University of Southern California Dissertations and Theses

Computer aided design and manufacture of membrane structures Fab-CAD

(USC Thesis Other)

Computer aided design and manufacture of membrane structures Fab-CAD

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI film s the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. T h e quality o f this reproduction is dependent upon the quality o f the cop y subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afiect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand com er and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back o f the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/321-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COMPUTER AIDED DESIGN AND MANUFACTURE OF MEMBRANE STRUCTURES Fab-CAD by Chandrashekar Ganti A Thesis Presented to the FACULTY OF ARCHITECTURE UNIVERSITY O F SOUTHERN CALIFORNIA In partial fulfillment of the Requirements for the Degree M ASTER OF BUILDING SCIENCE M ay 1996 Copyright 1995 Chandrashekar Ganti Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1380443 UMI Microform 1380443 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. u s e ® ARCHITECTURE APPROVAL FOR FINAL TYPING This thesis, written by G-AM TI C H A kl D R A S H ................ under the direction o f h X A Thesis Committee, and approved by all its members, has been presented to and accepted by the Dean o f The School o f Architecture, and is ready for final typing, m partial fulfillment o f the requirements for the degree of M A 3 T E & O F B U IL .D IM O S C t E M C E Dtan Date . ......................... .................. THESIS COMM! University of Southern California School of Architecture W att Hall 204 Los Angeles, California 90089*0291 (213)740-2723 Fax (213) 740-8884 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I solely dedicate this thesis to my wonderful wife, Khan, whose inspiration and support helped me throughout my endeavor. Shekar Ganti Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOW LEDGM ENTS: This is to express my gratitude to all those who have encouraged and supported this research. I extend my thanks to Dr. Tejav Deganayar whose ideas and work inspired this study. The program, Fab-CAD is developed around “Dynamic Relaxation", which is a computer program written by Dr. Deganayar to analyze tensile structures. I greatfully acknowledge my debt to Prof. Dr. G.G. Schierle, my thesis guide, for his dedicated assistance and continuous interest in my work. I further thank Prof. Marc Schiler and Prof. Dimitry Vergun for their critique and precious suggestions. This research has been greatly profited by Mr. Will Baylis of Eastman Technologies, who responded to my request for information. My special thanks to my parents and the School of Architecture, especially the Building Science Program. Finally, I deeply appreciate the cooperation and contribution of my wife, Kiran and my friend. Ramkumar without whom this research would not have been possible. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION ACKNOWLEDGMENT TABLE OF CONTENTS FIGURES AND TABLES V 1 : 1.1: INTRODUCTION 2 1.2: HISTORY 4 2 : MATERIALS AND METHODOLOGY 11 2.1: CABLES 12 2.2: CABLE NETS 19 2.3: MEMBRANES 26 2.4: MEMBRANE STRUCTURE FABRIC SPECIFICATION TABLE 39 CHAPTER 3 : DESIGN CONSIDERATIONS 41 3.1: EDGE CONDITIONS 41 3.2: SURFACES 42 * . SUPPORTING ELEMENTS 47 3.4: DESIGNING FOR DYNAMIC LOADS 48 3.5: ELASTIC BEHAVIOR OF CABLES 52 3.6: PRETENSIONING OF CABLES 52 3.7: MINIMAL SURFACE AREA 54 CHAPTER 4 : Fab-CAD 56 4.1: INTRODUCTION 56 4.2: INPUT DATA 58 4.3: STRESS ANALYSIS 78 4.4: PATTERN DESIGN 82 CHAPTER 5 : SAN DIEGO CONVENTION CENTER 96 (CASE STUDY) CHAPTER 6 : APPENDIX 103 6.1: TUTORIAL 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST O F FIGURES AND TABLES: CHAPTER 1 : Fig: 1.2 a~b: Conical tent 4 1.2 c-d : Kibitka 5 1.2 e-f: Black tent 6 CHAPTER 2: Fig: 2.1 a: Single strand cable 12 2.1 b: Multiple strand cable 12 2.1 c-d : Deflection o f cable under load 13 2.1 e-f: Distribution o f forces in cable and arches 14 2.1 g -j: Deflections in cable 15 2.1 k: Arch shapes 16 2.1 1 : Calculation o f cable length 18 2.2 a-e: Surface conditions 21 2.2 f-h: Net configurations 22 2.2 i-m : Mesh shapes 23 2.2 n: Square mesh along axis 24 2.2 p: Orthogonal cable net in square frame 24 2.2 q— r: Radial cable nets 25 Table------- 1 : Membrane structure fabric specification table 39 CHAPTER 3: Fig: 3.1 a: Edge cable 41 3.1 a: Edge beam 41 3.1 a: Edge arch 42 3.2 a: Wave shaped cable net 43 3.2 b-e: Point supported cable nets 44,45 3.2 f: Arch supported and edge cables 45 3.1 g: Arch supported and edge arches 45 3.2 h: Saddle shape with edge cable 46 3.2 i: Saddle shape with edge arch 46 3.2 j: Interrupted and uninterrupted frames 46 3.3 a: Pier supports 47 3.3 b: Guyed supports 47 3.3 c: Inclined guyed supports 48 3 4 a— e: Wind effect on cable nets 49,50 3.4 f: Double concave cables 50 3 4 g: Double convex cables 51 3.6 a: Pretensioning o f cables 53 3.7 a: Minimal surface 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4: Fig: 4.1 a~b: Flow chart — FabCAD 56,57 4.2 a: Geometric input 58 4.2 b— c: Load in positive and negative direction 60 4.2 d: Radial pattern 61 4.2 e: Linear pattern 61 4.2 f: Support elevation and location in space 62 4.2 g: Fabric weave pattern 62 4.2 h: Connectivity matrix 63 4.2 i: Cables with different span/dip ratio 64 4.2 j: Pattern configuration 65 4.2 k: Support location and elevation 67 4.2 1 : Material property dialogue box 67 4.2 m: Cable net 71 4.3 a: Dialogue box for stress analysis 80 4.3 b: Maximum and minimum display 81 4.3 c: Numeric value of stress printed on elements 81 4.4 a: T riangulation 82 4.4 b. Transformation from OCS to WCS 83 4.4 c: Compensation factor 85 4.4 d: Different types of patterns 86 4.4 e: Orientation of strips 88 4.4 f: Patterning process sequence 89 4.4 g: Annotation for manual cutting 90 4.4 h: Manual cutting table and cutting device 91 4.4 i: Manual cutter 91 4.4 j: Welding machine 91 4.4 k: Round knife 93 4.4 1 : CO2 laser 93 4.4 m: Computer controlled cutting machine 94 4.4 n: Flat bed plotter/cutting machine 94 Table------- 2: Property file 68 Table------- 3: Input file Table------- 4: Geometry file Table------- 5: Output file Table------- 6: Summary file CHAPTER 5: Fig: 5.1 a: Site plan 96 5.1 b: Rendered view of San Diego Convention Center 97 5.1 c: Wire-frame view o f San Diego Convention Center 98 5.1 d: Sectional elevation 100 5.1 e: Roof plan 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.1 INTRODUCTION 1.2 HISTORY 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.1 INTRODUCTION: (Paraphrased from Shaeffer, 1994: 49-53) The word STRUCTURE has been a modified English definition of what a man has lived within. The ancestors of this word can be traced down to anything that sheltered man, like tents, caves, pyramids, canopies c:c. Down the ages, man learnt to harness all the materials nature provided him with, to cater to his changing and ever growing needs. As the scale o f shelters increased from small to iarge, their complexity increased, which in turn, brought about a lot of research and solutions. The history o f structures has shown a gradual and very healthy development through long periods o f improvements and progress towards intelligent use o f materials. Most structures have been based on the principles of resistance to gravity. Heavy stone masses such as pyramids and elements like columns and beams have been stabilized by their own weight transferred to the ground and supporting members. A conventional tent, however, represents an exception. It is unstable under wind forces. It sags under snow and billows up under wind. Also the free span capacity of these structures has been very limited. This performance was acceptable for what existed then. Introduction o f new materials and sophisticated engineering methods initiated drastic changes. New systems such as space frames, shells, light weight tensioned fabric structures evolved. 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Expectations of these new systems in terms of their performance differed from the early traditional tents in that they: ► are usually permanent, unlike traditional tents. ► are expected not to fail. ► should not have wrinkles. ► should not flutter in wind. ► cover larger spans. ► could be more complex in terms of geometry. ► use high-strength materials. ► have anticlastic curvature to provide stability. All this demands more sophisticated analysis. Material developments have not only pushed the capabilities o f membranes to meet these demands but also helped in providing greater structural strength, envelope, insulation, flexibility and fire resistance. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.2 HISTORY OF TENSILE STRUCTURES (Paraphrased from Drew, 1976: 1-55 and Shaeffer, 1994: 49-53) TENTS: This word takes us way back into the past, intuitively recalling memories o f our ancestors. Evidences from the past, mammoth bones and tusks used as supports for animal hides prove that the tent sheltered man when no other form o f man made dwelling existed. The skin or velum o f early tents were of animal hides or, less frequently, birch bark pieces or latticed leaf fronds. Gradually these were replaced by felt or woven materials, such as wool or canvas. Contemporary materials include synthetic fabrics for velum and aluminum, fibreglass, steel as supporting elements. Until quite recently, most tents consisted o f three basic forms, conical or tepee shape, the wide-spread kibitka or yurt (which has cylindrical walls and a conical or domical roof) and the “black” tent (which has the velum tensioned into saddle shapes). J # : / | :f v I \ \ \ \ \ \ \ ' Fig. 1.2 a : Conical tent Fig. 1.2b: Conical tent framing (Drew, 1976 :7) (Drew, 1976 : 7) 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O f the three basic forms, the conical tepee form, is the oldest and saw widespread use across northern Europe, northern Asia and north America. As shown in figure 1.2a and 1.2b, this type o f tent consists of a conical framework o f inclined poles, arranged in a circle with their upper ends secured at the peak. Fig 1.2 c : Kibitka Fig 1.2 d : Kibitka Framing (Drew, 1976 : 28) (0 ^ i976 . 28) Figure 1.2c and 1 2d shows a conical kibitka which dates back to 2000 B.C. or earlier. Its shape has been the one most copied or adapted for later tents. For example, the parasol roof shape found in military tents. The kibitka is, essentially a limp covering draped over a light demountable wood frame. This frame comprises a low circular wall assembled from lengths of collapsible trellis, a roof- ring on a series o f radial roof ribs or struts spanning the gap between the top of the wall and the rim of the roof-ring. The roof-ring is the most important distinguishing feature of the kibitka for it is not found in any other type. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The black tent (figure 1.2e and 1.2f) is probably as old as the kibitka form. It got its name from the goats hair used to weave the velum. The loosely woven cloth permits the passage of air and its dark color provides a high degree o f shade. In the first two, the velum serves only as a barrier to the elements and is not an integral part of the structural system. In black tent, however, the amount of tension in the velum establishes its form and provides stability for supporting elements. In this manner, and because o f its anticlastic (opposite in sign) principal curvatures, it is related, from a structural point o f view, to contemporary fabric architecture. Fig. 1.2 e : Black tent: Type -1 (Drew, 1976.50) Fig. 1.2 f : Black tent: Type - 2 (Drew, 1976:50) 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Environmentally integrated tents have been used as elementary habitation since humankind’s early beginnings. As life progressed, expectations increased in terms o f quality. Man started looking for a definite and a stable way o f sheltering himself. Researchers were on the lookout for better materials, resistant to both fire and ultraviolet deterioration. Situations improved; larger spans needed to be covered and structures started becoming more and more complex. Modem technology catered to all these requirements. Even though, there is no direct connection between traditional tents and modem fabric architecture, there are fascinating technical and even visual parallels. There is an amazing similarity in the shapes o f some black tents and modem fabric structures. Due to pioneering heads like Frei Otto and many others, architecture took a very big leap from mass to membranes. Thus emerged the modem tensioned fabric era. In 1955, Otto designed a bandstand for the Federal Garden Exhibition in Kassel, Germany. He built several more complex canopies for various exhibitions including the entrance pavilion and dance pavilion at Cologne Federal Garden exhibition in 1958. In the Expo (1964), Lausanne: the restaurant pavillion was a feet o f engineering, achieved by G.G.Schierle and Marc J. Saugey. Its physical shape symbolized the Swiss mountains in one section and yatching in the other, thus blending membranes with the surrounding. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In 1976 Berger, a known name in this field, designed two significant fabric structures for the bicentennial celebration in Philadelphia, Pa. The Independence Mall Pavilion, covering more than 4000 square meters using eight tilted masts in two rows for clear span of approx. 35 meters, was one of the largest tensioned fabric spans in the world at the time it was constructed. Both the structures used vinyl coated polyester fabric. The largest fabric roof o f its time was the Haj Terminal at Jeddah, Saudi Arabia. It consists o f 210 identical cone-shaped canopies square in plan, measuring 45 meters on each side, covers approx. 47 hectares, and was completed in 1981. The next ten years saw the design and construction o f many successful tensioned fabric structures. Among the most notable are architect L. Gene Zeilmer's Good Shepard Lutheran Church in Fresno, Calif. (1981), Geiger Breger’s steel arched Lindsay park Sports Center in Calgary, Alberta (1983), the huge King Fahd Stadium in Riyadh, Saudi Arabia (1985), the Chene Park Amphitheater, Detriot, Mich., designed by architect Kent Hubbell (1990) and the new Pier Six Concert Pavilion, Baltimore, Md., designed by FTL Associates (1992). Not to forget the great Hall o f the Denver airport. This pace-setting fabric roof is 64 meters by 274 meters in plan. Convertible fabric roof is also being used these days, for instance, the one atop the Montreal Exhibition Pavillion. A giant inclined tower 168 meters tall forms a “skyhook" from which 26 cables suspend the fabric roof to cover a 200 by 120 meter opening in bad weather and retract the roof at other times to permit an exposed playing field. 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Outstanding qualities such as light weight, economy, fire-resistance, durability, ease o f erection, incombustibility and flexibility account for extensive use o f fabric structures in long span applications, huge spaces, stadiums, etc. As per the latest dictionary o f architecture, buildings are no longer just structural, functional or climatic necessities. Fabric, not only meets the structural and functional requirement, but also gives us a new way to express our architectural skin. Fabric lets us use large spans economically and creates a transcluency of the skin that allows daylight to enter the building in a controlled fashion and each technological improvement seems to expand its further use. As to the future o f fabric in architecture, architects believe that it is still in its infancy and has a potential far beyond what has been explored to date. The membrane structure which developed from the confines o f the lowly tent is now being recognized worldwide as one type of permanent architecture. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o ' ■ x ^ & * > * 2. M ATERIALS AND M ETHODOLOGY: (Paraphrased from Otto, 1967-69. 20-85. Schierle, 1968: 8-29. Thronton, 1992: 51-58. Youssef, 1995: Class 313 ). Tensioned fabric structures, as opposed to conventional structures, do not require the principles of gravity and their structural stability is defined by their own geometric shape. They are mainly composed o f cables and membranes stabilized by externally applied prestress forces and tensioning in mutually opposed curvature, an oppositional nature of two pieces of fabrics that create two sets of stress lines in a stable equilibrium. This is very critical to the stability of tensioned structure, unlike the flat nature o f conventional tents subjected to flutter under windload and deformation under asymmetrical loading. Tensioned fabric structures consist of primary members like cables, cable nets and membranes which in turn are supported by secondary members like masts, anchors and frames. Basically the membrane is attached to the boundary, which must be closed; if it is not, the fabric will tear and break. The boundary can be an element such as beam or a wall or more commonly, a cable. Concentrated point loads other than very small ones, cannot be supported by a membrane at a point because the local stresses are too high. In case of wave shapes, ridge or valley cables can be used but care must be taken to avoid chafing o f the membrane. An alternative to laying cables against the membrane is to place a ridge cable above a site joint and to suspend the membrane from the cable using clamp plates in the joint. 