Inelastic Drift Research Articles

A story shear-based adaptive pushover procedure for estimating seismic demands of buildings

In recent years some adaptive pushover methods have been proposed to include the effects of the higher modes and the changes in the vibration characteristics during the inelastic response. However, because of using the quadratic combination rules to combine the modal forces, the changes in the sign of the story components in the higher modes are removed. Consequently, the magnitudes of the applied loads in all story levels are positive and these adaptive methods are not superior to their non-adaptive counterparts. Here, an innovative adaptive pushover method, called “SSAP”, is proposed based on the story shears which takes into account the reversal of sign in the higher modes. In each step, the applied load pattern is derived from the instantaneous combined modal story shear profile. The sign of the applied loads in consecutive steps are changed and the structure is simultaneously pushed and pulled in different story levels. Another aspect of the proposed method is that at each step an assumed fundamental mode shape is derived from the load profile. Based on this adaptive fundamental mode shape and the energy concept, the multi degree of freedom system is converted into a single degree of freedom system. The proposed method is applied to two steel moment-frame buildings. The results show an admirable accuracy in prediction of peak inelastic drift response, especially where the effects of the higher modes are important. A combination of this method with the conventional pushover approach, called “SS–M1”, results in more accurate estimation of peak inelastic drift in all story levels compared to the other pushover approaches.

Estimating Inelastic Drifts and Link Rotation Demands in EBFs

When designing eccentrically brace frames (EBFs), the inelastic rotation of the links is estimated to ensure that links will not experience excessive rotations. Typically, design engineers amplify elastic analysis results to estimate EBF link inelastic rotations. Twelve EBF frames of different height (3-, 9-, and 18- story) and strength were designed and two types of analyses performed: static elastic analysis under the design base shear; and non-linear dynamic analysis under ten design-level earthquakes. Roof drifts, story drifts, and link rotations were estimated by amplifying values from the static elastic analyses, and then compared with average values from the dynamic analyses. Poor correlation was observed. For the 3-story frames, estimated link rotations were as much as 63% lower than the rotations observed in the dynamic analyses. For the 9- and 18-story frames, estimated link rotations were as much as two times greater than those observed in the dynamic analyses. Calibrated amplification factors were developed for better estimation of link inelastic rotation. It is demonstrated that amplifying only the shear component of the elastic story deformations will lead to more reasonable estimates.

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.

Design of steel plate shear walls considering inelastic drift demand

The unstiffened steel plate shear wall (SPSW) system has emerged as a promising lateral load resisting system in recent years. However, seismic code provisions for these systems are still based on elastic force-based design methodologies. Considering the ever-increasing demands of efficient and reliable design procedures, a shift towards performance-based seismic design (PBSD) procedure is proposed in this work. The proposed PBSD procedure for SPSW systems is based on a target inelastic drift and pre-selected yield mechanism. This design procedure is simple, yet it aims at an advanced design criterion. The proposed procedure is tested on a four-story test building with different steel panel aspect ratios for different target drifts under selected strong motion scenarios. The designs are checked under the selected ground motion scenarios through nonlinear response-history analyses. The actual inelastic drift demands are found to be close to the selected target drifts. In addition, the displacement profiles at peak responses are also compared with the selected yield mechanism. Future modifications required for this design procedure for different SPSW configurations are identified based on these test cases.

Friction Damped Posttensioned Self-Centering Steel Moment-Resisting Frames

A new connection for steel moment-resisting frames that incorporates posttensioning elements to provide a self-centering capacity along with friction mechanisms to dissipate energy is proposed and experimentally validated. The restoring force from the posttensioning elements in the connection makes the structure return to its undeformed state, even after experiencing large inelastic drifts. A bolt-prestressed friction mechanism with a frictional interface consisting of stainless steel and new nonasbestos organic break lining pads dissipates seismic input energy as the system undergoes lateral deformations. Cyclic tests were conducted to investigate the efficiency of the proposed friction interface and its performance under loading conditions that are expected during seismic loading. The test results showed that the frictional behavior is stable, repeatable, and predictable, although its friction coefficient is relatively low. Exterior and interior self-centering moment connections equipped with the proposed friction dampers were tested to study their structural behavior under cyclic loading. The results confirmed that friction damped posttensioned self-centering connections are capable of developing similar stiffness and strength characteristics to welded connections. They are also capable of undergoing large deformations with good energy dissipation characteristics, but without introducing inelastic deformations in the beams or the columns and without residual story drifts. Even at the ultimate stage, i.e., beyond the self-centering limit, the proposed connections can be detailed to exhibit a ductile response with the formation of flexural hinges in the beam sections, thus avoiding the sudden loss of strength and stiffness that occurs when the posttensioning elements are overloaded or when the beams buckle under excessive combined axial loads and bending moments.

