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Purpose – The purpose of this paper is to present a simplified hybrid modeling (HYMOD) approach
which overcomes limitations regarding computational cost and permits the simulation and prediction
of the nonlinear inelastic behavior of full-scale RC structures.
Design/methodology/approach – The proposed HYMOD formulation was integrated in a research...
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... Figures 2-4 show the different domains of the model that include the raft slab, the steel frame and the soil domain. It is noteworthy to state at this point that the raft slab and soil domains were discretized with the 8-noded isoparametric FE, while the frame was discretized through the use of the Natural Beam Column Flexibility Based (NBCFB) element [10]. It is also evident that the use of different dimensionality FEs requires special handling for connecting the columns with the raft slab. ...
... It is also evident that the use of different dimensionality FEs requires special handling for connecting the columns with the raft slab. This is done by applying the HYMOD approach (Hybrid Modeling), as it is described in [10]. Table 1: Upper and lower bounds for simulation parameters. ...
The fundamental period of a structure is an important intrinsic dynamic property of the structural system response. Current design codes use simplified empirical formulae to estimate the fundamental period, that generally do not account for the influence of plan geometry , cross-sectional properties of the specific structural elements, nor the properties of the soil the structures are founded on, and thus the effects of soil-structure interaction (SSI) are not accounted for. This research work investigates the fundamental period of unbraced steel framed structures of various geometric configurations, and multiple different steel column members, as well as the SSI effect. A new algorithm is also developed for the automated construction and analysis of finite element models. The proposed automated procedure is used to create a dataset that is used to train and test the predictive formulae for computing the fundamental period of steel structures with and without accounting for the SSI effect. The proposed 40-feature formula was found to derive an optimum coefficient of determination (R 2) with a value of 99.976% and an error that is less than 2%.
... This issue can be solved by performing modal analyses on structures discretized with the hybrid model (HYMOD) approach (Gravett et al., 2019) without compromising the accuracy of the model. The HYMOD approach was adopted for the development of the structures presented herein as described by Markou and Papadrakakis (2015). The HYMOD approach combines hexahedral and beam column finite elements as it is depicted in Figure 11 where it is shown how the coupling between the hexahedral and beam-column elements through kinematic constraints is performed. ...
... A total of 475 modal results were generated considering the minimum and maximum values in terms of geometry and soil material properties as seen in Table 5. Figure 14 shows different models that foresee the discretization of the soil domain through the use of hexahedral elements. (Markou & Papadrakakis, 2015). Three design formulae were generated using the NLR ML algorithm . ...
... The models were further modified to include the SSI effect where a soil domain was discretized with depths of 1, 5, 12.5, 22.5 and 37.5 m. The superstructure was discretized through the use of Natural Beam-Column Flexibility-based (NBCFB) finite elements (Markou & Papadrakakis, 2015), where the raft and soil domains were discretized through 8-noded isoparametric hexahedral finite elements. A total of 1,152 numerical results were produced for the final dataset that was used to train and test the closed-form solutions. ...
The design and analysis of structures is performed with the use of national and international design codes that usually suggest the use of semi-empirical formulae. Often the formulae are oversimplified, in some cases are not available to engineers, or are time-consuming and challenging to implement. The objective of this chapter is to demonstrate the use of artificial intelligence and machine learning to develop more accurate formulae for different types of applications related to structural design. The applications that are discussed in this work include predicting the shear capacity of reinforced concrete slender and deep beams without stirrups, calculating the fundamental period of reinforced concrete and steel structures, and predicting the deflection of horizontally curved steel I-beams.
... It is of significant importance that the first property of the adopted numerical modeling method to be the ability of objectively capturing the capacity of RC structural members by accounting for the most important physical phenomena that occur during the monotonic loading of these structural members (microcracking and macrocracking of concrete, simulate the 3D stress field within the concrete domain, steel rebar-concrete interaction, discretize the exact geometry of the structural member, steel yielding and steel rupture). For this reason, the 3D detailed approach that was initially proposed in (Markou and Papadrakakis 2013) and further developed and experimentally validated in (Markou and Papadrakakis 2015, Mourlas et al. 2017a, Mourlas et al. 2017b) is adopted herein for the needs of this research work. ...
