Uniform Damage Distribution Research Articles

Seismic design of reinforced concrete buildings equipped with viscous dampers using simplified performance-based approach

Passive control systems, such as Fluid Viscous Dampers (FVDs), have gained significant consideration in the design of earthquake-resistant structures. However, simple analysis and design methods are scarce for more practical and feasible implementation. This study provides a simplified procedure for performance-based seismic design of Reinforced Concrete (RC) special moment resisting frame using nonlinear FVDs. It adopts an extended performance-based design approach, focusing on maximum displacement along with floor acceleration to control the overall behavior of the structure. The fundamental principle of the method is to achieve the fully stressed (effect of FVDs on response indices) design approach to place dampers, which is attained by placing dampers among the storeys where drifts exceed the pre-decided performance limits. Further, a uniform damage distribution concept is followed to maximize the dampers' capacity. This study examines a rectangular-shaped RC SMRF with dampers to get the required performance when subjected to design basis and maximum considered earthquake levels. To check the efficacy, the proposed method is contrasted with a practical design method and a standard placement method employed in previous studies for RC structures with dampers. The analysis shows that the structure meets the performance targets of the design basis and the maximum considered level of earthquake hazards using the proposed step-by-step procedure. The comparison with the other two methods confirmed that the structure with dampers improved seismic behavior with the suggested process. Structural engineers can refer to the proposed method for the design of RC buildings with FVDs.

Grain size and orientation affected deformation inhomogeneity and local damage of hot-deformed Al-Zn-Mg alloy

The forming defects at elevated temperature caused by the microstructural evolution such as grain size, crystal orientations are the critical issue that induced deformation inhomogeneity and local damage which severely limits the application of Al-Zn-Mg alloys in thin-walled structure manufacturing. In this study, the hot deformation behavior and microstructural evolution were investigated via hot stretching tests, electron backscatter diffraction (EBSD) and the transmission electron microscopy (TEM) characterization. Then, an integrated multiscale constitutive model coupled dislocation density based crystal plasticity (CP) model and phase field method (PFM) was established through the reconstructed configuration of deformation gradient emphasized on a damaged part. The coupled CP-PFM model was numerically implemented into Düsseldorf Advanced Material Simulation Kit (DAMASK) software. Subsequently, a set of virtual polycrystalline RVE models assigned with different average grain sizes and two types of RVE models with realistic crystal orientations were constructed from EBSD data. The experimental and simulation results of the Al-Zn-Mg alloy under hot tensile loading showed that the grain size refinement leads to the increase of grain boundary density, which leads to the rapid increase of dislocation density, uniform damage distribution and better work hardening ability. In addition, the coordination of the activation of different slip systems between adjacent grains will lead to the uneven distribution of dislocation density and local damage.

Multi-level performance-based seismic design optimisation of RC frames

Conventional structural optimisation techniques often result in unconventional structural configurations, unrealistic structural elements and ignore actual construction costs. This paper presents an effective performance-based optimisation framework for minimising initial material costs of realistic multi-storey reinforced concrete (RC) frames, while satisfying pre-determined performance targets under multiple seismic hazard levels as well as a set of practical design and construction constraints. A new low computational-cost optimisation method is proposed to directly control specific response parameters at both the element and structural levels (i.e. plastic rotation and inter-storey drift). For the first time, the concept of Uniform Damage Distribution (UDD) is adopted to simplify the complex design optimisation problem of RC buildings with multiple design variables in terms of section sizes and reinforcement ratios. The optimum design solution is achieved by gradually redistributing materials from strong to weak parts of the structure, aiming to fully exploit the material capacity. The efficiency of the proposed optimisation framework is then demonstrated in the optimum designs of 3-, 5-, 10- and 15-storey RC frames under a set of six spectrum-compatible earthquake records. The results indicate that compared to structures designed by current codes, optimum solutions required up to 20 % and 43 % less concrete volume and steel reinforcement weight, respectively. It is also noted that due to more efficient use of materials, optimum structures exhibited considerably lower global damage index (up to 88 %), less maximum inter-storey drift (up to 58 %), and less maximum plastic rotations (up to 78 %). Sensitivity analysis on earthquake record selection shows that using a single earthquake record may not lead to reliable design solutions, in particular for tall buildings, and hence a set of spectrum-compatible records should be used in the optimisation process. This research will lead to more economical and safe design of multi-storey RC structures in seismic regions by developing a practical multi-level optimisation method with low computational costs.

