Integrated System for Steel Truss Bridge

Integrated System for Steel Truss BridgeAuthors:R. Pandia Raj, Research Student, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK, rp317@ V. Kalyanaraman, Professor, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai – 600 036, India, kalyan@iitm.ac.inA BSTRACTA number of authors have previously used genetic algorithms to optimize structural systems. This paper illustrates use of simple genetic algorithms for optimum design of large scale steel truss bridge superstructure for railway loadings. Object-Oriented Methodology is used to simplify the design software development process. Optimal design of practical structures is illustrated, considering system topology, configuration and member sizes represented by mixed design variables (continuous and discrete). Complex design domain requirements conforming to Indian Railways design standard consisting of constraints corresponding to material strength, buckling strength as well as fatigue strength limit have been considered and the objective function to be minimized represents the total cost of the superstructure including cost of fabrication. The paper also demonstrates the efficient integration of genetic algorithms for optimization with the design software, both implemented in an object-oriented environment.I NTRODUCTIONSteel truss girders are interesting as exciting structural forms. They have been used successfully in the intermediate and long span railway and highway bridges, since the internal forces in the members are essentially only tensile or compressive. However, mathematical representation of the design problem is complex.The computer assisted design process often requires integration of different computing methods such as database management, numerical analysis, optimization method, and even graphical representation. Incorporation of all these into a single environment make the software development process difficult. This is particularly so in the case of complete design of large scale complex system. Object-Oriented Methodology can simplify the software development process for the entire engineering of large scale practical structures – this paper will explain how.L ITERATURE S URVEYIn the last decade, Genetic Algorithms (GAs) has proved to be successful and powerful in solving various practical structural optimization problems (Jenkins 1991, 1992; Rajeev and Krishnamoorthy 1997; Adeli 1993; Ohsaki 1995; Rajan 1995; Galante 1996). By using GAs, which can deal with the mixed design variable problem, complex design domain requirement as well as complex constraint equations and objective function, one D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .can arrive at feasible optimal designs both from the mathematical as well as the practical point of view (Krishnamoorthy 2001; Pandia Raj and Kalyanaraman 2005). Recently, the object-oriented design and implementation of a core genetic algorithm library consisting of all of the genetic operators with an interface to a generic objective function is discussed by Krishnamoorthy et al. (2002). Cappello (2003) presents a method to find optimal topology and shape of structures. Renner (2003) gives an overview of applications of genetic algorithms to different domains of engineering design. Sivakumar et al. (2004) presents a new approach for the optimization of steel lattice towers by combining genetic algorithms and an object-oriented approach.For any system to be robust, they should possess an architecture that can easily incorporate any new software or hardware technology, as well as domain advances and should be able to integrate them with the existing ones without excessively disturbing the implementations already made in nearly seamless fashion. The object-oriented paradigm seems to be ideally suited to take care of these requirements (Miller 1991; Sause et al. 1992; Garrett et al. 1992; Abdalla et al. 1995; Moni et al. 1996; Sivakumar et al. 2004; Pandia Raj and Kalyanaraman 2005). This is due to the inherent modularity and extensibility obtained in the object-oriented system.The problem of system optimization requires a consideration of elements of the system, all design variables and constraint equations simultaneously. Whereas, the Object-Oriented Methodology represents the design space as a collection of nearly independent object modules. The difficulty in reconciling with these extremes might be the reason for the existence of a few applications of GAs based optimization procedures in an Object-Oriented environment. In the present work, details of a user-friendly software for structural optimization of steel truss girder bridge superstructure using GAs and integrated in the object-oriented environment is presented. This software can be used to perform both conventional and optimal design of steel bridge girder superstructure.B RIDGE D ESIGN S YSTEM (BDS)The software, named as Bridge Design System (Figure 1), consists mainly of four modules namely: master module, optimization module, FEA module, and data retrieval system (DRS). In the master module, data and methodology has been represented in an object-oriented