... According to the proposed modifications in Markou and Papadrakakis (2013), this problem was alleviated leading to small internal iteration numbers (per load increment) due to crack openings and other nonlinearities that occur during the analysis. Finally, the optimum algorithmic design of Reconan FEA allows for the computationally efficient solution of 3D detailed models under static and dynamic loading conditions efficiently (Markou and Papadrakakis 2013, Markou 2015, Markou and Papadrakakis 2015, Mourlas et al. 2017a, Mourlas et al. 2017b, Markou and AlHamaydeh 2018. ...
Calculating the shear capacity of slender reinforced concrete beams without shear reinforcement was the subject of numerous studies, where the eternal problem of developing a single relationship that will be able to predict the expected shear capacity is still present. Using experimental results to extrapolate formulae was so far the main approach for solving this problem, whereas in the last two decades different research studies attempted to use artificial intelligence algorithms and available data sets of experimentally tested beams to develop new models that would demonstrate improved prediction capabilities. Given the limited number of available experimental databases, these studies were numerically restrained, unable to holistically address this problem. In this manuscript, a new approach is proposed where a numerically generated database is used to train machine-learning algorithms and develop an improved model for predicting the shear capacity of slender concrete beams reinforced only with longitudinal rebars. Finally, the proposed predictive model was validated through the use of an available ACI database that was developed by using experimental results on physical reinforced concrete beam specimens without shear and compressive reinforcement. For the first time, a numerically generated database was used to train a model for computing the shear capacity of slender concrete beams without stirrups and was found to have improved predictive abilities compared to the corresponding ACI equations. According to the analysis performed in this research work, it is deemed necessary to further enrich the current numerically generated database with additional data to further improve the dataset used for training and extrapolation. Finally, future research work foresees the study of beams with stirrups and deep beams for the development of improved predictive models.
... During the last three decades, 3D detailed finite element modeling approaches have been proposed [1,2,5,17] for the analysis of structures with any geometry and type of loading. It is well known that beam-column and plane finite elements have significant simulation limitations when used to discretize 3D structures, as being unable to capture joint deformations and normal-shear stress coupling in three dimensions during a nonlinear analysis. ...
... It has to be mentioned that this concrete material model does not satisfy the 2 law of thermodynamics, since it was derived through regression on a large dataset of experimental results. However, it was found to be able to provide with acceptable numerical results when used to predict the structural response of RC structures [2,5,17,22] under monotonic and cyclic loading conditions. In this case, the physical laws were substituted by a large experimental dataset that incorporates the actual physical laws, instead of rigorous concepts or artificial physical laws. ...
The assessment of the nonlinear response of existing structures, or of new structural designs, to extreme loading conditions is of significant importance in achieving a safe and sustainable built environment. The accurate prediction of structural response of steel and steel-fibre reinforced concrete structures, that are expected to undergo ultimate limit state, monotonic and cyclic loading, is a challenging task, which is hindered by numerous modeling and numerical obstacles. As a consequence to this, the assessment of retrofitted reinforced concrete structures, is still conducted with the use of simplistic numerical models and semi-empirical design formulae. Although, quite a few 3D detailed modeling approaches have been proposed over the last two decades, they have a number of limitations that prevent them from their implementation, without simplifications, to the design of steel and fiber/steel reinforced concrete structures. In this work, the capabilities as well as the limitations of the recently published work on the subject will be critically presented, while different open problems will be discussed and remedies will be proposed to overcome these limitations. Furthermore, the development of a simulation tool with the ability to accurately and efficiently predict the structural performance of new designs and assess the bearing capacity of existing or retrofitted structures under extreme loading conditions, will also be discussed.
... However, such assessments before and after retrofitting are challenging, mainly because a) the progression of concrete damage and b) the effect of the retrofitting intervention are difficult to capture by existing models and simulation software. To address these drawbacks, the authors have recently proposed a new Hybrid Modelling (HYMOD) approach that provides numerically objective, accurate, and computationally robust solutions to the assessment of the ultimate carrying capacity of retrofitted structures [2]. The approach proved effective in modelling the seismic behaviour of a 4-storey RC building [3] subjected to pseudo-dynamic tests in bare and retrofitted conditions for which experimental data were available. ...
... (1) (2) where Ks and Gs are the secant forms of bulk and shear moduli, respectively. The secant forms of bulk, shear modulus and σid are expressed as functions of the current state of stress, which were derived by regression analysis of experimental data [40]. ...
