Vojko Kilar

Simple push-over analysis of asymmetric buildings

A simple method for the non-linear static analysis of complex building structures subjected to monotonically increasing horizontal loading (push-over analysis) is presented. The method is designed to be a part of new methodologies for the seismic design and evaluation of structures. It is based on the extension of a pseudo-three-dimensional mathematical model of a building structure into the non-linear range. The structure consists of planar macroelements. For each planar macroelement, a simple bilinear or multilinear base shear-top displacement relationship is assumed. By a step-by-step analysis an approximate relationship between the global base shear and top displacement is computed. During the analysis the development of plastic hinges throughout the building can be monitored. The method has been implemented into a prototype computer program. In the paper the mathematicalmodel, the base shear-top displacement relationships for different types of macroelements, and the step-by-step computational procedure are described. The method has been applied for the analysis of a symmetric and an asymmetric variant of a seven-storey reinforced concrete frame-wall building, as well as for the analysis of a complex asymmetric 21-storey reinforced concrete wall building. The influence of torsion on structural behaviour is discussed.

Effects of Horizontal and Vertical Mass-Asymmetric Distributions on the Seismic Response of a High-Rack Steel Structure

The paper examines the seismic response of an existing externally braced steel frame high-rack structure and analyses the effects of mass eccentricities that can be realistically achieved by asymmetric positioning of the stored payload. Apart from the symmetric, three different extreme payload distributions with varying occupancy levels have been considered, with the payload mass concentrated: (i) at the topmost part of the structure, (ii) at the upper corner of the structure and (iii) at the outermost edge of the structure. The seismic performance has been analysed by using unidirectional non-linear dynamic analyses as well as by non-linear static analyses, with the structures response observed in the cross-aisle direction in which it is possible to account for the effects of torsional twist. The results showed that most unfavourable payload eccentricities might increase the seismic risk leading to local instability of the rack columns. From a seismic point of view, a fully occupied structure does not present the most critical condition. It is obtained at an intermediate occupancy level, which allows more space to produce horizontal and/or vertical eccentricities. Very small occupancy levels in turn produce smaller induced seismic forces and might therefore not be of critical concern. The paper concludes that the payload distribution concentrated symmetrically at the topmost part is the most critical for the central part of the rack structure and that concentrating the payload eccentrically at the outermost edge is the most critical for the flexible side of the structure, while shifting the payload to one of the upper corners is generally not of critical concern.

Principles of Energy Efficient Construction and their Influence on the Seismic Resistance of Light-weight Buildings

Recently, an increasing trend of passive and low-energy buildings transferring from non earthquake-prone to earthquake-prone regions has thrown out the question about the seismic safety of such buildings. The paper describes the most commonly used details of energy efficient construction, which could be critical from the point of view of earthquake resistance. The paper focuses on the prevention of ground floor slab thermal bridge and presents a case study on the seismic response of multi-storey wooden buildings founded on the RC foundation slab lying on a thermal insulation (TI) layer made of extruded polystyrene (XPS). The structural response is investigated with reference to the following performance parameters: the buildings lateral top displacement, the ductility demand of the superstructure, the friction coefficient demand, the maximum compressive stress in the TI layer and the percentage of the uplifted foundation. A comparison between the response of models founded on a fixed base and models founded on a layer of TI with the same wooden crosslam structure differing in the number of storeys, strength capacity and subjected to earthquakes with different levels of seismic intensity is done. Regarding the buildings top displacements, the maximum compressive deformation in the TI layer, and the percentage of the uplifted foundation, the results have shown that the potentially negative influences of inserting the TI under the foundation slab could be expected only for high-rise buildings subjected to severe earthquakes. Oppositely, for the superstructures ductility demand and for the friction coefficient demand it was demonstrated that the largest demands could be expected in the case of low-rise buildings. The control of friction coefficient demand, which was recognized as critical parameter for analyzed wooden buildings, has shown that the capacity value could be exceeded yet in the case of moderate earthquake occurrence.