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The form o f the membrane structure must be in equilibrium and carry applied loads without overstressing the membrane. The properties of the above mentioned primary and secondary members help transferring the forces acting outside the principle axes by adjusting their form to redirect the forces into the principle axes. The applied load is transferred to the membrane in purely tensile stresses. The properties o f the primary members o f tensioned structures, like cables, cable nets, membranes are discussed below: 2.1 CABLE: A “cable" is defined as a member exclusively designed to take tension. It is a linear (one-dimensional) supporting system large in one direction and small in the other two. The term cable can imply— a single strand: (fig 2.1a) which consists o f a helical arrangement of individual wires around a central wire. a multiple strand cable: (fig 2.1b) which consists of a helical arrangement of a number o f strands around a central strand. Fig 2.1 a : Single strand cable Fig 2.1 b : Multiple strand cable (Schierle, 1968 : 8) (Schierle, 1968 : 8) 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A cable lacks bending stiffness and can carry only non-axial loads by forming a polygon. If a non-axial load is applied to a straight tie cable joining two points, it will stretch until the geometric change that takes place is such that the applied load is balanced by the tension in the cable. ORIGINAL POSITION 1 — DEFLECTED CABLE Fig. 2.1 c : Deflection of Cable under load (Youseef, 1995 : Seminar 313). The lower the elastic modulus of the cable, the tension will be less and the sag will be more. If the cable is pre-deflected in its initial geometry, both the tension in the cable and the deflection under applied load are reduced because the cable already has a geometry which can resist load. ORIGINAL POSITION I i — DEFLECTED CABLE Fig. 2.1 d : Deflection of prestressed cable under load (Youssef, 1995 : Seminar 313). 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The geometry of the system is defined by the length of the cables, the position o f the supports, and applied loads. The system will change its geometry depending on the magnitudes and location of loads. The shape adopted by a cable under a set of loads is known as the funicular shape. The term funicular is derived from the Latin word “rope." Only tension forces will be developed in the cable. DISTRIBUTIO’ ’ OF FORCES IN CABLES AND ARCHES T' T i i i Fig 2.1 e : CABLE FORCES: ONLY TENSION FORCES ARE DEVELOPED IN A CABLE. MAXIMUM FORCES OCCUR AT THE SUPPORTS. (Youssef. 1995 : Seminar 313). Fig. 2.1 f : ARCH FORCES: ONLY COMPRESSION FORCES ARE DEVELOPED IN AN IDEAL ARCH. MAXIMUM FORCES OCCUR AT THE SUPPORTS. (Youssef, 1995 : Seminar 313). A cable of constant cross section carrying its own dead weight will form into a catenary shape as shown in figure 2.1 g. Fig. 2.1 g : Catenary line Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A cable carrying a non-axial load that is uniformly distributed along the horizontal projection of the cable, as is the primary loading in a suspension bridge supporting a horizontal bridge deck, will form into a parabola, resulting in a parabolic line. ► 4 Fig. 2.1 h : Parabolic line A cable carrying concentrated point loads will form a series of straight line segments as shown in figure 2. li. I i '1 Fig. 2.1 i: Polygon line A cable subjected to a radial load will form a circular arc resulting in a circular tension line as shown below in figure 2. lj. Fig. 2.1 j : Circular line 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Combinations of different loadings will produce combined forms with the largest load producing the dominating shape. Comparable arch shapes for these same loadings are simply inversions of the shapes described above. If the neutral axis of an arch is identical to the funicular tension line for a given load condition, all forces applied will be resolved in pure compression. The arch determines the form of the structures and supports the membrane along its axis. ► 4 CATENARY LINE PARABOLIC LINE ► 4 CIRCULAR LINE POLYGON LINE Fig. 2.1 k : Arch shapes 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The magnitude o f the forces developed in the cable or arch depend on the relative depth o f the funicular shapes in relation to its length as well as its magnitude and the location o f the applied loads. If the sag of the cable or the rise of an arch is greater, the internal forces developed in the structure are smaller. Support reactions have both vertical and horizontal components which must be resisted by the foundation or some other element. These deflections affect the structural analysis because the changes in the geometry make the structure non-linear. A non-linear structure is one in which the response o f the structure to the load is not linear. If the loads on a structure o f linear elasticity and geometric response double, the stresses double: if the loads reverse the stresses reverse; and the effect of the changes in geometry is small enough to be ignored. This is not the case for non-linear structures, which require itterative analytical techniques. Analysis of Arches and Cables: Cflnggmraied. Loads; A cable can be conceived of as a continuous series discrete elements connected by hinges like a chain. These connections are such that the internal moments cannot be transmitted from one element to another. Generally, the function o f any structure can be defined as that o f carrying external loads to the ground. In a cable or a funicular shaped arch the external shear at a section is balanced by an internal resisting that is provided by the vertical component o f the 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. internal axial force developed in the cable or arch member. The external bending moment at the same section is balanced by an internal resisting moment that is provided by the couple formed by the horizontal component o f the axial force in the funicular member and the horizontal force acting at the support of the structure. Uniformly Distributed Loads; Since the funicular shape is constantly curving, a variant of the method of section may be used. Cable. Arch Length: It is important to know the total length of a cable or arch given its span and sag or rise. This length can be evaluated by considering the basic expression for the deformed cable shape. For a uniformly loaded cable with a horizontal chord. Let L be the total length o f the cable. (Consider both supports on the same level) Let Lh be the span, let h be the max sag. The total cable length is approx.: L toui = Lh (l+8/3h2 /Lh2 --32/5h4 /Lh4 ) L HORIZONTAL COMPONENT H OF TENSION' WL / 8h VERTICAL COMPONENT V OF TENSION = WL / 2 MAXIMUM CABLE FORCE T IS = 7h + V Fig. 2.11: Calculation of cable length 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Design of Arches and Cables: The forces in these structures, hence their size, are dependent on the amount of sag or rise related to the span o f the structure. The sag to span ratio determines the tension in the cable and the horizontal reaction in the support. The magnitude o f the forces increases as the sag decreases. The tension in the cable is maximum at the supports and decreases gradually, to minimum, at the center between the supports where it balances the horizontal support reactions. Given the sensitivity to the structural depth finding the most appropriate sag or rise becomes an optimization problem. As h increases the force in the cable decreases and thus the relative cross sectional area required also decreases. This increases the cable length. A depth equal to approximately one-third of the span o f the structure will be found to result in the minimum volume for a uniformly loaded structure. The exact sag or rise chosen is, however, dependant on the overall context in which it is used. Most cable structures used, have sag/span ratios between 1:8 and 1:10. Arch structures are usually deeper with rise/span ratios in the order 1:5. 2.2 CABLE NETS: ( Paraphrased from Otto, 1967-69: 20-85. Schierle, 1968: 8-29. Thronton, 1992: 51-58. Youssef, 1995: Seminar 313 ). A cable net consists o f a number o f cables forming a mesh. It is a surface support structure consisting o f one dimensional components rigid in tension. It is interesting to know that the smaller the size o f the mesh, the less is the freely suspended net capable o f taking up compressive forces. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cable nets can be typically subclassified into: ► Single curvature cable nets: in which the roofs are made by placing cables parallel to one another and using a surface formed by beams or plates to span between cables. ► Double curvature cable nets: in which a field of crossed cables of different and often reverse curvatures make up a primary roof surface. ► Double cable nets structure: in which interconnected double cables of different curvatures are used in the same vertical plane. For double curvature cable nets the centers of principle radii can be either on the same side o f the surface in which case the surface is synclastic or on the opposite side in which case it makes the surface anticlastic. Since a tension member requires curvatures to carry loads, it follows that if a structure is to resist positive and negative loads ( snow and wind ) it must be anticlastic. The formula for equilibrium is: P = ti/Ri + t:/R:, where P is the applied load, t is the tension, R is the radius. Cables are invariably prestressed; the materials have a certain amount o f initial stretch that must be pulled out, and prestressing improves load-carrying behavior. When load applied is zero, ti/Ri = b/R2 This system is in equilibrium and the two curvatures load each other by the same amount. If the load is applied to the system, ti is increased and the cables stretch in the direction o f Ri, while relieving some o f the tension t:. The load is thus shared between a reduction in one and increase in the other. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig 2.2 a: SYNCLASTIC OR Fig 2.2 b: ANTICLASTIC OR ELLIPTICAL SURFACE HYPERBOLIC SURFACE Fig 2.2 c: CONOID Fig 2.2 d: HYPERBOLOID Normal to surface Fig 2.2 e: \ ✓ t at cro ss point 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Various Net Shapes: The best known nets have tetragonal meshes of regular or irregular shape. Regular shapes may be squares (fig. 2.2f), parallelograms or rhombi (fig. 2.2g) and rectangles. A net with hexagonal or tetragonal meshes (fig. 2.2h) can form any surface. When the cable-net surface is spatially curved, the angles at the cable intersections vary. Fig. 2.2 f : Parallelogram Fig. 2.2 g . Rhombi Fig2.2 h : Hexagonal (Otto. 1967-69 : 28) (Otto, 1967-69 . 28) (Otto, 1967-69 : 28) Freely-sagging cable nets structures with tetragonal or hexagonal meshes are not rigid in shear. Tetragonal nets with tetragonal meshes can be extended diagonally under monoaxial stress, while nets with hexagonal meshes can be extended in any direction. If the net is required to be rigid in shear, but the effect o f the edge elements, the dead weight, or the rigidity o f the net lining is not sufficient, a triangular mesh must be chosen (fig. 2.2i). However, nets with uniform triangular meshes can only be simply curved. Spatially curved nets with triangular meshes must have different cable nets atleast in one direction. A freely suspended, triangular, spatially curved cable nets can be obtained by subdividing a net with rectangular or hexagonal meshes (fig. 2.2i). 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A certain rigidity can be obtained in nets with tetragonal meshes by inserting stiffening cable triangles (fig. 2.2j) or by means of rigid frames or panels (fig. 2.2k). This also applies to nets with hexagonal meshes (fig. 2.21). Many other regular shapes are possible as combinations o f octagonal, hexagonal, and tetragonal meshes (fig. 2.2m). Fig 2.2 i : Single triangulation (Otto, 1967-69 : 28) A : 4 f ' ,i ! \ ■ ■ • ’ _ i — * — . — i - : ' i— i t ' ; ' Fig. 2.2 j : Double triangulation (Otto, 1967-69 : 28) l -' u Fig. 2.2 k : Rigid frames (Otto, 1967-69 : 28) It is known that the triangle is one of the most stable shapes. However, nets with uniform triangular meshes cannot be extended in any direction. It cannot be fabricated flat on the ground and deformed in space. However, they can be simply curved. r - Fig. 2.2 1: Hexagonal mesh (Otto, 1967-69 : 28 ) Fig. 2.2 m : Combined mesh (Otto, 1967-69 : 28) 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.2n shows a cable net with square meshes only along the two central axes that are normal to each other; all other cables are curved. This type o f net can be fabricated flat on the ground and deformed in space. This mesh when subjected to load, shows large deformation; the straight cables redirect and transfer forces applied outside their own axes only after deformation. Fig. 2.2 n : Square mesh along axis Figure 2.2p shows an orthogonal cable net in a square frame. The cables o f an orthogonal net form vertical planes. The families of the cables are perpendicular to each other. The plan o f an orthogonal cable net therefore forms a square or rectangular grid. The task of prefabricating this net flat on the ground is rather difficult. The cable net itself is o f varying mesh size, unless it is tensioned in a plane. Fig. 2.2 p : Orthogonal mesh in square frame. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Apart from square frames, radial cable nets (a small area o f radial cable net is shown in fig 2.2q) are also very much in use. This best known form o f an asymmetrical cable net consists o f radial cables, extending from a center point, and circular ring cables. The cable lengths of the outer ring is always greater than those o f inner ones, unless there are subdivisions by steps as shown in fig 2.2q. shows a net o f radial and ring cables suspended between outer edge cables. Radial cable nets can also be inserted into nets with tetragonal or hexagonal meshes. Fig. 2.2 q Radial cable net (Otto, 1967-69 : 28) Among the many possible shapes, only nets with diagonal cables give equal angles o f cable intersection and geometrically similar meshes. Figure 2.2r Fig. 2.2 r . Radial and hexagonal net (Otto, 1967-69 : 28) 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3 MEMBRANES: (Thronton, 1992: 51-58 and Data compiled by Seaman corporation). In case of membrane structure, it is not possible to simply draw a shape in case of and then construct it, unlike the conventional one. A soap film between wire loops has a unique shape defined by boundaries- a membrane structure is the same. Its design is in four stages: sketch design, form-finding, analysis and detailed design. The first is to sketch a possible design which appears likely to satisfy both the functional criteria o f the overall structure and the specific technical requirements o f the membrane. It helps to construct a simple model using nylon stocking material. This is used to check the broad feasibility o f the design. It also helps to give an idea of the appearance. Computer models work fine but at this stage the physical model gives a more direct appreciation. Having decided on the basic form and established the boundary positions, the next stage is to establish the precise geometry. This process known as form-finding, uses computer programs. After the geometry has been defined, the structure is analyzed for various loading conditions, again using special computer programs. The design is checked to ensure that the fabric is neither overstressed nor goes slack under changes in load and that there is no ponding. Both the form-finding and analysis are time-consuming and rather tedious, so it is important that the geometry is defined as well as possible before starting. As with any structure, the analysis may show that changes are necessary for satisfactory structural performance. A minor change in the shape o f a boundary can result in 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. weeks of abortive work. The time for exploration of forms is the model stage. The cutting patterns are produced when a satisfactory geometry has been found. The pattern must take into account the physical properties, in warp and weft direction, o f the membrane and the degree of prestress it has to deal. Membranes can be typically classified into two categories: ► a simple cover without any support o f cable nets. ► skin for cable nets. The membranes are of, basically, two types: Woven membranes: A typical example, being, natural canvas. It comprises of fine mesh o f individual thread woven very close together. This accounts for its lateral stability. These can be deformed to a certain extent due to parallel displacement o f fibers. Homogenous membranes: These are membranes o f homogenous plastic skin and show a behavior very similar to a net of triangular mesh. A combination of both woven and homogenous membrane accounts for a woven fiber net with a homogenous coating, their structural behavior, being, very close to a homogenous membrane. The most commonly used materials in the membrane structures are: ► Fluoropolymer foils ► PVC coated polyester ► PTFE coated glass fibre Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fluoropolym er foils: Foils are thin, flexible sheets whose properties are the same in all directions. They were not used often used because they tend to be weak, develop large elongations, or are not very durable and degrade under ultraviolet (UV) light. However recent development of fluoropolymer foils are sufficiently strong and can be used in permanent structures. PVC coated polyester: PVC can be applied to all base cloth to protect them from damage and degradation, but it is mainly used with polyester. It is versatile and, by means of additives, can produce a cheap, flexible and fire-resistant coating. With newly created weaving technology, high tensile strength and high tear resistance can be obtained without weaving o f the base fabric. The weaving and coating process gives the fabric, exceptional stability under load with minimum of stretch and shrinkage over a wide range o f temperature and humidity conditions. Yams are designed to “rope up" to minimize progressive damage from tears or puncture. It does, however, suffer from the disadvantages o f retaining dirt and degrading with time. The PVC coating may contain a lot o f ingredients to achieve its performance so there are differences between materials from different manufacturers. Exposure to UV radiation can cause embrittlement due to the breakdown of the PVC. This can be reduced by the use o f stabilizing additives. Plasticizers help to give flexibility. