Extradosed bridges offer a competitive alternative to traditional systems used in spans ranging from 100 to 250 m. The trend in the world is the development of new materials and with it the design of thin structures, which is a challenging change for further development. Extradosed bridge is a relatively new type of construction (first in Odawara, Japan 1994), although there are many bridges of this type in the world, there are no strict design rules in terms of statics and even less in terms of dynamic behavior. To research this area closer, parametric analysis can be performed. Due to the complexity of this task and the non-linear coupling of the design parameters, it is necessary to approach it by an optimization method that, for predefined boundary conditions, optimizes the design response.

Footbridges are analyzed in terms of dynamic response for pedestrian comfort. This problem is solved mainly on light and at the same time rigid constructions, which are easily oscillated by pedestrian load. It is often solved on steel footbridges, but with the technological development of UHPC, we are capable nowadays to build relatively light and long span concrete footbridges. Behaviour of a thin concrete cross-section with its geometry is closer to steel structures, but at the same time we have to deal with rheological effects such as creep and shrinkage. There are many influences on the structure that can affect the dynamic behavior of the structure, including the non-linear behavior of the cable system. This paper presents an initial entry into the computational issues of more complex constructions that have more input influences.

A tuned mass damper (TMD) optimization can be performed under various assumptions and objectives. All the variables of the optimization, such as structural model, performance index and load type affect the optimal parameters of the TMD. This paper presents a new optimization method that implements straightforward performance index and allows taking load spectral characteristics into account. Thanks to the usage of modal coordinates, the method allows fast numerical optimization of TMD attached to large or complicated structures with numerous degrees of freedom. One of the complicated tasks while optimizing TMD is the choice of a performance index. In this paper, the mean value of potential energy stored in the elastic deformation of a structure under periodic load serves as a performance index, which leads to a low numerical complexity task if the optimization is performed in the frequency domain. The new method also allows a simple inclusion of load spectral characteristics and permits TMD optimization for any loading spectral range. When applied to a structure with a single degree of freedom, this method leads to H2 optimization in the case of white noise excitation. However, it is applicable to multiple degrees of freedom structures with single or multiple TMDs and any given load. The paper also presents several examples of numerical optimization of the TMD attached to both single and multiple degrees of freedom structures under various loads, including white noise excitation, pedestrian load, and earthquake strong motion.

A tuned mass damper is a device, which can be highly helpful while dealing with dynamic behaviour of structures. Its proper design is conditioned by knowledge of both loading and the structure properties. In many cases, the structure can be represented by single degree of freedom model, which simplifies the design and optimization of tuned mass dampers. Most of studies focus only on minimization of displacement of the main structure under harmonic force load, however, in many cases, different frequency response function would be more appropriate. This paper presents an extension of design formulas for the H∞ optimization of tuned mass dampers for damped structures and various frequency response functions.

Tuned mass damper is a device, which can be highly useful when dealing with excessive vibration and is widely used in many engineering fields. However, its proper design and optimization is a complicated task. This study uses mode superposition method to speed up the evaluation of dynamic response. The speed of response calculation allows for a quick calculation of frequency response function and numerical optimization of tuned mass dampers. This optimization method is demonstrated on a numerical example of a cable stayed footbridge. The example compares a simplified and widely used design method of tuned mass damper with numerical optimization.

The tuned mass damper (TMD) is an effective way to deal with excessive vibration of structures. Its high efficiency is, however, conditioned by proper design. The optimization of TMD is a complicated process, because a closed-form solution for its optimal parameters is known only for several simplified cases. This paper presents an approach of dynamic response calculation of structures with TMD in modal coordinates, which is suitable for repeated evaluations of response to harmonic load which is necessary in case of optimizing TMD parameters for large and damped systems.

The dynamic analysis of footbridges became common in recent years, but the approach to modelling pedestrian induced load is still inconsistent. This paper compares two different ways of modelling single pedestrian load. The response of the structure to stationary pulsating force is compared to the results given by the same force moving along simply supported beam. 300 randomly generated beams were used in this parametric study to describe the relation among these two approaches and parameters of the structure. The proposed formula was successfully applied to get more realistic estimation of response of the structure to a single walking pedestrian using stationary pulsating force.

