No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Design optimization of continuous partially prestressed concrete beams
Abstract
An effective formulation for optimum design of two-span continuous partially prestressed concrete beams is described in this paper. Variable prestressing forces along the tendon profile, which may be jacked from one end or both ends with flexibility in the overlapping range and location, and the induced secondary effects are considered. The imposed constraints are on flexural stresses, ultimate flexural strength, cracking moment, ultimate shear strength, reinforcement limits cross-section dimensions, and cable profile geometries. These constraints are formulated in accordance with ACI (American Concrete Institute) code provisions. The capabilities of the program to solve several engineering problems are presented.
... There are so many technical definitions of PPC structures given in the technical literature (Nilson 1976, Naaman 1977, Lee 1984, Nilson 1987, Naaman and Hamza 1993, Al-Gahtani et al. 1995, Agrawal and Bhattacharya 2010, Karayannis and Chalioris 2013. In this study, PPC is defined as the concrete that contains both conventional and prestressed reinforcement in both tension and/or compression regions that are considered in the load carrying capacity of the structure without conceding usability and safety requirements. ...
... In the study, the results of a comprehensive parametric study on prestress losses in prestressed and partially prestressed high strength concrete beams are reported. Al-Gahtani et al. (1995) dealt with an effective formulation for optimum design of twospan continuous PPC beams. Han et al. (1996) presented the minimum cost design of multispan PPC beams using discretized continuum-type optimality criteria (DCOC). ...
This paper deals with the optimum cost design of partially prestressed concrete I crosssectioned beams by using Genetic Algorithms. For this purpose, the optimum cost design of two selected example problems that have different characteristics in behavior are performed via Genetic Algorithms by determining their objective functions, design variables and constraints. The results obtained from the technical literature are compared with the ones obtained from this study. The interpretation of the results show that the design of partially prestressed concrete I crossectioned beams from cost point of view by using Genetic Algorithms is 35∼50 % more economical than the traditional ones (technical literature) without conceding safety.
... In the field of structural design several optimization applications can be found, such as, the researches of Al-Gahtani et al. [11], Albero et al. [12], Navarro-Rubio et al. [8], Castilho [13], and Castilho et al. [14] that applied optimization concepts to reduce the cost and weight of precast elements. Other applications in the field of structural engineering can be observed in Azad et al. [10] applied an optimization process for steel trusses under dynamic excitation. ...
Among the main contributors to CO2 emissions on the ozone layer, the construction industry contributes with a significant portion. This emission is generated largely by applying concrete construction systems and their variations. Therefore, it is important to use tools that allow the development of projects which mitigate the effects of harmful gas emissions into the atmosphere. Thus, this study applied an optimization algorithm called Firefly Algorithm (FA) to design precast and prestressed rectangular beams focusing on reducing CO2 emissions in the structural design phase. The Objective Function (OF) was defined as the total weight of CO2 emitted in each construction phase (production, transportation, and placement) and the structural design constraints are based on the design criteria established in ABNT NBR 6118. The problem optimization’s variables are geometric properties and mechanical beam's conditions, where the beam height, beam width, the proportion of height generates prestressing eccentricity, and the proportion of prestressing load were considered as design variables. Ten beams were analyzed, with different loadings, where each of these beams was submitted to the optimization process thirty times. For the proposed conditions, the ten beams had an average CO2 emission of 3282.59 kg, maximum and minimum carbon emission of 3630.52 kg and 2910.67 kg, respectively. The study resulted in a feasibility rate higher than 90%, showing that the optimization tool was efficient in the structural design phase focusing on sustainability. Concerning carbon emission, it is possible to verify a relationship between the increase of emission and the load since element with greater inertia tend to emit a greater amount of CO2. It was also possible to determine a regression between carbon emission and beam load.
... The single-objective optimization of continuous partially prestressed concrete beams was studied by Al-Gahtani et al. (1995). In doing so, the authors considered different cross sections and various profiles of the prestressing tendons. ...
