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Load models that account for Human-Structure Interaction (HSI) may be preferable to accurately predict the dynamic response of lightweight footbridges subjected to pedestrian actions. Representing each person within a crowd may not be practical in engineering design calculations as time-variant models with a large number of degrees of freedom have to be managed. In addition, high computational time may be required to achieve the steady-state response. In this sense, this paper proposes a novel approach to calculate the vertical steady-state response of footbridges from a time-invariant coupled crowd-structure system. Considering the model of the structure and a feedback model of the crowd, a total closed-loop Transfer Function (TF) of the coupled system is derived. Based on this frequency-domain interacting methodology, a step-by-step procedure is set to asses the vibration serviceability of lightweight footbridges due to harmonic excitations through simple algebraic operations. The proposal is used to study a Fibre Reinforced Polymer footbridge subjected to two streams of walking pedestrians. For this structure, a good compromise between experimental and numerical results is obtained in terms of vertical vibrations and TFs. To further validate the proposed approach, a pre-stressed concrete laboratory facility is also analysed, obtaining a satisfactory agreement between the experimental and numerical TFs. Thus, the proposed approach allows to evaluate lightweight footbridges under crowd-induced loads considering HSI in a simple and accurate manner, which is clearly geared to practice.

In the analysis of lightweight footbridges subjected to pedestrian actions, the vertical dynamic response is often overestimated when Human-Structure Interaction (HSI) is omitted. To account for the phenomenon, a Single- Degree of Freedom (DOF) system has been employed to represent a person. When dealing with a stream of people, this approach may lead to an expensive computational problem as several DOFs have to be managed. An alternative to overcome this issue is modelling the crowd as a distributed Mass-Spring- Damper-Actuator system acting on the structure. Hence, an equivalent time-invariant system with two DOFs can be obtained while considering HSI. This paper proposes a procedure to determine the resonant response of pedestrian structures subjected to a flow of walking pedestrians. Through the construction of a Transfer Function in the frequency domain, accounting for the parameters of the crowd and the structure, the dynamic analysis can be addressed by computing a simple algebraic multiplication. The proposed approach is applied to a lightweight Fibre Reinforced Polymer footbridge, which has been recently designed and built by the authors at the School of Civil Engineering – Universidad Politécnica de Madrid. A weak traffic class (0.2 pedestrians/m²) is the considered load scenario for the assessment of the structural acceleration response. As a good agreement between experimental and numerical results is shown, the proposal may be employed for the fast prediction of the dynamic response of other lightweight pedestrian structures at design stage.

Finite-element-model updating allows reducing the discrepancies between the numerical and the experimental dynamic behaviour of civil engineering structures. Among the different methods to tackle t...

Soil–structure interaction is a key aspect to take into account when simulating the response of civil engineering structures subjected to dynamic actions. To this end, and due to its simplicity and ease of implementation, the dynamic Winkler model has been widely used in practical engineering applications. In this model, soil–structure interaction is simulated by means of spring–damper elements. A crucial point to guarantee the adequate performance of the approach is to accurately estimate the constitutive parameters of these elements. To this aim, this article proposes the application of a recently developed parameter identification method to address such problem. In essence, the parameter identification problem is transformed into an optimization problem, so that the parameters of the dynamic Winkler model are estimated by minimizing the relative differences between the numerical and experimental modal properties of the overall soil–structure system. A recent and efficient hybrid algorithm, based on the combination of the unscented Kalman filter and multi-objective harmony search algorithms, is satisfactorily implemented to solve the optimization problem. The performance of this proposal is then validated via its implementation in a real case-study involving an integral footbridge.

A formulation in cylindrical coordinates of the nonlinear torsional wave propagation on a hyperelastic material characterized by Hamilton's strain energy function is proposed. The objective of this formulation is to study and assess soft tissues, taking into account both geometrical and physical nonlinearity. Specifically, this work analyzes the propagation of torsional shear waves through an isotropic axisymmetric medium, so the only non-zero velocity component is associated with the angular coordinate. To transform the equations from Cartesian to cylindrical coordinates, the covariant and contravariant transformations are employed. A transverse torsional wave propagating through a quasi-incompressible hydrogel from the emitter to the receiver is considered. As the close form solution is not straightforward, a numerical simulation using the Finite Difference Time Domain method is performed. The results are obtained for a realistic range of wave frequencies and nonlinear parameters for medical applications.