During the renovation of roof trusses and roof structures, damaged wood must be replaced with new wood. To keep the original material adjustment slab joints can be used. Unfortunately, this type of joint has not been observed from the structural perspective. The shape of the joint, the inclination of its faces, the type and the number of connectors still represent an unknown area. A simplified analytical model is briefly derived in the article and the effect of the face inclination is solved. The results obtained from experiments are compared with the results from the model.

The increase of vibration problems in modern footbridges shows that footbridges should no longer be designed for static loads only. Not only natural frequencies but also damping properties and pedestrian loading determine the dynamic response of footbridges and design tools should consider all of these factors. In this paper the pedestrian load models for serviceability verification of footbridges, which are missing in the current European codes, are presented. For simplicity reasons the proposed pedestrian load models are based on stationary pulsating loads instead of moving pulsating loads. It is shown that simplified procedure can be used in verification of the serviceability limit state related to vibration due to pedestrians. Footbridge vibrations don't cause usually structural problems, but if the vibration behaviour does not satisfy the comfort criteria, changes in the design or damping devices could be considered. The most popular external damping devices are viscous dampers and tuned mass dampers (TMD). The efficiency of TMD is demonstrated on the example of a footbridge prone to vibrations induced by pedestrians. It is shown that if the TMD is tuned quite precisely the reduction of accelerations can be very significant.

This work deals with the response of a linear undamped SDOF system exposed to a force with random amplitude, phase shift, or their combination. The first two moments, the mean value and the variance, of the response will be determined analytically through the Duhamel's integral, and compared to the numerical Monte Carlo simulations. Integration of associated equations of motion will be performed by the Newmark method of average acceleration.

This paper investigates effects of the seismic load to a structure. The article describes main methods of the definition and practical application of the seismic load based on the Standard Eurocode 8. There was made a comparison of all methods using the same structure. A simple two-storeyed concrete 2D-frame with fixed joints was chosen. A one another model with rigid beams for some calculations was defined. The second model can be used for hand-calculations as a cantilever with two masses. The paper describes main dynamic properties of the chosen structure. Seismic load was defined by lateral force method, modal response spectrum, non-linear time-history analysis and pushover analysis. The time-history analysis is represented by accelerograms. There were made linear and non-linear calculations.

Synchronized jumping is considered to be the most significant dynamic load on grandstand structures induced by humans. In order to accurately predict reliability and serviceability at the design stage, computational models with proper characterization of these kinds of external loads are required. In this contribution, we will focus on categorization and description of load, providing thus an overview of various approaches to simulate forces induced by a synchronized jumping crowds. Standard models, such as equivalent static load or simple approximations in time and frequency domain, will be recalled. Because the true load induced by a crowd is inherently random, more advanced models will be discussed as well. These are based on Monte Carlo generators or semi-analytical probabilistic models. Finally, all discussed approaches will be demonstrated on a simple test example.

Active spectators on grandstands can induce wide palette of loads ranging from hand-clapping or swaying to bobbing or synchronized jumping. Each of these loads may differ in its intensity, frequency range, and level of synchronization. All these aspects render the process of predicting the behaviour and performance of grandstands difficult, requiring proper modelling techniques. Although grandstands themselves can be successfully modelled by finite element method, the situation with human-induced loading is less transparent, and mathematical description of load have evolved over the years from equivalent static load through deterministic approximations in time and frequency domain to Monte Carlo (MC) generators. In this contribution, the most intensive kind of human activity exercised on grandstands—synchronized jumping—is focused on. In particular, the response of grandstands loaded by jumping active crowds that are randomly distributed in space is investigated. For simplicity, no passive spectators are considered. Two modelling approaches are used. First, direct MC simulation provides a reference solution. Second, a semi-analytical formulation employing theory of random processes provides response estimates and simplifying formulas. Finally, both approaches are demonstrated and compared on a simple example.

