Simplified Seismic Sidesway Collapse Capacity-Based Evaluation and Design of Frame Buildings with Linear Viscous Dampers

This article describes a simplified procedure for estimating the seismic sidesway collapse capacity of frame building structures incorporating linear viscous dampers. The proposed procedure is based on a robust database of seismic peak displacement responses of viscously damped nonlinear single-degree-of-freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed procedure is assessed by comparing its collapse capacity predictions on 272 different building models with those obtained from incremental dynamic analyses. A straightforward collapse capacity-based design procedure is also introduced for structures without extreme soft story irregularities.     

Equivalent Force Control Method for Real-time Testing of Nonlinear Structures

The equivalent force control (EFC) method replaces numerical iteration with a feedback control strategy to solve the nonlinear equations of motion using an implicit integration method for real-time substructure tests (RSTs). The method, however, requires the conversion of the equivalent forces to structural displacements using a conversion matrix. It is demonstrated in this article that with the use of a proportional-integral (PI) controller for the EFC, one has the convenience of choosing the initial stiffness matrix of a structure to construct the conversion matrix regardless of the properties and degree of nonlinearity of the system. The stability condition of the EFC using a PI controller has been derived with the Routh stability criterion. Methods for designing and tuning a PI controller for RST using EFC have been presented and excellent system performance has been obtained from numerical simulations and actual tests. The simulation results showed that the EFC method using a PI controller and the initial stiffness matrix to construct the conversion matrix can deliver excellent performance even for structural systems that develop a severe strain-softening behavior. Its superiority over iteration method proposed by Jung et al. [2007] Jung, R. Y., Shing, P. B., Stauffer, E. and Thoen, B. 2007. Performance of a real-time pseudo dynamic test system considering nonlinear structural response. Earthquake Engineering and Structural Dynamics, 36: 1785–1809.  [Google Scholar] was demonstrated through numerical simulation. This provides an efficient means to test nonlinear multiple-degrees-of-freedom structures.     

Parametric Sensitivity of Ground Motion Pulse Filter for Response Control of Base-Isolated Buildings

Recently, the authors have proposed ground motion pulse filters for designing effective active and semi-active controllers for base-isolated structures subject to near-field earthquakes. The controller design is realized by augmenting the structural system equation with state-space model of the pulse filter. It has been observed that the resulting controllers are capable of simultaneously reducing peak values of base displacement, superstructure drift, and accelerations of the base and the superstructure simultaneously within practical range of control forces. Since the pulse model depends on ground pulse period, ground pulse decay factor, and the pulse shape factor, a parametric sensitivity analysis is carried out to find pulse parameters for a broad range of earthquakes. It is found that the performance of the controller doesn't vary significantly if the pulse period is underestimated by 50% or overestimated by 20% with respect to the actual ground pulse period, the ground decay factor is between 0.15 and 0.35 and the pulse shape factor is between 1 and 3.     

Single-Degree-of-Freedom Characterization of Multi-Phase Passive Control Systems

A Multi-phase Passive Control System (MPCS) combines two passive control devices in order to offset the individual weaknesses and enhance structural performance, allowing the structure to respond effectively to varying levels of loading. Previous work involving a nine-story frame demonstrated the effectiveness of MPCSs but the fundamental understanding of the system was lacking. In order to more clearly understand the behavior and identify important parameters and parameter interactions, a single-degree-of-freedom (SDOF) non-linear dynamic study was performed. The results offer significant insight towards developing structural systems adaptable to multi-objective performance-based design procedures that meet higher performance standards than for ductility-based design.     

Direct Displacement-Based Seismic Design of Eccentrically Braced Steel Frames

A series of eccentrically braced frames (EBF) are designed and subjected to nonlinear analyses to highlight ambiguities and differences in current seismic design provisions for EBF structures. This provides motivation to implement better guidance for the checking of local displacement demand considerations and move towards a displacement-based design approach. A recently proposed direct displacement-based design (DDBD) procedure for EBFs is then described and further developed in this article through the calibration of a spectral displacement reduction factors that relate the displacement of an inelastically responding structure to that of the equivalent linear representation used in the DDBD of EBFs. Such an expression is calibrated as part of this study using an experimentally validated numerical model also proposed here for the EBF links such that the actual hysteretic behavior of the links is well represented. The DDBD guidelines are applied to EBF systems from 1–15 stories in height and their performance is verified via nonlinear dynamic analyses using two different sets of design spectrum compatible ground motions. The results of the study indicate the robustness of the proposed DDBD method in limiting the interstory drifts to design limits for a variety of EBF systems with short links, thus demonstrating that the proposed DDBD method is an effective tool for seismic design of EBFs.     

