Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Computer aided design and analysis of anticlastic membranes and cable nets
(USC Thesis Other)
Computer aided design and analysis of anticlastic membranes and cable nets
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
COMPUTER AIDED DESIGN AND ANALYSIS OF ANTICLASTIC MEMBRANES AND CABLE NETS by Mingsong Yin 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 1993 Copyright 1993 Mingsong Yin UMI Number: EP41435 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. Dissertation Publishing UMI EP41435 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 THE SCHOOL OF ARCHITECTURE UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-0291 This thesis, w ritten by Mingsong Yin under the direction o f h .i$........... Thesis Com m ittee, and approved b y all its m em bers, has been pre sented to and accepted b y the Dean of The School o f Architecture, in partial fulfillm ent of the require m ents for the degree o f MASTER OF BUILDING SCIENCE t _ D ate TH' •S Table of Contents List of Tables iv List of Figures v Acknowledgements viii Abstract ix Introduction 1 Chapter One Anticlastic Membranes and Cable Nets 1.1 General 3 1.2 Concepts 3 1.2.1 Definitions: Anticlastic Cable Nets and Membranes 3 1.2.2 Classifications 5 1.2.3 Materials: Cable and Membrane 7 1.3 Design Vocabulary 8 1.3.1 Boundary Conditions 8 1.3.2 Surface Conditions 10 1.4 Survey 11 Chapter Two Computer Program for Design and Anlysis of Membranes and Cable Nets 2.1 General 19 2.2 TRITRS 19 2.2.1 Functions 19 2.2.2 Input Data 21 2.2.3 Output Data 22 2.3 ISAP 23 Chapter Three Computer Simulation Correlation of Form, Prestress of Anticlastic Membranes 3.1 General 24 3.2 Cases Considered 24 3.3 Assumptions 26 ii 27 28 29 29 29 29 30 30 36 38 43 53 iii 3.4 Simulation Results 3.4.1 Compare Rigid Edge Beam and Flexible Edge Cable 3.4.2 Compare Membrane and Cable net 3.4.3 Compare Sag/Span Ratios 3.4.4 Prestress 3.4.5 Temperature Change 3.5 Conclusion 3.6 Recommendations Graphs Generated by ISAP Detailed Graphs of Analysis Cases Prestresses and Member Forces List of Tables TABLE PAGE Table 3-1 Graph List of Cable Nets and Membrane with Edge beam 27 Table 3-2 Graph List of Cable Net and Membrane with Edge Cable 28 Table 3-3 Graph List of Cable Nets with Temperature Increase 28 Table C-l Prestress and Force of Cable Nets and Membrane with edge Beam 54 Table C-2 Prestress and Force of Cable Nets and Membrane with Edge Cable 55 Table C-3 Prestress and Force of Cable Nets with Temperature Increase 56 List o f Figures FIGURE Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figire 1 Figure Figure Figure Figure Figure Figure Figure 3-1 Figure 3-2 Figure 3-3 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10 1-11 -12 -13 -14 -15 -16 -17 -18 PAGE 3 Anticlastic Surface Two Cables Cross Each Other 4 Two Series of Cable Cross Each Other 4 Net Diagonal to Border 5 Net Narallel to Border 6 Triangular Mesh Net 6 Cable 8 Rigid EdgeBeam 9 Flexible Edge Cable and Rigid Edge Arch 10 North Carolina State Fair Building 11 Ingalls Hockey Ring 12 West German Pavilion 13 Swimming Pool for the 1964 Tokyo Olympic, Japan 14 Stadium for 1972 Munich Olympics, West Germany 15 International Stadium, Riyadh, Saudi Arabia 16 Park District Recreation Complex, Hanover Park, Illinois 17 Concert Pavilion for Baltimore Harbor Place, Maryland 18 Lindsay Park Aquatic Center Calgary, Alberta, Canada 18 Cable Nets and Membranes with Rigid Edge Meam 25 Cable Nets and Membranes with Flexible Edge Cable 25 Graphs Correlating Form and Prestress as Percentage of Maximum 32 Force for Anticlastic Cable Nets and Membranes with Rigid Edge Beam Figure 3-4 Graphs Correlating form and Prestress as Percentage of Maximum 33 Force for Anticlastic Cable Nets and Membranes with flexible Edge Cable Figure 3-5 Graphs Comparing the Effect of Temperature Change on Anticlastic 34 Cable Net with Rigid Edge Beam Figure 3-6 Graphs Comparing the Effect of Temperature Change on Anticlastic 35 Cable Nets with Flexible Edge Cable Figure A-1(a) Plan of Grid Net Parallel to Border 39 Figure A-1(b) Axonometric and Sections of Grid Net Parallel to Border 40 Figure A-2(a) Plan of Grid Diagonal to Border 41 Figure A-2(b) Axonometric and Sections of Grid Net Diagonal to border 42 Figure B-1 Graph of Cable Net with Edge Beam, Sag/Span Ratio of 1:5 44 Figure B-2 Graph of Cable Net with Edge Beam, Sag/Span Ratio of 1:10 44 Figure B-3 Graph of Cable Net with Edge Beam, Sag/Span Ratio pf 1:15 45 Figure B-4 Graph of Membrane with Edge Beam, Sag/Span Ratio of 1:5 45 Figure B-5 Graph of Membrane with Edge Beam, Sag/Span Ratio of 1:10 46 Figure B-6 Graph of Membrane with Edge Beam, Sag/Span Ratio of 1:15 46 Figure B-7 Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:5 47 Figure B-8 Graph of Cable Net with Edge Cable,Sag/Span Ratio of 1:10 47 Figure B-9 Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:15 48 Figure B-10 Graph of Membrane with Edge Cable, Sag/Span Ratio of 1:5 48 Figure B-l 1 Graph of Membrane with Edge Cable, Sag/Span Ratio of 1:10 49 Figure B-12 Graph of Membrane with Edge Cable, Sag/Span Ratio of 1:15 49 Figure B-13 Graph of Cable Net with Edge Beam, Sag/Span Ration of 1:5, 50 With Temperature Increase 50 Degreee Figure B-14 Figure B-15 Figure B-16 Figure B-17 Figure B-18 Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:10, with Temperature Increase 50 Degree Graph of Cable Net with Edge Beam, Sag/Span Ratio of 1:15, with Temperature Increase 50 Degree Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:5, with Temperature Increase 50 Degree Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:10, with Temperature Increase 50 Degree Graph of Cable Net with Edge Cable, Sag/Span Ratio of 1:15, with Temperature Increase 50 Degree Acknowledgements I wish to thank the School of Architecture, Master of Building Science Program for providing a two-year teaching assistantship. Moreover, the Department also provides up-to-date research facilities and instruments. I would like to express my sincere gratitude to Professor G.G. Schierle for his friendly guidance in research. Appreciation is extended to Professors Marc Schiler and Doug Noble for reviewing this thesis. The friendship and support of fellow graduates student will always be remembered. Abstract Anticlastic membranes and cable nets are theoretically the most efficient structural system in which the members take tension only. The main concern is their stability. It is necessary to apply appropriate prestress to keep them stable. This thesis presents a study comparing, by computer simulation, the stability of three forms of variable sag/span ratios under five prestress levels. Moreover, it considers the effects of temperature change and its effect on prestress. The computer program TRITRS was used for structural analysis, based on the direct stiffness method for geometrically nonlinear structures. The ISAP computer program was used and augmented for pre- and post-processing. It is discovered that there is significant correlation among form, prestress and structural behavior. Analysis results are discussed and further research is recommended. Introduction The research for a means to make better and more efficient utilization of covered space has been one of the important objectives of architects and engineers. The demand for large-span roofs to provide unobstructed use of covered space has intensified the search for new solutions. Advances in material and construction technology have contributed significantly in finding answers to meet this need. Since the 1950s considerable research has been done in this area of rapid progress. Cable net and membrane systems, by virtue of their geometric proportions, are incapable of carrying compressive stresses. They also can not carry bending or twisting moments. The only force they can take is axial tension. If subjected to a compressive force, the element will become slack if they are without prestress. This may cause large local deformations and therefore instability, affecting the roof