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Design of weight-optimized space frame for the Canadian large adaptive reflector Chang, Ya-Ying 2000-07-07

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DESIGN OF WEIGHT-OPTIMIZED SPACE FRAME FOR THE CANADIAN LARGE ADAPTIVE REFLECTOR by YA-YING CHANG B.A.Sc, Civil Engineering, The University of British Columbia, 1998 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 2000 © Ya-Ying Chang, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Department DE-6 (2/88) ABSTRACT The Square-Kilometer Array (SKA) is an international project for building the next radio telescope. With a collecting area of one square-kilometer, the SKA will be 100 times more sensitive than current radio telescopes. The concepts for the SKA elements include nested phased arrays, large spherical reflectors, and many small parabolic antennas. The Large Adaptive Reflector (LAR) is the Canadian concept of building the SKA. The LAR is a long focal-length parabolic reflector which uses an airborne platform to support the focal receiver. The feed is held in plane by a tension-structure consisting of three or more tethers tensioned by the lift of a large helium-filled aerostat. The reflector is made up of segmented panels whose height and angle to zenith of segmented panels can be adjusted to focus on any point within zenith and azimuth angle coverage. Unlike conventional radio telescope, LAR is based on reflective optics thus the usable frequency range is limited by the surface accuracy of the reflector. Main structural components of the LAR are foundations, actuators (primary and secondary), main support structures, and reflector panels. This report includes investigation on the feasibility of using LAR antennas as elements to form the SKA, and the conceptual design of a triangular space frame, which is used as the main support structure. n CONTENTS ABSTRACT ii CONTENTS »LIST OF TABLES v LIST OF FIGURES vi ACKNOWLEDGEMENTS vi1 INTRODUCTION 1 1.1 Historical Background1.2 Research Objectives 4 2 DESIGN DEVELOPMENT 7 2.1 Grid Concept 9 2.1.1 Geometric Layout 1 0 2.1.2 Geometric Layout 2 1 2.1.3 Geometric Layout 3 2 2.1.4 Geometric Layout 4 13 2.2 Summary of Geometric Layouts 4 3 DESIGN OF MAIN SUPPORT STRUCTURES IV . 3.1 Loads 18 3.1.1 Dead Load3.1.2 Live Load3.1.3 Exceptional Loads 19 3.2 Selection Of Structural Types 20 3.3 Truss Design Considerations 2 3.3.1 Truss Design #1 4 3.3.2 Truss Design #2 26 3.3.3 Truss Design #3 7 3.3.4 Truss Design #4 8 3.3.5 Plane Truss Design Summary 29 3.4 Preliminary Design 31 3.4.1 Loads and Deflections 2 3.4.2 Static Analysis Results 5 3.5 Alternatives 36 in 3.5.1 Possible Configurations 38 3.5.2 Additional Requirements for the Main Support Structure Design 43 3.5.3 Structural Analysis 44 3.5.3.1 Combo #31 5 3.5.3.2 Combo #37 6 3.5.3.3 DRAO#l 47 3.5.3.4 Bridging System 8 3.6 Summary of Main Support Structure Designs 49 3.7 Weld Design 51 4 FINAL CONFIGURATION OF THE REFLECTOR 54 4.1 Structural Components4.1.1 Foundation 55 4.1.2 Primary Actuator4.1.3 Main Support Structure 58 4.1.4 S econdary Actuator4.1.5 Reflector Panel 9 4.2 Closure of the Reflector 60 5 CONCLUSION AND RECOMMENDATIONS 62 BIBLIOGRAPHY 64 Appendix A: Truss design calculation 65 Appendix B: Preliminary load deflection calculations 70 Appendix C: ANSYS input and output files 84 Appendix D: Alternative Configurations 93 Appendix E: ANSYS input and output files 99 Appendix F: Connection resistance 140 iv LIST OF TABLES Table 2.1: Required stroke for different focal lengths 8 Table 2.2: Total number of actuators versus different grid sizes 14 Table 2.3: Number of secondary actuators for different grid sizes 16 Table 3.1: Axial forces of Truss Design #1 25 Table 3.2: Member forces for Truss Design #2 6 Table 3.3: Axial force results of Truss Design #3 27 Table 3.4: Results of member forces for Truss Design #3 28 Table 3.5: Summary of loads for each Geometric Layout and grid size 33 Table 3.6: Masses of the alternative configurations 42 Table 3.7: Comparison of static analysis results 9 v LIST OF FIGURES Figure 1.1: Array Pattern of the SKA 2 Figure 2.1: Reflector surface variation for different incoming ray angles 7 Figure 2.2: Geometric Layout #1 10 Figure 2.3: Geometric Layout #2 1 Figure 2.4: Geometric Layout #3 2 Figure 2.5: Geometric Layout #4 13 Figure 2.6: Number of primary actuators and main support structures for different spans. 15 Figure 3.1: Types of trusses 23 Figure 3.2: Truss Design #1 4 Figure 3.3: Truss Design #2 6 Figure 3.4: Truss Design #3 27 Figure 3.5: Truss Design #4 8 Figure 3.6: Member force summaries 29 Figure 3.7: A Triangular Space Truss Frame 31 Figure 3.8: Typical Linear Truss 32 Figure 3.9: Maximum loads on primary actuators 34 Figure 3.10: Arrangement of preliminary design of space frames 37 Figure 3.11: Configuration of triangular modules 38 Figure 3.12: Various geometric configurations 9 Figure 3.13: Target position triangulation concept for the reflector panel measurement. 43 Figure 3.14: Combination #31 45 Figure 3.15: Combination #37 6 Figure 3.16: DRAO #1 7 Figure 3.17: Bridging System 48 Figure 4.1: Structural components 54 Figure 4.2: A hexagonal panel 9 Figure 4.3: Large Adaptive Reflector 60 Figure 4.4: An example of forming the entire reflector 61 vi ACKNOWLEDGEMENTS I would like to thank my thesis supervisor, Dr. Siegfried F. Stiemer, for his guidance and unwavering support during the preparation of this thesis. The technical advice and continual encouragement from Dave Halliday, P.Eng., Vice President of AGRA Coast Limited and Adjunct Professor of the Department of Civil Engineering, UBC, and David Lo, Chief Engineer, in particular, are sincerely appreciated. I would also like to thank all the staff at AGRA Coast Limited for their assistance and computer resources they have generously provided to my studies. In particular, I would like to thank K. Kiirschner, D. Dobmeier, J. Mitchell, K. Turpin, and P. Yu, who have consistently provided their assistance to me in many difficult situations. Special thanks to Dr. Peter Dewdney, Dr. Brent Carlson, and Dr. Bruce Veidt of the Dominion Radio Astronomy Observatory (DRAO) for their generous assistance throughout the project. vn Introduction 1 INTRODUCTION 1.1 HISTORICAL BACKGROUND Over the past thirty years, steady improvements in receiver sensitivity, digital processing speed, and imaging techniques have resulted in enhancements in sensitivity to all radio telescopes. Astronomers worldwide have a common acknowledgement that the next step in improving sensitivity is to increase the collecting area of the next telescope to one square-kilometer. Large gains in sensitivity are needed to map low-surface brightness emission from phenomena such as HI in the early universe, thermal and non-thermal emission from ionized gas in distant galaxies, and the ionized winds from starts in our own galaxy. This increasing in collecting area would make the telescope one hundred times more sensitive than the Very Large Array (VLA), the benchmark instrument at decimeter and centimeter wavelengths. It is not economical to build 100 VLAs; therefore, innovative techniques should be used to obtain that collecting area. In June 1996, the National Research Council (NRC) published the report "Canadian Radio Astronomy in the 21st Century - The Challenge" which examines the options for a future radio facility for Canada. In this report, it recommends adopting the Square Kilometer Array as the highest priority for a new national radio astronomy facility. Square Kilometer Array (SKA) is an international project of building a radio telescope array with a collecting area of one-square-kilometer. The array pattern of the SKA will approximately cover a circular region about 300km to 1000km in diameter, with a 1 Introduction concentration of elements in the center (Figure 1.1), therefore, a large sparsely populated region will be needed as a site for this array. The Square Kilometer Array Science Workshop took place two years later in Calgary, Canada. The concepts for the SKA antenna array elements include nested phased arrays, large spherical reflectors, and use of many small parabolic antennas. A particular achievement from the Canadian perspective is unanimous recognition that the SKA must cover short centimeter wavelengths, which will have considerable impact on the technology chosen for the SKA. Figure J.J: Array Pattern of the SKA. 2 Introduction After publishing the report in 1996, P. Dewdney, from the NRC Herzberg Institute for Astrophysics (HIA) in Penticton, BC, contacted researchers all over in Canada. He then organized several research teams from different Canadian universities and industry, which will work together in the next few years with a common objective: study on the realization of the LAR project. In February 1998, the Technical Group working on the development of the LAR held an organizational meeting in Calgary. Under the coordination of Dominion Radio Astrophysical Observatory (DRAO), sub-projects have been identified and the various groups started to work. 3 Introduction 1.2 RESEARCH OBJECTIVES Fully steerable paraboloidal reflectors (conventional design) have been widely used so the construction has been well optimized to minimize cost. The conventional design is limited to about 100m diameter because of the strength-to-weight ration of steel. The present technologies cannot provide larger increases in performance without very large cost. Therefore, new ides and innovations are required to bring down the cost of building large aperture telescope. There are two general ways to save in the cost: (1) eliminate the expensive rotating mechanical structure of steerable reflectors and (2) keep the structure close to the ground and supported by the ground to reducing the problems of gravitational loading. The concept LARGE ADAPTIVE REFLECTOR (LAR) was proposed by Legg, 1998. Its central idea is to use very large f/D (focal length to reflector diameter) ratio so the reflecting surface has very little curvature. An airborne platform is used to support the focal receiver. The basic requirements of the LAR include zenith angle coverage of ± 60°, azimuth angle coverage of 360°. It is designed to operate from 250MHz to 22GHz for a required target surface accuracy of 1mm rms. LAR must be capable of taking on a range of shapes which are sections of an offset paraboloid, so the overall shape of the reflector will consist of a segmented panels that could approximate to the ideal parabolic shape. The telescope is pointed by moving the focus and by simultaneously adjusting the shape of the reflector surface. 4 Introduction The ray angle, 9za, and the focal length, R, define the main geometry of the reflector. The equation below describes the surface of the reflector as a function of position (Legg 1998): x2 cos0!a +y2 cos 1 6_a 4R\ r x 1 + — sin 9, \ 2R (1.1) Where z is the height from the center panel, x and y are the coordinates of interest (x is parallel to the ray path and y is orthogonal to the ray path), R is the distance from the center of the reflector to the focus, and 9za is the zenith angle. The research objective is to investigate the feasibility of using LAR antennas as elements to form the SKA. The following aspects are also considered. 1. Consider innovative alternatives for the overall construction of the reflector, including the innovative use of materials and production techniques, include: an investigation of the feasibility and cost of panels a. Consider alternatives which could improve cost by taking advantage of natural structural bending to minimum actuation. b. Assess alternatives for actuators and determine the cost as function of actuator throw. 2. Consider the impact of reflector diameter and focal length on the actuator cost, and then the whole cost, including a cost versus diameter curve with varying assumptions of focal ratio and frequency of operation. 5 Introduction 3. Consider innovative alternatives for the overall construction of the reflector, including the innovative use of materials and production techniques, include: an investigation of the feasibility and cost of panels a. Consider alternatives, which could improve cost by taking advantage of natural structural bending to minimum actuation. b. Assess alternatives for actuators and determine the cost as function of actuator throw. 4. Consider the impact of reflector diameter and focal length on the actuator cost, and then the whole cost, including a cost versus diameter curve with varying assumptions of focal ratio and frequency of operation. Final parameters of operation to be determined by client. The current project consists of three phases; concept development, detail analysis and design optimization, and final design and documentation. The final reflector module size is a function of structural and cost optimization and will be determined by the project. 6 Design Development 2 DESIGN DEVELOPMENT Geometry of the reflector surface depends on the incoming ray angle the focal length of the receiver. The variations in panel elevation are calculated based on Equation 1.1 and Figure 2.1 below shows that the deflected shape of the reflector surface under operational conditions for a 200m diameter antenna with a focal length of 500m. 12.00 10.00 c CO P- 8.00 i a> 6.00 CD H -«—' O 4.00 Jj 2.0C 0.00 Projection Angle vs Height (for D= 200m) * aw"*" Ii 15 30 45 60 75 90 105 120 135 Projection Angle of Ray Path, Az (deg) 150 165 180 •Za=0 Za= 15 " Za= 30 —*<— Za= 45 •Za= 60 Figure 2.1: Reflector surface variation for different incoming ray angles. 1 y Design Development Table 2.1 is a summary of vertical travel required (also called "stroke") for a diameter up to 200m. Focal length (m) Max. Elevation (m) Min. Elevation (m) Required stroke (m) 500 10.000 2.301 7.699 1000 5.000 1.198 3.802 2000 2.500 0.612 1.888 Table 2. J: Required stroke for different focal lengths. From the geometric study of the reflector surface, it is observed that the required maximum actuator throw increases exponentially with the reflector diameter. socCs*r2 (2.1) Where s is the required actuator throw, and r is the radius of the reflector. The coefficient Cs varies with the focal of the reflector. To accomplish the change in surface shape and curvature, segmental panels should be used make up the reflector surface. These panels are supported on the ground by actuators, which will provide vertical travel to the panels under operational conditions. 8 Design Development 2.1 GRID CONCEPT Conventionally designed antenna uses a rigid backup structure to support reflector surface and the entire structure is steered by a mechanical rotating device, which sits on the ground. However, the design of LAR requires the implementation of segmental panels, considerations of how to place these segmental panels to form the entire reflector is essential. Different fundamental shapes for forming the reflector have been considered and the final choice was made based on that three points are required to identify a plane. Also, fewer actuators are required for a triangular grid than a square grid, or any other shapes. The center of the reflector has little variation in elevation when tracking the radio source, so the center portion of the reflector can be any desired shape. Several shapes for the centerpiece were evaluated. A circular centerpiece is not suitable for it has a curved edge, which would make the segmental panels to be different in size along the radial direction. If a square centerpiece is used, more supports (actuators) are needed than that of a pentagonal or hexagonal centerpiece. Another advantage of a pentagonal or a hexagonal centerpiece is that it can be brake-down into smaller triangular panels if this is required to achieve surface accuracy requirements. Four geometric layouts shown in the following sections were proposed for forming the entire reflector. The idea here is using triangles to map out the surface area of the reflector. 9 Design Development 2.1.1 Geometric Layout 1 The center of Layout #1 is a pentagon panel supported at the center and the corners. This layout is formed with equilateral triangles and two isosceles triangles (66° and 72°). The solid dots indicate the locations of actuators, and each triangle represents a main support structure. Total of five equilateral triangles will be used independently from the choice of grid size. The most often used triangles are in the 72° isosceles triangles. However, equal numbers of isosceles triangles are used for a span of 21m. The longest span will be ~1.2 times greater than the selected grid size. Figure 2.2: Geometric Layout #1. 10 Design Development 2.1.2 Geometric Layout 2 This layout is similar to Geometric Layout #1. Again, the centerpiece is a pentagonal panel. One equilateral triangle, one scalene triangle, and two isosceles triangles (46° and 72°) are used to form this layout. For this layout, the 72° isosceles triangle is used the most, followed by equilateral triangles. The longest span of this layout would be ~ 1.2 times greater than the selected grid size, i.e., the largest span is 24.7m for a grid size of 21m. Figure 2.3: Geometric Layout #2. 11 Design Development 2.1.3 Geometric Layout 3 Geometric Layout#3 has a hexagonal panel in the center and is mapped with only equilateral triangles. Due to its geometry, the design of main support structures and reflector panels are simplified. Figure 2.4: Geometric Layout #3. 12 Design Development 2.1.4 Geometric Layout 4 Starting with a pentagon in the center, Geometric Layout #4 is a combination of equilateral triangles with 3 different isosceles triangles (48°, 72°, and 84°). Similar to Geometric Layout #2, the 72° isosceles triangles are used the most which is followed by equilateral triangles. The longest span will be ~1.3 times longer than the selected gird size. For example, the maximum span will be 28. lm for a grid size of 21m. Figure 2.5: Geometric Layout #4. 