A PRACTICAL MODEL FOR SEISMIC ANALYSIS OF REINFORCED CONCRETE SHEAR WALL BUILDINGS

A simple macro-model for reinforced concrete shear walls is proposed, which consists of spring elements representing flexure and shear behaviour. The model for flexural behaviour is based on section analysis, while the model for shear behaviour is based on key parameters of the flexural behaviour. Four wall test specimens are selected to evaluate the reliability of the model. Modelling parameters for the backbone curves and the hysteretic rules are examined by conducting static and time history analyses, with the hysteretic response of a test specimen compared to that calculated using the proposed model. Results show some differences between measured and calculated shear force versus shear distortion relationships, but the model is acceptable because the differences do not significantly affect calculated global response. Parametric studies are also conducted to examine the influence of modelling parameters on seismic demand and capacity, which are the major design parameters for structural performance evaluation. Differences due to variation in modelling parameters are not significant, further indicating that the proposed model is reasonable.     

PREDICTION OF DAMAGE IN R/C SHEAR PANELS SUBJECTED TO REVERSED CYCLIC LOADING

In this paper, the damage prediction of shear-dominated reinforced concrete (RC) elements subjected to reversed cyclic shear is presented using an existing damage model. The damage model is primarily based on the monotonic energy dissipating capacity of structural elements before and after the application of reversed cyclic loading. Therefore, it could be universally applicable to different types of structural members, includeing shear-dominated RC members. The applicability of the damage model to shear-dominated RC members is assessed using the results from reversed cyclic shear load tests conducted earlier on eleven RC panels. First, the monotonic energy dissipating capacities of the panels before and after the application of reversed cyclic loading are estimated and employed in the damage model. Next, a detailed comparison between the analytically predicted damage and the observed damage from the experimental tests of the panels is performed throughout the loading history. Subsequently, the effects of two important parameters, the orientation and the percentage of reinforcement, on the damage of such shear-dominated panels are studied. The research results demonstrated that the analytically predicted damage is in reasonably good agreement with the observed damage throughout the entire loading history. Furthermore, the orientation and percentage of reinforcement is found to have considerable effect on the extent of damage.     

SEISMIC RELIABILITY ASSESSMENT OF EXISTING REINFORCED CONCRETE BUILDINGS

Structures designed according to earlier codes with inadequate seismic provisions have not performed satisfactorily during recent earthquakes. The seismic performance of an existing three-storey reinforced concrete building designed according to the 1963 ACI 313-63 is evaluated and compared to the performance of a similar frame designed according to current code provisions. Non-linear static and dynamic analyses of the reinforced concrete frames are conducted. In this study, a probabilistic approach is adopted where a large number of artificially generated ground motion records is used as input motion to the structure. The results of the analysis indicated the probability of various degrees of damage to be expected when the existing frame is subjected to different ground motion levels. This information is useful in the design of the required rehabilitation scheme to provide an identified level of protection.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

REHABILITATION OF REINFORCED CONCRETE COLUMNS USING CORRUGATED STEEL JACKETING

An experimental investigation was conducted to study the failure mode of existing reinforced concrete columns designed during the 1960s. The effectiveness of using corrugated steel jackets for enhancing the seismic flexural strength and ductility of these types of columns was examined. Three large-scale columns were tested under cyclic loading. The three columns represent existing column, current code-detailed column and rehabilitated column. The variables in the test specimens include the amount of column transverse reinforcement and jacketing of the column. The corrugated jacket was found to be effective in the rehabilitation of the selected existing structure, which does not meet the current seismic code requirements. A method is proposed for the design of the corrugated steel jacket to enhance the lap splice capacity and ductility of the column.     

