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The design of structures to resist progressive collapse primarily focuses on enhancing structural safety and robustness. However, given the low probability of accidental events, such designs often lead to a negative cost–benefit. To address this problem, this paper uses risk analysis to optimize the progressive collapse resistance design of steel frame structures. The elements' cross-section design for the progressive collapse resistance of steel frame structures is optimized using genetic algorithms and SAP2000 23, which identify the structural model with the minimum robustness index while ensuring safety. The results show that the risk-based robustness index can effectively assess the cost of progressive collapse design. More importantly, the optimization model can rapidly identify the most cost-effective structural design solution that complies with progressive collapse resistance guidelines, enhancing the simplicity and usability of the structure design optimization process. Additionally, the integration of the SAP2000 API with Python 3.8 automation streamlines the parameterization process, minimizes manual errors, and enhances the precision and efficiency of the structural design optimization. Finally, the model's effectiveness is validated through a case study, where the refined single-frame structure shows a reduction in initial construction and collapse-related costs by 2.4% and 9.1%, respectively. Meanwhile, the three-dimensional frame shows a 2.9% rise in initial costs but a 13.5% decrease in total collapse-resistant design costs, illustrating the model's ability to balance safety with cost-effectiveness. [ABSTRACT FROM AUTHOR]

The design of structures to resist progressive collapse primarily focuses on enhancing structural safety and robustness. However, given the low probability of accidental events, such designs often lead to a negative cost–benefit. To address this problem, this paper uses risk analysis to optimize the progressive collapse resistance design of steel frame structures. The elements’ cross-section design for the progressive collapse resistance of steel frame structures is optimized using genetic algorithms and SAP2000 23, which identify the structural model with the minimum robustness index while ensuring safety. The results show that the risk-based robustness index can effectively assess the cost of progressive collapse design. More importantly, the optimization model can rapidly identify the most cost-effective structural design solution that complies with progressive collapse resistance guidelines, enhancing the simplicity and usability of the structure design optimization process. Additionally, the integration of the SAP2000 API with Python 3.8 automation streamlines the parameterization process, minimizes manual errors, and enhances the precision and efficiency of the structural design optimization. Finally, the model’s effectiveness is validated through a case study, where the refined single-frame structure shows a reduction in initial construction and collapse-related costs by 2.4% and 9.1%, respectively. Meanwhile, the three-dimensional frame shows a 2.9% rise in initial costs but a 13.5% decrease in total collapse-resistant design costs, illustrating the model’s ability to balance safety with cost-effectiveness.

In order to study the effect of the support mode of a staggered truss system on the continuous collapse resistance performance of a steel structure, four finite element models were established based on the bracing arrangement of a five-story steel frame structure. The situations of different columns on the first floor removed were classified into eight scenarios, and five models of each scenario were analyzed with nonlinear dynamic analyses. Finally, a computational metric based on energy robustness was proposed to evaluate the robustness of the structure. The results of nonlinear dynamic analyses indicated that the staggered truss system significantly improved the resistance to progressive collapse of steel frame structures and effectively increased the redundancy of steel frame structures. All four bracing methods effectively reduced the vertical displacement at the point of failure, with the peak displacement at the point of failure reduced by a maximum of 84 percent and a minimum of 41 percent compared to a pure frame structure. Moreover, the staggered truss system can reduce some axial force peaks in the adjacent columns adjacent to the failed columns. The structural robustness coefficients of Model A, Scheme 1, Scheme 2, Scheme 3, and Scheme 4 are 1.144, 1.339, 1.306, 1.584, and 1.176, respectively, according to the proposed robustness calculation method, which shows that the braced steel frame structure has improved robustness over the original structure. The staggered truss system improves the robustness of the steel frame structure so that the steel frame structure has better resistance to progressive collapse. [ABSTRACT FROM AUTHOR]

Abstract The current advanced analysis techniques for steel frames generally use structural analyses with geometric and material nonlinearities to capture the collapse strength of the steel frame. Unfortunately, the true strength of a steel frame cannot be predicted with accuracy because of the uncertainties of the most significant design variables. Building codes of steel structures apply a resistance factor to account for the uncertainties present in the design variables and thus ensure a target level of structural reliability. This article examines the reliability of planar steel frames subject to gravitational loads by advanced structural analysis (second-order inelastic analysis). To calculate the collapse probability of planar steel frames, we utilized the first-order reliability method (FORM). The advanced analyses were performed using the program MASTAN2 and considered the geometric nonlinearities and inelasticity of the steel. The collapse probabilities of planar steel frames were evaluated and the adequacy of the resistance factor applied was discussed. The current inelastic design procedure of ANSI 360 reduces the yield strength and stiffness of all members by a factor of 0.90. Thus, the present study suggests that the adopted resistance factor must be equal to 0.85 for the target reliability index equal to 3.0, or it must be equal to 0.69 for the target reliability index equal to 3.8.

