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This paper deals with the estimation of maximum displacements in single-degree-of-freedom (SDOF) systems simulating typical steel structures by means of dimensional analysis. Peak deformation demands in bilinear systems (representative of moment resisting frames) are considered as well as additional pinching models depicting partially-restrained (P...
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... dimensionless response estimates for CB structures (solid curves) as well as their calculated values (markers) are depicted in Figures 8 and 9 whereas Table 8 presents the corresponding IQR and E values. As before, the model description in Table 8 follows the format CB-model where CB indicates concentrically-braced frames and model denotes the model as defined in Table 3. Equation 12 (see Table 2) was employed for all models and all regression terms were found to be statistically significant in each of the eleven models analysed. ...
Context 2
... dimensionless response estimates for CB structures (solid curves) as well as their calculated values (markers) are depicted in Figures 8 and 9 whereas Table 8 presents the corresponding IQR and E values. As before, the model description in Table 8 follows the format CB-model where CB indicates concentrically-braced frames and model denotes the model as defined in Table 3. Equation 12 (see Table 2) was employed for all models and all regression terms were found to be statistically significant in each of the eleven models analysed. ...
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... We determined the size of the experimental model to be 2.6 m × 1.4 m × 1.5 m (length × height × width). As shown in Table 2, according to the dimension analysis method [23,24] and the Buckingham quantitative method [25], the similar constants of other physical quantities were calculated. Based on the main similarity ratios of the model tests and repeated matching tests, the material ratios corresponding to the physical and mechanical parameters of each rock layer in the model were determined (see Table 3). ...
The southwestern region of China is close to the Eurasian earthquake zone. Many engineering areas in southwestern China are affected by earthquakes and are close to the epicenter of earthquakes that occur in this region. During earthquakes, slopes with weak interlayers are more likely to cause large-scale landslides. In response to the low stability of slopes with weak interlayers in reservoir dam areas, the dynamic response law and failure mechanism of weak interlayered slopes under the combined action of reservoir water and seismic forces were studied through shaking table model tests and finite element numerical simulation software. The height of the water level and the size of the seismic waves were changed during these tests. The research results indicate that seismic waves are influenced by weak interlayers and are repeatedly superimposed between the weak interlayers and the slope surface, resulting in an acceleration amplification effect that increases by approximately 1.8 times compared to homogeneous slopes. Vertical earthquakes have a significant impact on the dynamic response of slopes, and their peak acceleration amplification coefficient can reach 0.83 times the horizontal peak acceleration. The stability of weak interlayers during earthquakes is the worst within the range of the direct action of reservoir water. The failure mode of a slope is as follows: earthquake action causes cracking in the upper part of the slope, and as the earthquake increases in intensity, and the infiltration of reservoir water intensifies, the cracks expand. The soft and muddy interlayer in the front section of the slope forms a sliding surface, and ultimately, the sliding failure forms an accumulation body at the foot of the slope. In reservoir dam areas, the stability of a slope is closely related to the engineering safety of the reservoir dam. Therefore, when a strong earthquake and the water level in a reservoir jointly affect a weak-interlayer slope, the slope is in the stage of plastic deformation and instability. The stability of the slope may be overestimated, and the slope is likely vulnerable to sliding instability, which needs to be monitored and treated.
... Although many simplified seismic drift predictive models have been proposed for steel [8,9] or concrete structures [10,11], to our knowledge, simplified models for seismic demand estimations in timber buildings are rare. For example, Heresi and Miranda [12] developed an expression for the spatial correlation of 5%-damped average spectral pseudo accelerations for MIDR estimations on low-rise single-family wood-frame constructions for regional risk assessments. ...
... These parameters include the number of storeys, the panel fragmentation level, as well as the behaviour factors. Buildings of 6,8,12,16, and 20 storeys were considered. ...
... In general, it can be observed from Fig. 12, that the influence of T 1 /T m on RDR identified by Demirci et al. [13] has been learnt by our ML model leading to larger RDR demands in the region of shorter T 1 /T m period ratios. This trend is also consistent with previous studies for other structural types [8,66]. However, the sensitivity of RDR to T 1 /T m appears to be stronger in the model by Ref. [13] than in our newly proposed ML model, and this is specially evident at shorter periods. ...
