. Since prestress can be applied in horizontal cantilever concrete beams to improve the structural behavior and reduce deflection, could prestress also be used in high-rise buildings, which are vertical cantilevers from the ground, to reduce the lateral drift? lIQ IIIIX E ig LOAD LOAD SEAM SHEAR ■ MOMENT n LETT MOMENT OEFORM. HORIZONTAL SHEAR OEFORM. VERTICAL SHEAR OEFORM. Fig. 4-3 Structural behavior of cantilever beams. LOAO BUILDING SHEAR MOMENT LOAD MOMENT OEFORN. VERTICAL SHEAR DEFORM. Fig. 4-4 Structural behavior of high-rise buildings. HORIZONTAL SHEAR DEFORM. 44 4-4 Principles of reinforced and prestressed concrete Prestressing generates permanent stresses in a structure in order to improve its strength and stiffness under various service loads. The ultimate purpose of prestress is twofold: (1) “induce desirable strain and stress in the structure”; (2) “counterbalance undesirable strain and stress." (Lin, 1966) Reinforcement in reinforced concrete serves a function similar to prestress. Concrete is weak in tension and strong in compression. Therefore, it could not be able to withstand tensile stresses. In a simply supported beam of reinforced concrete, steel bars are placed at the bottom (Fig. 4-5); in cantilevered beams at the top (Fig. 4-6). Thus, the reinforcement is placed at the tension side of the beam in order to withstand the tensile stresses. If non-prestressed steel bars are placed in the concrete, the concrete may crack before the full strength of the steel is developed (Fig. 4-5). “By prestressing and anchoring the steel against in the concrete, the safe and economical utilization of the two materials can be achieved.” (Lin, 1966), as shown in Fig. 4-5 and Fig. 4-6. Namely, desirable strain and stress is induced in the structure and undesirable strain and stress is counterbalanced. Therefore, by means of prestress the structural behavior of buildings can be improved, to meet the requirements under different conditions. 45 Fig. 4-5 Prestressed simple beams. Fig. 4-6 Prestressed cantilever beams. 46 4-5 Prestressed cable systems Shown in Fig. 4-7 is a flexible wire supported at both ends and with a load P applied at its center. The wire on the left, without prestress, strains an amount e under the load P. The wire on the right is prestressed and strains only e/2 under the same load P, because half of its load is earned by the lower link through a reduction of prestress. For prestressed cable systems of similar symmetry conditions these observations can be made: Prestress reduces strain deformation to half. Compressive forces are absorbed through reduction of prestress. Prestress must be 50% of design stress to prevent slack members. Prestress above 50% compensates for creep and temperature changes. (Schierle, 1990) CO C u oo a . NOTE: P = LO AD PS = PRESTRESS e = STRAIN P I CO CO a. a. Fig. 4-7 Effect of prestress on strain. 47 4-6 Suspended structures and prestress With the effective use of high strength strands, suspended systems are rather efficient. Hangers are used instead of traditional columns to carry the floor weight (Fig. 4-8). The gravity load carried by hangers is transmitted via cantilevered trusses to a central core which carries it to the foundation. Since loads are directly carried by hangers in tension, the instability caused by buckling is eliminated, Therefore, the cross- sectional areas of the tensile members can be reduced to minimum. The hangers usually stop at the second floor, creating a column-free open space at the ground level for flexible use. Similar to the description for Fig. 4.7, prestress can reduce lateral drift. For example, as shown in Fig. 4.8, lateral drift is absorbed by increase of stress in the left hangers and by decrease of stress in right hangers. Without prestress the left hangers wound have to absorb the lateral drift alone. Because the right hangers between bottom floor and the anchor would get slack. Advantages and disadvantages of prestress for suspended structures and discussed below. Advantage of prestress • Prestress can reduce lateral drift since some of the load is carried in reduction of prestress. • Prestress increases the number of possible floors for each stack in suspended structures. The number of floors per stack is limited to about 10 . The reason for that is the strain difference between hangers and columns after floor loads are applied (Fig.4-10). As described in Chapter 4-5, prestress can reduce strain deformation to half. If prestress of 25 % of design stress is applied on the hangers, each stack of suspended structures may be able to carry up to 20 storeys; Thus increasing the freedom of suspended structures in architectural design. • Suspended systems can potentially have reduced drift due to prestress. The feasibility is investigated here. Several proposals are suggested and evaluated in the following chapters. Disadvantage of prestress • Additional long term compression due to prestress may require larger columns. The ultimate stress however, is not greater, but it is applied permanently rather than only during full loading. 