Seismic performance and damage assessment of CFDST frames with SBYC damper

Nowadays, the dual system consisting of moment resisting frame with energy dissipation devices was suitable to be employed for high-rise buildings in the area with high seismic intensities. Current investigations merely concentrated on the story drift as the main index to evaluate the seismic performance of such kind of system, which could not reveal the component damage state in a structure. It is more comprehensive to evaluate the seismic performance through the damage state of components. In this paper, the seismic damage of components in the dual system consisting of concrete filled double skin steel tubular (CFDST) moment resisting frame with shear -bending yielding coupling (SBYC) damper was analyzed. The damage factors of different components including CFDST column, semi-rigid joint and SBYC damper were determined based on existing test results. The nonlinear model of the dual system was established by Opensees and verified by the test results. Afterwards, the 20- and 10-story dual structures were designed with different strength of SBYC damper and moment resistances of joint. Parametric analyses were conducted on these two dual systems through the endurance time method. Further, the uniform damage ratio was defined to represent the uniform level of the damage distribution of the components. It found that increasing the strength of joint was beneficial for achieving a uniform damage distribution of SBYC damper, joint and SBYC damper. The analytical results were beneficial for the application of dual system and provided a reasonable method to evaluate the seismic performance and damage of dual systems.

Damage-based optimal control of steel moment-resisting frames equipped with tuned mass dampers

The efficacy of a tuned mass damper (TMD) in dissipating the seismic energy transmitted to a structure depends on the TMD’s and structure’s characteristics and the structural response(s) that the TMD is intended to control. This study presents an approach to designing TMDs considering seismic damage as a representative of structural response. Damage is quantified by the Park–Ang damage index, which integrates deformation-induced damages with the cumulative hysteretic energy dissipated by structural members. The design problem is formulated into an optimization framework. The objective function is assumed to be the maximum value of story damage averaged over an ensemble of independently applied, scaled historical ground motions, and constraints are defined such that an adjustably uniform distribution of the mean story damage along the height of the structure is achieved. The approach is demonstrated by finding the optimum design of a TMD for a 10-story inelastic steel moment-resisting frame (SMRF) using the passive congregation particle swarm and grey wolf optimization techniques and showing that the optimized TMD substantially mitigates local damage in beams and columns, achieves a more uniform damage distribution in stories, yields an improved balance of reduced drifts and accelerations in the structure, and reduces the seismic fragility of the SMRF at different performance levels.

Study of deformation and fracture of high strength steel sheet during conventional and robust trimming by conducting partial trimming tests

An instrumented trimming press equipped with D2 grade steel die inserts with sharp edges was used to conduct trimming tests on DP980 sheets with clearances of 10%, 20%, and 30% of the sheet thickness. Trimming tests were conducted either with or without a support pad placed under the scrap piece and the trimming force was measured as a function of penetration distance of the upper die. The progression of plastic deformation and fracture processes that occurred in the shear affected zone (SAZ) of DP980 were observed on the polished cross-sections of the sheet by performing partial trimming tests. During conventional trimming with 10% clearance, cracks propagated simultaneously from the upper and lower surfaces of the sheet toward each other. However, when the clearance was increased to 30%, the main crack was initiated from the upper surface and propagated toward the lower surface resulting in the formation of a tensile-type burr. At 30% clearance, the trimming test conducted with a support pad prevented bending of the scrap piece, resulting in a uniform damage distribution within the SAZ. Thus, an improved sheared edge quality is achieved at larger clearances.

Optimal distribution of friction dampers to improve the seismic performance of steel moment resisting frames

This study aims to develop a low computational cost framework to optimize the seismic performance of the steel moment-resisting frames (SMRFs) equipped with friction dampers at different performance levels. To achieve the optimal design of dampers in a structure, a novel approach called adaptive optimisation technique (AOT) is adopted. The basis of this method is to achieve a uniform distribution of damage (UDD) in the structure to exploit the maximum energy dissipation capacity of the dampers. The optimisation objective is to obtain the best position of friction dampers and minimize their slip-threshold force to satisfy a predefined inter-story drift (i.e. selected performance target). The efficiency of the proposed method is demonstrated through optimum design of 4, 8, and 16-story SMRFs subjected to a set of strong natural earthquake records. The unique features of AOT are examined including the high convergence rate, the independence of the optimal solution from an arbitrary starting point, and also the ability to perform multi-level performance optimisation. Finally, the dependency of the seismic optimisation methods to the selected design acceleration record, as a challenge in the practical seismic design process, is addressed by proposing a modification in the proposed adaptive formula. In addition, the results of the proposed method are compared with iterative, non-iterative, and some metaheuristic optimisation methods such as genetic algorithm (GA), particle swarm optimisation algorithm (PSO), and simulated annealing algorithm (SA). It is shown that the AOT can lead to optimum design solutions with significantly less computational costs (up to 98%) compared to the conventional techniques.