13 Design Development 2.2 SUMMARY OF GEOMETRIC LAYOUTS Three parameters were investigated in determining the optimal geometric layouts: 1. diameter versus actuator throw, 2. main support structure grid size verses number of actuators, and 3. panel size. The maximum throw (vertical travel of actuators) is a critical parameter for the reflector. As summarized in Table 2.1, a stroke of 7.7 meters is required if the focal length of the reflector is chosen as 500m and a diameter of 200m which controls the design of actuators. It is recommended that the altitude of airborne platform should not be lower than 500m. Table 2.2 shows the total number of actuators required verses grid size. Each triangle shown in Figure 2.2 to Figure 2.5 represents a main support structure and is supported by three vertical actuators at the nodes. Grid Size Layout # # 1 #2 #3 #4 9 m 476 476 517 476 12 m 291 301 313 291 15 m 196 196 211 196 18 m 136 141 151 141 21 m 101 116 121 111 Table 2.2: Total number of actuators versus different grid sizes. Since triangular units of size 9- 21 meters are the ranges under investigation, these units will have to be filled with smaller sub-structures to provide supports for individual panel, which will have to be individually actuated with short-stroke actuators (refer to as 14 Design Development secondary actuators in the following chapters) to compensate the errors in the primary actuation system. Of the four types of grids presented, only the equilateral triangle form (Geometric Layout #3) can be filled with a single panel. Geometric Layout #1 requires the smallest number of actuators and needs 3 types of unit triangles (as opposed to 1 type and 4 types for the other candidates). The final layout for the reflector will depend on the number of actuators, the type of actuators and the surface accuracy requirements. The results show that the most favorable choice is 21m grid of Geometric Layout #1 with sub structures. Figure 2.6 summaries the number of primary actuators and main support structures for Geometric Layout # 1. Primary Actuators v.s. Main support Structures Span (m) U Primary Actuators • Main Support Structures Figure 2.6: Number of primary actuators and main support structures for different spans. To keep the overall costs of the LAR structure under control, the number of primary actuators has to be minimized (i.e. its spacing has to be maximized). However, the load bearing capacity of a primary actuator is definitely limited; therefore, to achieve a 15 Design Development maximum feasible spacing of primary actuators, the weight of both the main support structure and the panel per unit has to be minimized. The grid size also effects the selection of panel sizes. A desirable size of the reflector panel is 5m, but for numerous grid sizes studied, only the 15m grid can be used with a 5m panel. Therefore, the number of secondary actuators required for each grid size is computed based on different panel sizes for different grid. The possible panel sizes of a 9m span are 3m and 4.5m and since the number of reflector panels should be minimized, panel size of 4.5m is used for computing the number of secondary actuators required. For a 12m span, possible panel sizes are 3m and 4m. A span of 18m can be used with a 4.5m panel or a 6.0m panel. For a 21m span, panel size of 4.5m or 5.25m are both acceptable. The summary of panel sizes verses number of secondary actuators is shown in Table 2.3. Grid Size (m) Panel Size (m) Number of Secondary Actuators 9 4.50 1345 12 4.00 2130 15 5.00 1410 18 4.50 1800 21 5.25 1290 7 able 2.3: Number of secondary actuators for different grid sizes. 16 Design Of Main Support Structures 3 DESIGN OF MAIN SUPPORT STRUCTURES Main support structures provide supports to secondary actuators and reflector panels. The elevation and angle of a support structure are adjusted continuously by controlling the movement of primary actuators to fit the paraboloid of revolution when tracking the radio source. The ideal main support structure is one that is light, stiff and with a minimum number of members. The final design of the main support structures should be cost-effective, easy to construct and easy to transport. To reduce the complexity of interactions, each triangular module should be rigid and independent from each other. The dimensions of a triangular module depend on the loads and surface accuracy requirements. From a practicality standpoint, a reasonable maximum depth for the main support structure is 1.8 m. Tilt component is used to correct for error in the position of the focus on the airborne platform but it is not included at this stage of study. 17 Design Of Main Support Structures 3.1 LOADS Dead loads and live loads are the two load cases considered for the design. Deflections due to dead loads are the error that could be compensated by measuring systems. 3.1.1 Dead Load Dead loads considered for the main support structure were self-weight of the main support structures and the weight of reflector panels. The weight of secondary actuators is negligible comparing to the weight of reflector panels. 3.1.2 Live Load Live loads include wind load and snow/ ice load. Only wind loading is considered when designing the main support structure because this is the component that would introduce error to the measuring system under operational condition. Wind load Wind load is applied perpendicular to the reflector panels and the gust wind factor is taken from NBC (assuming the site at Penticton). Wind load of 15m/s was applied, as for operational condition, to the entire reflector. The structural height was assumed to be 12.0m. Snow and ice load The reflector cannot be operating when snow is covering the reflector surface; therefore, the loading from snow will only increase the deflection of main support structures and it has no effect on measurement accuracy. 18 Design Of Main Support Structures Temperature Load Temperature load is not considered because the main support structures are covered by the reflector panels. In addition, the gap between these two structure components (main support structures and reflector panels) is large enough that there is no temperature gradient. 3.1.3 Exceptional Loads Some possible exceptional loads are earthquake load and impact loads (i.e. wind storms, hail, etc.) and it depends on the region where the radio telescope will be erected. Exceptional loads were no considered in this report. 19 Design Of Main Support Structures 3.2 SELECTION OF STRUCTURAL TYPES Three structural types are considered for forming the triangular module, and these structural types are discussed separately below. Plate girder A plate girder basically consists of flange plates and connected to a relatively thin web plate. It is used for long spans when rolled W sections or WWF shapes do not have the required flexural strength. The typical span lengths for plate girders are 20m to 100m. Since plate girders have very deep slender webs, transverse or longitudinal stiffeners may be used to increase the strength of the web. Usually, heavy concentrated loads and reactions are supported directly on bearing stiffeners. When designing plate girders with long span, economy may be achieved by reducing the area of flange plates where the bending moment is substantially less than the maximum. However, the cost of making flange splices must be balanced against the weight savings achieved. The compression flange may fail either by buckling or by yielding and will generally govern the flange design of a symmetrical plate girder (Handbook of Steel Construction 1997). The orientation of a main support structure depends on the radio ray path. The tilting of the main support structure will result in shifting the central of gravity of the structure, and this will introduce a secondary moment to the structure. Plate girders perform well under pure compression loads, but the secondary moment acting on the cross sectional area of 20 Design Of Main Support Structures plate girders might have warping effects on the structure. Moreover, it is difficult to construct sub-structures within a triangular unit formed with plate girders. Truss A truss is a built-up assembly of axially loaded tension ties and compression struts. It consists of a top and a bottom chord, connected to each other by vertical and /or diagonal web members. Angles, channels, double angles, and hollow structural sections are efficient truss members. Trusses generally are long slender structures, so they should be braced laterally to avoid buckling out of the plane of load. Truss depth is determined in relation to the span, loads, maximum deflection, etc., with increased depth reducing the loads in the chords and increasing the lengths of the web members. Efficient truss depths range from 0.08 to 0.12 of the span length. Open web steel joists Open web steel joists are standardized prefabricated trusses. There are three categories (Spiegel and Limbrunner 1997): 1. Open web steel joists, K-series: shallow trusses with parallel chords. For a span up to 60 feet with a depth of 8 inches to 30 inches. 2. Long span steel joists, LH-series: usually used for a span of 60-96 ft and a depth of 18-48 in. 3. Deep span steel joists, DLH-series: for span up to 144-ft with a depth of 52-72 in. Generally, open web steel joist are lighter than truss and thus has a lower unit cost ($/meter). Open web steel joists are commercially available, however, it cannot handle 21 Design Of Main Support Structures high compressive forces. Both custom-design trusses and open web steel joists can be used to form the triangular space frames. The selection between custom-designed trusses and open web steel joists will depend on the loads from reflector panels. 3.3 TRUSS DESIGN CONSIDERATIONS The preliminary design of the main support structure consists three linear trusses that form a space truss frame (or a triangular module) and is filled with subs-structures. Hollow structure section (HSS) is selected as the member type for savings in transportation and erection due to less weight than rolled plates. It also represents the most efficient use of a steel cross-section in compression. Two important points are considered when designing hollow structural sections (Packer and Henderson 1997). 1. Chords should generally have thick walls because the stiffer walls of chord members resist loads from the web members more effectively, and the connection resistance increases as width (or diameter) to thickness ratio of the chord decreases. 2. The connection resistance increases as the ratio of chord wall thickness to web wall thickness increases, so webs should have thin walls. In addition, thin web walls will require smaller fillet welds for a full strength joint. Large thin section for a compression chord is more efficient in providing buckling resistance, so for this member the final HSS wall slenderness will be a compromise between connection strength and buckling strength. 22 Design Of Main Support Structures Circular HSS are more expensive to fabricate than rectangular (or square) HSS. Connections of circular HSS require that tube ends be profile cut when the tubes are to be fitted directly together, unless the web tubes are much smaller than the chords. The most common planer trusses have Warren and Pratt web configurations which are efficient for spans over 20 meters. Longer spans might require two-way trusses which would involve primary trusses in one-direction and secondary trusses spanning between the primary ones. Common truss types are shown in the figure below. PR ATT VJERENOEEL BOWSTRING WARREN WARREN F)NK KNEE BRACE SCISSORS Figure 3.1: Types of trusses. 23 Design Of Main Support Structures 3.3.1 Truss Design #1 Warren truss provides the most economical solution since long compression web members take the advantage of the fact that HSS are very efficient in compression. Warren trusses also provide greater opportunities to use gap joints. This design is a typical warren truss (Figure 3.2). The distance between panel points is assumed to be 5.25m and the depth of the truss is 1.8m. Since the size of reflector panels has not yet defined, the load is calculated for a lightweight concrete panel with a thickness of 5.0 cm and an uncertainty factor of two is then applied. A concentrated load of 40kN is applied at all panel points except at the mid-span, where a concentrated load of 80kN was applied to taking into account of the load transferred from substructures. Elastic analysis is used assuming that all members are in jointed. ABC D E ,0 w. F G H I Figure 3.2: Truss Design #1. The member axial forces were determined by a pin-jointed analysis and are illustrated in Table 3.1. Negative value means the member is in compression and positive value means the member is in tension. Due to its geometry, the table shows the member forces for half of the truss. Top chords were under compressive loads and bottom chords were in tension. Web members were either in compression or in tension. 24 Design Of Main Support Structures Top Chord Fab -116.7 kN Fbc -291.7 kN Bottom Chord FfR 233.3 kN Fgh 350.0 kN Webs Faf 141.5 kN Fbf -141.5 kN Fbg 70.7 kN Fcg -70.7 kN Table 3. J: Axial forces of Truss Design #1. The maximum compression force is approximately 300kN for top chords, and the maximum tension force in the bottom chords is 350kN. Sixteen connections are required for this truss design, but due to its symmetry, one weld design can be applied to all connections. 25 Design Of Main Support Structures 3.3.2 Truss Design #2 Figure 3.3 shows Truss Design #2, which is based on Pratt truss configuration. Fourteen connections are required for this truss design. Figure 3.3: Truss Design #2. Same load conditions are applied to this design and the results show in Table 3.2. It is observed that the maximum tension force of approximately 250kN was found at the web labeled AF (and at EH by the symmetry of the design), which is twice of the forces in other webs. Since the tension forces in the diagonal webs of AF (and EH) and the bottom chords are approximately the same, these diagonal webs should be designed separately from the other webs. Top Chord Fab -233.3 kN Fbc -350.0 kN Bottom Chord Ffg 233.3 kN Webs Faf 246.7 kN Fbf -80.0 kN Fbg 123.3kN Fcg -80.0 kN Table 3.2: Member forces for Truss Design #2. 26 Design Of Main Support Structures 3.3.3 Truss Design #3 Truss Design #3 is a modified Pratt truss. It is assumed that the truss is simply supported. The angle between the top chord (member AJ3 for example) and the bottom chord (member AF) is 9.7 degrees. Between diagonal webs and bottom chords, the angle is 19.5 degrees. B C D E : :,•;•.•.•.^•.^:;•;';:;v^;':':'X\^^;:'^:v.-i^;:'N^• — kvi-n Jpp P G Figure 3.4: Truss Design #3. Table 3.3 shows the summary of member axial forces. By symmetry, the axial force in member Fae is the same as in member Fed, and this also applies to member Feh which equals to Faf. The result shows that the vertical web (CG) at the center of the truss is not required it bearings no load. Top Chords Fab -466.7 kN Fbc -466.7 kN Bottom Chords Fai 473.5 kN Ffg 118.4 kN Webs Fbf -40.0 kN Fcf 118.4 kN Fcg -120.0 kN 1'able 3.3: Axial force results of Truss Design #3. There are thirteen connections required for this truss design. Special connection design is required at the bottom of the truss. 27 Design Of Main Support Structures 3.3.4 Truss Design #4 This is a modified warren truss; it uses the concept of combining the above two designs. Due to the truss geometry, a vertical web member at node C will have zero force. In order to reduce the amount of material required for this design, the redundant web member is removed. F G Figure 3.5: Truss Design #4. The results of member forces are shown in Table 3.4. From this table, it is observed that all the top chords are in compression with a force of 233kN. The maximum tension force in the bottom chords is the same as Truss Design #1. Twelve connections are required for this design. Top Chords Fall -233.3 kN Fbc -233.3 kN Bottom Chords Ffg 350.0 kN Webs Faf 246.7 kN Fbf -40.0 kN Fcf -123.3 kN Table 3.4: Results of member forces for Truss Design #3. 28 Design Of Main Support Structures 3.3.5 Plane Truss Design Summary Forces in chords and webs were calculated with a formatted spreadsheet and the detailed calculations are shown in Appendix A. The comparison of member forces between the four designs is shown in the Figure 3.6. Truss Design #3 results in highest tension force in chord members. Truss Design #1 and #4 have the same tension force in the chords, however, the tension force in web is much smaller for Design SI. 600.0 400.0 z 200.0 (0 S 0.0 (0 m £ -200.0 -400.0 -600.0 Truss Member Forces Truss #1 Truss #2 Truss #3 •Chord - ten. - Chord - comp. -Web - ten. 350.0 233.3 ^^ -*"--• 350.0 —A 246.7 246.7 -^~~*118.4 -141.5 ^-80.0 ..-120.0 %LL2 —x — X -123.3 jm -233.31 -291.7 -350.0 --466.7 Truss #4 -Web - comp. Figure 3.6: Member force summaries. The dimensions of chords and webs are directly proportional to the maximum forces in the member. According to the design considerations, chords should have thick walls and webs should have thin walls. In another word, the favorable design would have higher forces in chords than in webs. Comparing the tension and compression forces in the members, Truss Design #3 requires a larger cross sectional area for the chords for the highest tension force in all designs, and a larger section is also required for the web to 29 Design Of Main Support Structures avoid buckling. For Design #2, the maximum tension force is higher in the webs than in the chords, which means the required cross sectional area for the webs might be larger than the chords. Truss Design #1 is selected for the preliminary design of space frame structures because of its simplification in connection design. 30 Design Of Main Support Structures 3.4 PRELIMINARY DESIGN The preliminary design of the main support structure consists three linear trusses that form a space truss frame (or a triangular module). Sub-structures are constructed within each triangular module to provide supports for secondary actuators and reflector panels. These sub-structures can also help to reduce the bending at the bottom of main support structures, thus reduce the deflection at the center of the triangular module. Design of sub-structures is similar to the main space truss; sub-structures have the same pipe diameter and depth as the main support space trusses. If necessary, circular pipes connecting to the top chords of the space trusses can be used, in addition to the substructure, to provide supports for the secondary actuators. Figure 3.7 shows the preliminary design of the space frame and Figure 3.8 on the next page shows a typical linear truss. Since each triangular modulus is independent from each other, every primary actuator may support up to a maximum of six triangular modules. Pipes Figure 3.7: A Triangular Space Truss Frame 31 Design Of Main Support Structures Figure 3.8: Typical Linear Truss In order to select suitable width (diameter) and thickness for chord and web members, simple static analyses were performed. The self-weight deflection and wind load deflection were considered for the LAR main support structures. Geometric studies were also carried out to investigate the problem of continual radial and tangential extension/ contraction of the reflecting surface resulting from changes in reflector shape during telescope operation. 3.4.1 Loads and Deflections In the preliminary design stage, the assumption is that the structure is very stiff. The structural performance of the different proposed configurations were evaluated on the basis of dead load and wind load deflections. Deflections due to the self-weight of the structure components are the parameters that can be compensated, so the effects due to dead load and wind load are considered separately. Microsoft Excel was used for the preliminary studies of loads and deflections of main support structures. The results are shown in Appendix B. No load factor is applied at the preliminary design stage. In order to optimize the design, numerous span lengths have been investigated. The span varies from 9 meters up to 21 meters in an increment of 3 meters (« 10 feet). 