49 fligid frame Suspended structure Fig. 4-8 Gravity transmission of rigid frames and suspended structures. Fig. 4-9 Suspended structures and prestress. Fig. 4-10 Strain differences between columns and hangers. 50 5. PROTOTYPES TESTED 5-1 Considered prototypes Table 5-1 and Fig. 5-1 illustrate prototype suspended structures that have been tested. Table 5-2 illustrates prototypes that were considered for testing but were not tested. Fig. 5-2 and 5-3 give plan dimensions for the prototypes tested. 51 Table 5-1 Selected structures for testing Profile Description A typical suspended system with hangers stopping at the second floor. Hangers without prestress are connected to top and bottom trusses. Hangers with prestress are connected to top and bottom trusses. Hangers without prestress are anchored to the ground. Hangers with prestress are anchored to the ground. 52 Table 5-2: Prototypes considered but not tested Profile Description Prestressed hangers are anchored to the central core at the foundation. Connecting the top and bottom truss, the hangers with prestress are anchored to the ground at an angle. Connecting the top and bottom truss, the hangers without prestress are anchored to the ground at an angle. Guy cables are anchored to the ground at an angle. Each beam is connected with guy cables. 53 5-2 Selected structures for testing According to the comparisons tabulated above, case 1, 2, 3, 4 and 5 were selected for testing based on the factors described in Table 5-1. 10-CSS 10-TASS 10-TASS+PS 10-GASS 10-GASS+PS 20-CSS 20-TASS 20-TASS+PS 20— G A S S 20-GASS+PS 30-CSS 30-TASS 30-TASS+PS 30-GASS 30-GASS+PS Fig. 5-1 Selected structures for testing 54 cn < o | | 30* l | , 40* | j ; 30* | | Fig. 5-2 Structural arrangement of test cases. M - M- - M -M- -W 2 0 ’ 2 0 ’ Fig. 5-3 Dimension of the centeral core of test cases. 55 6. CORRELATION OF MODEL AND ORIGINAL STRUCTURE Physical mpdel testing is used to provide evidence of behavior in cases where no well-known analytical procedures exist, or to confirm a particular technique. The correlations of model and original structure must be carefully identified before preparing and proceeding with tests. 6-1 Derivation of correlations The test model is related to the original structure by three scales; namely Sg = Geometric Scale = model dimension/original dimension = Lm/ Lo Sf = Force Scale = model force/original force = Pm/Po Ss = Strain Scale = model strain/original strain = EmlEo Force scale Sf for axial members unit strain £=A/L, strain A = PL/AE ,hence Force P = AEA/L, hence Pm Am Em (A/L)m Force Scale Sf = — = ------- x ------- Po AoEo (A/L)o (A/L)m Em Since Ss = ------- = ---— , hence (A/L)o T o Am Em Sf = --------- x Ss , or (1) AoEo AmEm Sf = --------- if Ss = 1 , or (2) AoEo Am Sf = ------- = SG 2 , if Em = Eo (3) Ao Force scale S f for bending members A unit strain £ = — , strain A L PL3 = K ----- , El hence EIA El A Force P = ------- = ------ x - L3K kl2 l , hence P m E m lm Force Scale Sf = — = ----- Po Eolo Lo2 (A/L)m X --- X ------- X Lm2 (A/L)o K K (A/L)m Since ------ = Ss , and (A/L)o Lo2 1 L m 2 Sg2 E m lm 1 Sf = ------- x ----- x Ss , Eolo Sg2 or (4) E m lm 1 Sf = ------- x ----- , Eolo Sg2 if Ss = 1 , or (5) Sf =Sg2, if Ss = 1, E m = Eo.and all member sizes are in geometric scale E = Modulus of Elasticity I = Moment of Inertia K = Constant of Integration m = Subscript for model o = Subscript for original 57 Emlm 1 In Equation (4) S f = --------- x --------- x Ss , Eolo Sg2 the composite moment of inertia for the model frame was computed as follows: Ic = I(lo + Ad2) (6) Since lo is small and negligible compared to the amount of Ad2 , the composite moment of inertia was computed as: Ic = XAd2, where (7) lc = Composite Moment of Inertia = Moment of Inertia of elements about their own centroid A = Cross-section area of elements d = Distance of element centroid to neutral axis 6-2 Numerical data For the tests presented here, the following scales/relating model to original structure, were selected and computed: Table 6-1. Scales for various test cases (See Table 6-3, 6-4 for more details) Scales No. storeys SG Geometric scale S F Force scale Ss Strain scale Frame Hangers 10 1:192 1:47710 1:42246 5:1 20 1:192 1:87080 1:84492 5:1 30 1:192 1:97683 1:126738 5:1 The strain scale was selected as 5:1 (5 times exaggerated) to better visualize the deformation and for better accuracy in measuring. According to the assumptions for materials and dimensions of components computed in Appendix C , the force scale was computed in Appendix D and tabulated in the following Tables 6-2 to 6-4: Table 6-2. Element sizes in model and original1 Element Location Original 10 20 30 a Beam (1)2 Roof Bottom w14x34 (340) w21x101 (2420) w16x36 (448) w21 x147 (3630) w16x45 (586) w30x132 (5770) ■ ■ H Int. Col. ( I) Roof Bottom - * ■ m w12x53 (425) w14x211 (3010) w12x65 (553) w14x342 (4900) w12x96 (833) w14x370 (5440) 4- 1 to Ext. Col. (I) (A ) 3 Roof Bottom n w12x53 (425) (15.6) w14x370 (5440) (109) w12x65 (553) (19.1) w14x665 (12400) (196) w12x87 (740) (25.6) w14x370 (14300) (215) 4r 1 4 Elastic Modulus 330 ksi 29000 ksi Hanger Cross-section Area 1.77x1 O'4 in2 12.6 in2 25.2 in2 37.8 in2 Elastic Modulus 12x10® psi 22x10® psi 1. (I): Moment of Inertia. 