cladding adversely. Therefore, the systems are generally designed with prestress such that any compressive force is absorbed by a reduction of prestress. The level of prestress must ensure that the entire system remains in tension under the worst conditions of loading. Many factors contribute to tension forces in elements. Foremost among them are structural form, prestress, load and temperature variation. A flat roof surface results in greater forces. With load, the tension in concave elements increases, while tension in convex elements decreases. So for a given prestress, when load increases to a given extent, the tension in convex elements would decrease to zero. It is significant to find the minmum prestress necessary to keep convex elements in tension under any given load. Temperature change also affects the stability of the structure because it effects prestress levels. If the temperature rises above normal, it will reduce prestress and vice versa due to the thermal expansion and contraction of the structural elements or members. l As mentioned above, the relations among form, prestress, load and temperature are important design criteria. This thesis presents findings on correlation of form, prestress and temperature for anticlastic membranes and cable nets. Chapter 1 is an introduction to concepts, form, prestress, design vocabulary, and a survey on the development of cable roofs. Chapter 2 introduces two interactive programs: TRITRS (Truss Iterations, Haug, 1971) a structural analysis program based on the finite deflection method; the other is a pre- and post processing program ISAP (Interactive Structural Analysis Processing) which generates the geometry for analysis and displays results. Chapter 3 presents 60 cases and simulates them with the two programs mentioned above, the results are presented and discussed. Further research is recommended. 2 Chapter One Anticlastic Membranes and Cable Nets 1.1 General This chapter will introduce the principles of anticlastic membranes and cable net structures. Concepts such as anticlastic surfaces, cable nets, membranes and prestress are discussed. Construction materials as well as their characteristics are intoduced. This chapter classifies the structures according to geometric configuration. Design vocabulary is included in this chapter. To illustrate the principles, a selected number o f structures are presented. 1.2 Concepts 1.2.1 Definitions Anticlastic Surface An anticlastic surface (or saddle shape) is a double-curved surface in which the main curvatures are in mutually-opposed directions with positive and negative radii at any point (figure 1-1). R — ; Figure 1-1 Anticlastic surface 3 Cable Nets Two cables that cross each other determine a point in space at their intersection. This point is statically stabilized (figure 1-2). Two series of cable that cross each other in a similar way form a series of polygons and series of statically stabilized points, which compose cable nets (figure 1-3). Figure 1-2 Figure 1-3 Two cables cross each other Two series of cables cross each other Membrane A membrane is a kind of tension roof. Usually it has two meanings: one is a self- supporting skin of flexible material such as natural canvas, or plastic fiber; the other is just a cover attached on cable nets. For the latter, the material includes flexible materials like canvas, fabric and plastic; semi-rigid material like sheet metal, lumber and plywood; rigid material like concrete panels, heavy plywood panels and rigid synthetic panels. In this thesis, the term membrane refers the former one. Anticlastic membranes and cable nets are anticlastic surfaces which consist of cable nets or membranes. It is one of a variety of tension roof systems which include suspended roof as well as tents. The characteristics of anticlastic cable nets and membranes is that they transfer applied loads in pure tensile stress to the supports and are stabilized by mutually opposed curvature which are named as concave and convex. Specifically speaking, the function of concave is to support gravity load, while that of convex is to stabilize the system. For wind load the reaction is reversed. Because cable nets and membranes are non-rigid, or flexible, they cannot take pressure or bending moment. When some members (either concave or convex) lose tension and get slack, the net will be unstable. To keep the structure stable, all or almost all members must retain tension. Therefore sufficient prestress has to be introduced to avoid members from becoming slack under loads. 1.2.2 Classifications Cable nets can have many kinds of configuration. Some of them are as follows: 1. Equal square grid net diagonal to border. Cables run in the general direction of the principal curvature from high-to-high points and from low-to-low points (figure 1- 4). Figure 1-4 Net diagonal to border 5 2. Equal square grid net parallel to border. Cables run in the general direction of the generating line or no curvature (figure 1-5) Figure 1-5 Net parallel to border 3. Triangular mesh net. Triangular nets can have mesh composed of 45/45/90 degree or 60/60/60 degree angles (figure 1-6). Figure 1-6 Triangular mesh net In 1967, Dr. G.G. Schierle did research on the three nets and compared their efficiency (Schierle, 1968). His model tests have proved the Net I (net diagonal to border) was most efficient and had the smallest deformation. The Net II (net parallel 6 to border) had the largest deformation and proved inefficient. This thesis continues research on Net I to find the minimum prestress needed to keep net and membrane stable. 1.2.3 Material Information regarding construction material employed in anticlastic cable nets and membranes is very important, since these materials are not as conventional as reinforced concrete or rolled steel. Cable net and membrane structures have usually a relatively high amount of elasticity. The elasticity allows the cable and membrane elongate under tension and temperature changes. Because of this characteristics, anticlastic cable net and membrane structures can adjust their shape and redistribute force under different loads. Cables The strength of cables is dependent upon cable composition. The basic component of a cable is wire drawn from high-strength steel rods. A minimum of 7 wires are then spun to form a strand. A minimum of 7 strands are assembled to form a wire rope. There are many kinds of strands and wire ropes. The usual configuration is to arrange six strands over a central core which is itself a strand or a rope (figure 1-7 a). Other strands include locked coil strand and parallel wire strand. The former one is usually shaped as a "Z". One or more of the outer layers consists of shaped wires (figure 1-7 b). The latter one consists of a set of wires assembled parallel to each other (figure 1-7 c). All the above ropes and strands have common mechanical properties: high breaking strength; capacity to transfer only tensile forces- no compression or moments. This is because of their small cross section in relation to length. 7 a b c Figure 1-7 Cable Membrane Membranes are similar in their behavior to that of cable nets. They can be regarded as a net of extremely fine mesh. Compared with width and length, membrane thickness is very small. Membranes only transfer tensile stress, they allow no compression or moments. Because of relatively high elasticity, they are fairly flexible. 1.3 Design Vocabulary A specific membrane or cable net is defined by environmental conditions. This section will illustrate some conditions which are related to investigation in this thesis: boundary conditions and surface conditions. 1.3.1 Boundary conditions Membrane and cable net structures may have three types of boundary conditions: edge beam, edge arch, and edge cable. 