ࡱ> Y q~bjbjWW ==Qn ]TNNNNN4DN78Rhhh~S "u  7777777$8:37 1 "S 37!h~R!!! Rh~ 7Rr 7!!#$3"6~/a2NN1X6`Vedran }ANI Tomislav JAN IJEV Jerolim ANDRI Author s addresses: Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb Ivana Lu ia 5, 10000 Zagreb , CROATIA Tel: +385 1 6168 122 Fax: +385 1 6156940 E-mail  HYPERLINK mailto:vedran.zanic@fsb.hr vedran.zanic@fsb.hr Case Studies in Structural Design and Optimization Case studies in structural design and optimization show, using ships built or designed in Croatia, that structural optimization is a mature tool offering significant savings to the shipyard : decrease in price of construction steel and weight, increase of deadweight, fast calculation of the most complex ships, obtaining of special class (by e.g BV )which assume 3-D FEM model. Full ship 3D FEM modeling permits response, safety evaluation, optimization, vibration analysis to be performed on a single FEM model. Modeling with large macroelemets (stiffened panel, bracketed beam, double wall element) allows fast development of the model. The models of large passenger and car/passenger ships, product carrier,double wall tanker and reefer/ro-ro ship are used to demonstrate those benefits. Key words: structural design, optimization, full ship 3D FEM modeling, single model Introduction to Full Ship Analysis and Optimization Purpose of the presentation of the following case studies in structural design and optimization is to show, using real ships built in Croatian shipyards, that: structural optimization is a mature tool offering significant savings to the shipyard, particularly if applications starts in early (concept) design stage. full ship 3D FEM modeling permits a number of different calculations to be performed on the single model (response, safety evaluation, optimization, vibration) that simplifies and speeds up the design process. modeling with large macroelets (stiffened panel, bracketed beam, double wall element) in the presented calculations allows fast development of the single finite element model (FEM) applicable in: a) ship design and construction The model is used for: calculation of response and safety analysis during development and approval of the classification documentation optimization of ship structure with the objective of decreasing (at least 3-7%) price of construction steel and with parallel increasing of structural safety and deadweight fast and accurate calculation of the stress concentrations at stress critical parts of the structure calculation of overall structural vibration (dry and wet modes) in the same FEM model generation of necessary stiffness and mass matrices for the forced vibration calculation for different parts of structure special calculations (docking, racking, extreme load, launching,..) b) shipping : The model is used for: fast calculation of structural safety in the case of ship conversion/refit estimation of necessary replacement of ship plating and stiffeners due to corrosion in a agreement with the classification society estimation of maximum allowed structural enfeeblement in the different phases of conversion Modern computers allow fast development of mathematical model of the complete structure (full ship modeling) and closely follow design process even with a possibility to accelerate it. It is obvious that is the time using that aproach when shipyards must recognize their interest in in a way of: decreasing price of construction steel decreasing of structural weight and increasing of deadweight increasing competitiveness of shipyard through possibility of calculation even the most complex ships (where the savings are greatest) possibility for shipowner to get special class (which assume 3-D FEM model) for maintenance of the ship. It is important to underline that direct expenses of these calculations are less than 10% of a savings that calculation brings (in the price of construction steel for only one ship in series). At the same time the designer has better overview