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This paper presents a new strengthening method for existing frames by using outside sub-structures, namely, precast bolt-connected steel-plate reinforced concrete (PBSPC) frame-braces. The working principles, numerical methods, and design procedures are presented, and case studies are carried out. The simulation results were consistent with the results from previous experiments, indicating the effectiveness of the numerical model. The design objective and procedure were put forward, and during the process, a coefficient η that considers the precast influences was considered. A practical engineering retrofitting was performed based on the proposed numerical model and design process, where the structure was subjected to the design basis earthquake (DBE) and maximum considered earthquake (MCE). The analyses demonstrated that the structural demands were clearly reduced within the thresholds, and the inner force was transferred from the existing building to the external sub-structure after strengthening. The incremental dynamic analysis (IDA) and fragility curves were plotted, illustrating the greater reliability in structural capacity and the lesser possibility of structural damage with the new upgrading form.

This paper discusses the optimal height-wise distribution of supplemental viscous dampers in multistorey building structures. Seismic excitation is modeled as stochastic stationary process and response statistics for linear structural systems are obtained through state-space analysis. For nonlinear damper applications statistical linearization is employed to accommodate a similar, state-space formulation. Emphasis is placed on three practical design issues: (i) realistic quantification of damper upfront cost based on damper force capacity rather than on the damping coefficient; (ii) investigation of bracing configuration schemes anchored at non-consecutive floor levels; and (iii) consideration of the cost of column strengthening required to accommodate the additional axial loads due to the supplemental damping system. Five different cost-based objective functions are defined to address these issues and the impact of each of them on the optimal damper distribution is examined in detail. Adjustments for estimation of peak responses when statistical linearization is used are also discussed. The optimal design problem considers the structural performance as a constraint, requiring that a target vibration suppression be achieved through the damper addition. An extension to a multi-objective design optimization is also discussed, incorporating the vibration suppression level as additional objective. The proposed approach is illustrated considering an actual Chilean 26-storey building subjected to an excitation compatible with the Chilean seismic hazard. Results show that damper distributions optimized considering realistic cost assessments are more efficient (with respect to cost-based design objectives) than distributions optimized considering simplified criteria. It is also demonstrated that consideration of practical issues such as column strengthening and feasible damper force capacity have a considerable influence on the optimal distribution. Finally, results also show that further cost reductions can be achieved with braces anchored at non-consecutive floor levels, and that such reductions are consistent with predictions given by approximate analytical expressions.

Shape memory alloy (SMA) has emerged as an alternative to conventional steel reinforcement for improving the seismic performance of bridges during an extreme earthquake. This paper presents the probabilistic seismic risk assessment of concrete bridge piers reinforced with different types of SMA (e.g. Ni-Ti, Cu-Al-Mn, and Fe-based) rebars. To achieve this objective, the bridge piers are designed following a performance-based approach. Ground motions with different probable earthquake hazard scenarios at the site of the bridge piers are considered. Probabilistic seismic demand models are generated using the response parameters obtained from incremental dynamic analysis. Considering maximum drift and residual drift as demand parameters, fragility curves are developed for five different SMA-RC bridge piers. Finally, seismic hazard curves are generated in order to compare the mean annual rate of exceedance of different damage states of different bridge piers. It is observed that all the bridge piers perform according to the design objective, and the performance of SMA-RC piers is significantly affected by the type of SMA used. The results show that all the SMA-RC piers have very low probability of collapse at maximum considered earthquake level. It is found that the bridge pier reinforced with FeNCATB-SMA (SMA-3) performed better as compared to the other SMA-RC piers.

Current structural design methods mostly emphasize the short-term structural behavior while neglect the long-term performance, social effects and environmental impacts. To address these problems, the Life-Cycle Design (LCD) method considering environmental impacts and structural deterioration could be adopted within the design process to ensure that the structural performance satisfies various objectives. Due to the complexity and the long lifespan of engineering structures, as well as the lack of standardized design approach, studies and application of LCD that cover all the design objectives are limited. This paper proposes a hierarchical LCD method for concrete structures by combining traditional design with green design and other engineering aspects. The design process is divided into six levels that cover the aspects of structural safety and reliability, durability, economic efficiency, local environment, social impacts, and global environment. The proposed design method is then applied to a reinforced concrete highway bridge in marine environment for the purpose of illustration, and a comprehensive comparison between traditional design and the hierarchical LCD approach is made within six design levels. A brief discussion on the hierarchical LCD framework and the future works is presented before conclusions are made.