1. Edge Beam The rigid straight edge is subject to a bending moment generated by the membrane tension (figure 1-8). The structural member for a straight edge may be a beam, girder 8 or truss. Quite heavy members are needed, especially for large structures, to resist the bending moment, this might reduce the integrity and efficiency of the structure. The large span capacity is accordingly limited for such a system. An advantage, however, of the straight edge is the simplicity in connecting it to adjacent elements such as side closures. By using the edge of a rigid structure such as bleachers of an arena, an adjacent building, or even a mountain side, a highly efficient system can be achieved with straight edges. Also the repetitive use of saddle shapes, with one straight edge forming the common border for two adjacent shapes, can be very efficient, since the bending moment in the edges is greatly reduced, tension force in adjacent nets being mutually absorbed. Net anchored into straight edge - beams Fig 1-8 Rigid edge beam 2. Edge Arch The edge arch transfers the loads imposed by the membranes and cable nets primarily under compression (figure 1-9). Some bending moments are generated when the neutral axis of an arch is not identical to the funicular pressure line caused by variation of load conditions. 3. Edge Cable The flexible curved edge cable supports a membrane and transfers the load imposed by the membrane under pure tension (figure 1-9). This is true for all load conditions. The edge cable adjusts its form to the funicular tension line for any condition. The edge of a membrane deformed in space assumes the shape of a funicular tension line which is deformed in space. The adjustable deformation of the edge cable under diverse loads can be minimized by applied pretension stabilizing the membrane and the edge cable. The tension developed in the edge cable varies according to its radius of curvature for any given unit load as generated by the pretensioned or loaded membrane. From e and slab anchor Edge cable Figure 1 -9 Flexible edge cable and rigid edge arch 1.3.2 Surface Conditions The anticlastic surface of membranes and able nets can be generated in various ways. This section illustrates one basic surface: saddle shapes. The anticlastic surface of saddle shapes is defined by any uninterrupted boundary which is not described in a plane. Various saddles are possible with respect to boundary conditions as described above and with respect to plan configurations. They may be on square bases, hexagonal bases, on bases with any number of sides, or bases of interrupted or uninterrupted curved borders. Saddle shapes may also be added in a repetitive manner by having rigid, straight adjacent edges, flexible cable adjacent edges, or open connections. 10 1.4 Historical Survey The oldest examples of tensile structures are tents and suspension bridges. Today they are supplemented by the tensile supporting surfaces for roof construction made of nets and membranes or of three-dimensional rope configurations. Anticlastic membrane and cable net structures were initiated in the 1950's. Since then, there has been rapid progress on both theoretical research and practice. Below are described selected number of structures varying in size and complexity, in location from warm to cool to damp climates, and in type of use. Figure 1-10 North Carolina State Fair Building North Carolina State Fair Building (figure 1-10) Architects: Nowicki and Deitrick Engineers: Severud-Elstad-Krueger This building is considered to be the first structure conceived and built on the principles of anticlastic cable net and membrane structures. The design was begun about 1950, construction being completed in 1953. Two concrete parabolic arches 11 cross each other over the two main entrances and form the boundary for a saddle shaped cable net. The arches are supported by a series of columns which form the side enclosure. The arches are nearly parallel to the concrete ring describing the upper rim of the bleachers. The cable net consists of bridge strands which are pretensioned by means of turnbuckles on either end. The supporting strands vary in size from 3/4 inch to 1-5/16 inches in diameter, while the stabilizing strands vary in size from 1/2 inch to 3/4 inch in diameter. The position and form of the parabolic arches result in the roof being almost flat toward the top of the arches. These flat parts needed to be stabilized against fluttering under windload by means of auxiliary guy cables. The cable net has a general mesh size 6 feet square. Supporting and stabilizing strands are mutually-connected at each cross point. The roof is covered with corrugated sheet metal. The architects originally intended to have a roof covering of neoprene-coated fabric with an outer film of sprayed-on aluminum for heat reflection. The actual roof weights 6 lbs/sqft. This building initiated the development of anticlastic membrane and cable net structures. ipffgi§g S U S M Figure 1-11 Ingalls Hockey Ring Ingalls Hockey Ring (figure 1-11) Architects: Eero Saarinen and associates Engineers: Severud-Perrone-Sturm-Bandel 12 Two saddle-shapes are supported by one vertical arch and two horizontal arches supported by side walls. A series of supporting strands of 15/16 inch diameter is pretensioned and stabilized by a series of stabilizing strands. The membrane consists of wood planking nailed to double wood purlins which are bolted to the strands. The arches form a counter-curvature at both ends. The cable net ends at the point of the change of curvature where it is fastened to horizontal steel trusses. Both entry areas are covered with a beam supported roof. The structure covers an area of 324x 183 feet. The supporting arch is stabilized by guy cables in addition to the membrane. The Hockey Rink was erected in 1958. Figure 1-12 West German Pavilion West German Pavilion (figure 1-12) Architects: Rolf Gutbrod, Frei Otto Engineer: Fritz Leonhard This two-acre cable net has been the most advanced example of anticlastic membranes. It was a point supported system. Eight steel masts with a maximum height of 120 feet supported the cable net as a point supported system. The cable net had a mesh size of 20 inches square and was prefabricated flat on the ground then deformed in space assuming anticlastic curvature. A plastic membrane 1/32 inch thick and fifty percent 13 translucent was suspended at a distance of about one foot beneath the cable net by means of spacers. This allowed independent tensioning of the cable net and the membrane. The cable net was supported by means of cable eyes which transferred the membrane force into the masts without excessive force concentrations. A similar eye acted as down pull of low points for interior water drainage. These eyes were covered with secondary cable nets to which transparent membranes were fastened. The engineering calculations were based on data from a structural test model and on wind tunnel tests simulating 120 mph winds. Structural details and erection procedures had been explored on a full-size prototype of one typical section of the pavilion. This prototype has been re-erected as a permanent structure in Stuttgart. Figure 1-13 Swimming Pool for the 1964 Tokyo Olympics, Japan Swimming Pool for the 1964 Tokyo Olympics, Tokyo, Japan (figure 1-13) This roof consists of a doubly curved network supported on main cables and concrete ring beams. The network has sharp changes of slope near the pylons. To accommodate this geometry, the main members are built-up I sections, bent to shape, 14 instead of cables. The deck for the roof consists of 0.18 in (4.5 mm) steel plates welded together. A special feature of the anchoring system is that the gravity anchors for the cables support only the vertical component of the tensile force. The horizontal component is transmitted between the anchor and the pylon by means of 4.9 by 9.4 ft (1.5 by 3.0 m) concrete struts, and between the pylons by the inspecting gallery under the pool, acting as a huge street. The main cables are installed with an oil damper system at each of the two pylons, to safeguard against the possibility of large amplitudes of vibration. Figure 1-14 Stadium for 1972 Munich Olympics, West Germany Stadium for 1972 Munich Olympics, West Germany (figure 1-14) This project is nearly 440 m long and 80 m wide and houses a variety of facilities such as arenas, an ice rink, and a swimming pool under one homogeneous, free- formed megaspace, which is 805,200 square feet. The roof is supported by 12 high masts from 131 feet (40 meters) to 262 feett (80 meters), meter) and 45 of 112 foot (34 meter) smaller masts. 