George T. Michaltsos

DYNAMIC STABILITY OF CABLE-STAYED BRIDGE PYLONS

This paper deals with the stability of the pylons of a cable-stayed bridge under the action of time-dependent loads, due to the vibration of the bridge deck. The stability of such problems of cable-stayed bridges is solved by a technique developed in the Laboratory of Metal Structures and Steel Bridges, of National Technical University of Athens (NTUA), as well as Bolotins technique for the solution of nonlinear problems of dynamic stability. Three cases are studied: pylons with damping, pylons under forced vibration, and pylons subjected to an arbitrary external dynamic load. Useful relations are established by the aforementioned solution method, examples for a variety of pylons are presented, and interesting results regarding the stability of each case are given in diagrams.

A new approach for loads moving on infinite beams resting on elastic foundation

The present work deals with the problem of the dynamic behavior of infinite beams resting on a Winkler-type elastic foundation under moving loads. The beam is subjected to a moving point load traveling with constant speed. Determining the effective length of the beam for a non-moving (static) load, and using the so-called quasi-stationary state of the beam, a solution is proposed with the aid of modal analysis and useful conclusions are obtained. Moving loads have a significant influence on the dynamic behavior of elastic or inelastic solid elements of an entire structure or parts of the structure, while they may produce strong vibrations on such systems, especially when high speeds are reached. The expressions obtained in this work allow the use of the same formulae for any values of speed or damping parameters. The analytical results obtained by the relations presented herein are compared to the ones given by Frýba in the relative chapter of his classic work. Finally, the possible speeds of moving loads that can be reached in the case of such types of beams are estimated and the application field of the gathered relations is determined.

CURVED-IN-PLANE CABLE-STAYED BRIDGES: A MATHEMATICAL MODEL

A mathematical model suitable for static and dynamic analyses of curved-in-plane cable-stayed bridges is proposed. By expressing the tensile forces of the cables in relation to the deck and pylon deformations, the problem is reduced to the solution of a beam curved-in-plane that is subjected to the usual permanent and external loads and to the tensile forces of the cables, the latter being functions of the deformation of the beam. The theoretical formulation presented is based on a continuum approach, which is suitable for the three-dimensional (3D) analysis of long span cable-supported bridges. Numerical examples will be analyzed to illustrate the applicability of the proposed approach.

ROCKING AND SLIDING OF ANCIENT TEMPLE COLUMNS UNDER EARTHQUAKE EXCITATIONS

This paper deals with the rocking and sliding behavior of a monolithic stone block or a system of stone blocks under earthquakes, a problem commonly observed for ancient temples in Greece and Southern Italy. The analysis for the above monolithic or multi-drum columns is conducted by a simple process based on generally accepted simplifications. The effects of column geometry, earthquake characteristics and restitution ratio due to impact are also studied herein. Furthermore, an analytical approach for the solution of the complete nonlinear equations of motion (including the one for the vertical earthquake excitation) for the subject considered is proposed. Finally, characteristic representative examples are presented with useful conclusions drawn. It was found that the stability criteria based on static conditions are reliable, while the corresponding dynamic criteria may lead to erroneous results.

