Light weight Scissor Deployable Structures.

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1 March 15, Volume 3 Special Issue, ISSN Light weight Scissor Deployable Structures. Mr. D.M. Jade 1 (M.E. student) Pr. G.R.Patil 2 Rajarshi Shahu College Engineering, Pune, Rajarshi Shahu College Engineering, Pune, Department Civil Engineering, Department Civil Engineering, S. P. university Pune. (INDIA) S. P. university Pune. (INDIA) ABSTRACT Deployable structure is any mechanism that can expand from enclosing a small area or volume to enclosing a larger area or volume. It combines rigid linkages and joints in a configurable closed loop mechanism. The primary element the closedloop deployable structure expansion is the 'Scissor linkage'. In Scissor deployable structures a 3 Dimensional model Scissor Bridge is developed that carries the moving load. That moving load is uniformly distributed over a bridge 2.8 m X 6. m. The Scissor Bridge consists Two Girdle Beams having width.5 m and height are maintained by SLE flats size mm X mm with angle 3, 45 and 6. The SLE flats and 4 mm X 75 mm X mm are connected with HTFG Bolts. The Girdle beam cross SLE connected with ISRO 25. The Light weight Scissor deployable Bridge is analysed using STAAD.Pro V8i. This result is compared to our design criteria with acceptable safety factor. The bridge would thus need to be optimized in order to improve its safety factor. The loading is thus moved back to the Centre the bridge as it may result in the most critical configuration. Then modified the other parameters are modified in order to try and optimize the structure. The analysis is carried out based solely on the static loads expected. Keywords Deployable Structures, ScissorLikeElement (SLE), Girdle Beam Element, Flats SLE and Structural Optimization INTRODUCTION Today s deployable structures have their members connected in the factory, so that they satisfy a set preassigned geometrical constraints. Erection is then operated by simply articulating the various components the structure. Other advantages are the ease transportation and storage, the minimum skill requirements for erection, dismantling and relocation, and the competitive overall cost. Bridge for use after earthquake and other emergency situations, temporary protective covers in remote construction sites or for curing concrete in cold environments, domes for sport facilities, exhibition structures or shelters for travelling theatres. Deployable structures are even greater interest in the aerospace industry, where severe constraints apply to both payload capacity space ships and to building time in space. Two types deployable structures have been designed and constructed in the past. (i) Structures that is stressfree in the folded configuration, during deployment, and in the deployed configuration. Need to be stabilized by external locking devices An innovative geometric design methodology allows for structures that exhibit a stable and stressfree state in both the initial and the final configuration. However, geometric compatibility requirements cause the development strains and stresses during the deployment procedure. The structural behavior the structures during that phase is highly nonlinear; hence the analysis presents difficulties for the structural engineer. Second order theory structural analysis frames with analytical methods. However, an analytical approach is already too complicated for plane structures with simple geometry and few 57

2 March 15, Volume 3 Special Issue, ISSN degrees freedom, and it is practically impossible to use it for these deployable space structures with their nonregular geometric configuration. Geometric properties deployable structures. The basic structural module deployable structures is the socalled ScissorLike Element (SLE). It consists two straight Flats SLEs connected to each other at an intermediate point with a pivotal connection and hinged at their end nodes to end nodes other SLEs Fig.1 A typical ScissorLike Element. Strict geometric constraints have to be satisfied in order to ensure the deployability the structure. Response deployable structures (Scissor Bridge) during deployment stage The structural behavior deployable structures during deployment is great interest due to its highly nonlinear nature. Therefore, both a qualitative understanding the behavior and a quantitative evaluation stresses occurring during deployment constitute an integral part the design deployable structures. The nature the strains and stresses develop in the members the structure during deployment defines the type kinematic assumptions that have to be made for this problem. These strains and stresses result from compatibility requirements between the members inner and outer SLEs. Furthermore, a small deformation has to take place before the structure can carry loads. The deployed configuration was used as initial state for the analysis, i.e. dismantling was simulated instead deployment. Nonlinear beam elements i.e. Girdle Beam have been used to mode1 inner SLEs, while outer SLEs that are only subjected to axial stresses were represented by truss elements. After introducing auxiliary coordinate systems, the master node/slave node technique was used to model the pivotal connections. variation structural quantities during deployment stage The loaddisplacement curve indicates a snap through type behavior for the structure. It can also be observed that the maximum values external load and member forces occur at different time steps. The axial force member 1 inner SLEs is the dominant load carrying mechanism. The distribution forces among members is very unbalanced, a fact that should be seriously taken into consideration during design. The steep slope the curves at the collapsed configuration corresponds to the sum the axial stiffness the members. Fig. 2 Member numbering for inner SLEs. 58