An accurate estimation of drift demands is crucial for designing and assessing structures under seismic loads. Given the novelty of massive timber buildings, predictive models for the estimation of drifts in mid- to high-rise CLT structures are lacking, particularly in the form of simple models suitable for preliminary design evaluations or regional seismic assessments. In this paper, we present and compare several Machine Learning (ML) models for the estimation of peak inter-storey and roof drifts in multi-storey Cross-Laminated Timber (CLT) walled structures. The ML techniques used include: Multiple Linear Regression, Regression Trees, Random Forest, K-nearest Neighbour, and Support Vector Regression. To this end, 69 structures spanning mid-rise to tall timber buildings are subjected to a large collection of acceleration records and used to create the training and testing datasets. Different structural configurations and behaviour factors, related to the assumed energy dissipation capacity of the buildings, are considered. A diversity of feature selection techniques informs our choice of parameters to the reduced input space leading to a set of six most efficient features: the spectral acceleration at the building’s fundamental period (Sa(T1)), the Peak Ground Velocity (PGV), tuning ratio (T1/Tm), behaviour factor (q), wall height (Hw), and the wall subdivision ratio (Wr). After verifying the high accuracy of our model predictions, the SHapley Additive exPlanation method (SHAP) is used to gain insight into the influence of key input features on the ML model outputs. Finally, our ML drift estimations are compared against previous proposals and design code assumptions, and the potential causes of disagreement are discussed.
... Furthermore, the pulse period (T p ), as a critical parameter of velocity pulse, has been validated to show a significant influence on seismic response [19][20][21][22][23], and the variation of T 1 /T p also has been found to display a strong correlation with the structural response (examples of T 1 /T p = 1 for structural response in elastic stage, and T 1 /T p ≈2 for structural response in plastic stage) [24][25][26]. Meanwhile, the seismic ductility spectra (SDS), a widely used method in the earthquake field, have been adopted by many scholars to investigate the ductility demand of structures with varied constitutive models subjected to near-field [23,[27][28][29][30] and far-field [31][32][33] earthquakes. ...
The seismic ductility spectra (SDS) method is a crucial tool to quickly evaluate the ductility demand of bridge columns with varied constitutive models. However, conventional SDS methods usually do not consider the characteristics of pulse-like excitations, which tend to cause severe structural damage. To address this challenge, near-fault pulse seismic ductility spectra (NFPSDS) based on Machine learning (ML) are developed in this study, where two ML models, i.e., the Random Forest (RF) and the artificial neural network (ANN), are utilized to map the relationship between seismic demand and a pulse-structure coupled index α 1-p (the structural fundamental period (T 1) relative to pulse period (T p)). Then, the influence of column parameters (such as fundamental period and longitudinal reinforcement ratio) and pulse parameters (such as pulse period and peak pulse velocity) on NFPSDS is quantitatively investigated. Thus, by employing the NFPSDS method, the reasonable design range of longitudinal reinforcement ratio can be obtained under different pulse periods and pulse velocities. Overall, the NFPSDS method significantly benefits the practice for seismic design of structures in near-fault regions.
... However, several unexpected features with very low collinearity with mod are also identified (e.g., 1 / m , PGD). The appearance of the mean ground-motion period, m , is in line with previous studies that highlighted its role in expected drift demands [66][67][68] and PGD may describe well drifts for taller buildings experiencing limited non-linear deformations. Besides, in contrast with the results from the other feature selection methods, the drop column importance shows that the behaviour factor ( ), maximum inter-storey drift at the first yield ( 1,max ) and several spectral accelerations for periods past the fundamental structural period have negative importance. ...
