László P. Kollár

Budapest University of Technology and Economics · Department of Structural Engineering

In addition to the two major earthquakes on February 6. 2023 more than 40 moderate (MW > 5.0) aftershocks were recorded by hundreds of stations in Turkey. Based on these records the rocking characteristics of the different locations can be evaluated. Design of rocking structures subjected to earthquakes can be carried out by using the overturning a...

The nonlinearity of the soil may considerably affect the response of structures subjected to seismic events. This paper aims to show under which circumstances geometry, soil, and earthquake-type; the nonlinearity is important. A simple model based on a 1D shear column was developed to calculate the maximum shear strain (γ) in the soil subjected to...

In dynamic analysis of complex systems usually simplified models are used. In case of floor vibration, an SDOF model is used to calculate the acceleration of the structure, in the seismic design of structures lumped parameter models are recommended to include the effect of the soil-structure interaction (SSI) in the analysis. Nonetheless, for rib s...

Recently several light‐weight, long span floors are built (e.g. steel‐framed structural systems), where the design is governed by vibration control. In these cases the acceleration due to human‐ or machine‐induced vibration can be very high, which may cause human discomfort. Long rectangular plates subjected to concentrated loads are often investig...

In this paper, the dynamical similarity of multi-block catenary arches and columns is discussed, which can be used for the simplified design of rocking arches. The basic hypothesis is that the dynamic response of multi-block arches and columns is similar when the shape of the arch follows the thrust line, i.e. it is a catenary arch. It is validated...

In this chapter, stresses and strains are discussed in both 2-D and 3-D, and then a few solutions will be shown under plane stress (or plane strain) condition, which have practical importance.

In this chapter first we discuss the analysis of composite cross sections, such as plywood, fiber reinforced plastics, reinforced concrete or composites. Then it is assumed that the materials of the constituents may behave in a nonlinear manner, which is essential for the analysis of typical building materials.

In this chapter, we consider cases, when unloaded structures are not stress free and/or their strains are not zero. The most important examples are change in temperature, shrinkage, creep, and prestress, which must be taken into account in the analysis of several civil engineering structures.

In this chapter, we take into account that due to the motion of structures inertia forces arise. It many cases, these forces result in the vibration of structures, which may increase the stresses and displacements substantially. It is even more significant when the load is periodic and resonance occurs. This is why the natural frequencies of the st...

As it was presented in the Introduction, when the change in geometry is taken into account in the equilibrium equations, the analysis becomes nonlinear. This effect, specifically for compressed structures, may increase stresses and displacements considerably and may even cause the loss of stability. These phenomena will be discussed in this chapter...

In this chapter, we focus on the membrane theory instead of a comprehensive shell theory. Bending of shells is treated approximately only as an edge disturbance. The basic behavior of shells together with the analyses of a few simple and important cases is presented.

In this chapter, we consider plates, which are loaded dominantly perpendicular to their midplane. Both isotropic and orthotropic plates are discussed, and the second one is the typical model of rib-stiffened floors. Static, buckling, and dynamic analyses are discussed, and the latter one is applied for the vibration control of floors. The analysis...

In Chapter 4, the plastic behaviour of cross sections was discussed. Here statically indeterminate structures are considered, which behave in an elastic-plastic manner. The lower bound (static) and the upper bound (kinematic) theorems are presented and applied for structural analysis.

In this chapter we consider bars (beams and columns), where one direction is substantially bigger than the other two. First in-plane problems are considered including the shear deformations. The shortcomings of the applied theories are emphasized. Then both Saint-Venant and restrained warping induced torque are presented and their role is discussed...

The most important energy principles are discussed in this chapter, which form the theoretical basis for most of the approximate (numerical) methods and may clarify the behavior of structures. Energy principles may also provide an alternative formulation of the governing equations of deformable structures.

In case of seismic design of structures the deformability and damping of the soil should be considered, which can be performed in several ways. The infinite soil half space can be approximated with the cone model, which gives constant values for the spring stiffnesses and dashpot characteristics, and an additional mass element for rocking motion. T...

Since damping in lightweight floors is usually low, dynamic amplification can be rather high. Long rectangular plates subjected to concentrated loads are often investigated by a replacement beam with a so called “effective width”. Although this approach is a reliable tool for static loads, the steady-state dynamic response of beams and long plates...