The current advanced analysis techniques for steel frames generally use structural analyses with geometric and material nonlinearities to capture the collapse strength of the steel frame. Unfortunately, the true strength of a steel frame cannot be predicted with accuracy because of the uncertainties of the most significant design variables. Building codes of steel structures apply a resistance factor to account for the uncertainties present in the design variables and thus ensure a target level of structural reliability. This article examines the reliability of planar steel frames subject to gravitational loads by advanced structural analysis (second-order inelastic analysis). To calculate the collapse probability of planar steel frames, we utilized the first-order reliability method (FORM). The advanced analyses were performed using the program MASTAN2 and considered the geometric nonlinearities and inelasticity of the steel. The collapse probabilities of planar steel frames were evaluated and the adequacy of the resistance factor applied was discussed. The current inelastic design procedure of ANSI 360 reduces the yield strength and stiffness of all members by a factor of 0.90. Thus, the present study suggests that the adopted resistance factor must be equal to 0.85 for the target reliability index equal to 3.0, or it must be equal to 0.69 for the target reliability index equal to 3.8. [ABSTRACT FROM AUTHOR]

In order to study the effect of the support mode of a staggered truss system on the continuous collapse resistance performance of a steel structure, four finite element models were established based on the bracing arrangement of a five-story steel frame structure. The situations of different columns on the first floor removed were classified into eight scenarios, and five models of each scenario were analyzed with nonlinear dynamic analyses. Finally, a computational metric based on energy robustness was proposed to evaluate the robustness of the structure. The results of nonlinear dynamic analyses indicated that the staggered truss system significantly improved the resistance to progressive collapse of steel frame structures and effectively increased the redundancy of steel frame structures. All four bracing methods effectively reduced the vertical displacement at the point of failure, with the peak displacement at the point of failure reduced by a maximum of 84 percent and a minimum of 41 percent compared to a pure frame structure. Moreover, the staggered truss system can reduce some axial force peaks in the adjacent columns adjacent to the failed columns. The structural robustness coefficients of Model A, Scheme 1, Scheme 2, Scheme 3, and Scheme 4 are 1.144, 1.339, 1.306, 1.584, and 1.176, respectively, according to the proposed robustness calculation method, which shows that the braced steel frame structure has improved robustness over the original structure. The staggered truss system improves the robustness of the steel frame structure so that the steel frame structure has better resistance to progressive collapse.

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This research is aimed at investigating the dynamic behaviour of, and to analyse the dynamic response and dynamic performance of steel frames strengthened with welded haunches subjected to a typical hydrocarbon blast loading. The structural dynamic analysis was carried out incorporating the selected blast load, the validated 3D model of the structures with different welded haunch configurations, steel dynamic material properties, and non-linear dynamic analysis of multiple degree of freedom (MDOF) structural systems. The dynamic responses and effectiveness of the reinforced connections were examined using ABAQUS finite element software. Results showed that the presence of the welded haunch reinforcement decreased the maximum frame ductility ratio. Based on the evaluation of the results, the haunch reinforcements strengthened the selected steel frame and improved the dynamic performance compared to the frame with unreinforced connections under blast loading, and the biggest haunch configuration is the "best" type. [ABSTRACT FROM AUTHOR]

