Dual‐plastic hinge design concept for reducing higher‐mode effects on high‐rise cantilever wall buildings

This paper explores the notion of detailing reinforced concrete structural walls to develop base and mid‐height plastic hinges to better control the seismic response of tall cantilever wall buildings to strong shaking. This concept, termed here dual‐plastic hinge (DPH) concept, is used to reduce the effects of higher modes of response in high‐rise buildings. Higher modes can significantly increase the flexural demands in tall cantilever wall buildings. Lumped‐mass Euler–Bernoulli cantilevers are used to model the case‐study buildings examined in this paper. Buildings with 10, 20 and 40 stories are designed according to three different approaches: ACI‐318, Eurocode 8 and the proposed DPH concept. The buildings are designed and subjected to three‐specific historical strong near‐fault ground motions. The investigation clearly shows the dual‐hinge design concept is effective at reducing the effects of the second mode of response. An advantage of the concept is that, when combined with capacity design, it can result in relaxation of special reinforcing detailing in large portions of the walls. Copyright © 2009 John Wiley & Sons, Ltd.     

Higher mode effects in frame pin‐supported wall structure by using a distributed parameter model

Frame pin‐supported wall structure is a kind of rocking structure, which releases constraints at the bottom of the wall. The wall is affiliated to the frame and can rotate around the hinge. Previous studies have investigated seismic performance (such as deformation pattern and plastic hinge distribution) of frame pin‐supported wall structure. Strength demand of this system was investigated through static pushover analysis. However, dynamic characteristics, especially higher mode effects, remain to be quantified. As demonstrated in several researches, higher mode effects have non‐negligible effects on seismic response. For this purpose, a distributed model for analyzing higher mode effects in frame pin‐supported wall structure was proposed, where the pin‐supported wall and the frame were simplified as a bending beam and a shear beam, respectively. The model was solved by differential equations derived from equilibrium and compatibility. Displacement and inner force distribution of frame pin‐supported wall structure in higher modes were quantified according to the model. Influence of critical parameters, such as wall stiffness and structure period, was assessed on higher mode effects. It was demonstrated that response in higher modes cannot be neglected in the design of frame pin‐supported wall structure. Capacity design based on the fundamental mode is not conservative, especially in the wall. Furthermore, pin‐supported walls tend to force the frame to vibrate in the rocking mode and suppress higher mode effects in the frame. Copyright © 2016 John Wiley & Sons, Ltd.     

Approximate modal decomposition of inelastic dynamic responses of wall buildings

Two approximate methods for decomposing complicated inelastic dynamic responses of wall buildings into simple modal responses are presented. Both methods are based on the equivalent linear concept, where a non‐linear structure is represented by a set of equivalent linear models. One linear model is used for representing only one vibration mode of the non‐linear structure, and its equivalent linear parameters are identified from the inelastic response time histories by using a numerical optimizer. Several theoretical relations essential for the modal decomposition are derived under the framework of complex modal analysis. Various numerical examinations have been carried out to check the validity of the proposed modal decomposition methods, and the results are quite satisfactory in all cases. Fluctuating bending moment and shear at any location along the wall height contributed by each individual vibration mode can be obtained. Modal contributions to shear and flexural strength demands, as well as the corresponding modal properties, under various seismic loading conditions can also be identified and examined in detail. Furthermore, the effects of higher vibration modes on seismic demands of wall buildings are investigated by using the modal decomposition methods. Several new insights into the complicated inelastic dynamics of multi‐story wall buildings are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

An experimental study of a damage‐controllable plastic‐hinge‐supported wall structure

The reinforced concrete (RC) shear wall serves as one of the most important components sustaining lateral seismic forces. Although they allow advanced seismic performance to be achieved, RC shear walls are rather difficult to repair once the physical plastic hinge at the bottom part has been formed. To overcome this, a damage‐controllable plastic hinge with a large energy dissipation capacity is developed herein, in which the sectional forces are decoupled and sustained separately by different components. The components sustaining the axial and the shear forces all remain elastic even under a rarely occurred earthquake, while the bending components yield and dissipate seismic energy during a design‐level earthquake. This design makes the behavior of the system more predictable and thus more easily customizable to different performance demands. Moreover, the energy dissipation components can be conveniently replaced to fully restore the occupancy function of a building. To examine the seismic behavior of the newly developed component, 3 one third‐scale specimens were tested quasi‐statically, including 1 RC wall complying with the current design codes of China and 2 installed with the damage‐controllable plastic hinges. Each wall was designed to have the same strength. The experimental results demonstrated that the plastic‐hinge‐supported walls had a better energy dissipation capacity and damage controllability than the RC specimen. Both achieved drift ratios greater than 3% under a steadily increasing lateral force.     