... A displacement control algorithm was implemented for all nonlinear analyses with the energy convergence criterion as expressed in Eq. 32. The energy convergence tolerance was set equal to 10 -5 , which is in line with the numerical implementations presented in [2,[36][37][38]44]. ...
The seismic assessment of reinforced concrete (RC) structures before and after retrofitting is a challenging task, mainly because existing numerical tools cannot accurately model the evolution of concrete damage. This article proposes an innovative numerical method suitable to model and assess the ultimate carrying capacity of RC structures. The modelling approach proposes a steel constitutive material model with a damage factor that accounts for accumulated damage within the surrounding concrete domain, which effectively captures bar slippage. The proposed method is validated with experimental results from full-scale cyclic tests on deficient bare and CFRP-retrofitted RC joints tested previously by the authors. The results indicate that the proposed simulation method captures the extreme nonlinearities observed in the tested RC joints, with acceptable accuracy and computational robustness. The results of this study are expected to contribute towards the development of more reliable numerical tools and design guidelines for efficient seismic assessment of RC structures before and after earthquakes.
... The methodology foresees the use of a computationally efficient and robust 3D modelling technique known as the HYMOD approach [7][8][9] in order to perform modal analysis to investigate the effect that SSI has on the fundamental period of RC structures. The overall approach foresaw the creation of a dataset comprising out of all the modal analysis results obtained from the various numerical models [1]. ...
The fundamental period of a structure is one of the key parameters utilized in the design phase to compute the seismic-resistant forces. Although the importance of seismic-resistant buildings is well understood it has been found that the current design code formulae, which are used to predict the fundamental period of reinforced concrete (RC) buildings are quite simplistic, failing to accurately predict the natural frequency, raising many concerns with regards to their reliability. The primary objective of this research project was to develop a formula that has the ability to compute the fundamental period of an RC structure, while taking into account the soil-structure interaction phenomenon. This was achieved by using a computationally efficient and robust 3D detailed modelling approach for modal analysis obtaining the numerically predicted fundamental period of 475 models, producing a dataset with numerical results. This da-taset was then used to train a machine learning algorithm to formulate three fundamental period formulae using a higher-order, nonlinear regression modelling framework. The three newly proposed formulae were evaluated during the validation phase to investigate their performance using 60 new out-of-sample modal results, where, in this work, additional validation models are created and used to test the predictive abilities of the proposed fundamental period formulae. The findings of this research report suggest that the proposed fundamental period formulae exhibit exceptional predictive capabilities for the understudy RC multi-storey buildings , where they outperform all existing design code fundamental period formulae currently in effect.
... The purpose of this work is to investigate deep-learning algorithms for the prediction of the shear strength of RC beams. For the needs of this research work, detailed 3D finite element (FE) modelling of RC structures is adopted [14,15,16,17,18], in order to develop a large database of results on slender RC beams without stirrups. The numerically generated data set is then used to train models to predict the beams' shear strength. ...
Data-driven models employing artificial intelligence approaches have been increasingly utilized in structural analysis and design problems over the past two decades. The main applications involve the processing of datasets, which are gathered from experimentally derived records or obtained numerically, in order to develop closed-form formulae or numerical tools predicting quantities related to structural response and mechanical behaviour. Given that datasets are difficult to assemble due to the limited available information and the high cost entailed to enrich them, exhaustively processing the available data to produce the best possible prediction models is an essential task of particular interest. For specific applications, this exhaustive computing task involves large numbers of iterations performed to train detailed prediction models with large numbers of parameters. Despite the intense computational demands of such problems, limited research work exists on the scaling-up of the utilized algorithms on supercomputers. In this work, a distributed training and hyperparameter tuning algorithm is proposed for the modelling of the shear strength of slender beams without stirrups. The training dataset comprises results obtained from the detailed modelling and analysis of several beams with non-linear finite elements using the Reconan software. The results presented in this research work highlight the importance of optimally utilizing computational power for the solution of such problems. The developed computer code is available on GitHub.
... where, (23) In the case of unloading, when the structure reaches zero deformation, a material deterioration of the steel reinforcement is estimated according to the following expression: ...
... s=0 and βc = 0) shows the following results in Fig. 12.29 comparing to the experimental ones in terms of P-δ curve. All the cyclic analysis can be conducted using the HYMOD approach that was presented in Chapter 10 as published in [22,23,24]. first (0,0) point within the function (it is omitted). ...