Over the last decades, performance-based design objectives have shifted towards damage control and continuity of operation after a design-level earthquake. In this context, the advantages of rocking have been applied to the development of a family of self-centring systems that can sustain large lateral deformations without noticeable damage. However, the bending moments and shear forces in uplifting structures can increase significantly due to the effects of higher modes, an issue to which timber structures are particularly prone. This paper assesses the seismic response of post-tensioned timber rocking walls combined with inerters as a means to control the rotation amplitude and suppress higher-mode effects on the system. To this end, a representative set of three post-tensioned rocking walled structures, comprising 3, 6 and 9 storeys, are designed following direct-displacement based design procedures. A simplified method to pre-dimension the inerter device is proposed and used to design a set of ball screw and gear inerters, with and without clutches. The performance of bare and protected structures with different levels of apparent mass ratios is assessed and compared considering a set of 7 records consistent with the displacement design spectrum. Special attention is paid to the resisting force developed in the inerter and the mechanism to transfer it safely to the structural diaphragm. Finally, a detailed performance-based assessment is conducted considering a database of 202 pulse-like ground motion records. It is concluded that the innovative combination of inerters and rocking is an efficient way to improve the seismic control of self-centring structures.

Existing self-centering braces are easily affected by machining errors, and the initial stiffness of the braces will obviously be less than the theoretical value, which is unfavourable for the seismic design and dynamic response control of the structure. Based on a theoretical analysis, the idea of using a rubber end plate to reduce the influence of machining errors is proposed in this paper, and the configuration of a self-centering buckling-restrained brace with rubber end plates (SC-BRB-REP) is formed. The quasi-static test shows that the SC-BRB-REP can not only effectively control the residual deformation but also substantially improve the ability to control the initial stiffness of the brace, and the difference between the actual initial stiffness and the theoretical initial stiffness is less than 8%. The seismic design process of the SC-BRB frame is established based on the concept of direct displacement-based design (DDBD). Through the hysteretic behaviour research of the brace and the dynamic time-history analysis of the structure, it is evident that the reduction in the initial stiffness of the brace will lead to the reduction in the bearing capacity, thus increasing the seismic response of the structure and even exceeding the expected design objective. The SC-BRB-REP improves the ability to control the initial stiffness, and its structural design parameters and actual seismic response are basically consistent with the expectations, which effectively improves the structural design accuracy.

In contrast to the single design objective associated with force-based design approaches of different seismic force resisting systems (SFRSs), performance-based seismic design (PBSD) allows the selection of more than one design/performance objective. Each performance objective is linked to a tolerable risk level associated with the considered SFRS experiencing a specific damage at a specified seismic hazard level (presented in the form of fragility curves). Similar to other SFRSs, damage of reinforced masonry structural wall (RMSW) SFRSs can be linked to their lateral displacements/drifts. As such, this study focuses on using a multivariate data analysis techniques, to develop a RMSW load-displacement (backbone) model. The backbone model is calibrated using a database of RMSW experimental test results, and the model is further utilized to investigate the influence of the wall geometrical and mechanical characteristics on altering the displacement of RMSW corresponding to different performance levels. These analysis results are subsequently used to develop RMSW seismic fragility bands to facilitate visualizing the risk (losses) associated with the resulting range of displacement (drift) demands, when the different RMSW ranges of characteristics are considered. The developed fragility bands are compared to the individual fragility curves currently adopted by the Federal Emergency Management Agency, FEMA P-58 pre-standards, Seismic Performance Assessment of Buildings. This comparison shows that the developed fragility bands significantly deviate from the individual fragility curves currently adopted by FEMA P-58 at each damage state. The developed backbone model and fragility-bands are expected to not only facilitate adoption of the RMSW SFRSs in the next generation of PBSD codes, but also to equip researchers and designers with a clear understanding of the different aspects governing RMSW systems seismic performance and the associated risk.