A numerical study on bolted end-plate connection using shape memory alloys

Superelastic shape memory alloys (SMAs) have the ability to recover their original shape after experiencing large strains. A new beam-to-column connection incorporating long shank SMA bolts is presented in this paper. By using the unique characteristics of SMAs, the connection possesses self-centering abilities. The 3D connection model is created using the software ANSYS, and Auricchio’s model is used to simulate the superelastic behavior of the SMA bolts. With cyclic loads applied on the beam ends, the behavior of the connection is studied. The results show the semi-rigid and moderate energy dissipation characteristics of the connection. Since the moment-carrying capacity of bolt cluster controlled below the elastic flexural capacity of connecting beam, a superelastic hinge forms just at the beam-to-column interface. The inelastic interstory drift angle of the connection reaches 0.035 rad, and 94% of the total rotations are recoverable upon unloading.

Multiobjective Optimization for Performance-Based Design of Reinforced Concrete Frames

In order to meet the emerging trend of performance-based design of structural systems, attempts have been made to develop a multiobjective optimization technique that incorporates the performance-based seismic design methodology of concrete building structures. Specifically, the life-cycle cost of a reinforced concrete building frame is minimized subject to multiple levels of seismic performance design criteria. In formulating the total life-cycle cost, the initial material cost can be expressed in terms of the design variables, and the expected damage loss can be stated as a function of seismic performance levels and their associated failure probability by the means of a statistical model. Explicit formulation of design constraints involving inelastic drift response performance caused by pushover loading is expressed with the consideration of the occurrence of reinforced concrete plasticity and the formation of plastic hinges. Due to the fact that the initial material cost and the expected damage loss are conflicting by nature, the life-cycle cost of a building structure can be posed as a multiobjective optimization problem and solved by the e-constraint method to produce a Pareto optimal set, from which the best compromise solution can be selected. The methodology for each Pareto optimal solution is fundamentally based on the Optimality Criteria approach. A ten-story planar framework example is presented to illustrate the effectiveness of the proposed optimal design method.

Feasibility study on a self-centering beam-to-column connection by using the superelasticbehavior of SMAs

High ductility in traditional beam-to-column connections is often coupled withbeam local buckling. These plastic local buckling deformations are difficult andvery costly to repair in any post-disaster reconstruction. This paper investigatesa new connection consisting of an extended end-plate, long shank SMA bolts,continuity plates, beam flange ribs and web stiffeners. Advanced 3D models oftraditional end-plate bolted connection and the SMA connection are created,and the behavior of the two types of connections is compared. The results showobvious cyclic elongations of the bolts in the SMA connection compared to thebeam local buckling in the traditional connection. Rather than the plastic hingeforming away from the column face in the traditional connection, a superelastichinge forms just at the beam-to-column interface in the SMA connection with themoment-carrying capacity of bolt cluster controlled below the elastic flexuralcapacity of the connecting beam. The connection deformations are recoverable uponunloading. Moreover, the SMA connection ductility is significantly influenced bythe length of the SMA bolts. For SMA bolts which are 1.2 times longer thanthe standard bolt, the inelastic interstory drift angle reaches 0.035 rad, whichindicates that the proposed connection can be designed with sufficient ductility.

Performance of a real‐time pseudodynamic test system considering nonlinear structural response

AbstractThis paper presents the implementation details of a real‐time pseudodynamic test system that adopts an implicit time integration scheme. The basic configuration of the system is presented. Physical tests were conducted to evaluate the performance of the system and validate a theoretical system model that incorporates the dynamics and nonlinearity of a test structure and servo‐hydraulic actuators, control algorithm, actuator delay compensation methods, and the flexibility of an actuator reaction system. The robustness and accuracy of the computational scheme under displacement control errors and severe structural softening are examined with numerical simulations using the model. Different delay compensation schemes have been implemented and compared. One of the schemes also compensates for the deformation of an actuator reaction system. It has been shown that the test method is able to attain a good performance in terms of numerical stability and accuracy. However, it has been shown that test results obtained with this method can underestimate the inelastic displacement drift when severe strain softening develops in a test structure. This can be attributed to the fact that the numerical damping effect introduced by convergence errors becomes more significant as a structure softens. In a real‐time test, a significant portion of the convergence errors is caused by the time delay in actuator response. Hence, a softening structure demands higher precision in displacement control. Copyright © 2007 John Wiley & Sons, Ltd.