Stadium grandstands are designed to support high dynamic loads due to the presence of spectators attending both sport and music events. In order to assess accurately the dynamic response of these s...

Due to the high strength-to-weight ratio of fibre reinforced polymers (FRPs), human-induced vibration problematic remains as a subject to be fully comprehended in order to extend the use of composites in Bridge Engineering. Thus, this paper studies an ultra-lightweight FRP footbridge, which presents excessive vertical vibrations when the fourth harmonic of a walking pedestrian is synchronised with the structure’s fundamental frequency. Focusing on the vertical bending mode, at 7.66 Hz, the bridge dynamic behaviour was assessed under the action of a single pedestrian crossing the facility at a step frequency of 1.9 Hz. As an over prediction of the footbridge response was computed using a moving force (MF) model available in a design guideline, a mass-spring-damper-actuator (MSDA) system was adopted to depict a walker. Hence, Human-Structure Interaction (HSI) phenomenon was considered. Employing the experimental results, parameters of the MSDA system were identified, leading to a HSI model that considers the first fourth harmonics of a walking human. Additionally, a parametric analysis was carried out, determining that the damping ratio of the human body and the load factor associated to the fourth harmonic are the most relevant parameters on the estimation of the response. The identified HSI model may be used as a first approximation to accurately predict the dynamic response of ultra-lightweight composite structures and should be extended to account for crowd-induced loads.

This paper presents the design, construction and structural response of a laboratory FRP footbridge. Pultruded elements, Glass-FRP profiles and Carbon-FRP strips, comprise the 10 m long simply supported structure, which linear mass is only 80 kg/m approximately. A value of L/200 (L being the length of the span) was the limit adopted for the long-term deflection at mid-span, and verifications at Ultimate Limit State were carried out according to the recommendations of the FRP manufacturer and the European Guideline to design FRP Structures. To construct the bridge, the following phases were completed: (i) bonding CFRP strips to the GFRP stringers, (ii) connecting the FRP elements, (iii) casting concrete at the support regions, and (iv) installing the deck. Once the construction finished, an experimental static and dynamic campaign was performed to assess the bridge structural behavior. As expected from the design stage, excessive vertical vibrations under different pedestrian actions (walking and bouncing) were measured.

Stay cables exhibit both great slenderness and low damping, which make them sensitive to resonant phenomena induced by the dynamic character of external actions. Furthermore, for these same reasons, their modal properties may vary significantly while in service due to the modification of the operational and environmental conditions. In order to cope with these two limitations, passive damping devices are usually installed at these structural systems. Robust design methods are thus mandatory in order to ensure the adequate behavior of the stay cables without compromising the budget of the passive control systems. To this end, a motion-based design method under uncertainty conditions is proposed and further implemented in this paper. In particular, the proposal focuses on the robust design of different passive damping devices when they are employed to control the response of stay cables under wind-induced vibrations. The proposed method transforms the design problem into a constrained multi-objective optimization problem, where the objective function is defined in terms of the characteristic parameters of the passive damping device, together with an inequality constraint aimed at guaranteeing the serviceability limit state of the structure. The performance of the proposed method was validated via its application to a benchmark structure with vibratory problems: The longest stay cable of the Alamillo bridge (Seville, Spain) was adopted for this purpose. Three different passive damping devices are considered herein, namely: (i) viscous, (ii) elastomeric, and (iii) frictions dampers. The results obtained by the proposed approach are analyzed and further compared with those provided by a conventional method adopted in the Standards. This comparison illustrates how the newly proposed method allows reduction of the cost of the three types of passive damping devices considered in this study without compromising the performance of the structure.