15 a b Figure 1-15 International Stadium, Riyadh, Saudi Arabia International Stadium, Riyadh, Saudi Arabia (figure 1-15) Architects: Lan Frazer and John Roberts Partners Engineers: Geiger-Berger Associates This project consists of a new international stadium covered with 480,000 square foot of Teflon-coated glass fiber fabric tension roof which is in a ring configuration having an outer diameter of 945 feet. Its 24 tent modules are arranged in a circle to provide 16 shade to the 60,000 seats plus concession areas and concourse. The roof is supported by 197 foot high masts and stabilized by a 440 foot diameter tension ring. Figure 1-16 Park District Recreation Complex, Hanover Park, Illinois Park District Recreation Complex, Hanover Park, Illinois (figure 1-16) Architects: The Shaver Partnerships Engineers: Bob D. Campbell Co. This 62,000-square-foot multipurpose recreational facility houses six tennis courts and a gymnasium that doubles as an auditorium. The tennis courts are covered by a translucent fabric roof, while the gymnasium and auditorium are covered by an insulated fabric roof. The roof is supported by steel arches. 17 Figure 1-17 Concert Pavilion for Baltimore Harbor Place, Maryland Concert Pavilion for Baltimore Harbor Place, Baltimore, Maryland (figure 1-17) This 19,000-square-foot pavilion on the harbor is the summer home of the Baltimore philharmonic orchestra and site of many summer concerts and other entertainment. The fabric roof is supported on seven masts with cable edges. Figure 1-18 Lindsay Park Aquatic Center Calgary, Alberta, Canada Lindsay Park Aquatic Center Calgary, Alberta, Canada (figure 1-18) Architects: Chandler Kennedy Engineers: Geiger-Berger Associates This facility was designed to enclose the Olympic Competition Pool, including diving and warmup pool, also track and field events, basketball, etc. The roof is a cable net over a trussed arch with tensioned Teflon-coated glass fiber fabric membrane. Chapter Two Computer Program for the Design and Analysis of Membranes and Cable Nets 2.1 General Principles of the anticlastic membranes and cable nets were discussed in chapter 1. This chapter will introduce computer programs to analyse these structures. There are two programs: TRITRS and ISAP. The former one is a structural analysis program based on the finite deflection method. The latter one is pre- and post-processing program which generates the geometry for analysing and display results. 2.2 TRITRS(TRUSS ITERATIONS) Paraphrased from from Dr. Haug (1971) TRITRS is a structural analysis program which computes shapes under prestress and load responses of cable net and membrane structures. Actually, it may be applied to any two- or three-dimensional truss type structure, that is one in which the members take axial forces only. It is expected that the structure will undergo large deflections and equilibrium is formulated using the deformed geometry. The program originated out of a study of geometrically nonlinear structures. It is initially written in Fortran IV by Dr. E. Haug and was modified slightly to Fortran 77 by the author and now runs on the Unix system. 2.2.1 Functions TRITRS uses the finite deflection method, which is a modification of the direct stiffness method of structural analysis. In the finite deflection method, joint 19 displacements are calculated based on the initial geometry, and then subsequent iterations correct those displacements to account for the geometrically nonlinear response of the structure. The program has 3 functions: 1) Calculation of the initial shape of the structures under prestress. 2) Calculation of new shapes after changes in member properties or prestress forces. 3) Calculation of deflections and member forces due to applied static loads, temperature changes, or turnbuckle tightening (change in length of members). At first the program finds the initial shape starting with a user defined approximate geometry, defined by x,y,z joint coordinates, connecting members, and bi-axial prestress. The program finds the exact form of equilibrium, based on an iterative algorithm that converges in usually about 5 to 20 iteration steps. After the initial form is defined, subsequent runs compute member stresses, joint displacements, and support reactions under applied load and/or temperature change as well as turnbackle motion, also in iterative analysis steps. Before a structure is analyzed, a numeric model for the structure must be set up. The structure consists of joints and members connecting the joints. A joint is defined by a number; a code, which indicates whether the joint is fixed or flexible; and its x, y, z coordinates with respect to a three-dimensional Cartesian coordinate system whose origin is located by the user. This system must be the same for all joints in the structure. Loads can be applied only at joints. A member is defined by a number and the joint numbers at each of its ends. Furthermore, each member is given a number specifing to which kind in a list of properties it belongs. Member properties consist of the cross-sectional area of the truss bar or cable net, or grid width of membranes, the elastic module, the prestress force, the member code 20 and the coefficient of the thermal expansion. The member code tells whether the member is to be a cable or membrane element which losses its stiffness when it goes into compression, a truss bar which takes compression, or a prestress member. Cable or membrane elements lose their force when going into compression. Struts or truss bar members take either tension or compression. Prestress members are responsible for the shape of cable nets. They pull with a constant specified prestress force and have no elastic stiffness. Thus, they may change their lengths without a change in force. 2.2.2 Input Data The data needed to analyse a structure include: Identification number (ID) Displacements and unbalanced forces convergence control number. Total number of joints and members. Joint number , its code and its x, y, z coordinates. Member number , its kind and corresponding joint numbers. Member properties: cross sectional area or width of member, elastic modulus of the material, initial prestress of member, member code, temperature expansion coefficient. Load applied on joints Temperature change and turnbuckle tightening. Convergence checking data. Among all the above data, the majority are joints and members. Coordinates of joints and relations between joints and members are calculated and set up by the program ISAP which produces a geometry data file. The file will be input into the TRITRS 21 program. Other data either can be edited into the geometry data file before TRITRS is run or input from a keyboard step by step while TRITRS is running. 2.2.3 Output Data The TRITRS output includes : New coordinates of joints and joint displacements. Member forces, new member lengths. Support reactions. 2.3 ISAP (Interactive Structural Analysis Processing) ISAP is a program developed by Dr. Schierle and augmented by the author which generates structure geometry model and graphically displays pre- and post-analysed structures as well as print it by a laser printer. The program is written in TurboBasic and runs on IBM PC , XT, AT, PS/2 286, 386, 486 & compatible computers. The ISAP program has 4 major functions: Model definition, Display, Plotting. Editing. 