The seismic design and assessment of Steel Moment Resisting Frames (SMRF) rely heavily on drifts. It is unsurprising, therefore, that several simplified methods have been proposed to predict lateral deformations in SMRFs, ranging from the purely mechanics-based to the wholly data-driven, which aim to alleviate the structural engi- neer’s burden of conducting detailed nonlinear analyses either as part of preliminary design iterations or during regional seismic assessments. While many of these meth- ods have been incorporated in design codes or are commonly used in research, they all suffer from a lack of consideration of the causal link between the seismic haz- ard level and the ground-motion suite used for their formulation. In this paper, we propose hybrid data-driven models that preserve this critical relationship of hazard- consistency. To this end, we assemble a large database of nonlinear response history analyses on 24 SMRFs of different structural characteristics. These structural mod- els are subjected to 816 ground-motion records whose occurrence rates and spectral shapes are selected to ensure the hazard consistency of our outputs. Two sites with different seismic hazards are examined to enable comparisons under different seis- mic demands. An initial examination of the resulting drift hazard curves allows us to re-visit the influence of salient structural modelling assumptions such as plastic resis- tance, geometric configurations and joint deterioration modelling. This is followed by a Machine Learning (ML)-guided feature selection process that considers struc- tural and seismic parameters as well as key static response features, hence the hybrid nature of our models. New models for inter-storey drift and roof displacements are then developed. A comparison with currently available formulations highlights the significant levels of overestimation associated with previously proposed non-hazard consistent models.
... By specifying the same values for this factor and the behaviour (force reduction) factor, q, for all steel structures, the equal displacements rule is effectively employed to predict inter-storey drift under all levels of excitation. A number of studies have proposed different methods for predicting global or peak inter-storey drift in steel frame structures (for example [6,10,11]), including studies which developed regression models from the results of large numbers of time history analyses [12][13][14]. In short, these studies have generally shown that for long period structures the equal displacements rule is generally conservative, but for shorter period structures the rule often under predicts drift. ...
This paper describes the development of regression equations to predict the peak inelastic drift and acceleration response of steel concentrically braced frame (CBF) building structures. A database of Engineering Demand Parameters (EDPs) is developed by performing a large number of nonlinear time-history analysis (NLTHAs) in OpenSEES for a set of 24 case study CBFs. A consistent and realistic set of mechanical models is achieved by designing each case study frame using Eurocode 8. Multi-variable regression models for peak drift and acceleration response at each storey level are fitted to the NLTHA results data. A nonlinear formulation and robust regression are employed to capture the influences of the Eurocode 8 behaviour factor and brace slenderness and overstrength limits on the EDP profiles over the height of a building. Comparison with existing models shows that the fitted regression equations achieve improved agreement with NLTHA results across a wide range of structural parameters. The regression models can be applied in performance-based design or assessment to predict the peak inelastic response of CBF structures without performing additional nonlinear analyses.
... Many alternative approaches exist to predict the nonlinear drift and acceleration response of structures to earthquake excitation, including those based on linear response like the equal displacements rule [4] for drift or the first mode reduced method [5] for acceleration, and methods based on examining single degree of freedom systems (for example [2]) or dimensional analysis (for example [6,7]. However, it is generally recognized that the most accurate method of predicting seismic response is to conduct NLTHA using multiple ground acceleration records. ...
This paper presents a rapid method for calculating the expected earthquake repair costs incurred by steel concentrically braced frame structures designed to Eurocode 8. The method adopts the FEMA P‐58 performance assessment methodology which is based on the predicting Engineering Demand Parameters (EDPs), such as peak inter‐story drift and peak floor acceleration, at various seismic hazard intensity levels of interest and then using these EDPs to calculate expected damage and associated economic losses. Typically, multiple nonlinear time history analyses (NLTHA) are employed to calculate the required EDPs, however this can be computationally expensive and technically challenging. This paper proposes the use of regression equations, developed from a large number of nonlinear analyses, as an alternative to NLTHA for EDP prediction. This allows loss assessment to be carried out without the need for multiple NLTHA, a process termed rapid loss assessment. The proposed equations are applied in loss assessment for three case study CBFs. It is shown that the economic losses predicted by the rapid method compare well with results obtained from conventional NLTHA‐based assessment.