A new model is presented for planar multi‐block arches subjected to earthquakes. The blocks are assumed to be rigid, and every interface between the blocks may split open and may close, ie, the blocks may impact to each other. During impact, both the classical Housner's approach and improved models with lower energy dissipation are considered. The...

Design of rigid monolithic columns for overturning cannot be performed with the classical response spectrum analysis. In this paper the responses of rocking blocks for different single and double pulses and real earthquake records are investigated. Based on our numerical and analytical results it is proposed that for real earthquake records the ove...

Presentation of the design method for rocking SDoF systems.

Overturning of rigid blocks on rigid foundations subjected to earthquakes in principle can be analyzed by simple replacement signals. The effect of a signal is generally characterized by its overturning curve. In this paper a new approach is presented, which is based on the overturning acceleration spectra (OAS). It is shown that an earthquake can...

In case of seismic design the deformability of the soil should be considered, which can be performed in several ways. Most of the methods do not take into account the finite dimensions of the soil, which results significantly different behavior than the spring-dashpot systems. For an infinite medium, which is used in many cases, there are no eigenm...

Long-span, light weight floors may show considerable vibration, which might disturb the occupants. The floor is often supported by beams, the stiffness of which may significantly reduce the natural frequency. For the simplified vibration analysis of floors, where the vibration is due to human activity, the natural frequency, the modal mass and the...

A new model is presented for multiblock columns subjected to earthquakes, which contains an impact and an opening model. Both in the impact and in the opening model, all the possible opening configurations are investigated because it was found that in many practical cases, unexpected patterns may occur. The model is purely mechanical: assuming rigi...

Housner published a simple model for the rocking block more than five decades ago (Housner in Bull Seismol Soc Am 53:403–417, 1963), which is widely used also for modeling stone and masonry columns and arches. In this paper we investigate the reasons of the well-known fact that experiments show lower energy loss during impact than it is predicted b...

Local buckling analysis of thin walled composite beams is presented, where the flanges are stiffened at their free edges. The web and the flanges are modelled by rotationally restrained long orthotropic plates. Explicit expressions are developed for the calculation of the lowest buckling load. For the stability of the flange distortional buckling,...

Explicit expressions are developed for the buckling analyses of rectangular plates subjected to uniaxial loads when the unloaded edges are rotationally constrained. Three types of constraints (and their combinations) are considered: rotational springs, stiffeners with torsional stiffness and stiffeners with warping stiffness. The results can be app...

A new numerical model is introduced to determine the planar motion of a dry-stone masonry column subjected to base excitation. The model and the numerical calculation were verified by experiments, where the multi-block motion had been recorded by a camera, and captured by image procession. The results of the numerical calculation and the tests are...

In this paper, expressions are developed which enable the designer to determine the load bearing capacity of concentrically loaded RC columns in a very simple manner. The 'reduction factor' (the ratio of the ultimate load of the column and that of the cross-section) is introduced. It is similar to that used for the calculation of steel, masonry and...

The majority of continuous girder bridges in regions of moderate seismicity were designed before the introduction of modern seismic codes that prescribe seismic design verification for such structures. The objective of this study is to investigate the seismic performance of typical Hungarian continuous girder bridges through a parametric study. A d...

Long-span (reinforced concrete, steel, composite, timber and timber-concrete) floors may show considerable vibration, which may disturb the occupants of such structures. The floor is often supported by columns and beams, which may reduce the natural frequency even in the range of human excitation. In this paper a model and simple explicit expressio...

A model and simple explicit expressions are developed for the calculation of the natural frequency of multi span (reinforced concrete, steel, composite, timber and timber-concrete) floors, which take into account the deflections of the supporting beams. The floor is modelled as an orthotropic plate, while the effect of the supporting beams is taken...

Introduction of the Eurocode 8 seismic design standard made earthquake resistant structural design obligatory in Hungary. Recent geophysical research concurrently led to significant increase in design peak ground acceleration values. Design of certain bridge structural members (e.g. bearings and surrounding structural details) is often governed by...

In the design of composite sections, beam theories are used which require the knowledge of the cross-sectional properties, that is, the bending-, the shear-, the torsional-, warping-, axial stiffnesses and the coupling terms. In the classical analysis, the properties are calculated by assuming kinematical relationships (e.g. cross sections remain p...