1) Model definition The program can generate two kinds of anticlastic cable nets and membrane structures. One is grid net parallel to border (figure A -l). The other is grid net diagonal to border (figure A-2). For both kinds, input data include: length of both x and y direction, height between the low points and high points. At first the program finds the total number of joints and members. For example, for the cable net parallel to border cable net, if there are nx bays in x direction and ny bays in y direction, the 22 total number of joints is: (nx + 1) * (ny + 1), the total number of members is : (nx+ l)*ny+(ny + l)*nx; For the cable net diagonal to border cable cable net, since both directions have the same bays, assume n= nx= ny, the total number of joints is 2*(n + l)2-2*n-l, total number of members is 4(n*(n + l). The program calculates the x, y, z coordinate of each joint, according to boundary conditions. Finally the program determines the members by connecting both end joints to each member. 2) Display The ISAP program graphically displays anticlastic membrane and cable net structures or truss structures in plan, elevation and axonometric. For axonometric display, different views can be chosen by selecting different angles and positions. Any direction elevation can be viewed by inputting corresponding angles to the x-axis in plan. Ten different colors are introduced to stand for different member forces . The forces are divided into ten groups. The colors are arranged from cool to warm and correspond to forces from low to high stress level ranges and stress level range members. Special consideration: yellow stands for compression members, white stands for zero or no force. 3) Plotting The program plots the plan, axonometric and elevation of structures by laser printer or ink plotter as they are shown on the screen. 4) Editing The program can edit text such as element nember and joint number on graph. 23 Chapter Three Computer simulation: Correlation of Form, Prestress and Temperature Change in Anticlastic Membranes 3.1 General In this chapter, I shall apply the TRITRS and ISAP programs to simulate anticlastic membranes and cable nets. First the cases will be considered, including determining boundary conditions and roof conditions. Secondly, some assumptions such as loads, prestress, dimensions and material elastic modules are made. Finally, simulation results are presented and conclusion are stated. 3.2 Cases Considered The anticlastic membranes and cable nets in this study were analyzed by TRITRS and generated by ISAP. The investigated structures include four different cases: 1) Cable net with rigid edge beam (figure 3-1). 2) Membrane with rigid edge beam (figure 3-1). 3) Cable net with flexible edge cable (figure 3-2). 4) Membrane with flexible edge cable (figure 3-2). All cases consist of two low and two high points. The high points were positioned to yield sag/span ratios at the line of principal curvature of 1:5, 1:10, 1:15. All structures are 50*50 ft in plan. Grid net is diagonal to border. Mesh size is 3.535*3.535 feet (figure 3-1 and 3-2). 24 3.5'x *3.5' 50' Plan Sag/Span: 1:5 Sag/Span: 1:10 Sag/Span: 1:15 Figure 3-1 Cable Nets and Membranes with Rigid Edge Beam 50' Sag/Span: 1:5 Sag/Span: 1:10 Plan Sag/Span: 1:15 Figure 3-2 Cable Nets and Membranes with Flexible Edge Cable 25 3.3 Assumptions The net cables were of 1 inch diameter strands, with metallic areas of 0.6 sq.in., and elastic modules of 24,000 ksi. Edge cables were of 3 inch diameter strands with metallic areas of 5.4 in2 and elastic modules of 23,000 ksi. The edge beam case was simulated with fixed joints along the edges, i.e. with infinite stiffness. Membranes were assumed of fabric bands of the same width as the cable mesh, with elastic modules of 6000/4500 pli in concave and convex (warp and fill) directions respectively. Prestress was applied equally in concave and convex directions, to approximate a minimal surface areas. Five levels of prestress were simulated, namely 30%, 40%, 50%, 60%, 70% of the maximum stress under load. The simulation was obtained iteratively by using a trial and error approach for each load case. The following loads were considered for the structure: Dead load: 15psf Live load: 25psf Total load: 40 psf This is equivalent to 0.5 k applied at each typical joint of the cable nets and equivalent intervals of the membranes. Load was prorated for smaller tributary areas along the edges. The load was applied downward and normal to the ground. Temperature change can cause redistribution of stress in elements. Higher temperature causes an increase in member lengths and a relaxation of stress. Reduction of prestress may be so large that stress in convex elements may become slack under load, causing 26 the anticlastic system to become unstable. So the initial level of prestress should be adjusted for expected temperature variations. In this thesis a 50 degree increase in temperature was considered to check whether they would cause slack elements. 3.4 Simulation Results The simulation compared maximum, average and minimum forces in both concave and convex elements for all cases. Analysis results are illustrated in figure 3-3 for cable nets and membranes with rigid edge beams, in figure 3-4 for cable nets and membranes with flexible edge cables, in figure 3-5 for cable nets with edge beam with 50°F temperature increase, and in figure 3-6 for cable net with edge cable with 50°F temperature increase. For detail of each case, table 3-1 lists graphs of cable nets and membranes with edge beam, table 3-2 lists graphs of cable nets and membranes with edge cable, table 3-3 lists graphs of cable nets with temperature increase. Table 3-4 lists prestress , member forces (maximum, average and and minimum) of cable nets with both edge beam and edge cable. Table 3-5 lists prestress, member force of membranes with both edge beam and edge cable. Table 3-6 lists prestress, member forces for cable nets with both edge beam and edge cable with a 50°F temperature increase. The main features of the results are as follows: Table 3-1 Graph List of Cable Nets and Membranes with Edge Beam Cable Nets Membranes Sag/Span Ratio Figure Sag/Span Ratio Figure 1:5 Figure B-l 1:5 Figure B-4 1:10 Figure B-2 1:10 Figure B-5 1:15 Figure B-3 1:15 Figure B-6 27 Table 3-2 Graph List of Cable Nets and Membranes with Edge Cable Cable Nets Membranes Sag/Span Ratio Figure Sag/Span Ratio Figure 1:5 Figure B-7 1:5 Figure B-10 1:10 Figure B-8 1:10 Figure B-l 1 1:15 Figure B-9 1:15 Figure B -l2 Table 3-3 Graph List of Cable Nets with Temperature Increase Edge Beam Edge Cable Sag/Span Ratio Figure Sag/Span Ratio Figure 1:5 Figure B -l3 1:5 Figure B -l6 1:10 Figure B -l4 1:10 Figure B -l7 1:15 Figure B-15 1:15 Figure B -l8 3.4.1 Compare Rigid edge beam and flexible edge cable. Generally speaking, the difference between rigid edge beam and flexible edge cable is minor, especially for sag/span ratio of 1:10. For concave elements, forces under the edge beam condition are higher than those under the edge cable condition. The order of difference for maximum, average, minimum forces is: smallest, moderate, largest. On the other hand, for convex elements, forces under the edge beam condition are lower than those under the edge cable condition. The order of difference from smallest to largest is: minimum, average, maximum. This means that the edge cable system has smaller maximum force in concave elements, but has bigger minimum force in convex elements. The edge cable system has the advantage of keeping elements from becoming slack, although the advantage is only 5.6 % for sag/span ratio of 1:10. 28 3.4.2 Compare Membranes and cable nets The difference between cable nets and membranes is obvious. Compared to cable nets, membranes need much less prestress. For the same prestress percentage, forces including maximum, average, minimum in concave elements and maximum force in convex element are much less than those in cable nets. The less the sag/span ratio, the more the difference. But the average and minimum forces in convex elements have a different behavior. They are higher in membrane than in cable nets, except for 70% prestress. This phenomena can be explain by elastic modules. The membrane has a lower E-modulus. This causes greater deformation and decreases tension. 