... The By applying the Buckingam Π-theorem, [38][39][40][41][42][43] Equation 3 can be conveniently reformulated in terms of dimensionless parameters, denoted as Π-terms. This approach permits the identification of the characteristic problem parameters that control the seismic response of the system also reducing the number of variables in Equation 3. ...
... The objective of the study is to evaluate how the circular frequency ω 0 , the frame damping ratio ξ, the parameter α, and the values of the target ductility demand of the BRBF and of the MRF, 8,9 respectively, μ bt and μ ft , affect the performance of the system. In order to achieve this objective, it is not possible to follow the approach conventionally followed in other studies, [39][40][41][42][43] where a free variation of the nondimensional problem parameters is considered. This is because the two nondimensional parameters related to the response, μ bt and μ ft , are defined by the design condition and hence fixed a priori rather than being observed. ...
Buckling‐restrained braces (BRBs) have proven to be very effective in improving the seismic performance of existing and new structures. They provide strength, stiffness and add energy dissipation to the structure. However, being BRBs characterized by a low post‐elastic stiffness, their use may lead to residual deformations hindering the building's reparability and to excessive cumulative ductility demand possibly compromising the residual capacity of BRBs. To overcome these drawbacks, BRB frames (BRBFs) can be coupled with moment‐resisting frames (MRFs) to form dual systems. If properly designed, MRFs acting as back‐up frames allow the control of the residual drifts and the optimization of the performance of the BRBs. The contribution of this study is to provide insights into the performance and residual capacity of BRBFs‐MRFs dual systems and to shed light on the influence of the main BRB's design parameters. To this end, a nondimensional formulation of the equation of motion is introduced for a single degree of freedom system, and an extensive parametric study is performed for a set of natural ground motion records with different characteristics and scaled to various intensity levels. This allows the investigation of a wide range of configurations, considering different levels of the relative strength and ductility demand of BRBFs and MRFs, and obtains useful information for their design. Finally, two case study frames, modeled as two‐dimensional nonlinear multi‐degree of freedom systems, are analyzed, and the results were compared to those obtained from the nondimensional formulation to show the capabilities and the limitations of the adopted methodology and of the SDOF approximation.
... Following this principle, dimensional analysis has been applied to a wide variety of problems in earthquake engineering including rocking structures 35,36 , steel structures 37 , seismic control devices 38,39 and fragility analysis 36,40 . Most of these studies have employed records with coherent pulses and clearly identifiable time and length scales 41 due to the difficulties associated with the selection of an adequate set of ground-motion time and length scale parameters for non-coherent earthquake actions 42,37 . ...
... As such, they follow a wealth of previous studies 9, 10,11,33,34 that have arrived to important findings based on non-degrading structural models. Indeed, non-degrading systems have been used to uncover the decisive property of self-similarity in the response of a variety of structures 33,34,42,37 , a property that, as has been demonstrated in this paper, also shapes the non-linear behaviour of bi-directionally loaded eccentric structures. ...
... Besides their physical insight, these self-similar relationships can also guide the formulation of predictive models by informing the choice of functional forms and set of parameters to be considered. Perhaps more importantly, given the underlying scale invariance associated with self-similarity, if the dimensionless relationships formulated on the basis of the uniform duration of coherent pulses could be extended to more realistic non-coherent records, lower dispersions in the response estimate are to be expected 55,37,40 . This is demonstrated in Figure 16 which presents the analysis of eccentric systems subjected Figure 16 for comparison purposes. ...