In this article, a model recently published by the authors is applied for the calculation of the axial resistance of centrically loaded fiber-reinforced plastic-confined rectangular concrete columns. The calculated results of our model agree well with the experimental data found in the literature. It is shown that the stiffness of the confinement h...

A new model for FRP confined concrete columns is applied for eccentrically loaded circular and centrically loaded rectangular cross-sections. A good agreement was found between the calculations and both our own experimental data and those found in the literature. The shortcomings of the existing models are demonstrated. Based on our calculations a...

Composite beams and columns are analyzed and designed either with explicit beam expressions or with numerical (e.g. FE) methods, both require the knowledge of the cross sectional properties, i.e. the bending-, the shear-, the torsional-, warping-, axial stiffnesses and the coupling terms. These properties are calculated either by using kinematical...

A new model for FRP confined concrete columns based on a sophisticated material model is presented. It was found that - on the contrary to most of the available literature - the stiffness of the confining material may have a significant effect on the concrete strength. The results are verified by experiments.

Approximate expressions to determine the lowest buckling load of short and long composite plates are presented. The plate is subjected to uniaxial compressive load. All the four edges of the plate are elastically restrained by springs or stiffeners. Explicit expressions for the calculation of the lowest buckling load are presented as a function of...

In this article, a new model for FRP-confined circular concrete columns based on a sophisticated material model is presented. With the aid of this model the effect of the stiffness of the confining material on the strength of the structure was investigated. It was found that: (i) in the case of a wide parameter range (low-stiffness confinement) the...

In this paper the available literature on FRP confined concrete columns is summarized and a new model and analysis is presented, which is based on an .,accurate" 3D plasticity concrete material law. Based on the new model, the effect of the stiffness of the FRP on the resistance of circular concrete columns is investigated. In the FRP the main dire...

An increase in the use of composite materials in areas of engineering has led to a greater demand for engineers versed in the design of structures made from such materials. This book offers students and engineers tools for designing practical composite structures. Among the topics of interest to the designer are stress-strain relationships for a wi...

Local buckling analysis of thin-walled open or closed section fiber-reinforced plastic beams is presented. In the analysis, the web is modeled as a long orthotropic plate with rotationally restrained edges. Explicit expressions were developed for the buckling analyses of rectangular (long) plates in a companion paper. These results are applied to d...

Explicit expressions are developed for the buckling analyses of rectangular (long) plates: for ‘linearly varying axial load’ the known results for hinged supports are corrected and new results are presented for built-in and constrained edges; for ‘shear load’ new results are presented for constrained edges; for ‘uniform compression’ new results are...

In this paper first explicit expressions are presented for the calculation of the buckling loads of long, rectangular composite plates with orthotropic layup. In these expressions uniform, linearly varying and shear loads are taken into account, the edges can be constrained, while the constraint coefficients can be different at the two edges. These...

Models were developed to calculate the mechanical properties of alpine skis. The skis considered are constructed of layers of materials which may include wood, foam, metal, plastics and fibre-reinforced composites. The ski may be manufactured with or without camber and sidecut. On the basis of the models, a computer code was written which yields th...

p>Slender building structures must be designed by taking into account the second order effects. Whether this effect is significant or not, can be decided by comparing the vertical load to the buckling load of the building. It was suggested by several researchers that second order effects can be neglected, when this ratio is below ten percent. This...

Overweight vehicles require permits to cross the highway bridges, which are designed for "design load vehicles" (prescribed in the national standards). A new, fast, and robust method is presented for the verification of bridges, which requires minimal input only: the axle loads, axle spacing, the bridge span(s), and the superstructure type. The bri...

In the design of composite sections beam theories are used, which require the knowledge of the cross sectional properties, i.e. the bending-, the shear-, the torsional-, the axial stiffnesses and the coupling terms. In the classical analysis the properties are calculated by assuming kinematical relationships, e.g. cross sections remain plane after...

The paper presents a theory for thin-walled, closed section, orthotropic beams which takes into account the shear deformation in restrained warping induced torque. In the derivation we developed the analytical (“exact”) solution of simply supported beams subjected to a sinusoidal load. The replacement stiffnesses which are independent of the length...