of the behavior of ship structures and the base for fast and rational decisions in design, building, launching and outfitting of the ship. Some of the ships presented in this paper, designed between 1985 to 1991 were some of the first examples of the analysis and optimization with programs SHIPOPT and MAESTRO. The program SHIPOPT ZAGREB VERSION was used in case studies 1 to 4 and program MAESTRO was used in case study 5. Program SHIPOPT was developed between 1975 and 1983 and its philosophy is given in the following: Hughes, O.F., Mistree, F., }ani, V.,  A Practical Method for the Rational Design of Ship Structures , Journal of Ship Research, 1980, Vol. 24, pp101-113. In the field of ship structures, the phrase practical design methods is usually interpreted as the use of simplified and easy-to-use formulas for the scantlings, obtained from the rules of a classification society. This approach saves time in the design office and it also saves time in the approval process. The disadvantage is that, because the rules are simple and are intended for a variety of design situations, they have large in-built margins, of unknown magnitude. They therefore do not give a truly efficient design, and the extra steel may represent a significant cost penalty in the life of the ship. More importantly these formulas involve a number of simplifying assumptions and can be used only within certain limits. The history of structural design abounds with examples of structural failures- in ships, bridges and aircraft which occurred because a standard simple rules was used, unknowingly, beyond its limit of validity. For this reason, and also for the potential cost benefits, structural designers are increasingly adopting a rational design procedures in which the designers seeks to determine, as comprehensively and rigorously as possible, the factors affecting the safety and performance of the structure throughout its life, and to use this information in determining a good design. This process involves far more calculations, but can be more than offset by using computers. In this case, rational design becomes automated, or computer-aided, structural design. If a quantitative measure of structural quality is given, the process leads to an optimal structural design. After development, this type of design procedure is in fact more practical then the earlier type. Automated optimization involves three main tasks: ANALYSIS: the calculation of the structural response (stresses, deflection,) and hence the demand on the individual members. For large complex structures such as ships, the required accuracy can be achieved only by a thorough analysis of the full 3-D structures (an entire compartment in the case of ship); using some form of the finite element method. EVALUATION: the accurate prediction of the critical or failure values of these responses ( for example ultimate strength of a stiffened panel) in other words, the evaluation of the capability of the structures as a function of the design variables. This requires an accurate and efficient method for determining the various modes of ultimate strength and other critical response values. OPTIMIZATION (or REDESIGN): the application of a systematic method for determining the design variables, which optimize a specified objective while satisfying the constraints. For the ship structures the constraints are numerous and many of them are highly nonlinear. Likewise the objective, such as least initial cost, is a nonlinear function of design variables. SHIPOPT was further developed in Zagreb as SHIPOPT ZAGREB VERSION. Detailed stress analysis, general superelements, graphic output, AFOSM reliability analysis were added in 1983-1991. Program MAESTRO developed by O.F.Hughes is an extension of SHIPOPT to multistructure, multimodule capability with excellent graphic pre and postprocessing. The sound philosophy of SHIPOPT / MAESTRO is best illustrated on calculations needed for passenger ships. Proceedings