3.4.3 Compare Sag/span ratio As expected, the sag/span ratio has a significant impact on forces. The less the sag/span ratio, the higher the forces in elements. The difference is much more in cable nets than in membranes. It is clear that the more flat the roof, the greater the generated forces. 3.4.4 Prestress The prestress is introduced to keep compressed elements in tension. The main concern is to keep convex elements in tension. For sag/span ratios of 1:5, 50% prestress can keep all elements in tension. For ratio of 1:10, 40% prestress can keep the system stable. For ratio of 1:15, 30 prestress can keep elements from becoming slack. 3.4.5 Temperature change With 50 degree increase in temperature, the tension in elements reduces considerably. For instance, for the cable nets with edge beam with 1:5 sag/span ratio, there is about 0.8k force decrease for the 50% prestress case, which means 9.4% decrease for 29 average force of concave elements and 48 % decrease for average force of convex elements, leading 3.6% elements slack. There are about 3.25 k force decrease for 60% prestress case, which means 29.6% decrease for average force of concave elements and 74% decrease for average force of convex elements, causing 2.5% elements to be unstable. There are 4.5 k force decrease for 70% prestress. For the last case, the minimum force is still positive and the system is stable, for the ratio of 1:10, 70% or more prestress can keep structure stable. For ratio of 1:15, the percentage of prestresss may be as low as 60%. So the effect of temperature change is significant in cable nets. 3.5 Conclusions The graphs and the above discussion demonstrate significant correlation between force, prestress and temperature. The edge cable system has the advantage of keeping elements from becoming slack. The membranes need much less prestress than the cable nets. The forces vary with sag/span ratios. The less the sag/span ratio, the higher the forces in elements. To keep cable nets stable, considering temperature increase 50°F, the minimum prestress as a percentage of maximum element force is 70% for sag/span ratio of 1:5, 60% for sag/span ratio of 1:10, 50% for sag/span ratio of 1:15. To keep membranes stable, the minimum prestress as a percentage of maximum element force is 50% for sag/span ratio of 1:5, 40% for sag/span ratio of 1:10, 30% for sag/span ratio of 1:15. In anticlastic membrane and cable net structure design, all the above factors ought to be considered to make final decisions. 3.6 Recommendations This thesis has investigated the correlation of form, prestress and temperature change for particular cable nets and membranes. There appears to be a general lack of 30 knowledge on free-form structural systems. Investigation of other forms is needed. To this aim, it is critical to develope a program which generates an approximate roof shape for any given border condition. In the above investigation, only static load is considered. It is obvious that dynamic load is an important factor for cable net and membrane structures. The information on dynamic response under time-dependent loads, such as wind and earthquake, is quite limited. This should be both through experimental study on models and observations on existing structures. A computer analysis program should be developed. 31 k N Sag/Span 1:15 CABLE NET 150" 140- ISO- 110 - 100- in 80- 5 e o ' 60- 30- 40 30 60 O 1 150- ISO" 1 2 0 " 00- 80- 60- 50- 70 30 40 5 0 60 Prestress as % of Maximum Force a Max force —I— Aver force — * — Min force MEMBRANE - 3 3 ■ 3 0 ■ 2 7 ■24 70 50 30 ■ 3 0 ■27 40 50 60 Prestress as % of Maximum Force Convex — B - Max force — Aver force - A - Min force Figure 3-3 Graphs correlating form and prestress as percentage of maximum force for anticlastic cable nets and membranes with rigid edge beam K ip s Sag/Span 1:15 CABLE NET MEMBRANE 150- 130- 120- 30- 20- 40 50 70 30 60 O I I 160' 140 130 120 ' *2 100' 8 0 ' 40' 30- 40 60 80 Prestress as % of Maximum force 30 ■ 3 0 ■ 2 7 70 40 60 60 Prestress as % of Maximum Force 30 Concave Max force Aver force Min force Convex Max force Aver force Min force Figure 3-4 Graphs correlating form and prestress as percentage of maximum force for anticlastic cable nets and membranes with flexible edge cable 33 K ip s Sag/Span 1:15 k N Sag/Span 1:15 ORIGINAL TEMPERATURE 160- 140- 1 1 0 - 100- in M - i 60- 2 0 - 30 60 0 1 % i 160- 140- 130- 120- 100- 90- 6 0 - 2 0 - 30 40 60 60 Prestress a s % of Maximum Force Concave ^ax force — Aver force Min force TEMPERATURE INCREASE 50 DEGREE ■ 3 3 -30 ■ 2 7 •■24 ■ 1 8 a ■12 S 60 33 •12 P restress a s % of Maximum force Convex Max force Aver force Min force Figure 3-5 Graphs comparing the effect of temperature change on anticlastic cable nets with rigid edge beam k N Sag/Span 1:15 ORIGINAL TEMPERATURE 160- 180- HO- 100- to § ~ rn 00- 70- 2 0- 30 60 60 O I 140 no- loo- 80- 70- 60- 30- 2 0 - 30 Prestress as % of Maximum force Concave Max force ■ Aver force • Min force TEMPERATURE INCREASE 50 DEGREE -30 ■ 2 7 -24 ■ ■ 9 60 70 30 40 50 ■ 3 3 ■ 3 0 •27 -24 70 40 50 60 Prestress a s % of Maximum force 30 Convex force — Aver force - A - Min force Figure 3-6 Graphs comparing the effect of temperature change on anticlastic cable nets with flexible edge cable K i p s Sag/Span 1:15 References 36 References Ambrose, E. James (1967), Building Structures Primer, John Wiley & Sons, Inc. New York. London. Sydney. Commission on Engineering and Technical Systems (1985), Architectural Fabric Structures, National Academy Press, Washington D.C. Grinter, Olinton E. (1962), Theory of Modern Steel Structures, The Macmillan Company. Haug, E. (1971), TRITRS Users Manual, University of California, Berkeley. International Conference of Building Officials (1991), Uniform Building Code. Krishna, Prem (1978), Cable-Suspended Roofs, McGraw-Hill Book Company. Lin, T.Y. (1989), Structural Concepts and Systems for Architects and Engineers, Van Nostrand Reinhold Company, New York. LSA 86 (1986), Lightweight Structures in Architecture , Proceeding, The first International Conference on Lightweight Structure in Architecture, Sydney, Austria. Schierle, G. Goetz (1968), Lightweight Tension Structures, Department of Architecture, University of California, Berkeley. Schierle, G. Goetz (1970), Prestressed Truss, Department of Architecture, University of California, Berkeley. Types and Grades of Wire Rope and Strand for Structural Applications. Vitruvius (1960), The Ten Books on Architecture, Translanted by Morris Hicky Morgan, Dover Publications Inc., New York. 37 Appendix A Graphs Generated by ISAP 38 Parallel Cable Net and Membrane Element number Joint number £ 6 E 6 r 200 170 180 190 2 1 0 1 2 0 100 140 150 160 179 19B 169 180 200 119 129 149 150 - 2 0 — 168 198 158 188 223 128 148 118 197 167 177 187 207 127 107 147 157 117 146 1 0 S 156 103 196 206 116 126 ■ 1 0 5 '—106- 175 195 105 185 205 125 145 115 125 156 m m 124 144 201 114 m 163 173 113 123 143 183 193 133 233 1 & 112 122 132 142 152 Plan View 1 21 220 1 2 0 219 119 218 118 217 117 216 116 215 115 214 114 213 113 212 1 1 2 2 1 1 1 1 1 Figure 2-1 (a) Plan of grid net parallel to border 39 Axonometric and Sections Figure 2-1 (b) Axonometric and sections of grid net parallel to border Diagonal Cable Net and Membrane Element number Joint number 221 R 9 — 1 5 7<p £13 1 9 -v> gi8 220 J23 217 q c B q 2 s q 4 7 q s o 2 C 6 J19 <406 195 1 ® q c & 157 > 7 7 > q i7 y to s <C E \109 A u \ \ Z J s m \ \ 4 1 A & \ \ 6 7 /{ & % V > N110 /4 2 3 \ ] 2 8 A z 1 \1 4 8 /4G 8 140 4 1 2 " 4 2 1 Plan View Figure 2-2 (a) Plan of grid net diagonal to border 41 Axonometric and Sections Figure 2-2 (b) Axonometric and sections of grid net diagonal to border 42 Appendix B Detailed Graphs of Analysis Cases 43 CABLE NET WITH EDGE BEAM Sag/Span 1:5 150 140 33 -30 130 120 -27 H O - 1 0 0 - 90 80- ■ 2 4 -21 -18 Z 70 60 -15 -12 50 40' -9 30 2 0 -3 60 70 40 50 Prestress as % of Maximum force Concave Max force — + — Aver force - x - M in force Convex - h - Max force - x - Aver force -A - M in force Figure B -l Graph correlating form and prestress as percentage of maximum force C A B L E N E T W IT H E D G E B E A M Sag/Span 1:10 33 150 