Seismic fragility was estimated for a controlled high-rise building using 200 kN magnetorheological (MR) dampers with direct performance-based design (DPBD) to assess seismic vulnerability and to validate the performance of the DPBD which was previously developed. The DPBD offers multiple control design layouts for various performance levels subjected to different hazard levels using multi-objective optimization approaches. These multiple control design layouts for the given performance levels need to be validated using random seismic excitations because those performance-based designs (PBD) had been devolved based on the specific strength of design objective earthquakes (i.e., hazard levels) from the DPBD. In order to evaluate those PBD cases using MR dampers, two different approaches for fragility estimation of the four PBD cases under two hazard levels are conducted: traditional approach using the overall maximum interstory drift and system reliability approach which considers multiple limit states associated with the maximum interstory drift for stories within the entire system. The results are compared using 41 earthquake ground motions. From this study, overall seismic fragility relations have been derived from extensive fragility analyses in terms of broad range of hazard levels for multiple performance levels which were achieved by new direct performance-based design using MR dampers. Moreover, it is observed that the multiple performance-based control design cases obtained from DPBD clearly show significant reduction in seismic vulnerability compared to the uncontrolled case. It also shows different seismic fragility estimates against seismic hazards reflecting the performance enhancement based on the initial objective of the DPBD. Based on the results, the system reliability approach can identify the stories that have close interstory drifts to the overall maximum value allowing for more accurate estimates of the seismic fragility of multi-story buildings.

Direct performance-based design methodology that incorporates traditional performance-based design and semi-active smart damping devices (i.e., magnetorheological (MR) damper) has been investigated through the application of multi-objective optimization. This design method achieves multiple objectives in which cost and efficiency are simultaneously optimized to achieve multiple performance levels subjected to multiple hazard levels. For numerical study, large-scale 200 kN MR dampers have been installed in a 9-story moment-resisting frame building to carry out multi-objective optimization using genetic algorithm. Minimum interstory drift during through nonlinear time history analysis and minimum number of MR dampers installed are considered as performance-based design objectives. Several MR damper location layouts have been obtained through the optimization. Nonlinear time history analyses have been carried out to evaluate performance of each MR damper device layout.

Structural systems are subject to uncertainties due to variability in many hard-to-control noise factors, which include external loads, material properties, and construction workmanship. Traditional structural design methodologies, although clearly recognizing the presence of uncertainty, omit robustness against the effects of uncertainty in the design process. First, if the actual uncertainties in the design process are underestimated, the design may fail to satisfy safety requirements. Second, to guarantee safety in the presence of high variability of the system response, the structural designer may be forced to choose an overly conservative, thus inefficient and costly design. When robustness against uncertainty is not treated as one of the design objectives, the trade-off between over-design for safety and under-design for cost-savings is exacerbated. This manuscript demonstrates that safe and cost-effective structural engineering designs maybe achieved by implementing Robust Design concepts originally developed in manufacturing engineering to consider robustness against uncertainty. This manuscript presents an optimization-based methodology for the application of Robust Design principles to structural design and demonstrates its application on an academic problem involving design of a reinforced-concrete frame.

Compared to structural base isolation, floor isolation is a more cost-effective and efficient means for seismic protection of vibration-sensitive equipment in a building structure. In this study, a multi-functional floor isolation system (FIS) that consists of several variable-stiffness sliding isolators, called polynomial friction pendulum isolators (PFPIs), is proposed and studied experimentally and numerically. Due to its variable-stiffness nature, the proposed PFPI-FIS is able to achieve multiple design objectives. This paper also demonstrates the procedure to design a prototype PFPI-FIS which meets the desired dual performance objectives for two-level seismic loads. The shaking table tests verify that the prototype system possesses the desired hysteretic property with variable stiffness, and the measured responses match very well with the simulated ones. Moreover, by considering ten ground motions that represent earthquakes with different spectral contents, the seismic responses of the prototype PFPI-FIS under these ground motions with different intensity level are simulated extensively. The simulated results demonstrate that the isolation performance of the PFPI-FIS does comply with the designated dual performance objectives, which yield either acceleration or displacement control depending on the earthquake intensity and isolator drift.