of 13th International Ship and Offshore Structures Congress, Edited by T. Moan, S.Berge , Trondheim, Norway, 1997. For passenger ships the modeling of large number of cut-outs in side plating is a problem when a global finite element analysis is planned at the preliminary stage. From the recent applications the analysis of a complete 3-D F.E. model of the hull seems to be the only practical and effective method. Idealizing each primary structural element and the main openings, these models are reaching 50 000-60 000 degrees of freedom for half ship symmetric in C.L. (Figure 8). Fig. 1 Finite element global model Macroelement modeling (stiffened panels, bracketed beams etc.) for the full ship models is far simpler than that for detailed meshes needed in NASTRAN or SESAM. Full ship macroelement mesh is also applicable for generation of boundary conditions for structural detail calculations and overall vibration analysis, at fraction of cost. In the sequel the flow chart of the design procedure is given. First three boxes represent the structural and optimization model formulation using Tables A, B ,C of input data samples. Next five boxes represent fast automatic analysis and optimization calculations. The last row of boxes contains reports and vibration analysis. As illustration five case studies are described through (A) objective, (B) mathematical details of structural analysis and optimization and (C) presentations of results of performed calculations. All analyses were performed at the Faculty of Mechanical Engineering and Naval Architecture University of Zagreb as an order from shipyards or design firms. Today for new and more complex type of vessels these calculations are necessary as given in e.g recommendations of International Ship and Offshore Structures Congress for passengers ships. We can thus safely conclude that their implementation, as a part of standard design procedure is a necessity rather than an option and that shipyards should benefit from these developments and presented experiences. DESIGN PROCEDURE  INPUT DATA (Table A) F.E.M MODEL - These data are supplied by the shipyard. GEOMETRY OF SHIPPRELIMINARY SCANTLINGSDESIGN LOADCASES (trim&stability book)RULES OF CLASSIFICATION SOCIETY (Table B) SAFETY MODEL - These data are adjusted to classification society requirments by FSB*. Failure modes in program MAESTRO and safety factors according to DnV. No. Limit state Description(1 PCSFPanel Collapse - Stiffener Flexure1.182PCCBPanel Collapse - Combined Buckling1.183PCMYPanel Collapse - Membrane Yield1.184PCSB Panel Collapse - Stiffener Buckling1.185PYTFPanel Yield - Tension Flange1.06PYTPPanel Yield - Tension Plate1.07PYCF Panel Yield - Compression Flange1.08PYCP Panel Yield - Compression Plate1.09,10PSPBPanel Serviceability - Plate Bending1.011PFLB Panel Failure - Local Buckling1.1112GCTGirder Collapse Tripping1.1813GCCFGirder Collapse Compression in Flange1.1814GCCPGirder Collapse Compression in Plate1.1815GYCFGirder Yield Compression in Flange1.3116GYCPGirder Yield Compression in Plate1.3117GYTFGirder Yield Tension in Flange1.3118GYTPGirder Yield in Tension in Plate1.3119-21FCPHFrame Collapse, Plastic Hinge1.522-24FYCFFrame Yield, Compression in Flange1.3125-27FYTFFrame Yield, Tension in Flange1.3128-30FYCPFrame Yield, Compression in Plate1.3131-33FYTPFrame Yield, Tension in Plate1.31 (TABLE C) SAMPLE OF OPTIMIZATION MODEL DATA These data are supplied by FSB* and approved by the designer of the ship. PROPORTIONALITYCONSTRAINTS MIN MAX CONSTRAINTDATATYPENo.ConstraintPositionNo.StrakePANEL1TS ( 0.6 TP*NSTPHSTSBF2TP ( TSmin13.2340131All strakes3TFF ( TFW1fix34HS* ( 20 TS*max223701552 TFW ( TFFBottommin13.2340136HF ( 2.5 HS + 752fix3745 TS ( HSmax22370152Bottom 8TFF ( 0.8 TFWmin13.232012strakes91.5 TFW ( TFFBilge3fix1max2234016 FSB* - Faculty of Mehanical Engineering and Naval Architeture, University of Zagreb, Croatia TP*- thickness of plating, TS*,HS*- thickness and hight of stiffener, e.t.c