140 130- -30 -27 120' 110 100- 90- 80 -24 -21 Z 70 60 50 -15 J l -12 -9 40 30 2 0 ' -6 60 70 50 30 40 Prestress as % of Maximum force Concave Max force — Aver force - x - M in force Convex Max force - x - Aver force -4k- M in force Figure B-2 Graph correlating form and prestress as percentage of maximum force 44 CABLE NET WITH EDGE BEAM Sag/Span 1:15 33 150- 140- 130 -30 -27 120 110 100 90 80 ■ 2 4 -21 Z 70 60 -15 -12 50 40 30 -6 2 0 70 40 60 30 50 Prestress as % of Maximum Force Concave Max force — t— Aver force M in force Convex - e - Max force - x - Aver force -A - M in force Figure B-3 Graph correlating form and prestress as percentage of maximum force M E M B R A N E W IT H E D G E B EA M Sag/Span 1:5 ■ 3 3 150 140 130 -30 -27 120 110 1 0 0 90 -24 -21 -18 80 Z 70- 60 50 40- -15 -12 30 2 0 -6 -3 - E 3 - 70 50 60 30 Prestress as % of Maximum Force Concave Max force — Aver force M in force Convex - e - Max force - x - Aver force -A - M in force Figure B-4 Graph correlating form and prestress as percentage of maximum force 45 MEMBRANE WITH EDGE BEAM Sag/Span 1:10 33 150- 140- -30 130 120' -27 1 1 0 - 100 90 80 •24 -21 -18 Z 70 60- 50- 40 30 2 0 -15 -12 - jK t 30 40 Prestress as % of Maximum Force 60 Concave -m - Max force — +— Aver force - x - M in force Convex - h - Max force - x - Aver force -*lr- M in force Figure B-5 Graph correlating form and prestress as percentage of maximum force M E M B R A N E W IT H E D G E B EA M Sag/Span 1:15 ■ 3 3 150 140- 130- 1 2 0 -30 -27 110 100 90 -24 -21 80 Z jc 70- 60 -15 -12 5 0 -- 40- 30 2 0 70 50 60 30 40 Prestress as % of Maximum Force Concave Max force — Aver force - x - M in force Convex - e - Max force - x - Aver force -*lr- M in force Figure B-6 Graph correlating form and prestress as percentage of maximum force 46 CABLE NET WITH EDGE CABLE Sag/Span 1:5 ■ 3 3 150 140' 130 120 -30 -27 110 100 90 24 -21 -18 Z 70 60- 50 40 -15 -12 30 2 0 ■ c * -d k r 40 60 70 30 50 Prestress as % of Maximum Force CONCAVE -m - Max force — Aver force - x - M in force CONVEX - B - Max force - X - Aver force -*lr- M in force Figure B-7 Graph correlating form and prestress as percentage of maximum force C A B L E N E T W IT H E D G E C A B L E Sag/Span 1:10 150 140- 130 •33 -30 -27 120 H O - 100- 90 -24 -21 80 Z 70- • 60- 5 0 -- 4 0 -- -15 -12 -9 30 2 0 IQ- 70 30 40 50 6 C Prestress as % of Maximum Force Concave Max force — I — Aver force - x - M in force Convex - e - Max force - x - Aver force -A - M in force Figure B-8 Graph correlating form and prestress as percentage of maximum force 47 CABLE NET WITH EDGE CABLE Sag/Span 1:15 33 150 140 130 120' -30 -27 110 100 90 80 •24 -21 Z j c 70 60 50 40 30 2 0 -15 -12 60 70 30 50 Prestress as % of Maximum force Concave -m - Max force - + - Aver force M in force Convex - s - Max force - x - Aver force -A - M in force Figure B-9 Graph correlating form prestress as percentage of maximum force M E M B R A N E W IT H E D G E C A B L E Sag/Span 1:5 33 150 140 130 120 110 100- 90 80- -30 .-2 7 •24 -21 70 60 50 40 -15 -12 30 2 0 70 60 40 50 30 Prestress as % of Maximum Force Concave Max force — Aver force M in force Convex - e - Max force - x - Aver force -A - M in force Figure B-10 Graph correlating form and prestress as percentage of maximum force 48 MEMBRANE WITH EDGE CABLE Sag/Span 1:10 150 140 130- 1 2 0 33 -30 -27 1 1 0 100- 90- z 80 70- 60 •24 -21 -18 -15 -12 50- 40 30- -6 2 0 70 30 40 60 50 Prestress as % of Maximum Force Concave Max force — Aver force -*r- M in force Convex - e - Max force - x - Aver force - ± - M in force Figure B -ll Graph correlating form and prestress as percentage of maximum force MEMBRANE WITH EDGE CABLE Sag/Span 1:15 ■ 3 3 150 140- 130 1 2 0 -30 -27 1 1 0 100 - 90' 80- -24 -21 Z 70 60 50- 40- -15 -12 30 2 0 ' 70 60 Prestress as % of Maximum Force 30 40 Concave Max force — Aver force M in force Convex - e - Max force ->€- Aver force -Ar- M in force Figure B-12 Graph correlating form and prestress as percentage of maximum force 49 TEMPERATURE INCREASE 50 DEGREE Cable Net W ith Edge Beam Sag/Span 1:5 150- 140- 130- 1 2 0 33 -30 -27 1 1 0 1 0 0 90 2 80 70- 60 ■ 2 4 -21 -15 -12 50 40 ■ m 30 2 0 1 0 -6 30 70 40 50 Prestress as % of Maximum force Concave Max force — I — Aver force -X - M in force Convex - e - Max force - X - Aver force -A - M in force Figure B-13 Graph correlating form and prestress as percentage of maximum force TEMPERATURE INCREASE 50 DEGREE Cable Net With Edge Beam Sag/Span 1:10 33 150 140 130 120 -30 -27 HO- 100- 90 -24 -21 -18 2 80 70 60 50 -15 -12 -9 40- 30 2 0 -6 50 6l Prestress as % of Maximum force 30 70 40 Concave -m~ Max force — f — Aver force - x - M in force Convex s - Max force - x - Aver force -A - M in force Figure B-14 Graph correlating form and prestress as percentage of maximum force 50 TEMPERATURE INCREASE 50 DEGREE Cable Net W ith Edge Beam Sag/Span 1:15 ■ 3 3 150 140- 130 1 2 0 - -30 -27 HO- 100- 90 80 ■ 2 4 -21 -18 70- 60 50- 40' -15 -12 30- 2 0 60 70 30 40 50 P re s tre s s a s % of M axim um fo rce Concave -m - Max force — + — Aver force M in force Convex - s - Max force - X - Aver force -ak- M in force Figure B-15 Graph correlating form and prestress as percentage of maximum force T E M P E R A T U R E IN C R E A S E 5 0 D E G R E E C a b le N et W ith E d g e C a b le S a g /S p a n 1 :5 33 150 140' 130 120 -30 -27 110 100' 90 80 ■ 2 4 -21 -18 70 60 50 -15 -12 40' 30 2 0 1 0 ■ a k - 40 60 70 50 30 P re s tre s s a s % of M axim um fo rce Concave -m - Max force — I — Aver force - x - M in force Convex - e - Max force - x - Aver force -ak- M in force Figure B-16 Graph correlating form and prestress as percentage of maximum force 51 TEMPERATURE INCREASE 50 DEGREE Cable Net W ith Edge Cable Sag/Span 1:10 150 140 •33 -30 130 120 -27 110' 100 •24 -21 90 80 -18 Z 70 60 50 40 -15 -12 30- 2 0 - m e 50 70 40 60 P re s tre s s a s % of M axim um fo rce Concave Max force — + — Aver force -*e- M in force Convex Max force -»*- Aver force -A - M in force Figure B-17 Graph correlating form and prestress as percentage of maximum force TEMPERATURE INCREASE 50 DEGREE C a b le N et With E d g e C a b le S a g /S p a n 1:15 30 40 50 60 70 P re s tre s s a s % of M axim um fo rce Concave Max force — + — Aver force M in force Convex - e - Max force - x - Aver force -afc- M in force Figure B-18 Graph correlating form and prestress as percentage of maximum force 52 Appendix C Prestresses and Member Forces 53 Table C -l Member Forces o f Cable Nets With Both Edge Beam and Edge Cable Cable Net With Edge Beam Sag/Span 1:5 Support Cable Stabilizing Cab e P.S. % Max Aver Min Max Aver Min Kips KN Kips kN kips kN kips kN kips kN kips kN 2.8 30% 9.389 41.74 7.68 34.13 5.82 25.86 2.53 11.25 1.12 4.96 0 0 3.85 40% 9.58 42.59 7.83 34.79 6.03 26.82 3.01 13.39 1.29 5.71 0 0 5 50% 10.07 44.74 8.27 36.75 6.34 28.17 3.79 16.86 1.75 7.77 0.002 0.01 7.7 60% 12.73 56.58 10.95 48.69 8.86 39.37 6.65 29.57 4.46 19.83 2.74 12.17 11.75 70% 16.72 74.33 14.98 66.61 12.73 56.58 10.85 48.25 8.53 37.91 6.84 30.39 Sag/Span 1:10 4.2 30% 13.85 61.56 12.58 55.93 8.11 36.06 2.89 12.84 0.45 1.99 0 0 5.6 40% 14.08 62.6 12.76 56.73 8.65 38.43 4.05 17.99 0.66 2.93 0 0 7.6 50% 15.13 67.23 13.69 60.85 9.71 43.15 5.98 26.6 1.69 7.51 0.381 1.69 11.2 60% 18.63 82.82 17.18 76.36 12.89 57.32 9.85 43.79 5.376 23.9 4.04 17.95 17.3 70% 24.57 109.2 23.12 102.8 18.61 82.7 16.21 72.07 11.61 51.61 10.2 45.35 S ag/Span 1:15 5.7 30% 19.03 84.58 17.23 76.85 9.5 42.24 4.58 20.37 0.37 1.66 0 0 7.7 40% 19.38 86.16 17.65 78.46 10.49 46.63 6.57 29.21 0.73 3.26 0 0 10.41 50% 20.86 92.73 19.06 84.72 12.32 54.77 9.3 41.35 2.37 10.55 0.65 287 15.5 60% 25.67 114.1 23.8 105.8 16.99 75.53 14.52 64.55 7.72 34.33 5.9 26.26 22.75 70% 32.57 144.8 30.65 136.2 23.92 106.3 21.91 97.39 15.31 68.05 13.45 59.78 Cable Net With Edge Cable Sag/Span 1:5 2.65 30% 8.82 39.19 6.53 29.01 2.99 13.33 4.29 19.11 0.94 4.18 0 0 3.69 40% 9.28 41.23 6.99 31.09 3.51 15.59 4.84 21.5 1.37 6.1 0 0 5.25 50% 10.52 46.76 8.22 36.54 4.77 21.19 6.11 27.14 2.58 11.45 0.36 1.58 7.7 60% 12.84 57.09 10.58 47.02 7.11 31.6 8.46 37.61 4.94 21.97 