Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

SEISMIC BEHAVIOUR OF PERIMETER AND SPATIAL STEEL FRAMES

The present study deals with the seismic performance of partial perimeter and spatial moment resisting frames (MRFs) for low-to-medium rise buildings. It seeks to establish perimeter configuration systems and hence the lack of redundancy can detrimentally affect the seismic response of framed buildings. The paper tackles this key issue by com-paring the performance of a set of perimeter and spatial MRFs, which were “consistently designed”. The starting point is the set of low-(three-storey) and medium-rise (nine-storey) perimeter frames designed within the SAC Steel Project for the Los Angeles, Seattle and Boston seismic zones. Extensive design analyses (static and multi-modal) of the perimeter frame buildings and consistent design of spatial frame systems, as an alternative to the perimeter configuration, were conducted within this analytical study. The objectives of the consistent design are two-fold, i.e. obtaining fundamental periods similar to those of the perimeter frames, i.e. same lateral stiffness under design horizon-tal loads, and supplying similar yield strength. The seismic behaviour of perimeter and spatial configuration structures was evaluated by means of push-over non-linear static analyses and inelastic dynamic analyses (non linear time histories). Comparisons be-tween analysis results were developed in a well defined framework since a clear scheme to define and evaluate relevant limit states is suggested. The failure modes, either local or global, were computed and correlated to design choices, particularly those concerning the strength requirements (column overstrength factors) and stiffness (elastic stability indexes). The inelastic response exhibited by the sample MRFs under severe ground motions was assessed in a detailed fashion. Conclusions are drawn in terms of local and global performance, namely global and inter-storey drifts, beam and column plas-tic rotations, hysteretic energy. The finding is that the seismic response of perimeter and spatial MRFs is fairly similar. Therefore, an equivalent behaviour between the two configurations can be obtained if the design is “consistent”.     

Robust Period-Independent Ground Motion Selection and Scaling for Effective Seismic Design and Assessment

A period-independent approach for the selection and scaling of ground motion records aimed at reducing demand variability is proposed for seismic response history analysis. The same set of scaled records can be used to study various structures at the same site regardless of their dynamic characteristics. The statistical robustness of the proposed and current approaches is compared through nonlinear inelastic dynamic analyses performed on single-degree-of-freedom systems and multi-story braced frames. The proposed approach leads to consistent response predictions with a limited number of records. This is advantageous for day-to-day structural design or assessment against code hazard-based seismic demand levels.     

Increasing Seismic Energy Dissipation of Steel Moment Frames Using Reduced Web Section (RWS) Connection

Connections of steel moment frames are vulnerable to brittle failure. Providing a perforation near the beam-ends is suggested as a potential method to improve seismic behavior of these structures. This article presents a numerical study on the energy dissipation of steel moment connections with perforated beam. Models with elongated circular openings of different dimensions and location are analyzed and compared based on the global and local damage indices, predicted failure time and dissipated energy. Results show that an RWS connection with a proper opening size can develop reasonable inelastic deformations and provide an acceptable seismic improvement to moment-resisting frames.     

PERFORMANCE-BASED SEISMIC RESPONSE OF FRAME STRUCTURES INCLUDING RESIDUAL DEFORMATIONS. PART II: MULTI-DEGREE OF FREEDOM SYSTEMS

The role of residual deformations when evaluating the performance of multi-storey frame structures subjected to ground motion is investigated in this paper. The limitations of damage indices available in the literature, either based on ductility, energy dissipation or a combination of both, in capturing such a significant aspect of the seismic response of frame structures are discussed. The concept of residual deformations as a critical complementary indicator to cumulative damage, introduced in a companion paper (Part I) for single-degree-of-freedom (SDOF) systems, is herein extended to multi-degree-of-freedom (MDOF) frame systems. The seismic performance of multi-storey frame structures, either representative of new designed or existing structures, is investigated, focusing on the response in terms of residual deformations. Residual deformations are shown to be sensitive to the hysteretic rule adopted, to the system inelastic mechanism as well as to the seismic intensity. The influence of higher modes and P-Δ effects on the final residual deformations is addressed. A combination of maximum drift and residual drift in the format of a performance matrix is used to define the system's global performance levels and is then extended to a framework for an alternative performance-based seismic design and assessment approach.     