Seismic Aspects of the Application of Thermal Insulation Boards Beneath the Foundations of Buildings

In recent years, there has been a significant increase in the construction of energyefficient buildings. These buildings are mainly characterized by their thermal envelope, which needs to follow the complete outer perimeter of the building without any interruptions, to avoid thermal bridges. It has been observed, however, that the specific new details which prevent the occurrence of thermal bridges can, in many cases, substantially affect the structural integrity of such buildings during earthquakes. This chapter deals with the seismic aspects of the application of thermal insulation (TI) boards beneath the foundations of buildings. For this purpose, the mechanical characteristics of the most commonly used material in practice (i.e., extruded polystyrene — XPS) were experimentally determined. Additionally, the shear behaviour of differently composed TI foundation sets was investigated and their friction capacity estimated. The authors have proposed a new solution for the foundation detail, which is based on controlling the sliding mechanism between the individual layers of TI boards in order to reduce the seismic forces induced on the superstructure. The proposed detail with a specially designed sliding layer surface is made of commonly used TI materials for modern passive houses, thus reducing the potential additional costs. The solution was verified by means of nonlinear dynamic analysis of several realistic building models and various friction coefficients between XPS boards. The selected results are presented in terms of fragility curves for the occurrence of sliding between the layers of XPS boards. Based on these curves, the desired seismic response scenario and level of protection of a building structure could be selected.

Assessing Numerical Error in Structural Dynamics Using Energy Balance

This work applies the variational principles of Lagrange and Hamilton to the assessment of numerical methods of linear structural analysis. Different numerical methods are used to simulate the behaviour of three structural configurations and benchmarked in their computation of the Lagrangian action integral over time. According to the principle of energy conservation, the difference at each time step between the kinetic and the strain energies must equal the work done by the external forces. By computing this difference, the degree of accuracy of each combination of numerical methods can be assessed. Moreover, it is often difficult to perceive numerical instabilities due to the inherent complexities of the modelled structures. By means of the proposed procedure, these complexities can be globally controlled and visualized in a straightforward way. The paper presents the variational principles to be considered for the collection and computation of the energy-related parameters (kinetic, strain, dissipative, and external work). It then introduces a systematic framework within which the numerical methods can be compared in a qualitative as well as in a quantitative manner. Finally, a series of numerical experiments is conducted using three simple 2D models subjected to the effect of four different dynamic loadings.

Assessment of the earthquake vulnerability of multi-residential buildings in Slovenia

The paper assesses the earthquake vulnerability of multi-residential buildings in Slovenia, although it is limited to the buildings that were built before 1981, in the time when the earthquake building codes were much less elaborated than today. In the paper, based on the building completion year, buildings are classified into different time periods, which are characterized by important historical events and bigger changes in earthquake building codes. The assessment of earthquake vulnerability is based on the data from the building completion year, number of storeys, prevailing structural material and the year of the last renovation as obtained from the last census of the population, households and apartments completed in 2002. The result is an estimation of the earthquake vulnerability of a building, also because for very similar buildings the earthquake resistance depends on the architectural design of a building, the amount and layout of its structural elements, foundations, soil profile and other influences. In the first part of the paper the multi-residential buildings are divided by age, material and number of storeys. In the second part, the assessment of the earthquake vulnerability of these buildings is divided into three classes: a) probably earthquake unsafe, b) probably earthquake less safe and c) probably earthquake safe. Additionally the earthquake vulnerability assessment is presented geographically by showing the earthquake less safe and unsafe buildings on the maps and charts for different communities in Slovenia. It has been concluded that the earthquake safety of many multi-residential buildings in Slovenia might be questionable, while we have detected also bigger differences between communities.