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Migration of these to the surface of the fabric, and subsequent loss, can also increase the brittleness o f the coating and cause a loss in the volume, which, in turn, induces cracking. Contact with solvents, oils and soaps can also lead to loss of the plasticizer. Cleaning the fabric can thus accelerate its decay if not carried out properly. Coatings such as acrylic lacquers and fluoropolymers like PVF (Tedlar) and PVDF help reduce plasticizer migration and retention of dirt. It does not wick moisture and bacteria into the yarns which can cause mildew, staining and deterioration o f coating, adhesion and fiber strength. Compared to PTFE, PVC coats are easier to pigment and to fill to vary the appearance. PVC fabrics have lower initial costs than PTFE but are less durable, require more frequent cleaning, and stretch more. The lower stiffness can be an advantage in that the finished membrane is more able to take up small errors in fabrication cr assembly. It is also more able to withstand bending without damage. Polyester substrate fabrics have relatively greater resistance than nylon-based substrate fabrics to many chemicals like HCL. PTFE coated glass fibre: PTFE is used to protect the glass fibre from physical damage and water, which weakens it. It has fewer ingredients than PVC because it has inherently better durability; it does not require plasticizer and UV absorbers. PTFE is flameproof and very durable, however, because of the high temperatures involved in the manufacture of the coated fabric, it can only be used with glass cloth. 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Because o f their lower elongation and susceptibility to damage, PTFE-coated glass fabrics are less tolerant of errors in construction. They are also more brittle and can be damaged by fluttering or flapping that would be acceptable in a PVC-coated roof. Structural properties: The structural properties of interest are: Strength Modulus (stiffness), which is the load/extension behavior o f the fabric measured biaxially because of the effects of crimp interchange. Tear strength, which is a measure o f the resistance of a fabric to the formation and propagation of a tear. Construction stretch, which is non-recoverable stretch caused by changes in the cloth. Dimensional stability which is the extent o f creep, temperature and moisture movement. These structural properties are affected by the weave and the materials used for the cloth and its coating. During weaving, one set o f threads, the warp, is held while another set, the weft, is passed through by means of a shuttle. During this process the warp is usually held straight while the weft goes up and down. If the fabric is subsequently loaded in the weft direction, these yams will straighten out causing an extension in the weft and contraction in the warp. This is the Crimp interchange. The yams also compact under load, which causes further extension. 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fire resistance: Many standards and methods for evaluating fire resistant characteristics o f fabrics have been developed. The requirements o f these standards are based upon sound engineering principles, research, and records o f test and field experience. One of the most accepted methods for testing is to apply a source o f flame, for a certain amount o f time to the fabric suspended vertically in a controlled chamber, remove the flame and look for self-extinguishing characteristics, the flame propagation, and the degree o f char. This is the type of testing outlined under: ► Standard Methods o f fire Test for Flame Resistance Textiles and Films, NFPA 701-1966, National Fire Protection Association. ► Flame Retardant Chemicals and Fabrics, extracted from the California and Administrative Code Title 19, Public Safety. ► Flame Test o f Flame Resistant Fabrics UL 241, developed by Underwriter Laboratories, Inc. ► Method 5903 Flame Resistance of Cloth: Vertical, Federal Test Method. The first three standards namely NFPA, California State Fire Marshall and UL 214 consists o f a small scale and a large scale test. These three standards outline the same method of testing. Method 5903 o f Federal Standard 191 is the same as the small scale test o f the other standards, except the gas used has a heat of 539+-7 BTU per cubic foot at 67 degrees. The first three standards require natural gas having a heat value o f 800-1000 BTU per cubic foot. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The fabrics meet the standards of small scale and large scale tests due to their chemical composition and coating techniques. Building regulations require wall and ceiling linings to be class 1 for rooms and class 0 for corridors and escape routes when tested to BS476: parts 6 and 7 as appropriate. Only glass-based fabrics can achieve class 0 since the substrate must not be a thermoplastic material. PVC and rubber coating are, by themselves, flammable and require the addition large amounts of flame-retardant materials to achieve highest performance. PVC-coated polyester can achieve the equivalent o f class 1. But the relevance o f these tests is to be seen, since in real fire the fabric bums through or the joints fail, thus allowing the fire to vent. Tests carried on PTFE revealed that the products o f combustion are highly toxic. However, the fabric will fail by perforation at the temperatures necessary to cause the PTFE to decompose allowing the flames and the smoke to vent. Also, recirculation of the primary decomposition products of the PTFE through a heated area generates extreme toxicity products. In view of this, the use o f PTFE fabric is accepted. Durability: The durability o f coated fabrics depend primarily on the coating. Recently available fluoropoylmer coatings have improved their life expectancy. PTFE-coated fabrics have been in service for almost 20 years and without known problems of degradation. The life expectancy o f PTFE-coated membrane structures is estimated at 20-25 years. Fluoroploymers foils are expected to have a life in excess o f 15 years. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Translucency: In many cases the transcluency is seen as a desirable quality o f fabric structure. This depends on the transcluency and the density o f the yarn and the coating. Typical percentages o f transcluencies are: Fluoropolymer foils upto 97 Silicon-coated glass fiber 15-30 PTFE-coated glass fiber 5-15 PVC coated polyester 8-30 The life of PVC-polyester fabric is inversely related to its translucency. A life o f 15 years may be achieved with 15 % translucency while a 30 % translucent fabric fails in almost half the time. Temperatures beneath a membrane depend on the particular circumstances. They are in order o f two or three degrees above outside ambient temperatures. The Building Regulations do not permit an uninsulated space to be heated by more than 25 W/m sq, which is insufficient to raise the temperatures by more than a few degrees. The main function o f a typical membrane roof is thus to provide shelter from rain, wind and sun. The membrane skin can reach low temperatures, particularly on clear winter nights when, because o f radiation to the sky, the fabric temperature can drop below the outside air temperature. This could result in condensation and even ice formation with water dripping on the space below as ice melts. Some insulation can be provided by the use of a second, lighter, skin o f fabric. Fluoropolymer foils have been used to form pressurized cushion structures. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. These foils can be treated with low emissivity coatings in a similar way to glass. Multiple skins with such coatings are capable of achieving very high insulation levels, in range of U=1.5-2.5 W/m sq deg C, although this reduced at the edges where the skins come together and at the frames. Such structures are best considered as components to replace glass or cladding panels. The geometry of a fabric roof is usually such that there is sufficient height for summer comfort to be achieved by the provision o f some opening vents at the high points. Seams: Both the analysis and the detailing must take account of the seams; which can be made in the shop or on site. The layout of joints affects the analysis because the properties o f the fabric in the warp direction are different from those in the weft direction. Seams are clearly visible and form an essential o f the architecture so their layout must be carefully chosen to coordinate with the overall design o f the roof as well being technically correct. Sewn shop-joints are not used on PTFE-coated glass. Its most common form o f seaming is heat welding using hot air, direct heating or radio frequency waves. They are coated with special compounds to permit welding capabilities. Site joints are necessary because o f limitations on the bulk o f membrane that can be handled on site. It may also be necessary to fit the membrane around the supporting structure. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mechanical seaming are more easily and reliably made on site as opposed to welded seaming. The most common form consists o f clamp plates or a double groove. Fabric attachment: The two chief types of attaching fabric to anchorages are sleeves and clamps. Sleeves are pouches to contain catenary cables, which are then connected to the fabric. The is the less expensive form of fabric attachment and results in free-form design. If a tighter connection between fabric and “hard" structure is required- for instance, roofs and skylights- a clamping system is used. Here the fabric is sandwiched between clamping bars or plates, which are then bolted to the hard structure. Large panel design: Nylon based fabrics are affected by the heat of welding to a greater degree o f welding than polyesters. Various welding situations may result in one panel ply shrinking from the heat slightly more than the other panel ply. Test welds should be made to optimize machine settings for control of panel dimensions. In some cases, particularly with nylon, very long seams should be cut slightly longer than the finished product and trimmed to size after welding. Elongation/stretch: Generally, fabrics show 10-13% elongation in the fill direction. Stretch in the warp direction is significantly lower. 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Initial evaluation o f stretch characteristics helps to design or pattern for stretch allowance to assure proper contour and shape in the finished product. Cutting: Fabric lays o f nylon are more susceptible than polyesters to humidity and temperature conditions affecting shrinkage o f panels. Nylon is hydroscopic and will gain moisture if allowed to lie on the moist floor and affect welding characteristics: this practice should be avoided. Polyester fabrics are more dimensionally stable in similar humidity conditions. Polyesters do have higher modulus than nylon and do require more patterning, but provide a much more dimensionally stable finished product. Reinforcing: Reinforces and/or patches for repair should consider the effect of fabric stretch under load. In general, reinforces should match warp to warp and fill to fill on the main panel to minimize internal shear between the reinforcement and panel. Erection: In case of complex structures the roof can be divided into a series of panels separated by elements of rigid structure. This can also simplify the analysis by converting a complex form into a series o f simpler repetitive forms. Boundary cables carry the load in the membrane back to attachment points. Such cables are in the form o f a catenary and are attached to plates at the comers. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The structure must be designed so that the interface between membrane and the hard structure can accept the tolerances in the manufacture of each and can accept the movements occurring as the roof is prestressed. Both depend on the particular form o f the roof, so it is impossible to generalize. The detailing o f the attachment points is one of the most important aspects o f design, both technically and visually. Details must allow the membrane to move under a load, avoid stress concentrations, avoid wrinkling and allow pre-stressing where necessary. It is * worth considering them in the design so that sufficient space can be allowed between the membrane and the supporting structure and so there is consistency in the detailing. As these details are at the edge, they are highly visible. Their contrast with the fabric can enhance the design if handled properly. The design must consider a prestressing method and provide the necessary details. A simple cone structure, for example, could be prestressed by pushing up the cone or by pulling out the edges. Membrane structures are relatively fragile. In general, they need to be laid out on a clean, level surface from which they can be pulled up. Nothing else should be allowed access while this is being done. After erection they should be protected from damage by other trades. Dirt, oil and smoke from fire and exhausts should be kept away. Ideally the fabric roof is the last element to be installed to complete the enclosure of a building. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Costs: In fabric industry, the cost curves works in reverse. The larger the span, the more cost efficient the structure. Cost analysis say that, at spans o f 700 ft., the tensile structure figure hovers around $ 33/sq. ft. In applications under 75ft., the cost of tensile structures is about $ 35-45/sq. ft. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission I I I TABLE -1 ; MEMBRANE STRUCTURE FABRIC SPECIFICATION TABLE Coated Fabric Weight Oz/sq.yd thick. (mils) Strip tensile lbs/in. Strain rate: in./minute. Dry Dry Wet Wet Wet Fill War]) Fill Trapezoidal Tear (lbs/in.) Warp Fill (m in) (min.) Solar transmission % High l.ow Sular reflectance % Flame out: seconds. Fire resistance Colors PTFE- coated fiber glass 37.5 avg. min. (32-38) 30,31 nominal 500- 410- 440, 360, 520, 430, 491, 433, 571, 513, 598 491 628 570 32-5, 34.4, 34.4, 35-8, 80 80 10-13 9+/-2 +1-2 67 (min.) 1 second Passes ASTM- E-136, ASTM- E-108: Class A White, alter sunlight exposure Silicon coated fiber glass. 36 avg. (16-42) 32 nominal 600 475 500 425 50 70 20+/-3 12 66 (min.) 3 seconds Passes ASTM- E -136, ASTM- E-108; Class A White or opaque PVC- coated Polyes ter 28 avg. min. (20-32) 400 350 65 65 Trans- As lucent, per as per color color depends on color 2 seconds Method 5910 meets CFMR, UL 214, NFPA- 701 Many colors Test FTMS 1915041 FTMS 191-5030 FTMS 191-5102 FTMS 191-5136 Tabic compiled from dala provided by Chemical Fabrics Corp., and Seaman Corp. 3. DESIGN CONSIDERATIONS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. DESIGN CONSIDERATIONS: 3.1 EDGE CONDITIONS: (Otto, 1967-69: 20-85. Schierle, 1968: 8-29. The edge elements of cable nets and membranes can be subjected to tension, bending or compression. Fig. 3.1 a: Edge cable (Schierle. 1968 : 25) Tension-loaded cables form the edge elements in figure 3.1a. In this case the edge cables transfer the load imposed by the membrane under pure tension, thereby assuming the shape o f a funicular tension line. The tension developed in the edge cable varies according to its radius of curvature for any given unit load as generated by the membrane. Fig. 3.1 b: Edge beam (Otto, 1967-69:41) Figure 3.1b shows the edge cable, supporting the membrane, subjected to bending due to tension in the membrane. The structural member for such an edge cable could be a beam. The size o f the members can help resisting the bending. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.1c shows the edge cable transfer the load, generated due to membrane, to its supports under compression. The funicular pressure line for an arch subjected to compression supporting a double curved membrane is a curve described in space for simplicity. The neutral axes o f an arch is better described in plane rather than in space. The deviation between the funicular pressure line and the neutral axis o f an arch causes a bending moment. Also, the neutral axis of an arch is same as the funicular pressure line for one load condition. Bending moments are caused by all variation from that load condition. 3.2 CABLE NETS AND MEMBRANE SURFACES: Various surface shapes are possible as per the tension induced in the cable nets and membranes. W ave shaped cable nets and m embranes: Repetition o f ridges and valleys define the anticlastic surface o f the wave shaped cable nets and membranes. 42 with permission of the copyright owner. Further reproduction prohibited without permission. Fig 3.2 a: Wave shaped cable net (Otto, 1967-69: 82) Cables (a) are stretched between two parallel rows of high points (H), and cables (b), between two parallel rows of low points (T) alternating with the high points (H). Cables (a) and (b) are then connected by transverse cables (c) at short intervals. The main cables (a) and (b) are thus subjected to tension. A continuous wave shaped cable surface is thus formed. Cables (a) form ridges and cables (b) form valleys in this surface. The interval between the transverse cables (c) can be decreased until they are close together (d). Cable nets (e) can also be stretched in the fields. They will form connections between cables (a) and (b). The principal directions o f the cable may be diagonal or parallel to the waves. Sharp ridges in wave-shaped cable nets and membranes can be caused by large forces. The wave crest corresponding approximately to the ridge line H-H is shown in dotted line in the adjacent figure, while the trough bottom, corresponding to the valley is shown by dots and dashes. The central longitudinal sectional is indicated by points. 