The paper investigates the effects of the geometrical imperfections in buckling analyses of plated steel elements at elevated temperatures and provides an alternative branch-switching procedure to perform post-buckling analyses without introducing initial imperfections into the model. This procedure is appealing since the choice of appropriate imperfections in classical analyses is not straightforward, above all at elevated temperature. Several numerical analyses show that the choice of the imperfections is not trivial and that the buckling mode may vary with temperature. They also show that the proposed branch-switching procedure is an interesting preliminary tool to understand the instability behaviour of steel structural members.

The purpose of this paper is to model the nonlinear dynamical response of steel frame structures subjected to impact loading. A 2D co-rotational rigid beam element with generalized elasto-plastic hinges is presented. The main idea is to integrate the concept of the generalized elasto-plastic hinge into the standard co-rotational framework by performing a static condensation procedure in order to remove extra internal nodes and their corresponding degrees of freedom. In addition, impact loading is applied through a contact model that is described in the rigorous framework of non-smooth dynamics. In this framework, equations of motion are derived using a set of differential measures and convex analysis tools, whereas Newton's impact law is imposed by means of a restitution coefficient in order to accommodate energy losses. An energy and momentum conserving scheme is adopted to solve the dynamical equations. The main interest of the current model is the ability to evaluate the geometrically nonlinear inelastic behaviour of steel structures with semi-rigid connections subjected to impact in a simple and efficient way, using only a few number of elements. The accuracy of the proposed formulation is assessed in three numerical applications.

In this paper, a simplified discrete model for calculating the modal parameters of the fundamental vertical mode of a simple beam on viscoelastic supports is proposed. Exact closed-form expressions for the fundamental natural frequency and modal damping ratio of the aforementioned coupled system are derived, as a function of the beam geometry and the foundation impedances. Using this model, the effect of the dynamic stiffness and dissipation capacity of the foundation-soil system on the modal characteristics of the fundamental vertical mode of the railway beam bridges is investigated and discussed. The proposed closed-form expressions, in combination with the impedance functions of different foundation-soil systems, can clarify the main features of dynamic SSI analysis of the railway beam bridges and lead to review the recommended modal damping ratios in the code provisions and design manuals.

The paper describes the development of a two-dimensional (2D) nonlinear beam finite element that includes advanced path-following capabilities for detecting bifurcation instability of steel elements subjected to fire loading. A co-rotational formulation was used for describing the beam kinematic. The degradation of the steel mechanical properties at high temperature according to the Eurocode 1993-1-2 was considered by integrating the material constitutive law based on a predetermined temperature field in the cross section. Advanced path-following methods were implemented to analyse the elastic-plastic post-buckling behaviour of compressed steel elements at high temperature without the need of introducing geometrical imperfections. To highlight the practical implications, a parametric analysis showed that the element could reproduce the EN1993-1-2 buckling curve. The obtained outcomes were validated against experimental and numerical data obtained with commercial software ABAQUS and SAFIR. 

This paper presents a numerical approach to evaluate the damping properties of a stay cable with an external viscous damper. The idea is to model the cable by using non-linear corotational beam elements and to study small vibrations around the static deformed equilibrium configuration. This gives a complex eigenvalue problem from which the modal damping ratios can be calculated. The performance of the proposed method is assessed through two numerical applications. Compared with the analytical methods based on differential equations widely used in the literature, the proposed non-linear finite element approach has the advantages that the effect of the sag is considered in an accurate way and that there is no limitation regarding the number and the value of the structural parameters that can be introduced in the model. 

This paper presents a full-scale dynamic testing on a simply supported railway bridge with integrated end-shields, by using a hydraulic exciter. Experimental frequency response functions are determined based on load controlled frequency sweeps. Apart from accurate estimates of natural frequencies, damping and mode shapes, the experimental testing also gives valuable information about the dynamic characteristics at resonance and amplitude dependent nonlinearities. Numerical models are used to simulate the dynamic response from passing trains which is compared to experimental testing of similar train passages. The results show that the bridge deck is partially constrained due to the interaction between the end-shields and the wing walls with the surrounding soil. Measurements at the supports also show that the flexibility of the foundation needs to be accounted for. An updated numerical model is able to accurately predict the response from passing trains. The response is lower than that predicted from the initial simulations and the bridge will fulfil the design requirements regarding vertical deck acceleration.

Precast and prestressed hollow core concrete slabs, that combine low self-weight and high strength, are often used for long span floors. However, this implies that the slabs are also confronted with the issue of human induced floor vibration serviceability. In this paper, experimental results from both hammer-impact and walking tests of a slab consisting of 6 hollow core concrete elements and of dimension 10 m × 1.2 m are presented. Comparisons with results Finite element results are performed. Three different walking paths and four numerical models taken from the literature for the single pedestrian load are considered. The results show that with transversal and diagonal walking paths, the vibrations due to the torsional mode of the slab can be higher than the ones due to the lowest bending mode. They show also that the four pedestrian loads give rather different numerical results.

This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Euler-Bernoulli beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It is rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through four numerical examples.

This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Bernoulli/Timoshenko beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It can be rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through two numerical examples.

The transient dynamic response of a steel beam-column subjected to impact loading is a complex phenomenon involving large localized plastic deformations and non-smooth contact interactions. Exposed to high intensity of the contact force generated from impact, the beam-column may undergo large displacement and inelastic deformation. Previous research has shown that a calibrated elasto-plastic single degree of freedom system is able to reproduce both the displacement and the force time-history of a steel beam subjected to non-impulsive loading or low-velocity impact. In these models, the static force-displacement curve is derived from either experiments or detailed 3D nonlinear analysis. Tri-linear resistance function has been extensively used to reproduce the different stages of the response including catenary effects. A rigorous treatment of such a complex problem calls for the use of non-smooth analysis tools to handle the impulsive nature of the impact force, the unilateral constraint, the impenetrability condition and the discontinuity of the velocity in a rigorous manner. In this paper, we present a non-smooth elasto-plastic single degree of freedom model under impact loading that permits the use of arbitrary resistance function. Adopting the non-smooth framework offers tools such as differential measures and convex analysis concepts to deal with unilateral contact incorporating Newton’s impact law. The mid-point scheme is adopted to avoid numerical unrealistic energy decay or blowup. Furthermore, the non-penetration condition is numerically satisfied by imposing the constraint at only the velocity level to guarantee energy-momentum conservation [1]. The explicit expression of resistance functions of the beam that are used in the SDOF model are obtained from a simplified nonlinear static analysis of two beam-column models. In the analysis, a linear relation between normal force and bending moment is assumed for the plastification of the hinges. Two proposals to simplify the explicit expressions of the model’s response behavior are given. Performing an energy-based analysis, we predict maximum displacement that is needed to absorb the kinetic energy arising from the impact for different coefficient of restitution. The numerical examples underline the validity of the model by showing good agreement with the predictions of reference models.