A quantifiable approach measuring the seismic structural collapse under sudden column removal is proposed using the interaction of the vertical collapse margin ratio (CMR V), the demand-to-capacity ratio (DCR) and the robustness (R). The assessment of CMR V needs the identification of the vertical maximum considered earthquakes. A classification of the ground motions based on the vertical-to-horizontal (V / H) ratios was used to obtain the vertical design spectrum. Six schemes of steel structures with various scenarios of sudden column removal were investigated to extract CMR V , DCR , and R. Then, a nonlinear regression analysis allows finding a general formulation of CMR V. A 15-story steel structure validates the proposed formulation of the CMR V. The two paths for estimating the minimum CMR V (CMR V, min) were the use of the recommended value of DCR and the minimum value of R inside the approximated CMR V expression, and the probabilistic distribution of CMR V, min from the analyses of different beam deformation states. The study of eighteen archetypes with 119 scenarios of sudden column removal reveals the value of the CMR V decreases when the V / H or/and DCR increase. The new maximum values of DCR with respect to R and its precise ranges are found with the use of the contour curves of CMR V, min. • The proposed classification of the vertical component of the earthquakes is based on the V / H ratio. • The structural safety diminishes with the increase of V / H ratio and DCR. • CMR V, min allows estimating the new range of values for DCR and R. • An improved value of DCR can reduce the structural cost while preserving the structural strength. [ABSTRACT FROM AUTHOR]

The objective of this paper was to evaluate the influence of initial flaws in the beam-column connections on the seismic performance of steel frame structures. The finite element models were constructed with different initial flaw lengths by ABAQUS. The initial flaw length was 0, 8, and 16 mm, respectively. The dynamic elastic-plastic time history analysis and the pushover analysis were conducted to obtain the probabilistic characteristics of seismic demand and seismic capacity. Seismic demands are quantified in terms of the maximum drift angle (RDA) and the displacement ductility ratio μ d . Moreover, the peak ground acceleration (PGA) was used for the pushover analysis. Formulas considering the influence of initial flaws on failure probability of a structure were derived for each length using different design basic acceleration of ground motion. The fragility curves were further constructed based on the data of seismic demand and capacity. The results show that the fragility of steel frame structures is similar across different seismic demand parameters. In addition, the analyses of fragility curves obviously indicate that the seismic fragility of steel frame structures increases as flaw length increases. Finally, the fragility of steel frame structures with initial flaws is consistent using different design basic acceleration of ground motion. [ABSTRACT FROM AUTHOR]

This research is aimed at investigating the dynamic behaviour of, and to analyse the dynamic response and dynamic performance of steel frames strengthened with welded haunches subjected to a typical hydrocarbon blast loading. The structural dynamic analysis was carried out incorporating the selected blast load, the validated 3D model of the structures with different welded haunch configurations, steel dynamic material properties, and non-linear dynamic analysis of multiple degree of freedom (MDOF) structural systems. The dynamic responses and effectiveness of the reinforced connections were examined using ABAQUS finite element software. Results showed that the presence of the welded haunch reinforcement decreased the maximum frame ductility ratio. Based on the evaluation of the results, the haunch reinforcements strengthened the selected steel frame and improved the dynamic performance compared to the frame with unreinforced connections under blast loading, and the biggest haunch configuration is the “best” type.

The post-tensioned energy dissipating connection for steel frames has drawn considerable attention because of its good seismic performance. Friction mechanisms, such as friction damped post-tensioned (FDPT) steel connections, are typically used to improve energy dissipating capacity. Many researchers have investigated the seismic behavior of FDPT through numerical or experimental method. Prior studies have indicated that the analysis by elaborate FE models is very time-consuming. To overcome this disadvantage, a friction element was first proposed based on general FE code and then incorporated into a simplified numerical model of PT connection to consider the effects of friction. The accuracy of results derived by this model was validated against prior experimental investigations. The effects of friction force value and initial PT force seismic behavior of FDPT connection was investigated. The geometric and material nonlinearities and strands can be considered in the modeling. A planar steel frame structure was established, and hysteretic analysis was conducted in the end. Results indicated the computational cost can be reduced significantly by this model. [ABSTRACT FROM AUTHOR]

To study the seismic performances of steel frame structures in traditional-style buildings, the pseudo-dynamic test was carried out on a 1/2 ratio model built in the areas with a seismic design intensity of eight. The input earthquake waves included El Centro, Lanzhou and Wenchuan, and the maximum peak accelerations of these ground motions were 70, 200, 400 and 620 gal (0.7, 2, 4 and 6.2 m/s2). The seismic responses such as displacement, reaction force, acceleration were recorded. The hysteretic behavior, energy dissipation capacity, time-history curves of acceleration and displacement, bearing capacity and stiffness degradation were analyzed. The results show that the traditional-style steel frame structure stayed in the elastic stage subjected to no more than 400 gal (4 m/s2) PGA. There was no obvious pinch phenomenon in the hysteretic loops and the structural energy dissipation increased significantly with the increase of the seismic wave amplitude. When the 9-intensity seismic wave was applied, some unique members in traditional-style buildings yielded, and the spectral characteristic of the input seismic wave had a great influence on the seismic response of the structure. The modal analysis and time-history analyses were applied to the structure, the vertical deformation of the second and third modes of the steel frame was larger than that of the first modal shape, the reaction force value of finite element was a little larger than that of the test under the same loading condition. When the structure subjected to more severe earthquake, some unique members in traditional-style buildings acted as the first earthquake fortification line and dissipate most energy, and  the structural most obvious reaction took place in advance or delayed a bit. [ABSTRACT FROM AUTHOR]