Plan irregular structures, whose complex response represents a generalization of the simpler de-coupled motion ascribed to symmetric buildings, make up a large proportion of the failures during major earthquakes. This paper examines the seismic response scaling of degrading and no-degrading eccentric structures subjected to bi-directional earthquake action and its relationship with the duration of the ground-motion by means of dimensional and orientational analyses. Structures with reflectionally symmetric stiffness distribution and mass eccentricity subjected to orthogonal pairs of ideal pulses are considered as the fundamental case. The application of Vaschy-Buckingham’s Π-theorem reduces the number of variables governing the peak orthogonal displacements leading to the emergence of remarkable order in the structural response. If orientationally consistent dimensionless parameters are selected, the response becomes self-similar. By contrast, when degradation is introduced, peak inelastic displacements are dramatically affected and the self-similarity in the response is lost immediately after the onset of inelastic deformations. Conversely, if the uniform duration, instead of the period, of the strong-motion is adopted as a time-scale, a practically self-similar response is observed. This offers unequivocal proof of the fundamental role played by the ground-motion duration in defining the peak displacement response of degrading structures even at small inelastic demands, although its importance increases with increasing deformation levels. Finally, the existence of complete similarities, or similarities of the first kind, are explored and the practical implications of these findings are briefly outlined in the context of real pulse-like ground-motions with varying degrees of coherency.
... Although they are regularly obtained from numerical searches of periodic stable solutions along the spectrum [43], in the present case FRFs were Each frame configuration was subjected to a series of four horizontal cycles. The resulting data is presented in Figure 14 FRFs are plotted in terms of roof drifts and accelerations since these response parameters are widely used as indicators of structural and non-structural damage [44,45]. By plotting the FRFs for a range of forcing amplitudes, a backbone curve is constructed. ...
Post-tensioned rocking frames have been proposed as damage-free seismic-resistant structures. However, currently available load resisting systems for rocking frames rely on sacrificial yielding components that accumulate damage during strong dynamic action. To address this shortcoming, this study proposes a novel thoroughly damage-avoidance solution by means of bracing elements with carefully controlled buckling behaviour. To this end, a proof-of-concept study is presented, whereby the elastic buckling response of buckling-enabled composite bracing (BECB) elements with circular-arc shaped cross-section is numerically investigated. Varying geometric properties are considered and validated against analytical approximations. Besides, a finite element study of a single-storey steel post-tensioned frame under static and dynamic actions is performed. The case study incorporates BECB elements made from glass-fibre reinforced polymer (GFRP). It is demonstrated that BECB enhances the non-linear static and dynamic response of rocking frames by providing stability and significantly reducing storey drifts and accelerations without accumulating damage.
... The By applying the Buckingam Π-theorem, [38][39][40][41][42][43] Equation 3 can be conveniently reformulated in terms of dimensionless parameters, denoted as Π-terms. This approach permits the identification of the characteristic problem parameters that control the seismic response of the system also reducing the number of variables in Equation 3. ...
... The objective of the study is to evaluate how the circular frequency ω 0 , the frame damping ratio ξ, the parameter α, and the values of the target ductility demand of the BRBF and of the MRF, 8,9 respectively, μ bt and μ ft , affect the performance of the system. In order to achieve this objective, it is not possible to follow the approach conventionally followed in other studies, [39][40][41][42][43] where a free variation of the nondimensional problem parameters is considered. This is because the two nondimensional parameters related to the response, μ bt and μ ft , are defined by the design condition and hence fixed a priori rather than being observed. ...
Buckling-restrained braces (BRBs) have proven to be very effective devices improving the seismic performance of existing and new building frames. They provide strength, stiffness and added damping to the structure, however, due to their low lateral post-elastic stiffness, their use may lead to excessive residual deformations which may hinder the building’s reparability. Moreover, excessive cumulative ductility demand in the BRBs may compromise the capability of withstanding multiple earthquakes. To overcome these drawbacks, BRB frames (BRBFs) can be coupled with moment-resisting frames (MRFs) to form a dual system. If properly designed, the MRF acts as a back-up frame and allows to control the residual drifts and optimize the performance of the BRBs. This paper attempts to provide insights into the performance and residual capacity of this type of dual systems and to shed light on the influence of the main BRB’s design parameters. A non-dimensional formulation of the equation of motion is derived and an extensive parametric study is carried out on a single-degree-of-freedom system subjected to a set of natural records with different characteristics and scaled to various intensity levels. This allows to investigate a wide range of configurations, considering different levels of the relative strength of the BRBF and MRF and their ductility demand, and to obtain useful information for the BRBs design.
