STRENGTH REDUCTION FACTORS FOR DUCTILE STRUCTURES WITH PASSIVE ENERGY DISSIPATING DEVICES

In recent years, current seismic codes started contemplating the design of structures with passive energy dissipating devices. One important issue for the rational seismic design of these devices and the structure that contains them is the formulation of numerical methods to estimate their design seismic forces. From the study of the dynamic response of single-degree-of-freedom systems subjected to accelerograms recorded in Mexico during the last two decades, expressions to estimate the strength reduction factor that should be used to reduce the elastic design strength spectra for 5 percent damping, to establish the design seismic forces for structures having different combinations of plastic and viscous energy dissipating capacities, are formulated.     

DUCTILITY REDUCTION FACTOR OF MDOF SHEAR-BUILDING STRUCTURES

In this paper, the results of recent studies on inelastic seismic response of MDOF shear-building structures are presented. In the last few decades, the concept of response modification factor R has been introduced and developed to account for inelastic nonlinear behaviour of structures under earthquakes. In this paper, an attempt has been made to adjust and extend this concept through introducing a modifying factor R _T . This factor is used for dynamic analysis of MDOF structures, including the calculation of inelastic response spectra. Sensitivity analysis was carried out to identify the parameters that have influence on R _T . It has been demonstrated that R _T is predominantly a function of number of stories, and accordingly a relationship has been suggested. Finally, an approximate approach has been developed for evaluating the seismic strength and ductility demands of MDOF structures.     

METHODOLOGY FOR THE PROBABILISTIC ASSESSMENT OF q FACTORS. A DAMAGE INDEX APPROACH

The objective of the present work is to present a methodology for the identification of relevant limit states, namely ultimate limit states leading to structural collapse, and for the assessment of design q factors (or force reduction factors) for reinforced concrete structures under seismic loading. It follows a probabilistic approach based on damage indices. The utilised nonlinear models, as well as the damage indices, which are those proposed by Miner and by Park and Ang, are.described. The methodology of analysis is presented emphasising its probabilistic characteristics. Some parametric studies are carried out, including the analysis of one regular plane frame reinforced concrete structure, designed for three different ductility classes (those proposed by Eurocode 8) and assuming different q factors in design. Results show how the chosen damage indices can be used as parameters to characterise the structural response and how the proposed methodology can be used to assess the design q factors. It is also shown that, for moderate seismic input, the three ductility classes are essentially equivalent in terms of maximum damage indices, but that for higher seismic levels the differences are evident, justifying the use of different q factors.     

SEISMIC SOIL-STRUCTURE INTERACTION: BENEFICIAL OR DETRIMENTAL?

The role of soil-structure interaction (SSI) in the seismic response of structures is reex-plored using recorded motions and theoretical considerations. Firstly, the way current seismic provisions treat SSI effects is briefly discussed. The idealised design spectra of the codes along with the increased fundamental period and effective damping due to SSI lead invariably to reduced forces in the structure. Reality, however, often differs from this view. It is shown that, in certain seismic and soil environments, an increase in the fundamental natural period of a moderately flexible structure due to SSI may have a detrimental effect on the imposed seismic demand. Secondly, a widely used structural model for assessing SSI effects on inelastic bridge piers is examined. Using theoretical arguments and rigorous numerical analyses it is shown that indiscriminate use of ductility concepts and geometric relations may lead to erroneous conclusions in the assessment of seismic performance. Numerical examples are presented which highlight critical issues of the problem.     

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.     

An Investigation of Characteristic Periods of Seismic Ground Motions

The design seismic base shear was obtained from the spectral elastic acceleration S_a divided by a system behavior factor R, accounting for ductility and overstrength. The behavior factor is currently taken as a constant for a given type of structures in various codes regardless of structural periods. In fact, the behavior factor is also a spectrum varying with the natural periods of structures. In order to understand the relationship between the spectral values and the corresponding characteristic periods in these two spectra, S_a and R_μ, this article carries out an investigation into the characteristic periods of 370 seismic ground motions from 4 site types. It is found that the periods T_ga at which the peak values appear in the S_a spectra are much less than the periods T _gR at which the R_μ spectra take a maximum value. Two characteristic periods are necessary to determine the seismic action if a more elaborate procedure is required in practice. Statistical study on these two periods is carried out for the 370 records, and results are presented. For site types A–D, the ratio of these two periods has a statistically averaged value of 5.5–6.7.

The maximum input energy S _EI , relative velocity S _v , power density P _SD , and the Fourier amplitude F _S spectra were constructed to determine their characteristic periods, respectively. These four spectra predict similar characteristic periods to T _gR . T _gR is very close to the characteristic period T _gd of the elastic displacement spectra.

Analysis of SDOF systems under combined harmonic excitations shows that the S_a spectrum is more sensitive to high-frequency excitations, while the displacement spectrum is more sensitive to long period excitations. For the elastic-plastic S_a spectra, peak values tend to appear at shorter periods even the amplitudes of the longer periods are greater than that of the shorter period. This provides an explanation on different characteristic periods in the S_a and R_μ spectra.     