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Point supported cable nets and membranes: Deformation o f membranes of any boundary condition in different directions due to one or more supporting points define the anticlastic surface of point supported structures. Cables are line components in which the forces act. Membranes form surfaces. The tensions in them are transmitted to boundaries. When the membrane is supported at a point, the tension in the membrane is extremely high at this point. With the true point load, i.e., with an infinitesimal supporting surface, and, therefore, infinitesimal edge length of the supporting surface, the membrane thickness is comparatively infinitesimal. This explains why even highly resistant membranes can be pierced by thin needles. Point supported membranes require an adequate contact area, as provided, by a sphere, a supporting shell or a supporting cone as shown in figure 3.2b. The membrane is thus stressed along the line of finite length, and not a single point. Fig. 3.2 b: Point supported cable nets (Otto, 1967-69: 69) I I 44 with permission of the copyright owner. Further reproduction prohibited without permission. A ,K ,h Fig. 3.2 c: Point supported cable net with Tetragonal meshes. (Otto. 1967-69: 69) ^ 7 > .> i \ v - c v Figure 3.2d and 3.2e shows shapes o f cable nets obtained by joining two, four or more cables. Fig. 3.2 d: Point supported with four cables (Otto. 1967-69: 69) Fig. 3.2 e: Point supported with two cables (Otto, 1967-69: 69) Arch supported cable nets and m em branes: Deformation of a membrane o f any boundary conditions due to one or more supporting arches define the anticlastic surface o f an arch supported structure. Fig. 3.2 f: Arch supported and edge cables (Otto, 1967-69: 64) Fig. 3.2 g: Arch supported and edge arches (Otto, 1967-69: 64) 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Saddle shaped cable nets and membranes: Saddle shapes are the most frequently used shapes. Various types of saddle shapes are possible with respect to different edge conditions. Fig. 3.2 h: Saddle shapes with edge cables (Otto, 1967-69: 54) Fig. 3.2 i: Saddle dhape with edge arch (Otto, 1967-69: 54) The frame, can be square shaped, hexagonal shaped on bases o f interrupted or uninterrupted borders as shown in figure 3.2j Fig. 3.2 j: Interrupted and Uninterrupted frames (Schierle, 1968 :26) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3 SUPPORTING ELEM ENTS: (Youssef, 1995 : Seminar 313) These elements typically support the cable in space and provide a means for transferring its vertical and horizontal thrusts to the ground. A basic design issue is whether to absorb the horizontal thrust involved directly through the foundations or by using a supplementary horizontal compression thrust. Fig. 3.3a : PIER SUPPORTS The vertical piers supporting the ends of the cable carry the vertical com ponents o f the cable reactions by axial com pression and the horizontal component by bending. This system is good for cables if relatively short span onlv. The greater the span L or the height H, the larger m ust be the supporting piers. J=> Basic force system. Note that the foundations must prevent the piers from overturning Fig. 3.3b : G U YED M ASTS The horizontal com ponent o f the cable thrusts are absorbed by diagonal guy cables and transferred to the ground. This vertical masts act in axial compression only. Inert osint forces 7V t f I T Free body diagram As the guy cable angle changes, the Basic force system. The m ast carry ot top o f cable mast. forces in the guy cable tend to increase, axial forces. The cable foundations must M ast forces also increase horizontally. prevent guy uplift and sliding. (Youssef, 1995 : Seminar 313) 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.3c : INCLINED GUYED MASTS: Inclining the masts causes them to pick up some o f the horizontal cable thrusts, thus Basic force system. The masts carry only downward forces. Cable foundations must prevent guy uplift and sliding. reducing the forces in the diagonal guy cable. (Y o u sse f, 1995 : S e m in a r 3 13) i r - s = T v The use o f horizontal compression struts is much less frequent because of the long unbraced length o f such members, which makes them highly susceptible to possible buckling since they are in compression. Required sizes for the struts would be very large and tend to offset any efficiencies gained by using a cable to span a long distance. In all the above figures, the sag chosen for the cable is a significant variable since pier or mast lengths are directly related to this value for a given functional enclosed cable height above the ground. The deeper the sag, the more substantial support members become. Sag/span ratios of around 1:8 to 1:10 are often used. 3.4 DESIGNING FO R WIND EFFECTS: (Youssef, 1995 : Seminar 313) A critical problem in the design of any cable roof structure is the dynamic effect o f wind. Consider the simple roof structure supported by cables in figure 3.4a. As the wind blows over the top o f the roof, a suction will be created. If the magnitude o f the suction force due to the wind exceeds the dead weight of the roof structure itself, the roof surface will begin to rise. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 As it begins rising and changing shape, the forces on the roof surface begin to change, since the magnitude and distribution of the wind forces on a body are dependant on the exact shape of the body. Flexible ro o f structure (cable-supported) Possible vibration modes Wind Wind Wind Fig. 3.4 a : W ind blowing over roof surface in its naturally deflected shape cause suction force to develop. T hese suction forces cause the flexible roof to begin rising. As the roof changes shape due As the roof moves up and down, to the suction forces, the effect the effect o f the wind alternately of the wind on the new shape produces suctions and pressures becomes one o f pressure rather causing further movements, than suction. This causes the A constant fluttering o f the roof to move downward again. roof results. (Youssef, 1995 : Seminar 313) Since the wind forces change due to the changing shape o f the roof, the flexible structure itself changes shape again, in response to the new loading. The process is cyclic. The roof shape will not remain in steady, but will flutter, as long as the wind is present. This problem can be solved by relying on the dead load to keep fluttering from occurring, or by using some sort of system of crossed or staying cables as shown in figure 3.4b, 3.4c, 3.4d, 3.4e. Wind suction Dead toad > Wind suction ’ f a = = s = =s=! ” Dead load Fig. 3.4 b : T he dead load o f the structure is m ade large to overcom e maximum possible suction forces due to wind. Resonance is also m ade unlikely. (Youssef, 1995 : Seminar 313> Fig. 3.4 c : Stayed cable structure: the guy cable are pretensioned. 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3 4 d : Crossed cables with opposite curvatures: cables are initially pretensioned. Vertical loads cause the tension in the upper cable to increase and those in lower cable to decrease. Fig. 3.4 e : Cable and arch structure: cables are pretensioned. (Youssef, 1995 : Seminar 313) The stability of a cable under a wind force is an important factor because of the phenomenon of flutter. There are several fundamental ways to combat flutter due to wind forces. One is to simply increase the dead load on the roof, thereby increasing cable tensions and changing natural frequencies. Another is to provide anchoring guy cables to the cables at the periodic points to tie the structure to the ground. A related method is to use some sort o f crossed-cable or double-cable system. The latter method is extremely interesting as it is possible to create an internally self-dampening system. Tie back cables Fig. 3.4 f : DOUBLE CONCAVE CABLES: Pretensioned cables are connected by secondary members. (Youssef, 1995 : Seminar 313) 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Structure using convex cables. Cable forces Forces on compression ring Fig. 3.4 g : Double convex cables Pretensioned cables are separated by compression struts. ;truts (Youssef, 1995 : Seminar 313) The problem o f roof flutter can be solved by using double-cable systems. In both cases shown above, the cable in the upper member is slightly different from that in the lower member. Therefore each member has a different frequency o f vibration, due to different tensions. This causes the whole assembly to be a self-damping mechanism, since neither cable can freely vibrate in its natural mode because o f the other cable. The natural frequency o f vibration o f a tight cable depends on the tension present in the cable. The natural frequency o f vibration of the lower cable will thus always tend to differ from the upper cable. As an external exciting force tends to cause either cable to vibrate in one o f its fundamental modes, the other cable will tend to damp out the vibrations in the cable, since it has a different natural frequency of vibration. The result is that any oscillations are damped out since neither cable can go into resonance because of the damping effect o f the other. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 3.5 ELASTIC BEHAVIOR O F CABLE NETS: (Schierle, 1968 8-29) Cables elongate under tension and temperature changes, due to the elasticity o f the materials. In comparison to rigid structures such as beams, shells etc., cable nets and fabric structures have a relatively high amount o f elasticity. On application of load along one direction, the cables in that direction elongate due to their elastic properties. This tension results in sag along that direction, while the cables in the opposite direction become slack. The sag/span ratio determines the magnitude o f forces developed in the cable and its supports. The increase in deformation causes new sag/span ratios, thereby reducing the tensions and the impact of load on cable tensions. This transfer is a very important factor in the structural efficiency o f cable nets structures. A structural disadvantage, however, results from the deformation o f the cables under load. The layer of cables in opposed curvature loses its stabilizing effect and the structure may be subjected to flutter. To avoid this effect, the cable must be pretensioned. 3.6 PRESTRESSING O F CABLES: Pretensioning is required to achieve structural stability in cable net structures. The amount o f prestress is governed by the consideration that under load normal to the cable nets, a minimal amount o f prestress remains in the cables o f the opposed cable curvature. 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Due to equilibrium of elasticity, the increase in tension along one direction is equal to the decrease along the opposed layer for cables o f equal dimensions, elasticity. This means that pretension must be atleast 50% o f the tension generated under ultimate load. However, the elasticity of boundary conditions demands higher values o f pretensioning. More elastic the boundary, more pretension will be required Several methods can be adopted for pretensioning. In cable nets having edge cables, pretensioning can be achieved by tensioning the edge cables. In cable nets with rigid borders, pretension can be applied to individual cables by means of mechanical devices. Another method involves pretensioning o f cable nets as a whole by displacing the edge condition after erection. • Pull Pe r i p h e r a l E d g e s . • P u l l Pe r i p h e r a l c a b l e s «Rjl l Br a c iu g c a b l e s P u s h u p a p e x . V • f ijL L u p S u s p e u s i o u c a b l e s . Fig. 3.6 a : Pretensioning of cables (Youssef, 1995 : Seminar 313 ) 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.7 M IN IM A L SURFACE AREA: (Schierle, 1968 : 23) ‘The one surface connecting the boundary edged with minimal amount of surface area is defined as the minimal surface.’ Anticlastic surfaces are always minimal for a given set of boundary conditions. This surface has mutually opposed curvatures, with positive and negative radii at any point. Minimal surfaces can be obtained by various methods in small scale models. Soap films form minimal surface connecting a given set of boundary conditions. Gravity results in small deformations o f the soap film. Measurements taken along two planes, along gravity and opposed to gravity should be recorded. The mean value gives a fairly accurate minimal surface. Minimal surfaces can be determined by: ► At any point on the surface, the sum of positive and negative radii equals zero. * • Surface tensions is equal in all directions throughout the surface. ♦ Fig 3.7 a: Minimal surface (Schierle, 1968:23) K .1 + £2 - 0 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Neglecting even the structure’s dead weight, minimal surface could be an ideal shape for any double-curved surface. In reality, however, minimal surfaces might not be the ideal shape due to varying load conditions. 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. Fab-CAD 4.1 INTRODUCTION: The program Fab-CAD is the short form of the word for fabric CAD which is a program for the computer aided design and manufacture of fabric structures. This program has been designed in different modules. They are basically categorized into pre-processor and post-processor modules. Fig. 4.1 a : Flow chart Form Finding | Pattern Design j Display Analysis Input-data Display Initial Form Fab-CAD Pre-processor Post-processor Main-processor The core uses a program Dynamic Relaxation method which has been written by Dr. Tejav Deganayar, who has significant contributions to the field o f fabric and membrane structures. This core has been written in the Fortran programming language. It was developed with an intention to integrate the DR program and the AutoCAD interface to run all the modules o f the program and to generate user friendly input and output of the program. 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AutoCAD is used as the parent software to generate all the graphical input. The graphical input data needed for the initial geometry can be easily generated and then, one can input the data to the main program for form finding and analysis CORE INPUT AutoCAD D.R OUTPUT AutoCAD Fig 4.1 b : Program flow chart AutoCAD is used for generating the input and the output because of its good graphic handling capabilities, which is very necessary for the Fab-CAD program. Entities such as lines, arcs, circles and text can be easily handled as graphical entity definitions or as "ASCII definitions. AutoCAD offers many possibilities to be customized in the autolisp programming language which has been developed to be used within AutoCAD. Autolisp programs do not require compiling by the user unlike Fortran, “C" etc.. System Requirements: A copy of AutoCAD rel.12 or higher for DOS or WINDOWS. ► 16 MB of memory or higher ► 20 MB of free hard disk space to load the Fab-CAD program ► VGA or SVGA monitor. ► Fab-CAD. 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2 INPUT DATA: The input data is the pre-processor module of the Fab-CAD program. Input data can be visualised in the form of a drawing prior to the processing of the data, hence the problems arising form incorrect input data can be tracked and corrected at an early stage of the process. Unlike some programs that allow input only by entering numbers, this program offers a graphic input method by way o f a CAD drawing and then converts it into the numerical format. The input data can be categorized into three types: l. Geometric Data; This involves specifying the widths o f the fabric in the fill and warp directions and the input geometry in the form of an AutoCAD drawing of boundaries. Fig 4.2 a : Geometric input 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. Material Properties: Material properties of all the components of the structure like the fabric, cables, supports etc. must be defined. The properties that need to be specified are as follows: a. Modulus of elasticity b. Area of cross section. c. Pretension d. Code 0=C able member 1 = Prestressed member, 2=Compression member, 3=Force density method for Prestressed members. e. Capacity : Indicates the max load capacity before failure of the material f. Title (Fill, warp, cable etc..) 3. Load Para; This specifies the load in the X, Y, Z directions. The signs of these values are to be considered to define the direction of the force. For eg. a load o f -0.10 in the z direction indicates a downward load ie. Gravity or snow load etc.. A load of + 0.10 in the direction indicates wind uplifting force. 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.2 b : Load in the -ve “z" direction (dead load or snow load). Fig. 4.2 c : Load in the +ve “z" direction (wind uplift load). (Note: The above figures 4.2a and 4.2b are exagerated for clarity ). Geometric Data: The fabric data is generated based on graphically defined boundary conditions, and surface conditions. There are a lot of variations in the surface conditions. Some of the very basic type are the saddle shapes, the radial shapes, arch supported shapes etc. The edge conditions are drawn graphically using the drawing tools like lines and arcs. The radii of the edge cables is determined by the span to dip ratio. The default value of the span/dip ratio is 10 although the user can change these values to get steeper curves or larger curves. Once the boundaries are defined, the infill fabric pattern is specified as the width of the fabric in the fill direction and in the warp direction and the angle o f the patterns (this is done as the fabric structures are analyzed as cable nets). 