STATISTICAL SEISMIC VULNERABILITY ASSESSMENT OF EXISTING REINFORCED CONCRETE BUILDINGS IN TURKEY ON A REGIONAL SCALE

A statistical procedure, called discriminant analysis, is used to develop a model for the preliminary assessment of the seismic vulnerability of low- to medium-rise (2-7 storey) reinforced concrete buildings. The earthquake damage data compiled in Düzce province after the 12 November 1999 Düzce earthquake formed the damage database. Number of storeys, minimum normalised lateral stiffness index, minimum normalised lateral strength index, normalised redundancy score, soft storey index and overhang ratio are selected as the basic damage inducing variables. Two discriminant functions are derived in terms of these variables considering immediate occupancy and life safety performance levels. In the proposed preliminary seismic vulnerability assessment model, the discri-minant scores obtained from these two discriminant functions are combined in an optimal way and axe used to classify existing buildings as “safe”, “unsafe” and “requires further evaluation”. The optimality criterion imposed into the model is the minimisation of the misclassification rate of damage states causing collapse. The validity of the proposed model is checked by using the seismic damage data associated with recent earthquakes that occurred in Turkey. The consistency between the observed damage distribution and the predictions of the proposed model supports the effectiveness of the proposed model.     

ARTIFICIAL ACCELEROGRAMS REPRESENTATIVE OF THE DAMAGE DISTRIBUTION ON A LOW-RISE SHEAR WALL

This study attempts to reproduce in an artificial way, at a given magnitude-distance couple, the statistical characteristics of damage caused by real accelerograms. The structure adopted is a low-rise shear wall, modelled as a nonlinear, one degree of freedom system with a degrading frequency as a function of a non-cumulative damage variable. Strong-motion records, contained in a large database, are characterised in terms of seismological and seismic parameters. Artificial accelerograms are generated from response spectra representative of real accelerograms belonging to different magnitude-distance zones. Although the mean damage is consistent, the low dispersion of damage caused by the artificial accelerograms with respect to that caused by the real accelerograms is highlighted. In order to reproduce the damage dispersion in addition to the mean damage, a generation method of representative artificial accelerograms is proposed. This method introduces the standard deviation drawn from attenuation relationships into a dispersion pre-process with respect to the regressed spectrum at a given magnitude-distance point. The method turns out to be capable of reproducing the statistical features of damage produced by real strong-motion records.     

ANALYSIS OF PORE PRESSURE GENERATION AND DISSIPATION IN COHESIONLESS MATERIALS DURING SEISMIC LOADING

The earthquake loading of a shallow foundation resting on top of a cohesionless layer creates cyclic variations in the shear force and overturning moment acting on the supporting soil. These loads induce a tendency for volume change which, in turn, depending on the drainage conditions and material permeability, may cause in addition to a cyclic pore pressure variation a progressive pore pressure buildup. The paper develops an efficient and elegant way, based on a multiple time scale analysis, of solving this fully coupled problem. The theoretical solution is implemented in a finite element code and is applied to predict the pore pressure development and dissipation under a bridge pier foundation for which it was essential to limit the pore pressure increase.     

A SUMMARY OF RESULTS OF SIMULATED SEISMIC LOAD TESTS ON REINFORCED CONCRETE BEAM-COLUMN JOINTS,BEAMS AND COLUMNS WITH SUBSTANDARD REINFORCING DETAILS

The results of some simulated seismic load tests on reinforced concrete one-way interior and exterior beam-column joints with substandard reinforcing details typical of buildings constructed in New Zealand before the 1970s are described. The tests were conducted using both deformed and plain round longitudinal reinforcement. The interior beam-column joint cores lacked transverse reinforcement and the longitudinal bars passing through the joint core were poorly anchored. The exterior beam-column joint units contained very little transverse reinforcement in the members and in the joint core. In one exterior beam-column joint unit the beam bar hooks were not bent into the joint core. That is, the hooks at the ends of the top bars were bent up and the hooks at the ends of the bottom bars were bent down. This anchorage detail was common in many older buildings constructed before the 1970s. In the other exterior beam-column joint unit the hooks at the ends of the bars were bent into the joint core as in current practice. The improvement in performance of the joint with beam bars anchored according to current practice is demonstrated. In addition, tests were conducted on interior joints with lap splices in the beam longitudinal reinforcement bars near the column face. The tests were conducted using both deformed and plain round longitudinal reinforcement. Tests were also conducted on columns with plain round bar longitudinal reinforcement and inadequate transverse reinforcement.