32 Design Of Main Support Structures Two load cases covered were: • The dead load includes the weight of reflector panels and space frames. Deflection of the truss is calculated based on the following equation. A = ^ (3..) 3S4EI • The wind load case only considers the operational load by assuming wind speed of 15m/s is acting on the entire reflector surface. Assuming structure elevation of 12.0m. The wind pressure is calculated based on the equation below (NBC 1995). P0=9o*ce*cg*cp (3.2) Where q0 = wind pressure at operational condition Ce = exposure factor Cg = gust effect factor Cp = pressure coefficient Table 3.5 shows the summary of loads that applied to a linear truss for different gird sizes. These values represent loads from the largest triangular unit of each Geometric Layout. For example, the largest triangular unit for Geometric Layout #1 is a 72° isosceles triangle. Grid Size 9 m 12m 15 m 18 m 21 m Panel Self-weight Load (kN/m) Layout #1 & #2 1.09 1.46 1.82 2.19 2.55 Layout #3 1.00 1.33 1.66 1.98 2.32 Layout #4 1.14 1.52 1.91 2.29 2.67 Wind Load (kN/m) Layout #1 & #2 0.44 0.59 0.74 0.88 1.03 Layout #3 0.40 0.54 0.67 0.81 0.94 Layout #4 0.46 0.62 0.77 0.93 1.08 Table 3.5: Summary of loads for each Geometric Layout and grid size 33 Design Of Main Support Structures From the deflection calculation results (Appendix B), a Hollow Structural Section (HSS) with a diameter of 168mm and a thickness of 7.2mm was selected for further static analysis which is presented in the next section. This hollow structural section weights 28.3 kg/m, Figure 3.8 shows the maximum loads from reflector panels for different grid sizes. 700 600 (A T3 co o 500 _l "53 400 c CO Q_ 300 um 200 E X 100 co 2 0 Maximum Loads on Primary Actuators • 630 r480 ^275 < r190 12 15 18 Grid Size [m] 21 24 Figure 3.9: Maximum loads on primary actuators 34 Design Of Main Support Structures 3.4.2 Static Analysis Results ANSIS-PC/LINEAR ver.5.4 was selected to carry out the static analysis of the preliminary design of the main support structure. The inputs and outputs of this analysis are shown in Appendix C. Assumptions for the static analysis are: • The span of 21m is used for minimizing the number of primary actuators and main support structures. • The distance between two panel points is assumed to be 5.25 meters. • HSS 168x8 is used for both chords and webs. • Panel weight is applied as a concentrated load of 20kN (assuming the reflector panel is made with light weight concrete and has a thickness of 5.0cm). Maximum displacement of the structure of 16.5mm is found at the center of the space truss with an applied load of 20kN per panel. It is estimated that 165 triangular modules were required to form the reflector and an estimated cost of $6.6M in Canadian Dollars. An increase in the panel distance of a truss could result in a decrease in the number of web members required and hence, the fabrication costs. The longer truss members, however, will be subjected to higher forces because of the greater panel distance. Optimization design of the main support structure is required to reduce the overall cost of the LAR per unit area. 35 Design Of Main Support Structures 3.5 ALTERNATIVES The preliminary design of the main support structure is rigid but is heavy. The cost of the main support structures comes from two parts: material and labor. By reducing the weight of space frames, the material cost can be reduced. However, the bigger portion of the cost is the labor cost for field welding, which is approximately constant for all similar designs. To reduce the labor cost, the number of members should be reduced. Looking closely at the arrangement of the main support structures, it is noted that the two adjacent space trusses are placed side by side (Figure 3.9) and they have to share secondary actuators. The sharing of secondary actuators will increase the difficulty of designing the main support structure and it will also increase of the cost of designing and fabrication. Other configurations for space truss frames are considered to reduce the cost of this structural component. 36 Design Of Main Support Structures Figure 3. JO: Arrangement of preliminary design of space frames. 37 Design Of Main Support Structures 3.5.1 Possible Configurations Because each space frame is independent, the trusses composing the sides of space frames would run side-by-side for adjacent space frames (Figure 3.10). To remove the redundant structure, a new concept is considered. By replacing space frames at alternate triangles and extending truss members to provide supports for secondary actuators at adjacent triangles can reduce the total number of space frame. However, the weight of each space frame might increase. Figure 3.11: Configuration of triangular modules. The big circles indicate the positions of primary actuators and the small circles represent the positions of the secondary actuators. The solid lines represent typical linear trusses. Thirty-one different configurations for the space frame were introduced and are illustrated in Figure 3.12. 38 Design Of Main Support Stmctures Figure 3.12: Various geometric configurations. 39 Design Of Main Support Structures Those alternative configurations for space frame structures are separated into two main groups: Group-A and Group-B. The main difference between the two groups is the number of structure members. Generally, a configuration from group A supports all the secondary actuators on that space frame (illustrated as solid lines in Figure 3.11). There will be three secondary actuators at the center of the adjacent triangle that still require supports, and this is where the Group B configurations fit in. Group A Group A configurations are further divided into 3 sub-groups. 1. Group-Al configurations have main space trusses placed closer to the center of the triangle than the original design. As mentioned in Section 3.4.2, the maximum displacement occurs at the center of a space frame. The idea here is to have the structure members closer to the place where the largest deflection will occur in order to reduce the amount of deflection. In this category, configuration #3 and #5 can only be used with configuration #4 and #6. 2. Starting with the original space frame on the top of the list, the configurations in Group-A2 all maintain the use of three linear trusses forming the space truss frame. The arrangements of sub-structure are somewhat different from the original design in all other possible forms. Three additional configurations were received from Brent Carlson, PhD, Research Council Officer, of DRAO on December 6, 1998; these configurations, labeled as "DRAO," fall into this category and are also included in Figure 3.12 to complete the list. 3. The third group (Group-A3) includes configuration #15 to #19. Instead of fully loading one space frame and removing the adjacent space frame as in Group-Al 40 Design Of Main Support Structures and A2, the load sharing systems between two adjacent triangular units are introduced. All of the configurations in this group have two typical trusses supporting the secondary actuators along two sides of a triangular unit, and sub structures are constructed to stiffen the structure and to support secondary actuators. Group B Group B layouts include configuration #20 to #28. These configurations are separated into Group-Bl and B2. Since the configurations in Group-A3 provide supports to the sharing actuators at only two sides of a triangular unit, a Group-Bl configuration is required to support the remaining actuators. Group-B2 configurations are designed to pick up the three actuators at the center of the neighboring triangular unit of a Group-Al (#1 and #2 only) or A2 configuration. Those configurations were investigated individually in order to select a feasible design for the main support structure. The main considerations are the rigidity of the structure and the field of view for the position accuracy measuring cameras. The weight of each configuration is calculated assuming the chord and web members have the same width and thickness (Table 3.6). Appendix D presents all the combinations of the layouts that demonstrated in Figure 3.11. The combination of configurations #11 and #27 (Combo #37) is the lightest among all other combination, thus requires the least amount of material. 41 Design Of Main Support Structures Group Configuration # Weight per unit (kg) 1 10500 2 12000 Al 3 9900 4 9300 5 10700 6 10100 7 13500 8 11500 9 11500 A2 10 10900 11 10300 12 11000 13 12500 14 11800 15 9100 16 7900 A3 17 8600 18 9600 19 9000 20 7300 Bl 21 6900 22 6600 23 5900 24 3800 25 4800 B2 26 4200 27 1900 28 3100 Table 3.6: Masses of the alternative configurations. 42 Design Of Main Support Structures 3.5.2 Additional Requirements for the Main Support Structure Design For measuring the surface of the LAR, the measuring scheme of using a CCD camera mounted on the ground to image the targets on the back of the panel is introduced. There will be three LEDs attached to the bottom surface of the panel. By measuring the global coordinates of the LEDs with the CCD camera each point on the panel surface and its global coordinates can be calculated. This concept is illustrated in Figure 3.13. In order for CCD cameras to scan the position of the targets, a clear view (also called as "field of view") is required. Figure 3.13: Target position triangulation concept for the reflector panel measurement. Precision Mounted" LEOs 5 m Reflector Panel Back Surface 43 Design Of Main Support Structures 3.5.3 Structural Analysis Due to the additional requirement, the main support structures should not block the filed of view for position accuracy measurements. All the configurations in Group-Al would not provide a clear view for CCD cameras, so these configurations are eliminated from further studies. Besides, configurations in Group-Bl are not rigid structures so they are also eliminated. Since Group-A3 configurations can only be used with a configuration from Group-Bl, these configurations are not applicable for further studies. From Figure 3.12, configuration #10 and #11 are the most suitable layouts for the LAR project. Configuration #10 is similar to the original space frame but without the use of circular pipes connecting top chords. This configuration has approximately the same stiffness as the original space frame but with a lighter weight. Configuration #11 is the lightest among the configurations in Group-A2, so it might worthwhile to study some combinations using these two configurations. ANSYS-PC/LINEAR version 5.4 was selected to carry out the static analyses of the space frames. FEM models for Combination #31, #32, #37 and DRAO #1 were built and analyzed separately to show the typical structural behaviors and properties. The boundary conditions used for the analysis at the three supports were: one fixed in all directions, one is only allowed to move in the radial direction, and one is allowed to move both in radial and tangential directions. 44 Design Of Main Support Structures 3.5.3.1 Combo #31 This combination is formed with the initial design with extended truss elements that act as cantilever beams. It is noted that greater displacements occur at the ends of these cantilever trusses. As a result, greater stroke is required for the secondary actuators. Besides, nine members were connected to the top chord at the mid-pan of the main linear trusses. This complex connection design will result in a higher probability of connection failure. The vertical webs can be removed to reduce the complexities of the connection. Figure 3.14: Combination #31 45 Design Of Main Support Structures 3.5.3.2 Combo #37 This combination is formed with a triangular space truss and is connected by two plane trusses through the center of the space truss. Connection between main planer trusses and substructures are simpler than Combo #31. For this configuration, the maximum number of members that have to connect together is five. However, since plane trusses are not braced, these trusses buckled out of the plane of the load; therefore, high deflections occur at the mid-span of trusses. Figure 3.15: Combination #37 46 Design Of Main Support Structures 3.5.3.3 DRAO #1 This is an idea of combining the two combinations above. The three linear plane trusses are independent from each other and are not linked rigidly. The mid-spans of the linear trusses is experiencing large deflection. The cantilever truss elements are the places where the displacement is at the maximum. Since the trusses are not braced laterally, they tend to buckle out of the plane of loads. Six members are connected at the top chord of the main linear truss. Figure 3.16: DRAO il 47 Design Of Main Support Structures 3.5.3.4 Bridging System The bridging system is similar to Combination #31 but instead of using cantilever trusses, a pair of parallel trusses is used as a bridge connecting two triangular modules. From the analysis on Combo #37, it is clear that a plane truss is not a rigid structure alone; therefore, a modified bridging space truss is introduced. The most complex connection for this configuration is at the place where the space truss is connected to the bridging trusses. The maximum member need to be connected can be reduced to eight if vertical webs are removed. Figure 3. J 7: Bridging System 48 Design Of Main Support Structures 3.6 SUMMARY OF MAIN SUPPORT STRUCTURE DESIGNS Various geometric configurations were laid out for the main backing structure. All of the alternate designs are lighter than the preliminary design. Four configurations were analyses separately by using FEM models. The static analysis results of combination #31, #37, DRAO#l, and Bridging system are presented in Appendix E. When the four combinations were not tilted and only the self-weight (space truss + panel weight) was encountered, the maximum dead load deflections were less than 30mm. Since the backing structures will be adjusted continuously when tracking the radio source, static analysis was also performed on these combinations with arbitrary angles up to 11 degrees. The tilt angles used were -11° about the x-axis (positive towards z-axis) and +6° about the y-axis (positive toward x-axis). The results are presented in the following table. Preliminary Design Combo #31 Combo #37 DRAO#l Bridging System Plane (mm) 16.5 21.9 22.7 25.6 20.7 Tilt (mm) 16.0 48.0 70.0 381.7 30.6 Weight per unit (kN) 368.0 417.6 463.5 401.4 430.5 Units required 165 95 95 95 95 Table 3.7: Comparison of static analysis results Generally speaking, the centers of gravity of the main support structure and the reflector panels shift when the space frame is tilted. The shifting of the center of gravity will introduce a secondary moment to some of the structure members depending on the configuration geometry, so the displacements for the tilt situation is generally greater. 49 Design Of Main Support Structures By comparing the four combinations, DRAO #1 was the lightest and combo #31 was the heaviest with a difference of ~20kN. The results also show that the performance the Bridging system is much stiffer than Combo #37 and DRAO #1. To select between Combo #31 and the Bridging System, one should not only compare the weight and performance of the structure. Even though the Bridging System is slightly stiffer than Combo #31, one the ideal design considerations is that the space frame structure should be light to save the material cost especially when a large quantity of space frame structure is required for the LAR. However, field labor cost for welding on site is another factor to consider when selecting a feasible space frame configuration. For Combo #31, up to nine member are connected together at one connection point. Comparing to Combo #31, the Bridging system will have seven members connected at the mid-span of the main space trusses. In summary, the Bridging System is more feasible than the other combinations for forming the LAR main support structure. 50 Design Of Main Support Structures 3.7 WELD DESIGN Welding costs are sensitive to joint geometry, weld type, and weld size. Joint configurations are increasingly expensive progressing from gap to complete overlap to partial overlap. Gap joints have the advantage of a single bevel cut and complete ease of fitting. Partial overlap joints have double cuts with minimum flexibility in fitting especially if both ends are partial overlaps. Circular HSS do not have large minimum gaps as a function of relative member widths; this makes it possible to employ small gaps as a function of web member wall thickness (Packer and Henderson 1997). Usually, gap connections (for K or N situations) are preferred to overlap connections because the members are easier to prepare, fit and weld. When overlap connections are used, at least a quarter of the height (dimension hi in the plane of the truss) of the overlapping member needs to be engaged in the overlap. An angle of less than 30 between a web member and a chord creates significant welding difficulties, and is not covered by the scope of these recommendations. 51 Design Of Main Support Structures Connection Resistance Calculation The factored resistance of axially loaded welded connections between circular hollow structure sections are calculated based on two failure criterions: chord plastification and punching shear. The connection resistance is calculated for Truss Design #1, as an example, and presented in Appendix F. Because of its geometry, the connection used for Truss Design #1 is K-gap connection. The equations for calculating the factored resistance based on chord plastification are shown below (Packer and Henderson 1997). N]" = ——-sin 0. F *t 2 ( rl \ v° ° ' 1.8 + 10.2^ i V do J sin 0. sin f?2 f(r,g')f(n') (3.3) (3.4) d0 S'=f (3.6) '0 0.2 r 0.024/2 V exp(0.5g'-1.33) + l Where Fy0 is the yield strength of the chord member do and to are the diameter and thickness of the chord respectively. 01 is the angle between the chord and the compression web. 02 is the angle between the chord and the tension web. g is the gap between two webs. (3.7) 52 Design Of Main Support Structures To check for punching shear, the following equation is applicable for all types of connections. N, = f vO . , r\ + sm0.A 2 sin2 0. (3.8) i J The index i =1 for compression web member, and i =2 for tension web members. HSS 164x4.8 is selected for chords and HSS 89x3.8 is used for webs. The sample hand calculations and a formatted spreadsheet printout are included in Appendix F. If the angle between chords and webs is smaller than 30 degrees, the equations above are no longer valid. 53 Final Configuration of the Reflector 4 FINAL CONFIGURATION OF THE REFLECTOR 4.1 STRUCTURAL COMPONENTS Major structural components of the reflector are foundations, actuators (primary and secondary), main support structures, and reflector panels. A briefly description of each structural component is included in the following sections. Figure 4.1: Structural components. 54 Final Configuration of the Reflector 4.1.1 Foundation The primary actuators exert mainly high compressive forces combined with small bending moments due to the tilt of the main support structures; therefore, these foundations can be dealt easily and cost-effectively by applying concrete standard techniques. 