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An explicit design procedure of cross-sections of framed tube high-rise buildings via an inverse problem approach is presented. In the formulation, interstory drift ratios and net deformations of beams are prescribed. The derived expressions clearly express the three-dimensional effect (tube effect) from the orthogonal frame. The expressions are helpful for the preliminary design because cross-sections are rationally and rapidly provided for a set of target deformations without trial-and-error repetition. In the proposed design method, a 2×2-bay basic model under a set of static horizontal loads is designed at first. Then, this 2×2-bay model is transformed into a multi-bay model. The second moments of cross-section of the multi-bay model can be obtained based on the equivalence of the responses of those two models in the case where the elongation of columns is neglected. In addition, assumptions of axial strains of columns are introduced to obtain the equivalent parameters of cross-sections of the 2×2-bay model. It is demonstrated through numerical examples that the proposed method has reasonable accuracy.

This paper aims to obtain an optimal viscous damper placement for a shear building model using H^∞ optimization. The H^∞ norm of the transfer function matrix of interstory drifts is adopted as the objective function. Since it represents the magnitude of vibration transfer, one can attenuate the gain of the frequency response by minimizing this norm. The sequential quadratic programming (SQP) method is employed for optimization. The proposed method is applicable to a multi-story shear building model as well. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

A simple evaluation method of building resilience is proposed, and the resilience of elastic-plastic high-rise buildings is evaluated under resonant long-duration ground motions. The concept of availability is incorporated into the evaluation model of the building resilience, which was proposed in the previous paper. Not only in-building components but also external factors such as lifelines and redundancy of facility systems are considered in the evaluation model. Based on the evaluation model, the following probabilistic indices are formulated: (1) the expected value of the total recovery time, (2) the expected values of the availability of the structural frame, facilities, and non-structural components just after an earthquake event, and (3) the maximum likelihood recovery curves (MLRCs) of the structural frame, facilities, and non-structural components. Numerical examples are presented for evaluating the resilience of elastic-plastic high-rise building models under a pseudo-multi impulse (PMI), which substitutes for resonant long-duration ground motions. Finally, the influences of the passive viscous dampers, the redundancy of facility systems, and the uncertainty of manpower to repair the components on the building resilience are clarified through the results of numerical examples.

An input velocity adjustment method of the critical double impulse (DI) is presented for efficient design of viscous dampers for elastic-plastic moment frames. The input velocity is adjusted so that the input energy to the lowest eigenmode under the critical DI is equal to those under the selected recorded ground motions. This adjustment makes the critical DI work as the active earthquake. The response bounding property of the critical DI is supported by, (1) the multi-modal property of the critical DI, (2) the usual excitation of the lowest mode response under recorded ground motions, (3) the large proportion of the instantaneous input energy to the total input energy in the critical DI. The proposed method can treat not only pulse-like near-fault ground motions but also ground motions of random nature. To validate the proposed method, the input energies and the maximum interstory drifts under the recorded ground motions and the critical DI with the adjusted input velocity are investigated for elastic single-degree-of-freedom (SDOF) models, elastic proportionally damped MDOF models, and elastic-plastic proportionally damped MDOF models. The optimization method presented in the previous paper is extended so that the critical DI can be treated for the design of viscous dampers for elastic-plastic moment frames.

A new model reduction method is presented for moment-resisting frames with viscous dampers. The proposed method considers (1) the interactive effect of added damping between the horizontal-vertical directions and (2) the direct effect with regard to the vertical direction different from the conventional static condensation method. When brace-type dampers are treated, these effects cannot be neglected originally. The proposed method gives a better correspondence of the fundamental eigenmode with that of the non-reduced moment frame than the static condensation method. In addition, the proposed reduced model can accurately evaluate the maximum interstory drifts of the non-reduced moment frame. The proposed model reduction method is formulated in the frequency domain. The frequency dependency of the stiffness matrix and the damping matrix of the reduced model is investigated. The influences of the added damping matrix by viscous dampers on the natural circular frequencies, the damping ratios and the participation vectors are also investigated. Finally, it is demonstrated through a numerical example that the displacement-based optimization of the damper allocation can be accurately and rapidly conducted by using the reduced models throughout the optimization process.

In this study, a model for the evaluation of a building's resilience and recovery time is proposed, and a new method is developed for the optimal viscous damper placement for a targeted resilience. The features of this model are as follows: 1) building components are categorized into systems in view of their functionality, 2) recovery time is regarded as a function of the damage to building components and human resources for repairing the components, 3) the model is applicable to structural design. This design method uses a type of real-coded genetic algorithm (GA). The effective use of a constraint on the sum of the added damper damping coefficients enables an efficient search for the solution.

