Alberto M. B. Martins

Optimum design of concrete cable-stayed bridges

The design of cable-stayed bridges involves a significant number of design variables and design objectives. The concrete cable-stayed bridge optimization is formulated here as a multi-objective optimization problem with objectives of minimum cost, minimum deflections and minimum stresses. A numerical method is developed to obtain the optimum design of such structures. This numerical method includes: structural analysis, sensitivity analysis and optimization. The structural analysis accounts for all the relevant effects (concrete time-dependent effects, construction stages and geometrical nonlinear effects). The structural response to changes in the design variables is achieved by a discrete direct sensitivity analysis procedure, and an entropy-based approach was used for structural optimization. The features and applicability of the proposed method are demonstrated by numerical examples concerning the optimization of a real-sized concrete cable-stayed bridge.

Optimum design of concrete cable-stayed bridges with prestressed decks

ABSTRACT This article presents an optimization-based numerical method for the design of concrete cable-stayed bridges with prestressed decks. This method includes a structural analysis module and a sensitivity analysis and optimization module. The structural analysis considers concrete time-dependent effects, construction stages and geometrical nonlinearities. The discrete direct method is used for sensitivity analysis and an entropy-based approach is used for structural optimization. The design is formulated as a multi-objective optimization problem with objectives of minimum cost, minimum deflections and stresses. Numerical examples concerning the optimization of a real sized cable-stayed bridge are presented to illustrate the applicability of the proposed method.

Sustainable Design Optimization of Reinforced Concrete Frames Considering CO2 Emission Minimization

Nowadays, the environmental consequences of global warming are of major concern. Worldwide, efforts are being made to reduce the CO2 (carbon dioxide) emissions in order to mitigate the greenhouse effect. Construction sustainability is gaining increasing relevance in the last years to cope with the large environmental impact of construction industry. Considering this the structural design should aim to obtain economical, structurally efficient and “environmentally-friendly” solutions. In this work a numerical model for the sustainable optimum design of reinforced concrete (RC) frames was developed. The structural analysis includes all the actions and relevant effects, namely, dead and live loads, the time-dependent effects and the geometrical nonlinearities. The analytical discrete direct method is used for sensitivity analysis. The sustainable design of RC frames is formulated as a multi-objective optimization problem with objectives of minimum construction cost, minimum CO2 emissions, minimum deflections and stresses and a Pareto solution is sought. The minimax solution is found by the minimization of a convex scalar function obtained through an entropy-based approach. The displacements and stresses design goals are established according to the Eurocode 2 recommendations for the design of framed structures. The design variables considered are the beams and columns cross-sectional dimensions and the steel reinforcement area. The features and applicability of the developed numerical model are demonstrated by a numerical example concerning the optimization of a real sized RC frame.

Optimization of Concrete Cable-Stayed Bridges with Discrete Design Variables

This work presents a procedure for finding the discrete optimum design of concrete cable-stayed bridges. The behaviour of this type of structures is governed by the stiffness of the load-bearing elements (towers, deck and cable stays) and the cable force distribution. In concrete bridges the stresses and deformations are significantly influenced by the construction sequence and by the concrete time-dependent effects. Furthermore, the geometrical nonlinear behaviour that arises when dealing with cables, large and flexible structures should also be considered in the analysis. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. The optimum design of cable-stayed bridges involves a significant amount of design variables and design objectives. It can be stated as the minimization of stresses, displacements and bridge cost. To solve the continuous design problem an equivalent multi-criteria approach was used transforming the original problem into the sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum can be obtained. This is followed by the rounding up or down of the continuous cross section variables to the nearest available discrete sections to find a discrete solution. Once the discrete design variables are fixed the solution is then improved by optimizing the cable installation forces (continuous variables) to meet the stress and displacements criteria. If this solution is infeasible, the segmental method is used to find the sizing variables which need to be modified. A concrete cable-stayed bridge example is presented to illustrate the proposed procedure.

Optimization of Extradosed Concrete Bridges

Extradosed bridges combine the main elements of both a prestressed box girder bridge (PBG) and a cable-stayed bridge. With their shallow cable-stays and stiff decks they represent an economic alternative to PBG bridges and cable-stayed bridges for main spans of 100 to 200 m. Their structural behavior combines the concepts of cable suspension and bending of the high stiffness box girder. The extradosed cable-stays introduce a highly effective prestress on the box girder which enhances its structural efficiency.

Fire Behaviour of Concrete Columns with Restrained Thermal Elongation

This paper presents the results of an experimental and numerical study to clarify the influence of the surrounding building structure in the fire behaviour of reinforced concrete columns with restrained thermal elongation. The parameters studied were: the longitudinal reinforcement ratio, the slenderness of the column and the stiffness of the surrounding structure to the column in fire. The experimental study was complemented by a numerical study carried out using the finite element program SAFIR. Simplified calculation methods proposed in EN1992-1-2 were also used to evaluate the fire resistance of the tested columns. From the application of the 500°C isotherm method, proposed in EN1992-1-2, it can be noticed that this method led to smaller values of the fire resistance than those obtained in the experimental tests. The tabulated data method A, proposed in EN1992-1-2, proved to be very conservative.