fashion for easy representation, incremental development and possible future modification. In the optimization module optimal design of various truss configurations has been formulated in an object-oriented environment. The FEA module analyses the truss girder superstructure for IRS loadings. The data retrieval system is used to fetch discrete section sizes from a database, as well as data used for design checking and fitness evaluation.O BJECT -O RIENTED M ODELINGIn object-oriented modeling, we first identify the classes and objects that are common to all applications within a given domain. For example, superstructure, substructure, foundation etc. are common to all types of bridges. The relationship between the classes and class hierarchy at the higher-level of abstraction has to be explored. Once the classes and objects are identified from the problem domain, the next task is to find out the D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .relation between the classes so that it can be modeled according to standard object-oriented notations.FIGURE 1S OFTWARE (BDS) A RCHITECTUREObject-Oriented Analysis (OOA) of Steel Truss BridgesFIGURE 2 OOA OF S TEEL T RUSS G IRDER S UPERSTRUCTURE (W HOLE / P ART H IERARCHY )The object-oriented analysis of steel truss girder superstructure is shown in Figure 2, and the hierarchy is termed as whole / part hierarchy. The whole structure is decomposed into whole / part until basic components are reached. The lower level abstraction of truss girder is difficult as the inter-dependency among the different components of the system is very high. For example, ‘Chord’, ‘Diagonal’, and ‘Vertical’ are highly inter-dependent as they model a type of ‘Main Vertical Truss’. As a result, the high inter dependency among the different components should be modeled accordingly even though the components can be modeled in separate classes. These can be modeled effectively by D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .using the concept of ‘aggregation’ relationship, which represents a physical containment. The truss girder superstructure is constructed of or contains many components like Main Vertical Truss, Floor System, Bracing System, Portal Bracing, Sway Bracing, Bearings, etc. The ‘aggregation’ relationship is also termed as ‘has’ relationship. Object-Oriented Design (OOD) of Steel Truss Bridges The first step in OOD is to identify the attributes and methods in all objects in greater detail, as well as their status namely whether they are private, protected or public innature. Subsequently, the sequence of message passing among different objects and their dynamic states are explored. The static as well as dynamic views of objects and their message passing can be represented using ‘object interaction’ diagrams. The significance of proper design process as well as design standards representations can be seen in this phase. Figure 3 shows the static view of class ‘Bracing System’. The subclasses ‘Top Lateral Bracing’ and ‘Bottom Lateral Bracing’ inherit public attributes and methods from the super class ‘Bracing System’. In addition to these inherited attributes and methods, the subclasses have their own attributes and methods.FIGURE 3S TATIC V IEW OF ‘B RACING S YSTEM ’ C LASSObject Interaction Diagrams (Dynamic View)The interaction diagrams capture the behavior, showing the pattern of interaction among objects. Sequencing of messages can be shown in two kinds of diagrams, sequence diagrams and collaboration diagrams.Sequence DiagramsA sequence diagram shows a set of messages arranged in time sequence. Each classifier role is shown as a lifeline - that is, a vertical line that represents the role over time through the entire interaction. Messages are shown as arrows between lifelines (Rumbaugh 1999). Figure 4 shows the sequence diagram of the design of Truss girder railway bridge superstructure. For simplifying the figure, only important messages are D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .shown. It is clear from the figure that the ‘Chord Member’, ‘Diagonal Member’ and ‘Vertical Member’ objects are created and their operations takes place only after the creation of ‘Main Truss Girder’ object (i.e. they are tightly coupled). Whereas, the design of floor system can be done in any order without affecting the overall main truss girder design process (i.e. they are loosely coupled). The diagram also clearly indicates that inner objects have a lesser life than their parent. Sequence diagrams help us not only to find interaction among objects, but also to assess the strength of these interactions (i.e. tightly coupled or loosely coupled).FIGURE 4S EQUENCE D IAGRAM FOR T RUSS G IRDER S UPERSTRUCTURE D ESIGN (D YNAMIC V IEW )Collaboration DiagramCollaboration diagram permits the software designer to see multiple roles that a class may play in various operations. This view can be constructed by taking the union of all the collaborations needed to describe all the operations of the class. In a collaboration diagram, the class is depicted by a rectangle with the name of the object in it, preceded by a colon and underlined. Arrows