Seismic Rehabilitation of Masonry Heritage Structures with Base-Isolation and FRP Laminates – A Case Study Comparison

The cultural and historical significance of architectural heritage buildings demands intrinsic considerations regarding appropriate conservation measures that need to be undertaken in order to restore or maintain their historical values. In this paper two contemporary seismic strengthening measures with varying degrees of invasiveness and strengthening efficiency are employed in a case study numerical simulation on a typical neo-renaissance masonry heritage building. The use of fibre reinforced polymer composites and the implementation of base-isolation was considered in the study in order to achieve the desired, code-based seismic protection levels. Non-linear static analyses with incremental increases in levels of seismic intensities were conducted on mathematical models of the fixed-base, FRP-strengthened and base-isolated variants of the structure. The comparison of results based on static pushover analyses for various ranges of seismic intensity was presented, while each strengthening measure was assessed in terms of its efficiency.

Proposal for Holistic Assessment of Urban System Resilience to Natural Disasters

Urban system is a complex mix of interdependent components and dynamic interactions between them that enable it to function effectively. Resilience of urban system indicates the ability of a system to resist, absorb, accommodate to and recover from the effects of a hazard in a timely and efficient manner. In the relevant literature, most studies consider individual components separately. On the other hand, the purpose of this paper is to assess the urban system as a whole, considering all relevant components and their interactions. The goal is a study of possibilities for holistic evaluation of urban system resilience to natural disasters. Findings from the preliminary study are presented: (i) the definition of urban system and categorization of its components, (ii) a set of attributes of individual components with impact on disaster resilience of the entire system and (iii) review of different methods and approaches for resilience assessment. Based on literature review and extensive preliminary studies a new conceptual framework for urban resilience assessment is proposed. In the presented paper, a conceptual model of urban system by abstraction of its components as nodes (buildings), patches - specific nodes with spatial properties (open space), links (infrastructures) and base layer (community) is created. In the suggested model, each component is defined by its own quantitative attributes, which have been identified to have an important impact on the urban system resilience to natural disasters. System is presented as a mathematical graph model. Natural disaster is considered an external factor that affects the existing system and leads to some system distortion. In further analyses, mathematical simulation of various natural disasters scenarios is going to be carried out, followed by comparison of the system functionality before and after the accident. Various properties of the system (accessibility, transition, complexity etc.) are going to be analysed with graph theory. The final result is going to be an identification of critical points and system bottlenecks as basis for further actions of risk mitigation.

Seismic Retrofitting of Historic Masonry Structures with the Use of Base Isolation—Modeling and Analysis Aspects

ABSTRACT The seismic retrofitting measures which are appropriate for buildings belonging to the architectural heritage are limited, since the extent to which such buildings are allowed to be altered is severely limited. In the paper the possibilities which exist for the implementation of base isolation in the case of the seismic upgrade of unreinforced masonry (URM) structures belonging to the valuable architectural heritage have been investigated. A new methodology for the modeling of URM buildings, based on an equivalent frame model with plastic hinges, was used for this purpose. A case study involving a typical neo‐renaissance masonry building is presented, in which base isolation is implemented, and a comparison is made with the response of the building in its original state. A refined approach for the selection of proper isolation devices is proposed which is based on the nonlinear static (pushover) analysis of such buildings and on the desired level of seismic protection, with reference to the code-based damage limit states. Additionally, the incremental nonlinear dynamic analyses were also applied in order to estimate what increases in seismic safety could be achieved if the employed base isolation system was used in the case of different seismic intensities.

A Framework for Structural Systems Based on the Principles of Statistical Mechanics

A framework is proposed in which certain well-known concepts of statistical mechanics and thermodynamics can be used and applied to characterize structural systems of interconnected Timoshenko beam elements. We first make the assimilation to a network of nodes linked by potential energy functions that are derived from the stiffness properties of the beams. Then we define a series of thermodynamic quantities inherent to a given structure (i.e., internal energy, heat, pressure, temperature, entropy, and kinetic energy). With the exception of entropy, all of them have the dimensions of energy. In order to test this new framework, a series of experiments was performed on four structural specimens within the elastic regime. Their configurations were taken from the seismic regulations known as Eurocode 8 in order to have a better based reference for our comparisons. The results are then explained within this new framework. Very interesting correlations have been found between the parameters given in the code and our concepts.