2. (A): Cross-section area. 60 Table 6-3. Lateral forces simulated on model Number of storey Location1 of model load (floor) Model load (lb) Original load2 (lb) Force scale3 10 9.2 1.25 59850 1:47710 5.0 1.12 53583 20 .41 36167 18 .40 35371 20 15 .34 29433 1:87080 11.6 .34 30083 6.3 .34 29416 30 .53 52350 27.5 .37 3645 30 23.1 .39 38100 1:97683 17.6 .36 24783 9.6 .36 34800 1. Location of the resultant force was computed in Appendix F 2. From Appendix A: SDG 3. For calculation see Appendix 0 61 Table 6-4. Hanger prestress on model No. of floor Mo1 Original overturning moment 00 SF 2 Force scale for hangers 1 Mo 1 pg3 _ — x — x Sf x — 2 70’ 6 (lb) 10 63846.5 1:42246 1.8 20 182415.2 1:84492 2.57 30 343589.8 1:126738 3.23 1. From Appendix A: SDG 2. For calculation, see Appendix D. 3. Hanger prestress was computed as 1 Mo 1 PS = — x -----x SF x -- .where 2 70' 6 PS = Hanger prestress Mo = Overturning moment on central core (From SDG : Appendix A) SF = Force scale for hangers The above formula was derived as follows: The central core consists of 6 typical bays, then Original cross-section. Overturning moment on each bay = Mo, / 6 Distance AC = 70’ (Fig. 6-1) Prestress was 1/2 of design stress, therefore 1 Mo 1 PS = — x x — 2 70’ 6 Convert to model prestress by multiplying by the Force scale SF, then 1 Mo 1 PS = — x — x SFx — 2 70’ 6 62 7. MODEL BUILDING AND TESTING 7-1 Model building A bay of the primary structure of different stories was built in a geometric scale of 1:192 (1”=16’) to simplify the testing. The beams and columns of the frame were cut in scale and glued together. Then the frame was glued to a wood board through 2 holes (Fig. 7-2). A table (Fig.7-1) was built for testing. A section paper pasted on a card board was attached to the vertical plywood for reading the lateral drift of the top floor. In addition, for drift-reading convenience, a small piece of plastic cut at an angle was glued to the beam of the top floor to function as a indication needle (Fig. 7-2). Sand cups suspended from the frame were used to simulate the lateral loads, which were computed by the SDG Program (Schierle,1987) and converted by the force scales shown in Table 6-1. To simplify the testing procedure, the sand cups were hung every three or four floors, based on the calculations in Appendix E to simulate the lateral forces on each floor and the overturning moments for the building. 63 7-2 Test procedure Testing was done in the following sequence of steps: (Fig. 7-1 and Fig. 7-2) Test cases for CSS: * Marked the locations to apply the lateral forces. • Suspended fishing lines through pulleys to the frame at marked locations. * Prepared sand cups on a platform. * Hooked the sand cups by S hooks to the fishing lines. * Slowly lowered the platform until the sand bags, simulating lateral forces, were totally suspended by the fishing lines. * Marked and recorded lateral drift. Test cases for GASS: • Held strings (hangers in original) with screws which were fixed to the top of the back board. • Drilled holes in base for anchoring strings. • Introduced the anchor strings through the holes on the base. • Glued the strings to the base. • Let glue dry ( for at least 10 hours). • Cut the strings from screws. • Prepared sand cups on the platform. • Hooked the sand cups by S hooks to fishing lines . • Slowly lowered the platform until the sand cups, simulating lateral forces, were suspended by the fishing lines. • Marked and recorded lateral drift. Test cases for TASS • Cut the strings from the base to remove ground anchors, so the strings were connected to top and bottom truss only. • Marked and recorded lateral drift. Test cases for GASS+PS: • Attached strings (hangers in original) with screws which were fixed to the back board for temporary anchorage. • Introduced the strings through the holes on the base. • Filled sand bags to simulate the prestress of hangers. • Hooked the sand bags by S hooks to the strings. • Glued the strings to each beams end. • Glued the strings to the base. • Let glue dry ( for at least 10 hours). • Cut the strings from screws on back board. • Released the sand bags used for prestress. • Prepared sand cups on the platform. • Hooked the sand cups by S hooks to fishing lines . • Slowly lowered the platform until the sand cups, simulating lateral forces, were suspended by the fishing lines. • Marked and recorded lateral drift. Test cases for TASS+PS • Cut the strings from the base to remove ground anchors, so the strings were connected to top and bottom truss only. • Marked and recorded lateral drift. 