Case Study 1: Structural Design, Analysis and Optimization of Passenger/Car Ferry (LOA=169 m, 11 decks) Newbuilding Yard no. SPLIT 356/357 A) Objective of case study is to demonstrate: fast development of structural optimization model for weight critical design cost sensitivity study with respect to frame spacing (800, 850 and 900 mm) (B) Structural analysis and optimization is performed for 12 frame spacings dominating scantlings for 0.6L of the ship. Modified program SHIPOPT-ZAGREB VERSION is used. FEM model : 3D optimization model : 1490 degrees of freedom per quarter space (1076 active), 485 macroelements + 5 superelements and 34 ord. elements. 2D centerplane model frame 10-179 and 2D cross section shear flow model are used for determination of cross section loads. Feasibility (evaluation) model : 19404 safety criteria in 49 strakes, 3 loadcases. Safety factors are adjusted to DnV requirements for direct calculation. Optimization process : 492 design variables, 291 fixed by designer, 141 blocked at minimal or maximal prescribed values, 5725 failure criteria. 4 cycles of optimization. C) Results of performed calculations Problem of structural adequacy is solved by simultaneously resolving 49 unsatisfied failure criteria of the very sophisticated prototype. Weight decrease of 600 kg/m has been achieved for the critical weight constrained design, as compared to the minimal weight prototype, giving 60 tons of weight reserve to the designer. Sensitivity study shows that the cost of structure per meter is rather insensitive to frame spacing, in a given interval, due to the cancellation of the effects of structural modifications and smaller number of web frames. Result was produced in one day during negotiations with ship owner. Fig. 2 Longitudinal Section and Optimization Procedure Fig. 3 Loading due to passengers cars Fig. 4 Dangerous zones of failure criteria (see Table B) Case Study 2: Structural Design, Analysis and Optimization of Ro-Ro Ship (470000 cbft) Newbuilding Yard no. ULJANIK 389/390 (A) Objective of case study is to demonstrate: development of two coordinated structural models for optimization and analysis of details torsional loads and racking analysis deformation analysis regarding hatch covers fast redesign for new of lashing system (B) Structural analysis and optimization are preformed for one quarter of typical hold space (repetitive module) dominating cargo space scantlings from frame 51 to frame 140. Second FEM model is developed between frames 35 and 65 to analyze strength deck discontinuity. Modified program SHIPOPT-ZAGREB VERSION is used. FEM model 1: 1183 degrees of freedom per quarter hold (1076 active), 2 models of boundary conditions symmetric and antisymmetric, 496 macroelements,1 superelement with 142 elements. Feasibility (evaluation) model : 40600 safety criteria in 43 strakes, 10 loadcases (2 nonsymmetric). Safety factors are adjusted to BV requirements for direct calculation. Optimization process : 448 design variables, 353 active, 115 blocked at minimal or maximal prescribed values, 12 cycles of optimization. (C) Results of performed calculations Problem of structural adequacy (starting from design with 115 unsatisfied failure criteria) is solved, including nonsymmetrical loads together with weight decrease of 1056 kg/m. Reinforcements at the stress concentration areas are specified Obtained results show that hatch deformations are within limits Obtained results show that lashing system can be improved. Entirely new optimized design is obtained in a single day. Fig. 5 Longitudinal Section and Optimization Procedure Fig. 6 Symmetric loadcase 1 Fig. 7 Non-symmetric loadcase 4 Case Study 3: Structural Design, Analysis and Optimization Product Carrier (39500 tdw) Newbuilding Yard no. ULJANIK 387/388 Objective of case study is to demonstrate: Minimization of cost/weight of structure Change of classification society safety criteria. Prototype is classed according to DnV and is smaller. New