The reinforcing details were close to identical to those in an existing seven storey reinforced concrete building that was designed and built in New Zealand in the late 1950s.

The test results give an indication of the performance of beam-column joints and members with the above now out-of-date reinforcing details.

The test results reported are a summary of results reported in a number of publications written since 1994.     

DUCTILITY AND LOAD CARRYING CAPACITY PREDICTION OF STEEL BEAM-TO-COLUMN CONNECTIONS UNDER CYCLIC REVERSAL LOADING

Abstract

The economy and reliability of steel-framed buildings in seismic areas depend basically on the hysteretic behaviour of its individual components, such as members and joints. With reference to the latter, despite the recent semi-continuous frame approach (which appears generally very convenient for the design of low- and medium-rise steel buildings), the present state of knowledge does not allow for a complete understanding of the behaviour and the low-cycle fatigue life of beam-to-column connections under dynamic loads.

This paper presents a criterion for the definition of the low-cycle fatigue strength of steel connections, and proposes two approaches for the design of steel frames in seismic zones via the assessment of the fatigue damage, which is evaluated alternatively on the basis of either the ductility or of the load carrying capacity.     

MODELLING OF RC MEMBERS UNDER CYCLIC BIAXIAL FLEXURE AND AXIAL FORCE

A model is proposed for the incremental force-deformation behaviour of reinforced concrete sections and members, under generalised load or deformation histories in 3D, including cyclic loading, up to ultimate deformation. At the section level the model is of the Bounding Surface type and accounts for the coupling between the two directions of bending and between them and the axial direction. For the construction of the member tangent flexibility matrix on the basis of the section tangent flexibility matrix, a piecewise-linear variation along the member is assumed for the nine terms of the tangent section flexibility matrix. Model parameters are derived on the basis of available test results for: (a) the force-deformation response under cyclic biaxial bending with normal force; (b) the hysteretic energy dissipation; (c) the secant-to-yield member stiffness, and (d) the ultimate deformation of the member under cyclic biaxial load paths.     

STRUCTURAL CONTROL ALGORITHMS IN EARTHQUAKE RESISTANT DESIGN

The dynamic finite element equations of a two-dimensional structure made of axial-flexural frame elements with tendon-driven actuators have been derived. A critical review of classical optimal control theory is made with respect to its application to the control of structure under seismic excitations. Seven control algorithms, including two newly proposed algorithms, have been described, investigated and discussed. The need of an optimal observer, Kalman filter, is discussed. The validity of separation theorem applicable to the optimal stochastic control of structure for earthquake resistance is shown. How the control system perform under the circumstances of actuator saturation is also shown. Several numerical examples are worked out to demonstrate and compare the efficiency and limitations of those control algorithms.     

ANALYSIS,TESTING AND DESIGN OF STEEL ROOF DECK DIAPHRAGMS FOR DUCTILE EARTHQUAKE RESISTANCE

An experimental program was conducted to study the inelastic response of steel roof deck diaphragms for low-rise steel buildings subjected to seismic loading. Tests were performed on 3.6 m×6.1 m diaphragm specimens made of corrugated steel deck panels. The parameters examined were the thickness and configuration of the sheet steel panels, the type and spacing of the fasteners, the applied loading history and the influence of end lap joints. Diaphragms built with screwed side lap fasteners and nailed deck-to-frame connectors exhibited a pinched hysteretic behaviour, but could sustain large inelastic deformation cycles with limited strength degradation. This type of diaphragm construction could be designed to resist earthquake effects in the inelastic range. Higher shear resistance and less pinching was observed for systems that included welded with washer connections. However, their strength decreased rapidly after the peak load was reached, and hence, these systems should be designed for limited inelastic response. Deck systems with button punched side laps and frame welds without washers showed a brittle response and should be designed to remain elastic under severe earthquake motions. The inelastic demand was found to increase when the spacing of the fasteners was reduced. Specimens constructed with an internal overlap joint exhibited extensive warping of the cross section mainly due to the shorter panel length.     