This paper is concerned with the cost minimization of prestressed concrete beams using a special differential evolution-based technique. The optimum design is posed as single-objective optimization problem in presence of constraints formulated in accordance with the current European building code. The design variables include geometrical dimensions that define the shape of the cross section and the amount of prestressing steel. A special (μ¿+¿¿)-constrained differential evolution method is performed in order to solve the optimization problem. Its search mechanism depends on several mutation strategies whereas an archiving-based adaptive tradeoff model is in charge of selecting a specific constraint-handling technique. Finally, numerical examples are included to illustrate the application of the presented approach.
... Over the last two decades, studies on the design optimization of granular-solid prismatic beams have received considerable attention. Prakash et al. (1988); Ezeldin (1991); Quiroga and Arroyo (1991); Erbatur et al. (1992); Al-Gahtani et al. (1995); ; Lepš and Šejnoha (2003); Barakat et al. (2003); Govindaraj and Ramasamy (2005) and Kwak and Noh (2006) attempted to seek optimal shape of beam cross-sections. They highlighted the potential savings in material, either directly or indirectly through various optimization techniques analogous to shape and sizing methods. ...
Topologically optimized granular-solid structures from additive manufacturing processes have impending applications as lightweight load bearing structures. To facilitate application, a procedure for characterizing optimal structural performance is devised for the design optimization of ‘end-use’ functional structures. An approach capable of realizing this objective is presented and demonstrated for horizontal prismatic beams produced from Nylon-12 granular-solid polymer, by Selective Laser Sintering (SLS). It combines topology (or layout) optimization, calibration of material parameters, and finite element (FE) modelling. The metamorphic development (MD) method forms the basis of an adaptive growth and degeneration optimization by material distribution approach. Experimental measurements are used to calibrate a bimodulus constitutive Drucker–Prager (D–P) model. Simply-supported three-point bending (3PB) tests are used to assess the fidelity of optimized beams on the basis of numerically predicted performance.
This paper presents a comprehensive contribution to the design of doubly reinforced prestressed concrete I-beams by means of cost optimization. The objective function, which is the sum of the costs of the cross-section’s constituents (concrete, reinforcement steel, prestressing steel, and formwork), is subjected to design constraints according to Eurocode 2 provisions. These constraints involve serviceability and ultimate limit states, along with current rules of practice, and take into consideration long-term effects such as creep and shrinkage to accurately depict the structural behavior of the I-beam. A combination of gradient-based and metaheuristic optimization techniques is employed to solve the nonlinear optimization problem. An illustrative example demonstrates the efficacy of the optimal design model and its merited gain compared to the conventional design method. The results highlight the significance of certain constraints that are often overlooked in the literature, along with a study of sensitivity to cost fluctuations. An investigation of the results showed that the proposed model can provide practical guidelines for initial geometry selection to achieve more economical conventional designs. Moreover, the model’s simple and practical implementation holds potential for extension to other types of prestressed structures.
Post-tensioned method is a technique commonly used all over the world to prevent cracks and minimize deflections produced by externally applied loads. In post-tensioned, stress is added after concrete placement and appropriate hardness and strength are achieved. By a post-tensioned method greater loads, greater spans, control the cracks and smaller size of members can be achieved. This paper reviews some previous research studies on post-tensioned concrete beams. From this literature; it was concluded that the ultimate load capacity for a beam with a bonded tendon is higher if compared to the same beam with the unbonded tendon. The higher ultimate capacity for the bonded beam is due to the additive stiffness obtained by tendon-concrete bond. For external prestressed beam, the results showed that using draped tendon profile increases the flexural resistance as compared to straight tendon profile.