Repairs to historical timber structures include connecting existing beams and new beams. Older ways of making the connection need to be used to ensure authenticity of the beam. In most cases, e.g. floor structures, the second limit state – serviceability – is of decisive importance. The new connection softens the beam and increases the displacement. The most widely-used joint is a scarf joint with two or more bolts or dowels. It is not clear whether greater obliquity of its cheeks is desirable, or the effect of different numbers of bolts on the stiffness of the beam. In Germany, a scarf joint with four bolts is recommended, but there is no validation for this from the structural perspective. The behaviour of joints with two bolts or with four bolts seems to be the same. In the process of repairing historically valuable timber structures, the most widely-used joint is with wooden dowels. One pin can be combined with two dowels, or two dowels with one pin. There is currently no relevant information available about the behaviour of the joint, although practical engineers require such information. A theoretical solution requires simplifications, and these are derived from experimental results. The force method (based on the elastic strain energy) is used for a theoretical solution for a statically indeterminate structure. The results of numerical analysis are very encouraging. The final changes in the stiffness of repaired beams in comparison with the original beams are in very good agreement with experimental results.

This paper is concerned with the selected aspects, which are discovered during a design stage of cable and membrane structures, known as “form-finding” process. The aim of this paper is the understanding of the basic principles of the form-finding process and their explanation of the very simple examples. The use of the finding a shape of a tension membrane that is in static equilibrium as an analogy with the search condition of minimal surfaces is explained. The basic principles are demonstrated on simple 2D example, in which the finding a stable minimal surface passes in the finding a stable minimal length.

The increase of vibration problems in modern footbridges shows that footbridges should no longer be designed for static loads only. Not only natural frequencies but also damping properties and pedestrian loading determine the dynamic response of footbridges and design tools should consider all of these factors. Footbridge vibrations don’t cause usually structural problems, but if the vibration behaviour does not satisfy the comfort criteria, changes in the design or damping devices could be considered. The most popular external damping devices are viscous dampers and tuned mass dampers (TMD). The paper presents the basic principles of optimal TMD configuration and design procedure. The efficiency of TMD is demonstrated on the example of a footbridge prone to vibrations induced by pedestrians. It is shown that if the TMD is tuned quite precisely the reduction of accelerations can be very significant.

The bearing capacity of a scarf joint depends on the length of the joint and the type of connection. It is possible to use circular bolts or squared dowels. Both connection tools used in the repairs of historic timber structures are made of wood according to the requirements of the heritage authority.

The first case study used in this work is an existing seven-storey unreinforced masonry building (representing a typical residential building located in the district of L ́Example in Barcelona). The accuracy of the non-linear static procedures was evaluated by comparison with non-linear dynamic analyses for seven ground motion records and different levels of seismic intensity. The results obtained from the analyses showed good performance of the static pushover methods on the analysed building. The second case study used in this work is a two-storey unreinforced masonry building which was tested at ELSA in Ispra, Italy. First a modal response spectrum analysis was carried out. Subsequently, non-linear static analysis was performed using two different computer programmes. The results of the present work were compared with experimental results.

This paper presents a practical application of form-finding process of cable-membrane structures. The dynamic relaxation method with kinetic damping is used as the computation method for numerical analysis. A brief description of the construction, a description of the models and the way of solving tasks will be introduced. The correct operation of the implemented algorithm will be compared with a commercial program.

In this contribution, we employ non-stationary filtered Gaussian processes as an enrichment of a periodic mean value in order to approximate crowd loads on grandstands. Our work generalizes previous considerations where the superposition of a mean value and a stationary filtered Gaussian noise was used, and helps therefore to better predict the response of a structure mainly in the transition stages. We specify general theory of stochastic differential equations within the context of grandstands by recalling particular moment equations, and demonstrate its benefits or drawbacks on two simple examples. Overall performance is measured in terms of the second moment evolutions in time and in terms of the total up-crossings of the system's response compared to previously developed stationary approximation and Monte Carlo simulation. Throughout, only an active part of a crowd is considered.