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In simple inelastic structures subjected to severe base motions, the maximum acceleration response is bound by the yield strength and is inversely proportional to its mass. It can be demonstrated that a similar effect is approximately produced in structures with multidegrees of freedom. In strong structures, the maximum acceleration response is dependent on the intensity of the earthquake. However, if the strength of the structure is reduced, the maximum acceleration response and associated forces in its structural and nonstructural components can be substantially reduced. If some of the structural columns (carrying gravity loads) are allowed to rock, providing very small resistance to lateral loads, it is possible to reduce the strength of the global structural system and limit the global accelerations in seismic events. However, before overturning such columns may have substantial resistance which may void the effectiveness of weakening. The objective of this study is to (1) develop a simplified analytical model for rocking columns from fixity to overturning; (2) build the computational tools to simulate the behavior of structures including such rocking columns; and (3) examine the global nonlinear static response of a weakened structure. An analytical model is developed using an equivalent ftexibility approach, which considers rigid body rotations and flexural deformations. Physical experiments of rocking columns were performed, and the results are used for the calibration and validation of analytical models. An analytical model of a 1:3 scaled structure is developed using IDARC2D modified in this study to evaluate several alternatives of weakening using rocking columns. DOI: 10.1061/(ASCE)ST.1943-541X.0000154 CE Database subjeet headings. Columns; Nonlinear analysis; Structural analysis; Inelasticity; Ground motion. Author keywords: Rocking columns; Weakening structures; Flexibility approach; Nonlinear static analysis.

This paper presents a rational and efficient analytical approach for predicting the nonlinear in-plane flexural behavior of longitudinally posttensioned hollow block masonry shear walls under the action of reversed cyclic lateral loading. The present approach is based on a modified fiber-element (microelement) model of the longitudinally (vertically) posttensioned slender hollow block concrete masonry shear walls with ungrouted cells (i.e., ungrouted longitudinal posttensioning steel) that employs realistic cyclic constitutive rules tbr the constituent materials. The approach also accounts for the 'rocking' type of motion encountered in such walls when subjected to cyclic load reversals in the postcracking range of masonry. The present microelement modeling approach is also valid for slender hollow block masonry shear walls with unprestressed longitudinal steel reinforcement. An important objective of the study is to rationally model the effect of the absence of bond between the longitudinal reinforcing steel (posttensioned or unprestressed) and surrounding masonry, as well as the effect of posttensioning of longitudinal steel on the nonlinear in-plane force-displacement behavior of slender hollow block masonry shear walls subjected to reversed cyclic lateral loading. The proposed approach is implemented to model the in-plane hysteretic force-displacement response of slender posttensioned/reinforced hollow block concrete masonry shear wall specimens with ungrouted cells that were tested under quasi-static reversed cyclic lateral loading. The theoretical predictions are compared with available experimental results for validating the proposed microelement modeling approach. CE Database subject headings: Fibers; Post tensioning; Masonry; Shear walls; Lateral loads; Cyclic loads.

The hybrid simulation test method is a versatile technique for evaluating the seismic performance of structures by seamlessly integrating both physical and numerical simulations of substructures into a single test model. Using hybrid simulation, the seismic response of complex structural systems partitioned into multiple large-scale experimental and numerical substructures at networked geographically distributed experimental and computational facilities can be evaluated. A scalable framework with a fault-tolerant distributed controller is presented to support the implementation of advanced hybrid testing methods with distributed substructures. The control strategy is based on a multithreaded simulation coordinator for parallel communication with remote sites and an event-driven controller at each remote experimental site to implement continuous loading. The distributed controller provides faster rates of testing and improved accuracy in the simulation results. The effectiveness of the proposed framework is demonstrated by computing the earthquake response of a six-span bridge model with multiple remote experimental and numerical column substructures distributed within NEES laboratories across the United States. Further, the distributed tests were implemented using a secure network link between the testing sites that was developed for the NEES cyber infrastructure. DOI: 10.1061/(ASCE)0733-9445(2008)134:4(535) CE Database subject headings: Dynamic tests; Experimentation; Hybrid methods; Simulation; Structural response; Seismic effects; Bridges.