3 March 15, Volume 3 Special Issue, ISSN Fig. 3 Reloading pattern Girdle Beam Element 1 and 2 along with plate Element Parameters affecting the structural behavior during deployament stage The behavior deployable structures during the deployment procedure. The next point interest for the analyst, and especially for the designer is to obtain information about how several parameters affect the response scissor bridge. optimize the design process by taking full advantage the features deployable structures and by minimizing their limitations. Parameters investigated here are the geometry the Girdle Beam structure, the cross section inner and outer SLEs, Properties Angle section used in Girdle beam (), Plate size and thickness, angle SLE, and the length to stiffness ratio the members. Choosing a large crosssection Angle section and Flats SLE in order to be on the safe side when loading the structure in the deployed configuration increases the stiffness the structure and therefore the stresses that develop during deployment Fig.4 Deflection Scissor Deployable Bridge X 75X X75X X75X (3 Degree) (45 Degree) (6 Degree) 6 M Span SLE (Deflection MM) 6 M Span 12 SLE 6 M Span 14 SLE 6 Mspan 16 SLE 59

4 March 15, Volume 3 Special Issue, ISSN X75X (3 X75X (45 X75X (6 Degree) Degree) Degree) 6 M Span SLE (Max. Axial Forces ) 6 M Span 12 SLE 6 M Span 14 SLE 6 M span 16 SLE Fig.5 Maximum Axial forces Scissor Deployable Bridge The lower centre node structure was fixed against horizontal and vertical motion, while the upper centre node could only move vertically and subjected to a vertical concentrated load that is recorded on the vertical axis the graph. The horizontal axis records the relative vertical displacement between the two centre nodes. Fig.6 SLE with Discrete Member Width Fig.7 Deformation Flats SLEs Due to Discrete width It was further assumed that at the pivotal connection there is a small gap between the Flats SLEs caused by a tiny margin in the length the pin and by the extensibility its material. In other words, the pin which is under tension elongates slightly so that there is no contact between the two Flats SLEs at the connection. This led us to the deformed configuration one the Flats SLEs an SLE demonstrated in Fig. 8 The Flats SLE can be thought as consisting six segments. The first and the sixth are in the slots the end hubs and are in contact with these hubs only at their end points. Segments 2 and 3 and segments 4 and 5 are separated by the contact points with the other Flats SLE the SLE. Segments 3 and 4 are separated by the pin. Because the elongation the pin, there is no continuous contact surface between the two Flats SLEs. 6

5 March 15, Volume 3 Special Issue, ISSN Fig.8 Details Deformation Flats SLEs Due to their Discrete Width Fig.9 Maximum Bending Moment Scissor Deployable Bridge M Span SLE (MAXIMUM SHEAR FORCEs ) 6 M Span 12 SLE 6 M Span 14 SLE X75X (3 Degree) X75X (45 Degree) X75X (6 Degree) 6 M span 16 SLE Fig. Maximum shear Forces Scissor Deployable Bridge The assumed deformed configuration a Flats SLE due to the discrete cross section width. Let (X, Y) be a global Cartesian coordinate system, while (Xi, Yi), i = 1,..., 6 are local systems for each the six segments. v = ( b h b) / 2 (1) v 1 = b / 2 =.5b (2) v 2 = k b (3) 61

6 March 15, Volume 3 Special Issue, ISSN where k = numerical factor slightly larger than.5 that depends on the extensibility the pin at the pivotal connection. For (2) and (3), it is inherently assumed that the two Flats SLEs are approximately the same length and the same stiffness. It can further be assumed that the six segments that constitute the Flats SLE have cubic shapes, expressed in the local coordinate systems as v(xi) = a i X 3 i + b i X 2 i + c i X i + d i, i = 1,....,6 (4) Then the slope is given by v'(x i ) = 3a i X 2 i + 2b i X i + c i ; i = 1,..., 6 (5) while the bending moment distribution is M(Xi) = EI (6a i X i + 2b i ) ; i = 1,....,6 (6) The 24 unknown coefficients ai, bi, ci, di, i = 1,..., 6 can be calculated from boundary conditions; known end displacements at each segment; moment and slope continuity at interfaces between segments; and zero moment at the two ends due to the hinged connections. These boundary conditions result in a system the 24 linear equations for the 24 unknowns. The system can be solved with Gauss elimination. Then, the bending moment and shearforce diagrams can be obtained and the concentrated transverse forces can be calculated as shown in Fig.11, where Fig. 11 Deformation, Moment, Shear, and Free Body Diagrams Flats SLE V i = 6 a i EI; i = 1,...,6 (7) Where, F i = 6 (a i a i1 ) EI; i = 1,..., 7 (8) a = a 7 = (9) It should be noted however, that the lengths Li, i = 1,...,6 are not constant along the height the beam. Referring to Fig.11, the lines contact between the two beams the SLE are not perpendicular to the longitudinal axes the beams. Therefore, we should either use some average values for the lengths Li, or calculate the exact values Li refer to a specific longitudinal fiber the beam, and then integrate along the height h the beam. Result and Discussion In deployable structures, Two Girdle Beam is spacing at 2.8 m c/c and Scissor Bridge having span 6. m over the Girdle beam a 3 mm thick plate are attached to a Beam element having nodes for Finite Element Analysis. The overall Plate size is 6. m X 3. m X 3 mm. 62