Behavior Factor for Performance-Based Seismic Design of Plane Steel Moment Resisting Frames

Simplified expressions to estimate the behavior factor of plane steel moment resisting frames are proposed, based on statistical analysis of the results of thousands of nonlinear dynamic analyses. The influence on this factor of specific structural parameters, such as the number of stories, the number of bays, and the capacity design factor of a steel frame, is studied in detail. The proposed factor describes the seismic strength requirements in order to restrict maximum storey ductility to a predefined value. Interrelation studies between maximum storey ductility and the Park-Ang damage index are also provided for the damage-based interpretation of the performance levels under consideration. Realistic design examples serve to demonstrate the ability of the proposed factor to convert conventional force-based design to a direct performance-based seismic design procedure.     

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.     

Design of Passive Viscous Fluid Control Systems for Nonlinear Structures Based on Active Control

A practical procedure is developed for the design of passive control systems using viscous fluid dampers for nonlinear structures. The design methodology takes advantage of the modification of the damping, strength, and stiffness properties of the structure to achieve the desired relative displacement and absolute acceleration response. For this purpose, a study of poles in the complex plane is used to determine the required changes in the dynamic properties of nonlinear structures. Furthermore, a relatively simple relation between the ductility demands of highly damped single- and multiple-degree-of-freedom (SDF and MDF respectively) systems is established to reduce the computational burden of the proposed design method.     

SEISMIC DESIGN OF BASE-ISOLATED STRUCTURES USING CONSTANT STRENGTH SPECTRA

This paper presents the concept of constant strength design spectra for the design of base-isolated structures; particularly those structures using isolators with a bilinear hys-teretic behaviour when subjected to dynamic loading. The constant strength design spectra relate peak accelerations, velocities, displacements and effective isolated natural periods for bilinear systems with a given yield strength and post yield stiffness. Constant strength design spectra could be useful for the design of base isolators with bilinear hysteretic behaviour, as these devices can be designed for fixed yield strength and post yield stiffness. The concept of constant strength design spectra and its application for the design of base isolated structures is illustrated with case studies of specific structures.     

AN ALGORITHM FOR COMPUTING ISODUCTILE RESPONSE SPECTRA

The computation of constant ductility (or isoductile) response spectra for single-degree-of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a “check-reject” approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.     

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.     

INELASTIC SEISMIC RESPONSE ANALYSIS BASED ON ENERGY DENSITY SPECTRA

Energy balance is used to characterise the seismic energy in inelastic structures where energy input to the structure is decomposed into strain energy, kinetic energy, damping energy, and plastic energy. The exact quantification of plastic energy is derived based on force analogy method for moment-resisting frames. A method of generating energy density spectra is then proposed based on yield displacement of a single degree of freedom system. The effects of different structural vibration characteristics are then studied on energy density spectra. These effects include variations of yield displacement level, earth-quake scaling factor, and damping ratio, which proves to be useful in improving the basic understanding of energy characteristics in structural dynamic response. Finally, the use of energy density spectra is demonstrated on a multi-degree of freedom structure to show the practical applications of these spectra.     

CALIBRATION OF FORCE REDUCTION FACTORS OF RC BUILDINGS

A comprehensive study is undertaken to assess and calibrate the force reduction factors (R) adopted in modern seismic codes. Refined expressions are employed to calculate the R factors “supply” for 12 buildings of various characteristics represent a wide range of medium-rise RC buildings. The “supply” values are then compared with the “design” and “demand” recommended in the literature. A comprehensive range of response criteria at the member and storey levels, including shear as a failure criterion, alongside a detailed modelling approach and an extensively verified analytical tool are utilised. A rigorous technique is employed to evaluate R factors, including inelastic pushover and incremental dynamic collapse analyses employing eight natural and artificial records. In the light of the information obtained from more than 1500 inelastic analyses, it is concluded that including shear and vertical motion in assessment and calculations of R factors is necessary. Force reduction factors adopted by the design code (Eurocode 8) are over-conservative and can be safely increased, particularly for regular frame structures designed to lower PGA and higher ductility levels.     

METALLURGY OF BRONZE USED IN TOOLS FROM MACHU PICCHU,PERU*

Although the tin‐bronze artisans’ tools found at Machu Picchu appear to have been cast to their final shape, examination of their microstructures shows that they were forged and annealed. As found, the tools were broken or cracked due to poor ductility of the bronze. Rolling and annealing of samples of bronze formulated with sulphur and iron additions to replicate the metal used at Machu Picchu show that the minimum amount of deformation needed to induce the observed recrystallization is a 12% reduction in thickness. The sulphur and iron impurities retard nucleation of new grains during annealing, but do not inhibit subsequent grain growth. Tensile tests show that while up to 10% porosity in cast bronze has no effect on hardness or initial strain‐hardening rate, it reduces the tensile strength and ductility enough to embrittle the metal. Hardness is an inadequate indicator of the strength properties of cast bronze intended for use in tools or weapons. The results show that when the metalsmiths at Machu Picchu started making bronze tools for use by stone and woodworkers, they had not mastered the art of making metal with adequate strength properties for this service. The forging and annealing procedure they used did not enhance the mechanical properties of their tools, and may reflect an inherited metallurgical tradition.     