Approximate closed-form maximum interstory drifts under the critical pseudo-double impulse (PDI) are derived for undamped multi-story shear building models with bilinear hysteresis by using the proposed updated mode-controlled energy-based approach (UMEA). PDI was proposed in the previous paper to simulate the critical responses of elastic-plastic MDOF models under near-fault fling-step motions. Although a double impulse (DI) is treated as a ground motion, PDI is treated as a set of impulsive lateral forces. PDI excites only the fundamental-mode responses of elastic proportionally-damped MDOF models because the fundamental participation vector is applied to the influence coefficient vector of PDI. UMEA is a kind of displacement control analyses, and the displacement increment, which is proportional to the fundamental mode evaluated by the tangent story stiffnesses, is given to the model. It is demonstrated that UMEA effectively captures the main characteristics of the maximum interstory drifts under the critical PDI and the critical one-cycle sine wave because most of the kinetic energy, which the fundamental mode has just before yielding, is given to the plastic fundamental mode just after yielding except for the case that the post-yielding stiffness is almost zero. The use of UMEA leads to much more efficient estimation of the maximum interstory drifts than the time-history response analysis because UMEA requires only 2N-time evaluations of the elastic and plastic fundamental modes at most for N-story shear mass models with bilinear hysteresis. It is shown through numerical examples that the maximum interstory drifts under the critical PDI and the corresponding one-cycle sine wave correspond well to those evaluated by the proposed method. It is also shown that the correspondence of the responses of elastic-plastic MDOF models under recorded near-fault motions and the estimated responses by the proposed method is fairly good.

A new concept of a “lower-bound transfer function (LBTF)” and a new frequency-domain optimal damper design method are presented. LBTF expresses an ideal performance for response control in the frequency domain under a constant sum of added damping coefficients (or the total cost of dampers). The effectiveness of the damper design for each mode can be captured visually through plotting the transfer function amplitudes of the model and the LBTF. An efficient generation method of LBTFs is also proposed. The proposed design method provides designs with multimodal adaptability (effective for multimodes). It does not require much computational load to implement the method since the optimization is conducted in the frequency domain, and the first-order or second-order sensitivities of the objective function can be derived analytically. The proposed design and the fundamental mode optimal damper placement are compared for shear-mass systems and moment-resisting frames through the transfer functions and the incremental dynamic analysis (IDA). It is demonstrated that the proposed designs effectively reduce the floor acceleration responses and the elastic deformation responses. Moreover, it is shown that the proposed designs can effectively reduce the elastic–plastic responses although the optimization is conducted for linear elastic models.

A new method of optimal damper design is presented for elastic–plastic planar frame structures under large-amplitude earthquake ground motions. The transformation of a moment frame into the 1st-mode equivalent shear mass system leads to an efficient search of the optimal damper placement along the building height for the elastic–plastic moment frame. In the optimization procedure, a linear elastic bare frame is transformed into the 1st-mode equivalent shear mass system first. Then the optimization of the damper placement is conducted for the elastic shear mass system. After that, the damped shear mass system is inversely transformed into the elastic–plastic moment frame with the added dampers. This inversely transformed damper system in the moment frame is employed as an initial design and the local search-based optimization is conducted for the efficient distribution of dampers not only along the building height, but also among the different bay. The proposed method greatly reduces the computational task in the whole optimization procedure because only a limited number of time-history response analyses is required for elastic–plastic moment frames. It is demonstrated through numerical examples that the proposed method efficiently provides the damper designs with high accuracy. Finally, the importance of using the large-amplitude ground motions for damper optimization is demonstrated through the incremental dynamic analysis (IDA) for the optimally designed models.

The viscous-hysteretic hybrid (HVH) damper system recently introduced by one of the authors has a clear property that, when the hysteretic dampers with gap mechanism become active (stiffness element starts working), the acceleration of building frames with this damper system as a stopper attains large values in spite of the advantageous feature to prevent excessive deformation. It is therefore desired that both the maximum interstory drift and the maximum acceleration exhibit an acceptable value with appropriate compromise. The double impulse as a simplified version of one-cycle sine wave as a representative of the main part of near-fault ground motions can simulate the maximum interstory drifts properly. However, it cannot simulate the maximum accelerations due to its impulsive nature. In this case, the sine wave corresponding to the double impulse can play an important role in the reliable simulation of the maximum accelerations. Even in such circumstance, the analysis using the double impulse is important because it enables to obtain the critical timing of the input, i.e. the nonlinear resonant frequency of the sine wave without repetition. The investigations on the criticality of the sine wave corresponding to the critical double impulse show that the critical timing of the double impulse leads to the nonlinear resonant frequency of the sine wave in view of the maximum interstory drift, the maximum top acceleration and the maximum relative acceleration for the constant input acceleration and the constant input velocity except for some cases. It is demonstrated finally that the index in terms of the maximum interstory drift and the maximum acceleration can be introduced as an appropriate parameter for deriving the optimally compromised gap quantity of hysteretic dampers with gap mechanism for various input velocity levels and various hysteretic damper stiffness ratios.

The optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading is of great concern in the structural design of building structures. The research started around 1980 and many investigations have been conducted. A comprehensive review on this subject is made in this article. After the description of essential features of the optimal design problem of nonlinear building structures under earthquake ground motions, analysis types of optimization problems are explained and the significance of the dynamic pushover analysis is discussed from the viewpoint of analysis of limit states under earthquake ground motions of magnitude larger than the code-specified level. Then, the categorization by the response of frames and dampers was made. In this categorization, several subjects are discussed first: 1) Optimal design of bare nonlinear building frames under seismic loading, 2) Optimal design of nonlinear dampers for elastic building frames under seismic loading, 3) Optimal design of linear dampers for nonlinear building frames under seismic loading, 4) Optimal design of nonlinear building frames with specified nonlinear dampers under seismic loading, 5) Optimal design of nonlinear dampers for specified nonlinear building frames under seismic loading, 6) Simultaneous optimization of elastic-plastic building structures and passive dampers. Finally, the classification of researches in view of solution strategies is conducted for providing another viewpoint.

The critical responses are investigated for a high-rise building with a deformation-concentration seismic control system under double and multi impulses representing pulse-type and long-duration ground motions, respectively. The critical responses were studied for an elastic-plastic multi-degree-of-freedom (MDOF) shear building model under a double impulse and a multi impulse in the previous papers. However, it seems difficult to derive the critical response for a realistic three-dimensional (3-D) nonlinear frame model with a deformation-concentration seismic control system under such double and multi impulses. The criteria on the criticality of the double and multi impulses for the elastic-plastic MDOF shear building model derived in the previous research are extended to this realistic controlled 3-D frame model by regarding the sum of base story shear forces of both main and sub buildings as a key quantity. In the analysis, the concepts of “Double Impulse Pushover (DIP)” and “Multi Impulse Pushover (MIP)” introduced before are used effectively for clarifying the progressive performances for the increasing input level. The analyses of total input energy, frame hysteretic energy and damper dissipation energy are conducted and the criticality of the input derived based on the above-mentioned criteria is investigated in detail.

A new method of robust damper design is presented for elastic-plastic multi-degree-of-freedom (MDOF) building structures under multi-level ground motions (GMs). This method realizes a design that is effective for various levels of GMs. The robustness of a design is measured by an incremental dynamic analysis (IDA) curve and an ideal drift response curve (IDRC). The IDRC is a plot of the optimized maximum deformation under a constraint on the total damper quantity vs. the design level of the GMs. The total damper quantity corresponds to the total cost of the added dampers. First, a problem of generation of IDRCs is stated. Then, its solution algorithm, which consists of the sensitivity-based algorithm (SBA) and a local search method, is proposed. In the application of the SBA, the passive added dampers are removed sequentially under the specified-level GMs. On the other hand, the proposed local search method can search the optimal solutions for a constant total damper quantity under GMs’ increased levels. In this way, combining these two algorithms enables the comprehensive search of the optimal solutions for various conditions of the status of the GMs and the total damper quantity. The influence of selecting the type of added dampers (oil, hysteretic, and so on) and the selection of the input GMs on the IDRCs are investigated. Finally, a robust optimal design problem is formulated, and a simple local search-based algorithm is proposed. A simple index using the IDRC and the IDA curve of the model is used as the objective function. It is demonstrated that the proposed algorithm works well in spite of its simplicity.

A pseudo-double impulse (PDI) is proposed as an extension of the ordinary double impulse (DI) as a substitute of a one-cycle sine wave. PDI is treated as a set of impulsive lateral forces while the ordinary DI was introduced as an impulsive ground acceleration. The deformation and acceleration responses of multi-degree-of-freedom (MDOF) models under DI largely exceed those under the corresponding one-cycle sine wave as a main part of a near-fault ground motion. This is because DI has multiple frequency components and the higher-mode responses are excited. While the influence coefficient vector of the ordinary DI consists of 1 at every component, the influence coefficient vector of PDI is set to be proportional to the undamped fundamental natural mode. Therefore, the fundamental-mode response is mainly excited and the higher-mode responses are hardly excited by PDI. The displacement responses, the velocity responses and the input energy under DI and those under PDI are derived here for both elastic proportionally and non-proportionally damped MDOF models. The critical timing under PDI is also derived. The critical timing can be obtained by the time-history response analysis without repetition. It is demonstrated through the time-history response analysis that the distributions of interstory drifts and floor accelerations under the critical PDI correspond well to those under the critical one-cycle sine wave. Moreover, it is shown that, as far as the input level is large, the critical input period of PDI and that of the one-cycle sine wave correspond well. Since this procedure is not limited to elastic models, the proposed procedure helps to efficiently estimate the critical responses under the one-cycle sine wave for elastic-plastic MDOF models. Finally, the responses under recorded near-fault ground motions are compared with those under PDI. It is shown that the correspondence of the response under PDI and that under the recorded ground motions is fairly good althoug