Presented in this paper is an optimal capacity design method for steel building frameworks by adopting a nonlinear response history analysis procedure as the evolution tool for the structures under extreme earthquake loading. Minimum structural weight, minimum seismic input energy, and maximum hysteretic energy of fuse members are identified as design objectives. The design constraints include plastic deformation limit on every frame member and total deformation limit on each inter-story drift. The design optimization method employs a multi-objective genetic algorithm to search for optimal member section sizes from among commercially available steel section shapes. The design method is illustrated in details for a three-story eccentrically-braced steel frame.

A preference-based optimal design approach for the actively controlled adjacent structures is proposed in this study. For the vibration control of connected adjacent structures subject to earthquake excitations, there exist many objective functions that are in conflicts with each other. It involves suppression of dynamic responses of the two structures and simultaneous minimization of control efforts such as control force, power and energy. Conventional optimal design technique has some difficulties in designing well-balanced control system between multiple objectives of performance and cost so as to exhibit the best performance on reducing incompatible responses of the coupled system with minimum control efforts. In the proposed method, the concept of degree of desirability and the preference function are introduced. By using the designers’ preference, each design objective is aggregated and multi-objective optimization problem is formulated as finding the best compromising solution between structural control performance and control requirements. It is demonstrated in numerical example that the proposed approach is able to successfully mitigate the seismic impacts on both buildings by effectively utilizing and balancing the required control resources. As a result, the proposed system shows superior control performance to the conventionally designed control system in spite of using smaller control force, power and energy.

This paper compares the simulation results of three methods of using the commercial finite element package ABAQUS to model the very large deflection behaviour of steel structures with realistic endplate joints in fire. The results of a set of fire tests on restrained steel beam–column assemblies were used to check the accuracy of these different modelling methods. In the first modelling method, the fire exposed structural members, including the connections, were simulated using detailed solid elements to enable detailed behaviour of the structure to be faithfully represented. In the second method, the unexposed segments of the columns were represented by conventional line (beam) elements, the joints were represented using springs (Connector Elements) based on the component based method, and the beam was modelled using solid elements. In the third method, the joints were modelled using springs as in the second method and the beam and columns were simulated using line (beam) elements. As expected, the detailed simulation method was extremely time-consuming, but was able to produce accurate results. The simulation results from the second and third methods contained some inaccuracy, but depending on the simulation objective, their simulation results may be acceptable. In particular, the third simulation method was very efficient, suitable for simulating complete frame structures under very large deflections in fire. This paper will compare results from the three different simulation methods for different parts of the structure, including the fire exposed beam, the connection components and the columns, through different stages of fire exposure, from initial exposure to fire to the development of catenary action in the beam. From these comparisons of simulation results, this paper will recommend appropriate methods of modelling steel framed structures with realistic joints for different design objectives.

This paper presents a robust method for semi-deterministic topology and geometry design of trusses supporting distributed loads, giving due considerations to the load domain. The load-bearing nodes are not treated as basic nodes and the number and location of these nodes are considered as design variables. These quantities affect both the truss and the distributed load domains. The method developed for the integrated design of trusses supporting distributed loads is based on introducing a new parameter that can be treated as an additional design objective or constraint in truss design problems. This parameter can be used as a reliable substitute for the load domain objectives in a semi-deterministic integrated design. A case study is carried out to demonstrate the efficiency of the proposed design method.