Design and Assessment Spectra for Retrofitting of RC Buildings

This article presents a novel approach for deriving Retrofit Design Spectra (RDS) that are intended for use in preliminary development and assessment of seismic upgrading scenarios of existing structures. The new spectral representation relates the characteristics of the intervention method chosen as the core of the upgrading strategy, with the ductility and strength demand of the retrofitted structure. The methodology utilized for the derivation of the RDS is based on the Capacity Spectrum Method where the capacity curve is described by relationships for global and local intervention methods that are parameterized in terms of fundamental response quantities. The proposed spectra provide direct insight into the complex interrelation between the characteristics of the intervention method and the implications of the upgrading scenario on demand. Alternative retrofit solutions are thus assessed in an efficient way. A case study is used to illustrate practical application of the new approach.     

Seismic Overstrength of Shear Walls in Parking Structures with Flexible Diaphragms

The objective in current design practice for parking structures is that energy is dissipated through the formation of plastic hinges at the base of shear walls while floor diaphragms remain elastic and are vertically supported by a combination of shear walls and gravity resisting columns. Unfortunately, this objective is not always achieved due to inaccuracies in current methods for calculating demands on shear walls and in calculating the capacity of shear walls (IBC 2003 International Building Code. International Conference of Building Officials. Whittier, CA.  [Google Scholar], ACI code). When demands are overestimated and capacity underestimated, then diaphragm can fail prior to flexural yield of shear walls as was observed in several parking structures in the 1994 Northridge earthquake.

Eigenvalue and inelastic dynamic response analyses were performed in order to investigate the effects of diaphragm flexibility on wall responses and of wall overstrength on diaphragm responses. The elongated periods of parking structures due to diaphragm flexibility were found to significantly decrease seismic force demand on shear walls relative to what is calculated using codes of practice in which diaphragms are assumed to be rigid. This leads to the over design of shear walls, which further compounds the problem by preventing the flexural yielding of these walls and thereby driving inelastic response to diaphragms. Various degrees of diaphragm flexibility, shear wall layout, seismic zone, and the number of stories were considered in these analyses.

Inelastic static pushover analyses were preformed to investigate the design and capacity evaluation of shear walls. The results illustrate that the shear capacity of walls may be close to twice that calculated by codes of practice. The largest overstrengths were observed in shear walls with low height-to-length ratios in which a significant portion of the lateral load was taken by direct strut action to the foundation and without placing demands on the longitudinal tension reinforcement in the shear walls. The article concludes that methods in codes of practice for calculating shear wall demands and capacities need to be improved if good seismic performance of parking structures is to be achieved.     

Seismic Performance Assessment of Steel Frames with Shape Memory Alloy Connections,Part II – Probabilistic Seismic Demand Assessment

This article is the second of two companion articles that evaluate the seismic performance of steel moment-resisting frames with innovative beam-to-column connections that incorporate shape memory alloy (SMA) elements to enhance the energy dissipation characteristics of such frames. Building upon the finite element models of the three- and nine-story frames that were developed in the first article, the seismic demands on partially restrained frames with and without SMA elements are evaluated within a probabilistic framework. The results of this evaluation, expressed in the form of demand hazard curves, depict the effectiveness of the SMA connections in enhancing building performance over a range of demand levels. Martensitic SMA connections are most effective in controlling deformation demands on the frame from high levels of seismic intensity. In contrast, the recentering capability of superelastic SMA connections make them most suitable for reducing residual deformations in the structure, a reduction that is achieved at the expense of increased deformation demands during strong excitation. However, neither connection is uniformly beneficial at all hazard levels, suggesting that SMA systems must be tailored to the specific performance objectives for the building structural system.     

Reliability-based Strength Amplification Factors for Structures with Asymmetric Yielding

A reliability-based methodology to estimate strength amplification factors for structures with asymmetric yielding is proposed. The approach is based on structural demand hazard analyses. Nonlinear time-history analyses of tridimensional simplified systems are carried out. The effects of two orthogonal components of the seismic ground motions and soil-structure interaction, are considered. Results show that the expected ductility demand of systems with asymmetric yielding may be much higher than those of symmetric systems. A simplified mathematical expression (which is function of the ratio between the fundamental vibration period of the system and that of the soil, ductility demand, and level of asymmetric yielding) is proposed to estimate the amplification factors. The expression is applied successfully to a 9-story reinforced concrete building exhibiting asymmetric yielding produced by tilting.     

Use of Cumulative Ductility Spectra Within a Deformation-Control Format for Seismic Design of Ductile Structures Subjected to Long Duration Motions

Due to the large economical losses derived from recent seismic events, design methodologies that are based in the explicit control of the dynamic response of structures have been formulated. This article introduces, within the framework of performance-based design, a numerical methodology for the seismic design of structures that are expected to undergo severe cumulative plastic demands. The methodology explicitly considers and integrates: (1) the structural and non-structural performance of the building; (2) the life safety limit state; and (3) the prevention of low cycle fatigue.