A computationally efficient structural topology optimization framework is proposed for design of steel frame structures with user-defined factors of safety against overall structure (global) and individual member instabilities. The objective function is minimization of either compliance or the maximum of von Mises stresses within the frame structure. Within optimization, overall structure buckling modes are found via an eigenvalue analysis, a subset of “pseudo modes” are identified using a newly proposed methodology and are discarded to obtain a set of real eigenvalues. Moreover, individual member buckling loads are estimated with Euler buckling analysis and are aggregated into a single constraint. The minimum of each instability constraint is then estimated with separate differentiable negative p-norm functions. Sensitivities of these newly developed constraints are explicitly derived for application of gradient-based optimizers. The topology of four frame structures featuring moment-resisting connections and member cross-sectional properties mapped from the American Institute of Steel Construction design manual are optimized with the proposed algorithm to verify its effectiveness in optimizing structural performance while maintaining factors of safety against overall and individual member instabilities. The interaction effects of preventing instabilities at different safety levels and the choice of objective function on the final designs and their performances are investigated. [ABSTRACT FROM AUTHOR]

Post-tensioned (PT) self-centering beam-column connections has been developed for its good seismic performance. Many researchers have investigated its mechanical behavior by numerical or experimental method. Prior researches have indicated that the analysis by elaborate FE models is very time consuming. To overcome this disadvantage, a simplified numerical model was established in this paper. The accuracy of results derived by this model was validated against prior investigations on interior PT connections with top-and-seat angles. Influence of initial PT force on mechanical behavior of PT connection was investigated. The Geometric and material nonlinearities, and strands can be considered in the modeling. A planar steel frame structure was established and hysteretic analysis was conducted. Results indicated that the computational cost can be greatly reduced by this model. [ABSTRACT FROM AUTHOR]

Real-time hybrid simulation (RTHS) offers an economical and reliable methodology for testing integrated structural systems with rate-dependent behaviors.Within a RTHS implementation, critical components of the structural system under evaluation are physically tested, while more predictable components are replaced with computational models under a one-to-one timescale execution. As a result, RTHS implementations provide a more economical and versatile alternate approach to evaluating structural/rate-dependent systems under actual dynamic and inertial conditions, without the need for full-scale structural testing. One significant challenge in RTHS is the accurate representation of the physical complexities within the computational counterparts. For RTHS, the requirement for computational environments with reliable modeling and real-time execution capabilities is critical. Additionally, the need of a flexible environment for implementation and easy integration of such platforms with remaining RTHS components has also been established. An open-source computational platform, RT-Frame2D, for the RTHS of dynamically excited steel frame structures has been developed to satisfy these demands. The computational platform includes both adequate modeling capabilities for the nonlinear dynamic analysis of steel frame structures under real-time execution, and a versatile design to allow its efficient integration within a RTHS framework. Comparisons of RT-Frame2D modeling capabilities with those of a well-known simulation tool, in addition to challenging experimental implementations based on several RTHS scenarios, are performed herein to verify the accuracy, stability, and real-time execution performance of the proposed computational platform. [ABSTRACT FROM AUTHOR]

The main problem in performance-based structures is the extremely high computational demand of time-history analyses. In this paper, an efficient framework is developed for solving the performance-based multi-objective optimal design problem considering the initial cost and the seismic damage cost of steel moment-frame structures. The Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed as the optimization algorithm to search the Pareto optimal solutions. For improving the time efficiency of the solution algorithm, the Generalized Regression Neural Network (GRNN) is utilized as the meta-model for fitness approximation, and a specific evolution control scheme is developed. In this scheme, in order to determine which individuals should be evaluated using the original fitness function and which by the meta-model, the Fuzzy C-Mean (FCM) clustering algorithm is used to choose the competent individuals rather than choosing the individuals randomly. Moreover, the computational burden of time history analyses is decreased through a particular wavelet analysis procedure. The constraints of the optimization problem are considered in accordance with the FEMA codes. The results obtained from numerical application of the proposed framework demonstrate its capabilities in solving the present multi-objective optimization problem. [ABSTRACT FROM AUTHOR]