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

A static predictor of seismic demand on frames based on a post‐elastic deflected shape

Predictors of seismic structural demands (such as inter‐storey drift angles) that are less time‐consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square‐root‐of‐sum‐of‐squares (SRSS) rule by taking a first‐mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post‐elastic first‐mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single‐degree‐of‐freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third‐mode response for long‐period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright © 2006 John Wiley & Sons, Ltd.     

Response of tall cantilever wall buildings to strong pulse type seismic excitation

This paper investigates the seismic response of tall cantilever wall buildings subjected to pulse type ground motion, with special focus on the relation between the characteristics of ground motion and the higher‐modes of response. Buildings 10, 20, and 40 stories high were designed such that inelastic deformation was concentrated at a single flexural plastic hinge at their base. Using nonlinear response history analysis, the buildings were subjected to near‐fault seismic ground motions and simple closed‐form pulses, which represented distinct pulses within the ground motions. Euler–Bernoulli beam models with lumped mass and lumped plasticity were used to model the buildings. The response of the buildings to the closed‐form pulses fairly matched that of the near‐fault records. Subsequently, a parametric study was conducted for the buildings subjected to three types of closed‐form pulses with a broad range of periods and amplitudes. The results of the parametric study demonstrate the importance of the ratio of the fundamental period of the structure to the period of the pulse to the excitation of higher modes. The study shows that if the modal response spectrum analysis approach is used — considering the first four modes with a uniform yield reduction factor for all modes, and with the square root of sum of squares modal combination rule — it significantly underestimates bending moment and shear force responses. A response spectrum analysis method that uses different yield reduction factors for the first and the higher modes is presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Blind modal identification of output‐only structures in time‐domain based on complexity pursuit

Output‐only modal identification is needed when only structural responses are available. As a powerful unsupervised learning algorithm, blind source separation (BSS) technique is able to recover the hidden sources and the unknown mixing process using only the observed mixtures. This paper proposes a new time‐domain output‐only modal identification method based on a novel BSS learning algorithm, complexity pursuit (CP). The proposed concept—independent ‘physical systems’ living on the modal coordinates—connects the targeted constituent sources (and their mixing process) targeted by the CP learning rule and the modal responses (and the mode matrix), which can then be directly extracted by the CP algorithm from the measured free or ambient system responses. Numerical simulation results show that the CP method realizes accurate and robust modal identification even in the closely spaced mode and the highly damped mode cases subject to non‐stationary ambient excitation and provides excellent approximation to the non‐diagonalizable highly damped (complex) modes. Experimental and real‐world seismic‐excited structure examples are also presented to demonstrate its capability of blindly extracting modal information from system responses. The proposed CP is shown to yield clear physical interpretation in modal identification; it is computational efficient, user‐friendly, and automatic, requiring little expertise interactions for implementations. Copyright © 2013 John Wiley & Sons, Ltd.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic performance of a 1 : 15‐scale 25‐story RC flat‐plate core‐wall building model

Earthquake simulation tests were conducted on a 1 : 15‐scale 25‐story building model to verify the seismic performance of high‐rise reinforced‐concrete flat‐plate core‐wall building structures designed per the recent seismic code KBC 2009 or IBC 2006. The following conclusions can be drawn from the test results: (1) The vertical distribution of acceleration during the table excitations revealed the effect of the higher modes, whereas free vibration after the termination of the table excitations was governed by the first mode. The maximum values of base shear and roof drift during the free vibration are either similar to or larger than the values of the maximum responses during the table excitation. (2) With a maximum roof drift ratio of 0.7% under the maximum considered earthquake in Korea, the lateral stiffness degraded to approximately 50% of the initial stiffness. (3) The crack modes appear to be a combination of flexure and shear in the slab around the peripheral columns and in the coupling beam. Energy dissipation via inelastic deformation was predominant during free vibration after the termination of table excitation rather than during table excitation. Finally, (4) the walls with special boundary elements in the first story did not exhibit any significant inelastic behavior, with a maximum curvature of only 21% of the ultimate curvature, corresponding to an ultimate concrete compressive strain of 0.00638 m/m intended in the displacement‐based design approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Generalized force vectors for multi‐mode pushover analysis of torsionally coupled systems

A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Modified consecutive modal pushover procedure for seismic investigation of one-way asymmetric-plan tall buildings

The effects of higher modes and torsion have a significant impact on the seismic responses of asymmetric-plan tall buildings.A consecutive modal pushover(CMP) procedure is one of the pushover methods that have been developed to consider these effects.The aim of this paper is to modify the(CMP) analysis procedure to estimate the seismic demands of one-way asymmetric-plan tall buildings with dual systems.An analysis of 10-,15-and 20-story asymmetric-plan buildings is carried out,and the results from the modified consecutive modal pushover(MCMP) procedure are compared with those obtained from the modal pushover analysis(MPA) procedure and the nonlinear time history analysis(NLTHA).The MCMP estimates of the seismic demands of one-way asymmetric-plan buildings demonstrate a reasonable accuracy,compared to the results obtained from the NLTHA.Furthermore,the accuracy of the MCMP procedure in the prediction of plastic hinge rotations is better than the MPA procedure.The new pushover procedure is also more accurate than the FEMA load distribution and the MPA procedure.     