indicate the messages sent by the objects and their direction and the sequences are indicated by numbering the messages. Figure 5 shows the collaboration between ‘ObjMainTrussGirder’, ‘ObjFloorSystem’, ‘ObjBridgeRules’, ‘ObjStringer’, ‘ObjStringerBracing’, ‘ObjXGirder’ and ‘ObjSteelBridgeCode’ objects to design the floor system of truss girder superstructure deck. The necessary data for floor system design is supplied by the main truss girder object.Floor system object interacts with bridge rules objects to get loads for stringers and cross girder design. Steel bridge code, stringer and cross girder objects are created in floor system object. Stringer object designs the stringer girder and checks the stresses and deflection by interacting with steel bridge code object. Stringer object also creates a stringer bracing object and designs it. Cross girder designs the cross girder after receiving D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .stringers reaction from floor system object and checks stresses and deflection with steel bridge code object.1: Create MainTrussGirder Object2: Create FloorSystem Object and Pass DataFIGURE 5C OLLABORATIOND IAGRAM S HOWING F LOOR S YSTEM D ESIGNObject oriented design methods emphasize the proper and effective structuring of complex systems. The object oriented design, by using the model of the domain obtained from OOA, generates a blueprint for completely implementing the system in a programming environment.O PTIMAL D ESIGN F ORMULATIONSThe design variables, objective function, a set of constraints that define the limits on the design problem have to be identified.Design VariablesThe sizing design variables considered in this study are either cross-sectional dimensions using continuous variable for lateral dimensions and discrete design variables for thickness. The standard cross section is described in terms of integer pointing to a row in a table of available cross sections. A boolean variable is used to specify parallel chord system and non parallel chord system.A typical truss configuration used in Indian Railway (Figure 6) is taken for illustrating member grouping, selection of cross sections, identification of continuous and discontinuous variables, choice of different bracing patterns and their influence on the string length used to represent the design variables.There are three different top chord member, four bottom chord member, three diagonals and four vertical members, taking advantage of symmetry. The shape of the member is kept the same for members belonging to the same type. In addition to this, D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .there is one group each for each type of end diagonal, stringers, cross girders, portal girder, sway girder, bottom lateral bracings and top lateral bracings. Thus 21 different member groups are identified for this particular problem. Number of different possible shapes exists for each type of members. A discrete variable for representing a cross section of each member in the truss girder such as top chords, bottom chords, end diagonals, diagonals, verticals, portal girders, sway girders, top lateral bracings and bottom lateral bracings is used in the genetic model. Thus up to 9 discrete variables are needed to represent the shape of the cross sectionFIGURE 6S KELETON OF A T HROUGH T YPE S TEEL T RUSS R AILWAY B RIDGE S UPERSTRUCTUREFrom the fabrication and aesthetic point of view, it is required to keep a few parameters constant throughout the bridge. The possible web bracings are also numbered to be represented as discrete variables. For instance, width of all the main members (top and bottom chords) is generally kept constant so as to be able to connect them properly to gusset plate. For continuous design variable values sixty four (26) possibilities are considered, whereas for discrete design variable values eight (23) possibilities are considered.Objective FunctionIn the present study, the aim is to minimize the cost expressed as the objective function. The total cost of superstructure comprises material costs and fabrication costs. Joints costs depend upon the number of joints, the number of members joining at the node and the forces to be transferred at the joint. In the present study, various web bracing configuration is considered in the genetic evolution process. The constrained form of the optimization problem can be formulated as⎟⎟⎠⎞⎜⎜⎝⎛∑∑+×⎟⎟⎠⎞⎜⎜⎝⎛∑××====j mj m n j n r r st N i i i C C l A MinimizeC 111ρ (1)Subject to the following constraints: D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .Material strength, buckling strength as well as fatigue strength limit.Deflection limit.Where C = objective function; A i , l i and ρ = area, length and weight density of the ith member, respectively; C st = cost of steel per kN; n mj = number of members meeting at the nodes and C r = cost of joining each member depending upon its force.The objective of the optimum design problem is to minimize the total cost of the superstructure, which is represented by (1).ConstraintsAn optimal solution is the best solution among a set of feasible solutions, which satisfy all