ship is classed according to LR Selection of design loadcases for many alternate loading combinations for this type of ship (caustic soda, oil products). (B) Structural analysis and optimization are preformed for 3D model of five hold spaces dominating cargo space scantlings from frame 48 to 168. Modified program SHIPOPT-ZAGREB VERSION is used. FEM model: 1567 degrees of freedom per quarter model for 120 frame spaces, 562 macroelements, 60 elements and 3 superelements. Feasibility (evaluation) model : 78300 safety criteria in 19 strakes, 10 loadcases (according to LR and ULJ365). Safety factors are adjusted to LR requirements for direct calculation. Optimization process : 147 design variables, 107 active, 7 cycles of optimization (3 preliminary, 4 final). 1330 failure criteria constrain the feasible design space. 57 variables are blocked on prescribed minimum. (C) Results of performed calculations Structural mass is decreased for 1470 kg/m or 172 t for cargo space when scantlings are standardized in accordance with shipyard practice (215 t for nonstandardized optimum). Problem of structural adequacy ( starting from infeasible design with 22 unsatisfied failure criteria) is simultaneously resolved. Differences between class. societies are recorded. Preliminary modeling and loadcase selection should start as soon as possible. Analysis should constantly follow, support and simplify the decision making to the designer. Quality assurance and savings of this type can be even greater than material savings. Fig. 8 Longitudinal Section and Optimization Procedure Fig. 9 Web frame modeling-strakes and nodes Fig. 10 Loadcase 5 -testing of central tank Case Study 4: Structural Design, Analysis and Optimization of Tanker for oil (70000 TDW) Newbuilding Yard no. ULJANIK 406/407 (A) Objective of case study is to demonstrate: Fast development of the design model variants for optimization and analysis of details Double wall modeling (FEM element +safety criteria) for ship sides General superelement application instead of equivalent stiffness modeling Automatic detailed stress analysis (DSA) of critical regions Graphic output for safety analysis for global model and DSA regions (B) Structural analysis and optimization are preformed for cargo space from frame 77 to frame 197. Modified program SHIPOPT-ZAGREB VERSION is used. FEM model : 3D model is developed between frames 77 and 137 ( representing cargo space scantlings from frame 77 to frame 197 ).It includes 3648 DOF, 1170 macroelements, 16 superelements, 167 standard elements. Second FEM model is developed for new ships depth, width of double wall, bulkhead and deck structure. Feasibility (evaluation) model Safety analysis (including FEM response analysis) is preformed for modified structure. It includes 90070 safety checks for 6 loadcases, one nonsymmetric, according to DnV requirements. Optimization process : 288 design variables, 114 active, 51 blocked at minimal or maximal prescribed values, 6 cycles of optimization. (C) Results of performed calculations Weight of preliminary design (4260 t) is reduced to 3901 t (3766 t nonstandardized opt.). Savings of 359 t per ship are obtained or 8.5% of the weight of preliminary design. Considerable modifications of the structural model, even for the changes in cross section geometry, are performed following the head designers requests. Extended superelement and double wall modeling are found practical. DSA and the graphic output additions to SHIPOPT have greatly improved communication with the designer. Fig. 13 HMH stresses of outer plating Fig. 11 Longitudinal Section and Optimization Procedure Fig. 12 Superelements in bilge tank side Fig. 14 Detailed stress analysis-HMH stresses Case Study 5: Full Ship Structural Analysis of First Class Passenger Vessel Design (800 passengers, 40000GRT) NVC-NAVIS CONSULT, Rijeka (A)Objective of case study is to demonstrate: Advantages and necessity of full ship modeling for modern passenger