The paper presents a method for comparing the mechanical effects of overweight and design load vehicles on bridges. There is no restriction on the arrangement of the axles and on the size of the axle loads. The bridge may be a simple span bridge, a continuous girder, a truss girder, or an arch. Even for a very complex bridge structure the only requ...

The paper presents a new simple and reliable method for comparing the effects of the over- weightand the design load vehicles on bridges. There is no restriction on the arrangements of the axles and on the size of the axle loads. The bridge may be a single span, multi span, arch bridge, frame bridge, or a truss girder, with arbitrary length. The on...

The paper presents the summary of beam theories of thin-walled open and closed section composite (fiber reinforced plastic) beams and columns which take into account both the transverse and the torsional shear deformations. Simple expressions are presented to determine the cross sectional properties required in the solution of practical problems su...

Long-span lightweight floors like timber slabs may show considerable vibration, which may disturb the occupants. Timber-concrete composite floors are representing an economical alternative where timber joist are built with reinforced concrete slab using shear connectors. These structures, which can be applied both as building floors and bridge deck...

Recently, design against earthquake events gains significant importance in Hungary. The authors completed independent earthquake resistant design of two Hungarian Danube bridges that are under construction. Our experiences are discussed in this paper.The analysis is in accordance with the European standard Eurocode 8. The paper briefly summarizes t...

Preface List of symbols 1. Introduction 2. Displacements, strains, stresses 3. Laminated composites 4. Thin plates 5. Sandwich plates 6. Beams 7. Beams with shear deformation 8. Shells 9. Finite element analysis 10. Failure criteria 11. Micromechanics Appendix A. Cross-sectional properties of thin-walled composite beams Appendix B. Buckling loads a...

In this paper an approximate earthquake analysis is presented for multistory building structures. The building is stiffened by an arbitrary combination of lateral load-resisting subsystems (shear walls, frames, trusses, coupled shear walls, cores). We consider stories with identical stiffnesses and masses, however the mass at the top floor may be d...

Models were developed for calculating the mechanical characteristics and the on-snow performance of snowboards.The snowboards are constructed of layers of materials which may include wood, foam, honeycomb, fibre-reinforced composites and polymeric materials.The models pertaining to the mechanical characteristics provide the bending and torsional st...

The local buckling analysis of fiber reinforced plastic (FRP) composite open and closed thin-walled section beams and columns is presented. Explicit expressions are developed for axially loaded and for bent box-, I-, C-, Z-, and L-members. These simple, explicit formulas contain the width and the bending stiffnesses (D11, D22, D12, D66) of each wal...

In this paper replacement beams of building structures are developed, and the stiffnesses of the replacement beams are derived. The analysis is robust and can be used for slender and wide structures consisting of frames, trusses, shear walls, or coupled shear walls. The utility of the derived replacement beam is demonstrated through the examples of...

A beam theory for open and closed section, thin-walled, composite beams is presented. The layup of each wall segment is arbitrary, the effects of shear deformation and restrained warping are neglected. Closed form expressions are developed for the calculation of the 4×4 stiffness matrix. It is also shown that the local bending stiffnesses of the wa...

This paper compares the results of different beam theories with finite element calculations and determines simple rules which designers may apply to insure simplified theories give acceptable results. Specifically, we analyze the effect of shear deformation and restrained warping. For thin-walled beams with layups that may be symmetrical or unsymme...

Closed form solutions are derived for the buckling loads of unidirectionally loaded rectangular orthotropic plates with (1) free and built-in unloaded edges and (2) free and rotationally restrained unloaded edges. These expressions can be used in the design of local buckling of the flanges of fiber-reinforced plastic beams. The accuracies of the fo...

This paper presents the results of experiments performed on masonry beams subjected to four-point bending. Four types of fiber-reinforced plastics (FRP) were used as reinforcement material: chopped glass fiber with epoxy resin,chopped glass fiber with polyester resin,glass fabric cloth with epoxy resin, and glass fabric cloth with polyester resin....

This paper presents a simple model to predict the load-deflection curve of a fiber-reinforced plastic (FRP) reinforced masonry beam subjected to bending and axial loads. Delamination growth is modeled by using an energy balance approach. It is shown that continuously growing delamination results in highly nonlinear behavior.