Modeling and Control of the CSCEC Multi-Function Testing System

In order to promote the research and development on evaluating the seismic performance of structures, China State Construction Engineering Corporation (CSCEC) planned to construct a large-scale loading testing facility, the Multi-Function Testing System (MFTS). This facility can perform full-scale, real-time, 6-degree-of-freedom static and dynamic testing of rubber bearings and many types of structural components including long columns, shear walls and cross shape joints. The basic performances of the MFTS are a clearance of 9.1 m × 6.6 m × 10 m for specimen installation, maximum x-directional displacement 1500 mm, maximum y-directional velocity 1570 mm/s and maximum z-directional compressive load 108 MN. The system configuration and performance specifications of the MFTS are presented in this paper. The inverse kinematics model and the nonlinear model of the hydraulic servosystem of the MFTS are built. A modified feedback forward kinematics algorithm is developed for real-time control of the MFTS. Internal force characteristics of the loading system are analyzed. The internal force control method based on real-time solution of basis of internal force space is proposed for the system with large motion ranges. The motion controller combining position control loop and internal force control loop is developed. To meet the requirement of simultaneously imposing vertical compressive load and horizontal displacement, a mixed load and displacement controller is designed, where a direct force control loop is used to improve the response speed of the force control and reduce spatial dynamic coupling effects. Finally, a dynamic bearing testing is performed. The test results demonstrate that the system using the proposed controller has good abilities on position tracking, force balance, and load following.     

CONCEPT AND DEVELOPMENT OF HYBRID SOLUTIONS FOR SEISMIC RESISTANT BRIDGE SYSTEMS

The development of alternative solutions for precast concrete buildings based on jointed ductile connections has introduced innovative concepts in the design of lateral-load resisting frame and wall systems. Particularly efficient is the hybrid system, where precast elements are connected via post-tensioning techniques and self-centring and energy dissipating properties are adequately combined to achieve the target maximum displacement with negligible residual displacements. In this contribution, the concept of hybrid system is extended to bridges as a viable and efficient solution for an improved seismic performance when compared with monolithic counterparts. Critical discussion on the cyclic behaviour of hybrid systems, highlighting the most significant parameters governing the response, is carried out.

The concept of a flexible seismic design (displacement-based) of hybrid bridge piers and systems is proposed and its reliability confirmed by quasi-static cyclic (push-pull) and nonlinear time-history analyses based on lumped plasticity numerical models.     

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.     

Probabilistic Calibration and Experimental Validation of the Seismic Design Criteria for One-Story Concrete Frames

This article investigates the seismic performance of one-story reinforced concrete structures for industrial buildings. To this aim, the seismic response of two structural prototypes, a cast-in-situ monolithic frame and a precast hinged frame, is compared for four different levels of translatory stiffness and seismic capacity. For these structures an incremental nonlinear dynamic analysis is performed within a Monte Carlo probabilistic simulation. The results obtained from the probabilistic analysis prove that precast structures have the same seismic capacity of the corresponding cast-in-situ structures and confirm the overall goodness of the design criteria proposed by Eurocode 8, even if a noteworthy dependency of the actual structural behavior from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of pseudodynamic tests on full-scale structures. The results of these tests confirm the overall equivalence of the seismic behavior of precast and cast-in-situ structures. Moreover, two additional prototypes have been designed to investigate the seismic behavior of precast structures with roof elements placed side by side. The results of these further tests show that an effective horizontal diaphragm action can be activated even if the roof elements are not connected among them, and confirm the expected good seismic performance of these precast systems. Finally, the results of the experimental tests are compared with those obtained from nonlinear structural analyses. The good agreement between numerical and experimental results confirms the accuracy of the theoretical model and, with it, the results of the probabilistic investigation.     