66 Plan view screw back-board fishing lines sand cups strings temp. platform sand bags Front view Side view Fig. 7-1 Test preparation. / - Pointer _ l [ k _ z = Q $ t — .............. - glued -X Frame anchorage strings . I Base Glued hole _ _ ________ ... , Fig. 7-2 Model details. 8. TEST RESULTS AND SUMMARY 8-1 Numeric test results Table 8-1. Test model drifts (inches) 1 2 3 4 5 CSS TASS TASS+PS GASS GASS+PS Cable • • • • • Bottom truss • • Ground • • Prestress • • 10 .11 .11 .11 .06 .06 storey 100% 100% 100% 55% 55% drift (reduction) (0%) (0%) (0%) (45%) (45%) 20 .21 .20 .19 .16 .1 1 storey 100% 95% 91% 76% 52.% drift (reduction) 0%) (6%) (9%) (24%) (48%) 30 .51 .42 .44 .29 .26 storey 100% 82% 86% 57% 51% drift (reduction) (0%) (18%) (14%) (43%) (49%) % 8-2 Graphic test results The test results are Illustrated in Table 8-2 to visualize lateral drift for the various test cases. Table 8-2 Graphic test results 10 story 20 story 30 story C S S T A S S T A S S + P S G A S S G A S S + P S C S S T A S S T A S S + P S G A S S G A S S + P S C S S T A S S TA S S + P S G A S S G A S S + P S 69 I l 8-3 Summary of results The drift measured on CSS is assumed as 100% in order to compare the results from the other test described below. • The drifts reduction on TASS for 10, 20, and 30 stories was 0%, 5%, and 18% respectively. This reveal the efficiency of truss anchorage increases with building height. Zero reduction measured for 10 storey might be due to the small scale of the model. Even 10% reduction is hard to measure on the model. • If prestress is applied on TASS+PS, the drifts is further reduced by 0%, 10%, and 16%, for 10, 20, and 30 stories based on Table 8-1 The efficiency also increases with building height. Zero reduction for 10 storey is as above. • Drift reduction on GASS was much greater than that of TASS. Namely 55%, 76%, and 57% for 10, 20, and 30 stories respectively due to better height/width ratio. GASS can reduce lateral drift more efficiently. The efficiency also increases with building height. When lateral forces are applied, the ground remains at rest,while the bottom truss in TASS rotates with the deformation of the core frame. • Among all tests, GASS+PS exhibits the best overall drift reduction of 49% for 30 stories and the best drift reduction of 31% due to prestress for 20 stories. Due to ground anchors for 30 stories. The height-to-width ratio is significantly decreased from 9.8:1 to 5.6:1. • To apply prestress on the structure, hangers must be anchored somehow. Comparing TASS+PS with GASS+PS, identical prestress is applied, but, ground anchors provide a substantial improvement of height-to-width ratio, and hence less drift. Therefore, ground anchors are effective to improve stability. • Comparing GASS+PS to GASS, the prestress reduces drift by 32% (computed as1 - 52 / 76 x 100%) for 20 stories. 9. CONCLUSIONS AND RECOMMENDATIONS 9-1 Conclusions Ground anchors exhibit the best results. Because the height-to- width ratio is considerably decreased by the hangers anchoring to the ground. The fact that slenderness ratio affects the stiffness of structures is proven again. The effect of prestress to reduce the lateral drift, if the hangers are not anchored to the ground, is not as much as expected, but is quite good for 20 stories with ground anchors. To reduce lateral drift in suspended high-rise structures through anchors and prestress, these conclusions can be made: • If the hangers are anchored to the ground or truss without prestress, no extra compression is generated in the core columns. • If an open ground level is not essential, hangers, either with or without prestress, can be extended and anchored to the ground to reduce lateral drift. • If a support-free ground level is necessary, hangers, either with or without prestress, can be anchored to the bottom truss to reduce lateral drift, but to a lesser degree than with ground anchors. 72 • If only some hangers are anchored to the ground and are connected to a belt truss then the ground floor remains relatively unobstructed. • If the hangers are prestressed, extra compression will, be generated in core columns under average load; but ultimate compressive stress remains the same as described in Fig. 4-7. Therefore, without increasing the column size, prestress can be applied. • Prestress allows to increase the number of floors to be suspended per stack. The number of floors per stack is normally limited to 10, due to the strain difference between hangers and core columns under gravity load (Fig. 4-8). As mentioned in chapter 4-4, prestress can reduce strain deformation to half, thus more floors can be suspended per stack.This extends the freedom of architectural design for suspended structures. • With reduced weight, suspended high-rise structures experience reduced seismic forces. • If hangers are anchored to the ground, the lateral stiffness for wind and seismic forces is considerably improved. • For drift reduction of suspended structures, anchoring hangers to the ground is most effective. 