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The patterns differ depending on the shape of the structure. The linear patterns are used for hypars and the radial patterns are used for tent-like shapes. A combination o f these shapes also can be used. The width of the fabric pattern is determined on the basis of availability of the fabric material. Usually the fabrics are available in the range of 40-60 inches in width and 120-150 feet in length. Each category o f element has to be placed on different layers as the DR program reads the material data unique on each layer for the form finding process. The fabric patterns consist of fibers in the fill and the warp direction and since the material is not homogeneous like plastic, the characteristic properties differ although not very significantly, but large enough such that if neglected can cause deformations or wrinkles in the structure. The fabric weave in cross section is continuous in one direction and the one perpendicular goes in the form of a sine curve weaving between the fibers. This causes the fabric to elongate more in one direction in which the fibers run continuous and less in the other direction in which the fabric runs like a sine curve. Fig. 4.2 d : Radial pattern - tent shapes Fig. 4.2 e : Linear pattern - hypars Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4 .2 f : Support elevation and location in space. Fig. 4.2g : Fabric weave pattern Once the fabric and the edge conditions have been determined the support locations and elevations have to be specified as shown in the figure 4.2e. General theory of the form finding is that the geometric input consist of finite elements which are simple line entities connected to each other by nodes. The nodes on the other hand can be considered to be connected to each other by 2, 3, or 4 line elements. The connectivity matrix o f the geometry in fig 4.2g can be thus determined as follows. The cable elements also have to be broken down as composed of line elements. Node no Connectivity 1 2 29 49 45 32 46 32 55 40 54 39 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V - -iL 45 1 ,1 ~ .''T V - • ^ T I ; b i _ * „ , — , v \ -------—------- 7 ? »\ \ i ' >s Fig. 4.2 h : Connectivity between nodes and elements Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Program description: The Fab-CAD program offers tools to generate the input data and the geometric data in the form of user friendly prompts and dialogue boxes. All the programs start with an “F" in the beginning of the file name to differentiate it from AutoCAD and autolisp programs. The extension of .LSP indicate a lisp file generated in Autolisp programming language. Please refer to the appendix for the detailed listing o f all the programs. Fcable.lsp : This program helps to draw the edge cables or boundaries of the fabric structure. It draws all these cables by default on the layer L03. The program prompts the user for two points in the drawing area, and then the span/dip ratio o f the cable by default being 10 which is an ideal ratio. The program then draws the cable between the two points and then gives an option to mirror it, just in case the user intends to have the curvature on the opposite side. -1 die LiH tfew Data Q ftlll . Ml* till* ?* |< a l l # o « T « 3 I ItU'TlR A / \ 10 / \ 5P*N/DP**7 / \ P 2 fr> ! H , i_l--- io a a e a d w ie a c a l* C g M M d Fig. 4 .2 i: Cables with different span/dip ratios 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Command: Fcable (enter) Enter first point: PI (enter) Enter second point: P2 (enter) Enter SpatvDip ratio : <J0>: 10 (enter) Do you want to flip the cable: y/n ?. : n (enter) The above sequence can be repeated to draw all the other cables. Fpat.lsp: This routine is adopted to draw the infill fabric pattern with specific pattern widths. The user is prompted for the pattern width and the angle o f the pattern. The program then hatches the boundary with the specified pattern and transfers the lines in the fill direction to layer L01 and the lines in the warp direction on layer L02 and changes their color to RED and GREEN respectively. This hatch is different from other hatch patterns from AutoCAD in a way that they are composed o f small line elements discontinuous between intersection points. m Fig. 4.2 j : Pattern configuration 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Command : Fpat (enter) Enter the width in the fill direction : 48 (enter) (note : units are inches). Enter the width if the warp direction : 48 (enter) (note : units are inches). Angle o f pattern : 45 (enter) Fjoin.lsp: This module breaks the edge cables at the point where it intersects the pattern lines in the fill and warp direction. This is intentional so as to create discrete elements from point to point. Command :Fjoin (enter) Flin.lsp: This program converts the small arc generated by the Fjoin.lsp into line elements as the core program “Dynamic Relaxation" requires that all the elements should be line elements. This means that even the arc should be a segmented line composition. Command : Flin (enter) Fnode.lsp This program prompts the user for the support location and elevation in space. The supports are drawn in the form of small circles on the layer SXYZ. Command: Fnode (enter) How many nodes : 4 (enter) Show node diameter : 10 (enter) Show support location: click a point on the screen (enter) Elevation in “ Z" : 180 (enter) The last two steps are repeated 4 times and there by drawing 4 nodes at places shown by the user and at the elevation specified. 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V Fig. 4.2 k : Support location and elevation Fddprop.lsp: This program prompts the user for the material properties of the cable and the fabric in the fill and warp direction. It offers a user friendly dialogue box for the input of the data. A r n m C A D I M C W M M I . D W G I E l l * g ilt t f c w Q t t a Q p t o a t !• • • » ..................... ' * - 7 ~ 'r s m n r * ' • ' 1 ti— H*„ t {e\wana\wVMM» M M t t a t * .- m t V M M i***. i .* m m m |u j , MOTMtt ji* j m c m n t d m x MM fZST MM. |m .M r.tm 'l“ “ t W M t jt M > j : « m » j « - . Z i- m W k -' jaon 1 tM « |l P « m p i» . . . * * . } amttr j u « ■ ■ . v . - . - t w . v . v . - S v K ’j i m 7' W? 3 , ; f a n i t - t i nan 1y t U J \ Fig. 4.21: Material property dialogue box 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. After the user enters the data and the file name in the edit box, the program creates a material property file with an extension of KEP as shown in fig 4.21. Table -2 : Property file . Prop.kep Material Modulus Width Pre- Code Capacity Title Tension 2.0 48.000 .300 10.00 Fill 2.0 48.000 .500 10.00 Warp 24000.0 150 .000 24.00 Cable This file is used as a property file in the following step which helps in running the form finding program. Network.lsp: This program is a part of the core program written by Dr. Tejav Deganayar. It processes the data obtained in the above steps and returns it to the core written in Fortran to run the form finding program. Once the user defines the material properties, he is only prompted for the input file name. The input file name is usually six characters long and the extension is always .INP. for eg. TRY222.inp Command: Input file name ? Try222.inp 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The program then shifts into text mode and performs the calculations. The number o f nodes and elements are displayed and the user is prompted as follows. Cable 126 126 Support 4 4/ Update Elevation (All : only 2 : No) : ALL Problem title: fa b Read properties from a file: (Y N) ?. : Y Property file name : Prop.kep The Dynamic Relaxation program then finds the shape depending on the factors defined in the material file and gives the output in the form a DXF file that can be visualized in AutoCAD. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Program files: The program gives an out put o f 7 files and they are as follow: (Note: Try222 is only an example o f a file nam e, this changes file to file but the extensions remain the same). TRY222.INP Input file TRY222.GEO Geometry file TRY222.REC Record file TRY222.0UT Output file TRY222.SUM Summary file TRY222.MOD Model file TRY222.RES Residual file TRY222.DXF Data exchange format file A brief description o f some important files is given below. TRY222.INP : Input file containing the material properties, node co-ordinates in the x,y and z , and forces in the x, y, and z. TRY222.GEO: This file has the geometric definition o f the model, it contains the node positions, connectivity matrix o f all the elem ents, pretension and product of modulus of elasticity and area of cross section. TRY222.REC: This is a program file. TRY222.QUT: This file contains a combination o f the INP and GEO files that contains all the nodal and connectivity data along with the material properties. TRY222.SUM: This file contains the member statistics that include the max, min, and average of the forces and the shear force at the critical nodes. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TRY222 MOD: This file consist of the the nodal data , and node co-ordinates in X , Y , Z direction, and the layer on which the different members are located. TRY222.RES: This file consists of the member connectivity between nodes and the residual stress in each of the members. TRY222.DXF: This file is a graphic file that can be viewed and used for visualization. This file format is compatible with many graphic applications. The cable net below is a simple example of an input model. The model is composed of simple line elements connected between nodes. The out put files from the program are attached in the following pages. Sample c A 4 7/ 10 Fig. 4.2 m : Simple cable net 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T a b l e - 3 : INPUT FILE SAMPLE 0 33 56 3 5000 .0001000 I 2 .0 48 .000 . 100 2 2 .0 48 .000 . 100 3 2400 .0 .100 .000 1 0 6 5 .8 1 1 6 8 .1 6 3 2 111 1 7 .8 1 1 9 3 .9 9 7 3 0 94 .091 4 5 . 9 9 7 4 0 1 1 3 .8 1 1 26 .277 5 0 1 3 5 .9 7 7 -2 .003 6 111 1 6 1 .8 1 1 -5 0 .0 0 3 48 7 0 2 5 7 .8 1 1 6 8 .1 6 3 8 111 3 0 5 .8 1 1 9 3 .9 9 7 9 0 2 2 9 .5 3 1 4 5 .9 9 7 10 0 2 0 9 .8 1 1 2 6 .2 7 7 11 0 • 1 8 7 .6 4 5 - 2 .0 0 3 12 0 6 5 .8 1 1 1 1 9 .8 3 1 13 0 9 4 .0 9 1 1 4 1 .9 9 7 14 0 1 1 3 .8 1 1 1 6 1 .7 1 7 15 0 1 3 5 .9 7 7 1 8 9 .9 9 7 16 111 1 6 1 .8 1 1 2 3 7 .9 9 7 48 17 0 2 5 7 .8 1 1 1 1 9 .8 3 1 18 0 229 .531 1 4 1 .9 9 7 19 0 2 0 9 .8 1 1 1 6 1 .7 1 7 20 0 1 8 7 .6 4 5 1 8 9 .9 9 7 21 0 2 5 7 .8 1 1 9 3 .9 9 7 22 0 2 0 9 .8 1 1 1 4 1 .9 9 7 23 0 2 0 9 .8 1 1 9 3 .9 9 7 24 0 1 6 1 .8 1 1 1 8 9 .9 9 7 25 0 1 6 1 .8 1 1 1 4 1 .9 9 7 26 0 1 6 1 .8 1 1 9 3 .9 9 7 27 0 2 0 9 .8 1 1 4 5 .9 9 7 28 0 1 6 1 .8 1 1 - 2 .0 0 3 29 0 1 6 1 .8 1 1 4 5 .9 9 7 30 0 6 5 .8 1 1 9 3 .9 9 7 31 0 1 1 3 .8 1 1 45 .997. 32 0 1 1 3 .8 1 1 9 3 .9 9 7 33 0 1 1 3 .8 1 1 1 4 1 .9 9 7 1 3 1 2 2 3 3 1 3 3 4 3 ' 4 3 5 4 5 3 6 5 6 3 7 8 7 3 9 7 8 3 10 9 9 3 11 10 10 3 6 11 11 3 12 2 12 3 13 12 13 3 14 13 14 3 15 14 15 3 16 15 16 3 17 8 17 3 18 17 18 3 19 18 19 3 20 19 20 3 16 20 21 1 21 17 0 51 1 1 1 10.00 FILL 10 .00 WARP 24.00 CABLE .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 . 00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00.000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 . 00000 .00000 .00000 .00000 .00000 .00000 .00000 1 1 1 0 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 1 22 23 23 1 19 22 24 2 20 24 25 2 22 25 26 2 23 26 27 2 8 21 28 2 18 22 29 2 21 23 30 1 27 10 31 2 11 28 32 2 27 29 33 2 9 27 34 1 7 21 35 1 23 27 36 1 30 12 37 1 1 30 38 1 • 31 4 39 1 32 31 40 1 33 32 41 1 14 33 42 1 24 16 43 1 25 24 44 1 26 25 45 1 29 26 46 1 28 29 47 1 6 28 48 2 5 28 49 2 31 29 50 2 3 31 51 2 15 24 52 2 33 25 53 2 13 33 54 2 32 26 55 2 30 32 56 2 2 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table - 4 : GEOMETRY FILE 1 0 0 . 6987293S47246381E + 02 2 111 0 .1 7 8 1 1 0 0 0 0 0 0 0 0 0 0 0 E+02 3 0 0 . 1004421907770967E+03 4 0 0 .1 2 0 8 0 8 0 7 6 5 3 1 2 022E+03 5 0 0.1408434820880208E+03 6 111 0 .1618110000000000E+03 7 0 0 .2537490635275363E+03 8 111 0 .3058110000000001E+03 9 0 0 .2231798092229034E+03 10 0 0 . 202813 923468 7979E+03 11 0 0 . 1827785179119792E+03 12 0 0 .6 9 8 7 2 9 3 6 4 7 2 4 6 3 7 8 E+02 13 0 0.1004421907770966E+03 14 0 0 .1208080765312022E+03 15 0 0 .1 4 0 8 4 3 4 8 2 0 8 8 0 2 0 8 E+03 16 111 0 .1618110000000000E+03 17 0 0 .2537490635275362E+03 18 0 0 .2231798092229034E+03 19 0 0 .2028139234687979E+03 20 0 0 .1 8 2 7 7 8 5 1 7 9 1 1 9 7 9 3 E+03 21 0 0 .2536955174333786E+03 22 0 0 .2025231947662210E+03 23 0 0 .2023381293945965E+03 24 0 0 .1618110000000000E+03 25 0 0 . 1618110000000000E+Q3 26 0 0 .1618110000000000E+03 27 0 0 .2025231947662210E+03 28 0 0 .1618110000000000E+03 29 0 0 .1 6 1 8 1 1 0 0 0 0 0 0 0 0 0 0 E+03 30 0 0.6992648256662152E+02 31 0 0 .1 2 1 0 9 8 8 0 5 2 3 3 7 7 92E+03 32 0 0 .1 2 1 2 8 3 8 7 0 6 0 5 4 0 3 5E+03 33 0 0 . 1210988052337792E+03 0 . 8251243652054468E+02 0 . 93 99700000000003E+02 0 .6 4 9 1 9 0 3 1 6 3 975699E+02 0 .4 6 6 9 8 8 6 8 16728198E+02 0 . 1770774150284478E+02 -0 . 5 000300000000001E+02 0 . 8251243652054471E+02 0 .93 99700000000003E+02 0 .6 4 9 1 9 0 3 1 6 3 975692E+02 0 .4669886816728197E+02 0 .1770774150284473E+02 0 .1054 815634794553E+03 0 . 1 2 3 0 7 4 9683602431E+03 0 .1 4 1 2 9 5 1 3 18327180E+03 0.1702862584971553E+03 0 .2379970000000000E+03 0 . 1 0 5 4 815634794553E+03 0 .123 074 9683602431E+03 0 .1412951318327181E+03 0 .1 7 0 2 8 6 2 5 8 4 9 7 1 5 5 4 E+03 0 . 9399700000000003E+02 0.1227595099364224E+03 0 . 9 3 9 9 7 00000000003E+02 0.1701745641387414E+03 0 .1 2 2 5 0 0 0 0 1 5 7 8 7 3 83E+03 0 .9399700000000003E+02 0 .6523449006357765E+02 0 . 1781943586125857E+02 0 .6 5 4 9399842126172E+02 0 .9 3 9 9 7 0 0 0 0 0000003E+02 0 . 6523449006357768E+02 0 .9 3 9 9 7 0 0 0 0 0 0 0 0 0 03E+02 . 0 .1 2 2 7 5 9 5 0 9 9 3 64224E+03 11678 8 0 9 2 2 4 6 8 7 8 9E+ OOOOOOOOOOOOOOOOE+ 1 879623619996446E+ 2450941842361756E+ 3 1 7 6 8 7 7081298090E+ 0 .4800000000000001E+ 0 .1167880922468788E+ OOOOOOOOOOOOOOOOE+ 1879623619996445E+ 2450941842361756E+ 3176877081298089E+ 1 1 67880922468787E+ 1879623619996446E+ 2450941842361759E+ 31768770812 98092E+ 0 .4800000000000001E+ 0 .1167880922468789E+ 1 8 79623619996447E+ 2450941842361760E+ 3 1 76877081298091E+ 1141836167755056E+ 2180612343926110E+ 2019562758165998E+ 3233947626736503E+ 2411318831208287E+ 2249751758368065E+ 2180612343926110E+ 3233947626736503E+ 2 411318831208286E+ 1141836167755056E+ 2180612343926110E+ 2019562758166001E+ 2 180 6 1 2 3 4 3 926110E+ 1 3 1 2 0 .2 9 6 2 2 1 6 1 3 7828448E+00 0 . 2400000000000000E+03 2 3 3 1 0 .33 204 90627075404E+00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 3 3 4 3 0 . 2 5 0 9 4 6 3 S94085S56E+00 0 . 2400000000000000E+03 4 3 5 4 0.3261205727672591E+ 00 0 . 2400000000000000E+03 5 3 6 5 0 .2827748619887722E+00 0.2400000000000000E+03 6 3 7 8 0.2962216137S27823E +00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 7 3 9 7 ' 0 .33204 90627078724E+00 0.2400000000000000E+03 8 3 10 9 0 . 2 S 0 9 4 63594085556E+00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 9 3 11 10 0 .3 2 6 1 2 0 5 7 2 7 6 7 5 9 1 3 E+00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 10 3 6 11 0 .2827748619885375E+00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 11 3 12 2 0 .2 9 6 2 2 1 6 1 3 7 8 2 6 5 7 1E+00 0 .2 4 0 0 0 0 0 0 0 0 OOOOOOE+O3 12 3 13 12 0 . 3 3 2 0 4 90627077302E+00 0 .2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+03 13 3 14 13 0 . 2509463594089225E+00 0 .2 4 0 0 0 0 0 0 0 0 OOOOOOE+O3 14 3 15 14 0 . 3261205727672118E+00 0 .2 4 0 0 0 0 QOOOOOOOOOE+O3 15 3 16 15 0 . 2827748619887723E+00 0 .2400000000000000E+03 16 3 17 8 0 .2 9 6 2 2 1 6 1 3 7 8 3 1 5 7 8 E+00 0 .2400000000000000E+03 17 3 18 17 0 .3 3 2 0 4 9 0 6 2 7 0 7 3 029E+00 0 .2 4 0 0 0 0 0 0 0 0 OOOOOOE+O3 18 3 19 18 0 .2 5 0 9 4 6 3 5 9 4 0 8 6 4 7 3 E+00 0 .2 4 0 0 0 0 0 0 0 0 OOOOOOE+O3 19 3 20 19 0 .3 2 6 1 2 0 5 7 2 7 6 7 7 8 12E+00 0.2400000000000000E+03 20 3 16 20 0 .2 8 2 7 7 4 8 6 1 9 8 8 3 966E+00 0 .2400000000000000E+03 21 1 21 17 0 . 1000000000000000E+00 0 .9 6 0 0 0 0 OOOOOOOOOOE+02 22 1 22 23 0.1000000000000000E+ 00 0.9600000000000000E+ 02 23 1 19 22 0 .1000000000000000E+00 0 .9600000000000000E+02 24 2 20 24 0.1000000000000000E+ 00 0 .9 6 0 0 0 0 OOOOOOOOOOE+02 25 2 22 25 0 .1000000000000000E+00 0 . 9 6 0 0 0 0 OOOOOOOOOOE+02 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 2 23 26 0 . 27 2 8 21 0 . 28 2 18 22 0 . 29 2 21 23 0 . 30 1 27 10 0 . 31 2 11 28 0 . 32 2 27 29 0. 33 2 9 27 0. 34 1 7 21 0 . 35 1 23 27 0 . 36 1 30 12 0 . 37 1 1 30 0 . 38 1 31 4 0 . 39 1 32 31 0 . 40 1 33 32 0. 41 1 14 33 0 . 42 1 • 24 16 0 . 43 1 25 24 0 . 44 1 26 25 0 . 45 1 29 26 0. 46 1 28 29 0 . 47 1 6 28 0. 48 2 5 28 0 . 49 2 31 29 0 . 50 2 3 31 0 . 51 2 15 24 0 . 52 2 33 2-5 0 . 53 2 13 33 0 . 54 2 32 26 0 . 55 2 30 32 0 . 56 2 2 30 0 . 1000000000000000E+00 1000000000000000E+00 lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOQOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO 10000000000000OOE+OO 1000000000000000E+00 1000000000000000E+00 lOOOOOOOOOOOOOOOE+OO 100000000000 0000E+00 lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO lOOOOOOOOOOOOOOOE+OO 0 .9 6 0 0 0 0O000000000E+02 0 . 9 6 0000000000000OE+02 0 . 9 6 0 0 0 0 0 00000000OE+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+02 0.9600000000000000E+02 0 . 9600000000000000E+02 0 . 9600000000000000E+02 0.9600000000000000E+02 0. 9600000000000000E+02 0 .9600000000000000E+02 0.9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+02 0 .9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+02 0 .9600000000000000E+02 0 . 9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 OE+02 0.9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+02 0. 