Nonlinear Performance of Explicit Pseudodynamic Algorithms

A previously published explicit method has been proved to have the same numerical properties as those of constant average acceleration method for linear elastic systems. Although its application to the pseudodynamic testing of nonlinear systems with high frequency modes has been conducted and thus unconditional stability for nonlinear systems was indicated, there is still lack of an analytical proof. In order to explore the nonlinear performance of this explicit pseudodynamic algorithm, a new parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change between the stiffness at the end of a time step and the initial stiffness. This parameter enables basic analysis and error propagation analysis for a nonlinear system. In addition, it can also be applied to construct the rough guidelines to select an appropriate time step to conduct a pseudodynamic test although it is almost impossible to achieve this goal using the currently available techniques for a nonlinear system. Analytical results reveal that this algorithm can have unconditional stability for instantaneous stiffness softening and linear elastic systems while it has conditional stability for instantaneous stiffness hardening systems. The proposed rough guidelines for selecting a time step to yield a reliable pseudodynamic test are confirmed with numerical examples.     

Considering Soil-Nonlinearity Effect on Seismic Performance Evaluation of Structures based on Pushover Analysis

According to the most of current seismic codes, nonlinear soil behavior is commonly ignored in seismic evaluation procedure of the structures. To contribute on this matter, a pushover analysis method incorporating the probabilistic seismic hazard analysis (PSHA) is proposed to evaluate the effect of nonlinear soil response on seismic performance of a structure. The PSHA outcomes considering soil nonlinearity effect is involved in the analysis procedures by modifying the site-specific response spectrum. Results showed that incorporation of nonlinear soil behavior leads to an increase in displacement demand of structures which should accurately be considered in seismic design/assessment procedure. Results of implemented procedure are confirmed with the estimated displacement demand including soil-structure interaction (SSI).     

Numerical Characteristics of Explicit Method for Nonlinear Systems

Numerical properties of the Newmark explicit method in the solution of nonlinear systems are evaluated by introducing a parameter, which is named the instantaneous degree of nonlinearity, to monitor the variation of stiffness with time. Stability analysis reveals that the upper stability limit is inversely proportional to the square root of the instantaneous degree of nonlinearity and thus it is no longer equal to 2 for nonlinear systems. In fact, it is shrunk as instantaneous degree of nonlinearity is larger than 1 while it is enlarged as instantaneous degree of nonlinearity is less than 1. It is also proved that the satisfaction of stability limits for each time step implies a stable computation in the complete step-by-step integration procedure. Accuracy analysis shows that the relative period error is increased with the increase of the instantaneous degree of nonlinearity for a given product of the initial natural frequency and time step. Furthermore, a rough guideline is proposed for accurate integration of nonlinear systems and its appropriateness is confirmed with numerical examples.     

Estimating the Higher-Mode Response of Ductile Structures

While the importance of higher-mode actions is appreciated within the engineering community, the affect that ductile nonlinear response has on higher-mode characteristics and the subsequent implications this has for design has received little attention. In this article, the manner in which the higher-mode response of frame-wall structures is affected by inelastic behavior is closely examined and a means of accounting for this in design is proposed. The work focuses firstly on the characteristics of the higher modes present at the development of peak response and then considers how these characteristics would affect the total forces in the building. The study utilizes a series of nonlinear time-history analyses of two different groups of RC frame-wall structures subject to a suite of real records. It is shown that a new modal analysis approach that incorporates transitory inelastic modal characteristics gives significantly improved predictions of peak base shear in frame-wall structures than more traditional modal analysis methods which use elastic higher-mode characteristics. The issues associated with the use of transitory inelastic modal characteristics are discussed and various challenges that would need addressing for the prediction of other response parameters and structural types are identified.     

Identification of Suitable Limit States from Nonlinear Dynamic Analyses of Masonry Structures

Performance-based earthquake engineering, developed over the last decades for the design and assessment of other structures, can also be applied for masonry structures if the particularities of masonry are incorporated into the procedure. According to this methodology, structural performance can be assessed according to damage states which are identified through displacement/damage indicators. While various methods for the identification of limit states from the results of nonlinear static analyses exist, the identification of damage states from the results of nonlinear dynamic analyses is still uncertain. This article investigates a number of criteria allowing to identify the attainment of significant limit states from the results of time history analyses, in terms of appropriately identified response quantities. These criteria are applied to five building prototypes and their results are compared. A comparison with the limit states derived from nonlinear static analyses is also made.     