4.1.2 Primary Actuator Primary actuators are the linking between the foundations and the main support structures. Their main functions are configuring the shape of the reflector and supporting the main support structures. The primary actuators only move vertically; hence, any reflector surface stretch is achieved with shear and universal joints on the primary actuator crown. The shear forces will cause bending within the primary actuator and these moments need to be transferred to the foundations. Larger throws are usually more complex to construct, associate with higher cost, and may take longer to activate. The type of actuators will depend on accuracy, feasibility, accessibility for maintenance, and the cost. Several possible types of actuators are considered for the LAR project which include water pontoon, Airstroke, and hydraulic actuation and are discussed separately below. a) The water pontoon actuation is having several water ponds at desired radial distances from the center of the reflector. Stroke is provided by releasing water in and out of the water ponds. The advantages of this method are that water is 55 Final Configuration of the Reflector inexpensive and the water pontoon is easy to construct. The disadvantage of this method is that water surface is exposed, so evaporation rate might influence the accuracy of movements. This method is not suitable for the LAR project because for the required stroke of 8 m, it requires a great amount of water for the system. a) The Airstroke idea is using air springs for actuation. These air springs are rubber/fabric flexible bellows which contains a column of compressed air. A single air spring can provide up to 22.5kN of linear force and a stroke up to 35cm. Also, it is permissible to stack Airstrokes to increase stroke. The actuation fluid may be filled with liquid or gas. The advantage of Airstroke is that air is readily available. The disadvantage of Airstroke is that air is fairly sensitive to temperature changes so the accuracy might be affected. In addition, there might be a damping/ resonance problem. Besides, this is a new technology introducing to the telescope design. b) Hydraulic actuation is similar to air actuation but it uses water as the actuation media but water is used instead of air. Hydraulic actuation is a proven technology and it is commercial available. These hydraulic actuators will be contained in telescoping cylinders. The cost is about $70,000 per cylinder. If use hydraulic actuators at every supporting location, 240 cylinders will be required for the proposed geometric layout. One problem occurs when analyzing the structure: the total radial stretch is about 60 cm. For 21 m grid, the radial stretch (max. stretch « 26 cm) and tangential stretch (max. 56 Final Configuration of the Reflector stretch « 16 cm) are too large to be compensated if using vertical actuators. Possible solutions for this problem are 1) using smaller grid sizes to average out the stretch per triangular unit; however, the number of primary actuators required increases, and 2) using sloping actuators. By using smaller grid size (to about 9 m), the amount of stretch per triangular unit is negligible. However, the number of primary actuators increases dramatically. On the other hand, if use sloping actuators moving in the desirable direction (from 1 degree up to 5 degrees depending on the location), the amount of radial stretch per triangular unit is reduced from 260 mm to about 70mm. However, one challenge arises with sloping actuators: telescoping cylinders cannot take lateral loads. To solve this problem, we proposed three solutions: 1. Build a support structure and let the cylinder resting on the top of the structure. The actuators in sliding along the structure in the pre-determined direction. 2. Use pistons inside the cylinders to take the moments. 3. Pinned both the top and bottom of the cylinder so that the cylinders take only axial loads. The innovative design of the primary actuators is using a jacking system as shown in Figure 4.1. The arrangement of the jacking system allows the use of sturdy pipe columns with minimum manufacturing cost. The sequence of jack movement is as follows: when the lower pins are engaged, the lower jacks start to extend. Meanwhile, the upper pins immediately extract and upper jacks retract bringing upper ring down. Then upper pins are engaged in next set of slotted holes. Upper jacks then extend at double the average 57 Final Configuration of the Reflector raising velocity and start carrying load. At the same time, the lower jacks contract at the raising velocity. At the end of the stroke the lower pins are again set and the cycle is repeated continuously to raise the actuator. 4.1.3 Main Support Structure The main support structure supports the secondary actuators and the reflector panels. The elevations and angles of the main support structures are adjusted continuously by controlling the movement of primary actuators to fit the paraboloid of revolution. Each main support structure is a space frame, which is formed with linear trusses and sub structures. The linear trusses and the sub-structures are connected rigidly through welding. The design optimization was discussed in Chapter 3. 4.1.4 Secondary Actuator Secondary actuators are required for compensating inaccuracy of the primary actuation system. These actuators also provide supports for reflector panels and are shared by adjacent panels. The number of secondary actuators depends mainly on the number of reflector panels. Since the required strokes for secondary actuators are much less than that for the primary actuators, commercial products of electrical/ mechanical actuators can be used. Two types of actuators are considered: ball screw actuators and ACME screw actuators. Rubber bearings can be used to connection this structural component to reflector panels. 58 Final Configuration of the Reflector 4.1.5 Reflector Panel Reflector panels make up the reflecting surface of the telescope. The requirements for the reflector panels are that they are inexpensive, easy to construct, and stiff enough to meet the surface accuracy requirements. Different types of constructions and materials are investigated in order to minimize the overall manufacturing cost and to attain the required high precision collecting surface. Hexagonal panel is chosen for it has larger area than a triangular panel and it requires one less support than a rectangular panel. Each panel is support by three secondary actuators at alternate corners. The preliminary design of the reflector panel has a flat-to-flat distance of 5.25m. A possible construction technique is to use steel-fiber reinforced concrete with an embedded steel frame (Ktirschner 1999). Figure 4.2: A hexagonal panel. 59 Final Configuration of the Reflector A possible arrangement of a LAR is shown in Figure 2.8. This picture shows the radio signals come in to the reflector at different angles. These signals are reflected by the reflector panels to the focal receiver, which is lifted by a helium-filled aerostat. Figure 4.3: Large Adaptive Reflector 4.2 CLOSURE OF THE REFLECTOR After selecting the most cost-effective configuration for the main support structure, it is important to layout the combination on the proposed main support structure grid to form the entire reflector. It is noted that the number of triangular units around a circumference is an odd number. If the main support structures are used in a pair, it requires an even number of triangular modulus around a circumference. If one of the combinations is used for the main support structure, the pair of choice will not be able to close up and form the 60 Final Configuration of the Reflector entire reflector. Special designs are required for Geometric Layout #1, #2 and #4 (see Chapter 3). An example of using four different space frame structures to form the entire reflector is shown in Figure 4.4. This form is based on using the Bridging System discussed in Section 3.5.3.4. To fill all of the triangular units, two other space frame configurations other than the proposed Bridging System are needed. Figure 4.4: An example of forming the entire reflector. 61 Conclusion and Recommendations 5 CONCLUSION AND RECOMMENDATIONS Numerous Geometric Layouts were proposed for the Large Adaptive Reflector. Geometric Layout #1, which used three different triangle types, requires the least number of primary actuators when comparing to the other three Geometric Layouts. To form the entire reflector structure, if a 21m-grid size of Geometric Layout #1 is used, it requires 101 primary actuators and 165 triangular units. Thirteen different reflector panel types are needed for Geometric Layout #1. The number of secondary actuators is independent from the design of main support structure, but the grid size and reflector panel size control the number of secondary actuators. Triangular space frames form the main support structure. Three different linear truss designs were evaluated to optimize the design for space frame structure. As discussed in section 3.3.5, Truss Design #1 is superior than the other three designs because of its simplified design of weld connections. Thirteen K-gap connections will be used. The original design of the space frame was estimated to be $6.6 million. This cost is composed by material cost and field labor cost. The optimization of this structural component was done through minimizing the amount of steel used in the construction and reducing the number of connections. For the various space frame configurations, the Bridging System is the most promising design. The maximum dead load displacement is 20.7mm (compared to 16.5mm for the original design) when the system is placed in elevation, and the maximum displacement is increased to 30.6mm (compared to 16.0mm for the original design) when it is tilted at the maximum tilt angle of 11 degrees in the 62 Conclusion and Recommendations radial direction and 6 degrees in the tangential direction. The weight of the Bridging System, including self-weight of the space frame and weight of reflector panels, is ~ 431kN. Even though the weigh of the Bridging System is heavier than the preliminary design, the number of space frame structures required is reduced by a factor of 1.7. In summary, the Bridging System is a feasible solution for the space frame structure for the LAR. The design can still be optimized by examining the trade-offs between structural member dimensions and the deflections of the structure. For example, as the diameter and thickness of the chords decreases, the moment of inertia of the space frame decreases and this leads to a significant increase in deflection of the structure. The increase in deflection would result in an increase stroke for the secondary actuators. Since the bridging trusses are spanning over two space frames, they are actually 'floating' on top of these two space frames. The orientation and position of the bridging trusses are mainly depend on the bridged space frames. Although rubber bearing may be used for connecting the two structural elements (the main space truss and the bridging trusses) of the Bridging System, detail design of the connection is required to check the adequacy of rubber bearing connections if this configuration is selected as the main support structure. Another aspect should put into consideration is the fact that the reflector surface changes its shape when tracking radio signals. As the zenith angle increases, the reflector is actually "closing up." Further studies on the behavior of the reflector are needed to approach the problem of stretching and contraction of space frame structures. 63 BIBLIOGRAPHY Brent Carlson, "Geometry Study and Simulation of a Laser-Free Surface Measurement Technique for the Large Adaptive Reflector," 15 Oct. 1998, <http://www. drao.nrc.ca/science/ska/#documents> (20 Oct. 1998). Kai Kiirschner, "Conceptual Design of the Large Adaptive Reflector Panel for the Square Kilometer Array" (Diplomarbeit/ Master's thesis, University of Stuttgart, 1999). T.H., Legg, "A Proposed New Design For a Large Radio Telescope", Astronomy and Astrophysics Supplement 130 (1998): 369-379. J.A. Packer and J.E. Henderson, Hollow Structural Section Connections and Trusses, 1st ed. (Markham, Ontario: Canadian Institute of Steel Construction, 1992), 41-42, 47-92, 323-41. E. Seaquist, C. Carignan, P.E. Dewdney, A.R. Taylor, and C. Wilson, "Canadian Radio Astronomy in the 21st Century - The Challenge," The Second Report of the NRC Planning Committee for a New National Facility for Radio Astronomy (1996), <http://www.drao.nrc.ca/science/ska/#documents> (15 June 1998). Leonard Spiegel and George .F. Limbrunner, Applied Structural Steel Design, 3rd ed. (New Jersey, Ohio: Prentice Hall, 1997), 361-71, Handbook of Steel Construction, 6th ed. (Alliston, Ontario: Canadian Institute of Steel Construction, 1997). National Building Code of Canada, 11th ed. (Ottawa: NRCC, 1995), 145-46. 64 Appendix A APPENDIX A: TRUSS DESIGN CALCULATION FORMATEED SPREADSHEET PRINTOUT OF TRUSS DESIGNS Appendix A PROJECT LAR SECTION 1 TITLE Truss Design #1: Member Forces DATE 3/02/00 FILE Truss 1 .xls TIME 10:51 AM Case 1: Typical Wairen Truss INPUT Dead load Total length (=span) Unit length Unit depth Modulus of elasticity Angle btw chord & web reactions web length MEMBER FORCES FORCE SUMMARY Max. tension force Max.comp. force chord length required web length required effective length (chord) effective length (web) PRELIMINARY SELECTION Chord Max. tension force Max.comp. force required area Web Max. tension force Max.comp. force required area DL L UL U„ E • RF Faf Fab Fbf Ffg Fbg Fbc Fcg Fgh Fch Fed MaxF Mini" lenc lenw KLc KLw MTFc MCFc Ac MTFw MCFw Aw atan(Ud/(U,72)) -DL*(L/UL+2)/2 sqrt(UdA2+(UL/2)"2) (DL+RF)/sin(0) Faf*COS(6)*-l Faf*-1 Faf*COS(6)-Fbf*cos(9) DL/sin(6)-Fbf Fab+(Fbf-Fbg)*cos(8) Fbg*-1 Ffg+(Fbg-Fcg)*cos(6) 2*DL/sin(6)-Fcg Fbc+(Fcg-Fch)*cos(9) max(Faf,Fab,Fbf,Ffg,Fbg,Fbc,Fcg,Fgh,Fch,Fcd) min(Faf,Fab,Fbf,Ffg,Fbg,Fbc,Fcg,Fgh,Fch,Fcd) 7*UL 8*w,, 0.9*UL*1000 0.75*wL*1000 max(Fab,Ffg,Fbc,Fcg,Fgh,Fcd) min(Fab,Ffg,Fbc,Fcg,Fgh,Fcd) M'I'Fc*1000/(0.9*Fy) max(Faf,Fbf,Fbg,Fcg,Fch) min(Faf,Fbf,Fbg,Fcg,Fch) MTFw*1000/(0.9*Fy) Fy yield strength Note: Positive in tension; negative in compression -40 21 5.25 1.8 200000 0.6 120.0 3.2 141.5 -116.7 -141.5 233.3 70.7 -291.7 -70.7 350.0 -70.7 -291.7 350.0 -291.7 36.8 25.5 4725 2387 350.0 -291.7 1111.1 141.5 -141.5 449.1 350.0 kN Mpa rad kN m kN kN kN kN kN kN kN kN kN kN kN kN mm mm kN kN mm2 kN kN mm2 Mpa 66 Appendix A PROJECT Large Adaptive Reflector SECTION 1 TITLE Plane Truss Design #2: Member Forces DATE 3/13/00 FILE Truss 2.xls TIME 10:18 AM Case 2: Pratt Truss INPUT Dead load DL -40 [kN] Total length (=span) L 21 [m] Unit length uL 5.25 [m] Unit depth ud 1.8 [m] Modulus of elasticity E 200000 [Mpa] Angle btw chord & web • atan(Ud/UL) 0.33 [rad] reactions RF -DL*(L/UL+2)/2 120.0 [kN] web length wL sqrt(Ud"2+(UIy2)A2) 3.2 [m] MEMBER FORCES F»f (DL+RF)/sin(9) 246.7 [kN] Fab - Faf*cos(6)*-l -233.3 [kN] FM Faf*sin(9)*-1 -80.0 [kN] Fbc F»b-Fbg*cos(0) -350.0 [kN] Fbg (DL-Fbf)/sin(9) 123.3 [kN] Ffg Faf*cos(9) 233.3 [kN] Fcg 2*DL -80.0 [kN] FORCE SUMMARY Max. tension force VlaxF = max(Faf,Fab,Fbf,Fbc,Fbg,Ffg,Fcg) 246.7 [kN] Max.compression force VlinF min(Faf,Fab,Fbf,Fbc,Fbg,Ffg,Fcg) -350.0 [kN] Length of the chords Lc 6*UL 31.5 M . Length of the webs U 4*wL+3*Ud 18.1 [m] equivalent length required Vllen = Lc+L„ 49.6 [m] Preliminary Selection Yield stress Fy 350.0 [Mpa] (1) Top Compression Chord max. compression force MCF min(Fab,Fbc) -350.0 [kN] KLtc 0.9*UL*10A3 4725 mm] (2) Bottom Tension Chord max. tension force MTF MAX(Ffg) 233.3 [kN] KLbc - 0.9*wL*10A3 2865 [mm] required area Abc MTF/(ft9*Fy)*10A3 741 [mm2] (3) Web max. tension force MTFW Max(Faf,Fbf,Fbg,Fcg) 246.7 [kN] max. compression force MCF. Min(Faf,Fbf,Fbg,Fcg) -80.0 [kN] effective length (diag.) KL„ 0.75*wL*10A3 2387.1 mm] required area A„ MTF„/(0.9*Fy)*10A3 783.1 mm2] effective length (vert.) KL„ OJ5*2*Ud*10A3 2700.0 mm] effective length (vert.) KU 0.75*U„*10A3 1350.0 mm] Note: Positive in tension; negative in compression 67 Appendix A PROJECT Large Adaptive Reflector SECTION 1 TITLE Plane Truss Design #3: Member Forces DATE 3/21/00 FILE Truss 3.xls TIME 12:05 PM Case 3: Modified Pratt Tinss INPUT Dead load DL -40 [kN] Total length (=span) L 21 [m] Unit length uL 5.25 [m] Unit depth ud 0.9 [m] Modulus of elasticity E 200000 [Mpa] Angle btw chord & web • atan(UyUL) = 0.17 [rad] reactions RF -DL*(L/UL+2)/2 = 120.0 [kN] web length wL sqrt(Ud"2+(U!y2)A2) = 2.8 [m] MEMBER FORCES F.f (DL+RF)/sm(9) = 473.5 [kN] Fab = Fai*cos(0)*-1 = -466.7 [kN] Fbf DL = -40.0 [kN] Ft, Fab = -466.7 [kN] Ffg Fbf/SlN(e)/2+F„ = 355.1 [kN] F,t 0.5*Fb(/SIN(6)*-l = 118.4 [kN] Fgh F* = 355.1 [kN] F[h FCf = 118.4 [kN] 2*DL-(Fch+Fcf)*sin(9) = -120.0 [kN] Fed Fbc+(FcrFch,*cos(9) = -466.7 [kN] FORCE SUMMARY Max. tension force MaxF - max(Faf,Fab,Fbf,Fbc,Ffh,Fcf,Fgh.Fch,Fcg,Fcd) = 473.5 [kN] Max.compression force MinF = min(Faf,Fab,Fbf,Fbc,Ffh,Fcf,Fgh,Fch,Fcg,Fcd) = -466.7 [kN] Length of the chords Lc 4*UL+4*wL = 32.1 [m] Length of the webs Lw 2*wL+4*Ud = 9.2 [m] equivalent length required Mien Lc+Lw = 41.3 [m] Preliminary Selection Yield stress Fy ' 350.0 [Mpa] (1) Top Compression Chord max. compression force MCF min(Fab.Fbc.Fcd) = -466.7 [kN] KL,C 0.9*UL*10A3 = 4725 [mm] (2) Bottom Tension Chord max. tension force MTF MAX(Faf.Ffh.Fgh) = 473.5 [kN] KLhc = 0.9*wL*10A3 = 2497.5 imm] required area Abc MTF/(0.9*Fy)*10A3 = 1503.1 [mm2] (3) Web max. tension force MTF„ Max(Fbf,Fcf,Fcg,Fch) = 118.4 [kN] max. compression force MCFW Mm(Fbf.Fcf.Fcg,Fch) = -120.0 [kN] effective length (diag.) KLW 0.75*wL*10A3 = 2081.3 [mm] required area A„ MTFv,/(0.9*Fy)*10A3 = 375.8 [mm2] effective length (vert.) KLvi = 0.75*2*Ud*10A3 = 1350.0 [mm] effective length (vert..) KLv2 = 0.75*Ud*10A3 = 675.0 [mm] Note: Positive in tension; negative in compression 68 Appendix A PROJECT LAR SECTION 1 TITLE Truss Design #4: Member Forces DATE 3/21/00 FILE Truss 4.xls TIME 12:07 PM • Case 4: Modified W'airen Truss INPUT Dead load DL kN Total length (=span) L 21 m Unit length uL 5.25 m Unit depth ud 1.8 m Modulus of elasticity E 200000 Mpa Angle btw chord & web • atan(U/UL) = 0.330 rad reactions RF -DL*(L/UL+2)/2 = 120.0 kN web length wL sqrt(UdA2+U,,A2) = 5.55 m MEMBER FORCES Ftf (DL+RF)/sin(9) = 246.7 kN Fab -Ftf*cos(6) = -233.3 kN Fbc Ft = -233.3 kN Fbf DL = -40.0 kN Fcf -Fbf/sin(9)-Ftf = -123.3 kN F% (FuJ-cf)*cos(6) = 350.0 kN Fcg (-FCd+Fbe)/cos(e)+Fcf = -123.3 kN Fed FDT = -233.3 kN Fdg DL = -40.0 kN Fde -F,g*cos(0) = -233.3 kN F* (DL+RF)/sin(6) = 246.7 kN FORCE SUMMARY Max. tension force VlaxF = max(Faf,Fab!Fbc,Fbf,Fcf,Fig,Fcg,Fcd) = 350.0 kN Max.compression force MinF min(Faf,Fab,Fbc,Fbf,Fcf,Ffg,Fcg,Fcd) = -233.3 kN equivalent length required Mien = 6*UL+4*wL+2*Ud = 57.3 m equivalent length required lenc 6*UL = 31.5 m equivalent length required ienw = 4*wL+2*Ud = 25.8 m PRELIMINARY SELECTION Yield strength F, 350 Vlpa (1) Top Chord (Compression) max. comp. Force MCF min(Fab,Fbc,Fcd,Fde,Ffg) = -233.3 kN KLcl 0.9*UL*1000 = 4725 mm (2) Bottom Chord (Tension) max. tcsion. Force VITF = max(Fab,Fbc,Fcd,Fde,Ffg) = 350.0 kN required area Ad, MTF/(0.9*F),)*10a3 = 1111.1 mm2 slcndemcss ratio SR 300.0 effccitve length <*Lbc UL*2*1000 = 10500 mm required radius of gyration ; = CLbc^SR = 35.0 mm (3) Web (i) Compression max. comp. Force Mwc v!in(Faf,Fcf,Fcg,Feg) = -123.3 kN KLWC 0.75*wL*10A3 = 4163 mm (ii) Tension max. tesion. Force MAX(Faf,Fcf,Fcg,Feg) = 246.7 kN required area A„ Mwr/(0.9*Fy)*10A3 = 783.1 mm2 (iii) Vertical max. comp. Force Mwv f(min(Fbf,Fdg)<0,min(Fbf,Fdg),0) = -40.0 kN KLwv 0.75*Ud*10A3 = 1350 mm Note: Positive in tension; negative in compression. 