9 6 0 0 0 0 0 000000000E+02 0.9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 OE+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 OE+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0E+02 0 .9600000000000000E+02 0 .9 6 0 0 0 0 0 0 0 0 0 0 0 000E+02 0.9600000000000000E+02 0 .9 6 0 0 0 0 OOOOOOOOOOE+02 0 .9600000000000000E+02 0 .9600000000000000E+02 0 .9600000000000000E+02 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table - S : OUTPUT FILE NETWORK (V e r:2 .6 0 > (G e n e ra l I n f o r m a t i o n ] P a g e : l P r o j e c t : SAMPLE D a t e -.06-FEB-96 NUMBER OF NODES = 33 NUMBER OF ELEMENTS = 56 NUMBER OF MATERIALS = 3 NUMBER OF ITERATIONS = 5000 CONVERGANCE TOLERANCE =.000100000 MATERIAL PROPERTY TABLE TYPE AREA PRE-TEN CODE CAPACITY ( k i p s / i n ) ( in c h e s ) (k ip s ) 2.0 2.0 ( k s i) 24000 .0 48.0 0 0 0 48.0000 (S q .in ) 0 .1 0 0 0 0 .1 0 0 0 0.1000 (k ip s) 0.0000 1 1 ( p l i ) 1 0 .0 0 0 10 .000 (k s i) 2 4 .0 0 0 DESCRIPTION FILL WARP CABLE 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table - 6 : SUMMARY FILE Minimum Z - D is p la c e m e n t ( a t Node: 16) = 0 .0 0 0 0 0 0 Maximum Z - D is p la c e m e n t ( a t Node: 24) = 3 2 .3 3 9 4 7 6 NETWORK ( V e r : 2 .6 0 ) [ R e a c t i o n s ] P a g e : 8 P r o j e c t : SAMPLE D a t e : 0 6 - F E B - 96 SUPPORT REACTIONS NODE CODE X-REACTION Y-REACTION Z-REACTION 2 111 0 .6 6 3 0 .0 0 0 6 i l l 0 .0 0 0 0 .6 2 4 0 H I - 0 .6 6 3 0 .0 0 0 16 H I 0 .0 0 0 - 0 .6 2 4 0 .148 -0 .149 0 .148 -0 .149 STATIC CHECK SUM OF THE APPLIED LOADS SUM OF THE SUPPORT REACTIONS 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0011 NUMBER OF SLACK MEMBERS NETWORK (Ver.-2.60) [Member S t a t i s t i c s ] P a g e : 9 P r o j e c t : SAMPLE D a t e :0 6 -FEB - 96 MEMBER STATISTICS • .................. MAXIMUM TYPE FORCE S . F . 1 0.100 100.00 2 0.100 100.00 3 0 .3 3 2 7 2 .2 8 AT 21 24 7 (N o te : S .F . S t a n d s f o r S a f e t y F a c t o r ) MINIMUM ■ FORCE S .F . 0.100 100.00 0.100 100.00 0.2 5 1 9 5 .6 4 AT 47 56 8 - AVERAGE ----- FORCE S . F . 0.100 10 0.00 0.100 1 0 0.00 0.298 8 0 .6 4 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3 Stress Analysis: Stress analysis is a critical step in the design of fabric structure. The behavior o f the structure in response to loads like dead load, snow load, and wind uplift have to be considered to design membrane strength and elasticity. The thickness and the quality of the fabric used depends on the span and the intended use of the structure and so does the allowable stresses. During erection the possibility of the workmen getting on top of the fabric to work on it has to be considered, bolting and fabric attachment to other components of the structure has to be done on the field by getting on top of these membranes. Architectural fabrics are good in taking dead loads in die range 50-100 lbs/sqft. Care has to be taken to prevent tears, once a tear develops the fabric shears along the line o f the tear and may cause collapse or damage. A secondary system of support can be considered to take care of the fabric failure. Some of the standard information is given below to help in the design. Water collection on top the fabric can also cause undesirable stresses, water should be channeled out like any other structure. Although the architectural fabric is water proof, it is undesirable for water to collect and stagnate as it can be seen from the under side due to the translucency of the material. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress Display Module: The stress visualization in a fabric structure is very helpful because only alphanumeric values in the form of long data outputs is not very versatile in finding the critical stress areas. It is rather a situation of a needle in a hay stack. The FabCAD program uses a method of color coding method to identify members which fall in a certain stress value range. The user can specify the range for e.g. 1-10 or 1-15. The program then takes the maximum and the minimum values of the stresses from the data files and divides them into 10 to 15 ranges and then based on the user specification of the color, the program assigns a color code to each range and generates a color hard copy on a color printer or on the screen. Apart from the colors, the program can also print the numeric values of the stresses on each line element in the structure. A combination of color and numeric designation can also be adopted to get better results. Although the user can customize the ranges and the color values the program offers default values. The advantage of this program is that it can be targeted to look for a certain range of stress values that are critical. The high stress areas or the members with slack in them can be located easily even in complex geometry as the colors can be customized to be assigned to these members. The numeric designation helps on normal printers that do not have the color option. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Program Description: Fstress.lsp This program basically compiles data from the GEO (geometry file) and formats in way, that it collects all the data for stresses and all the data for the geometry separately and then it loops through the data and draws each line again but with a new color and a stress range value printed on it. The stress range and color have to be specified initially. The max and min stresses in the membrane are displayed in a message box, refer fig 4.3c Command: Fstress (enter) Select the .GEO file: select a geometry file (enter) Enter range limit value: <10> : 10 (enter) t a f C A D • [ U M W M C O I ^ flic E4H yiew Qaia Q ptisni |jc la L h l JS nun* h t» n i.a M fonM nd ttrM * B f»l S iJM M ! •/ Fig. 4.3 a. Dialogue box for stress analysis 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A t t o C A D • H J K H A U t D I ^ " A m O W N e w e t* . I ' ^ M lIM M p i r * r r n f " ! X £ 7 4 * l J M k - W X ^ :-y F ig .: 4.3 b Max and Min stress display m i ro 34 5 1 ® < } A ^ I m I c _ fl 0 ) c b < $ Q & $ ® 3*-'' T m I ? , T g ; . i ir i ( ? , ( •» -' < ? < j > -a a -L a 3 > $ q i a - i . f f l ; ~W -tpr ^ o> <i 3> f f l 1 a \ 0 1 m Fig. 4.3 c : Numeric values of stress printed on the elements 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4 PATTERN DESIGN: (Paraphrased from Hangleiter and Grundig, 1986 : 60) The point is that, strips o f serially connected triangles can be deformed into flat sheets without stretching. Pattern cutting is a post processor module in the Fab- CAD program. The process consists of first using a triangulation method to divide every strip o f fabric into small triangles. The process asks the user to draw the diagonals as shown in the figure below. After the user has drawn the diagonals, the program takes over the process of transposing each triangle from the 3d-space coordinates to the world coordinate system. The triangles are connected serially to reconstruct the strip flat on the ground. Fig. 4.4 a: Triangulation 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (OCS)’ ’ In the OCS of each triangle all the vertices have the “ z " The theory of triangulation is based on the fact that the triangle is a very stable shape and the three vertices o f the triangle form a plane which forms the “Object coordinate system, component as zero and thus the form a single plane. The triangles are transposed piece by piece to the World Coordinate system and are serially arranged to construct the pattern flat on the ground. 7 f Fig. 4.4 b : Transformation from OCS to WCS 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Com pensation Factor: The object o f the design process is produce a structure that will assume a shape when it is prestressed. This implies that cables and the fabric must be fabricated smaller so that they will fit together when prestressed. Patterning must include a compensation for elastic elongation due to prestress. This compensation is done at the end o f the patterning process. The compensation depends on the moduli of elasticity in the fill and the warp direction. Each strip of fabric is treated as a block and the X-direction (warp) and the Y-direction (fill) or vice versa. They are scaled according to their respective modulus of elasticity. If El and E2 are the moduli of elasticity in the fill and the warp direction then, using the formula for the modulus o f elasticity o f a material we have. E= Stress/strain therefore, E = (P/A) x ( L /aL) aL = PL/EA Cross multiplying, we have E Modulus of elasticity (PLI -Pounds / linear inch) P Applied force A Area of the member (Inches) aL Change in length L Original length 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thus, the change in length in both the fill and the warp direction can be computed given the values of their moduli o f elasticity, area, stress and original length. All o f this information can be found once the analysis of the membrane is complete. The file with the extension of GEO is used to get all of the above information. The moduli o f elasticity is taken from the input file. i — C'j > > \\ s i_U M WARP -DIRECTION Fig. 4.4 c : Compensation factor XI - X2 = LI change in length in the warp direction. Y1 - Y2 = L2 change in length in the fill direction 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Characteristics of patterns: a. The geometry o f the membrane structure which is the result o f the form finding determines the orientation o f the membrane strips. --for shapes such as a hyperbolic paraboloid or hypars and saddle-shapes the strips are generally parallel to each other and run in the principal direction o f the forces. — for shapes that are tent-like or which show humps or peaks, the orientation of the strips are radial. -f o r some cases a combination o f both, radial and parallel are used. V / V Fig. 4.4 d : Different Types o f patterns 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b. The orientation o f the strips has to be fixed in such a direction, that the warp and the fill directions follow the direction o f the principal stresses and principal curvatures. c. The widths o f the membrane strips depend on different factors: -on width of the fabric manufactured usually about 52 -56 inches wide. -on a maximum strip width for ease o f production and for minimal lengths of seams -greater the curvature of the surface, the smaller the strip width will have to be, to limit distortion when the strips are flattened into the plane. d. Minimizing the waste The strip boundaries should be straight and as parallel as possible. This requirement can be fulfilled selecting geodesic lines as seam edges. The main requirement for the best membrane strips which will be sewn in order to generate the surface are that those strips are straight as possible in order to avoid a change o f the prestress which might cause wrinkles in the material or an overstressing. These requirements are contradictory to a certain extent because only narrow strips o f changing width according to changes o f curvature, guarantee small distortions while wide and straight strips minimize the amount o f material. A compromise has to be found selecting those strip boundaries which allow for wide and undistorted strips. 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The strip boundaries can be calculated following the geodesic lines on the surface. For small parallel strips boundaries, the geodesic lines should be as parallel as possible. This is only feasible if the curvature of the shape doesn’t change too much along the geodesic lines. It is therefore an essential task to find those geodesic lines as strip boundaries which make full use of the material and which keep the influence of the distortion small. Fig. 4.4 e : Strips arranged to fit within the width o f the fabric Orientation o f stnps minimize the wastage of material e. Interesting visual patterns can be achieved by using seam orientation, enhancing the effect o f the fabric structure. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PROCESS SEQUENCE: The whole process of pattern cutting can be understood by a flow chart as shown below. FORM FINDING TRIANGULATION GEODESIC LINES J ■\L / ! /_L\ \ FLATTENING THE STRIPS ) Fig. 4.4 f : Pattering process sequence 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CUTTING O F PATTERNS: The Fab-CAD program generates an output that can be used both for manual cutting and computer guided lasers and rotary knives. M anual cutting: The program generates an output in the form shown below, in which each strip of the pattern is laid out on the plane and one edge along the length of the strip is aligned with the material which is usually 52-56 inches wide and 150-200 feet long. Each unique strip o f the pattern is annotated to identify one piece from the other. A convenient grid of usually 2 feet, 4 feet or 6 feet can be chosen to mark the various points on the material from which the strip is going to be cut. The material is held down on the cutting tables with adhesives tape and the pattern strips are cut using blades or electric cutting machines operated by hand. In some cases where the fabrics are too long and wide to be cut on the table, they are cut by using paper templates put on the ground. Manual cutting requires the co- ordiantes set off on the pattern. 1*1.65 . T M 4S J7 Grids are marked on the cutting table \ to assist in cutting. The co-ordinates \ are given every 18 to 24 inches or at end points o f lines forming the curve. / x = 0 i K * = . 1 0 0 Fig. 4.4 g : Anotation for manual cutting 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Time Factor: It usually takes about 4-5 hours per strip o f approx. 25-30 feet long and 52-56 inches wide. There are also other factors that determine the time taken, like number o f people working on it etc.. The manual cutting method is the most commonly used but the disadvantages o f this method is that the accuracy cannot be maintained and the curves are not very smooth at the edge o f the strip. These small inaccuracies can aggravate the stresses in the fabric and can also cause wrinkles. (Photographs, Courtesy : Academy Tents). Fig. 4.4 h : Manual cutting table and cutting device Fig. 4.4 I : M anual cutter O Fig. 4.4 j : W elding machine 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C om puter Aided Pattern cutting: (Photgraphs, Courtesy : Eastman Technologies ) The process o f pattern cutting has been drastically modified using computers. The production speed and accuracy can be easily checked and controlled. Plotters as an output device has been known for a long time but the fact that the same pen holding and drafting device can hold lasers and rotary knives has been an investigation in this part o f my research. The fab-CAD program can also write out file format that can be genetically read by flat bed plotters. The program can write out files like DXF, HPGL, IGES or STL (stereo lithography) which are the common formats for input to many CAD-CAM machines. Flat bed plotters have proved to be an asset to the textile industry. Flat bed plotters work on the same concept as the normal plotters, the only difference being that they can substitute pens with sharp cutting knives that can easily cut fabrics or polyester materials. They can be 17 feet wide and upto 150 feet in length. These plotters can cut fabrics upto accuracies of +/- 0.05 inches. They can cut fabrics in the excess of 50 inches per second, thereby increasing the production capacity tremendously. C utting devices: The carriage will accept several different cutting devices. Electrically driven round knives, rotary pressure knives, reciprocative textile knives and laser cutters have all been successfully installed on these plotters. Ultrasonic and wateijet cutting devices are being tested for future implementation. A powerful vacuum holds the material in place atop the cutting table which ensures that the fabric does not develop wrinkles or encounter slippage during the cutting. 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.4 k : 1" round knife in the cutting process. Fig. 4.4 1 : Cutting of pattern using CCte laser. The heat of the laser seals as it cuts and as a result there are no loose fibers at the edges. The laser leaves the edges brown due to the burning effect. Speed and accuracy are some o f the advantages using the laser knife. 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.4 m: Fully computer controlled Cutting machine. The carriage can hold lasers, rotary knives and other cutting tools. The machine can also be put into manual mode or partial mode. The fabric is held down by powerful vaccum pumps located on the under side o f the table. Fig. 4.4 n : Control panel on the flat bed plotter/cutting machine and joystick for minute manoevers. 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The Fab-CAD program outputs the file into the format that is best suited to the cutting device. The most popular file format is the DXF-Data exchange format, an ASCII format that can be read by most graphic application. The IGES (Initial Graphics Exchange Specification) is device independent, system independent, and has a degree o f version independence that makes it suitable for data transferes. IGES is superior if you are translating to or from a CAD/CAM system that doesn’t support DXF or supports it poorly. The program can also output an STL (Stereolithogrphy) which can be read by many Steriolithograp Apparatus. In this case the pattern is coverted into a solid by giving the actual thickness defination, the STL file coverts the solid into small triangulations, this helps to get good accuracy especially if the pattern is to long. Lastly the program can also output a HPGL a commonly used file format for plotting. In this case the cutting knife is assumed to replace the pen in the carriage and cuts instead o f drawing. The architectural fabric is thick as compared to regular fabric. It should be treated as a metal sheet with the same guage and programs designed to take account of the same. Neglecting the thickness factor can result in wear and tear o f cutting knives or may result in just indentation on the fabric surface, instead of a cut. Especially the laser when used for cutting needs to consider material thickness and adjust the speed so that the laser beam stays at a point on the fabric just enough time to cut it. Slow laser can bum the fabric and fast might just graze the surface and indent it, instead o f cutting it. The cutting device considers the surface o f the material and the thickness to adjust the speed and pressure. 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 5.1 a: Site Plan (Canty, 1990: Architectural Record) 5. SAN DIEGO CONVENTION CENTER: San Diego, California. OWNER: Port o f San Diego ARCHITECTS: Arthur Erickson and Associates ENGINEERS: John Martin and Associates (Structural) Horst Berger Partners (Tent Structure) GENERAL CONTRACTOR. Tuto— Saliba— Perini FABRIC ROOF: Birdair Inc. 