Computer analysis of structures has traditionally been carried out using the displacement method combined with an incremental iterative scheme for nonlinear problems. In this paper, a Lagrangian approach is developed, which is a mixed method, where besides displacements, the stress resultants and other variables of state are primary unknowns. The method can potentially be used for the analysis of collapse of structures subjected to severe vibrations resulting from shocks or dynamic loads. The evolution of the structural state in time is provided a weak formulation using Hamilton's principle. It is shown that a certain class of structures, known as reciprocal structures, has a mixed Lagrangian formulation in terms of displacements and internal forces. The form of the Lagrangian is invariant under finite displacements and can be used in geometric nonlinear analysis. For numerical solution, a discrete variational integrator is derived starting from the weak formulation. This integrator inherits the energy and momentum conservation characteristics for conservative systems and the contractivity of dissipative systems. The integration of each step is a constrained minimization problem and it is solved using an augmented Lagrangian algorithm. In contrast to the traditional displacement-based method, the Lagrangian method provides a generalized formulation which clearly separates the modeling of components from the numerical solution. Phenomenological models of components, essential to simulate collapse, can be incorporated without having to implement model-specific incremental state determination algorithms. The state variables are determined at the global level by the optimization method. CE Database subject headings: Lagrange's equations; Collapse; Structural safety; Simulation.

A method is suggested to reduce the structural seismic response using viscous dampers with their effect magnified with mechanical levers (lever arms). The lever arms are used to magnify the drift and the drift velocities transferred from the structure to the dampers thus producing larger energy dissipation in smaller devices. The increase of energy dissipation in each unit results in a reduction of the number of units necessary to achieve the same reduction in structural response, or it results in a reduction of the size of dampers required for the same purpose. The use of the proposed technique permits one to reduce the number of frame bays obstructed by diagonal or Chevron bracing elements. An optimal design procedure, based on the linear quadratic regulator (LQR) technique, is proposed in this study to obtain the initial properties of the viscous dampers. The study presents the amplification and the contribution of the construction details to such amplification. A seven-story structure model with the proposed system was simulated numerically in order to check the damping efficiency. The numerical example shows that using the lever arms for dampers' connection, it yields significant reduction in the structural response, very close to that designed according to the LQR strategy. CE Database subject headings: Damping; Seismic response; Structural response; Optimization.

In an attempt to trace the collapse of structures in seismic events, this paper discusses an alternative approach to the formulation and solution of the large deformation inelastic problem in planar frame structures. A beam-column element that includes the effect of geometric and material nonlinearities is developed using the flexibility approach. The formulation uses force interpolation functions and the principle of virtual forces in rate form. It is formulated in the context of the state space approach, where the global system of conservation equations and the local constitutive equations are solved simultaneously. The differential-algebraic system solver is used to solve the resulting system of equations. Numerical examples are presented to illustrate the functionality of the analysis using the newly formulated approach. DOI: 10.1061/(ASCE)0733-9445(2002)128:12(1575) CE Database keywords: Collapse; Deformation; Framed structures; Inelastic action.

The modeling of deteriorating hysteretic behavior is becoming increasingly important, especially in the context of seismic analysis and design. This paper presents the development of a versatile smooth hysteretic model based on internal variables, with stiffness and strength deterioration and with pinching characteristics. The theoretical background, development, and implementation of the model are discussed. Examples are shown to illustrate the features of the model. Many inelastic constitutive models in popular use have been developed independently of each other based on different behavioral, physical, or mathematical motivations. This paper attempts to unify the concepts underlying such models. Such a holistic understanding is essential to realize limitations in application of inelastic models and to extend 1D models to 3D models featuring interaction between various stress resultants.

A procedure for evaluating the seismic performance and retrofit of existing low-to-midrise reinforced concrete (RC) buildings is proposed. The procedure is derived from the well-known capacity spectrum method and is intended to provide practicing engineers with a methodology for estimating the margin of safety against structural failure. A series of seismic story demand curves is established from modal superposition analyses wherein changes in the dynamic characteristics of the structure at various response phases ranging from elastic to full failure mechanism are considered. These demands are compared to the lateral story capacities as determined from an independent inelastic pushover analysis. The distribution of lateral forces used in the progressive pushover analysis is based on stiffness dependent incremental story shear demands and forms a critical aspect of the methodology. The proposed technique is applied to a one-third scale model, three-story reinforced concrete frame building that was subjected to repeated shaking table excitations, and that was later retrofitted and tested again at the same intensities. This study indicates that the procedure can provide reliable estimates of story demands versus capacities for use in seismic performance and retrofit evaluation of structures.

Torsion in base-isolated structures with inelastic elastomeric isolation systems due to bidirectional lateral ground motion is studied. In a companion paper by the writers, torsional coupling in sliding base-isolated structures was investigated. in this paper, which is the second part of the sequence, torsional coupling in elastomeric base-isolated structures is investigated. Various multistoried structural systems with elastomeric isolation systems are investigated, with the objective of studying the influence of: (1) The flexibility of the superstructure; (2) the ratio of uncoupled torsional to lateral frequencies; (3) stiffness eccentricity in the superstructure; (4) eccentricity in the isolation system; (5) higher mode effects; and (6) number of bearings in the isolation system. Response to different ground motions is also studied. The results are used to explain: 1) The behavior of actual buildings; and (2) some inconsistencies in the conclusions of previous studies. It is shown that, although the total superstructure response is reduced significantly due to the effects of elastomeric base isolation, torsional amplification can be significant depending on the isolation and superstructure eccentricity and the lateral and torsional flexibility.