Multi-level performance-based design optimisation of steel frames with nonlinear viscous dampers

This paper presents a practical multi-level performance-based optimisation method of nonlinear viscous dampers (NVDs) for seismic retrofit of existing substandard steel frames. A Maxwell model is adopted to simulate the behaviour of the combined damper-supporting brace system, with a fractional power-law force–velocity relationship for the NVDs, while a distributed-plasticity fibre-based section approach is used to model the beam-column members thus incorporating the nonlinearity of the parent steel frame in the design process. The optimum height-wise distribution of the damping coefficients of NVDs satisfying given performance requirements is identified via a uniform damage distribution (UDD) design philosophy. The efficiency of the proposed multi-level performance-based design optimisation is illustrated through nonlinear time-history analysis of 3-, 7- and 12-storey steel frames under both artificial and natural spectrum-compatible earthquakes. Sensitivity analysis is performed to investigate the effects of initial height-wise damping distribution, convergence factor and uncertainty in design ground-motion prediction on the optimisation strategy. The efficiency of the final optimum design solution is also investigated by using drift-based, velocity-based, and energy-based UDD approaches to identify the most efficient performance index parameter for optimisation purposes. It is found that regardless of the selected performance parameter, the optimum damping distribution identified by the proposed methodology leads to frames exhibiting lower maximum inter-storey drift, local damage (maximum plastic rotation) and global damage index compared to an equal-cost uniform damping distribution. However, using drift-based UDD approach generally results in a better seismic performance. It is shown that the proposed UDD optimisation method can be efficiently used to satisfy multiple performance objectives at different intensity levels of the earthquake excitation, in line with performance-based design recommendations of current seismic codes. The proposed method is easy to implement for practical design purposes and represents a simple yet efficient tool for optimum seismic retrofit of steel frames with NVDs.

Performance-based seismic design of moment resisting steel frames: Adaptive optimisation framework and optimum design load pattern

In this study, a performance-based optimisation framework is proposed for optimal cross-sectional distribution of steel moment resisting frames (MRFs) subject to earthquake excitations. For the first time, the concept of uniform distribution of damage (UDD) is adopted for the complex optimisation of moment resisting steel frames under dynamic earthquake excitations. To enhance the computational efficiency of the optimisation process, a novel adaptive algorithm is proposed, where the power functions change based on the demand to capacity ratio of the structural elements. The framework is then used for optimisation of 3, 5, 7, 10 and 15-storey steel MRFs under a set of representative earthquake records. Maximum plastic rotations and strength-based demand to capacity ratios are considered as the main performance parameters for deformation-controlled and force-controlled members, respectively. The results indicate that the proposed method is very efficient at improving the seismic performance of the designed structures in only a few steps by satisfying all the prescribed performance targets. It is shown that, for the same performance level, the optimum design frames require up to 38% less structural-weight compared to their code-based design counterparts. The average storey shear force distributions of the optimum frames under the design spectrum-compatible earthquakes are then used to obtain more efficient lateral load patterns for seismic design of steel MRFs. It is shown that by adopting the proposed load pattern in the conventional seismic design process, the frames exhibit significantly (up to 70%) less global damage compared to the similar frames designed based on code suggested load pattern.