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART I: BARE STRUCTURES

Abstract

Eurocode 8 is applied for the complete design of 26 multi-storey reinforced concrete buildings to study its operationally and compare the implications of trading strength for ductility through designing the same structure for a different Ductility Class. The difference between the conventional full Capacity Design of columns in bending and the relaxed one allowed by Eurocode 8 is quantified, and the implications on the column capacities are examined. About half of the designed buildings, representative of the class of regular frames, are subjected to nonlinear dynamic response analyses to spectrum-compatible motions with intensities up to twice that of the design motion. Nonlinear modeling is very simple, but gives satisfactory agreement with available quasistatic or pseudodynamic test results on full scale structures. Results show that the three Ductility Classes of Eurocode 8 are essentially equivalent in terms of material quantities and seismic performance. Within the limitations of the nonlinear modelling, the response results suggest very satisfactory performance of structures designed to Eurocode 8, even under twice the design motion intensity. Softening of the structure due to concrete cracking and steel yielding significantly reduces the seismic force demands and contributes to the satisfactory performance, despite the increased P — 6 effects. Another important contributor to the good performance is the significant overstrength of the members considered in the analyses with their average as-built properties. Beam overstrength due to the contribution of the slab to flexural capacity is large enough to overcome the effects of the application of the relaxed Capacity Design rule to columns in bending. However, the resulting column plastic hinging does not lead to drift concentrations suggesting formation of storey-sway mechanisms.     

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART II: INFILLED STRUCTURES

The effects of masonry infills on the global seismic response of reinforced concrete structures is studied through numerical analyses. Response spectra of elastic SDOF frames with nonlinear infills show that, despite their apparent stiffening effect on the system, infills reduce spectral displacements and forces mainly through their high damping in the first large post-cracking excursion. Parametric analyses on a large variety of multi-storey infilled reinforced concrete structures show that, due to the hysteretic energy dissipation in the infills, if the infilling is uniform in all storeys, drifts and structural damage are dramatically reduced, without an increase in the seismic force demands. Soft-storey effects due to the absence of infills in the bottom storey are not so important for seismic motions at the design intensity, but may be very large at higher motion intensities, if the ultimate strength of the infills amounts to a large percentage of the building weight. The Eurocode 8 provisions for designing the weak storey elements against the effects of infill irregularity are found to be quite effective, in general, for the columns, but unnecessary and often counterproductive for the beams.     

MODELLING OF RC BEAM-COLUMN JOINTS AND STRUCTURAL WALLS

The deformation of beam-column joints may contribute significantly to drift of reinforced concrete (RC) frames. In addition, failure may occur in the joints due to cumulative concrete crushing from applied beam and column moments, bond slip of embedded bars or shear failure as in the case of existing frames with nonductile detailing. When subjected to earthquake loading, failure in RC structural wall is similar to failure of frame joints as it may occur due to cumulative crushing from high flexural stresses, bond slip failure of lap splice, shear failure or a combination of various mechanisms of failure. It is important to include these behavioural characteristics in a simple model that can be used in the analysis of RC frames and RC walls to predict their response under earthquake loading and determine their failure modes.

Global macro models for the beam-column joint and for RC structural walls are developed. The proposed models represent shear and bond slip deformations as well as flexural deformations in the plastic hinge regions. The models are capable of idealising the potential failure mechanism due to crushing of concrete, bond slip or shear with allowance for the simultaneous progress in each mode. The model predictions are compared with available experimental data and good correlation is observed between analytical results and the test measurements.     

ELASTIC AND INELASTIC RESPONSE OF TUNNELS UNDER LONGITUDINAL EARTHQUAKE EXCITATION

This paper addresses the problem of the behaviour of underground tunnels subjected to longitudinal earthquake excitation. State-of-the-art solutions, which are relative to infinite length tunnels in the stationary case, with linear models for both the ground and the structure, are first recalled. These models are either static or dynamic; results generally indicate large strains, often incompatible with reinforced concrete structures, and small crack widths.