In this work, we sought to study the behavior of prestressed concrete wind-turbine tower in circular cross-section. The idea was to use Genetic Algorithm to obtain a structural optimization of the projected tower. Thus, a tower with the shape of a conical section was obtained, which minimizes the appearance of stress concentrations in the structure. The tower has a tapered profile to reduce the area subjected to wind thus lower the total weight and applied moment. It will also enhance the dynamic response of the tower and improve its overall stability. Steel tubular wind turbine towers are most widely utilized for wind turbines, however, the use of concrete material is becoming more attractive for wind towers because concrete towers are more stable for buckling failure. As the turbine size is growing and the towers are rising in height, steel towers are required to be sufficiently strong and stiff, consequently leading to high construction costs. Therefore, the prestressed concrete wind-turbine tower has a reduced construction cost compared to the steel tubular wind turbine towers or the self-supporting steel truss towers with a maximum height of 150 m. For this, Computer-Aided Engineering (CAE) tools were used and a 100 m prestressed concrete tower system for a wind turbine was optimized. It is concluded that the model met all the restrictions described and represents an economy in raw material and greater simplicity of design in relation to the octagonal model used for comparison. A new structural methodology was described for the study and application of prestressed concrete to replace the steel towers currently used.
Recent earthquakes, especially those in Chile (2010) and Christchurch (2011), have demonstrated the unexpected performance of buildings designed according modern seismic design codes. These incidents strengthen the cause for moving towards performance-based design codes rather than serviceability and strength design. This chapter deals with optimal design of RC frames, a widely used structural type around the world, considering both the initial cost and structural performance as problem objectives. Initial cost comprises the total cost of materials and workmanship for structural components, while structural performance is measured by a two-level approach. First, each design is checked for acceptability according to existing codes, and next performance is quantified in terms of maximum interstory drift obtained from nonlinear inelastic dynamic analysis. This multi-objective, multi-level approach allows one to investigate the implications of the selection of design parameters on the seismic performance while minimizing the initial cost and satisfying the design criteria. The results suggest that structural performance varies significantly within the acceptable limits of design codes and lower initial cost could be achieved for similar structural performance.
The focus of this work is a novel application of configurational forces to tendon layout optimisation problems in prestressed concrete beams. To this end, the application of the method of the configurational forces is extended to two-dimensional plane stress analysis. The optimum tendon position is obtained by iteratively arriving at vanishing configurational forces. The performance of the optimisation algorithm is illustrated by means of numerical examples.
The concept of configurational forces has been explored recently as an optimisation tool. Configurational forces are the derivative of the energy with respect to the initial coordinates of the material. Solving for a zero residual of configurational forces implies that no further energy can be released by changing the material positions. Configurational forces are used to optimise tendon layouts in pre-stressed concrete beams. The dual set of equilibrium equations is derived and implemented in a finite element code. Inequality constraints are added in order to ensure that the optimal tendon position is always located within the cross-section.
Los tableros de vigas prefabricadas de hormigón pretensado se utilizan habitualmente en todo el mundo para resolver estructuras de viaductos y de pasos superiores sobre carreteras. Son escasos los trabajos de inestigación encaminados a la optimización económica de estas estructuras, donde la mayoría se han centrado en la reducción de las fuerzas de pretensado y han padecido de un signo considerablemente teórico, sin mejorar el aprovechamiento de los recursos que requieren, lo que ha dificultado su aplicación sobre los proyectos de ejecución. En la búsqueda bibliográfica, no se ha encontrado trabajo alguno enfocado a la optimización heurística económica de este tipo de estructuras. Ante el hueco existente en el espectro de la investigación, el enfoque de este trabajo está basado en la aplicación de distintas técnicas de optimización económica a esta tipología. Se han elegido técnicas metaheurísticas para poder plantear el problema lo más completo posible, donde se define todo el tablero y sus armados, y se realizan las comprobaciones que marca la normativa española. Se han analizado diferentes proyectos con esta tipología estructural, donde se han estudiado diseños de vigas artesa de distintos fabricantes, elegiendo una de ellas como modelo para realizar el presente estudio, y dejando la opción para adaptar la tipología a cualquiera de los otros diseños que se fabrican. A continuación se ha desarrollado un programa informatico en lenguage FORTRAN que incluye diferentes módulos: generación de la estructura, comprobación estructural y evaluación económica. El estudio se realiza sobre un tablero de 12 metros de ancho, con 11 de calzada, luz entre apoyos de 35 metros, y separación entre vigas de 6 metros. El estudio de los métodos heurísticos sobre el tablero, se realiza mediante la comparación de ocho distintos tipos de algoritmos: la estrategia de saltos múltiples aleatorios (RW), tres métodos de búsqueda local y cuatro de búsqueda poblacional.