Refined Seismic Design Method for RC Frame Structures to Increase the Collapse Resistant Capacity

In current structural design codes, elastic vibration modes are used for seismic design. However, when a structure is subjected to strong earthquakes and inelastic response or even when collapse damage is observed, the damage state is always unevenly distributed along the height of the structure. Such a phenomenon implies the materials of stories with elastic response and slight damage are not fully utilized. In this paper, a new practical and effective method, which improves collapse resistant capacity by making full use of materials, is proposed for reinforcement concrete (RC) frame structures at a structural collapse state. In this method, incremental dynamic analysis (IDA) is used to evaluate the structural collapse capacity. Tangent_ratio (TR) is formulated based on the IDA curves, and the longitudinal reinforcement of columns is modified based on the TR to achieve uniform distribution of damage along the height of building. Fewer variables are optimized and constraints of the provisions in current codes are considered, which makes the proposed procedure more computationally efficient and practical. The proposed method is employed on a 5-story RC frame structure to illustrate its feasibility and practicality. Comparison work indicates that the refined seismic design method can significantly increase the collapse resistant capacity and decrease the maximum inter-story drift ratio response under strong ground motion in a few iterative steps without a cost increase.

New lateral load distribution pattern for seismic design of deteriorating shear buildings considering soil-structure interaction

The current code-conforming seismic lateral load patterns are implicitly derived based on the dynamic solutions of fixed-base elastic structural systems, without considering the effects of hysteretic characteristic and soil-structure-interaction (SSI). Consequently, such lateral force patterns may not be applicable for the seismic design of nonlinear deteriorating structural systems. In this study, the analytical model was constructed using the shear building model. The peak-oriented modified I–K model and sway-rocking (S-R) model were employed to simulate the deteriorating behavior and SSI effects, respectively. A practical optimization design procedure for optimal lateral load pattern was developed based on the uniform damage distribution. The influence of main parameters on the new lateral load pattern was comprehensively investigated, including the parameters of the S-R model and the peak-oriented modified I–K model, ground motion excitations, fundamental period, target ductility, damping ratio and so on. The quantified expression of the new lateral load distribution was proposed as a function of fundamental period, the target ductility, aspect ratio and shear wave velocity. The results show that the structures designed according to the proposed lateral force pattern experienced obviously less damage than the code-conforming pattern.

Consideration of strength-stiffness dependency in the determination of lateral load pattern

The lateral load pattern used in design can significantly influence the distribution of strength and stiffness and consequently the distribution of damage along the height of the structure. The distribution patterns provided in seismic design codes are primarily derived from the fundamental elastic mode of vibration without considering the inelastic behavior of structures. This code-based load pattern causes concentrated damage in some stories, while leading to inefficient use of materials in other stories. Therefore, recent studies have employed optimization algorithms to develop lateral load patterns that achieve a uniform distribution of damage over all stories. These algorithms usually determine the distribution of strength along the height to achieve a particular ductility, while the stiffness is assumed to be constant. This assumption is contrary to the strength-stiffness dependency in steel or RC elements, hence causing some errors in the proposed load patterns. This paper presents an innovative algorithm to consider strength-stiffness dependency in the development of a lateral load pattern used for the design of moment frames. The proposed algorithm is implemented in MATLAB with supplementary OpenSees codes called in for nonlinear dynamic analysis. To reduce the computational cost of the nonlinear dynamic analysis during the optimization process, original n-bay frames are represented by simplified single-bay frames. The algorithm is implemented 800 times for 5 multi-story building models, 4 target ductility level, and 40 earthquake ground motions, with each implementation requiring a large number of trial and error iterations. The analysis results are processed to achieve two new lateral load patterns, which are evaluated using three original frames subjected to different ground motions. The results demonstrate that the moment frames designed by the proposed load patterns exhibit a more uniform distribution of ductility along the building height compared to the structures designed by the previously proposed lateral load patterns.

A practical methodology for optimum seismic design of RC frames for minimum damage and life-cycle cost

The design criteria in current seismic design codes are mainly to control lateral displacements and provide adequate strength to sustain expected design load combinations. However, to achieve the most economic design solutions, the life-cycle total cost (TLCC), which includes both initial structural cost and expected damage cost, should be also considered for the probable earthquakes during the lifetime of the structure. In the present study, the TLCC of the buildings is used as the main objective function for optimum seismic design of reinforced concrete (RC) frames. First, it is demonstrated that the blind increase of the reinforcement ratios does not necessarily reduce the displacement demands and the damage costs. Subsequently, a practical methodology is developed for the optimum seismic design of RC frames based on the concept of uniform damage distribution (UDD). Using an adaptive iterative procedure, the distribution of inter-storey drifts and TLCC of the floors is modified along the height of the structure. To demonstrate the efficiency of the method, 5, 8 and 12 storey RC frames are optimized using the proposed algorithm. The results indicate that, while all predefined performance targets are satisfied, the maximum inter-storey drift ratio and TLCC of the frames are considerably reduced (up to 56% and 45%, respectively) only after a few steps. The proposed method should prove useful for more efficient performance-based design of RC frames in practice.