Steel frame structures often use exposed column-base plate connections. Studies on such connections have mainly focused on the mechanical properties along the strong axis. Thus, the seismic performance evaluation for the weak axis direction, which may cause insufficient structural safety, has been underestimated. The present study discusses the results of eight cyclic loading tests along the minor axis of exposed column-base plate connections. Then, the effects of the axial compression ratio, the size of the column section, the diameter and the arrangement of anchor bolts, the thickness of the base plate, and any stiffeners on the connection's seismic performance are quantified. It was found that the failure mode is breaking of the anchor bolts except for two specimens with torn welding lines. Also, all hysteretic curves are the slip type with the highest ductility coefficient of 10.49. The experimental results are used to build a numerical model based on the finite element method. Also, the stiffness calculation formula for the weak axis direction is derived using the component method. In addition, a technique for predicting a column's moment-rotation curve is proposed. It will be shown that the results of this technique agree well with those of the finite element model and with the experimental data. [Display omitted] • The exposed column-base connections along minor axis were investigated by cyclic loading test. • Failure modes and seismic performance of exposed column-base connections along minor axis were presented. • The formulas for the initial rotational stiffness of connections along minor axis were derived. • A numerical model was established using the component method based on loading experiments. • The moment-rotation curve for the weak axis direction with an H-shaped steel column was predicted. [ABSTRACT FROM AUTHOR]

A beam–column element formulation and solution procedure for nonlinear inelastic analysis of planar steel frame structures under dynamic loadings is presented. The spread of plasticity is considered by tracing the uniaxial stress–strain relationship of each fiber on the cross section of sub-elements. An elastic perfectly-plastic material model with linear strain hardening is employed for deriving a nonlinear elemental stiffness matrix, which directly takes into account geometric nonlinearity and gradual yielding. A solution procedure based on the combination of the Hilber–Hughes–Taylor method and the Newton–Raphson method is proposed for solving nonlinear equations of motion. The nonlinear inelastic time-history responses predicted by the proposed program compare well with those given by the commercial finite element package known as ABAQUS. Shaking table tests of a two-story steel frame were carried out with an aim to clarify the inelastic behavior of the frame subjected to earthquakes generated by the proposed program. A more practical analysis method for seismic design can be developed by comparing it with the presented frames for verification. [ABSTRACT FROM AUTHOR]

A damage-based seismic design procedure for steel frame structures is formulated as an optimization problem, in which minimization of the initial construction cost is treated as the objective of the problem. The performance constraint of the design procedure is to achieve "repairable" damage state for earthquake demands that are less severe than the design ground motions. The Park-Ang damage index is selected as the seismic damage measure for the quantification of structural damage. The charged system search (CSS) algorithm is employed as the optimization algorithm to search the optimum solutions. To improve the time efficiency of the solution algorithm, two simplifying strategies are adopted: first, SDOF idealization of multi-story building structures capable of estimating the actual seismic response in a very short time; second, fitness approximation decreasing the number of fitness function evaluations. The results from a numerical application of the proposed framework for designing a twelve-story 3D steel frame structure demonstrate its efficiency in solving the present optimization problem. [ABSTRACT FROM AUTHOR]

This study presents a new empirical model to estimate the base shear of plane steel structures subjected to earthquake load using a hybrid method integrating genetic programming (GP) and simulated annealing (SA), called GP/SA. The base shear of steel frames was formulated in terms of the number of bays, number of storey, soil type, and situation of braced or unbraced. A classical GP model was developed to benchmark the GP/SA model. The comprehensive database used for the development of the correlations was obtained from finite element analysis. A parametric analysis was carried out to evaluate the sensitivity of the base shear to the variation of the influencing parameters. The GP/SA and classical GP correlations provide a better prediction performance than the widely used UBC code and a neural network-based model found in the literature. The developed correlations may be used as quick checks on solutions developed by deterministic analyses. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a performance-based optimal seismic design of frame structures is presented using the ant colony optimization (ACO) method. This discrete metaheuristic algorithm leads to a significant improvement in consistency and computational efficiency compared to other evolutionary methods. A nonlinear analysis is utilized to arrive at the structural response at various seismic performance levels, employing a simple computer-based method for push-over analysis which accounts for first-order elastic and second-order geometric stiffness properties. Two examples are presented to illustrate the capabilities of ACO in designing lightweight frames, satisfying multiple performance levels of seismic design constraints for steel moment frame buildings, and a comparison is made with a standard genetic algorithm (GA) implementation to show the superiority of ACO for the discussed optimization problem. [Copyright &y& Elsevier]