SEISMIC ENERGY DEMAND IN STEEL MOMENT FRAMES

The present paper investigates the seismic energy demand in steel moment-resisting frames. The frames, with 3, 6 and 10 storeys, and 4 and 8 spans, are designed according to current seismic code provisions. The energy response (energy quantities and their distributions) in the frames subjected to an ensemble of six earthquake ground motions recorded on different soil conditions, is investigated by nonlinear time history analysis. The study concludes that (1) the results of energy response can be developed into a rational method of seismic evaluation and design for steel moment-resisting frames; (2) the energy concept based on the single-degree-of-freedom has limitations when extended to the realistic structural system for design purposes; and (3) it is necessary to develop the energy-based approach for seismic evaluation and design based on the seismic response of a realistic multi-degree-of-freedom structural system.     

EVALUATION OF THE SEISMIC PERFORMANCE OF EXISTING RC BUILDINGS: II. A CASE STUDY FOR REGULAR AND IRREGULAR BUILDINGS

The results of a parametric study are presented, concerned with the evaluation of the structural overstrength, the global ductility and the available behaviour factor of existing reinforced concrete (RC) buildings designed and constructed according to past generations of earthquake resistant design codes in Greece. For the estimation of these parameters, various failure criteria are incorporated in a methodology established to predict the failure mode of such buildings under planar response, as described in detail in a companion publication. A collection of 85 typical building forms is considered. The influence of various parameters is examined, such as the geometry of the structure (number of storeys, bay width etc.), the vertical irregularity, the contribution of the perimeter frame masonry infill walls, the period of construction, the design code and the seismic zone coefficient. The results from inelastic pushover analyses indicate that existing RC buildings exhibit higher overstrength than their contemporary counterparts, but with much reduced ductility capacity. The presence of perimeter infill walls increases considerably their stiffness and lateral resistance, while further reducing their ductility. Fully infilled frames exhibit generally good behaviour, while structures with an open floor exhibit the worst performance by creating a soft storey. Shear failure becomes critical in the buildings with partial height infills. It is also critical for buildings with isolated shear wall cores at the elevator shaft. Out of five different forms of irregularity considered in this study, buildings with column discontinuities in the ground storey exhibit the worst performance. Furthermore, buildings located in the higher seismicity zone are more vulnerable, since the increase of their lateral resistance and ductility capacity is disproportional to the increase in seismic demand.     

ANALYTICAL MODELS FOR BRICK MASONRY INFILLED R/C FRAMES UNDER LATERAL LOADING

Proposed in this paper are two analytical models for predicting the inelastic response of unreinforced brick masonry infills in reinforced concrete frames subjected to mono-tonic and reversed cyclic loading. The first model is based on the traditional diagonal strut concept, while the second one is a simple isoparametric element with shear deformation only. All the essential characteristics of the hysteretic behaviour of the panel, including strength and stiffness degradation, pinching and slippage, are explicitly taken into account. The models are implemented in a general-purpose program for the inelastic time-history analysis of structures, and are used for studying the seismic behaviour of typical multistorey frames with various arrangements of infill panels, including structures with an open ground storey. The results of the analysis are in agreement with both experimentally observed behaviour and with experience regarding seismically damaged buildings.     

Seismic Design and Response of Framed Structures with Stiffening Bracing Systems

Stiffening Bracing System (SBS) is proposed as an alternative to conventional braced frames. SBS is intended to reduce the floor accelerations while maintaining uniform inter-story drift along the building height. The system ensures that additional damping devices distributed over the building’s height work efficiently. An iterative design procedure is developed to maintain a desired target performance. The procedure accounts for higher mode effects and supplemental damping. A series of nonlinear response history analyses on braced frames with various heights demonstrated the adequacy of the proposed procedure in achieving target structural performance and seismic demand prediction.     