69 Appendix B APPENDIX B: PRELIMINARY LOAD DEFLECTION CALCULATIONS SPREADSHEET PRINTOUTS OF DEAD LOAD AND WIND LOAD DEFLECTIONS Appendix B LAR - DEAD LOAD AND DEFLECTIONS Assumptions: 1. Material for the panel is lightweight concrete. 2. Assume that the panel thickness = 2 inches. Lightweight Concrete^ _16 psf Max Unit Angle Max Unit Angle Triangular Area per Triangular Unit (ftA2) 9 12 15 18 21 (rad) (deg) Unit Size 30 40 50 60 70 1.26 72 Layout #1 414.6 737.1 1151.8 1658.6 2257.5 1.26 72 Layout #2 414.6 737.1 1151.8 1658.6 2257.5 1.05 60 Layout #3 377.6 671.2 1048.8 1510.3 2055.7 1.47 84 Layout #4 433.6 770.8 1204.4 1734.4 2360.7 Angle Angle Total Weight oer Trianaular Unit (lbs) (rad) (deg) 30 40 50 60 70 1.26 72 Layout #1 6634 11794 18429 26537 36120 1.26 72 Layout #2 6634 11794 18429 26537 36120 1.05 60 Layout #3 6041 10740 16781 24165 32891 1.47 84 Layout #4 6937 12333 19271 27750 37771 Angle Angle Weight Supported by Each Truss (lbs)* (rad) (deg) 30 40 50 60 70 1.26 72 Layout #1 2211 3931 6143 8846 12040 1.26 72 Layout #2 2211 3931 6143 8846 12040 1.05 60 Layout #3 2014 3580 5594 8055 10964 1.47 84 Layout #4 2312 4111 6424 9250 12590 Angle Angle Eguivalent Uniformly Distributed Load (lbs/ft) (rad) (deg) 30 40 50 60 70 ( 1.26 72 Layout #1 74.9 99.9 125 150 175 1.26 72 Layout #2 74.9 99.9 125 150 175 1.05 60 Layout #3 68.2 90.9 114 136 159 1.47 84 Layout #4 78.3 104 131 157 183 Angle Angle Triangular Unit Size Moment (Ibs-ft) (rad) (deg) 30 40 50 60 70 1.26 72 Layout #1 8425 19971 39005 67401 107030 1.26 72 Layout #2 8425 19971 39005 67401 107030 1.05 60 Layout #3 7672 18185 35518 61375 97461 1.47 84 Layout #4 8810 20883 40788 70481 111922 (ft) Note: - *Three trusses per triangular unit. -Area per Triangular Unit Size: Total Weight per Triangular -Unit: -Eguivalent Uniformly Distributed Load: Area = ^-*sin(max UnilAngle)*(3.28l)2 Weight = A rea * 16psf Weight w = 3*L -Moment: Moment •• w. *L2 where L is the triangular unit size. 71 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE Elastic Modulus, E = Depth, h = 29000 6 ksi ft Equivalent Uniformly Distributed Load (lbs/m Geometric Layout 30 40 50 60 70 1 &2 74.9 99.9 125 150 175 3 68.2 90.9 114 136 159 4 78.3 104 131 157 183 Top/ Bottom Chord: Pipe Diameter Wt per Pipe Total Wt of Pipes A I d = h/2 l+AdA2 (in) (lbs/ft) (lbs/ft) (inA2) (inA4) (in) (inA4) 3 7.58 15.16 2.23 3.02 36 2893.1 3-1/2 9.11 18.22 2.68 4.79 36 3478.1 4 10.79 21.58 3.17 7.23 36 4115.6 5 14.62 29.24 4.30 15.2 36 5588.0 6 18.97 37.94 5.58 28.1 36 7259.8 8 28.55 57.1 8.40 72.5 36 10959 10 40.48 80.96 11.9 161 36 15583 12 49.56 99.12 14.6 279 36 19201 Web Pipe: Pipe Spacing = 11.5 Wall Total Weight of Web Pipes (lbs/ft) Pipe Diameter Wt of Pipe Thickness I 30 40 50 60 70 (in) (lbs/ft) (in) (inA4) (ft) (ft) (ft) (ft) (ft) 1-1/4 1.68 0.140 6708 3.10 2.93 2.83 2.76 2.72 1-1/2 2.27 0.145 6948 4.19 3.96 3.83 3.73 3.67 2 3.65 0.154 7379 6.74 6.37 6.15 6.01 5.90 2-1/2 5.79 0.203 9727 10.7 10.1 9.8 9.5 9.4 3 7.58 0.216 10350 14.0 13.2 12.8 12.5 12.3 3-1/2 9.11 0.226 10829 16.8 15.9 15.4 15.0 14.7 4 10.79 0.237 11356 19.9 18.8 18.2 17.8 17.4 5 14.62 0.258 12362 27.0 25.5 24.6 24.1 23.6 6 18.97 0.280 13416 35.0 33.1 32.0 31.2 30.7 8 28.55 0.322 15429 52.7 49.8 48.1 47.0 46.2 72 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE. DEFLECTION DUE TO DEAD LOAD ONLY. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 30 ft Depth, h = 6 ft_ Top/ Bottom Chord Diameter Web Pipe Diameter (in) 1-1/4 1-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4)' (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 9601 93.2 0.155 86.5 0.144 96.6 0.161 9841 94.2 0.153 87.5 0.146 97.7 0.162 3-1/2 10186 96.2 0.151 89.5 0.140 99.6 0.156 10426 97.3 0.149 90.6 0.142 100.7 0.158 4 10824 99.6 0.147 92.9 0.137 103.0 0.152 11063 100.7 0.145 94.0 0.139 104.1 0.153 5 12296 107.2 0.139 100.5 0.131 110.7 0.144 12536 108.3 0.138 101.6 0.132 111.7 0.145 6 13968 115.9 0.132 109.2 0.125 119.4 0.136 14208 117.0 0.131 110.3 0.126 120.4 0.138 8 17667 135.1 0.122 128.4 0.116 138.5 0.125 17907 136.2 0.121 129.5 0.117 139.6 0.126 10 22292 159.0 0.114 152.3 0.109 162.4 0.116 22531 160.0 0.113 153.3 0.110 163.5 0.117 12 25909 177.1 0.109 170.4 0.105 180.5 0.111 26148 178.2 0.109 171.5 0.106 181.6 0.112 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 10272 96.8 0.150 90.1 0.140 100.2 0.156 12620 100.7 0.127 94.0 0.119 104.2 0.132 3-1/2 10857 99.8 0.147 93.1 0.137 103.3 0.152 13205 103.8 0.125 97.1 0.117 107.2 0.130 4 11495 103.2 0.143 96.5 0.134 106.6 0.148 13842 107.2 0.124 100.5 0.116 110.6 0.128 5 12967 110.9 0.136 104.2 0.128 114.3 0.141 15315 114.8 0.120 108.1 0.113 118.2 0.123 6 14639 119.6 0.130 112.9 0.123 123.0 0.134 16987 123.5 0.116 116.8 0.110 126.9 0.119 8 18338 138.7 0.121 132.0 0.115 142.1 0.124 20686 142.7 0.110 136.0 0.105 146.1 0.113 10 22962 162.6 0.113 155.9 0.108 166.0 0.115 25310 166.5 0.105 159.8 0.101 170.0 0.107 12 26580 180.7 0.109 174.0 0.105 184.2 0.111 28928 184.7 0.102 178.0 0.098 188.1 0.104 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (in"4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 13243 104.0 0.125 97.3 0.117 107.5 0.130 13243 106.9 0.129 100.2 0.121 110.3 0.133 3-1/2 13828 107.1 0.124 100.4 0.116 110.5 0.128 13828 109.9 0.127 103.2 0.119 113.3 0.131 4 14465 110.5 0.122 103.8 0.115 113.9 0.126 14465 113.3 0.125 106.6 0.118 116.7 0.129 5 15938 118.1 0.118 111.4 0.112 121.5 0.122 15938 120.9 0.121 114.2 0.114 124.4 0.125 6 17610 126.8 0.115 120.1 0.109 130.2 0.118 17610 129.6 0.118 122.9 0.111 133.1 0.121 8 21309 146.0 0.109 139.3 0.104 149.4 0.112 21309 148.8 0.111 142.1 0.106 152.2 0.114 10 25933 169.8 0.105 163.1 0.100 173.3 0.107 25933 172.7 0.106 166.0 0.102 176.1 0.108 12 29550 188.0 0.102 181.3 0.098 191.4 0.103 29550 190.8 0.103 184.1 0.099 194.2 0.105 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Deft. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 15472 116.4 0.120 109.7 0.113 119.8 0.124 16478 123.4 0.120 116.8 0.113 126.9 0.123 5 16944 124.0 0.117 117.3 0.111 127.5 0.120 17950 131.1 0.117 124.4 0.111 134.5 0.120 6 18616 132.7 0.114 126.0 0.108 136.2 0.117 19622 139.8 0.114 133.1 0.108 143.2 0.117 8 22315 151.9 0.109 145.2 0.104 155.3 0.111 23321 159.0 0.109 152.3 0.104 162.4 0.111 10 26939 175.8 0.104 169.1 0.100 179.2 0.106 27946 182.8 0.104 176.1 0.101 186.3 0.106 12 30557 193.9 0.101 187.2 0.098 197.3 0.103 31563 201.0 0.102 194.3 0.098 204.4 0.103 Note: -w1 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #1 & #2. -w3 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #3. -w4 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #4. -Deflection: . ,4 384C7 73 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE. DEFLECTION DUE TO DEAD LOAD ONLY. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 40 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 1-1/4 1-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 9601 117.9 0.620 109.0 0.573 122.5 0.644 9841 119.0 0.610 110.0 0.578 123.5 0.649 3-1/2 10186 121.0 0.599 112.1 0.555 125.6 0.622 10426 122.0 0.591 113.1 0.560 126.6 0.627 4 10824 124.4 0.580 115.4 0.538 128.9 0.601 11063 125.4 0.572 116.5 0.543 130.0 0.606 5 12296 132.0 0.542 123.1 0.505 136.6 0.560 12536 133.1 0.535 124.1 0.509 137.6 0.565 6 13968 140.7 0.508 131.8 0.476 145.3 0.525 14208 141.8 0.503 132.8 0.480 146.3 0.528 8 17667 159.9 0.457 151.0 0.431 164.4 0.470 17907 160.9 0.453 152.0 0.434 165.5 0.473 10 22292 183.7 0.416 174.8 0.396 188.3 0.426 22531 184.8 0.414 175.8 0.398 189.3 0.429 12 25909 201.9 0.393 193.0 0.376 206.5 0.402 26148 202.9 0.392 194.0 0.378 207.5 0.404 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 10272 121.4 0.596 112.5 0.552 125.9 0.619 12620 125.1 0.500 116.2 0.464 129.7 0.518 3-1/2 10857 124.4 0.578 115.5 0.537 129.0 0.599 13205 128.2 0.490 119.3 0.456 132.7 0.507 4 11495 127.8 0.561 118.9 0.522 132.4 0.581 13842 131.5 0.479 122.6 0.447 136.1 0.496 5 12967 135.5 0.527 126.5 0.492 140.0 0.545 15315 139.2 0.459 130.3 0.429 143.8 0.474 6 14639 144.2 0.497 135.2 0.466 148.7 0.513 16987 147.9 0.439 139.0 0.413 152.5 0.453 8 18338 163.3 0.449 154.4 0.425 167.9 0.462 20686 167.1 0.407 158.1 0.386 171.6 0.419 10 22962 187.2 0.411 178.3 0.392 191.7 0.421 25310 190.9 0.381 182.0 0.363 195.5 0.390 12 26580 205.3 0.390 196.4 0.373 209.9 0.398 28928 209.1 0.365 200.2 0.349 213.6 0.373 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 13243 128.2 0.489 119.3 0.455 132.8 0.506 13243 130.9 0.499 122.0 0.465 135.5 0.516 3-1/2 13828 131.3 0.479 122.4 0.446 135.9 0.496 13828 134.0 0.489 125.0 0.456 138.5 0.505 4 14465 134.7 0.470 125.7 0.439 139.2 0.486 14465 137.3 0.479 128.4 0.448 141.9 0.495 5 15938 142.3 0.451 133.4 0.422 146.9 0.465 15938 145.0 0.459 136.1 0.431 149.6 0.473 6 17610 151.0 0.433 142.1 0.407 155.6 0.446 17610 153.7 0.440 144.8 0.415 158.3 0.453 8 21309 170.2 0.403 161.3 0.382 174.7 0.414 21309 172.9 0.409 163.9 0.388 177.4 0.420 10 25933 194.0 0.377 185.1 0.360 198.6 0.386 25933 196.7 0.383 187.8 0.365 201.3 0.392 12 29550 212.2 0.362 203.3 0.347 216.8 0.370 29550 214.9 0.367 205.9 0.352 219.4 0.375 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 15472 140.3 0.457 131.3 0.428 144.8 0.472 16478 146.9 0.450 138.0 0.423 151.5 0.464 5 16944 147.9 0.440 139.0 0.414 152.5 0.454 17950 154.6 0.435 145.7 0.409 159.2 0.447 6 18616 156.6 0.424 147.7 0.400 161.2 0.437 19622 163.3 0.420 154.4 0.397 167.9 0.432 8 22315 175.8 0.397 166.9 0.377 180.3 0.408 23321 182.5 0.395 173.5 0.375 187.0 0.405 10 26939 199.6 0.374 190.7 0.357 204.2 0.382 27946 206.3 0.372 197.4 0.356 210.9 0.381 12 30557 217.8 0.360 208.9 0.345 222.4 0.367 31563 224.5 0.359 215.6 0.345 229.1 0.366 Note: -w1 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #1 & #2. -w3 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #3. -w4 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #4. -Deflection: A_ 5wL' ~ 3MEI 74 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE. DEFLECTION DUE TO DEAD LOAD ONLY. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 50 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 10272 .146.1 1.75 135.0 1.62 151.8 1.82 12620 149.7 1.46 138.6 1.35 155.4 1.52 3-1/2 10857 149.2 1.69 138.0 1.57 154.9 1.76 13205 152.8 1.43 141.6 1.32 158.5 1.48 4 11495 152.5 1.63 141.4 1.52 158.3 1.70 13842 156.2 1.39 145.0 1.29 161.9 1.44 5 12967 160.2 1.52 149.0 1.42 165.9 1.58 15315 163.8 1.32 152.7 1.23 169.5 1.36 6 14639 168.9 1.42 157.7 1.33 174.6 1.47 16987 172.5 1.25 161.4 1.17 178.2 1.29 8 18338 188.1 1.26 176.9 1.19 193.8 1.30 20686 191.7 1.14 180.5 1.075 197.4 1.18 10 22962 211.9 1.14 200.8 1.077 217.6 1.17 25310 215.5 1.049 204.4 0.995 221.2 1.077 12 26580 230.1 1.066 218.9 1.014 235.8 1.09 28928 233.7 0.995 222.5 0.948 239.4 1.019 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 13243 152.8 1.42 141.6 1.32 158.5 1.47 13243 155.3 1.44 144.2 1.34 161.0 1.50 3-1/2 13828 155.8 1.39 144.7 1.29 161.5 1.44 13828 158.4 1.41 147.2 1.31 164.1 1.46 4 14465 159.2 1.36 148.0 1.26 164.9 1.40 14465 161.7 1.38 150.6 1.28 167.5 1.43 5 15938 166.8 1.29 155.7 1.20 172.5 1.33 15938 169.4 1.31 158.3 1.22 175.1 1.35 6 17610 175.5 1.23 164.4 1.150 181.2 1.27 17610 178.1 1.25 167.0 1.17 183.8 1.29 8 21309 194.7 1.125 183.5 1.061 200.4 1.16 21309 197.3 1.14 186.1 1.076 203.0 1.17 10 25933 218.6 1.038 207.4 0.985 224.3 1.065 25933 221.1 1.050 210.0 0.997 226.8 1.077 12 29550 236.7 0.987 225.6 0.940 242.4 1.010 29550 239.3 0.997 228.1 0.951 245.0 1.021 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 DeH. I w1 Den. w3 Den. w4 Den. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (in"4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 15472 164.6 1.31 153.4 1.22 170.3 1.36 16478 171.0 1.28 159.9 1.195 176.7 1.32 5 16944 172.2 1.25 161.1 1.171 177.9 1.29 17950 178.7 1.23 167.5 1.150 184.4 1.27 6 18616 180.9 1.20 169.8 1.123 186.6 1.23 19622 187.4 1.176 176.2 1.106 193.1 1.21 8 22315 200.1 1.104 188.9 1.043 205.8 1.136 23321 206.6 1.091 195.4 1.032 212.3 1.121 10 26939 224.0 1.024 212.8 0.973 229.7 1.050 27946 230.4 1.016 219.3 0.966 236.1 1.041 12 30557 242.1 0.976 231.0 0.931 247.8 0.999 31563 248.6 0.970 237.4 0.926 254.3 0.992 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Den. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 20676 194.7 1.160 183.6 1.094 200.4 1.194 22689 210.9 1.145 199.7 1.084 216.6 1.176 8 24375 213.9 1.081 202.7 1.024 219.6 1.110 26388 230.0 1.074 218.9 1.022 235.7 1.100 10 29000 237.7 1.010 226.6 0.962 243.5 1.034 31012 253.9 1.008 242.7 0.964 259.6 1.031 12 32617 255.9 0.966 244.7 0.924 261.6 0.988 34630 272.1 0.968 260.9 0.928 277.8 0.988 Note: -w1 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #1 & #2. -w3 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #3. -w4 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #4. -Denection: ,.. A = 384£7 75 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE. DEFLECTION DUE TO DEAD LOAD ONLY. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 60 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm)' (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 10272 170.9 4.25 157.6 3.92 177.8 4.42 12620 174.5 3.53 161.1 3.26 181.3 3.67 3-1/2 10857 174.0 4.09 160.6 3.78 180.9 4.25 13205 177.5 3.43 164.1 3.17 184.4 3.57 4 11495 177.4 3.94 164.0 3.64 184.2 4.09 13842 180.9 3.34 167.5 3.09 187.7 3.46 5 12967 185.0 3.64 171.6 3.38 191.9 3.78 15315 188.5 3.14 175.2 2.92 195.4 3.26 6 14639 193.7 3.38 180.3 3.15 200.6 3.50 16987 197.2 2.97 183.9 2.76 204.1 3.07 8 18338 212.9 2.96 199.5 2.78 219.7 3.06 20686 216.4 2.67 203.0 2.51 223.3 2.76 10 22962 236.7 2.63 223.4 2.48 243.6 2.71 25310 240.3 2.42 226.9 2.29 247.1 2.49 12 26580 254.9 2.45 241.5 2.32 261.8 2.52 28928 258.4 2.28 245.0 2.16 265.3 2.34 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 13243 177.4 3.42 164.0 3.16 184.3 3.55 13243 179.9 3.47 166.5 3.21 186.8 3.60 3-1/2 13828 180.5 3.33 167.1 3.09 187.3 3.46 13828 183.0 3.38 169.6 3.13 189.8 3.51 4 14465 183.8 3.25 170.4 3.01 190.7 3.37 14465 186.3 3.29 173.0 3.05 193.2 3.41 5 15938 191.5 3.07 178.1 2.85 198.3 3.18 15938 194.0 3.11 180.6 2.89 200.9 3.22 6 17610 200.2 2.90 186.8 2.71 207.0 3.00 17610 202.7 2.94 189.3 2.75 209.6 3.04 8 21309 219.4 2.63 206.0 2.47 226.2 2.71 21309 221.9 2.66 208.5 2.50 228.7 2.74 10 25933 243.2 2.40 229.8 2.26 250.1 2.46 25933 245.7 2.42 232.3 2.29 252.6 2.49 12 29550 261.4 2.26 248.0 2.14 268.2 2.32 29550 263.9 2.28 250.5 2.165 270.7 2.34 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 15472 189.1 3.12 175.7 2.90 196.0 3.23 16478 195.4 3.03 182.0 2.82 202.3 3.13 5 16944 196.8 2.97 183.4 2.76 203.6 3.07 17950 203.1 2.89 189.7 2.70 209.9 2.99 6 18616 205.5 2.82 192.1 2.64 212.3 2.91 19622 211.8 2.76 198.4 2.58 218.6 2.85 8 22315 224.6 2.57 211.2 2.42 231.5 2.65 23321 230.9 2.53 217.5 2.38 237.8 2.60 10 26939 248.5 2.36 235.1 2.23 255.3 2.42 27946 254.8 2.33 241.4 2.21 261.6 2.39 12 30557 266.7 2.23 253.3 2.12 273.5 2.29 31563 273.0 2.21 259.6 2.10 279.8 2.26 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 20676 218.9 2.70 205.5 2.54 225.8 2.79 22689 234.7 2.64 221.3 2.49 241.5 2.72 8 24375 238.1 2.49 224.7 2.35 244.9 2.57 26388 253.9 2.46 240.5 2.33 260.7 2.52 10 29000 262.0 2.31 248.6 2.19 268.8 2.37 31012 277.7 2.29 264.3 2.18 284.6 2.34 12 32617 280.1 2.19 266.7 2.09 287.0 2.25 34630 295.9 2.18 282.5 2.08 302.7 2.23 Note: -w1 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #1 & #2. -w3 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #3. -w4 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #4. -Deflection: . 5wL A = 384£7 76 Appendix B THE LARGE ADAPTIVE REFLECTOR PANEL WEIGHT AND THE WEIGHT OF THE BACKUP STRUCTURE. DEFLECTION DUE TO DEAD LOAD ONLY. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 70 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 10272 195.8 9.02 180.2 8.30 203.8 9.39 12620 199.3 7.47 183.6 6.89 207.3 7.77 3-1/2 10857 198.9 8.67 183.2 7.99 206.9 9.01 13205 202.3 7.25 186.7 6.69 210.3 7.54 4 11495 202.2 8.32 186.6 7.68 210.2 8.65 13842 205.7 7.03 190.1 6.50 213.7 7.30 5 12967 209.9 7.66 194.3 7.09 217.9 7.95 15315 213.3 6.59 197.7 6.11 221.3 6.84 6 14639 218.6 7.07 203.0 6.56 226.6 7.32 16987 222.0 6.19 206.4 5.75 230.0 6.41 8 18338 237.7 6.13 222.1 5.73 245.7 6.34 20686 241.2 5.52 225.6 5.16 249.2 5.70 10 22962 261.6 5.39 246.0 5.07 269.6 5.56 25310 265.1 4.96 249.4 4.66 273.1 5.10 12 26580 279.8 4.98 264.1 4.70 287.8 5.12 28928 283.2 4.63 267.6 4.38 291.2 4.76 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3-1/2 13828 205.2 7.02 189.6 6.49 213.2 7.30 13828 207.7 7.11 192.1 6.57 215.7 7.38 4 14465 208.6 6.82 193.0 6.31 216.6 7.08 14465 211.1 6.90 195.4 6.39 219.0 7.16 5 15938 216.2 6.42 200.6 5.96 224.2 6.66 15938 218.7 6.49 203.1 6.03 226.7 6.73 6 17610 224.9 6.04 209.3 5.62 232.9 6.26 17610 227.4 6.11 211.8 5.69 235.4 6.33 8 21309 244.1 5.42 228.5 5.07 252.1 5.60 21309 246.6 5.48 230.9 5.13 254.6 5.65 10 25933 268.0 4.89 252.3 4.60 275.9 5.03 25933 270.4 4.93 254.8 4.65 278.4 5.08 12 29550 286.1 4.58 270.5 4.33 294.1 4.71 29550 288.6 4.62 273.0 4.37 296.6 4.75 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 15472 213.8 6.54 198.1 6.06 221.8 6.78 16478 220.0 6.32 204.3 5.87 227.9 6.55 5 16944 221.4 6.18 205.8 5.75 229.4 6.41 17950 227.6 6.00 212.0 5.59 235.6 6.21 6 18616 230.1 5.85 214.5 5.45 238.1 6.05 19622 236.3 5.70 220.7 5.32 244.3 5.89 8 22315 249.3 5.29 233.7 4.95 257.3 5.46 23321 255.5 5.18 239.9 4.87 263.5 5.35 10 26939 273.1 4.80 257.5 4.52 281.1 4.94 27946 279.3 4.73 263.7 4.47 287.3 4.86 12 30557 291.3 4.51 275.7 4.27 299.3 4.63 31563 297.5 4.46 281.9 4.23 305.5 4.58 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 20676 243.4 5.57 227.8 5.21 251.4 5.75 22689 258.8 5.40 243.2 5.07 266.8 5.56 8 24375 262.6 5.10 246.9 4.79 270.6 5.25 26388 278.0 4.98 262.4 4.70 286.0 5.13 10 29000 286.4 4.67 270.8 4.42 294.4 4.80 31012 301.9 4.61 286.2 4.37 309.8 4.73 12 32617 304.6 4.42 289.0 4.19 312.6 4.53 34630 320.0 4.37 304.4 4.16 328.0 4.48 Note: -w1 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #1 & #2. -w3 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #3. -w4 is the total dead load (panel weight and backup structure weight) supported by each truss for geometric layout #4. -Deflection: . 