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.     

Capacity Design of Coupled RC Walls

Capacity design aims to ensure controlled ductile response of structures when subjected to earthquakes. This article investigates the performance of existing capacity design equations for reinforced concrete coupled walls and then proposes a new simplified capacity design method based on state-of-the-art knowledge. The new method is verified through a case study in which a set of 15 coupled walls are subject to nonlinear time-history analyses. The article includes examination of the maximum shear force in individual walls in relation to the total maximum shear force in the coupled wall system, and subsequently provides recommendations for design.     

Non-Iterative Equivalent Linearization Based on Secant Period for Estimating Maximum Deformations of Existing Structures

The capacity spectrum method of ATC-40 uses the secant period as the equivalent period of equivalent linear systems. Therefore, it results in a direct graphical comparison. The maximum inelastic displacement and acceleration demands of structures can be simultaneously obtained from the intersection of the demand and capacity diagrams. However, for evaluation of existing structures, the demands need to be determined through iterations since the equivalent period and damping of the equivalent linear systems currently available are both a function of the (displacement) ductility ratio, which is unknown and is the target of evaluation. In addition, the equivalent damping used in the capacity spectrum method is independent of periods of vibration. It may lead to poor estimations of maximum responses especially for short-period systems. This article proposes two equivalent linear systems based on the secant period to estimate the maximum displacement and acceleration responses of existing structures. Both the recommended equivalent period and damping are defined by the strength ratio (elastic lateral strength/yield lateral strength), rather than the ductility ratio. Because the strength ratio of existing structures is a known parameter, the maximum displacement and acceleration responses of these structures can be determined without iterations. Besides, effects of periods of vibration on the equivalent linear systems are also included in this study. The equivalent damping is derived from statistical analyses for bilinear single-degree-of-freedom (SDOF) systems with different periods of vibration, strength ratios and post-yield stiffness based on 72 earthquake ground motions recorded on firm sites. Procedures and examples for applications of the proposed equivalent linear systems on nonlinear static analysis procedures are also provided.     

Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings

The first step in a hysteretic energy-based design approach of performance-based design is the estimation of hysteretic energy demand in the structure. A nonlinear response-history analysis of the multi-degree of freedom model gives an accurate estimation, but it is not suitable for adopting in design. Two alternative methods, based on the concepts of modal pushover analysis (MPA) and 2D-MPA, are proposed in this article for uniaxial plan-asymmetric structures. Application studies show that both methods are efficient. While the 2D-MPA-based method is more accurate, the MPA-based method is more suitable for design adoption. Significant conclusions are given for prospective application of these methods.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

Seismic Performance and Modeling of a Half-Scale Base-Isolated Wood Frame Building

The concept of base isolation is a century old, but application to civil engineering structures has only occurred over the last several decades. Application to light-frame wood buildings in North America has been virtually non existent with one notable exception. This article quantitatively examines issues associated with application of base isolation in light-frame wood building systems including: (1) constructability issues related to ensuring sufficient in-plane floor diaphragm stiffness to transfer shear from the superstructure to the isolation system; (2) evaluation of experimental seismic performance of a half-scale base-isolated light-frame wood building; and (3) development of a displacement–based seismic design method and numerical model and their comparison with experimental results. The results of the study demonstrate that friction pendulum system (FPS) bearings offer a technically viable passive seismic protection system for light-frame wood buildings in high seismic zones. Specifically, the amount and method of stiffening the floor diaphragm is not unreasonable, given that the inter-story drift and accelerations at the upper level of the tested building were very low, thus resulting in the expectation of virtually no structural, non structural, or contents damage in low-rise wood frame buildings. The nonlinear dynamic model was able to replicate both the isolation layer and superstructure movement with good accuracy. The displacement-based design method was proven to be a viable tool to estimate the inter-story drift of the superstructure. These tools further underscore the potential of applying base isolation systems for application to North America's largest building type.