Optimum seismic design of multi-story buildings for increasing collapse resistant capacity

The distribution patterns of equivalent static seismic lateral forces used in current structural design codes are mostly derived from elastic vibration modes. Such force patterns may not be consistent with actual conditions when structures behave into the inelastic range or even into the collapse stage. In this study, a new design method for multi-story buildings that uses an optimum lateral force pattern is proposed based on the concept of uniform damage distribution at the collapse state of these buildings. To reduce the computational cost of statistical analyses for deriving the optimum lateral force pattern, the non-linear story behaviors are represented by a story shear-deformation model with tri-linear relationships. Systematic parametric analyses are performed to study the influences of various ground motion parameters (site condition, magnitude, distance to rupture, and near-fault effect) and structural parameters (number of stories, fundamental period, damping ratio, post-yielding stiffness, ductility, and degrading stiffness) on the optimum lateral force pattern. Formulas for the optimum lateral force pattern that are applicable for practical seismic designs are provided. The collapse resistant capacities of structures designed using the proposed and conventional methods are compared by fragility analyses. Results show that the proposed method increases the seismic collapse resistant capacity of structures under the same construction cost.

Interrupted tension-tension fatigue behavior of angle-ply GFRP composite laminates

The effect of load interruptions on the tension-tension fatigue behavior of angle-ply (±45)2S glass/epoxy composite laminates was investigated. The cyclic loading was interrupted for two hours at regular cycle intervals, corresponding to 20% of the fatigue life under continuous loading at the same maximum cyclic stress level. Fatigue stiffness was partially restored after each loading interruption due to the recovery of the viscoelastic polymeric matrix. This repeated material stiffening at the beginning of each loading block delayed crack growth. Crack blunting further delayed damage growth and caused a more uniform damage distribution throughout the specimen volume. By applying interrupted fatigue loading, the rates of stiffness degradation and energy dissipation per cycle decreased due to the delayed damage growth. In addition, more uniform damage growth throughout the specimen volume increased the specimen’s capacity to accumulate damage, which led to a lower stiffness at failure, greater energy dissipation per cycle at failure and higher total dissipated energy of specimens subjected to interrupted loading. The specimens loaded under interrupted fatigue therefore exhibited longer fatigue lives than those continuously loaded. This enhancement of fatigue life increased at higher stress levels but almost disappeared at low levels. It was thus concluded that fatigue design allowables, if determined on the basis of continuous fatigue, are conservative in the case of interrupted fatigue.

Performance-based optimisation of RC frames with friction wall dampers using a low-cost optimisation method

Friction-based dampers can be considered as one of the suitable passive control systems for seismic strengthening and rehabilitation of existing substandard structures due to their high adjustability and good energy dissipation capability. One of the main issues in the design of these systems is to obtain the magnitude of the maximum slip force and the distribution of slip forces along the height of the building. In this study, a practical performance-based optimisation methodology is developed for seismic design of RC frame buildings with friction energy dissipation devices, which allows for an accurate solution at low computational cost. The proposed method aims at distributing the slip loads of the friction dampers to achieve a uniform distribution of damage along the height of the building. The efficiency of the method is evaluated through the optimum design of five different low to high-rise RC frames equipped with friction wall dampers under six natural and six synthetic spectrum-compatible earthquakes. Sensitivity analyses are performed to assess the reliability of the method using different initial height-wise slip load distributions, convergence parameters and earthquake records. The results indicate that optimum frames exhibit less maximum inter-storey drift (up to 43%) and global damage index (up to 75%), compared to uniform slip load distribution. The method is then developed to obtain the optimum design solution for a set of earthquakes representing a design spectrum. It is shown that the proposed method can provide an efficient tool for optimum seismic design of RC structures with friction energy dissipation devices for practical purposes.