5wL A = 384£7 77 Appendix B LAR - Wind Loads and Deflections WIND LOAD ACTS ON THE MAIN SUPPORT STRUCTURE ALONE. Elastic Modulus, E = Depth, h = Operational: Survival: 6.58 22.8 29000 6 psf psf ksi ft Total Area per Triangular Unit (ftA2) Max Unit Angle Max Unit Angle 9 12 15 18 21 (rad) (deg) Triangular Uni Size 30 40 50 60 70 1.26 72 Layout #1 414.6 737.1 1152 1659 2257 1.26 72 Layout #2 414.6 737.1 1152 1659 2257 1.05 60 Layout #3 377.6 671.2 1049 1510 2056 1.47 84 Layout #4 433.6 770.8 1204 1734 2361 Wind Load (lbs/ft)* Geometric Layout 30 40 50 60 70 (ft) 1 &2 30.3 40.4 50.5 60.6 70.7 3 27.6 36.8 46.0 55.2 64.4 4 31.7 42.3 52.8 63.4 74.0 Top/ Bottom Chord: Pipe Diameter Wt of Pipe A I d = h/2 l+AdA2 (in) (lbs/ft) (inA2) (inA4) (in) (inA4) 3 7.58 2.23 3.02 36 2893.1 3-1/2 9.11 2.68 4.79 36 3478.1 4 10.79 3.17 7.23 36 4115.6 5 14.62 4.30 15.2 36 5588.0 6 18.97 5.58 28.1 36 7259.8 8 28.55 8.40 72.5 36 10959 10 40.48 11.9 161 36 15583 12 49.56 14.6 279 36 19201 (m) (ft) Web Pipe: Pipe Diameter Wt of Pipe Wall Thickness I Total Weight of Web Pipes (lbs/ft) 30 (ft) 40 (ft) 50 (ft) 60 (ft) 70 (ft) (in) (lbs/ft) (in) (inA4) 1-1/4 1.68 0.140 8709 3.30 3.13 3.03 2.96 2.91 1-1/2 2.27 0.145 9020 4.45 4.23 4.09 4.00 3.93 2 3.65 0.154 9580 7.16 6.80 6.58 6.43 6.33 2-1/2 5.79 0.203 12628 11.4 10.8 10.4 10.2 10.0 3 7.58 0.216 13437 14.9 14.1 13.7 13.4 13.1 3-1/2 9.11 0.226 14059 17.9 17.0 16.4 16.1 15.8 4 10.79 0.237 14743 21.2 20.1 19.4 19.0 18.7 5 14.62 0.258 16050 28.7 27.2 26.3 25.8 25.3 6 18.97 0.280 17418 37.2 35.3 34.2 33.4 32.9 8 28.55 0.322 20031 56.0 53.2 51.4 50.3 49.5 * Assuming wind load is acting perpendicular to the entire triangular unit. 78 Appendix B THE LARGE ADAPTIVE REFLECTOR WIND LOAD ACTS ON THE BACKUP STRUCTURE ALONE. DEFLECTION DUE TO WIND LOAD. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 30 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 1-1/4 1-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 11602 30.3 0.042 27.6 0.038 31.7 0.044 11913 30.3 0.041 27.6 0.038 31.7 0.044 3-1/2 12187 30.3 0.040 27.6 0.036 31.7 0.042 12498 30.3 0.039 27.6 0.036 31.7 0.042 4 12825 30.3 0.038 27.6 0.034 31.7 0.039 13136 30.3 0.037 27.6 0.034 31.7 0.039 5 14297 30.3 0.034 27.6 0.031 31.7 0.035 14608 30.3 0.033 27.6 0.031 31.7 0.035 6 15969 30.3 0.030 27.6 0.028 31.7 0.032 16280 30.3 0.030 27.6 0.028 31.7 0.032 8 19668 30.3 0.025 27.6 0.022 31.7 0.026 19979 30.3 0.024 27.6 0.022 31.7 0.026 10 24293 30.3 0.020 27.6 0.018 31.7 0.021 24604 30.3 0.020 27.6 0.018 31.7 0.021 12 27910 30.3 0.017 27.6 0.016 31.7 0.018 28221 30.3 0.017 27.6 0.016 31.7 0.018 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 12473 30.3 0.039 27.6 0.035 31.7 0.041 15521 30.3 0.031 27.6 0.028 31.7 0.033 3-1/2 13058 30.3 0.037 27.6 0.034 31.7 0.039 16106 30.3 0.030 27.6 0.027 31.7 0.031 4 13696 30.3 0.035 27.6 0.032 31.7 0.037 16744 30.3 0.029 27.6 0.026 31.7 0.030 5 15168 30.3 0.032 27.6 0.029 31.7 0.033 18216 30.3 0.027 27.6 0.024 31.7 0.028 6 16840 30.3 0.029 27.6 0.026 31.7 0.030 19888 30.3 0.024 27.6 0.022 31.7 0.025 8 20539 30.3 0.024 27.6 0.021 31.7 0.025 23587 30.3 0.021 27.6 0.019 31.7 0.021 10 25163 30.3 0.019 27.6 0.018 31.7 0.020 28212 30.3 0.017 27.6 0.016 31.7 0.018 12 28781 30.3 0.017 27.6 0.015 31.7 0.018 31829 30.3 0.015 27.6 0.014 31.7 0.016 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 16330 30.3 0.030 27.6 0.027 31.7 0.031 16330 30.3 0.030 27.6 0.027 31.7 0.031 3-1/2 16915 30.3 0.029 27.6 0.026 31.7 0.030 16915 30.3 0.029 27.6 0.026 31.7 0.030 4 17552 30.3 0.028 27.6 0.025 31.7 0.029 17552 30.3 0.028 27.6 0.025 31.7 0.029 5 19025 30.3 0.025 27.6 0.023 31.7 0.027 19025 30.3 0.025 27.6 0.023 31.7 0.027 6 20697 30.3 0.023 27.6 0.021 31.7 0.024 20697 30.3 0.023 27.6 0.021 31.7 0.024 8 24396 30.3 0.020 27.6 0.018 31.7 0.021 24396 30.3 0.020 27.6 0.018 31.7 0.021 10 29020 30.3 0.017 27.6 0.015 31.7 0.017 29020 30.3 0.017 27.6 0.015 31.7 0.017 12 32638 30.3 0.015 27.6 0.014 31.7 0.016 32638 30.3 0.015 27.6 0.014 31.7 0.016 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 18859 30.3 0.026 27.6 0.023 31.7 0.027 20165 30.3 0.024 27.6 0.022 31.7 0.025 5 20331 30.3 0.024 27.6 0.022 31.7 0.025 21638 30.3 0.022 27.6 0.020 31.7 0.023 6 22003 30.3 0.022 27.6 0.020 31.7 0.023 23309 30.3 0.021 27.6 0.019 31.7 0.022 8 25702 30.3 0.019 27.6 0.017 31.7 0.020 27009 30.3 0.018 27.6 0.016 31.7 0.019 10 30327 30.3 0.016 27.6 0.015 31.7 0.017 31633 30.3 0.015 27.6 0.014 31.7 0.016 12 33944 30.3 0.014 27.6 0.013 31.7 0.015 35250 30.3 0.014 27.6 0.013 31.7 0.014 Note: -w1 is the wind load acting on geometric layout #1 & #2. -w3 is the wind load acting on geometric layout #3. -w4 is the wind load acting on geometric layout #4. -Deflection: . 5wL A = 384£7 79 Appendix B THE LARGE ADAPTIVE REFLECTOR WIND LOAD ACTS ON THE BACKUP STRUCTURE ALONE. DEFLECTION DUE TO WIND LOAD. Elastic Modulus, E = 29000 ksi Triangular Unit Size =40 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 1-1/4 1-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 11602 40.4 0.176 36.8 0.160 42.3 0.184 11913 40.4 0.171 36.8 0.160 42.3 0.184 3-1/2 12187 40.4 0.167 36.8 0.152 42.3 0.175 12498 40.4 0.163 36.8 0.152 42.3 0.175 4 12825 40.4 0.159 36.8 0.145 42.3 0.166 13136 40.4 0.155 36.8 0.145 42.3 0.166 5 14297 40.4 0.143 36.8 0.130 42.3 0.149 14608 40.4 0.140 36.8 0.130 42.3 0.149 6 15969 40.4 0.128 36.8 0.116 42.3 0.134 16280 40.4 0.125 36.8 0.116 42.3 0.134 8 19668 40.4 0.104 36.8 0.094 42.3 0.108 19979 40.4 0.102 36.8 0.094 42.3 0.108 10 24293 40.4 0.084 36.8 0.076 42.3 0.088 24604 40.4 0.083 36.8 0.076 42.3 0.088 12 27910 40.4 0.073 36.8 0.067 42.3 0.076 28221 40.4 0.072 36.8 0.067 42.3 0.076 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 12473 40.4 0.163 36.8 0.149 42.3 0.171 15521 40.4 0.131 36.8 0.120 42.3 0.137 3-1/2 13058 40.4 0.156 36.8 0.142 42.3 0.163 16106 40.4 0.127 36.8 0.115 42.3 0.132 4 13696 40.4 0.149 36.8 0.136 42.3 0.156 16744 40.4 0.122 36.8 0.111 42.3 0.127 5 15168 40.4 0.134 36.8 0.122 42.3 0.141 18216 40.4 0.112 36.8 0.102 42.3 0.117 6 16840 40.4 0.121 36.8 0.110 42.3 0.127 19888 40.4 0.103 36.8 0.093 42.3 0.107 8 20539 40.4 0.099 36.8 0.090 42.3 0.104 23587 40.4 0.086 36.8 0.079 42.3 0.090 10 25163 40.4 0.081 36.8 0.074 42.3 0.085 28212 40.4 0.072 36.8 0.066 42.3 0.076 12 28781 40.4 0.071 36.8 0.065 42.3 0.074 31829 40.4 0.064 36.8 0.058 42.3 0.067 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 16330 40.4 0.125 36.8 0.114 42.3 0.131 16330 40.4 0.125 36.8 0.114 42.3 0.131 3-1/2 16915 40.4 0.121 36.8 0.110 42.3 0.126 16915 40.4 0.121 36.8 0.110 42.3 0.126 4 17552 40.4 0.116 36.8 0.106 42.3 0.121 17552 40.4 0.116 36.8 0.106 42.3 0.121 5 19025 40.4 0.107 36.8 0.098 42.3 0.112 19025 40.4 0.107 36.8 0.098 42.3 0.112 6 20697 40.4 0.099 36.8 0.090 42.3 0.103 20697 40.4 0.099 36.8 0.090 42.3 0.103 8 24396 40.4 0.084 36.8 0.076 42.3 0.087 24396 40.4 0.084 36.8 0.076 42.3 0.087 10 29020 40.4 0.070 36.8 0.064 42.3 0.073 29020 40.4 0.070 36.8 0.064 42.3 0.073 12 32638 40.4 0.062 36.8 0.057 42.3 0.065 32638 40.4 0.062 36.8 0.057 42.3 0.065 Web Pipe Diameter (in) Top/ Bottom Chord 4 5 Diameter I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 18859 40.4 0.108 36.8 0.098 42.3 0.113 20165 40.4 0.101 36.8 0.092 42.3 0.106 5 20331 40.4 0.100 36.8 0.091 42.3 0.105 21638 40.4 0.094 36.8 0.086 42.3 0.099 6 22003 40.4 0.093 36.8 0.084 42.3 0.097 23309 40.4 0.087 36.8 0.080 42.3 0.091 8 25702 40.4 0.079 36.8 0.072 42.3 0.083 27009 40.4 0.076 36.8 0.069 42.3 0.079 10 30327 40.4 0.067 36.8 0.061 42.3 0.070 31633 40.4 0.064 36.8 0.059 42.3 0.067 12 33944 40.4 0.060 36.8 0.055 42.3 0.063 35250 40.4 0.058 36.8 0.053 42.3 0.060 Note: - w1 is the wind load acting on geometric layout #1 & #2. -w3 is the wind load acting on geometric layout #3. -w4 is the wind load acting on geometric layout #4. -Deflection: , . 5wL 80 Appendix B THE LARGE ADAPTIVE REFLECTOR WIND LOAD ACTS ON THE BACKUP STRUCTURE ALONE. DEFLECTION DUE TO WIND LOAD. Elastic Modulus, E = 29000 ksi Triangular Depth, h = Unit Size = 50 ft 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 12473 50.5 0.499 46.0 0.454 52.8 0.522 15521 50.5 0.401 46.0 0.365 52.8 0.419 3-1/2 13058 50.5 0.477 46.0 0.434 52.8 0.498 16106 50.5 0.386 46.0 0.352 52.8 0.404 4 13696 50.5 0.454 46.0 0.414 52.8 0.475 16744 50.5 0.372 46.0 0.338 52.8 0.389 5 15168 50.5 0.410 46.0 0.374 52.8 0.429 18216 50.5 0.342 46.0 0.311 52.8 0.357 6 16840 50.5 0.370 46.0 0.337 52.8 0.386 19888 50.5 0.313 46.0 0.285 52.8 0.327 8 20539 50.5 0.303 46.0 0.276 52.8 0.317 23587 50.5 0.264 46.0 0.240 52.8 0.276 10 25163 50.5 0.247 46.0 0.225 52.8 0.259 28212 50.5 0.221 46.0 0.201 52.8 0.231 12 28781 50.5 0.216 46.0 0.197 52.8 0.226 31829 50.5 0.196 46.0 0.178 52.8 0.204 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 16330 50.5 0.381 46.0 0.347 52.8 0.398 16330 50.5 0.381 46.0 0.347 52.8 0.398 3-1/2 16915 50.5 0.368 46.0 0.335 52.8 0.385 16915 50.5 0.368 46.0 0.335 52.8 0.385 4 17552 50.5 0.355 46.0 0.323 52.8 0.371 17552 50.5 0.355 46.0 0.323 52.8 0.371 5 19025 50.5 0.327 46.0 0.298 52.8 0.342 19025 50.5 0.327 46.0 0.298 52.8 0.342 6 20697 50.5 0.301 46.0 0.274 52.8 0.314 20697 50.5 0.301 46.0 0.274 52.8 0.314 8 24396 50.5 0.255 46.0 0.232 52.8 0.267 24396 50.5 0.255 46.0 0.232 52.8 0.267 10 29020 50.5 0.214 46.0 0.195 52.8 0.224 29020 50.5 0.214 46.0 0.195 52.8 0.224 12 32638 50.5 0.191 46.0 0.174 52.8 0.199 32638 50.5 0.191 46.0 0.174 52.8 0.199 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 18859 50.5 0.330 46.0 0.300 52.8 0.345 20165 50.5 0.309 46.0 0.281 52.8 0.323 5 20331 50.5 0.306 46.0 0.279 52.8 0.320 21638 50.5 0.288 46.0 0.262 52.8 0.301 6 22003 50.5 0.283 46.0 0.258 52.8 0.296 23309 50.5 0.267 46.0 0.243 52.8 0.279 8 25702 50.5 0.242 46.0 0.220 52.8 0.253 27009 50.5 0.230 46.0 0.210 52.8 0.241 10 30327 50.5 0.205 46.0 0.187 52.8 0.215 31633 50.5 0.197 46.0 0.179 52.8 0.206 12 33944 50.5 0.183 46.0 0.167 52.8 0.192 35250 50.5 0.177 46.0 0.161 52.8 0.185 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Deft. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 24678 50.5 0.252 46.0 0.230 52.8 0.264 27291 50.5 0.228 46.0 0.208 52.8 0.238 8 28377 50.5 0.219 46.0 0.200 52.8 0.229 30990 50.5 0.201 46.0 0.183 52.8 0.210 10 33002 50.5 0.189 46.0 0.172 52.8 0.197 35614 50.5 0.175 46.0 0.159 52.8 0.183 12 36619 50.5 0.170 46.0 0.155 52.8 0.178 39232 50.5 0.159 46.0 0.144 52.8 0.166 Note: -w1 is the wind load acting on geometric layout #1 & #2. -w3 is the wind load acting on geometric layout #3. -w4 is the wind load acting on geometric layout #4. -Deflection: , . 5wL A = 384£7 81 Appendix B THE LARGE ADAPTIVE REFLECTOR WIND LOAD ACTS ON THE BACKUP STRUCTURE ALONE. DEFLECTION DUE TO WIND LOAD. Elastic Modulus. E = 29000 ksi Triangular Depth, h = Unit Size = 60 ft 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 12473 60.6 1.24 55.2 1.13 63.4 1.30 15521 60.6 1.00 55.2 0.91 63.4 1.04 3-1/2 13058 60.6 1.19 55.2 1.08 63.4 1.24 16106 60.6 0.96 55.2 0.88 63.4 1.01 4 13696 60.6 1.13 55.2 1.03 63.4 1.18 16744 60.6 0.92 55.2 0.84 63.4 0.97 5 15168 60.6 1.02 55.2 0.93 63.4 1.07 18216 60.6 0.85 55.2 0.77 63.4 0.89 6 16840 60.6 0.92 55.2 0.84 63.4 0.96 19888 60.6 0.78 55.2 0.71 63.4 0.81 8 20539 60.6 0.75 55.2 0.69 63.4 0.79 23587 60.6 0.66 55.2 0.60 63.4 0.69 10 25163 60.6 0.62 55.2 0.56 63.4 0.64 28212 60.6 0.55 55.2 0.50 63.4 0.57 12 28781 60.6 0.54 55.2 0.49 63.4 0.56 31829 60.6 0.49 55.2 0.44 63.4 0.51 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft)- (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 16330 60.6 0.95 55.2 0.86 63.4 0.99 16330 60.6 0.95 55.2 0.86 63.4 0.99 3-1/2 16915 60.6 0.92 55.2 0.83 63.4 0.96 16915 60.6 0.92 55.2 0.83 63.4 0.96 4 17552 60.6 0.88 55.2 0.80 63.4 0.92 17552 60.6 0.88 55.2 0.80 63.4 0.92 5 19025 60.6 0.81 55.2 0.74 63.4 0.85 19025 60.6 0.81 55.2 0.74 63.4 0.85 6 20697 60.6 0.75 55.2 0.68 63.4 0.78 20697 60.6 0.75 55.2 0.68 63.4 0.78 8 24396 60.6 0.63 55.2 0.58 63.4 0.66 24396 60.6 0.63 55.2 0.58 63.4 0.66 10 29020 60.6 0.53 55.2 0.49 63.4 0.56 29020 60.6 0.53 55.2 0.49 63.4 0.56 12 32638 60.6 0.47 55.2 0.43 63.4 0.50 32638 60.6 0.47 55.2 0.432 63.4 0.50 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. . w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 18859 60.6 0.82 55.2 0.75 63.4 0.86 20165 60.6 0.77 55.2 0.70 63.4 0.80 5 20331 60.6 0.76 55.2 0.69 63.4 0.80 21638 60.6 0.72 55.2 0.65 63.4 0.75 6 22003 60.6 0.70 55.2 0.64 63.4 0.74 23309 60.6 0.66 55.2 0.60 63.4 0.69 8 25702 60.6 0.60 55.2 0.55 63.4 0.63 27009 60.6 0.57 55.2 0.52 63.4 0.60 10 30327 60.6 0.51 55.2 0.46 63.4 0.53 31633 60.6 0.49 55.2 0.45 63.4 0.51 12 33944 60.6 0.46 55.2 0.42 63.4 0.48 35250 60.6 0.44 55.2 0.40 63.4 0.46 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inA4) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 24678 60.6 0.63 55.2 0.57 63.4 0.66 27291 60.6 0.57 55.2 0.52 63.4 0.59 8 28377 60.6 0.55 55.2 0.50 63.4 0.57 30990 60.6 0.50 55.2 0.46 63.4 0.52 10 33002 60.6 0.47 55.2 0.43 63.4 0.49 35614 60.6 0.43 55.2 0.40 63.4 0.45 12 36619 60.6 0.42 55.2 0.39 63.4 0.44 39232 60.6 0.39 55.2 0.36 63.4 0.41 Note: -w1 is the wind load acting on geometric layout #1 & #2. - w3 is the wind load acting on geometric layout #3. -w4 is the wind load acting on geometric layout #4. -Deflection: 4 5wL A = 38467 82 Appendix B THE LARGE ADAPTIVE REFLECTOR WIND LOAD ACTS ON THE BACKUP STRUCTURE ALONE. DEFLECTION DUE TO WIND LOAD. Elastic Modulus, E = 29000 ksi Triangular Unit Size = 70 ft Depth, h = 6 ft Top/ Bottom Chord Diameter Web Pipe Diameter (in) 2 2-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3 12473 70.7 2.68 64.4 2.44 74.0 2.81 15521 70.7 2.16 64.4 1.96 74.0 2.25 3-1/2 13058 70.7 2.56 64.4 2.33 74.0 2.68 16106 70.7 2.08 64.4 1.89 74.0 2.17 4 13696 70.7 2.44 64.4 2.23 74.0 2.56 16744 70.7 2.00 64.4 1.82 74.0 2.09 5 15168 70.7 2.21 64.4 2.01 74.0 2.31 18216 70.7 1.84 64.4 1.67 74.0 1.92 6 16840 70.7 1.99 64.4 1.81 74.0 2.08 19888 70.7 1.68 64.4 1.53 74.0 1.76 8 20539 70.7 1.63 64.4 1.48 74.0 1.70 23587 70.7 1.42 64.4 1.29 74.0 1.48 10 25163 70.7 1.33 64.4 1.21 74.0 1.39 28212 70.7 1.19 64.4 1.08 74.0 1.24 12 28781 70.7 1.16 64.4 1.06 74.0 1.22 31829 70.7 1.05 64.4 0.96 74.0 1.10 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 3 3-1/2 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 3-1/2 16915 70.7 1.98 64.4 1.80 74.0 2.07 16915 70.7 1.98 64.4 1.80 74.0 2.07 4 17552 70.7 1.91 64.4 1.74 74.0 1.99 17552 70.7 1.91 64.4 1.74 74.0 1.99 5 19025 70.7 1.76 64.4 1.60 74.0 1.84 19025 70.7 1.76 64.4 1.60 74.0 1.84 6 20697 70.7 1.62 64.4 1.47 74.0 1.69 20697 70.7 1.62 64.4 1.47 74.0 1.69 8 24396 70.7 1.37 64.4 1.25 74.0 1.43 24396 70.7 1.37 64.4 1.25 74.0 1.43 10 29020 70.7 1.15 64.4 1.05 74.0 1.21 29020 70.7 1.15 64.4 1.05 74.0 1.21 12 32638 70.7 1.03 64.4 0.93 74.0 1.07 32638 70.7 1.03 64.4 0.93 74.0 1.07 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 4 5 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 4 18859 70.7 1.77 64.4 1.62 74.0 1.86 20165 70.7 1.66 64.4 1.51 74.0 1.74 5 20331 70.7 1.65 64.4 1.50 74.0 1.72 21638 70.7 1.55 64.4 1.41 74.0 1.62 6 22003 70.7 1.52 64.4 1.39 74.0 1.59 23309 70.7 1.44 64.4 1.31 74.0 1.50 8 25702 70.7 1.30 64.4 1.19 74.0 1.36 27009 70.7 1.24 64.4 1.13 74.0 1.30 10 30327 70.7 1.10 64.4 1.00 74.0 1.15 31633 70.7 1.06 64.4 0.96 74.0 1.11 12 33944 70.7 0.99 64.4 0.90 74.0 1.03 35250 70.7 0.95 64.4 0.86 74.0 0.99 Top/ Bottom Chord Diameter Web Pipe Diameter (in) 6 8 I w1 Defl. w3 Defl. w4 Defl. I w1 Defl. w3 Defl. w4 Defl. (in) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) (inM) (lbs/ft) (mm) (lbs/ft) (mm) (lbs/ft) (mm) 6 24678 70.7 1.36 64.4 1.23 74.0 1.42 27291 70.7 1.23 64.4 1.12 74.0 1.28 8 28377 70.7 1.18 64.4 1.07 74.0 1.23 30990 70.7 1.08 64.4 0.98 74.0 1.13 10 33002 70.7 1.01 64.4 0.92 74.0 1.06 35614 70.7 0.94 64.4 0.86 74.0 0.98 12 36619 70.7 0.91 64.4 0.83 74.0 0.96 39232 70.7 0.85 64.4 0.78 74.0 0.89 Note: -w1 is the wind load acting on geometric layout #1 & #2. -w3 is the wind load acting on geometric layout #3. -w4 is the wind load acting on geometric layout #4. -Deflection: A = -5wL4 iUEI 83 Appendix C APPENDIX C: ANSYS INPUT AND OUTPUT FILES PRELIMINARY DESIGN OF THE SPACE FRAME STRUCTURE Appendix C create /title, LAR-Backup Structure , August 06, 1999 Created by Ya-Ying Chang LAR Finite Element Model for LAR Backing Structure Rev Date Note: Equilateral Triangle (21m) SECTION 1: Definition of elements, materials and sections Define element type et,l,pipel6„„0„2 et,2,mass21 ! ! Define material properties of steel mp,ex, 1,200 ! Young's modulus in kN/mm2 mp,dens,l,7.85e-12 ! density in kN-secA2/mmA4 (w/a =9810 mm/secA2) mp,nuxy,l,0.3 ! Poisson's ratio mp,gxy, 1,79.29  shear ratio in kN/mm2 mp,alpx, 1,11.7e-6 ! thermal expansion coeff. / deg. C I ! Define shapes in mm, mm ! r,no,OD,Tkwall r,l 1,168,7.112 !Top/Bottom Chords r,12,168,7.112 !Web r,13,0.001825,0.001825,0.001825 !Panel mass per actuator ! Specify coordinate system and material 1=============================================================== (SECTION 2: Geometry definition !