ships. The structural strength calculation for the first class passenger vessel in fulfillment of requirements for direct calculation of the classification society Registro Italiano Navale. Application of single model for design optimization, design evaluation for class requirements, detailed stress analysis of substructures and overall ship vibrations analysis. (B) Structural analysis and evaluation is performed for full ship model. Program MAESTRO is used. Full ship 3D FEM MAESTRO model and 3D FEM NASTRAN models for critical structural details are generated in accordance with : (1) R.I.N.A requirements for direct calculation (2) International Ship and Offshore Structures Congress (ISSC 1997) recommendations. FEM model : Full ship 3D half model has approximately. 5000 grid points having approximately 30 281 degrees of freedom . 7615 stiffened shell macroelements, 8208 bracketed beam macroelements, 357 bar and pillar elements, 442 triangles, 90 brackets and 108 superelements were generated in the half model. Full model is almost double in size. The preliminary fine mesh NASTRAN model for windows comprised 15935 grid points and 16947 Q4 elements. Two test quasistatic loadcases are generated using given weight distribution and adjusted to the longitudinal weight distribution from the corresponding GHS calculation. Feasibility (evaluation) model : 502 590 safety criteria checks in 5 substructures having in total 31 3D FEM moduli, for 2 test ladcases. Safety factors are adjusted to RINA requirements for direct calculation. (C) Results of performed calculations The case study shows that complex full ship model of the 13-deck passenger vessel is possible to generate simultaneously with the structural design process and development of classification documentation (E.g.: results have shown shear buckling in longitudinal bulkhead at 2080 from CL. Careful analysis of windows between decks 7 and 8 has to be performed. Deck beams in way of pillars in recess region require special consideration). Full ship analysis does not require modeling of loads at structural cut end sections. Gross-errors due to unknown normal and shear stress distribution are thus avoided( Parallel calculation with SESAM of 3D part of the structure was greatly misleading regarding stress levels, as anticipated by Italian designers and ISSC recommendations). Full model can immediately be used for calculation of other loadcases required by class. society obtained from the 6 DOF seakeeping analysis for extreme sea states. Racking loads for the heeled ship as well as the docking loads can also be considered. Overall ship vibration analysis using automatic generation of added mass and other masses for vibration calculation can immediately be performed. Optimization of any of 31 structural module can now be preformed like in Case Study 1. Fig. 15 Longitudinal Section CONCLUSION Main areas of implementation and benefits of the procedure are outlined in the introduction. The case studies have proved the following additional points: Problem of structural adequacy starting from infeasible design/prototype is solved in all case studies together with simultaneous weight decrease giving the weight reserve to the designer. Considerable modifications of the structural model, even changes in cross section geometry, lashing system etc. are quickly performed following the head designers requests. Sensitivity study regarding change in cost due to some modification of the structure can be produced in short time (e.g one day) even during negotiations with ship owner. Full ship analysis does not require modeling of loads at structural cut end sections. Gross-errors due to unknown normal and shear stress distribution are thus avoided. The complex full ship model can be generated simultanously with development of classification documentation. These means that structural modeling and loadcase selection should start as soon as possible and analysis should constantly follow, support and simplify the decision making to the designer. To benefit from the presented modern design procedure it is necessary to quickly form teams consisting of the shipyards structural designers and experts in 3-D FEM modeling required for direct calculation and structural optimization. This can be important element of shipyards competitiveness regarding cost and time savings. REFERENCES Proceedings of 13th International Ship and Offshore Structures Congress, Edited by T. Moan, S.Berge , Trondheim, Norway, 1997. O.F. Hughes, F. Mistree, V.