Tobia Zordan

TOPOLOGY OPTIMIZATION OF BRIDGES SUPPORTED BY A CONCRETE SHELL

Abstract A shell-supported footbridge was designed by shaping an anticlastic membrane in compression between deck and foundations. Since it would be subject to biaxial compression, it was appropriate to be made of concrete because concrete strength could be exploited and crack propagation prevented. With reference to Musmeci’s work, a form-finding algorithm shaped the shell as a tension structure with same loads, restraint reactions and internal normal forces, but with the opposite sign. Using a finite element (FE) model of the shell, unwished bending moments (and therefore tensile stresses) were, however, found, because of second order displacements and (contrary to a tension structure) because of the bending stiffness of the reinforced concrete (RC) shell. Tensile stresses were progressively eliminated by removing material from the shell regions where unwished bending moments occurred. For this purpose, topology optimization with the Solid Isotropic Material with Penalization (SIMP) method was used, and different shell structures with cavities for different values of given volume reduction were obtained. Appropriate indexes for structural response were defined, and an optimization index was finally used to identify the most suitable pattern of cavities along the shell.

Equivalent Viscous Damping of Bilinear Hysteretic Oscillators

AbstractAn improved formula to determine the equivalent viscous damping ratio of a single-degree-of-freedom (SDOF) bilinear oscillator is proposed in this paper, which simultaneously considers the influence of the initial period, ductility ratio, and strain hardening ratio. A large number of parameters are considered in order to present comprehensive results. Based on the assumption of secant stiffness, several equivalent linearization approaches are evaluated through parametric analyses. Then, optimization analyses are performed using a genetic algorithm to identify the variation trend of optimal damping ratios. A new formula of an equivalent viscous damping ratio is proposed by nonlinear regression analyses of the optimal damping ratios. Finally, the proposed approach is validated and the results show that the proposed approach leads to better estimates of maximum inelastic displacement response in the entire parameter space considered in this study when compared with other equivalent linearization appr...

Finite element model updating of a tied-arch bridge using Douglas-Reid method and Rosenbrock optimization algorithm

Abstract Condition assessment of bridges has become increasingly important. In order to accurately simulate the real bridge, finite element (FE) model updating method is often applied. This paper presents the calibration of the FE model of a reinforced concrete tied-arch bridge using Douglas-Reid method in combination with Rosenbrock optimization algorithm. Based on original drawings and topographie survey, a FE model of the investigated bridge is created. Eight global modes of vibration of the bridge are identified by ambient vibration tests and the frequency domain decomposition technique. Then, eight structural parameters are selected for FE model updating procedure through sensitivity analysis. Finally, the optimal structural parameters are identified using Rosenbrock optimization algorithm. Results show that although the identified parameters lead to a perfect agreement between approximate and measured natural frequencies, they may not be the optimal variables which minimize the differences between numerical and experimental modal data. However, a satisfied agreement between them is still presented. Hence, FE model updating based on Douglas-Reid method and Rosenbrock optimization algorithm could be used as an alternative to other complex updating procedures.

Application of Topological Optimization to Bridge Design

AbstractRecently, structural optimization has become an important tool for structural designers, because it allows a better exploitation of material, thus decreasing a structure’s self-weight and saving material costs. Moreover, structural optimization helps the designer to find innovative design solutions and structural forms that not only better exploit material but also give the structure greater aesthetic value from an architectural point of view. In this article, the seismic retrofitting of a bridge originally designed in reinforced concrete is illustrated, showing how lightening the bridge superstructure, rather than reinforcing the already completed foundations and abutments, allowed these latter features to resist greater seismic actions as required in the recent update of the Italian seismic code. Therefore, besides using the steel-concrete composite typology, the bridge superstructure was lightened through structural optimization. After having optimized the thickness of webs and flanges, it was ...

Bridge Structural Optimization Through Step-by-Step Evolutionary Process

In this paper, the structural optimization process aiming to reduce the weight of the superstructure of a five span arch bridge, built in the Province of Venice, Italy, and spanning the Piave River in the town of San Donà, is presented. The original project, with a pre-stressed concrete superstructure, was re-considered during construction because of the following two unexpected events. First, the approved new seismic national regulation became effective when the bridge was already partially built. As a result, existing foundations became unable to withstand the prescribed new seismic action. Furthermore, the Venice Water Authority, responsible for the management of the river spanned by the bridge, declared that erection phases without any provisional supports and scaffolding resting on the riverbed, as foreseen by the original project, should be preferred. Between the two possible identified design strategies able to deal with the mentioned problems, namely, the strengthening of the foundations or the lightening of the superstructure, the second option was chosen, on the basis of engineering judgement concerning the simplification of construction procedures, timing and budget. The search for the lightest possible solution, with the restraint given by the approved aesthetics of the original design and the need of keeping within the former budget, brought to the conclusion that an evolutionary structural optimization (ESO) process could be suitably applied to a composite steel and concrete superstructure.