7 March 15, Volume 3 Special Issue, ISSN Table 1 : Details Girdle Beam connections with span 6. m and Angle Flats SLE Designatio Ixx Iyy n (M3 ) (M3 ) Span Whole Syste m (mm) Thick ness ( mm) Flats Size (mm X mm) x x x x x x x x x x x x Angle Flats SLE Lengt h Flats ( mm ) No. SLE unit s Self Weight Girdle Beam ( ) Cross sectiona l Area Girdle Beam (mm2 ) The Scissor are developed with 4 X 75 X mm and ScissorLikeElement Flat mm X mm and Length Flat SLE depends on angle SLE units i.e. 3, 45 and 6 are connected using HTFG Bolts. The Light weight Scissor deployable Bridge are Analyzed using STAAD.Pro V8i the optimization are carry out for design deployable bridges. 63

8 March 15, Volume 3 Special Issue, ISSN Fig. 12 Comparison Angle SLE vs. Safe Load Sr. No Span whole system Fig. 13 Comparison deflection vs. Safe Load Table 2: Result Scissor Deployable structures using 4 X 75 Xmm Angle No. Designat Max. Stress ion deflectio SLE SLE angles n mm 1 6M 3 2 6M M M M M X75 X75 X75 X75 X75 X75 Max. Axial forces Fx Max. Shear forces Fy Max. Bending Moments My knm Max Comp N/mm2 Max Tens N/mm2 Safe Load ( )

9 March 15, Volume 3 Special Issue, ISSN M M M 6 6M M M 6 16 REFERENCES X75 X75 X75 X75 X75 X [1] Gantes, C., Logcher, R. D., Connor, J. J., and Rosenfeld, Y. (199b). "Developing new concepts and design procedures for deployable structures." Res. Rep. No. R97, Dept. Civ. Engrg., Massachusetts Inst. Tech., Cambridge, Mass. [2] Gantes, C., Logcher, R. D., Connor, J. J., and Rosenfeld, Y. (1993). "Geometric design deployable structures with discrete joint size." Int. J. Space Struct., 8(2/3). [3] Torstenfelt, B. (1983). "Contact problems with friction in general purpose finite element computer programs." Comp. Struct., 16(14), [4] Seismic Assessment Concentrically Braced Steel Frames with Shape Memory Alloy Braces, Jason McCormick, S.M.ASCE 1 ; Reginald DesRoches, M.ASCE 2 ; Davide Fugazza 3 ; and Ferdinando Auricchio 4. [5] Design Structures with Seismic Isolation. Farzad Naeim, Ph.D., S.E. Vice President and Director Research and Development, John A. Martin and Associates, Inc., Los Angeles, California. [6] Minimum design loads for buildings and other structures, ASCE Standard ASCE/SEI 75, American Society Civil Engineers & ISBN [7] I. Ario, m. Nakazawa, y. Yanaka, I. Tanikura, and S. Ono, Development a prototype deployable bridge based on origami skill., fuji, japan. [8] Bati, S.B., T. Rotunno and M. Tupputi. "Deployable Structures: A New Kind SelfLocking Mechanism." Conference Proceedings IASSAPCS. Beijing, China, 6. [9] Hanus, J.P. Investigation a Deployable Military Bridge System with a Fiber Reinforced Concrete Deck Doctor Philosophy, University WisconsinMadison, USA. 7. Advisor: Pr. L.C. Bank [] M. Nakazawa and I. Ario, Mechanical Property Deployable Emergency Bridge Based on the Scissors Structures, Journal safety problems, vol. 5 () (in Japanese). 65