73 9-2 Recommendations for future research The relative stiffness between hangers and the frame is one of the most important factors that must be matched in the test model. A major concern must be to find suitable materials and the best combination of hangers and frame. The strain scale and force scale for hangers and the frame must be identical for each test case, or as close as possible, to simulate the structural behavior in reality, for test results to be reliable. For better accuracy of test results, models of a larger scale and of an E modulus equal to the original structure are recommended. It would also be better to use a more accurate device to read the lateral drift. Instead of static models computer analysis could be used to investigate the effect of anchorage and prestress to reduce lateral drift. New functions can be added to existing programs for input of prestress, or a new one can be created. Lateral drifts can be shown on screen numerically and graphically. Seismic and wind forces could be input and applied on a structure by simply setting the degree of an earthquake or wind speed. Thus, it will be very easy to visualize the lateral stiffness of structures with different layouts under various service loading to achieve an optimal structural design. For construction feasibility, methods of applying prestress and anchorage are recommended for future research. Architectural application should be further investigated to explore the full potential of suspended structures. 10. ARCHITECTURAL APPLICATIONS The aim of this chapter is to propose possible architectural applications of suspended structures. It is hoped that the investigated suspended structures in this thesis provide a basis for feature research and creative integration of structure in architectural design for synergy of form and structure. Description Profile Volume variation Identical structural layout with different architectural floors allows free floor arrangements. \ Bridge-house Floors can be suspended under a bridge and used as visitor centers or gift shops. 77 Description Profile Historic preservation Historic buildings can coexist with new suspended structures which can provide open exterior space on the lower floors. Mix-use Different structural bases accommodate different architectural functions, such as offices and apartments. 78 Profile Description \ / / \ zsz S / V Free interior space arrangements An impressive atrium can be created by free interior space arrangements. Long span and future expansion Double towers in conjunction with belt trusses allow a smaller width/height ratio and better lateral stiffness. Atrium can be used as conference room, theater and auditorium for which long span is required and can be also used for future expansion by suspending more floors. 79 Profile Description \ V s / \I / 1 i / k / \ A \ Free space arrangement Each single tower can be used for single or multi-functions. Space between two towers may be used for natural lighting. By various heights of towers, the skyline can be more interesting and impressive. Open space on the ground level can be used for public. Existing structure utilization The existing structure of suspended bridges can suspend floors above bridges for visitor centers or restaurants without too much new construction. 80 Profile Description Sea right utilization Multi-core suspended structures can be built on water and used for hotels and restaurants or for museum of sea life. Construction under water can be reduced by the features of suspended structures. Higher single stack With prestressed hangers, each single stack is capable of suspending up to 20 storeys of floors by reducing the deflection defference between frame and hangers. 81 REFERENCES Ackerknecht D. & Assaf S., 1986 TALL BUILDINGS IN URBAN CONTEXT, College of Environmental Design, University of Petroleum & Minerals Dhahran, Saudi Arabia AISC, 1990 MANUAL OF STEEL CONSTRUCTION, 8th Edition, American Institute of Steel Construction, Inc., Chicago. Ambrose, J. and Vergun, D., 1990 SIMPLIFIED BUILDING DESIGN FOR WIND AND SEISMIC FORCES, John Wiley and Sons, New York. Ambrose, J. and Vergun, D., 1987 DESIGN FOR LATERAL FORCES, John Wiley and Sons, New York. Ambrose, J., 1988 BUILDING STRUCTURES, John Wiley and Sons, New York. Aregger, H., 1967 HIGHRISE BUILDING AND URBAN DESIGN, F.A.Praeger, New York Beedle, C. S., 1988 SECOND CENTURY OF THE SKYSCRAPER,Van Nostrand Reinhold, New York. Council on Tall Buildings and Urban Habitat., 1980 TALL BUILDING CRITERIA AND LOADING, American Society of Civil Engineers, New York. Council on Tall Buildings and Urban Habitat., 1980 TALL BUILDING SYSTEMS AND CONCEPTS, American Society of Civil Engineers,New York. Fattal, S. G., 1983 EVALUATION OF CONSTRUCTION LOADS IN MULTISTORY CONCRETE BUILDINGS, U.S. Dept, of Commerce, National Bureau of Standards Hart, F., 1978 MULTI-STORY BUILDINGS IN STEEL, John Wiley