The lateral-torsional response of base-isolated structures, with sliding isolation system due to bidirectional lateral ground motion, is studied. The objective of the study is to identify the key system parameters that lead to significant torsional coupling in sliding base-isolated structures. The analysis procedure adopted can capture the highly nonlinear behavior of sliding systems in plane motion. The nonlinear biaxial stick-slip characteristics of sliding bearings and the velocity dependence of coefficient of friction are accounted for. The study considers multi-storied structures with variable number of bearings subjected to the effects of earthquakes with various frequency content and different peak ground accelerations. It is shown that, although the total superstructure response is reduced significantly due to the effects of sliding base isolation, torsional coupling can be significant depending on the superstructure eccentricity and the lateral-torsional flexibility of the superstructure and the base.

An experimental study, performed to evaluate the feasibility of using a sliding isolation system with uplift restraint devices for medium-rise buildings subject to column uplift, is presented. A Teflon-disc sliding bearing with built-in uplift restraint devices is described. A quarter-scale, 52-kip (231-kN) model of a six-story structure was isolated using the sliding isolation system with uplift restraint devices. The model had a slender configuration with ratio of height to width of 4.5. The slender configuration was chosen to ensure column uplift. Shake-table tests, involving strong motions with different frequency contents and peak table accelerations as high as 0.6 g, were performed. The shake-table test results show that the sliding isolation system is effective in reducing the structural response and uplift forces, by reducing the lateral floor accelerations and overturning moments, and that the uplift restraint system is effective in resisting uplift forces. An analytical model for predicting the response is developed. Comparisons between the predicted and observed responses are presented., The use of a sliding isolation system with uplift restraint devices for medium-rise buildings subject to column uplift was evaluated. Shake-table tests were conducted on a quarter-scale model of a six-story steel-braced frame that was isolated using the sliding isolation system. Results show that the system is effective in decreasing overturning moments and resisting uplift forces. A model for the behavior of the structure on the sliding system was also developed.

Damage of nonstructural components during past seismic events was shown to be not only a critical threat to life safety in extreme cases but also led to substantial reduction of functionality of buildings and other facilities. Because of the complex construction of nonstructural and architectural components, current standards provide only limited guidance for the seismic design. Suspended ceiling systems are among the less understood important nonstructural/architectural components in buildings for which design standards provide limited guidance. To understand the dynamic behavior of suspended ceiling systems, a series of full scale shake table tests of 20 ft × 53 ft and 20 ft × 20 ft ceiling systems were conducted at the Structural Engineering and Earthquake Simulation laboratory (SEESL) at University at Buffalo (UB). For the full scale dynamic testing, a new test frame providing a continuous suspended ceiling area of 1,060 ft2 was constructed on the tandem shake tables and was equipped with an open-loop shake table compensation procedure. The combined designs of the physical frame and of the shake table motion controllers allowed simulating the required floor/roof motion according to ICC-ES AC156 standard at the roof of the test structure. Various test configurations were selected in order to determine the influence of different system conditions and the effects or efficiency of various protective systems required by the current standard ASTM E580 for seismic design. Based on the test data and the failure mechanisms observed, damage states are defined, and fragility curves are developed. The results of the fragility analysis show that a ceiling system becomes more vulnerable as (a) it is subjected to multi-directional input motions, (b) heavier tiles are installed, (c) the size of a ceiling area increases, and (d) lateral restraints are not installed. In addition, simplified numerical models that can capture the special behavior of ceiling systems are developed and presented in a companion paper. This paper presents the experimental study of large area suspended ceiling systems involving test setup and configurations, test motions generated by a unique control system, and basic lessons gained from the experiments. [ABSTRACT FROM AUTHOR]

Due to the complex and heterogeneous construction of suspended ceiling systems, current standards provide only limited guidance for their seismic design. Simplified uniaxial numerical models of suspended ceiling systems are developed based on the experimental observation. Main runners with tributary ceiling area and grid connections in the longitudinal direction are modeled using lumped-masses and nonlinear connection springs. The proposed numerical models can be used as simple computational tools to explore the dynamic behavior and to estimate the design forces. Possible changes to the current standard design that suggest a more rational distribution of ceiling inertia forces are also discussed. [ABSTRACT FROM AUTHOR]