Los tableros losa de hormigón pretensado son una tipología habitualmente empleada en España para resolver estructuras de pasos superiores. Su optimización presenta un gran interés para conseguir diseños más económicos, que permitan un mayor aprovechamiento de los recursos que requieren. Las contribuciones a esta materia son escasas y han adolecido de un carácter extemadamente teórico que ha dificultado su aplicación por parte de ingenieros proyectistas. El objetivo de este trabajo ha sido el de aplicar técnicas de optimización estructural a esta tipología. Se han empleado técnicas metaheurísticas, puesto que permiten plantear el problema de un modo más complejo, aprovechando par una definición completa de tablero y de todos sus componentes, al tiempo que ha permitido imponer todas las comprobaciones que la normativa exige para este tipo de estructuras. Para definir las características del problema ha sido necesario distinguir entre los tableros aligerados y los macizos, dado que ha resultado imposible considerar a uno un caso particular del otro. Se ha implementado un programa informático que incluye las siguientes funciones: generación aletatoria de un tablero, comprobación automática de un tablero, evaluación de su coste a partir de las mediciones completas de todos sus componentes y tres algoritmos de optimización heurística implementados basados en tres metaheurísticas, pertenecientes a los denominados algoritmos de mejora local. Para la calibración de los algoritmos se han efectuado pruebas con diferentes parametrizaciones. La comparación de los resultados ha permitido descartar el algoritmo OBA pormostrar una menor eficacia para las parametrizaciones ensayadas. Los algoritmos SA y TA, por el contrario, muestran resultados muy similares, por lo que han efectuado pruebas de inferencia estadística consistentes en diferentes test de hipótesis. Los resultados no han sido capaces de determinar la heurística más eficaz de las dos.
It is found that for a wide range of unit costs of formwork both approaches lead to approximately similar results provided the unit cost ratio of concrete to steel is above 60 (where cost of concrete is per cubic yard and steel per pound). However, if a cost ratio much below 60 prevails, substantial savings can be achieved by using a minimum cost approach instead of the usual minimum weight approach, which is the aim of the hand design procedure. The minimum weight approach is extended one step further in this study by combining the conditions minimizing the section moduli and the practicality condition which constrains the prestressing force to remain inside the concrete section; this results in a simple algorithm which will systematically lead to the minimum weight feasible slab or rectangular beam. The direct search technique that was used in the computerized optimization algorithm for minimum cost gave satisfactory results.
"Introduction to Optimum Design " is the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level within engineering departments of all disciplines, but primarily within mechanical, aerospace and civil engineering. The basic approach of the text is to describe an organized approach to engineering design optimization in a rigorous yet simplified manner, illustrate various concepts and procedures with simple examples, and demonstrate their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB are featured throughout as learning and teaching aids. The 3rd edition has been reorganized and enhanced with new material, making the book even more appealing to instructors regardless of the level they teach the course. Examples include moving the introductory chapter on Excel and MATLAB closer to the front of the book and adding an early chapter on practical design examples for the more introductory course, and including a final chapter on advanced topics for the purely graduate level course. Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable.Applications of the methods for structural, mechanical, aerospace and industrial engineering problems.Introduction to MATLAB Optimization Toolbox.Optimum design with Excel Solver has been expanded into a full chapter.Practical design examples introduce students to usage of optimization methods early in the book. New material on several advanced optimum design topics serves the needs of instructors teaching more advanced courses.
A unified bridge design optimization theory has been developed by a research team composed of personnel from the College of Engineering, Louisiana State University working in close collaboration with engineers from the Louisiana Department of Highways. The theory, useful in the design of multispan, simply supported highway bridges considers simultaneously the structure and the geometry of the bridge. Soil and terrain conditions, construction costs, shape, and other parameters can be investigated simultaneously with dynamic programming, an optimization technique applicable to serial systems of the type to which these structures belong.