and Sons, New York. 82 Hawaiian Dredging & Construction Co.,1975 PAN PACIFIC TALL BUILDINGS CONFERENCE, Hawaiian Dredging & Construction Co. Hawaii Hutchinson Ross Pub. Co., 1983 DEVELOPMENTS IN TALL BUILDINGS, Hutchinson Ross Pub. Co, New York. Huxtable, A.L., 1984 THE TALL BUILDING ARTISTICALLY RECONSIDERED: THE SEARCH FOR A SKYSCRAPER STYLE, Pantheon Books, New York. Jencks, C., 1980 SKYSCRAPERS, SKYPRICKERS, SKYCITIES, Rizzoli , New York. Libby, J.R.,1977 MODERN PRESTRESSED CONCRETE, Van Nostrand Reinhold Company, New York. Lin.T. Y.,1966 DESIGN OF PRESTRESSED CONCRETE STRUCTURES, John Wiley and Sons, Inc., New York. Monfried, A. E., 1990 TECHNICS: HIGH-PROFILES, PROGRESSIVE ARCHITECTURE, February, 1990 Popov, E. P.,1968 INTRODUCTION TO MECHANICS OF SOLIDS, Prentice-Hall, Inc., Englewood Cliffs, N.J. Schierle, G. G., 1990 Prestressed Trusses: Behavior Analysis and Design, PROCEEDING FORTH RAIL BRIDGE CENTENARY CONFERENCE, Chapman and Hall, London. Schierle, G. G., 1990 StarCADD USER’S MANUAL, Schierle Associates, Los Angeles Schierle, G. G., 1990 LECTURE NOTES ON STRUCTURES, University of Southern California 83 Schierle, G. G., 1987 SDG: SEISIMIC DESIGN GRAPHS, US Department of Housing and Urban Development, Washington, D.C. Schmertz, M. F., 1975 OFFICE BUILDING DESIGN, John Wiley and Sons, New York. Schueller, W „ 1977 HIGH-RISE BUILDING STRUCTURES, John Wiley and Sons, New York. Shultz, E., 1959 OFFICES IN THE SKY, Bobbs-Merrill, Indianapolis. Taranath, B. S., 1988 STRUCTURAL ANALYSIS AND DESIGN OF TALL BUILDINGS, McGraw-Hill, New York. U.S. Dept, of Commerce, National Bureau of Standards, 1975 PRE-DESIGN ANALYSIS OF ENERGY CONSERVATION OPTIONS FOR A MULTI-STORY DEMONSTRATION, U.S. Dept, of Commerce, National Bureau of Standards, Washington. Vance, M. A., 1981 SKYSCRAPERS: A BIBLIOGRAPHY OF RECENT BOOKS AND PERIODICAL ARTICLES, Vance bibliographies, Monticello. Williams, S., 1989 HONG KONG BANK—THE BUILDING OF NORMAN FOSTER’S MASTERPIECE, Jonathan Cape Ltd, London. 84 Appendix A: SDG SAMPLE STRUCTURE Sonp/ Coefficient Occup.Importance St-ruc t . £ tiffness Soi1 Profi3e Fac:tor 4/ 2: 1-00 I j 1.00 K : O .68 S: 1.50 X/Y Time Period T X/Y Factors CS X/Y Base Shear V X/Y 0vert. Clement M S.000 / 2.000sec 0.07 / 0.07 96E / 9621c 18194 1 / 181941k? Length X: 40ft Width Y: 40ft Height H: 260ft No of Levels; 2 0 ftrea/floor(sq ft) Dead weight(psf) Floor height-Cft) From Level to Level 10000.00 100.00 1 3.00 1 £0 Concrete shear wall # 1 : 36,000 plf Concrete shear wall # 2 : 28,800 plf Concrete shear wall # 3 : 24,000 plf Concrete shear wall # 4 : 19,200 plf Concrete shear wall # 5 : 14,400 plf C o n c r e t e s - h e a r w a. 1 1 # 6 : 12,000 plf Concrete shear wall # 7 : 9,600 plf WARNING: See UPC 2312. j for moment frame rpquireir£ ! ' ■ ' t S WARNING: See UBC 3312, j for heights abe ve 3 60 fee Force Fx/Fy Shear Vx /Vy 0vertur n Moment M> ; /My per Level in X/ V D i r ec: t i one. Fir F (K > Fy(K> 7;c(K> ' Vy (K ) Mr< K * ) My< K “> 1 3-9 3.9 961.7 961 .7 181,940.7 181?940.7 2 7.9 7.9 957.7 957.7 169,4 39.0 169,439.0 3 11.8 11.8 949.9 949.9 156,930.6 156,935.6 4 15.8 15.S 933.0 938.0 144,640.5 144,640.5 5 19.7 19.7 922.3 922.3 132,446.1 132,446.2 6 23.6 £3.6 902.6 902.6 120,456.4 120,456.4 7 27.6 £7.6 879.0 879.0 108,722.7 108,722.7 S 31.5 31.5 851.4 851 .4 97,296.2 97,296.2 9 35.4 35.4 919.9 819.9 36,223.0 86,228.0 10 .39.4 39.4 784.4 784.4 / 5 , 569 . 5 75,569.5 11 43.3 43.3 745.1 745 . 1 65,371.7 65,271.7 12 47.3 47.3 701.7 701 .7 55,685.9 55,685.9 13 51.2 51.2 654.5 654.5 46,563.3 46,563.2 14 55.1 55.1 602.3 603.3 36,055.0 33,055.0 15 59.1 59.1 548.1 548. 1 30,£12.3 30,218.3 16 63.0 63.0 489.1 489. 1 23,086.4 £3•086.4 17 67.0 67.0 426.1 426.1■ 16,723.4 16,728.4 18 70 . 9 70.9 359.1 359. 1 11,139.6 11,189.6 19 74.8 74.8 288.2 288.2 6-521.1 6,523.1 20 213-4 213.4 213.4 £13.4 2,774.2 8,774.2 8 5 Appendix B: CAFA Col Col. Shear Ext. Int. Ext. Moment Ext. Int. Ext. i F 3 . 2 - a 0 . 1-9 4BO 85 2 4 0 .4 2 1 F 1 . , 1569 q 6 3:1.23. 52 1 5 6 9 .9 6 ? FI , 22°.. 1-5 4 9 9 . . 90 ■ 979.. 45 2 FI . 1 3 6 7 , 6 2 5117.. 85 1 5 6 3 .6 3 F3 . 2 2 '”’ . . 47 4 7 4 .9 5 2 3 7 .4 7 3 FI . t 5 3 9 ,7Q 3087,, 17 , t ; _ 7 (-, 4 F t 934., 32 46,9. 05 .93 4 52 4 F 1 t 53 1 . . . .6 1 7 0 4 9 ,9 7 1 5 3 1 . . 6 1 s .r F t , 970.. 3 7 4 6 1 .1 5 230., 57 5 F I .- 1. 5 0 5 , 94 7 9 9 - 7 . 4 7 1 505.. 94 7 F I . . 27'5,. 4‘5 4 5 1 .3 0 7 2 5 .6 5 6 FI. 1 4 77, 9 2 5 9 7 3 .4 5 14 77 9? ~r F"! . 2 1 9 .7 3 4 3 9 ,5 0 2 1 9 „ 75 , 7 n . • 1 4 3 ’~ ‘"7 795.4,, " i1 3 1 45 5. “77 n F ' i ' 91 7 9 3 4 9 5 ,7 0 9 1 , 85 8 FI . 1 790 „ "? 7 : 9 7 4 7 r>5 1 TQf, 7 9 9 FI . 2 0 4 .9 7 409.. 95 9 0 4 .9 7 9. .Ft : ‘7 d...2 : ; ; - a .. . 7 73.4.. .4 7 .. ■ : 779 . . 54. to F I . . 1 96 . 1 . 7 3 9 9 .7 5 1 96., 1 2 1 0 F t . 1 2 B ? .n i 2549., 62 i :?b? . 0 1 1 1 Ft .1.86. 27 3 7 2 .5 5 1 8 6 . , 27 1 . 1 F I . . 17.1.7 C )< ;) t b 5 "7 1 1 7 .9 9 1 2 FI , , 1 7 9 . 4 3 3 5 0 ,9 0 1 7 5 .4 5 1 ? FI. . . I . 