}ani: A Pratical Method for the Rational Design of Ship Structures , Journal of Ship Research, 24, 1980. O. F. Hughes: Ship Structural Design, John Wiley & Sons, Inc. 1983. O.F. Hughes, F. Mistree, V. }ani: Theoretical and Users Manual for SHIPOPT, University of New South Wales, Sydney, 1979. MAESTRO Version 7.1 , Program documentation, Proteus engineering, Stensville, MD, USA, 1996. MSC/NASTRAN Version 70.5, Program documentation, MacNeal-Schwendler GmbH, Muenchen, Germany, 1998. V. }ani, T. Jan ijev : Structural Design and Analysis of Passenger/Car Ferry "AMORELLA" Newbuilding Split 357/358, Tehical Report, Faculty of Mechanical Engineering and Naval Architecture, Univesity of Zagreb, Zagreb, 1986. V. }ani, T. Jan ijev: Frame Spacing Study of Passenger/ Car Ferry, Newbuilding Split 358, Techical Report, Faculty of Mechanical Engineering and Naval Architecture, Univesity of Zagreb, Zagreb, 1989. V. }ani, T. Jan ijev: Design, Optimisation, Analysis of Product Carrier for "Uljanik Shipyard", Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 1987. V. }ani, T. Jan ijev: Safety Analysis of Product Carrier, for "Uljanik" - Shipyard Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 1987. V. }ani, T. Jan ijev, G. Tokin, V. Salamon, B. Smiljani: Structural design and analysis of Reefer Ro-Ro, for "Uljanik" - Shipyard, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 1988. V. }ani, T. Jan ijev, G. Tokin: Safety Analysis of Reefer Ro-Ro, for "Uljanik" - Shipyard, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 1988. V.}ani, T. Jan ijev, K. }iha: Structural Optimisation of Double Skin Tanker for Oil, for "Uljanik" - Shipyard, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 1990. V.}ani, N.Naran a: Prora un sigurnosti i funkcionalne upotrebljivosti konstrukcije RTOP 'Petar Kreaimir IV' u neoateenom i oate enom stanju, Izvjeataj 19-088, Brodarski institut, Zagreb, 1995. }ani V.,Jan ijev T., Andri J.: "Global Finite Element Model of Large Passenger Ship", for Nuovi Cantieri Apuania, Marina di Carrara, Italia and NVC-Navis Consult-Rijeka, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb , Zagreb, 1998.  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All X2s reserved.`Shape.hlp!#18170&n }  tN`s@1 6lUa0G k!Aw!>6MMLi9 j  NomT)!!1(Au?F81ih `Cost4O1,Enter the cP associated with.Pis process01` $##[#,fP.00AZM YQDup3(O1 )WdT ofGSstepTXAm{_?4n` ResourPPBO1:)Wnumb,PPpeople0quir@Pto2Pm,`teGStask0n!$S 1 Link To Pa_geO1|b9`ano/Pr p,`TS`#`Q{k` /drpsh?dw y0_o3|eDocumsen Pq`mddh'`Qoo@mb?6i6_,Ų? 8?}E F$,#B$Ī_- ;_ªCTG@CH+<Ȫ}CG+;ê;23F hTA@* ?<I?NXfx** <Ebb{b b NeH . 3 3 (32 2? 1u% 6|Wr_U>(. $z 3eConnect the side of onbjoamanor. se horizontal flipget 9"'."H"&\h_T@@,4+?> ?P u `u `@  xubu `{u {A@u` Zu b?   *|43?J,R5_VG #(L@)࿺YAF&IX *M%V%a " r'`rL`-}@N& @" +$| u`S.' ' R 0O贁/Nk?ck'!b`4 `3 a0 A`9Copyright 1995 Visio Corporation. All 2s reserved.`Shape.hlp!#18145(dL1lUxE510*Ev ! P@  "   A<-LA rj Cr pAA" "<-'BB!HG":OPG (AtCeG [A`BzID~QPQO`p $P03933;333; t;; t 3LConnect the bottom of one objoanor.mb?6i6贁N{?p= ףp?SH"&\h_T@@@'}6@,?,+FP~   u_ z}u `u `bu `u @ػAu` Qu b?   ,u?5 4J0V5cBch"{zt@t wL@NAQoAIP ?F$MN%?b rL`-}@F& @ #$ u`S.}' }' V0O贿Nk?Gk)4&4 b+ D4 D3 as0 A`9Copyright 1995 Visio Corporation. All 2s reserved.`Shape.hlp!#181450H0 l^|U)5h1qm0*Gy @4@ F@# hzG2rw TC @Cr@@ AEA"B]D5EOOOQC" QH"EA+E2JWDIH?ADB^InCOطPhU'p )44/~_n" LS SQ AfC Y bYAQcEDAA\5? D1DQ!zwaC ! `Y Posi1 of Arm }ps'Fߖ8#BT19 ;|תC5G@C+;OC4H+0:F hTA@* ?