Seismic Performance of Square High-Strength Concrete Columns in FRP Stay-in-Place Formwork

The use of high-strength concrete (HSC) in seismically active regions poses a major concern because of the brittle nature of the material. The confinement requirements for HSC columns may be prohibitively stringent since they require proportionately greater confinement than columns of normal-strength concrete. An alternative to conventional confinement reinforcement is the use of fiber reinforced polymer (FRP) casings, in the form of a stay-in-place formwork. This paper investigates the use of stay-in-place FRP formwork as concrete confinement reinforcement for HSC columns with square cross sections. Large scale HSC building columns, encased in FRP casings, were tested under simulated seismic loading. The columns had 270 mm square sections and concrete strengths up to 90 MPa. The casings were manufactured from carbon FRP and epoxy resin. The unique aspects of the test program were the introduction of the corner radius as a test parameter, and the presence of internally placed FRP crossties, integrally built with column casings, to improve the effectiveness of concrete confinement. Results indicate that the deformation capacity of HSC columns can be improved significantly by using FRP casings. The results further indicate that the confinement effectiveness of columns is significantly affected by the corner radius of casings. Additionally, the confinement efficiency can be improved with the use of FRP crossties. The columns developed inelastic drift capacities of up to 11%, demonstrating the usefulness of FRP stay-in-place formwork in improving deformability of HSC columns.

Optimal seismic performance-based design of reinforced concrete buildings using nonlinear pushover analysis

Performance-based design using nonlinear pushover analysis, which generally involves tedious and intensive computational effort, is a highly iterative process needed to meet designer-specified and code requirements. This paper presents an effective computer-based technique that incorporates pushover analysis together with numerical optimization procedures to automate the pushover drift performance design of reinforced concrete (RC) buildings. Steel reinforcement, as compared with concrete materials, appears to be the more cost-effective material, that can be effectively used to control drift beyond the occurrence of first yielding and to provide the required ductility of RC building frameworks. In this study, steel reinforcement ratios are taken as design variables during the design optimization process. Using the principle of virtual work, the nonlinear inelastic seismic drift responses generated by the pushover analysis can be explicitly expressed in terms of element design variables. An optimality criteria technique is presented in this paper for solving the explicit performance-based seismic design optimization problem for RC buildings. Two building frame examples are presented to illustrate the effectiveness and practicality of the proposed optimal design method.

Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads

AbstractThis paper presents an effective optimization technique for the elastic and inelastic drift performance design of reinforced concrete buildings under response spectrum loading and pushover loading. Attempts have been made to develop an automatic optimal elastic and inelastic drift design of concrete framework structures. The entire optimization procedure can be divided into elastic design optimization and inelastic design optimization. Using the principle of virtual work, the elastic drift response generated by the response spectrum loading and the inelastic drift response produced by the non‐linear pushover loading can be explicitly expressed in terms of element sizing design variables. The optimization methodology for the solution of the explicit design problem of buildings is fundamentally based on the Optimality Criteria approach. One ten‐story, two‐bay building frame example is presented to illustrate the effectiveness and practicality of the proposed optimal design method. While rapid convergence in a few design cycles is found in the elastic optimization process, relatively slow but steady and smooth convergence of the optimal performance‐based design is found in the inelastic optimization process. Copyright © 2004 John Wiley & Sons, Ltd.

Recent Findings from Phase V of the United States–Japan Cooperative Earthquake Research Program

Recent Findings from Phase V of the United States–Japan Cooperative Earthquake Research Program

Seismic Behavior of Composite Concrete Filled Steel Tube Column-Wide Flange Beam Moment Connections

The results of an experimental research study involving the testing of ten full-scale moment resisting connections under simulated seismic loading conditions are presented. Each test specimen modeled the interior joint of a moment resisting frame consisting of square concrete filled steel tube columns and wide flange steel girders, where energy dissipation was designed to occur either primarily in the beams or in the connection panel zone during a severe earthquake. The results of the study indicate that moment resisting connection details can be economically designed that enable more than 0.045 rad of inelastic story drift to develop under cyclic loading. These details include split-tee connections without a shear tab, weak panel zone connections, and extended tee connections. Panel zone shear yielding and local buckling are shown to be a ductile mode of response, with minimal strength deterioration occurring in the connection. The use of interior diaphragms in the column is shown to locally stiffen the joint, but also lead to strain concentrations and fracture of the beam flanges at their weld access holes. Furthermore, strain concentrations develop at connection details that lack a gradual transition in geometry and result in a reduction in connection ductility.

Seismic performance of steel moment frames with reduced beam sections

This paper presents an investigation on the seismic performance of steel moment-resisting frames with reduced beam sections (RBS), and addresses the design issues related to the RBS frames. Nonlinear static and time history analyses of eight frames (three- and ten-story steel moment frames with different RBS configurations are conducted. The 1940 Imperial Valley (El Centro station, 0.32 g PGA) and the 1994 Northridge (Newhall station, 0.59 g PGA) ground motions factored to 0.3 g and 0.6 g are used in the time-history analyses. Global and local performances of the frames are discussed in terms of plastic deformation, inelastic drift ratio, as well as strength demand. The quantitative indices, such as flange reducing rate and location of the RBS, are recommended for seismic design practice.