Errors caused by peak factor assumptions in response‐spectrum‐based analyses

The modal combination rules commonly used in response spectrum analyses implicitly assume that the peak factor associated with the response quantity of interest is equal to the peak factors of the contributing modal responses. In this paper, we examine the validity of this assumption and demonstrate that it causes the modal combination rules to over‐represent the contribution of the higher modes of vibration to the total response and under‐represent the contribution of the lower modes. Consequently, a response‐spectrum‐based analysis can yield a biased estimate for the peak value of a response quantity when two or more well‐separated modal frequencies make significant contributions to the total response. To correct this potential bias in response‐spectrum‐based estimates, we develop a procedure for estimating the peak factors that is suitable to the response spectrum analysis calculations commonly used in the current design practice. Examples are presented to demonstrate the proper use and potential impact of the proposed procedure. Copyright © 2015 John Wiley & Sons, Ltd.     

The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions

This paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings subjected to bi-directional seismic ground motions taking the effects of higher modes and torsion into account. Multi-stage and single-stage pushover analyses are carried out in both X and Y directions. Inelastic seismic responses obtained by multi-stage and single-stage pushover analyses for X and Y directions are combined using the SRSS combination scheme. The final seismic responses are determined by enveloping the combined results of multi-stage and single-stage pushover analyses. To evaluate the accuracy of the proposed procedure, it is applied to two-way unsymmetric-plan tall buildings which include torsionally stiff and torsionally flexible systems. The results derived from the CMP procedure are compared with those from nonlinear response history analysis (NL-RHA), as a benchmark solution. Moreover, the advantages of the proposed procedure are demonstrated by comparing the results derived from the CMP to those from pushover analysis with uniform and fundamental effective mode distributions. The proposed procedure is able to accurately predict amplification or de-amplification of the seismic displacements at the flexible and stiff edges of the two-way unsymmetric-plan tall buildings by considering the effects of higher modes and torsion. The extended CMP procedure can accurately estimate the peak inelastic responses, such as displacements and storey drifts. The CMP procedure features a higher potential in estimating plastic hinge rotations at both flexible and stiff sides of unsymmetric-plan tall buildings under bi-directional seismic excitation when compared to the uniform and fundamental effective mode force distributions.     

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion,including its evaluation for tall buildings

The modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of modal pushover analysis using generic frames

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2003; 32:1795. The recently developed modal pushover analysis (MPA) has been shown to be a significant improvement over the pushover analysis procedures currently used in structural engineering practice. None of the current invariant force distributions accounts for the contribution of higher modes—higher than the fundamental mode—to the response or for redistribution of inertial forces because of structural yielding. By including the contributions of a sufficient number of modes of vibration (generally two to three), the height‐wise distribution of responses estimated by MPA is generally similar to the ‘exact’ results from non‐linear response history analysis (RHA). Although the results of the previous research were extremely promising, only a few buildings were evaluated. The results presented below evaluate the accuracy of MPA for a wide range of buildings and ground motion ensembles. The selected structures are idealized frames of six different heights: 3, 6, 9, 12, 15, and 18 stories and five strength levels corresponding to SDF‐system ductility factor of 1, 1.5, 2, 4, and 6; each frame is analysed for 20 ground motions. Comparing the median values of storey‐drift demands determined by MPA to those obtained from non‐linear RHA shows that the MPA predicts reasonably well the changing height‐wise variation of demand with building height and SDF‐system ductility factor. Median and dispersion values of the ratios of storey‐drift demands determined by MPA and non‐linear‐RHA procedures were computed to measure the bias and dispersion of MPA estimates with the following results: (1) the bias and dispersion in the MPA procedure tend to increase for longer‐period frames and larger SDF‐system ductility factors (although these trends are not perfect); (2) the bias and dispersion in MPA estimates of seismic demands for inelastic frames are usually larger than for elastic systems; (3) the well‐known response spectrum analysis (RSA), which is equivalent to the MPA for elastic systems, consistently underestimates the response of elastic structures, e.g. up to 18% in the upper‐storey drifts of 18‐storey frames. Finally, the MPA procedure is simplified to facilitate its implementation in engineering practice—where the earthquake hazard is usually defined in terms of a median (or some other percentile) design spectrum for elastic systems—and the accuracy of this simplified procedure is documented. Copyright © 2003 John Wiley & Sons, Ltd.     

A cantilever beam analogy for quantifying higher mode effects in multistorey buildings

This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.