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig 5.1 b: Rendered View San Diego Convention Center Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F i g 5.1 c : S a n D ieg o Convention Center (Paraphrased from Associated Construction publication, 1989: 20-26. Kay, 1989: San Diego Union. Canty, 1990: Architectural Record. Data provided by San Diego Convention Center, Communications Dept.) The challenge in creating a successful convention center is to induce an efficient, stimulating environment for the communication o f information and ideas at formal and social levels. The San Diego climate and waterfront settings offered a rare opportunity to meet that challenge in creating a truly unique facility- unlike any other in the world. The convention center at San Diego, rises above the mundane requirements of the project, featuring all the necessities required to accommodate large meetings and events. It incorporates the latest technology in concrete, metal, glass and tensile fabric systems to synthesize operating efficiency with the beauty o f the place. Located on 11.2 acres o f waterfront site near downtown San Diego, the center has a total of 1,700,000 sq.ft including 2000 cars, two level garage below grade. The building consists 250,000 sq.ft o f open air flat floor exhibit area, 100,000 sq.ft o f open air flat floor exhibit covered by the largest clear, span, cable-stayed tensile structure in the United States at its time. The 100,000 sq.ft of meeting rooms can be subdivided into 35 separate spaces for various utilities. The $118 million facility features novel conciete fins and a fabric roof over half the building to give it a nautical motif. 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Superstructure: Angular concrete fins, rise 120 ft high, creating a archway inside to accommodate the lobbies and vertical circulations. The fin beams, 6'-6" wide and 3’-10” deep are placed at 50 ft intervals along the periphery of the building. The main exhibit halls, having a floor area of about 254,000 sq.ft and a clear height o f 30 ft, are designed for live loads upto 350 lbs\sq.ft. Huge transverse steel trusses in the hall, to hold the concrete roof slab with loads upto 150 lbs\sq.ft, are held on the diagonal arms o f the internal steel column clusters placed at a distance o f 134 ft. Shear walls, 70 ft high, are placed along the periphery o f the building. The exterior light colored concrete has been sand blasted and curved green tinted glass fills the area between the fins along the side of the structure, giving the building a elegant transparency. Fig. 5.1 d: Sectional elevation (Canty, 1990: Architectural record) 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Tensile roof: (Canty, 1990: Architectural Record) The 100,000 sq.ft o f open-air space, topped by a tensile fabric roof, exploits the Southern California's benign climate and the center’ s prominent site at the edge o f the San Diego bay. The Teflon coated glass fibre roof covers the outdoor space, held 90 ft. above the deck by an elegant web of cables. The roof has 15 percent translucence to let light in with minimum heat gain, reducing lighting and cooling costs while increasing the aesthetic value of interior spaces. The reflective surface o f roof becomes luminous when backlit, creating a dramatic effect at night. The dynamism o f tensile fabric systems is that the whole structure is designed to move and flex.’ Because a tensile structure flexes in response to changing forces, lateral loads are absorbed primarily by the roof itself. The roofs aerodynamic shape helps deflect wind loads upto 70 mph in the bay area and minimize its load on ground. The glass fibre o f the roof weighs only 2 Ibs/sq.ft, roughly 1/15 of a steel framed roof structure and only 1/40 o f a concrete roof. Fig. 5.1 e: Roof plan (Canty, 1990: Architectural record) 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The roof comprises o f five fabric modules, each 50 ft. wide. Valley cables spanning between pairs o f concrete fins form the module along the long edge. Suspension cables in the center line o f each module, carry two flying poles or struts. The cables fork just above the membrane to reach the top of two adjacent fins, where they are anchored. The two masts, forming the high points, with the sequence o f high and low points along the edge, create a very stable saddle or antisynclastic shape. A smaller "flyover" roof is suspended above the center of the main tent to protect its ventilation openings from rain. The secondary roofing fabric is attached to the mast-heads at its edges and anchored to the fins. The edges along the longer side are held up by a steel framework running along the center o f the roof. The steel framework forks at its ends to create a dynamic entrance canopy. Stabilizing cables run along the length o f the fabric. Together, the precisely calculated forms o f ridge and valley cables create a structurally stable shape capable of sustaining heavy loads. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES Burkhardt Berthold (1971): Canty Donald Drew Philip Geiger David Herzog Thomas (1990): (1976): (1988): (1977): Hangleiter. U : (1986): Proceedings, & & Grundig. L. Otto Frei Schierle G.G. Shaeffer R.E. Thronton John (1967-69): (1968): (1994): (1992): Youssef Nabhi: California Builder (1989): & Engineer Institute o f Lightweight Structures IL5 Volume one, Architectural Record, McGraw-Hill, Inc. (Aug). Tensile Archilecture:WestView Press, Colorado. Building Design & Cowsrrwc//oH: published by Oxford University Press, NY (May) Pnuematic Structures. A hand book of Inflatable Architecture. “ Cutting Pattern fo r Membranes": LSA86, Sydney. Tensile Structures: Cable Structures, volume two. Light weight Tension Structures. Fabrics & Architecture. (Sept-Oct) Architects Journal: Membrane Structures: part 1 (Sept) Getting Design on Site, Membrane Structures: part2 (Sept). Seminar on Structures, course 313 Dept. O f Architecture, USC. Associated Construction Publication North edition, (Sept). IL Expo '67 Montreal: German Pavillion (1968) Stuttgart, published in co-operation with the German Ministry of Federal Property. The Architectural Fabrics o f the Future: Data compiled by Seaman Corporation. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. APPENDIX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.1 TUTORIAL This tutorial explains the Dynamic relaxation software by taking a simple example of a Hyperbolic Paraboloid. This tutorial assumes that the user has some knowledge of AutoCAD Rel. 12 or higher, although the commands are explained in every section. Z=0' Saddle shape View 60’ square in plan STEP: 1 Start Autocad and begin a new drawing called TENSILE (or any name ). --C:\acad (enter) -O nce you are into the main menu of autocad go to menu FILE open a NEW drawing. -E n ter the drawing name as TENSILE. 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STEP:2 In this step we will set up the grid and the snap settings and define the limits of our drawing. -Com m and : Grid (enter) : 48 (enter) -Com m and : Snap (enter) : 48 (enter) -Com m and : Limits (enter) : Lower left comer (0,0) : Upper right comer (2000,2000) -Com m and : Zoom (enter) : All (enter) S T E P :3 In this step we will create some layers on which to draw the different components of the tensile structures. Basically there are 4 layers. 1. L01 this is the layer on which the fabric in the warp or horizontal direction is drawn. It has color RED 2. L02 this is the layer on which the fabric in the fill direction is drawn. It has color GREEN, 3. L03 is the layer on which the cables are drawn. It has color CYAN. 4. SXYZ this is the layer on which the supports are drawn. It has color WHITE. 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (NOTE: All the layer names are in upper case and the "0" is the number zero in the layer name). To add these new layers go to the top of the screen to DATA. Under DATA go to Layers. At the bottom rectangular edit box, put the mouse cursor and hit the first mouse button to activate the window. Type the layer name L01 and hit new on the top of the edit box. This adds the layer L01 to the top window. To change the color go Set color box and choose RED. Do the similar steps to get all the 4 layers mentioned above. Once you have got all the layer names and the specific layer color set up for all the layers, make the layer L01 the current by clicking in the box Current. Click on the OK button to exit the layer window. Layer Control Cunant Layer L03 ' s * Slate i i i l t e i i i M netate 0 On . . white CONTINUOUS L S I On, . ted C O N T IN U O U S L02 On . . gieen CONTINUOUS L03 On . . cyan CONTINUOUS SXYZ On . . white CONTINUOUS jjn lo c fc □ & et C olor,. Sot Unto.. M M w j Select & H Hog, f C i w w t " ] Renege "~j F lteir \ |lo i r 0,1 1 S d - 1 1 O K j Cancel | Help.., I Layer window o f AutoCAD for Windows. 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S T E P :4 In this step we will create the mesh. This program requires the mesh to be composed of small elements like lines which join together to form a mesh. --Make sure the grid is on by pressing the F7 function key, also set the Snap on by pressing the F9 key. --Command : Line (enter) : From p o in t: (Pick a grid point approx at the lower left comer o f the g rid ). : To p o in t: (select a point one grid point to the right of the first p o in t) : (enter) --Change the layer to L02 by going to the settings on top of the screen and then to layer control. Make layer L02, the current layer by clicking on the current layer. -Com m and : Line: (enter) ( Draw a line one grid point in the vertical direction, starting at the left end o f the horizontal line ). : To p o in t: ( Point in the vertical direction and click on the mouse button ). : (enter) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STEP : 5 In this step we will generate a mesh composed of the two lines above forming a single unit of the mesh. Command : Array (enter) : R (enter) : Select objects: (select both the lines) (enter) : No of rows: 30 : No of columns: 30 : Distance between rows: 48 : Distance between columns: 48 : (enter) lUaiilw: - imm W S S B S m 1 gOraaad •d«ne*l • PCirwaad GRID: 48" X 48" Horizontal --Red , Vertical — Green Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STEP : 6 In this step you are going to create the edge cable needed for the tensile structure. Command : Layer (enter) : Set (enter) : Layer name to s e t: L03 This will set the layer L03 as the current layer with the color cyan. Now let us start drawing the arcs to make up the boundary in plan. (At this point make sure that the snap and grid are both on by pressing the F7 and F9 key resp). Command : Arc (enter) : 3Point (enter) : Start p o in t: Pick a point PI approx at one of the grid point at the bottom. : 2nd p o in t: Point at the point P2 at the left side. : End p o in t: Pick a point P3 at the mid of the grid. : (enter) -C om m and : M irror (enter) : Select objects to m irro r: Select the arc drawn. : First point of mirror line : Pick the 2nd point. : Second point of mirror line : Drag your mouse to the right and pick a point. : Delete old objects : No 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. — Command : Mirror (enter) : Select ob ject: Pick both the objects(enter) : First point of mirror line : Pick the point at top : Second point of mirror line : Pick at the bottom point : Delete old objects: No At this point your fig should look like the figure below. —— r a Q p t l o n s I o o l s H e l p mmm B Y L A Y E R X Y> W A V / \ / \ r Y y s s lA k J < > 1 V y s 1 S. ,i j , F 2 * / \ / \ / \ r V - V P I C o aM n d • C a n c e l* ..... I H H W I I i m i M I I H I H I I I I I I I I H M I I I I I H I B n H ^ g j j l C o aaan d 1 | t m b " ; Arc 2 is the mirror o f 1, 3 and 4 are the mirror o f 2 and 1 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S T E P :7 In this step we are going to use some edit commands to trim unwanted lines. --Command : Trim (enter) : Select cutting edges: select all the 4 cyan colored arcs, (enter) : Select objects to trim : Select all the red and the green line touching the cyan colored arcs at the outer edge one by one. ( Note: If the image is too small to select the objects to trim, use the zoom window command from the top menu under display. This is called transparent zooming so as to prevent you from leaving the command trim. Once you are within the magnified zoom you can move around to other places to trim using the pan command ). --Command : Erase (enter) : Select objects to erase : Select all the unwanted lines around outside the mesh to clean up the space. — Command : Redraw (enter) S T E P :8 In this step we will replace all the arc by lines as the program only deals with lines and join each connecting element o f cyan line to the red or green endpoints to create a link . --Command : Erase (enter) : Select objects: Select all the 4 arcs one after the other. :(enter): Erase all the cyan arcs. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -C om m and : Osnap (enter) : Endpoint (enter) -C om m and : Line (enter) : From p o in t: Stan at bottom and point at each endpoint on the red and green line and complete all the link. (Note : make sure all the links join from end to end and the cyan line elements form a closed link). A u to C A D -E F -T U T .D W G I "1 £He Edit yiew gala Options Iools Help 1 1 1 ■ SYLA.YER w A A A \ 17" C om m and: nj , f a m a r mMMii.yiilj;, . Replace the arcs with line segments between the red and green lines to form a closed polygon. 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STEP : 9 In this step we will create the support points i.e the low and high points in the tensile structure. First we will change the viewing direction to make it easy to work in the "Z" axis. Command : Viewpoint (enter) : 1, 1, 1 (enter) Now let us draw small circle at all the node points, on the layer SXYZ to represent the high and low points. Command : Circle (enter) : Radius : 1 (enter) : Center p o in t: pick the bottom point at the tip of the hypar. Similarly create a circle on all the node points. In this example we will create PI and P3 as our high points having "Z" co-ordinates as 8 feet and 15 feet respectively, and P2 and P4 as low points having “ Z = 0 fe e t" PI — 8 feet P3 — 15 feet Command : Move (enter) : Select o b ject: select the circle at PI (enter) : Base p o in t: 0,0,0 (enter) : Second p o in t: 0,0,8' (enter) similarly move P3 to 15 feet in the "Z" direction . 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Now your figure should look like the one in figure below with PI & P3 higher in space than P2 & P4 on the ground plane. *utaaM M i~T or.pw a ■ file Edit View Data Qptlons loots Help BY lA Y tA P 2 : Z=0 P I : Z=81 P4:Z=0 ■land <H-aneel* a la n d ... i M s l B M I S T E P : 10 In this step we will join the cable lines ( cyan colored ) to the high points. We have to trim the cyan colored lines meeting at the nodes and connect the last joint to the support at a height. Command : Select the lines that need to change their intersection points to the center point o f the circle in space. This will activate the grip mode then click the common grip point to move all the line to the point in space. 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This step can be done using any other command as well, the only intent is to get the line endpoints to connect in space to the circle center. Repeat the above steps to join links at the Pt3. Now your figure should look like the figure above. ifrrto C W » ffrT O T .P W O I I f e i 0 * . V ■ D IM il b y u ^ r .M & M f io il ConAand • C a n c e l" E S fCOAMABd ' ..... Command : Save (enter) : File name : TENSILE (enter) 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ST E P: 11 In this step we will run the actual DR software within AutoCAD which does the form finding. Type the following line at the command or load it from the applications menu under tools. Command : (load "network.lsp") (Note: include the open and close parenthesis ). Command : NETWORK (enter) : Input file name : TE ST O l.IN P (ENTER) Note: The file should be 6 characters long excluding the extension of .INP This will run the DR program and switch the screen too text mode and will ask you for Data input of the materials. CABLE 126/ 126 SUPPORT 4/ 4/ UPDATE ELEVATION (Y/N)? Y PROBLEM TITLE .FORM READ PROPERTIES FROM A FILE (Y/N)? N MODULUS OF ELASTICITY 1 = 2 CROSS SECTIONAL AREA 1 = 48 PRETENSION 1 = 0.2 CODE 1 = 1 CAPACITY 1 = 10 TITLE 1 = FILL 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MODULUS OF ELASTICITY 2= 2 CROSS SECTIONAL AREA 2= 48 PRETENSION 2 = 0 .2 CODE 2 = 1 CAPACITY 2 = 10 TITLE ~ 2 = W ARP MODULUS OF ELASTICITY 3=2400 CROSS SECTIONAL AREA 3= 0.15 PRETENSION 3 = 0 CODE 3 = 0 CAPACITY 3 = 2 4 TITLE 3 = CABLE After entering all the data the screen will return to the AutoCAD screen end the drawing Command: End (enter) The computer will return to the command p ro m p t. C :\> C D DR (ENTER) ( OR the directory in which DR.EXE is located ). C :\D R > DR (ENTER) PROBLEM TITLE : TESTOI (Note: Do not use the extension INP above ). The programme will shift to the graphic screen and compute from the give data the form of the tensile structure. It will generate a DXF file called TEST01.DXF Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Start AutoCAD again and open a new drawing called Newform. Now at the command prompt type the following. Command : dixfin (enter) In the File box type : C:\dr\test01 (enter) The form generated will be displayed. You can look at it in different angles by changing the view point. To change the angle of the view, go to the Display on the top menu and select Vpoint -3d select your desired angle and view the new form. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Comparison of lateral performance: Residential light wood framing versus cold-formed steel framing