A robust stochastic design framework is discussed for design of mass dampers. The focus is on applications for the mitigation of the coupled heave and pitch response of Tension Leg Platforms under stochastic sea excitation. The framework presented fully addresses the complex relationship between the coupled dynamics of the platform, the stochastic excitation and the vibration of the dampers. Model parameters that have some level of uncertainty are probabilistically described. In this probabilistic setting, the system reliability is adopted as the design objective. Stochastic simulation is considered for evaluation of the system model response and the overall reliability performance. This way, all nonlinear characteristics of the structural response and environmental excitation are explicitly incorporated into their respective models. An efficient algorithm is discussed for performing the challenging stochastic design optimization. The ideas are illustrated in an application involving a tension leg platform with closely spaced frequencies for the heave and pitch degrees of freedom.

The robust reliability-based design of Tuned Liquid Column Dampers (TLCD) and Liquid Column Vibration Absorbers (LCVA) under earthquake excitation is studied. The design objective is the minimization of the probability of failure, where failure is defined as the first-passage of the dynamical system trajectory out of a hypercubic safe region in the space of the performance variables. These variables correspond to response characteristics of the system that are considered important. Versions of the approach are described for the case of a nominal model and the case considering model uncertainty. In the latter case the concept of robust probability of failure is employed which considers a set of possible models for the dynamic system. The nonlinear characteristics of the damper response are addressed by including the excitation intensity as an uncertain parameter in the system description. An analytical approximation is used for the reliability estimation that allows for computationally efficient, gradient-based design optimization. Numerical issues are discussed. The validity of the reliability approximation is checked by comparing the results to those derived through direct Monte Carlo simulation of the nonlinear model. Applications to dynamical systems with single and multiple degrees of freedom are presented. For the latter case, other standard control synthesis methods are also considered and significant differences are illustrated between them and robust reliability-based design. Although this study focuses on optimization of TLCDs and LCVAs, it shows the efficiency of the proposed methodology for other systems that also involve model uncertainty.

In this paper, some useful guidelines for designing tuned liquid column dampers (TLCDs) for damped single-degree-of-freedom structures under a white noise type of wind excitation are proposed as quick guidance for industrial practice. These guidelines contain two major parts that serve two respective purposes. One is the design table that provides the list of necessary optimal parameters as well as the corresponding response reduction to be used as the design reference. The other is the empirical formula for reliably predicting the basic properties of TLCDs, especially for head loss coefficients, to ensure the design objectives can be achieved. In the first part, the solutions of optimal parameters in the design table are obtained through numerical optimization, by which it is also found that for a given mass ratio and horizontal length ratio, using a uniform cross-section for all columns can always achieve the best performance. To construct the prediction formula in the second part, TLCD property tests using free vibration and harmonic forced vibration techniques via a shake table are performed and the experimental results thus calibrated are used. Consequently, a modified formula to predict head loss coefficients for TLCDs with sharp-edged elbows is proposed as a guideline for designers. Finally, an example of the TLCD design is demonstrated by following the guidelines presented.

In this study, a direct displacement design procedure for steel frames with buckling-restrained braces (BRBs) is presented. The proposed structure system is composed of a hinge-connected main structure, which is designed to remain elastic under seismic load, and BRBs resisting all lateral loads. At seismic event, the BRBs dissipate dynamic energy through stable hysteretic behavior. A displacement-based seismic design procedure is applied to model structures to check the applicability of the design procedure. Two artificial earthquake records are generated from a design spectrum, and the response spectra constructed based on the earthquake records are utilized in the design process. Time-history analyses are carried out to confirm that the maximum displacements coincide with the target displacements. The results show that the seismic performance of the 3- and 5-story model structures designed in accordance with the proposed method coincide well with the given design objectives.

The design objectives in current building codes address life safety, control damage in minor and moderate earthquakes, and prevent collapse in a major earthquake. However, the actual reliability of the design in achieving the objectives is not known. There is a general agreement among researchers and professionals that future seismic design needs to be based on achieving stated multiple performance objectives. Future seismic design practice will be based on explicit performance criteria that can be quantified, considering multiple performance and hazard levels. There are several challenges to be addressed before procedures for performance-based design can be widely accepted. The development in performance-based design in seismic engineering will be directed towards the definition of performance objectives, a general design methodology, issues of ground motion modeling, and demand and capacity evaluations.