=============================================================== ILocal systems local,ll,0„„-30 local,12,0,10500,-18186.5335,0,-30,10,10 local,13,0„„30 !n,1000,0,0,0 local,90,0,10500,-18186.5335,0„-ll,6 (Consider till of the space frame csys,90 n, 1,0,0,0 n,2,-5250,0,0 n,3,-10500,0,0 n,4,-15750,0,0 n,5,-21000,0,0 n,6,-2625,0,-1800 n,7,-7875,0,-1800 n,8,-10500,0,-1800 n,9,-13125,0,-1800 n,10,-18375,0,-1800 n,l 1,-13125,-4546.633375,0 n,12,-l 1812.5,-2273.3166875,-1800 n, 13,-14437.5,-6819.9500625,-1800 n,31. -21000,0,0 n,32,-18375,-4546.63338,0 n,33,-15750,-9093.26675,0 n,34,-13125;-13639.90013,0 n,35,-10500,-18186.5335,0 85 Appendix C n,36,-19687.5,-2273.31669,-1800 n,37,-17062.5,-6819.95006,-1800 n,38,-15750,-9093.26675,-1800 n,39,-14437.5,-l 1366.58344,-1800 n,40,-l 1812.5,-15913.21681,-1800 n,41,-10500,-9093.26675,0 n,42,-13125,-9093.26675,-1800 n,43,-7875,-9093.26675,-1800 n,61,-10500,-18186.5335,0 n,62,-7875,-13639.90013,0 11,63,-5250,-9093.26675.0 n,64,-2625,-4546.63338,0 n,65,0,0,0 n,66,-9187.5,-15913.21681,-1800 n,67,-6562.5,-l 1366.58344,-1800 n,68,-5250,-9093.26675,-1800 n,69,-3937.5,-6819.95006,-1800 n.70,-1312.5,-2273.31669,-1800 11,71,-7875,-4546.633375,0 n,72,-6562.5,-6819.9500625,-1800 n,73,-9187.5,-2273.3166875,-1800 l type,l real. 11 en. 1,1,2 en;2,2,3 en,3,3,4 en,4,4,5 en,5,6,7 en,6,7,8 en,7,8,9 en,8,9,10 en,9,l,6 en, 10,6,2 en,l1,2,7 en:12,7,3 en, 13,3,8 en,14,3,9 en, 15,9,4 en, 16,4,10 en,17,10,5 en, 18,3,11 en,19,ll,33 en,20,3,12 en,21,ll,12 en,22,ll,13 en,23,13,33 en, 124,8,12 en,I25,12,13 en,126,13,38 en,127,10,36 engen,30,2,30,l,23 engen,30,2,30,124,127 engen,30,2,30,31,48 en,79,71,3 en,80,63,72 86 Appendix C en,81,71,72 en,82,71,73 ^1,83,73,3 en, 184,68,72 en,185,72,73 en, 186,73,8 en,187,70,6 en,101,2,64 en,102,2,71 en, 103,71,64 en, 104,71,11 en,105,71,41 en,106,ll,41 en, 107,4,11 en,108,4,32 en,109,ll,32 en,l 10,41,62 en,lll,41,34 en, 112,34,62 I type,2 [panel real, 13 en,24,l en,25,2 en,26,3 en,27,4 en,28,ll engen,30,3,30.24,28 nail eall /ANG, 1 ,-30.0,XS,l eplot /eof be csys, 11 nail nrotal,all nsel,s,node„ 1,61,30 nsel,a,node„5,65,30 d,l,ux,0,,„uy,uz d,61,ux.0,,„uz d,31,uz,0 cp,2,all,l,65 cp,next,all,31,5 cp,next,all,61,35 ! nail eall /eof deadL nail eall acel,„9810 /eof post ! Postprocessing 87 Appendix C /format,,„4 /output,prel_r,rst prrsol csys,0 esel,u,type„2 etable,fxi,smisc,l etable,fyi,smisc,2 etable,fzi,smisc,3 etable,mxi,smisc,4 elable,myi,smisc,5 etable,mzi,smisc,6 etable,fxj,smisc,7 etable,fyj,smisc,8 etable,fzj,smisc,9 etable,mxj,smisc, 10 elable,myj,smisc,ll etable,mzj,smisc,12 pretab,fxi,fyi,fzi,mxi,myi,mzi pretab,fxj,fyj,fzj,mxj,myj,mzj etable,eras esel,s,type„2 etable,fxi,smisc,l etable,fxj,smisc,2 pretab,fxi,fxj /output /output,prel_d,dsp prdisp /output nsel,all esel,all /eof main /clear /prep7 *use,create *use,bc eplot *use,deadl /eof 88 Appendix C Preliminary Design No tilt. Date: August 11, 1999 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 1 0.0 0.0 122.4 0.0 0.0 0.0 31 0.0 0.0 123.1 0.0 0.0 0.0 61 0.0 0.0 123.9 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 369.3 0.0 0.0 0.0 89 Appendix C Preliminary Design No tilt. Date: August 11, 1999 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 0 0 0 0 2 0.5486 0.5778 -10.36 10.39 3 1.461 0.669 -14.8 14.89 4 2.373 0.5778 -10.36 10.65 5 2.922 -1 88E-09 0 2.922 6 3.35 1.935 -5.597 6.804 7 2.277 1.453 -13.27 13.54 8 1.461 1.006 -14.8 14.91 9 0.6449 1.453 -13.27 13.36 10 -0.4281 1.935 -5.597 5.938 11 1.69 0.7113 -15.77 15.87 12 1.338 1.073 -15.41 15.5 13 1.2 0.8351 -15.41 15.48 31 2.922 -1.88E-09 0 2.922 32 2.147 0.1862 -10.36 10.58 33 1.612 0.9306 -14.8 14.92 34 1.235 1.766 -10.36 10.58 35 1.461 2.53 0 2.922 36 -0.4289 1.934 -5.597 5.937 37 0.5252 1.245 -13.27 13.34 38 1.32 0.7619 -14.8 14.88 39 1.341 -0.1678 -13.27 13.34 40 1.46 -1.338 -5.597 5.937 41 1.461 1.108 -15.77 15.87 42 1.323 0.6221 -15.41 15.48 43 1.598 0.6221 -15.41 15.5 61 1.461 2.53 0 2.922 62 1.687 1.766 -10.36 10.65 63 1.31 0.9306 -14.8 14.89 64 0.7747 0.1862 -10.36 10.39 65 0 0 0 0 66 1.462 -1.338 -5.597 5.938 67 1.58 -0.1678 -13.27 13.36 68 1.602 0.7619 -14.8 14.91 69 2.396 1.245 -13.27 13.54 70 3.351 1.934 -5.597 6.804 71 1.232 0.7113 -15.77 15.83 72 1.721 0.8351 -15.41 15.53 73 1.584 1.073 -15.41 15.53 MAXIMUM ABSOLUTE VALUES NODE 70 35 41 41 VALUE 3.351 2.53 -15.77 15.87 90 Appendix C Preliminary Design Tilt angles of -11 (radial) and 6 (tangential) degrees Date: August 11, 1999 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 1 0.0 0.0 122.4 0.0 0.0 0.0 31 0.0 0.0 123.1 0.0 0.0 0.0 61 0.0 0.0 123.9 0.0 0.0 0.0 TOTALVALUES VALUE 0.0 0.0 369.3 0.0 0.0 0.0 91 Appendix C Preliminary Design Tilt angles of -11 (radial) and 6 (tangential) degrees Date: August 11, 1999 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES ODE UX UY uz USUM [mm] [mm] [mm] [mm] 1 0.0 0.0 0.0 0.0 2 -0.5 -1.1 -10.0 10.0 3 -0.1 -1.9 -14.2 14.3 4 1.2 -1.3 -9.9 10.1 5 2.6 -0.4 0.0 2.6 6 2.6 1.1 -6.0 6.7 7 0.8 -0.6 -13.0 13.1 8 -0.1 -1.6 -14.3 14.3 9 -0.8 -0.6 -12.7 12.8 10 -1.1 1.2 -5.3 5.6 11 0.1 -2.1 -15.1 15.3 12 -0.2 -1.7 -14.8 14.9 13 -0.3 -1.9 -14.7 14.8 31 2.6 -0.4 0.0 2.6 32 1.1 -1.8 -10.0 10.2 33 0.2 -1.7 -14.2 14.3 34 0.3 0.0 -9.9 9.9 35 1.5 2.5 0.0 2.9 36 -0.6 0.9 -5.7 5.8 37 -0.5 -1.1 -12.8 12.9 38 0.0 -1.9 -14.1 14.3 39 0.4 -2.4 -12.5 12.7 40 1.2 -2.1 -4.7 5.3 41 0.0 -1.7 -15.1 15.2 42 -0.1 -1.9 -14.7 14.8 43 0.1 -1.9 -14.8 14.9 61 1.5 2.5 0.0 2.9 62 0.8 0.0 -9.8 9.9 63 -0.1 -1.6 -14.1 14.2 64 -0.3 -1.6 -10.0 10.1 65 0.0 0.0 0.0 0.0 66 1.2 -2.3 -4.5 5.2 67 0.3 -2.5 -12.3 12.6 68 0.1 -1.9 -14.1 14.3 69 1.0 -1.2 -13.0 13.1 70 2.4 1.0 -6.1 6.7 71 -0.3 -2.0 -15.1 15.2 72 0.4 -1.8 -14.8 14.9 73 0.2 -1.5 -14.9 15.0 MAXIMUM ABSOLUTE VALUES NODE 6 35 11 11 VALUE 2.6 2.5 -15.1 15.3 92 Appendix D APPENDIX D: ALTERNATIVE CONFIGURATIONS ALTERNATIVE CONFIGURATION COMBINATIONS 93 Appendix D Combination #24) qx^ o o o £} O V*" I A Combination #6: C#2 «#24) w Y ° Combination #11:(#3&#4) 4 —'—77 Combination #2:(#1 &#25) V Combination #7: (#2 S #25) Q O O O JQ tY1 Combination #12:(#5 S#6) CpL,^ Q <j> Q Jp "\AVJS Combination #3 a #2ef) O O O V er'* J & o o Combination #8: (#2 S#26) O O O O O t3 <5 5 3>i& Confcination #13 (#7 S#24) Cbmbination #4: (# 1 & #27) 9 o <? o o / 1 \ Combination #9: (#2 &#27) O O ^ o O OLyJS p \> Q Combination #14:(#7 S#25) O o o Combination #5 :(# 1 S #28) Q Q Q Q O 7 Combination #10: (#2 &#28) © O O O Q gr3 5 Jog Combination #15: (#7 S#26) jjijjL POO JO 94 Appendix D Combination #16: (#7 a #27) O q O O p \ o Q C> Combination #21: (#8 a #27) © o ^ o O P1—b poo d—o—4J o—o X <\ p X ° Combination #26: (#9 a #27) a o <o o o t v 6 o Y a b Combination #17: (#7 a #28) <£! O O O O Combination # 18: (#8 & #24) Combination #22: (#8 a #28) O O O O R—^—h—0—0 / \ / \ Combination #27: (#9 a #28) O O o O A G—Q V o b Combination #28: (#10 a #24) O O O X> a / Combination # 18: (#8 a #25) f o Combination #24:|?f9 a #25) Combination #29: (#10 a#25) a o o .0 Combination #20: (#8 a #26) O O O J© Combination #26: (#9 a #26) O O O Combination #30: (#10 a #26) SjL o o o j© A/ * Z: o 95 Appendix D Cont.in3t.ion #31 :(# 10 S #27) Qa^oQ p & 0 \> o Combination #36: (#11 S #27) D q a O H—°—» Combination #37: (#11 S #28) o o o O 0 (3—o—o— Combination #38: (#12 S #24) O O O j£> /AY Combination #41: (# 12 S #27) Q O <^ o O !> <J O O O G^o—o—©-% Combination #42: (#12 S#28) ^ o o o O cy^-o—o—0-^%) Combination #43: (# 13 & #24) ° ° 9 j£> 0/ J^b. \i I O Combination #34: (# 11 S #25) p ° ° <^—a—1>—a—© Combination #39: (#12 S #25) O r>^^0 / A Combination #44: (# 13 & #25) /A XT ° Of—O Q—o—® Combination #35: (# 11 & #26) O £> O J0 Combination #40: (#12 & #26) ° ° ° -jam JO" o ,6* ^—V \ {J1-© ° &—© O 0 Combination #45: (# 13 & #26) QL O 0 a ..0 -O 0—o—^») 96 Appendix D Combination #46 (#13 S#27) 4 ° o V A —o—a—£) Combination #47 (# 13 & #28) Q o o 0 O fJP—O O O—^1 Combination #48: (#143 #24) d A b « o o o o*q' Combination #51 :(#14 3 #27) Q o Q o O p p b o O O O—-£) Combination #52:(#14S#28) o o o O (3^—0 O O Combination #53: (#15 &#20) -o—n—o—£> Combination #58: (#15 &#23) Q——°—P—G o o o Q) Combination #57: (#16 &#20) / \ Q Q o o O Combination #58:(#16 & #21) O O O O O O O Combination #49: (# 14 & #25) 0 4. © b C3=—o 6—0—5© Combination #54:(#15 &#21) Combination #59: (#16 fi#22) ^—O o ^_£) —o—ic^ 6 o O o o 0 6 Combination #50: (#14& #26) Q o o o j0 b xx jx o pi 6 'fc* I o jeAe^ b Combination #55:(#15 &#22) -o o O—H£> . ^b f y\\ Combination #60: (#16 S#23) 6 o o o 97 Appendix D Combination #61: (#17 & #20) -O o o—£j§| O O O Combination #86: (# 18 & #21) ^-^—9 O 4 I ,6 O Combination #71: (#19 S#22) A 6 J . o Coronation #62: (#17 &#21) o O O "^f fc a a Combination #67: (#18 S #22) Qt7-o & o—30 o o o Is Combination #72: (#19 a #23) ^ O p O 4 V \ / ° \ \ / C q o o o o o g Combination #63: (#17 a #22) 0 / A \ f ° Combination #68: (# 18 & #23) /AY" (J o a o Combination #73: (#4 a #5) {ft^ O <j> & £) o /i\ ar\ 6 rx> /AN. W Combination #64: (#17 a #23) 0F o o o Combination #69: (#19 S #20) -*—?—°-^o 0 n 'ti, 6 o LT ° © o Combination #74: (#3 a #6) &...... «i 0 ^ — o /\>\^oA,V/S> Qr6 o i vO Combination #66. (#18 a #20) o o o ~ & Combination #70 :(# 19 & #21) 6 k W o c o o o is 98 Appendix APPENDIX E: ANSYS INPUT AND OUTPUT FILES ANSYS INPUT FILES AND OUTPUT FILES FOR CONFIGURATIONS: COMBO #31, COMBO #37, DRAO#l, AND THE BRIDGING SYSTEM 99 Appendix E Input file tor Combination #31 create /title, LAR-Backing Structure (Combo#31), Dec 14, 1998 ! Created by Ya-Ying Chang ! LAR ! Finite Element Model for LAR Backing Structure SECTION 1: Definition of elements, materials and sections Define element type et,l,pipel6„„0„2 et,2,mass21 ! Define material properties of steel mp,ex, 1,200 mp,dens,l,7.85e-12 mp,nuxy, 1,0.3 mp,gxy, 1,79.29 mp,alpx,l,11.7e-6 I ! Define shapes in mm, mm ! r,no,OD,Tkwall nil, 168,7.112 r, 12,168,7.112 r, 13,0.001825,0.001825,0.001825 Specify coordinate system and material SECTION 2: Geometry definition ! Young's modulus in kN/mm2 ! density in kN-secA2/mmA4 (w/a =9810 mm/secA2) ! Poisson's ratio ! shear ratio in kN/mm2 ! thermal expansion coeff. / deg. C ! Top/Bottom Chords !Web ! Panel mass per actuator Define nodes Assuming 5.25m Flat Panels, 21m Triangular Unit node,#,x,y,z csys,0 local,! 1,0„„,-11,6 n, 1,7875,4547,0 n,2,13125,4547,0 n,3,10500,9093,0 n,4,13125,-4547,0 n,5,18375,13640,0 n,6,0,9093,0 n,7,11813,-2273,-1829 n,8,17063,11367,-1829 n,9,2625,9093,-1829 n,10,0,0,0 n, 11,20,0,0 n,12,5250,0,0 n, 13,10500,0,0 n,14,15750,0,0 n,15,20980,0,0 n,20,21000,0,0 ! Center points (top) Cantilever truss points (top) ! Cantilever truss points (bottom) ! Top chord 100 Appendix E n;21,20990,17,0 n,22,18375,4547,0 n,23,15750,9093,0 n,24,13125,13640,0 n,25,10510,18169,0 n,30,10500,18187,0 n,35,10,17,0 n,34,2625,4547,0 n,33,5250,9093,0 n,32,7875,13640,0 n,31,10490,18169,0 n,40,2635,0,-1829 ! Bottom chord n,41,7875,0,-1829 n,42,10500,0,-1829 n,43,13125,0,-1829 n,44,18365,0,-1829 n,45,19683,2282,-1829 n,46,17063,6820,-1829 n,47,15750,9093,-1829 11,48,14438,11367,-1829 n,49,l 1818,15905,-1829 n,50,9183,15905,-1829 n,51,6563,11367,-1829 n,52,5250,9093,-1829 n,53,3938,6820,-1829 n,54,1318,2282,-1829 n,60,6563,6820,-1829 n,61,9188,2273,-1829 n,62,l 1813,2273,-1829 n,63,14438,6820,-1829 n,64,13125,9093,-1829 n,65,7875,9093,-1829 mat,l ! Circular HSS type,l real, 11 en,l,10,11 en,2,ll,12 en,3,12,13 en,4,13,14 en,5,14,15 en,6,15,20 en, 11,20,21 en,12,21,22 en,13,22,23 en,14,23,24 en,15,24,25 en,16,25,30 en,21,30,31 en,22,31,32 en,23,32,33 en,24,33,34 en,25,34,35 en,26,35,10 en,33,l,13 en,34,2,13 en,35,2,23 101 Appendix E en,36,3,23 en,37,3,33 en,38,l,33 en,41,40,41 en,42,41,42 en,43,42,43 en,44,43,44 en,45,45,46 en,46,46,47 en,47,47,48 en,48,48,49 en,50,50,51 en,51,51,52 en,52,52,53 en,53,53,54 en,55,40,54 en,56,44,45 en,57,49,50 en>30'4>13 ! Cantilever sections en,31,5,23 en,32,6,33 en,91,4,7 en,92,7,13 en,93,7,42 en,94,5,8 en,95,8,23 en,96,8,47 en,97,6,9 en,98,9,33 en,99,9,52 en,135,52,60 en,136,60,61 en,137,61,42 en, 138,42,62 en,139,62,63 en,140,63,47 en, 141,47,64 en,142,64,65 en, 143,65,52 type,l real, 12 en,61,11,40 ! Truss webs en,62,12,40 en,63,12,41 en,64,13,41 en,65,13,42 en,66,13,43 en,67,14,43 en,68,I4,44 en,69,15,44 en,71,21,45 en.72,22,45 en.73,22,46 en,74,23,46 en,75,23,47 en,76,23,48 102 Appendix E en,77,24,48 en,78,24,49 en,79,25,49 en,81,31,50 en,82,32,50 en,83,32,51 en,84,33,51 en,85,33,52 en,86,33,53 en,87,34,53 en,88,34,54 en,89,35,54 en,121,33,60 en,122,l,60 en,123,l,61 en,124,13,61 en,125,13,62 en, 126,2,62 en, 127,2,63 en, 128,23,63 en,129,23,64 en, 130,3,64 en,131,3,65 en,132,33,65 type,2 ! Panels real, 13 en,101,10 en,102,12 en,103,13 en, 104,14 en,105,20 en, 106,22 en,107,23 en, 108,24 en, 109,30 en,l 10,32 en,l 11,33 en, 112,34 en,113,l en, 114,2 en.115.3 en, 116,4 en, 117,5 en, 118,6 ! Define boundary conditions nail eall local,90,0„„-30 nrotat,all d,10,uz,0„30,10 d,20,uy,0„30,10 d,30,ux,0 /view„0,-l,l /pbc,all,l eplot /eof 103 Appendix E (===============================================: ! Section 3: Loads |===============================================: ! Load Case 1: Gravity Load acel„,9810 /eof post ! Postprocessing /format„„4 /output,etruss_t,rst prrsol csys,0 esel,u,type„2 etable,fxi,smisc, 1 elable,fyi,smisc,2 etable,fzi,smisc,3 etable,mxi,smisc,4 etable,myi,smisc,5 elable,mzi,smisc,6 etable,fxj,smisc,7 etable,fyj,smisc,8 etable,fzj,smisc,9 etable,mxj,smisc,10 etable,myj,smisc,ll elable,mzj,smisc, 12 prelab,fxi,fyi,fzi,mxi,rnyi,mzi pretab,fxj,fyj,fzj,mxj,myj,mzj etable.eras esel.s,type..2 etable,fxi,smisc,l etable,fxj,smisc,2 pretab,fxi,fxj /output /output, etruss_t, dsp prdisp /output nsel.all esel,all /eof 104 Appendix E Combo #31 No tilt Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 10.0 0.0 0.0 139.2 0.0 0.0 0.0 20.0 0.0 0.0 139.2 0.0 0.0 0.0 30.0 0.0 0.0 139.2 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 417.6 0.0 0.0 0.0 105 Combo #31 No tilt Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 -1.7 2.9 -19.8 20.1 2 -1.6 2.2 -19.8 20.0 3 -1.1 2.6 -19.8 20.0 4 -2.6 2.0 -21.6 21.8 5 -0.5 1.9 -21.6 21.7 6 -1.4 3.8 -21.6 21.9 7 -2.7 2.7 -20.4 20.8 8 -1.0 1.5 -20.4 20.5 9 -0.8 3.6 -20.4 20.8 10 0.0 5.2 0.0 5.2 11 0.0 5.2 -0.1 5.2 12 -0.6 3.9 -13.4 13.9 13 -2.2 2.5 -19.6 19.9 14 -3.8 2.6 -13.6 14.3 15 -4.5 2.6 -0.1 5.2 20 -4.5 2.6 0.0 5.2 21 -4.5 2.6 -0.1 5.2 22 -3.1 2.7 -13.4 14.0 23 -1.1 2.0 -19.6 19.7 24 -0.4 0.5 -13.6 13.6 25 0.0 0.0 -0.1 0.1 30 0.0 0.0 0.0 0.0 31 0.0 0.0 -0.1 0.1 32 -0.8 1.2 -13.4 13.4 33 -1.2 3.2 -19.6 19.9 34 -0.4 4.6 -13.6 14.4 35 0.0 5.2 -0.1 5.2 40 -4.4 2.2 -7.2 8.7 41 -3.2 2.6 -17.6 18.1 42 -2.3 2.7 -19.6 19.9 43 -1.3 2.0 -17.8 17.9 44 0.0 0.4 -7.3 7.3 45 0.3 0.2 -7.2 7.2 46 -0.7 1.1 -17.6 17.6 47 -1.2 1.8 -19.6 19.7 48 -1.1 3.0 -17.8 18.1 49 -0.4 5.0 -7.3 8.8 50 -0.3685 5.305 -7.159 8.918 51 -0.6086 4.078 -17.59 18.07 52 -1.015 3.219 -19.58 19.87 53 -2.153 2.693 -17.79 18.12 54 -4.15 2.393 -7.298 8.73 60 -1.361 3.103 -19.68 19.97 61 -1.946 2.723 -19.64 19.93 62 -2.003 2.428 -19.68 19.93 106 Appendix E NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 63 -1.371 2.105 -19.64 19.8 64 -1.102 2.189 -19.68 19.83 65 -1.139 2.896 -19.65 19.89 MAXIMUM ABSOLUTE VALUES NODE 20 50 6 6 VALUE -4.5 5.3 -21.6 21.9 107 Appendix E Combo #31(Tilted) ANSYS OUTPUT FILE Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [KN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 10 0.00 0.00 140.1 0.00 0.00 0.00 20 0.000 0.000 139.2 0.00 0.00 0.00 30 0.000 0.000 138.3 0.00 0.00 0.00 TOTAL VALUES VALUE 0.000 0.000 417.6 0.00 0.00 0.00 108 Appendix E Combo #31 (Tilted) ANSYS OUTPUT FILE THE FOLLOW DEGREE OF FREEDOMS RESULTS IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 -2.3 0.0 -19.1 19.2 2 -5.8 0.4 -19.0 19.9 3 -2.7 3.2 -19.9 20.4 4 30.7 17.7 -27.6 44.9 5 -1.4 -2.4 -21.5 21.6 6 -3.2 38.9 -27.9 48.0 7 5.8 4.8 -21.4 22.6 8 -2.1 -2.6 -20.0 20.2 9 -2.6 10.6 -21.6 24.2 10 0.5 4.9 0.0 4.9 11 0.5 4.9 -0.1 4.9 12 -1.5 6.1 -13.5 14.9 13 -3.7 -0.7 -18.5 18.8 14 -4.8 11.1 -15.0 19.3 15 -4.2 2.5 -0.1 4.9 20 -4.2 2.4 0.0 4.8 21 -4.1 2.4 -0.1 4.8 22 3.4 4.4 -14.5 15.5 23 -2.6 -1.4 -19.1 19.3 24 5.0 1.7 -14.5 15.5 25 0.0 0.0 -0.1 0.1 30 0.0 0.0 0.0 0.0 31 0.0 0.0 -0.1 0.1 32 1.4 -3.2 -12.8 13.2 33 -2.8 -0.3 -18.7 18.9 34 -4.4 3.9 -13.0 14.2 35 0.4 4.9 -0.1 4.9 40 -4.6 3.4 -6.4 8.6 41 -4.6 -0.7 -16.2 16.9 42 -3.9 -0.7 -18.5 18.9 43 -2.8 4.2 -18.0 18.7 44 -0.6 4.8 -8.1 9.4 45 4.8 1.7 -7.8 9.3 46 0.1 -0.9 -17.4 17.4 47 -2.8 -1.7 -19.0 19.3 48 -0.3 1.1 -18.0 18.1 49 1.9 5.1 -8.5 10.1 50 1.9 2.0 -7.8 8.3 51 0.3 -0.8 -17.2 17.3 52 -2.8 -0.4 -18.7 18.9 53 -5.9 0.8 -16.5 17.6 54 -6.5 2.3 -6.0 9.1 60 -4.2 -1.1 -18.6 19.1 61 -5.0 -1.5 -18.3 19.1 62 -6.1 0.5 -18.7 19.7 63 -4.2 -0.6 -19.0 19.4 64 -2.8 0.1 -19.3 19.5 109 Appendix E NODE UX [mm] 65 -2.8 MAXIMUM ABSOLUTE VALUES NODE 4 VALUE 30.7 UY UZ USUM [mm] [mm] [mm] -0.9 -18.7 19.0 6 6 6 38.9 -27.9 48.0 110 Appendix E Input file for Combination #37 create /title, LAR-Backing Structure (Combo#37), Dec 14, 1998 LAR Finite Element Model for LAR Backing Structure Rev Date: August 20, 1999 Note: tilt angle increase to 11 degrees SECTION 1: Definition of elements, materials and sections Define element type et,l,pipel6„„0„2 et,2,mass21 ! ! Define material properties of steel mp.ex, 1,200 ! Young's modulus in kN/mm2 mp,dens,l,7.85e-12 ! density in kN-secA2/mmA4 (w/a =9810 nim/secA2) mp,nuxy, 1,0.3 ! Poisson's ratio mp,gxy,l,79.29  shear ratio in kN/mm2 mp,alpx,l,11.7e-6 ! thermal expansion coeff. / deg. C ! Define shapes in mm, mm ! r.no,OD,Tkwall r,l 1.168,7.112 !Top/Bottom Chords r,12,168,7.U2 !Web r,13,0.001825,0.001825,0.001825 IPanel mass per actuator Specify coordinate system and material SECTION 2: Geometry definition Define nodes Assuming 5.25m Flat Panels, 21m Triangular Unit node,#,x,y,z local, 11,0„„,-11,6 n, 1,7875,4547,0 ! Center points (top) n,2,13125,4547,0 n,3,10500,9093,0 n,7,5250,4547,-1800 n,8,10500,4547,-1800 n,9,15750,4547,-1800 n, 10,0,0,0 ! Top chord n,ll,20,0,0 n,12,5250,0,0 n, 13,10500,0,0 n,14,15750,0,0 n,15,20980,0,0 n,20,21000,0,0 n,21,20990,17,0 111 Appendix E n,22,18375,4547,0 n,23,15750,9093,0 n,24,13125,13640,0 n,25,10510,18169,0 11,30,10500,18187,0 11,35,10,17,0 n,34,2625,4547,0 n,33,5250,9093,0 n,32,7875,13640,0 n,31,10490,18169,0 n,40,2635,0,-1800 ! Bottom chord n,41,7875,0,-1800 n,43,13125,0,-1800 n,44,18365,0,-1800 n,45,19683,2282,-1800 n,42,18375,4547,-1800 n,46,17063,6820,-1800 n,47,15750,9093,-1800 n,48,14438,11367,-1800 n,49,11818,15905,-1800 n,50,9183,15905,-1800 n,51,6563,11367,-1800 n,52,5250,9093,-1800 n,53,3938,6820,-1800 n,67,2628,4551,-1800 n,54,1318,2282,-1800 11,60,6563,6820,-1800 n,61,9188,2273,-1800 n,62,11813,2273,-1800 n,63,14438,6820,-1800 n,64,13125,9093,-1800 n,65,7875,9093,-1800 n,71,15750,9093,0 n,72,21000,9093,0 n,73,26250,9093,0 n,74,13125,13640,0 n,75,18375,13640,0 n,76,23625,13640,0 n,77,28875,13640,0 n,81,18375,9093,-1800 n,82,23625,9093,-1800 n,83,15750,13640,-1800 n,84,21000,13640,-1800 11,85,26250,13640,-1800 mat,l ! Circular HSS type,l real, 11 en,l,10,11 en,2,ll,12 en,3,12,13 en,4,13,14 en,5,14,15 en,6.15,20 en, 11,20,21 en,12,21,22 en,13,22,23 112 Appendix E en, 14,23,24 en,15,24,25 en, 16,25,30 en,21,30,31 en,22,31,32 en,23,32,33 en,24,33,34 en,25,34,35 en,26,35,10 en,27,22,42 en,30,l,34 en, 31,1,2 en,32,2,22 en,33,3,33 en,34,3,23 en,41,40,41 en,42,41,43 en,43,43,44 en,44,42,45 en,45,42,46 en,46,46,47 en,47,47,48 en,48,48,49 en,50,50,51 en,51,51,52 en,52,52,53 en,53,54,67 en,54,53,67 en,55,40,54 en,56,44,45 en,57,49,50 en,58,7,67 en,59,9,42 en,97,7,8 en,98,8,9 en,151,47,64 en, 152,64,65 en,153,65,52 en,154,71,72 en,155,72,73 en,156,81,82 en, 157,74,75 en, 158,75,76 en,159,76,77 en, 160,83,84 en,161,84,85 en,171,72,75 en, 172,72,76 en, 173,81,83 en, 174,82,85 type, 1 real, 12 en,61,11,40 ! Truss webs en,62,12,40 en,63,12,41 en,64,13,41 113 Appendix E en,65,34,67 en,66,13.43 en,67,14,43 en,68,14,44 en,69,15,44 en,71,21,45 en,72,22.45 en,73,22,46 en,74,23,46 en,75,23,47 en,76,23,48 en,77,24,48 en,78,24,49 en,79,25,49 en,81,31,50 en,82,32,50 en,83,32,51 en,84,33,51 en,85,33,52 en,86,33,53 en,87,34,53 en,88,34,54 en,89,35,54 en.91,7,34 en.92,1,7 en,93,l,8 en,94,2,8 en,95,2,9 en,96,9,22 en,129,23,64 en,130,3,64 en,131,3,65 en,132,33,65 en,133,71.81 en,134,81,72 en,135,72,82 en, 136,82,73 en, 13 7,74,83 en, 138,83,75 en, 139,75,84 en, 140,84,76 en, 141,76,85 en,142,85,77 type,2 ! Panels real, 13 en,101,10 en,102,12 en,103,13 en, 104,14 en, 105,20 en, 106,22 en, 107,23 en, 108,24 en, 109,30 en,l 10,32 en,lll,33 114 Appendix E en,112,34 en,113,l en,114,2 en,115,3 en, 116,72 en,117,73 en, 118,75 en,l 19,76 en, 120,77 ! Define boundary conditions local,90,0„„-30 nsel,s,node„ 10,30,10 nrotat,all d,10,uz,0„30,10 d,20,uy,0„30,10 d,30,ux,0 nsel,s,node„71,74,3 nsel,a,node„23,24,l local,20,0„„30 csys,20 nrotat,all cp,2,uz,23,71 cp,next,uz,24,74 nsel,s,node,,73,77,4 local,21,0,„',-30 nrotat,all d,73.ux,0„77,4,uz nail eall /view„0,-l,l /pbc,all,l eplot /eof load 1===================== ! Section 3: Loads !===================== ! Load Case 1: Gravity Load acel,„9810 /eof post /format,, f„ 3 /output,com37,out /output /eof 115 Appendix E Combo #37 No tilt. Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm 10 0.0 0.0 115.7 0.0 0.0 0.0 20 0.0 0.0 129.0 0.0 0.0 0.0 30 0.0 0.0 142.8 0.0 0.0 0.0 73 0.0 0.0 32.9 0.0 0.0 0.0 77 0.0 0.0 43.1 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 463.5 0.0 0.0 0.0 116 Appendix E Combo #37 No tilt. Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 -2.7 4.4 -16.7 17.5 2 -3.2 3.8 -18.0 18.6 3 -1.8 2.4 -20.4 20.6 7 -3.9 2.3 -14.7 15.4 8 -3.4 1.0 -17.7 18.1 9 -2.9 -0.2 -17.2 17.5 10 -2.8 6.1 0.0 6.7 11 -2.8 6.1 0.0 6.7 12 -3.2 5.9 -7.4 10.0 13 -4.0 5.2 -10.4 12.3 14 -4.9 4.3 -7.4 9.9 15 -5.2 3.0 0.0 6.1 20 -5.2 3.0 0.0 6.1 21 -5.2 3.0 -0.1 6.1 22 -3.5 3.2 -16.1 16.8 23 -2.0 1.9 -22.5 22.7 24 -0.8 0.5 -16.1 16.1 25 0.0 0.0 -0.1 0.1 30 0.0 0.0 0.0 0.0 31 0.0 0.0 -0.1 0.1 32 -1.0 1.2 -11.3 11.4 33 -1.7 3.1 -16.5 16.9 34 -2.4 5.1 -12.3 13.5 35 -2.8 6.1 -0.1 6.7 40 -5.2 2.3 -4.0 7.0 41 -4.5 1.3 -9.5 10.6 42 -2.9 -0.7 -16.1 ' 16.4 43 -3.6 0.1 -9.5 10.2 44 -2.8 -1.3 -4.0 5.1 45 -2.6 -1.5 -8.7 9.2 46 -2.8 0.2 -20.6 20.8 47 -2.7 1.4 -22.5 22.7 48 -2.6 2.7 -20.7 21.0 49 -2.0 4.9 -8.7 10.2 50 -2.0 5.4 -6.1 8.4 51 -2.6 4.6 -14.9 15.8 52 -3.0 4.0 -16.5 17.2 53 -3.5 3.3 -15.4 16.2 54 -4.7 2.6 -6.7 8.6 64 -2.8 2.1 -21.5 21.8 65 -3.0 3.5 -18.5 19.1 67 -3.9 2.8 -12.3 13.2 71 0.4 0.8 -22.5 22.5 72 0.3 -0.1 -12.2 12.2 117 Appendix E NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 73 0.1 0.2 0.0 0.3 74 1.1 -3.0 -16.1 16.4 75 0.9 0.2 -14.0 14.0 76 0.4 -0.2 -8.6 8.6 77 0.1 0.2 0.0 0.2 81 4.0 1.0 -17.5 17.9 82 4.3 -0.7 -6.2 7.6 83 2.0 -0.2 -15.3 15.4 84 2.5 0.8 -11.7 12.0 85 3.0 0.0 -4.5 5.4 MAXIMUMABSOLUTE VALUES NODE 15 10 47 47 VALUE -5.2 6.1 -22.5 22.7 118 Appendix E Combo #37 Tilt angles of -11 (radial) and 6 (tangential) degrees Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 10 0.0 0.0 116.4 0.0 0.0 0.0 20 0.0 0.0 129.2 0.0 0.0 0.0 30 0.0 0.0 142.0 0.0 0.0 0.0 73 0.0 0.0 33.4 0.0 0.0 0.0 77 0.0 0.0 42.5 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 463.5 0.0 0.0 0.0 119 Combo #37 Tilt angles of -11 (radial) and 6 (tangential) degrees Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 -2.7 4.4 -16.7 17.5 2 -3.2 3.8 -18.0 18.6 3 -1.8 2.4 -20.4 20.6 7 -3.9 2.3 -14.7 15.4 8 -3.4 1.0 -17.7 18.1 9 -2.9 -0.2 -17.2 17.5 10 -2.8 6.1 0.0 6.7 11 -2.8 6.1 0.0 6.7 12 -3.2 5.9 -7.4 10.0 13 -4.0 5.2 -10.4 12.3 14 -4.9 4.3 -7.4 9.9 15 -5.2 3.0 0.0 6.1 20 -5.2 3.0 0.0 6.1 21 -5.2 3.0 -0.1 6.1 22 -3.5 3.2 -16.1 16.8 23 -2.0 1.9 -22.5 22.7 24 -0.8 0.5 -16.1 16.1 25 0.0 0.0 -0.1 0.1 30 0.0 0.0 0.0 0.0 31 0.0 0.0 -0.1 0.1 32 -1.0 1.2 -11.3 11.4 33 -1.7 3.1 -16.5 16.9 34 -2.4 5.1 -12.3 13.5 35 -2.8 6.1 -0.1 6.7 40 -5.2 2.3 -4.0 7.0 41 -4.5 1.3 -9.5 10.6 42 -2.9 -0.7 -16.1 16.4 43 -3.6 0.1 -9.5 10.2 44 -2.8 -1.3 -4.0 5.1 45 -2.6 -1.5 -8.7 9.2 46 -2.8 0.2 -20.6 20.8 47 -2.7 1.4 -22.5 22.7 48 -2.6 2.7 -20.7 21.0 49 -2.0 4.9 -8.7 10.2 50 -2.0 5.4 -6.1 8.4 51 -2.6 4.6 -14.9 15.8 52 -3.0 4.0 -16.5 17.2 53 -3.5 3.3 -15.4 16.2 54 -4.7 2.6 -6.7 8.6 64 -2.8 2.1 -21.5 21.8 65 -3.0 3.5 -18.5 19.1 67 -3.9 2.8 -12.3 13.2 71 0.4 0.8 -22.5 22.5 72 0.3 -0.1 -12.2 12.2 120 Appendix E NODE UX [mm] 73 0.1 74 1.1 75 0.9 76 0.4 77 0.1 81 4.0 82 4.3 83 2.0 84 2.5 85 3.0 MAXIMUM ABSOLUTE NODE 33 VALUE 54.UY UZ USUM [mm] [mm] [mm] 0.2 0.0 0.3 -3.0 -16.1 16.4 0.2 -14.0 14.0 -0.2 -8.6 8.6 0.2 0.0 0.2 1.0 -17.5 17.9 -0.7 -6.2 7.6 -0.2 -15.3 15.4 0.8 -11.7 12.0 0.0 -4.5 5.4 VALUES 13 23 23 62.7 -34.1 70.0 121 Appendix E Input file for DRAO#l create /title, LAR-Backing Stnicture (DRAO#l), August 14, 1999 LAR Finite Element Model for LAR Space Frame Structure (Tilted) Rev Date Note SECTION 1: Definition of elements, materials and sections Define element type et,l,pipel6„„0„2 et,2,mass21 ! ! Define material properties of steel mp,ex, 1,200 ! Young's modulus in kN/mm2 mp,dens,l,7.85e-12 ! density in kN-secA2/mmA4 (w/a =9810 mm/secA2) mp,nuxy,l,0.3 ! Poisson's ratio mp,gxy, 1,79.29  shear ratio in kN/mm2 mp,alpx,l,11.7e-6 ! thermal expansion coeff. / deg. C ! ! Define shapes in mm, mm ! r,no,OD,Tkwall r,ll,168,7.112 (Top/Bottom Chords r,12,168,7.112 !Web r,13,0.001825,0.001825,0.001825 IPanel mass per actuator Specify coordinate system and material SECTION 2: Geometry definition Define nodes Assuming 3.5m Flat Panels, 21m Triangular Unit node,#,x,y,z local,ll,0,„„-ll,6 n, 1,7875,4547,0 ! Center points (top) n,2,13125,4547,0 n,3,10500,9093,0 n,4,13125,-4547,0 I Cantilever truss points (top) n,5,18375,13640,0 n,6,0,9093,0 n,7,14438,-2273,-1829 ! Cantilever truss points (bottom) n,8,15750,13640,-1829 n,9,1313,6820,-1829 n, 10,0,0,0 ! Top chord n, 11,20,0,0 n,12,5250,0,0 n,13,10500,0,0 n,14,15750,0,0 n, 15,20980,0,0 n,20,21000,0,0 n,21,20990,17,0 n,22,18375,4547,0 n.23,15750.9093.0 122 Appendix E 11,24,13125,13640,0 n,25,10510,18169,0 n,30,10500,18187,0 n,35,10,17,0 n,34,2625,4547,0 n,33,5250,9093,0 n,32,7875,13640,0 n,31,10490,18169,0 n,40,2635,0,-1829 11,41,7875,0,-1829 n,42,'15750,0,-1829 n,43,13125,0,-1829 11,44,18365,0,-1829 n,45,19683,2282,-1829 n,46,17063,6820,-1829 n,47,13125,13640,-1829 n,48,14438,11367,-1829 n,49,11818,15905,-1829 n,50,9183,15905,-1829 n,51,6563,11367,-1829 n,52,2625,4547,-1829 n,53,3938,6820,-1829 n,54,1318,2282,-1829 n,61,5250,4547,-1829 n,62,14438,2273,-1829 n,63,11813,11367,-1829 mat,l type,l real, 11 en,l,10,11 en,2,ll,12 en,3,12,13 en,4,13,14 en,5,14,15 en,6,15,20 en, 11,20,21 en,12,21,22 en,13,22,23 en,14,23,24 en, 15,24,25 en, 16,25,30 en,21,30,31 en,22,31,32 en,23,3'2,33 en,24,33,34 en,25,34,35 en,26,35,10 en,33,l,34 en,34,2,14 en,35,3,24 en,41,40,41 en,42,41,43 en,43,42,43 en,44,42,44 en,45,45,46 en,46,46,48 ! Bottom chord ! Circular HSS 123 Appendix E en,47,47,48 en,48,47,49 en,50,50,51 en,51,51,53 en,52,52,53 en,53,52,54 en,55,40,54 en,56,44,45 en. 5 7,49,50 en,30,4,14 ! Cantilever sections en,31,5,24 en,32,6,34 en:37,52,61 en,38,42,62 en,39,47,63 en,91,4,7 en,92,7,14 en,93,7,42 en,94,5,8 en,95,8,24 en,96,8,47 en,97,6,9 en,98,9,34 en,99,9,52 type,l real, 12 en.61,11,40 ! Truss webs en,62,12,40 en,63,12,41 en,64,13,41 en,65,14,42 en,66,13,43 en,67,14,43 en,68,14,44 en,69,15,44 en,71,21,45 en.72,22,45 en,73,22,46 en, 74,23,46 en,75,24,47 en,76,23,48 en,77,24,48 en, 78,24,49 en,79,25,49 en,81,31,50 en,82,32,50 en,83,32,51 en,84,33,51 en,85,34,52 en,86,33,53 en,87,34,53 en,88,34,54 en,89,35,54 en,12U,61 en,122,34,61 en, 123,2,62 124 Appendix E en, 124,14,62 en,125,3,63 en, 126,24,63 type,2 ! Panels real, 13 en,101,10 en,102,12 en,103,13 en, 104,14 en, 105,20 en,106,22 en, 107,23 en,108,24 en,109,30 en,110,32 en,lll,33 en.l 12,34 en,113,l en,114,2 en,115,3 en, 116,4 en, 117,5 en, 118,6 ! Define boundary conditions local,90,0„„-30 nsel,s,node„ 10,30,10 nrotat,all d,10,uz,0„30,10 d,20,uy,0„30,10 d.30.ux,0 nail eall /view„0,-l,l /pbc,all,l eplot /eof load (===================================== ! Section 3: Loads !===================================== ! Load Case 1: Gravity Load acel„,9810 /eof post /format„f„3 /output,drao_t,out /output /eof I 125 Appendix E DRAO#1 No tilt. Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 10 0.0 0.0 133.8 0.0 0.0 0.0 20 0.0 0.0 133.8 0.0 0.0 0.0 30 0.0 0.0 133.8 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 401.4 0.0 0.0 0.0 126 Appendix E DRA0#1 No tilt. Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 0.6 3.2 -25.0 25.2 2 -2.9 3.9 -25.1 25.6 3 -2.4 0.3 -25.2 25.3 4 -4.4 3.6 -13.5 14.7 5 -1.2 -1.2 -13.4 13.5 6 0.9 4.4 -13.6 14.3 7 -0.6 1.3 -13.3 13.4 8 -1.1 3.4 -13.3 13.8 9 -2.8 2.3 -13.4 13.9 10 0.0 4.9 0.0 4.9 11 0.0 4.9 -0.1 4.9 12 -0.5 4.7 -11.9 12.8 13 -1.9 4.2 -17.4 18.0 14 -3.5 3.3 -13.4 14.3 15 -4.2 2.4 -0.1 4.9 20 -4.2 2.4 0.0 4.9 21 -4.2 2.4 -0.1 4.9 22 -4.0 1.9 -11.9 12.7 23 -3.1 0.9 -17.4 17.7 24 -1.4 0.0 -13.5 13.5 25 0.0 0.0 -0.1 0.1 30 0.0 0.0 0.0 0.0 31 0.0 0.0 -0.1 0.1 32 0.0 0.6 -11.9 11.9 33 0.2 2.1 -17.4 17.6 34 0.4 3.9 -13.4 14.0 35 0.0 4.9 -0.1 4.9 40 -3.9 1.8 -6.4 7.7 41 -2.9 1.7 -15.6 16.0 42 -0.4 1.0 -13.5 13.5 43 -1.3 1.3 -16.7 16.8 44 0.2 0.6 -7.2 7.3 45 0.4 0.5 -6.4 6.4 46 -0.3 1.4 -15.6 15.7 47 -0.9 3.8 -13.5 14.0 48 -0.8 2.9 -16.7 16.9 49 -0.8 4.6 -7.3 8.6 50 -0.8 5.0 -6.4 8.1 51 -1.5 4.2 -15.6 16.2 52 -3.2 2.3 -13.5 14.0 53 -2.6 2.9 -16.7 17.1 54 -3.7 1.9 -7.3 8.4 61 -3.4 1.9 -19.1 19.5 62 0.1 1.0 -19.2 19.2 63 -1.3 4.3 -19.2 19.7 127 Appendix E MAXIMUM ABSOLUTE VALUES NODE 4 50 3 2 VALUE -4.4 5.0 -25.2 25.6 128 Appendix E DRAO#1 Tilt angles of -11 (radial) and 6 (tangential) degrees Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN GLOBAL COORDINATES NODE FX FY FZ MX MY MZ [kN] [kN] [kN] [kN-mm] [kN-mm] [kN-mm] 10 0.0 0.0 134.5 0.0 0.0 0.0 20 0.0 0.0 133.8 0.0 0.0 0.0 30 0.0 0.0 133.1 0.0 0.0 0.0 TOTAL VALUES VALUE 0.0 0.0 401.4 0.0 0.0 0.0 129 Appendix E DRAO#1 Tilt angles of -11 (radial) and 6 (tangential) degrees Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES )DE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 -46.1 29.8 -40.6 68.3 2 163.1 314.2 -143.0 381.7 3 322.3 -4.9 -3.6 322.4 4 -147.8 322.3 -20.0 355.2 5 148.7 293.3 -141.5 358.0 6 5.8 55.9 -9.2 57.0 7 -72.4 257.4 -35.4 269.7 8 133.0 173.6 -88.9 236.0 9 -34.2 38.8 -9.0 52.6 10 0.1 4.8 0.0 4.8 11 0.1 5.2 -0.2 5.2 12 -1.6 150.0 -40.0 155.2 13 -3.5 276.6 -70.2 285.4 14 -4.7 228.3 -57.0 235.3 15 -4.1 3.3 -0.2 5.3 20 -4.1 2.4 0.0 4.7 21 -3.3 2.8 -0.3 4.3 22 184.6 104.0 -51.9 218.1 23 248.4 136.9 -70.6 292.3 24 154.1 83.8 -46.3 181.4 25 0.5 0.2 -0.2 0.6 30 0.0 0.0 0.0 0.0 31 0.5 -0.3 0.0 0.5 32 59.0 -37.0 -10.8 70.5 33 9.8 -7.7 -16.5 20.7 34 -43.6 26.6 -13.2 52.7 35 -0.2 5.0 -0.1 5.0 40 ' -4.4 51.3 -15.0 53.7 41 •' -4.3 205.8 -54.4 213.0 42 -1.8 210.7 -53.9 217.4 43 -2.9 261.3 -66.7 269.6 44 -0.6 114.2 -29.2 117.8 45 100.5 54.7 -27.8 117.7 46 226.5 124.0 -64.0 266.1 47 136.0 77.3 -43.1 162.2 48 203.3 112.9 -60.4 240.2 49 55.0 34.2 -19.9 67.7 50 55.0 -29.6 -6.4 62.8 51 43.9 -26.4 -14.9 53.4 52 -52.2 28.2 -12.6 60.7 53 -29.1 14.6 -15.8 36.2 54 -48.5 26.9 -6.4 55.9 61 -53.8 20.6 -24.3 62.5 62 74.5 249.1 -95.0 276.8 63 220.4 33.0 -21.7 223.9 130 Appendix E MAXIMUM ABSOLUTE VALUES NODE 3 4 2 2 VALUE 322.3 322.3 -143 381.7 131 Appendix E Input file for the Bridging System create /title, LAR-Backup Structure , August 06, 1998 Created by Ya-Ying Chang LAR Finite Element Model for LAR Backing Structure Rev Date Note: Equilateral Triangle (21 m) SECTION 1: Definition of elements, materials and sections Define element type et,l,pipel6„„0„2 et,2,mass21 I ! Define material properties of steel mp,ex, 1,200 ! Young's modulus in kN/mm2 mp.dens,l,7.85e-12 ! density in kN-secA2/mmA4 (w/a =9810 mm/secA2) mp.nuxy, 1,0.3 ! Poisson's ratio mp,gxy,l,79.29  shear ratio in kN/mm2 mp.alpx, 1,11.7e-6 ! thermal expansion coeff. / deg. C ! ! Define shapes in mm, mm ! r,no,OD.Tkwall r.l 1,168,7.112 !Top/Bottom Chords r, 12,168,7.112 !Web r,13,0.001825,0.001825,0.001825 !Panel mass per actuator ! Specify coordinate system and material 1=============================================================== !SECTION 2: Geometry definition 1==========================================^=== ! Local systems local, 11.0„„-30 local,12,0,10500,-18186.5335,0,-30,10,10 local, 13,0„„30 !n, 1000,0,0,0 local,90,0,10500,-18186.5335,0„-ll,6 csys,90 n, 1,0,0,0 n,2,-5250,0,0 n,3,-10500,0,0 n,4,-15750,0,0 n,5,-21000,0,0 n,6,-2625,0,-1800 n,7,-7875,0,-1800 n,8,-10500,0,-1800 n,9,-13125,0,-1800 n,10,-18375,0,-1800 n,ll,-13125,-4546.633375,0 n,31,-21000,0,0 n,32,-18375,-4546.63338,0 n,33,-15750,-9093.26675,0 n,34,-13125,-13639.90013,0 n,35,-10500,-18186.5335,0 n,36,-19687.5,-2273.31669,-1800 132 Appendix E n,37,-17062.5,-6819.95006,-1800 n,38,-15750,-9093.26675,-1800 n,39,-14437.5,-11366.58344,-1800 n,40,-11812.5,-15913.21681,-1800 n,41,-10500,-9093.26675,0 n,61,-10500,-18186.5335.0 n,62,-7875,-13639.90013,0 n,63,-5250,-9093.26675,0 n,64,-2625,-4546.63338,0 n,65,0,0,0 n,66,-9187.5,-15913.21681,-1800 n,67,-6562.5,-l 1366.58344,-1800 n,68,-5250,-9093.26675,-1800 n,69,-3937.5,-6819.95006,-1800 n,70,-1312.5, -2273.31669,-1800 n,71,-7875,-4546.633375,0 n,72,-7875,-13639.90013,-1800 ! Bridging system n,201,-5250,-9093.26675,0 n,202,0,-9093.26675,0 n,203,5250,-9093.26675,0 n,204,-2625,-9093.26675,-1800 n,205,2625,-9093.26675,-1800 n,211,-7875,-13639.90013,0 n,212,-2625,-13639.90013,0 n,213,2625,-13639.90013,0 n,214,7875,-13639.90013,0 n,215,-5250,-13639.90013,-1800 n,216,0,-13639.90013,-1800 n,217,5250,-13639.90013,-1800 ! type.i real, 11 en, 1,1,2 en,2,2,3 en,3,3,4 en,4,4,5 en,5,6,7 en,6,7,8 en,7,8,9 en,8,9,10 en,9,l,6 en, 10,6,2 en, 11,2,7 en,12,7,3 en, 13,3,8 en,14,3,9 en,15,9,4 en,16,4,10 en, 17,10,5 en, 18,3,11 en, 19,11,33 en,20,8,ll en,21,11,38 en,22,10,36 en,23,8,38 133 Appendix E engen,30,2,30,l,23 engen,30,2,30,31.48 en,79,71,3 en,80,68,71 en,81,71,8 en,82,70,6 en,83,68,8 ! type,l real 11 en,501,201,202 en,502,202,203 en,503,204,205 en,504,201,204 en,505;204,202 en,506,202,205 en,507,205,203 en,511,211,212 611,512,212,213 en,513,213,214 en,514,215,216 en,515,216,217 en,516,211,215 en,517,215,212 en,518,212,216 en,519,216,213 en,520,213,217 en,521,217,214 en,522,204,215 en,523,205,217 en,524,202,212 en,525,202,213 type,2 Ipanel real, 13 en,24,l en,25,2 en,26,3 en,27,4 en,28,ll engen,30,3,30,24,28 en,508,202 en,532,212 en.533.213 nail eall /ANG, 1 ,-30.0,XS,l eplot /eof addne local,15,0,10500,-18186.5335,0„,10 csys,15 nsym,x,100,l,ll,l nsym,x,100,31,41,l nsym,x,100,61,72,l type,l real, 11 134 _____ Appendix E engen, 100,2,100,1,23 engen,100,2,100,31,53 engen,100,2,100,61,78 en,179,171,103 en,180,168,171 en,181,171,108 en, 182,170,106 en,183,168,108 type,2 real, 13 engen, 100,2,100,24,28 engen.30,2.30,124,128 /eof be csys, 11 nail nrotat,aIl nsel,s,node„ 1,61,30 nsel,a,node,,5,65,30 nsel,a,node„62,63,l nsel,a,node„201,211,10 d,l,ux,0,,„uy,uz d,61,ux,0„„uz d,31,uz,0 d,201,ux,0„211.10 cp,2,all,l,65 cp,next,all,31,5 cp,next,all,61,35 cp,next,uz,201,63 cp,next,uz,211,62 ! nsel,s,node„203,214,ll csys, 13 nrotat,203,214,ll d,203,ux,0„„uz d,214.ux.0,,„uz nail eall /eof deadL nail eall acel„,9810 /eof post ! Postprocessing /format.,,,4 /output,etruss3,rst prrsol csys,0 esel,u,type„2 etable,fxi,smisc,l etable,fyi,smisc,2 etable,fzi,smisc,3 etable,mxi,smisc,4 etable,myi,smisc,5 135 Appendix E elable,mzi,smisc,6 etable,fxj,smisc,7 etable,fyj,smisc,8 etable,fzj,smisc,9 etable,mxj,smisc, 10 etable,myi,smisc,l 1 etable,mzj,smisc,12 pretab,fxhfyi,fzi,mxi,myi,mzi pretab,fxj,fyj,fzj,mxj,myj,mzj etable,eras esel,s,type,,2 etable,fxi,smisc,l etable,fxj,smisc,2 pretab,fxi,fxj /output /outpul,etruss3,dsp prdisp /output nsel.all esel,all /eof main /clear /prep7 *use,create *use,bc eplot *use,deadl /eof 136 Appendix E Bridging System No tilt. Date: Dec 20, 1998 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN NODE FX FY [kN] [kN] 1 0.0 0.0 31 0.0 0.0 61 0.0 0.0 201 -0.2 0.1 203 0.2 0.1 211 0.2 -0.1 214 -0.2 -0.1 TOTAL VALUES VALUE 0.0 0.0 GLOBAL COORDINATES FZ MX MY MZ [kN] [kN-mm] [kN-mm] [kN-mm] 130.2 0.0 0.0 0.0 116.8 0.0 0.0 0.0 143.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 14.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 25.3 0.0 0.0 0.0 430.5 0.0 0.0 0.0 137 Appendix E Bridging System No tilt. Date: Dec 20, 1998 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM [mm] [mm] [mm] [mm] 1 0.0 0.0 0.0 0.0 2 0.5 0.6 -11.5 11.5 3 1.9 1.4 -16.3 16.5 4 3.2 0.8 -11.3 11.7 5 3.7 0.5 0.0 3.8 6 3.7 3.1 -6.1 7.8 7 2.7 2.5 -14.9 15.4 8 1.8 2.1 -16.4 16.6 9 1.1 2.3 -14.7 15.0 10 0.1 2.7 -6.0 6.6 11 2.2 1.4 -18.4 18.6 31 3.7 0.5 0.0 3.8 32 3.2 0.8 -11.4 11.8 33 2.1 1.7 -16.5 16.7 34 2.1 3.3 -11.6 12.2 35 2.4 4.1 0.0 4.7 36 0.0 2.7 -6.1 6.6 37 0.8 2.0 -14.9 15.1 38 1.4 1.4 -16.6 16.7 39 1.4 0.5 -15.1 15.2 40 1.3 -0.9 -6.2 6.4 41 2.2 1.7 -19.8 20.0 61 2.4 4.1 0.0 4.7 62 2.4 3.2 -14.9 15.4 63 2.1 1.3 -20.5 20.7 64 0.7 0.3 -14.0 14.0 65 0.0 0.0 0.0 0.0 66 1.3 -0.9 -8.0 8.2 67 1.6 0.7 -19.0 19.1 68 1.8 1.7 -20.5 20.7 69 2.6 2.4 -18.4 18.8 70 3.7 3.1 -7.5 8.9 71 1.9 1.2 -19.7 19.8 201 -0.3 -0.6 -20.5 20.5 202 -0.5 0.3 -11.2 11.2 203 -0.6 1.0 0.0 1.2 204 2.9 -0.9 -16.0 16.2 205 3.2 1.2 -5.7 6.7 211 0.9 1.5 -14.9 15.0 212 0.6 -0.3 -13.2 13.2 213 0.1 0.6 -8.2 8.2 214 -0.2 0.3 0.0 0.4 215 1.5 -0.1 -14.3 14.3 216 2.0 -0.3 -11.1 11.3 217 2.5 0.8 -4.3 5.1 138 Appendix E MAXIMUM ABSOLUTE VALUES NODE 6 35 68 68 VALUE 3.723 4.084 -20.54 20.69 139 APPENDIX F: CONNECTION RESISTANCE FORMATETTED SPREADSHEET FOR CONNECTION RESISTANCE CALCULATION 140 Appendix F PROJECT LAR SECTION 1 TITLE Weld Resistance DATE 3/02/00 FILE Truss 1.xls TIME 11:08 AM Case 1: Typical Warren Truss [INPUTS yield strength angle MEMBER SELECTION Chord: ?•;•>:•; diameter thickness area mass parameter check Web: .•;:;:•:<.,; diameter thickness area mass parameter check Fy do to A0 Mc Chk1 d, ti A, Mw Chk2 = if(d0/to<50,"O.K.","Too slender") if(d,/t, <50,"O.K.","Too slender") 350 Mpa 34.4 deg 168 mm 4.78 mm 2460 mm2 19.3 kg/m O.K. 73 mm 3.81 mm 828 mm2 6.5 kg/m O.K. Resistance Calculation At Panel Point B effective length (chord) KLc = 4725 mm effective length (web) KLw = 2387 mm A = d,/(2*SIN(61*PI0/180)) = 65 mm B = d,/(2*SIN(6,*PI0/180))  65 mm C = SIN(erPIO/180)A2/SIN(2*ei*PIO/180) = 0.34 D = do/2 = 84 mm eccentricity e = C"(A+B+g)-D  -31 mm gap g = 25 mm g' = g/to  5 CK = 0.26 Nop = -300.00 kN n = Nop/(A0*Fy)*1000 = -0.35 fn' = 1+0.3*n-0.3*nA2  0.86 connection resistance N, = CK,(to/t,)*(1/sin(e,*piO/180))"fn'*A,"Fy/1000 = 144 kN web comp. resistance Cr = 172 kN comp. Force in web CFw = 141.5 kN resistance check Chk3 = if(min(N1 ,Cr)>CFw,"O.K."."Failure") = O.K. eccentricity check Chk4 = if(e/dO>=-0.55,if(e/dO<=0.25,"O.K.","Select e"),"Select e") = O.K. punching shear Np5 = Fy/sqrt(3)*t0*piO*d,*(1+SIN(e,*PIO/180))/(2*SIN(e,*PIO/180)A2)/1000 = 543.0 kN Weight Calculation chord length required lenc = 36.75 m web length required lenw = 25.46 m total weight of chords Wc = lenc'Mc = 709 kg total weight of webs Ww = lenw'Mw  166 kg total weight W = Wc+Ww  S7S kg Note: - CK is taken from Figure 3.14 of "Design Guide for Hollow Structural Section Connections" by Packer & Henderson. - Cr is taken from Section 4 of "Steel Handbook of Construction", sixth ed. 141 Appendix F PROJECT LAR SECTION 1 TITLE Weld Resistance DATE 3/02/00 FILE Truss 1.xls TIME 11:49 AM Case 1: Typical Warren Truss INPUTS yield strength angle MEMBER SELECTION Chord: •;<;••:»!.? diameter thickness area mass parameter check Web: diameter thickness area mass parameter check Resistance Calculation lAt Panel Point C effective length (chord) effective length (web) Fy do to A0 Mc Chk1 d, ti A, Mw Chk2 eccentricity gap connection resistance web comp. resistance comp. Force in web resistance check eccentricity check punching shear Weight Calculation chord length required web length required total weight of chords total weight of webs total weight KLc KLw A B C D e 9 g' CK Nop n fn' N, Cr CFw Chk3 Chk4 Nos lenc lenw Wc Ww W if(do/t0<50,"O.K.",'Too slender") if(d,/t, <501',O.K.',,'Too slender") d1/(2*SIN(01*PIO/18O)) d,/(2*SIN(6,*PIO/180)) SIN(e,*PI0/180)A2/SIN(2"e,*PI0/18O) d0/2 C"(A+B+g)-D g/to Nop/(A0*Fy)*1000 1+0.3*n-0.3*nn2 CK*(t0/t,)*(1/sin(erpiO/180))*fn'*A,*Fy/1000 if(min(N1,Cr)>CFw,"O.K.","Failure") if(e/d0>=-0.55,if(e/d0-==0.25,"O.K.","Select e"),"Select e") Fy/sqrt(3) Vpi0*d,*(1 +SIN(9,*PI()/180))/(2*SIN(9, *PIQ/180)A2)/1000 lenc'Mc lenw*Mw Wc+Ww 350 Mpa 34.4 deg 168 mm 4.78 mm 2460 mm2 19.3 kg/m O.K. 88.9 mm 3.81 mm 1020 mm2 8.0 kg/m O.K. 4725 mm 2387 mm 79 mm 79 mm 0.34 84 mm -22 mm 25 mm 5 0.26 -300.00 kN -0.35 0.86 177kN 172 kN 70.7 kN O.K. O.K. 661.3 kN 36.75 m 25.46 m 709 kg 204 kg 313 kg Note: - CK is taken from Figure 3.14 of "Design Guide for Hollow Structural Section Connections" by Packer & Henderson. - Cr is taken from Section 4 of "Steel Handbook of Construction", sixth ed. 142 

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