PDF

Hebel design analysis program

PDF

Interactive C++ program to generate plank system lines for timber rib shell structures

PDF

Catalyst: A computer-aided teaching tool for stayed and suspended systems

PDF

A proposed wood frame system for the Philippines

PDF

A statical analysis and structural performance of commercial buildings in the Northridge earthquake

PDF

Determine the optimum block type for use in Saudi Arabia

PDF

Acoustics of the Bing Theater, USC: Computer simulation for acoustical improvements

PDF

A method for glare analysis

PDF

Emergency shelter study and prototype design

PDF

Statistical analysis of the damage to residential buildings in the Northridge earthquake

PDF

Eccentric braced frames: A new approach in steel and concrete

PDF

Guidelines for building bamboo-reinforced masonry in earthquake-prone areas in India

PDF

Computer aided design and analysis of anticlastic membranes and cable nets

PDF

Investigation of sloshing water damper for earthquake mitigation

PDF

A visual and digital method for predicting discomfort glare

PDF

The response of high-rise structures to lateral ground movements

PDF

Computer aided form-finding for cable net structures

PDF

Bracing systems for tall buildings: A comparative study

PDF

Computer aided value conscious design

Asset Metadata

Creator Ganti, ChandraShekar (author)

Core Title Computer aided design and manufacture of membrane structures Fab-CAD

School (School of) Architecture

Degree Master of Building Science / Master in Biomedical Sciences

Degree Program Building Science

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

Tag Architecture,engineering, civil,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Schierle, G. Goetz (committee chair), Schiler, Marc E. (committee member), Vergun, Dimitry (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-3141

Unique identifier UC11337063

Identifier 1380443.pdf (filename),usctheses-c16-3141 (legacy record id)

Legacy Identifier 1380443.pdf

Dmrecord 3141

Document Type Thesis

Rights Ganti, ChandraShekar

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