Stability of Steel Columns with Non-Uniform Cross-Sections

In this work, non-uniform steel members with or without initial geometrical or loading imperfections, that are loaded by axial forces applied concentrically or eccentrically and by concentrated moments applied at the ends or at intermediate points, are studied. More specifically, steel members with varying cross-sections, tapered or stepped or members consisting by two different tapered parts are considered. The formulation presented in this work is based on solving the governing equation of the problem through a numerical method where the eigenshapes of the member are employed. A failure plasticity criterion is introduced for members especially the short ones that will never reach the elastic critical buckling load. Although only the simply supported beam-column case is studied herein, it is obvious that the method can be extended to multi-span beams and frames, by employing the corresponding eigenshapes. Useful diagrams are presented for both the critical buckling loads and the equilibrium paths showing the influence of the main characteristics of the beam-column. non-uniform steel members with or without imperfections (of any form), loaded by axial forces (concentrically or eccentrically applied) and by concentrated moments applied at its ends or intermediate points are studied. The steel members with cross-section that may vary along the length, can be tapered or stepped or they can be members consisting by two unequal tapered parts. The imperfections considered may have any form. The formulation presented in this paper is based on solving the governing equation of the problem through the Galerkin method using the eigenshapes of the member. A plasticity failure criterion is introduced for stub or short members that will never reach the elastic critical buckling load. Although in this paper only the simply supported single-span beam-column is studied, it is obvious that the formulation presented may be extended to any type of frame members or frames using the corresponding eigenshapes. The results are presented in the form of diagrams either for the critical buckling loads or for the equilibrium paths, showing the influence of the main members characteristics, as for example the cross-sectional variation law, the interme- diate loads and bending moments or the existing imperfec- tions on the above mentioned buckling loads and equilibrium paths. Although these diagrams are derived for a simply sup- ported beam-column they can be readily employed for the design of steel frames with such members through the use of the equivalent buckling length factor concept.

Eigenfrequencies and Critical Speeds on a Beam due to Travelling Waves

A dynamic load, suddenly applied at a point of a beam, produces a local disturbance that propagates or diffuses to the rest of the beam. This propagation takes place with a speed depending on the material and geometrical characteris- tics of the beam. It has been demonstrated that an impulsive disturbance involving shear and moment will result in two wave types, one that propagates with the shear wave velocity and a second that propagates with a moment-wave velocity. It is observed that tampering with the cross-section of the beam may result to equal shear wave and moment-wave veloci- ties and the two types of disturbances will travel together along with additionally interfering shear waves from beams ends reflections. In this paper, the effect of the traveling waves on the dynamic characteristics of a beam is studied. A complete beam model is presented, which motion is governed by the Timoshenko equation. Two main cases are exam- ined, namely a simply supported beam, and a beam resting on a Winkler-type elastic foundation. Analytical results are presented in graphical form showing the influence of the traveling waves on the eigenfrequencies and critical speeds of such a beam and useful conclusions are drawn.

Nonlinear stability of a simplified model for the simulation of double suspension roofs

Abstract The present work deals with the nonlinear static as well as dynamic stability aspects of an initially imperfect dissipative 2-mass, 3–DOF model under step loading, introduced as a simplified simulation of a class of double-suspension roofs. Employing a fully nonlinear straightforward analysis it is found that global stability, being the main feature of double-suspension roofing systems, is captured by the proposed autonomous conservative model. For realistic combinations of the geometric, stiffness and damping parameters involved the model dealt with is always associated with a stable point attractor response and does not experience either snapping or large amplitude horizontal motions, contrary to recent findings reported for single suspended roof models. Finally, various mathematical and visualization obstacles were encountered, to be overcome by modern commercial software.

A Numerical Approach to the Non-convex Dynamic Problem of Steel Pile-Soil Interaction under Environmental and Second-Order Geometric Effects

The paper deals with a numerical approach for the dynamic soil-pile interaction, considered as an inequality problem of structural engineering. So, the unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects and second-order geometric effects for the pile behaviour due to preexisting compressive loads are taken into account. The numerical approach is based on a double discretization and on mathematical programming. First, in space the finite element method (FEM) is used for the simulation of the pile and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and finally a nonconvex linear complementarity problem is solved in each time-step.

Mathematical modeling for seismic response of steel bridges with internal damping systems

The present work deals with internal damping systems aiming to reduce the torsional and torsional-flexural modal amplitudes in steel bridges with open or closed cross sections. The effect of internal damping systems on the vibration modes and modal amplitudes is studied using simple models of bridges subjected to earthquake actions and useful results are gathered that can be used for design purposes.

DYNAMIC BEHAVIOR OF TELESCOPIC CRANES BOOM

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.