... 22 P-δ curve. 20-noded hexahedral mesh.23 Deformed shape prior to failure. ...
Reconan FEA v2.00 software manual.
... The constitutive model is based on the experimental findings of Kotsovos and Newman [3] and a mathematical approach described in Kotsovos and Pavlovic [4]. This model is also used for the analysis of large-scale structures as described in Markou et al. [5], where a 4-storey RC building specimen was modeled through the Hybrid Modeling (HYMOD) approach [6,7]. The under study RC building [5] was retrofitted with RC infill walls and carbon fiber reinforced polymer (CFRP) jacketing at its base, where three different load histories were applied until the frame reached its ultimate capacity. ...
... T g l C = T C T (6) where T is the transformation matrix consisted by the direction cosines that define the relative orientation of the local to global axis. The factor Dc is a damage factor proposed in [11], describing the accumulated energy loss due to the number of times a crack has opened and closed. ...
Advanced numerical methods for seismic assessment of existing substandard reinforced concrete (RC) structures have significantly evolved in the last two decades. Nonetheless, existing numerical tools have numerous limitations (e.g. numerical instabilities, applicable only in 1D or 2D problems, computationally demanding, etc.) and lack of objectivity and accuracy in providing robust, numerically accurate and objective solutions. As a result, new numerical approaches are necessary to solve some of these limitations. This paper presents a detailed 3D modelling approach that solves some of the current model-ing limitations. The approach is used to predict the experimental results from i) a substandard RC joint with inadequate detailing subjected to cyclic loading, and ii) the same RC joint rehabilitated and retrofitted with carbon fiber reinforced polymer (CFRP) sheets and subjected to cyclic loading. It is shown that the proposed numerical method reproduces the experimental results of both substandard and CFRP retrofitted specimens in a robust and computationally efficient manner. Current research is investigating the behavior of more RC components and full-scale retrofitted structures. This study contributes towards providing engineers and researchers with an advanced analytical tool to study the cyclic nonlinear behaviour of substandard RC structures.
... In order to overcome the numerical limitations derived from the high computational demand of the 3D detailed modeling, the HYMOD method is implemented in this research work as it was proposed by Markou and Papadrakakis [9], while the proposed modal algorithm [8] was programmatically optimized for the needs of this research work to be able to manage largescale numerical problems. The HYMOD approach and its main assumptions are presented in the next section. ...
... The HYMOD approach adopted in this work is based on the formulation presented by Markou and Papadrakakis [9], which was also extended in [8] in order to analyze large-scale RC structures submitted to cyclic loading conditions. Based on the proposed framework of Markou and Papadrakakis [9], the element types that are combined, are the isoparametric hexahedral element and the natural Beam-Column Flexibility-Based (NBCFB) fiber element. ...
... The HYMOD approach adopted in this work is based on the formulation presented by Markou and Papadrakakis [9], which was also extended in [8] in order to analyze large-scale RC structures submitted to cyclic loading conditions. Based on the proposed framework of Markou and Papadrakakis [9], the element types that are combined, are the isoparametric hexahedral element and the natural Beam-Column Flexibility-Based (NBCFB) fiber element. The NBCFB element is a one-dimensional element and the 8-noded isoparametric hexahedral element is a three-dimensional element that consists of 24 degrees of freedom (dof). ...
Nonlinear dynamic modeling of full-scale mid-and high-rise reinforced concrete structures through the use of the 3D detailed approach that foresees the use of hexahedral elements with embedded rebars is not yet feasible due to numerous reasons. The two main numerical problems that do not allow for this type of analysis to be performed, are the numerical instabilities that immerse when the opening and closing of cracks initiates during the dynamic analysis and the excessive computational demand that is required even when dealing with small numerical models. This work will present the computational response of a newly developed algorithm that is used herein to perform modal analysis of large-scale models. The under study algorithmic development is a part of a project that aims towards alleviating the prementioned numerical constraints in regard to performing nonlinear dynamic analysis of full-scale reinforced concrete structures. An extensive numerical investigation is presented that foresees the performance of modal analysis on different full-scale reinforced concrete structures that are discretized with the Hybrid Model (HYMOD) approach. Based on the numerical investigation findings, the developed algorithm was found to be computationally efficient offering a robust numerical tool for performing modal analysis of large-scale numerical models.