The paper compares the ‘‘exact’’ solution of mid-plane symmetric rectangular plates to approximate ones obtained by assuming orthotropy or Huber orthotropy. It shows under which conditions the approximate solutions can be used for the bending, buckling and vibration analyses of composite plates.

A model was developed to calculate the turning characteristics of alpine skis. The skis considered are constructed of layers of materials which may include wood, foam, metal, plastics and fibre-reinforced composites. The ski may be manufactured with or without camber and sidecut. The model simulates the motion of a skier of given height, weight and...

The paper compares the "exact" solution of mid-plane symmetric rectangular plates to approximate ones obtained by assuming orthotropy or Huber orthotropy. It shows under which conditions the approximate solutions can be used for the bending. buckling and vibration analyses of composite plates.

The paper presents the analysis of the natural frequency of thin-walled open section composite beams. Vlasov's classical theory of thin-walled beams is modified to include both the transverse shear and the restrained warping induced shear deformations. A simplified, approximate solution is also presented, in which the effect of the shear deformatio...

The paper presents the stability analysis of axially loaded, thin-walled open section, orthotropic composite columns. Vlasov's classical theory is modified to include both the transverse (flexural) shear and the restrained warping induced shear deformations. In addition to the bending stiffness matrix a (3×3) shear stiffness matrix is introduced. A...

Closed form approximate formulas are presented for the calculation of the buckling load of rectangular orthotropic plates with clamped and/or simply supported edges. The solution is based on the Ritz method assuming one term approximation.

Closed form approximate formulas are presented for the calculation of the buckling load of rectanglar orthotropic plates with clamped and/or simply supported edges. The solution is based on the Ritz method assuming one term approximation.

Seismic analysis of buildings stiffened by frames, trusses, shear walls or coupled shear walls is presented. The regular bents are modelled by replacement sandwich beams. Design charts are presented which enable the designer to determine the period of vibration, base shear, bending moment, top deflection and maximum story drift index very easily.

The analysis of symmetric(plane) bracing earthquake resistance structures was presented.The members of the shear walls rigid frames and braced frames were same at each level and the level of stiffness was same at individual levels. Formulas based on the replacement continua was presented which enable the designer to determine the period of vibratio...

In this investigation, a procedure is developed for determining the effectiveness of composite materials in retrofitting masonry buildings to reduce seismic damage. The reinforcement considered is a thin layer of fiber-reinforced composite applied to the wall in a wallpaper-like fashion. Models were developed which predict the behavior of masonry w...

In a previous paper, models are described for estimating the deformations and failures of masonry walls reinforced with composites when the wall is subjected to static, in-plane shear and normal loads. In this follow-up investigation, tests were performed to assess the accuracies of these models. Three types of test specimens were constructed: i) w...

Coated fiber optic sensors operating on interferometric principles have recently been considered for measuring strains and temperature inside composite materials. Owing to the complex interactions between the sensor and the material surrounding it, the relationship between the sensor output and the strains and temperature inside the material cannot...

Embedded fiber optic sensors operating on interferometric principles have recently been considered for measuring strains and temperature inside isotropic and orthotropic (composite) materials. Owing to the complex interactions between the sensor and the material surrounding it, the relationship between the sensor output and the strains and temperat...

This paper presents the stability analysis of simply supported and cantilever, thin walled, open section, orthotropic composite beams subjected to concentrated end moments, concentrated forces, or uniformly distributed load. In the analysis, both the transverse shear and the restrained warping induced shear deformations are taken into account. An e...

SUMMARY In the engineering practice it is very important that the structures have an adequate safety against the loss of stability. One form of the loss of stability is the lateral torsional buckling of beams. Solutions were worked out in the past to determine the critical load of a simple beam. There are structures where the above mentioned formul...

High-rise buildings are investigated for earthquake using the continuum method. A replacement Timoshenko-beam is analyzed using the Response Modal Analysis with Mode superposition. Design charts are presented which enable the designer to determine easily and quickly the base shear force, the overturning moment, the top displacement and the maximum...

The buckling of isotropic and composite cylinders due to induced moments was investigated. The cylinder wall may be of solid or of sandwich construction. Expressions were derived for the critical buckling moment. Numerical examples for aluminum and glass-epoxy composite cylinders are presented which show that induced moments are unlikely to result...