For finite length tunnels, in this study the dynamic solution for the linear case is developed and it is shown that maximum strain is an increasing function of the tunnel length so that, in many situations, the behavior of the lining is satisfactory also under the aspect of crack formation. When the nonlinear behaviors of the tunnel and soil are taken into account, segments of reinforced concrete tunnels, after cracking, may undergo considerable relative displacement, undesired both for serviceability and ultimate limit states. After review of the constitutive relationship for the ground, a parametric study on the crack openings for an example tunnel is presented. It is shown that crack widths computed with linear static analyses underestimate the real value for tunnels embedded in stiff grounds and that the lining longitudinal reinforcement can reduce crack width so as to cope with serviceability and ultimate limit states.     

A FIBRE FINITE BEAM ELEMENT WITH SECTION SHEAR MODELLING FOR SEISMIC ANALYSIS OF RC STRUCTURES

The paper describes the formulation of a non-linear, two-dimensional beam finite element with bending, shear and axial force interaction for the static and dynamic analysis of reinforced concrete structures. The hysteretic behaviour of “squat” reinforced concrete members, in which the interaction between shear and flexural deformation and capacity is relevant for the overall structural performance, is emphasised. The element is of the distributed inelasticity type; section axial-flexural and shear behaviours are integrated numerically along the element length using a new equilibrium-based approach. At section level a “hybrid” formulation is proposed: the axial-flexural behaviour is obtained using the classic fibre discretisation and the plane sections remaining plane hypothesis, the shear response instead is identified with a non-linear truss model and described with a hysteretic stress-strain relationship. The latter contains a damage parameter, dependent on flexural ductility, that provides interaction between the two deformation mechanisms. The element has been implemented into a general-purpose finite element code, and is particularly suitable for seismic time history analyses of frame structures. Analytical results obtained with the model are compared with recent experimental data.     

ENERGY-BASED TECHNIQUE FOR SEISMIC PERFORMANCE ASSESSMENT OF INTERIOR BEAM-COLUMN JOINTS

For investigating the seismic behaviour of monolithic beam-column joints, a new technique of assessment of joint performance, termed the Shear Deformation Energy Index, is presented in this paper. Previous research efforts in this field were evaluated and the relative merits and drawbacks of each approach were highlighted. Primary variables influencing the seismic behaviour of joints were studied in the experimental phase of the current study. This included pseudo-static testing of nine interior beam-column sub-assemblages with different joint configurations. The parametric investigation of primary variables was complemented by studying the behaviour of specimens of eight different experimental programmes. For easy application of the technique in design practice, the Index is graphically represented versus its main variables in a design chart, referred to as the Performance Chart.     

ESTIMATION OF NEAR-SOURCE GROUND MOTION AND SEISMIC BEHAVIOUR OF RC FRAMED STRUCTURES DAMAGED BY THE 1999 ATHENS EARTHQUAKE

On September 7, 1999 an earthquake with magnitude M _W =5.9 occurred close to the city of Athens in Greece. More than 80 buildings collapsed, about 150 deaths and hundreds of injuries were reported. Soon after the event a damage investigation was carried out by two of the authors in the most heavily struck areas. The most serious damages were observed in the northern suburbs of Athens, where reinforced concrete frames and masonry buildings represent the prevalent construction systems. The hysteretic energy demands imposed on RC buildings should have been rather severe considering the structural systems characteristics and the inadequate construction details. However, over-strengths, redundancy and especially the presence of infill walls, provided a significant increase of the seismic capacity and contributed to the survival of many buildings.

The objective of the present work is to reproduce and analyse the response of typical RC frames subjected to the 1999 Athens earthquake in areas where the observed damage was particularly severe but no recordings of the ground motion were available. After a general overview of the seismotectonic environment, seismological data, observed macro-seismic intensities, structural typologies and observed building behaviour, an attempt is made to identify representative excitations in the meizoseismal area. Specifically, the required accelerograms are obtained by modifying available records so as to reproduce a given global energy content and to be consistent with the observed damage. To study the seismic response of RC models, the obtained accelerograms are used to perform nonlinear dynamic analyses.