Damage controlled optimum seismic design of reinforced concrete framed structures

In this paper, an innovative procedure is proposed for the seismic design of reinforced concrete frame structures. The main contribution of the proposed procedure is to minimize the construction cost, considering the uniform damage distribution over the height of structure due to earthquake excitations. As such, this procedure is structured in the framework of an optimization problem, and the initial construction cost is chosen as the objective function. The aim of uniform damage distribution is reached through a design constraint in the optimization problem. Since this aim requires defining allowable degree of damage, a damage pattern based on the concept of global collapse mechanism is presented. To show the efficiency of the proposed procedure, the uniform damage-based optimum seismic design is compared with two other seismic design procedures, which are the strength-based optimum seismic design and the damage-based optimum seismic design. By using the three different seismic design methods, three reinforced concrete frames including six-, nine-, and twelve-story with three bays are designed optimally under a same artificial earthquake. Then, to show the effects of the uniform damage distribution, all three optimized frames are used for seismic damage analysis under a suite of earthquake records. The results show that the uniform damage-based optimum seismic design method renders a design that will suffer less damage under severe earthquakes.

Seismic optimization design for uniform damage of reinforced concrete moment-resisting frames using consecutive modal pushover analysis

In this study, a practical optimization procedure is developed for uniform damage design of reinforced concrete moment-resisting frames using consecutive modal pushover analysis based on the framework of performance-based earthquake engineering. Consecutive modal pushover, which can capture the higher-mode effect well, is employed to derive the inelastic seismic demands of structures subjected to considered seismic hazards. Furthermore, the optimization problems are formulated using the profile of inter-story drift ratios and component hinge rotations to redistribute the steel reinforcements from components with low damage to ones that experience high damage under the constant-cost constraint, until a state of uniform damage distribution prevails. By applying the proposed design procedure to two prototype frames with five and eight stories designed using the Chinese Seismic Design Code (GB 50011-2010), the efficiency of the method as well as the variation of steel reinforcements is demonstrated. The seismic performances of final solutions and prototype frames are compared through nonlinear dynamic analysis for scenarios of 22 ground motions matching well with the code-compliant spectrum. The results show that the proposed method allows for a significant reduction of maximum story drifts combined with more evenly distributed story drifts and component hinge rotations, indicating better seismic performance for the optimized structures.

Optimum lateral load distribution for seismic design of nonlinear shear-buildings considering soil-structure interaction

The lateral load distributions specified by seismic design provisions are primarily based on elastic behaviour of fixed-base structures without considering the effects of soil-structure-interaction (SSI). Consequently, such load patterns may not be suitable for seismic design of non-linear flexible-base structures. In this paper, a practical optimisation technique is introduced to obtain optimum seismic design loads for non-linear shear-buildings on soft soils based on the concept of uniform damage distribution. SSI effects are taken into account by using the cone model. Over 30,000 optimum load patterns are obtained for 21 earthquake excitations recorded on soft soils to investigate the effects of fundamental period of the structure, number of stories, ductility demand, earthquake excitation, damping ratio, damping model, structural post yield behaviour, soil flexibility and structural aspect ratio on the optimum load patterns. The results indicate that the proposed optimum load patterns can significantly improve the seismic performance of flexible-base buildings on soft soils.

Effects of uncertainties on seismic behaviour of optimum designed braced steel frames

Concentrically braced steel frames (CBFs) can be optimised during the seismic design process by using lateral loading distributions derived from the concept of uniform damage distribution. However, it is not known how such structures are affected by uncertainties. This study aims to quantify and manage the effects of structural and ground-motion uncertainty on the seismic performance of optimum and conventionally designed CBFs. Extensive nonlinear dynamic analyses are performed on 5, 10 and 15-storey frames to investigate the effects of storey shearstrength and damping ratio uncertainties by using the Monte Carlo simulation method. For typical uncertainties in conventional steel frames, optimum design frames always exhibit considerably less inter-storey drift and cumulative damage compared to frames designed based on IBC-2012. However, it is noted that optimum structures are in general more sensitive to the random variation of storey shear-strength. It is shown that up to 50% variation in damping ratio does not affect the seismic performance of the optimum design frames compared to their code-based counterparts. Finally, the results indicate that the ground-motion uncertainty can be efficiently managed by optimizing CBFs based on the average of a set of synthetic earthquakes representing a design spectrum. Compared to code-based design structures, CBFs designed with the proposed average patterns exhibit up to 54% less maximum inter-storey drift and 73% less cumulative damage under design earthquakes. It is concluded that the optimisation procedure presented is reliable and should improve the seismic performance of CBFs.