the constraints imposed upon them. In GAs based optimal design process, the constraints can be implicit constraints - the lower and upper bounds values for design variables or explicit constraints - functional constraints imposed on material strength, buckling strength as well as fatigue strength limit, deflection limit, and the unsupported projection of any plate.The genetic algorithms can be used for optimizing unconstrained objective functions. In this implementation of GAs the constrained problem is converted into unconstrained problem, using penalty function, to obtain an augmented objective function and fitness values, as given below:()c aug P C f +×=1 (2) ()()()()∑×+×+×=i implicit d deflection s stress c P C P C P C P (3) Where f aug = Augmented Objective Function; C = Objective function given by Eq. 6; P c = Total penalized constraints violations; C stress , C deflection and C implicit = stress, defection and implicit constraint violations respectively; and P s , P d and P i = penalty factors for stress constraints, deflection constraints and implicit constraints, respectively.To evaluate the fitness, F i , of a solution, the value of the augmented objective function has to be subtracted from a large number. Usually this large number is taken as the sum of the maximum and minimum objective function values in the population (4).i aug i f f f F ,min max −+= (4) Where f max , f min = maximum, minimum value of augmented objective function in a generation.O PTIMIZATION M ODULEThe optimization module is implemented entirely in object oriented environment with the GAs process implemented using the concepts of object oriented method. The core GAs attributes and methods, which are independent of the problem domain, are completely encapsulated and the access to the GAs process from outside is given only through a well-defined interface. The features available in object-oriented models such as D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I V E R S I T Y o n 11/17/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .‘aggregation’ make the interface implementation easier. Figure 7 shows the schematic diagram, representing the object-oriented implementation of GAs process. Object-oriented implementation of GAs as methods in a class by abstracting the problem-independent genetic operations part and the problem-dependent function evaluation part has enabled effective encapsulation, inheritance and better memory management.FIGURE 7O BJECT -O RIENTED I MPLEMENTATION OF G ENETIC A LGORITHMSS UMMARY A ND C ONCLUSIONSThe GAs based optimal design formulation presented in this paper is certainly not new. One of the early applications of GAs to engineering design problems is the optimization of gas pipeline control by Goldberg (1983) and GAs has been used in much work since; a recent application of GAs in a large scale practical structure has been explained by Krishnamoorthy (2001). Although application of GAs in steel truss girder is not new, the present paper does give a new and simple implementation procedure for the entire engineering of steel truss girder bridge superstructure, and outlines it in an object oriented fashion. A novel feature is the use of an object technology to model both conventional and optimal design system.An important feature of this paper is that it links GAs into computer aided design software in a single environment. The computer aided design software has not been used as extensively by the profession as the computer aided analysis software due to the inability of this software to capture the complex process of design, which is an open ended problem.The aim of this work is not just applying GAs for optimal design of steel truss girder bridge superstructures, but answering questions such as when a large scale practical structure optimization involves with complex design requirments, considering system topology, configuration, and member sizes represented by mixed design variables. Of particular relevance here is that the GAs based optimal design formulation is efficiently integrated with a conventional design software, both implemented in an object oriented environment.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C H A N G 'A N U N I VE R S I T Y o n 11/17/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s re s e r v e d .A CKNOWLEDGEMENTWe gratefully acknowledge the support of the DST and RDSO, Ministry of Indian Railways.R EFERENCE [1] Abdalla, J. A. and G. H. Powell, An object design frame work for structural engineering. Engineering with Computers , 11, 213-226, 1995.[2] Adeli, H . and Cheng, N., Integrated genetic algorithm for optimization of space structures. J. Aerosp. Eng., 6(4), 315-328, 1993.[3] Bridge rules . Rules specifying the loads for design of super-structure and sub-structure of bridges and for assessment of the strength of existing bridges. Ministry of Railways, Government of India, New Delhi, 1964.[4] Cappello, F., and Mancuso, A ., A genetic algorithm for combined topology and shape optimisations. Computer-Aided Design 35, 761–769, 2003.[5] Chen, S.Y., and S. D. 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