Attainment of an integral abutment bridge through the refurbishment of a simply supported structure

Maintenance problems related to existing bridges represent a matter of major concern for road authorities that are recently accepting major construction or retrofitting costs when an initially increased expense would turn out to be economically favourable in a long period. Temporal performance of structures does not depend just on the related performance of construction materials, but is deeply affected by detailing, coupling, static scheme (with the consequent state of stress and deformation) and finally by the boundary conditions (such as environmental condition, volume and kind of traffic). Integral abutment bridge (IAB) concept, as explained in the following, with the elimination of all bearings and expansion joints seems to adequately respond to the mentioned functional demands with potentially limited maintenance problems during service life of the structure. After a concise description of the state of the art and possible inconvenience with IABs, the paper will present the transformation of a simply supported bridge into a IA structure on a total length of roughly 400 m using glued connections at piers and abutments.

Optimization Indexes to Identify the Optimal Design Solution of Shell-Supported Bridges

As a structural optimization technique, topology optimization is an important tool for helping designers to determine the most suitable shape of a structure. With this powerful tool, designers can define families of candidate solutions by modifying the input volume reduction (VR) ratio, reducing the structural weight as much as possible. However, finding the best compromise between material savings and structural performance among these candidate solutions is a critical issue for designers. To deal with this issue, an optimization index (OI) is presented in this paper. It provides a mathematical procedure that highlights the best choice among several candidate solutions obtained by the optimization procedure. The index was originally defined in a previous study on the structural optimization of composite steel-concrete bridges. In this paper, a generalized version of the original optimization index is introduced and used to investigate a particular aspect related to concrete shell-supported bridges. Starting from three shell-supported footbridges, the shapes of which are the final result of form-finding optimization procedures, different starting models are defined, and each is characterized by different edge-stiffening conditions. Despite using an anticlastic shell shape, unavoidable tensile stresses occur because of the thickness of the shell, variations in the material, the loading of the deck, and other factors. For each starting model, a finite-element topological optimization conducted with the solid isotropic material with penalization (SIMP) method is performed to minimize the weight (i.e., volume) of the shell by a certain percentage. According to the results obtained from topology optimization, the proposed generalized optimization index (OI*) analytical formulation is discussed in detail, and its effectiveness is validated.

Optimal Design of Pile Foundation in Fully Integral Abutment Bridge

In order to resolve the durability problem of expansion joints and bearings, the integral abutment bridge (IAB) has become more and more popular. For integral abutment bridge, choosing a suitable pile foundation type is a challenging problem, because the substructure is fixed with superstructure to bear the load together. In this paper, the design of the pile foundation in a fully integral abutment bridge (FIAB) in China was analyzed. A finite element model was built by the commercial software MIDAS considering soil-structure interaction and construction stage simulation. A sensitive analysis was carried out to investigate the influence of different pile foundation types on the mechanic performance of the IAB. The results show that when the circular pile is used, the stress of pile, negative moment and tensile stress of girder are smaller than those when the rectangular pile is used. With the increase of pile diameter, the stress and displacement of pile decrease, while the bending moment of pile and the negative moment and tensile stress of girder increase. For rectangular piles, with the increase of cross-sectional length-width ratio, the bending moment of pile, negative moment and tensile stress of girder decrease; while the stress and displacement of pile increase.

A Project Supported by the IABSE Foundation in Togo

Currently the project has entered the fourth phase and the courses have started. Classes are given by professors coming from Lomé University and focus on the following subjects: Drawing; Structural Design and Analysis; Hydraulics and Plants; Civil Engineering Practice; Business and Management. Control indicators to check the effectiveness of each step of the project have been established. IABSE Foundation is receiving regular reports, upon which the single payments of the total sum allocated are transferred. An intense and effective communication between the YOVO Association in charge of the project and the IABSE Foundation has been established, before and after the beginning of the project. All the funds distributed by the IABSE Foundation have been spent on the project without any leakage or loss: the money has reached the addressees in a straight and efficient way.

Design Service Life Determination for Bridge Structural Elements

Through definition of design service lives for bridges and their elements, element classification according to structural systems, durability type research as well as investigations of their actual operating lives and recommended design service lives in specifications home and abroad, a direct method and also a simplified one were proposed in order to determine design service lives of bridge structural elements based on life-cycle cost analysis. In direct method, element service life schemes were established, and then the one with optimal economy could be selected through life cycle cost calculation of each scheme. In the simplified method a calculation formula was presented, for applying which the classification and evaluation of the influence coefficients were discussed and recommended foundational design service lives of bridge elements were brought forward based on professional investigations. In the end, a certain sea-crossing project was used as an example to illustrate the process of design service life determination for bridge structural elements.