The progressive collapse of steel frame structures under the blast load was investigated using LS-DYNA. The multi-material Eulerian and Lagrangian coupling algorithm was adopted. A fluid-structure coupling finite element model was established which consists of Lagrange element for simulating steel frame structures and concrete ground, multiple ALE element for simulating air and TNT explosive material. Numerical simulations of the blast pressure wave propagation, structural dynamic responses and deformation, and progressive collapse of a five-story steel frame structure in the event of an explosion near above ground were performed. The numerical analysis showed that the Lagrangian and Eulerian coupling algorithm gave good simulations of the shock wave propagation in the mediums and blast load effects on the structure. The columns subjected to blast load may collapse by shear yielding rather than by flexural deformation. The columns and joints of steel beam to column in the front steel frame structure generated enormous plastic deformation subjected to intensive blast waves, and columns lost carrying capacity, subsequently leading to the collapse of the whole structure. The approach coupling influence between structural deformation and fluid load well simulated the progressive collapse process of structures, and provided an effective tool for analyzing the collapse mechanism of the steel frame structure under blast load. [ABSTRACT FROM AUTHOR]

In this article, a harmony search algorithm is presented for optimum design of steel frame structures. Harmony search is a meta-heuristic search method which has been developed recently. It is based on the analogy between the performance process of natural music and searching for solutions of optimization problems. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress Design (ASD) specifications, maximum (lateral displacement) and interstorey drift constraints, and also size constraint for columns were imposed on frames. The results of harmony search algorithm were compared to those of the other optimization algorithms such as genetic algorithm, optimality criterion and simulated annealing for two planar and two space frame structures taken from the literature. The comparisons showed that the harmony search algorithm yielded lighter designs for the design examples presented. [ABSTRACT FROM AUTHOR]

Seismic resilience is a new approach in earthquake engineering, which addresses technical, organizational, social, economic and environmental aspects. The main purpose of a resilience system is to reduce economic or operational casualties, so as to return the community or the damaged system to natural conditions in the shortest possible time. Schools and education centers are especially important when it comes to designing seismic-resistant buildings, as they require higher safety margins than other buildings. Due to the inadequacy and lack of precision in previous structural regulations, many Iranian schools require rehabilitation as well as increased resiliency. For this research, a high school located in Zanjan city in Iran, as a sample of 5120 Iranian steel frame school buildings, is investigated for seismic resilience evaluation. Various schemes are considered for the retrofitting process. The nonlinear analysis is conducted for each scheme, while the reliability analysis is performed using FORM and the sampling method, all of which are effective and reliable methods that can assign the appropriate and feasible strategy for the retrofitting process. The reliability analysis shows retrofitting with the X-braced system to be the optimal retrofitted scheme because it has the lowest losses and highest seismic resilience indices. To examine the accuracy of common methodologies for assessing the resilience index, two common procedures of resiliency evaluation are chosen, and their resiliency parameters are compared. The results indicate that extracting resiliency parameters by means of vulnerability curves is more reasonable and accurate than using resilience curves. The results of this study could help stakeholders better select the appropriate option for retrofitting operations by considering account resiliency parameters, structural deficiency, and disaster risk reduction mitigations. • Typical high schools were considered for resilience evaluation. • Loss estimation modified corresponding to local economic conditions, were used in the function of resilience. • Two common procedures of resiliency evaluation are chosen, and their resiliency parameters are compared. • The reliability calculations are done due to the different limit state functions considering the materials, ground motion records, and hazard levels uncertainty. • The optimal option for retrofitting operation with the lowest damages and the highest resiliency, is characterized. • Resiliency curves are extracted by two methods and the best methodology for resiliency analysis is proposed. [ABSTRACT FROM AUTHOR]