In this manuscript, it is presented, a case-study about the assessment of the seismic behaviour of Veronicas Market. Its structure, initially constituted by steel trusses supported on masonry walls, was subsequently modified by the addition of a mezzanine supported on reinforced concrete piers. Applying the capacity spectrum method, based on an updated nonlinear finite element model, the performance levels of both the original and modified structure have been compared to assess the effects originated by the change in the transmission mechanism of the seismic loads., En este artículo, se presenta, un caso en estudio sobre la evaluación del comportamiento sísmico del Mercado de Verónicas. Su estructura, originalmente constituida por cerchas metálica apoyadas sobre muros de fábrica fue posteriormente modificada por la incorporación de una entreplanta con pilares de hormigón armado. Aplicando el método del espectro de capacidad, con base en un modelo calibrado no-lineal de elementos finitos, se han comparado los niveles de desempeño de la estructura original y modificada para valorar los efectos originados por el cambio en el mecanismo de transmisión de las cargas sísmicas.

Finite element model updating has become a key tool to improve the numerical modelling of existing civil engineering structures, by adjusting the numerical response to the observed experimental behaviour of the structure. At present, model updating is mostly conducted using the maximum likelihood method. Following this approach, the updating problem can be transformed into a multi-objective optimization problem. Due to the complex nonlinear behaviour of the resulting objective functions, metaheuristic optimization algorithms are normally employed to solve such optimization problem. However, and although this is nowadays a well-established technique, there are still two main drawbacks that need to be addressed for practical engineering applications, namely: (i) the high simulation time required to compute the problem; and (ii) the uncertainty associated with the selection of the best updated model among all the Pareto optimal solutions. In order to overcome these limitations, a new collaborative algorithm is proposed herein, which takes advantage of the collaborative coupling among two optimization algorithms (harmony search and active-set algorithms), a machine learning technique (artificial neural networks) and a statistical tool (principal component analysis). The implementation details of our proposal are discussed in detail throughout the paper and its performance is illustrated with a case study addressing the model updating of a real steel footbridge. Two are the main advantages of the newly proposed algorithm: (i) it leads to a clear reduction of the simulation time; and (ii) it further permits a robust selection of the best updated model.

The finite element model (FE) updating is a calibration method that allows minimizing the discrepancies between the numerical and experimental modal parameters. As result, a more accurate FE model is obtained and the structural analysis can represent the real behaviour of the structure. However, it is a high computational cost process. To overcome this issue, alternative techniques have been developed. This study focuses on the use of the unscented Kalman filter (UKF), which is a local optimization algorithm based on statistical estimation of parameters taken into account the measurements. The dome of a real chapel is considered as benchmark structure. A FE model is updated applying two different algorithms: (i) the multi-objective genetic algorithm and (ii) a hybrid unscented Kalman filter-multi-objective genetic algorithm (UKF-MGA). Finally, a discussion of the results will be presented to compare the performance of both algorithms.

Wind action can induce large amplitude vibrations in the stay cables of bridges. To reduce the vibration level of these structural elements, different types of passive damping devices are usually installed. In this paper, a motion-based design method is proposed and implemented in order to achieve the optimum design of different passive damping devices for stay cables under wind action. According to this method, the design problem is transformed into an optimization problem. Thus, its main aim is to minimize the different terms of a multi-objective function, considering as design variables the characteristic parameters of each considered passive damping device. The multi-objective function is defined in terms of the scaled characteristic parameters, one single-function for each parameter, and an additional function that checks the compliance of the considered design criterion. Genetic algorithms are considered as a global optimization method. Three passive damping devices have been studied herein: viscous, elastomeric and friction dampers. As a benchmark structure, the Alamillo bridge (Seville, Spain), is considered in order to validate the performance of the proposed method. Finally, the parameters of the damping devices designed according to this proposal are successfully compared with the results provided by a conventional design method.

Using a multi-objective optimization algorithm avoid the use of weighting factors to balance the different residuals in a finite element model updating procedure under the maximum likelihood method. By using this approach, the fittest model is not unique and a set of solutions that form a curve, so-called Pareto optimal front, is obtained. Within this paper, first a review of the state of the art on the criteria used to determine the most adequate model among all the solutions of the Pareto front is presented. Subsequently, a case study of a real footbridge is considered. A finite element model of the footbridge is updated based on its experimental modal parameters. The Non- Dominated Sorting Genetic Algorithm is used to obtain the Pareto front. Since all the solutions in the Pareto front are non-dominated, the selection of the best candidate requires a reasonable criterion. Herein, different procedures to select the best updated model are discussed.