Pseudo-Dynamic Testing and Analytical Modeling of AAC Infilled RC Frames

Two concrete frames were tested by the PsD procedure. One frame was bare and the other was infilled with AAC blocks in the middle bay. The objective was to determine the effect of AAC infills on the seismic performance of reinforced concrete frames and developing an AAC strut model. Based on the test results, it was found that AAC infill panels did not modify the deformation response of the RC test frame significantly; however, shear in diagonal strut must be considered in boundary column design. A shear design procedure is proposed for the boundary columns in infilled frames. The drift limits of AAC infill panels measured during the tests were 0.005, 0.008, and 0.014 during diagonal cracking, corner crushing, and severe damage states, respectively.     

Effect of Hysteresis Type on Drift Limit for Global Collapse of Moment Frame Structures Under Seismic Loads

Seismic analyses of 3-, 9-, and 20-story moment resisting frame (MRF) buildings with 5 hysteresis models were conducted. The objectives of the study were to study the effect of the hysteresis type on the global collapse drift limit, seismic demand, and capacity/demand ratio for MRF structures under seismic loads. The results show that strength degradation significantly decreases the global drift limit and the safety of the structure, whereas, the existence of stiffness degradation or pinching has small effect. The results suggest that the global drift limit for a building is not likely to be the collapse limit state (CLS) which will most likely be governed by local collapse.     

Developing Representative Dual Loading Protocols for the Columns of Steel Special Moment Frames based on the Seismic Demands on These Members

The column members of steel moment frames undergo high axial forces as well as inelastic rotations during a severe seismic event. The boundaries of these simultaneous structural demands on the columns of special moment frames have been investigated in this research. Based on the results of this investigation, dual cyclic loading protocols have been developed that represent both axial force and lateral deformation demands. Contrary to other loading scenarios that have been implemented in previous studies on steel columns, the loading protocols developed in this study include simultaneous axial and lateral loading cycles with varying amplitudes. The level of axial forces and story drifts tolerated by the columns of some typical Special Moment Frames (SMFs) has been investigated through performing nonlinear dynamic analyses. These frames have been selected with several configurations and different number of stories. The results of the nonlinear dynamic analyses have been processed to assess cumulative and instantaneous seismic demands on the columns of the chosen typical frames. Subsequently, dual cyclic loading protocols have been developed such that exerting these loading protocols on individual steel columns can result in structural effects close to the general seismic demands assessed in this study. Two separate dual loading protocols have been introduced for Design Earthquake (DE) and Maximum Considered Earthquake (MCE) seismic intensity levels.     

A Simplified Drift-Based Assessment Procedure for Regular Confined Masonry Buildings in Seismic Regions

This article presents a simplified procedure for assessing the seismic performance of existing low-to-medium rise confined masonry (CM) buildings, which are a typical construction type in Latin-America. The procedure consists of the estimation of the peak roof and first-story inelastic drift demand of CM buildings. The expected peak inelastic displacement demand is related to drift-based fragility curves, which express the probability of being or exceeding two key damage states in the masonry panels, developed from a relatively large experimental database. The proposed procedure could be very useful for obtaining rapid estimates of expected performance during future earthquake events and for assessing the seismic vulnerability of regular confined masonry structures.     

Lightly Reinforced Walls Subjected to Seismic Excitations: Interpretation of CAMUS 2000–1 and 2000–2 Dynamic Tests

In this article a study is presented of the inelastic seismic performance of two 5-story reinforced concrete wall specimens, which were tested in the context of the CAMUS 2000 program. The structure has been sized and detailed following the French PS92 code. To investigate the simplifying assumptions made in design, a 3-D refined nonlinear analysis was conducted. Particular aspects of the behavior of the two tested specimens are presented and then test results are compared with numerical predictions. The experimental-analytical comparisons not only demonstrate the accuracy of the time-history analysis model, but also allow obtaining more detailed information about the behavior of the specimen when it is subjected to seismic excitation. The significant effect of degradation of the stiffness and strength of the wall suggests that it is always important that design procedures are derived from numerical modeling and experimental observations.     

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.     