2.74 12.17 11.75 70% 16.76 74.49 14.58 64.83 11.11 49.37 12.47 55.42 8.96 39.85 6.85 30.44 Sag/Span 1:10 4.1 30% 13.65 60.67 10.97 48.77 4.34 19.28 6.89 30.66 0.92 4.1 0 0 5.55 40% 13.91 61.82 11.46 50.95 4.95 21.99 7.56 33.59 1.27 5.63 0 0 7.59 50% 15.29 67.98 12.92 57.43 6.53 29.03 9.15 40.69 2.69 11.94 0.402 1.79 11.2 60% 18.63 82.81 16.35 72.69 9.991 44.43 12.61 56.06 6.19 27.49 3.91 17.39 17 70% 24.13 107.3 22.05 98.01 15.75 70 18.34 81.53 12.02 53.39 9.87 43.88 Sag/Span 1:15 5.6 30% 18.81 83.63 15.05 66.92 5.54 24.61 9.13 40.59 1.01 4.5 0 0 7.65 40% 19.06 84.72 15.91 70.73 6.51 28.94 10.24 45.5 1.49 6.63 0 0 10.35 50% 20.61 91.59 17.83 79.24 8.68 38.59 12.45 55.32 3.33 14.82 0.202 0.898 15.1 60% 25.05 111.4 22.29 99.1 13.35 59.35 17.04 75.75 8.11 36.07 5.26 23.39 22.55 70% 32.06 142.5 29.46 130.9 20.82 92.55 24.39 108.4 15.79 70.21 13.21 58.73 54 Table C-2 Member Forces o f Membranes With Both Edge Beam and Edge Cable Membrane With Edge Beam Sag/Span 1:5 Support Membrane Stabilizing Membrane P.S. % Max Aver Min Max Aver Min Kips KN Kips kN kips kN kips kN kips kN kips kN 2.38 30% 7.92 35.19 6.3 28.02 3.28 14.57 2.3 10.24 0.62 2.74 0 0 3.38 40% 8.376 37.24 6.75 30.02 3.82 16.98 3.29 14.64 1.15 5.13 0 0 4.82 50% 9.56 42.52 8.02 35.66 5.18 23.03 4.73 21.04 2.67 11.88 1.43 6.36 6.75 60% 11.22 49.89 9.76 43.39 7.05 31.32 6.67 29.64 4.71 20.93 3.51 15.59 9.8 70% 13.92 61.89 12.56 55.83 10.04 44.61 9.72 43.22 7.91 35.15 6.76 30.06 Sag/Span 1:10 3.05 30% 10.06 44.71 8.28 36.83 3.77 16.76 3.35 14.91 0.92 4.1 0 0 4.25 40% 10.56 46.93 8.98 39.91 4.82 21.41 4.42 19.65 2.12 9.41 0.97 4.32 5.7 50% 11.36 50.5 9.95 44.22 6.17 27.44 5.78 25.69 3.68 16.34 2.6 11.56 7.5 60% 12.54 55.73 11.26 50.07 7.89 35.08 7.52 33.44 5.61 24.94 4.6 20.47 10 70% 14.38 63.91 13.24 58.85 10.32 45.85 9.99 44.39 8.28 36.79 7.35 32.68 Sag/Span 1:15 3.15 30% 10.41 46.28 8.84 39.29 3.98 17.68 3.89 17.28 1.95 8.65 0.77 3.41 4.35 40% 10.79 47.96 9.4 41.8 5.03 22.34 4.82 21.44 3.09 13.74 2.02 8.96 5.75 50% 11.42 50.77 10.18 45.25 6.3 28.02 6.02 26.78 4.47 19.89 3.49 15.56 7.45 60% 12.37 54.98 11.26 50.06 7.89 35.11 7.61 33.82 6.19 27.53 5.31 23.63 9.8 70% 13.93 61.93 12.96 57.62 10.15 45.12 9.87 43.89 8.61 38.25 7.82 34.78 Membrane With Edge Cable Sag/Span 1:5 2.15 30% 7.28 32.34 5.69 25.33 2.52 11.19 3.36 14.93 0.61 2.7 0 0 3.05 40% 7.63 33.9 6.14 27.28 3.04 13.53 3.85 17.13 1.03 4.59 0 0 4.3 50% 8.59 38.21 7.23 32.14 4.26 18.94 4.98 22.13 2.28 10.13 1.27 5.66 6.1 60% 10.11 44.95 8.87 39.44 6.07 26.98 6.66 29.59 4.13 18.37 3.21 14.28 8.7 70% 12.41 55.14 11.29 50.21 8.71 38.71 9.13 40.59 6.82 30.32 5.93 26.38 Sag/Span 1:10 2.85 30% 9.63 42.78 8.01 35.59 3.56 15.81 4.68 20.79 0.74 3.31 0 0 4.05 40% 10.03 44.6 8.68 38.59 4.51 20.03 5.55 24.65 1.74 7.73 0.77 3.4 5.35 50% 10.76 47.82 9.58 42.59 5.73 25.49 6.63 29.48 3.11 13.81 2.2 9.74 7.25 60% 12.12 53.89 11.00 48.94 7.58 33.69 8.29 36.84 5.14 22.84 4.29 19.12 10.05 70% 14.31 63.59 13.29 59.08 10.34 45.95 10.82 48.09 8.12 36.11 7.38 32.81 Sag/Span 1:15 3.05 30% 10.24 45.52 8.85 39.32 4.51 20.05 5.53 24.59 1.49 6.65 0.55 2.44 4.25 40% 10.66 47.37 9.41 41.81 5.45 24.22 6.37 28.32 2.62 11.64 1.75 7.77 5.65 50% 11.35 50.43 10.19 45.31 6.63 29.47 7.42 32.98 4.02 17.86 3.22 14.29 7.45 60% 12.4 55.14 11.37 50.35 8.23 36.59 8.86 39.38 5.87 26.09 5.15 22.88 9.85 70% 14.05 62.47 13.14 58.41 10.46 46.49 10.9 48.48 8.37 37.19 7.73 34.36 55 Table C-3 Member Forces o f Cable Nets With Temperature Change 50°F Cable Net With Edge Beam Sag/Span 1:5 Support Cable Stabilizing Cable P.S. % Max Aver Min Max Aver Min Kips kN Kips kN kips kN kips kN kips kN kips kN 2.8 30% 8.98 39.91 7.39 32.88 5.19 23.05 1.83 8.13 0.79 3.52 0 0 3.85 40% 9.05 40.21 7.44 33.08 5.29 23.54 1.96 8.71 0.84 3.75 0 0 5 50% 9.13 40.59 7.49 33.33 5.43 24.15 2.11 9.39 0.91 4.04 0 0 7.7 60% 9.43 41.9 7.71 34.25 5.86 26.04 2.61 11.61 1.15 5.1 0 0 11.75 70% 12.11 53.81 10.32 45.89 8.26 36.72 5.99 26.62 3.83 17 2.09 9.32 Sag/Span 1:10 4.2 30% 13.49 60.01 12.24 54.42 6.81 30.26 0.63 2.82 0.19 0.88 0 0 5.6 40% 13.54 60.21 12.32 54.77 7.15 31.77 0.65 2.89 0.22 0.97 0 0 7.6 50% 13.7 60.91 12.46 55.46 7.695 34.21 1.91 8.47 0.329 1.463 0 0 11.2 60% 14.34 63.76 12.96 57.63 9.05 40.21 4.87 21.64 0.89 3.99 0 0 17.3 70% 20.01 88.95 18.56 82.48 14.19 63.11 11.34 50.42 6.82 30.34 5.48 24.35 Sag/Span 1:15 5.7 30% 18.67 82.99 16.71 74.29 7.61 33.84 0.39 1.77 0.11 0.46 0 0 7.7 40% 18.78 83.49 16.94 75.28 8.33 37.03 1.89 8.43 0.15 0.68 0 0 10.41 50% 19.03 84.6 17.29 76.87 9.52 42.29 4.61 20.49 0.38 1.67 0 0 15.5 60% 21.23 94.37 19.43 86.39 12.68 56.38 9.72 43.21 2.8 12.45 1.06 4.73 22.75 70% 28.11 124.9 26.21 116.5 19.42 86.31 17.14 76.19 10.41 46.27 8.57 38.11 Cable Net With Edge Cable Sag/Span 1:5 2.65 30% 8.64 38.39 6.43 28.58 2.89 12.89 4.21 18.68 0.86 3.84 0 0 3.69 40% 8.89 39.53 6.75 29.89 3.29 14.63 4.61 20.48 1.14 5.05 0 0 5.25 50% 9.89 43.94 7.78 34.60 4.41 19.58 5.74 25.51 2.14 9.49 0 0 7.7 60% 12.01 53.38 10.06 44.72 6.71 29.84 8.06 35.81 4.41 19.62 1.69 7.51 11.75 70% 15.66 69.63 13.99 62.21 10.69 47.54 12.05 53.56 8.36 37.18 5.57 24.76 Sag/Span 1:10 4.1 30% 13.42 59.66 10.43 46.41 3.73 16.61 6.23 27.67 0.64 2.86 0 0 5.55 40% 13.48 59.94 10.73 47.72 4.08 18.15 6.62 29.44 0.80 3.57 0 0 7.59 50% 13.68 60.82 11.29 50.22 4.78 21.27 7.39 32.85 1.16 5.14 0 0 11.2 60% 15.83 70.36 13.78 61.27 7.55 33.57 10.18 45.25 3.54 15.73 0.93 4.11 17 70% 21.16 94.08 19.31 85.81 13.19 58.67 15.81 70.29 9.19 40.83 6.47 28.75 Sag/Span 1:15 5.6 30% 18.51 82.24 14.23 63.25 4.73 21.02 8.18 36.34 0.69 3.05 0 0 7.65 40% 18.57 82.57 14.87 66.09 5.41 24.01 8.98 39.93 0.96 4.27 0 0 10.35 50% 18.79 83.53 15.94 70.84 6.64 29.52 10.39 46.22 1.53 6.78 0 0 15.1 60% 22.06 98.04 19.54 86.86 10.77 47.88 14.51 64.52 5.13 22.79 1.59 7.11 22.55 70% 28.74 127.8 26.54 117.9 18.16 80.73 21.79 96.86 12.65 56.22 9.32 41.44 56
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Computer aided value conscious design
PDF
A computer teaching tool for passive cooling
PDF
Energy performance and daylighting illumination levels of tensile structures in an extreme climate
PDF
Investigation of sloshing water damper for earthquake mitigation
PDF
The Indian Himalayan building energy code as a step towards energy conservation
PDF
Computer aided form-finding for cable net structures
PDF
Investigation of seismic isolators as a mass damper for mixed-used buildings
PDF
A proposal for the Indian National Lighting Code
PDF
Passive cooling methods for mid to high-rise buildings in the hot-humid climate of Douala, Cameroon, West Africa
PDF
Computer aided design and manufacture of membrane structures Fab-CAD
PDF
Terrace housing: A conscious solution
PDF
The response of high-rise structures to lateral ground movements
PDF
A method for glare analysis
PDF
Computer modelling of cumulative daylight availability within an urban site
PDF
WAHHN: Web based design: Wind and human comfort for Thailand
PDF
Qualitative and quantitative natural light in atria and adjacent spaces
PDF
DS(n)F: The design studio of the (near) future
PDF
Hebel design analysis program
PDF
From nescience to science and beyond: A critical investigation of 'building' in cyclone prone areas
PDF
Return to the moon: MALEO, Module Assemby in Low Earth Orbit: A strategy for lunar base build-up
Asset Metadata
Creator
Yin, Mingsong
(author)
Core Title
Computer aided design and analysis of anticlastic membranes and cable nets
Degree
Master of Building Science
Degree Program
Building Science
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
engineering, architectural,OAI-PMH Harvest
Language
English
Contributor
Digitized by ProQuest
(provenance)
Advisor
Schierle, Gotthilf Goetz (
committee chair
), Noble, Douglas (
committee member
), Schiler, Marc (
committee member
)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c20-299829
Unique identifier
UC11258338
Identifier
EP41435.pdf (filename),usctheses-c20-299829 (legacy record id)
Legacy Identifier
EP41435.pdf
Dmrecord
299829
Document Type
Thesis
Rights
Yin, Mingsong
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
Tags
engineering, architectural