Seismic performance of cover-plate strengthened frames

This paper summarizes results and conclusions of a case study of cover-plate strengthened frames with two, five and ten stories. The study begins with the comparison of a test results from a cover-plate connection assembly specimen with results using a detailed nonlinear finite element analysis (FEA) model. With a strong correlation to the test specimen, more FEA models are generated and analysed in order to (a) examine the local behavior of cover-plate profiles; various and (b) compare their performance to the simplified structural models that will be used in the static and time history analysis of those of the frames. With the reliable simple structural model of the cover-plate connection assemblies capturing both elastic and inelastic behavior, such a model is incorporated into frames to perform nonlinear static and time history analyses. Nine frames (two-, five- and ten-story steel moment frames with and without a cover plate) are the designed for the study. For comparative purposes, the 1940 Imperial Valley (El Centro station, 0·32g PGA) and the 1994 Northridge (Newhall station, 0·59g PGA) ground motions factored to 0·3 and 0·6g are used in time-history analyses. Global and local performance of frames are discussed in terms of plastic deformation distribution, story shear force and inelastic drift ratio. Copyright © 1999 John Wiley & Sons, Ltd.

Circular High-Strength Concrete Columns under Simulated Seismic Loading

Behavior of high-strength concrete columns with concrete strengths of up to 90 MPa was investigated experimentally. Large-scale columns were tested under different levels of constant axial compression and incrementally increasing lateral deformation reversals. The columns had a circular cross section and circular transverse reinforcement. Different volumetric ratios and grades of steel were used to confine the core concrete. The results indicate that the deformability of high-strength concrete columns can be improved significantly through confinement. Inelasticity drift capacity of columns can be improved to levels well beyond those usually expected during strong earthquakes. The improvements can be achieved with volumetric ratios of confinement. inelastic drift capacity of columns can be improved to levels well beyond those usually expected during strong earthquakes. The improvements can be achieved with volumetric ratios of confinement steel that are typically used for normal-strength concrete columns, provided that higher grades of steel are used. Furthermore, analytical techniques commonly employed for analysis of normal-strength concrete columns can also be used for high-strength concrete columns, if proper material models are incorporated, reflecting stress-strain characteristics of high-strength concrete and reinforcing steel.

Inelastic Deformation of One-Story Asymmetric-Plan Systems Subjected to Strong Earthquake Ground Motions

Inelastic response of one-story building systems with eccentricity is investigated based on linear static and nonlinear dynamic analyses using asymmetric-plan systems simultaneously subjected to strong earthquake ground motions in the x- and y-directions. Inelastic story drift ratios in the x- and y-directions are evaluated considering shear and torsional strength capacity and the corresponding shear force and torsional moment acting in each direction of asymmetric-plan system. Response analysis of one-story systems with one-axis plan asymmetry and varying parameters such as uncoupled lateral vibration period, torsion-to-lateral frequency ratio, rigidity and strength eccentricities, and shear and torsional strength capacity ratio is carried out and compared with those of corresponding one-story symmetric systems. In addition, inelastic response of one-story building systems with two-axes eccentricity including a L-shape asymmetric-plan system is also investigated.

Seismic [formula omitted] effects in mesium height moment resisting steel frames

An analytical investigation of the P- Δ effects in medium height steel moment resisting frames to selected earthquake motions is reported. The frames with various design drifts and fundamental natural periods were designed according to the load provisions for New Zealand seismic risk zone A of the Draft Code of Practice for General Structural Design and Design Loading for Buildings, DZ4203. The effect of strength degradation was investigated. Dynamic magnification factors for the member forces and displacement are also presented. Limits for the maximum plastic hinge rotation, inelastic drift, curvature ductility, displacement ductility and prediction of maximum plastic hinge rotation based on the inter-storey drift are suggested.

P-delta effects in medium height moment resisting steel frames under seismic loading

An analytical investigation of the P-delta effects in medium height steel moment resisting frames excited by selected earthquake motions is reported. The frames with various design drifts and fundamental natural periods of free vibration were designed according to the loadings provisions for New Zealand's highest seismic risk zone (Wellington) of the Draft Code of Practice for General Structural Design and Design Loading for Buildings, DZ4203 [10] as issued as a "Draft for Comment" in May 1986. The effect of strength degradation was investigated. Dynamic magnification factors for the member forces and displacement were also observed. Limits for the maximum plastic hinge rotation, inelastic drift, displacement magnification and prediction of maximum plastic hinge rotation based on the inter storey drift are suggested.