Quasi-Static Testing of RC Infilled Frames and Confined Stone-Concrete Bearing Walls

This article presents an experimental investigation of the seismic performance of gravity load-designed RC infilled frames and confined bearing walls of limestone masonry backed with plain concrete. Five infilled frames and two bearing walls were constructed at one-third scale and tested using reversed cyclic lateral loading and constant axial loads. Effects of openings, axial loading, and infill interface conditions were examined using quasi-static experimentation. The two structural systems exhibited similar lateral resistance and energy dissipation capacities with higher global displacement ductility for the infilled frames. Hysteretic behavior of the infilled frame models exhibited pinching of the hysteretic loops accompanied by extensive degradation of stiffness whereas loops of the bearing walls were free of pinching. Test results confirmed the beneficial effect of axial loading on lateral resistance, energy dissipation, and ductility of the bearing walls. Higher axial loading resulted in a substantial decrease in ductility with no significant effect on lateral resistance of the infilled frames. Openings within the infill panel reduced significantly the lateral resistance of infilled frames. Using dowels at the infill panel interfaces with the base block and bounding columns enhanced the maximum load-carrying capacity of infilled frames without impairing their ductility.     

Modeling and Seismic Response Analysis of Italian Code-Conforming Single-Storey Steel Buildings

ABSTRACT

This article describes the structural design, nonlinear modeling, and seismic analysis of prototype single-storey non-residential steel buildings made of moment-resisting portal frames in the transverse direction and concentric braces in the longitudinal direction. Various design parameters (building geometry, seismic hazard, foundation soil category) and different modeling assumptions (bare frame model, model including cladding elements, ground motions including vertical accelerations, and modeling uncertainties) were considered to investigate their effects on the simulated seismic performance.     

Displacement-Based Assessment of Non Ductile Exterior Wide Band Beam-Column Connections

Results from testing two half-scale exterior wide band beam-column sub-assemblages under cycles of lateral displacement are presented in this article. The first subassemblage represents the current level of detailing adopted in low to moderate seismic regions, such as Australia, for connections where seismic provisions are not normally a consideration in design. Minor (inexpensive) detailing changes in the reinforcement distribution and anchorage were introduced to the second test specimen. These changes significantly improved the connection performance in terms of increased displacement capacity and a reduction in strength deterioration. Using a displacement-based assessment approach to assess primary moment-resisting band beam frames of up to eight stories, it was found that the current level of detailing is adequate for the drift demands resulting from the expected Australian seismicity for a 500-year return period. However, for the displacement demands corresponding to a 2500-year return period, the frames sited on very soft soils and frames over four stories sited on intermediate soils would require improved detailing such as that used in the second sub-assemblage. A strength hierarchy of strong column-weak beam was assumed in this assessment.     

Multi-Component Seismic Response Analysis – A Critical Review

Issues related to multi-components seismic response analysis are critically reviewed and their implications with respect to the current codified approaches are studied. The issues specifically addressed are: (1) the directions of earthquake forces to excite a structure when the direction of the potential epicenter is known; (2) different commonly used combination rules to obtain the critical response when responses are available in different directions; and (3) the applicability of the combination rules for elastic and inelastic analyses. Based on an extensive parametric study consisting of three-dimensional 1-, 3-, 8-, and 15- story buildings made of moment-resisting steel frames and 20 recorded earthquakes, it is observed that the principal components produce larger responses than the normal components. The 30% and SSRS rules generally underestimate the axial loads in columns. The 30% combination rule is slightly better than the SSRS rule. For both rules, the uncertainty in the estimation of the axial loads in terms of COV is very large (about 25%). The statistics obtained for axial loads and total base shear indicate that the combination rules are applicable for both elastic and inelastic cases. The critical response could be obtained for an orientation different from that of the principal components. The differences are found to be slightly greater for the scaled earthquakes producing a considerable inelastic behavior. Considering the enormous amount of efforts needed to address the directionality effect, it is believed that the responses obtained by the principal components will be acceptable in most cases; however, for critical structures the components should be rotated to obtain the critical responses.