The primary purpose of this paper is to discuss an interactive design and analysis algorithm for prestressed concrete girders. Prestressed concrete highway bridge girder design is used for the prototype computer program to simplify the incorporation of design code requirements and loading conditions. The computer code can be extended to include other prestressed concrete girder applications. The second purpose arises from the search for the optimum prestressed concrete girder design. Linear programming is discussed as a possible method to arrive at the optimum girder cross-section and prestressing strand design. However, manufacturing standardization and techniques make selection of the optimum crosssection, prestressing force, and strand centroid eccentricity by mathematical methods rather academic. Therefore, design optimization, to be practical, must be based on standard cross-sections and prestressing strand position templates. The algorithm, guided by the engineer, selects, from tabulated standard crosssections and associated combinations of prestressing forces and eccentricities, the cross-section, prestressing force, and eccentricity to satisfy the problem constraints. The kern boundaries are calculated in the analysis portion of the algorithm. The engineer, using the kern boundaries, determines the path of the strands by specifying the strand hold-down points and associated strand centroid eccentricity. The algorithm also provides for shear reinforcement, dead load deflections at transfer and after placement of the slab, and auxiliary nonprestressed tension reinforcement at transfer.
A method is developed for the optimum design of prestressed indeterminate beams with uniform cross section. Optimum values of prestressing force, tendon configuration and cross sectional dimensions are determined subject to constraints on design variables and stresses. A transformation of variables is employed to reduce the optimization to a solution of a linear programming problem.The method is suitable for practical design of structures with no restriction on the number and types of loading conditions, tendon configuration or number of prestressing stages. Applications of the proposed method are illustrated by examples.
A comprehensive method for minimum cost design of simply supported, uniformly loaded, partially prestressed concrete beams is presented. Nine design variables are used—six geometrical dimensions, area of prestressing steel and area of tensile and compressive mild reinforcement. The optimum design is in accordance with ACI 318/77. The imposed constraints are on the four flexural stresses, initial camber, dead and live load deflections, ultimate shear and ultimate moment capacity with respect to both the cracking moment and the applied load. The nonlinear optimization is performed using the Penalty- Functions method coupled with Quasi-Newton unconstrained optimization techniques. The method, successfully applied to several design problems, both cracked uncracked, clearly indicates that numerical optimization can be used to solve design problems of interest to practicing engineers.
A computer approach to the optimal design of structural concrete beams is presented. The approach allows the optimization for a variety of possible merit functions, considers all relevant limit state constraints by any standard code (as well as other desirable engineering and construction requirements) and is valid for reinforced, prestressed and partially prestressed concrete members. The problem formulation and a nonlinear programming technique for its solution are briefly described. Four numerical examples illustrate some of the capabilities of the optimization program: (1) Minimizing the amount of reinforcement for a given concrete section; (2) assessing the effect of steel cost ratios on optimal solutions; (3) optimizing the section shape of partially prestressed concrete beams; and (4) analysis of given designs with regard to all relevant criteria.
An integer programming formulation for the minimum cost design of precast, prestressed concrete simply supported beams is developed. The cross section and gridwork within which strands must be placed are assumed given, and the design problem is to determine the concrete strength and the number, location, and draping of strands that minimizes the total cost of the beam. Constraints limit release and service load stresses, ultimate moment capacity, cracking moment capacity, and release camber. A box girder for a multibeam highway bridge is designed to demonstrate the computer program written to implement the methodology.
A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.
Computational procedures for optimal design of large complex systems are described. Requirements of a good algorithm are discussed. A general design optimization model applicable to several classes of problems is defined. Several optimization algorithms are outlined and differences between them are highlighted. Modern algorithms generate and use approximate Hessian of the Lagrange function to calculate the search direction. They are quite reliable and become extremely efficient when a potential constraint strategy is incorporated into them. Based on recent experience with them, they are recommended for general engineering design applications. Several other computational aspects are also discussed, such as robust implementation of algorithms, use of knowledge base in providing consulting and diagnostic support to the designer, interactive use of optimization, and role of a database and database management system in design optimization.
Optimal design of continuous prestressed concrete girders
- Hussain
A study of mathematical programming methods for structuralmization
- Belgundu
Interactive IDESIGN Program
- Arora