147 A 7 2 ? B O ,35 1 1.47 7,2 1.5 Ft . .16 7„ 6 ? 327.. 25 1.65. 62 15 F t, 1 . C )7 0 ;. 7 71.27 „ 1 7 1 ,170 76 1 4 F t , 1 R7 301. . 6,5 1.50. 89 . 1 4 FI . 9 ;:o 7 _ -7 9 1 9 6 0 .7 7 ^ C ,.,. 1 Ft . 7 -7 4 , | • , I 3 7 . 0 5 1.r- " F t . H9P . . 07 1 731 . . ‘ 5 ^ ri,., i F t „ 1. 2 "-'.. 5 ”7 944.. 55 1 2 2 . . 2 1 7 1 6 F t . . ■ 7 O.1 . . 0 9 1.589 ‘--f 7,') J . . 99 I n .1.06.. 32 2 ! . 3 0 5 1 O 6 , 5.7 1 7 F t . 9 9 9 ■ , • J 7Rfl. 3 "I1 .7 59. 4 1 ’ 9 F t . 8 9 . 7 7 1 7 9 .5 5 8 9 . 77 1 p r . : r 1 , O _ ' v c | . ! 1 F , " 7 t 9 Ft . . 7 ? . 03 144. J O O fS 1 0 1 ...1 . . !-> -? /.. 90 F! , S3 73 106.. 70 •"Vi p i . y l ' i " 1 7 9 9 -r I-:,-.; : i . , i ”7 Col. Axial Force Ext. Int. Ext. i F I . . 4.359 4-7 7? C i „ 0 0 4552.. 4 7 2 FI , | 3 0 4 „OO 47 3 2 .5 0 3 F I . 391. 4 , 9 7 ! 2 8 R,OO 3 9 1 4 ,5 0 4 r-i . 9 7 2 .OO 3 5 9 9 _ 7 ,5 F I , > :}iV . 7 9 9 5 6 .OO 3289 . , 59 0 Fi 9 9 8 4 ,R4 2 4 0 .OO 7 0 , 3 4 . 04 3 FI , 76, f f- 3 7 7 7 4 „ OO 7 6 8 7 .5 5 8 F I . 3 7 0 ^ /|. 708,, 0 0 7 3 9 8 .1 4 9 FI 2 1 1 9 5.6 1 . 9 2 . OO 9 1 1 8 .5 6 1 O FI 1 8 4 ° .9 4 1 76.. OO .1849. 84 1 1 F t . 1 5 9 ”- . 9R I 6 0 „0 0 1 5 9 3 ,7 8 .1 2 F i - 1 330 . 1 6 1 4 4 .0 0 1 350.. .! 6 . 1 . 3 F t .. . 1 . 1 .9 1 76 1 2 8 .OO 1 1 2 1 .7 6 3 4 Ft. . O f" ) 1.7 7 ‘7 1 1 2 . 0 0 9 0 9 .7 7 1 3 F I ~ 7 - ] '-'7 9.6. OO 7 1 4 .7 5 1. 5 F! ="7 r- 80.. 0 0 3 3 7 ,6 9 t FI . 7 9-7 6 4 . O'”' 7 R 0 . °7 v 1 8 Ft . . 2 4 5 , 7 7 4 8 ,. 00 2 4 5 .3 7 4*9 FI . ■ { 77 j 0 7 2 . OO I 3 2 . 19 ‘ ’ O ' A FI. . 49 764? 1 6 , OO 4 2 ,6 8 8 6 Beam Beam Shear Ext. Int. Ext. Moment Ext. Int. Ext. 1. !r '! . 31. 7 . P7 31, Q 0 2 31 9,. 97 1 f"1 ■ j 3 1 9 3 99 71.33. 99 FI . . 31 F s 00 3 1 0 .OO 31 S., OO 7 F! . . 3 - t i a 41 '31 1 4 -.. 4 1 . 9 1 1 4 - 4 1 Ft 31 4 . . f - > 0 31'4. BO 31.4 . BO ~.r F I . . “TOP 2> . 40 ’ 3 0 8 ? . , 40 ■tar? - -O 4 FI , 3 1 O 3 : ! . 310.. 31 71 0 , 71. 4 FI . . 30 93 . 3 9 30 9 7,. 903-7.. 99 9 FI .. .30:: 33 304., 55 3 0 4 ’. 55 u : r F I ? 9 7C' . o ‘; ? 9 7 9 . . BO POTQ 6 F I .. ? 9 7 : 31 2 9 7 , 51. 797., 51 3 F -3 - '■QoQ « = ;,“) 9 9 0 9 „ 3 r' 7 9 AO '9;"i 7 FI , 1 O 3B9., 19 7 0 9 .1 9 f : ! 7 8 9 9.. 70 ? G 70 o F'! . f , o 3 7 9 .3 9 2 7 c; _ 5 0 P F I . p 73 0 .3 3 ?' 7 7 0 - 9 3 ;?79o . ? V? FI , 3 i ! '■ '! "7 1 . 7 0 2 . 7 1 2 6 R .71 9 F ! '•n .' < ■ • • • , .j t:-- . .• . . . < P 4 •{ <4 p i • ? 1 . 77 1.0 FI "'4. '. . 56 2 5 6 .5 6 3 5 6 .5 6 1 ‘~ - F ‘» . . 4. nr'i ? 3 r>0,. OO 9 r - “ fn 1 1 '. if 1 i 1 F I , P 4 3 ■ 1 . 7 2 4 3 .1 2 243.. 1 2 1 i n ? 7 p9 . . 01 • 77 6 3 , 01 P'74 ^ ■ < 1 i p FT . 7 2 8 .4 0 2 7 B „40 7 2 8 . 4.0 1 Fi ?-“■ * 1 p 3 9 9'? 1 . B. 99 '”'3 1 c 'f . 1 3 1 i 2 i'-.> 3 3 2 1 2 , 3 9 7 .1 . 2 . 39 t - -1,-v r ■ " 1 4 . FI. 1 75 t? 1 95 . . 1 2 1 9 5 . 17 ! - r t < ^ ’ i“.l‘r _ t:'\ ' • 1 FI |7 1 3 ■ ■ ■ 1 . 7 6 . 56 1 7 6 .5 4 1 ’ 1' • • ' " , • ! : ■ ■ .‘i . ; 1 ■ i 6 F 1 .. j 7 7 156.79 15 6 .73 - t 1 .. 0 • • ! 9, 1 1 . : r 7 FI .. ■ | ’ 1 3 5 5 9 j ,:^o • ? • • • > ‘ . i ■ I ■ ; -p; i p FI. . 1 . ! 3 . 1 . ° I 1 7 1 . 9 1 . 1 3 . . 1 9 ■ t c ■ r i 1 , . "v 1 c ? FT p.-! 21 w , 51. 619 . 31 '! t.'- 1 ■ " 1 ‘ . -... - j, 1 :.' i . .1 _ _ ____ n n . 4 "5 P ” 42,.7v ? 4 2 . 49 r ; ? 87 Appendix C: Frame Analysis by Portal Method The uniform vertical load is assumed to be as follows: L.L. = 20 psf D.L. =100 psf Total = 120 psf tributary width for a typical bay =19 ft uniform load = 120x19 = 2280 plf = 2.28 klf BEAM DESIGN: Find max. positive and negative beam moments. (Fixed-end support) -M = 0.045wL2 = 0.045x2.28x202 = 41.04 kip*ft +M = 0.08wL2 = 0.08x2.28x202 = 72.96 kip*ft BOTTOM beams Find required section modulus. Max.+M = 72.96 kip*ft Max.-M = 41.04+3121.8/6 = 561.34 kip*ft (GOVERNS) M 561.34X12 S= -— = -------------------= 312 in3 F5 36x.6 from AISC; try w2 1 x147 where Sx = 329 in3 >312 in3 88 Find beam shear, due to gravity V = wL/2 = 2.28x20/2 = 22.8 k due to lateral forces V = 312.18/6 = 52.03 k Total beam shear V = 22.8+52.03 = 74.83 k The shear stress must be less than 40% of the yield stress. (ie. .0.40x36 ksi = 14.40 ksi) For w21x147; A = 22.06x0.72 in2 V 74.83 f ------- 4 7 1 ksj < 1 4 4 o.K. A 22.06x0.72 ROOF beams Find section modulus. Max.+M =72.96 kip*ft Max.-M =41.04+352.6/6 = 99.81 kip*ft (GOVERNS) M 99.81X12 S = — = ------------------- 56 in3 Fb 36x.6 from AISC; try w16x36 where Sx = 56.5 in3 > 56 in3 89 Find beam shear. due to gravity V = wL/2 = 2.28x20/2 = 22.8 k due to lateral forces V = 35.26/6 = 5.9 k Total beam shear V = 22.8+5.9 = 28.7 k The shear stress must be less than 40% of the yield stress. (ie. .0.40x36 ksi = 14.40 ksi) For w16x36; A = 15.86x0.295 in2 V 28.7 f = --------------------------= 6.13 ksi < 14.4 ksi O.K. A 15.86x0.295 INTERIOR COLUMN DESIGN tributary floor area = (70/6)x20 = 233.3 ft2 Interior columns at BOTTOM total gravity load =120 psfx20 floor = 2400 psf = 2.4 ksf total axial force =233.3x2.4 = 560 k 90 Int. cols. N (k) lateral 3128.12x12/6 =6256.8 gravity 560 assume KL = 13 ft. from AISC, try w14x342 Bx = 0.181 (AISC, 1990) Peq. =P + BxMx =560 kip+0.181x6256.8 k*in =1692 kips < 1963 Kips = Pallow O.K. Interior columns at ROOF total gravity load = 1 2 0 psfxl floor = 1 2 0 psf = 0 . 