<I?NXfx** <Ebb{b b NeH J <3󎻂3;󿇻0 M; jn;9 A 30ߙ;u 3?Connect the side of onhape totop or bottoma;nor.b?6i6S?t= ףp?5H"&th_T@@@@,?>,FP u `u `bqu `u z xuA@u` Qu b  {  *?5=@@?@?R:G5T}/ Y  \}@X!u }B@*E#?U CBGrC+C1H+@F hTA@* ?<I?NXfx** <Ebb{b b NeH Z L33;󿆻 +&+3933;3^LLR'ewr;n; aU.,+30 838Connect the bottom of one objotopanor.H" &\h_T@@,,?G,?P bA@quu` Zu `u `b?u `u u  >u ?}x"  R*4O>O@,%R5_G_IG  L@)WAI %%a qrL`-@& ^T u`%.p {'a    R'nx$k!be$ # a0O_Nk?c+0 A`9Copyright 1995 Visio Corporation. All H2s reserved.`Shape.hlp!#18145(עolU %1 0*=0R`6 8,пp;r4I! 7Cu @r ;BuI @AQ@)W$FJ#qr@DP@?&Dm@E 8BfDA> A"F$;B )\(?cAH)F!%(BTfl`}%;w[]& F@C#3|%D8%RSH+S+;H5:QF hTA@* ?<I?NXfx** <Ebb{b b NeH { m3󎻂x{ ߳833߃!߳-B {D {W aV;^_ my331zeoVa33; ;~ xpxd ;({n >:{HG 3nConnector with up to 5 legs. Use c shapes by point2, dynamic glue methods.Vmbؿ?n:mؿ8io6?l?7 H"&\hT@?Z,4,FFP u `u `u `u `A@bxu/bu` Z?u b .%   &  4()4@G4?[en:/JV541# # &(. /7/I/[$d ~az" !@ / +/P" ///% L@C/"*zWAAI0k?4Њ5?b rL`-@6 0u`.@Dr1 4 0 _@@rJA1= 73 QHRB 0 ^0g4 -G7G1b"D A2q@?OFF n2=lU ! aAQFP4*PV&@S P0!:PP]gP30 C73Ob F@ E(OP"C0S8TAVRBQRETV80`np?WSL3 A@n` C[pa~a @ CQI< @rQYV"QoXfT`UPSedR@o`sf}ck bgcobVQ(ip{[EgS!VpGjKUn3b0a263sAbTpl3uS(L3!lVh=gE\+GPLQqa@qBX"7`p$^CvPB7P`N!Rp m0(Wdn 128tqe@@Bpg@AQ ;4IBufo`ug`i@ d@בܟQq[Bk  B:NB g3T.cdCT8c` Arm Position!fR f@@BEhϖ/ٟj  ,lFJW(lLp1"R%,FEԯt﯀uϖ5 Av @>.wF8VX(Tl0as%/:asп=P}d $YVYV@"m~rvf`n@X\gO`o@q)Sxxr&Sĉm@d5#((5Pxsús< h1p ?)?*X-:}p;X"F߂I#BlJ D;'Kf_ @|OSVG+;OS4H+=SF hTA@* ?<I?NXfx** <Ebb{b b NeH u w$?p%7]o OThis symbol represents thenchronization of two or more parallel opers.b??:i6@ t??Y4D H , 'whT@?@@@Z>?H>'?P/6%{?HQuw` ?u {l_b} "7    @r"  44  FFFL@}b`Shape.hlp!#18125A`9Copyright 1995 Visio Corporation. All s reserved.F-lUq#a a! ?SVH4-V!H/Tߊl/"-v6/+@!Z-/|/!/"%-rC o3 8vQd o10o3 D >v20g6 1R /Z v #b300)@h 2."ӡ M?_>It3dB?>4$dB6 }N8 5nE"< ? OD &O8Cp +(%,cB_v/d  %RUQ}.0n2PB2  0P"-210L `Connec Loc&Hof_,x__a_Uj1o1T  U9@L _g*%ao6oHo eoUof?\pLoi[o{Y(hS1r4-L[bUvgSsQ8AlBO`=Ot3sOa44685<O_D_8Ei_>Ut3[446D75<(DB8CmosTPu+()*+ux&z^/"`Cost4,Enter the c associated withis processr` $###,.00SnZDu( d2 ofڣstep稶nm/ ResourB:numbTpeoplequirӠtoŠmte^ڣtaskn */a%Custom Propertiz80SetSe sel`Ӡs`>Btb v0` Link To Pagei2`̰ano r pX#` /drpshdw yvoόDocuWmen!͉dX'c~cq};[FRR#39 >&SXGU~S+S=H+SF hTA@* ?<I?NXfx** <Ebb{b b NeH @ 23 ߄3; +33;<G ;G cddbr cW 30GS-+$ 3eConnect the side of onbjoamanor. se horizontal flipget 9"'."H"&\h_T@?,@5+4+?P u `u `@  xubu `u {A@u` Zu b $  , =3?,V9cBZK (C L@WYAJ&I\ Q%JZ%a " r'`~rL`-@R& @& /$ u`.' $' V0O贁Nk ?gkx'! b d4 d3 a0 A`9Copyright 1995 Visio Corporation. All 2s reserved.`Shape.hlp!#18145hP}lUxI5180*Ev !T@ @ &  0`A@-PAr Cr tAA"0"@-'BB!HG!">OTG QxCiG _AdB~IDQPU>`p $@/_n"nLC C @VCTS byA!c!m`Y" DA  d1@CAW `X Posi1 of Ar5m0b?贁N{8i6??p= ףp }%3 FY#Z ; [XGxSH+yS+>;4_.F hTA@* ?<I?NXfx** <Ebb{b b NeH ; -3󎻂3;󿇻39& ).p&O% _ Lw 333A~n?  3?Connect the top or bottom of one shapside anor.b?6i68?SgM߿H"&th_T@@@'}63?>,FۿP u `u `bqu `{u z x~uA@ u` Qu b G ,?5=(OO?xA >GmP=s!*3vLm%P AQAI 5? $%?b i L`-@ &# [ u`.@*r 5 !0O?Nk?,ml$$O!b+4 3 a70 A`9Copyright 1995 Visio Corporation. All T2s reserved.`Shape.hlp!#18145  {{lUE,110*7&=W  }@V!u }=AGF@!N&W+ }p~#F_#_` ;aAGES+;FS/H +uSF hTA@* ?<I?NXfx** <Ebb{b b NeH u ςw wwwww 1pw1ppSeI .< w0/JThis symbol represents the start or end of a program flow.evironm.b??6i6p:m?:?l4DH"'\h_T@W?@@54u44?P +q5~>~G(  u` HF@ u q~bbFeM MIL@`P>|IQc -*-)  ) /?S A`9Copyright 1995 Visio Corporation. All p"s reserved.r`Shape.hlp!#18115_'R9 lU0%a_`bb "%%U{)r< zW6 3a  rr/160r;0H38F* 0k3,!"23  2l2H`/iG?=d33 F?;0r`}Iop mrT!()r*R0QuGO"O%n `Cost4g!,Enter the csP associated withPis process IA A` $###,P.00r0QZO]`YmQDuR#h ~WdT ofSstepRX0Qm_W$nmQ ResourPBg!:~WnumbP`people qu[irPtoPm`{teStask q kKW L@ ) +A`9Copyright 1995 Visio Corporation. All F"s reserved.`Shape.Hlp!#18195 klUpka+ # @,?i. 0 0!-/@,=@?R=/%'BY? (>(5rr 0#(@4MwQ@a(}l!i$/:b1#Bw?4"@H?gg@E!A21A3WYFOp0"OD_h% pIA}@.5UbRQu>$1 +CQ"6@2 3` Lin?e Posi`! 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