1 2 ksf total axial force =233.3x0.12 = 28 k Int. cols. N (k) M (k*ft) lateral 205x12/6 =1410 gravity 28 91 assume KL = 13 ft. from AISC, try w12x65 Bx = 0.217 Peq. =P + BxMx =28 kip+0.217x1410 k*in =334.5 kips < 348 Kips = Pallow O.K. Exterior columns at BOTTOM Int. cols. N (k) M (k*ft) lateral 4404.2/6 1564.1x12/6 =735.7 =3128.4 gravity 1 0 0 2 x1 2 0 x2 0 / 1 2 3121.8x12x0.5/6 = 2 0 0 0 =3121.8 total 2735.7 6250.2 from AISC, try w14x665 Bx = 0.17 Peq. =P + BxMx =2735.7 kip+0.17x6250.2 k*in =3798.2 kips < 3855 Kips = Pallow O.K. Exterior columns at ROOF Int. cols. N (k) M (k*ft) lateral 35.26/6 352.64x12/6 =5.76 =705.6 gravity 1 0 0 2 x1 2 0 / 1 2 352.64x12x0.5/6 = 1 0 0 =352.8 total 105.76 1058.4 from AISC, try w12x65 Bx = 0.217 Peq. =P + BxMx =105.76 kip+0.217x1058.4 k*in =335.43 kips < 348 Kips = Pallow O.K. For all columns: fa fb — + — < 1 Fa Fb where Fb = 0.6x36 ksi = 21. 6 ksi Interior columns at BOTTOM fa Pact./A Pact. Fa Pall./A Pall. 560 = -------- = 0.29 1963 M 6256.8 fb «•-— = --------- = 11.19 S 559 fa fb 11.19 -----+ ------= o.29 + -----------= 0.806 < 1 O.K. Fa Fb 2 1 . 6 Interior columns at ROOF fa Pact./A Pact. Fa Pall./A Pall. 32.4 = -------- = 0.093 348 M 1410 fb ------ ------------ =16.04 S 87.9 94 fa fb 16.04 + = 0.093 + = 0.855 < 1 O.K. Fa Fb 21.6 Exterior columns at BOTTOM fa Pact./A Pact. Fa Pall./A Pall. 2735.7 -------------= 0.71 3855 M 4406.4 fb = ------ 3.832 S 1150 fa fb 3.832 .— + ---- = o.71 + ------------ 0.887 < 1 O.K. Fa Fb 2 1 . 6 Exterior columns at ROOF fa Pact./A Pact. Fa Pall./A Pall. 105.8 = ---------- = 0.304 348 M 1058.4 fb = ----- = = 12.04 S 87.9 95 fa fb 12.04 + ----- = 0.304 + ------------ 0.861 < 1 O.K. Fa Fb 21.6 Analysis summary Beam Int. columns Ext., columns Roof Bottom w16x36 w21x147 w12x65 w14x342 w12x65 w14x665 Strand size: tributary area = 35 ft x 15 ft D.L. = L.L. = 100+20 = 120 psf total load at top floor = 35x15x120x20 =1260000# =1260 K Required metallic area Ao: P 1260 Ao = ---- = ----------- = 25.2 in2 F 50 (Allowable tensile stress =50 ksi) APPENDIX D: Force scale for Frame Emlm 1 Sf = x x Ss , or (4) Eolo Sg2 Composite I of model and original were computed as Ic = Z(lo + Ad2) (6 ) Considering a single bay, lo is small and negligible in comparison to the amount of Ad2, hence, the moment of inertia can be computed as: Ic = 2Ad2 (7) Em2AmDm2 1 Dm 2 Sf = --------------- x x Ss, since,--------- = Sg: E02A0D02 Sg2 D o2 Em Am Sf = x Ss , E0A0 2 From Table 6-2 Ext. roof column, w12x65, I = 553 in4 Ext. bottom column, w14x665, I = 12400 in4 553+12400 I ave. 6426 jn4 2 97 w14x426 Average w14x398 I (in4) 6600 6426 6000 A(in2) 125 X 117 The average cross-section area of the column can be computed as: 6600-6426 6426-6000 125 - X X - 117 X = 123.2 in2 330 x 2.47 x 10' 2 Sp = x 5 2900 x 123.2 5 435403 1 = -— .......... = 1: 87080 87080 98 Force scale for hangers: E modulus of strings: (for 30# strings with d = 0.015”) PL E = ------ AAL P = 6.89# L = 8’ AL = 2.5/8 = 0.31” A= jcd2 /4 = 0.015 2X7t/4 = 1.77x10'4 6.89x8x12 E = --------- = 12,000,000 1.77x10‘4x0.31 2 0# strings with d=0.0118” are selected for model tests Am Em Sf = ---------- x Ss , AoEo tcxO.01 182/4x1 2,0 0 0 ,0 0 0 = ..........................................X 5 2 5.2x2 2 x10 6 SF = 1 :8 4 4 9 2 99 Appendix E: Locations of lateral forces on model Form Appendix A: SDG program 5 zones were divided and the loads and locations computed as follows: Zone Floors Load (K) Load location (floor-height) 1 1—9 177.2 6.3 2 10—13 181.2 11.6 3 14—16 177.2 15.0 4 17—19 212.7 18.0 5 2 0 213.4 2 0 .0 Overturning M = Force x Lever arm, hence M = XFxH ( H = height above the ground) H = M/F, hence Locations of lateral forces on model were computed: 9x35.4+8x31.5+7x27.6+6x23.6+—+1 x3.9 Zone 1 : H = .............................................................. = 6.3 177.2 10x39.4+11 X43.3+12x47.3 Zone 2 : H = ............................................. = 11.6 181.2 14x55.1+15x59.1+16x63 Zone 3 : H = ----- —- = 15.0 177.2 17x67+18x70.9+19x74.8 zone 4 : H = ................. - = 18.0 212.7 20x213.5 Zone 5 : H = .................= 20.0 213.4 100 Appendix F: Glossary CSS Conventional Suspended Structure TASS Truss Anchored Suspended Structure T ASS+PS Truss Anchored Suspended Structure w/ Prestress GASS Ground Anchored Suspended Structure G ASS + PS Ground Anchored Suspended Structure w/ Prestress 101
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Kuo, Ping-hung
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Effect of anchorage and prestress to reduce lateral drift in suspended high-rise structures
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Master of Building Science
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Building Science
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