Effective Stiffness Ratio Research Articles

Optimized machine learning models for prediction of effective stiffness of rectangular reinforced concrete column sections

To evaluate the response of a reinforce concrete (RC) building subjected to nonlinear dynamic loading, it is recommended to use effective stiffness of the members. Currently, design codes and practices provide an empirical fraction of un-cracked stiffness to consider the effect of reduced stiffness in cracked sections. However, it is imperative to conduct an accurate assessment of effective stiffness as it directly affects the distribution of forces and various demands in nonlinear dynamic analyses. Manual calculation of effective stiffness based on strength is a time-consuming process. Therefore, the present study attempts to estimate the effective stiffness ratio of rectangular column sections using machine learning algorithms with ensemble learners namely, Adaptive Boosting (AdaBoost), Random Forest (RF), Extreme Gradient Boosting (XGBoost), Decision Tree (DT) and Categorical Gradient Boosting (CatBoost) using a database of 226 samples of nonlinear dynamic analysis results, obtained from previous work of the author. Additionally, Bayesian Optimization has been used for optimal hyperparameter selection. The results of the present study exhibit that the CatBoost model outperforms other considered machine learning models with R2 value of 0.9921 and 0.9966. A sensitivity analysis based on SHAP has also been implemented to establish the correlation between input parameters and output parameters.

A Prediction Model for the Calculation of Effective Stiffness Ratios of Reinforced Concrete Columns.

Nonlinear dynamic analyses of reinforced concrete (RC) frame buildings require the use of effective stiffness of members to capture the effect of cracked section stiffness. In the design codes and practices, the effective stiffness of RC sections is given as an empirical fraction of the gross stiffness. However, a more precise estimation of the effective stiffness is important as it affects the distribution of forces and various demands and response parameters in nonlinear dynamic analyses. In this study, an evolutionary computation method called gene expression programming (GEP) was used to predict the effective stiffness ratios of RC columns. Constitutive relationships were obtained by correlating the effective stiffness ratio with the four mechanical and geometrical parameters. The model was developed using a database of 226 samples of nonlinear dynamic analysis results collected from another study by the author. Subsequent parametric and sensitivity analyses were performed and the trends of the results were confirmed. The results indicate that the GEP model provides precise estimations of the effective stiffness ratios of the RC frames.

Electroconductive Melt Electrowritten Patches Matching the Mechanical Anisotropy of Human Myocardium

AbstractCardiac patches represent a promising strategy for the treatment of myocardial infarction (MI). Here, an electroconductive cardiac patch that conforms to the mechanics of human myocardium is fabricated. By melt electrospinning writing (MEW), it is possible to fabricate an auxetic patch that can overcome the limited range of elasticity seen in conventional square patch designs. The auxetic patches can accommodate the strains and stresses exhibited by the human myocardium during diastole and systole. It is shown that the geometry of the auxetic patches can be fine‐tuned to reflect anisotropic mechanical properties. The anisotropic ratio of effective stiffness (E1/E2) of the auxetic patches agrees with the directionally‐dependent mechanics of the heart. Furthermore, in situ polymerization of doped‐polypyrrole (PPy) on the auxetic patches confers electroconductive properties close to those reported of human myocardium. This approach demonstrates the potential use of a rational design of PPy‐coated patches for their use as cardiac patches.

Influence of effective stiffness on the performance of RC frame buildings designed using displacement-based method and evaluation of column effective stiffness using ANN

In the analysis and design of reinforced concrete (RC) buildings, member stiffness is generally taken as the gross stiffness, or as the effective stiffness as an empirical approximate fraction of gross stiffness. However, actual stiffness is strength dependent. Improper approximation of member stiffness affects the distribution of forces and deformation demands which lead to inaccurate structural response evaluation. Thus, the use of actual effective stiffness based on strength is very important in nonlinear analyses to evaluate the actual performance of the building under seismic conditions. A series of RC frame buildings have been designed using displacement-based method. The designed building have been subjected to nonlinear analyses incorporating three categories of stiffnesses, namely, gross stiffness, effective stiffness as per FEMA-356, and, actual effective stiffness based on strength. The results of nonlinear time history analysis show that the buildings analysed with gross stiffness exhibit very conservative drift and high performance level in comparison with those of buildings with effective stiffness based on strength. FEMA specified effective stiffness ratio yielded drift and performance level in between those with gross stiffness and effective stiffness based on strength. It is noted that, the estimation of actual effective stiffness for column sections is a tedious process. Therefore, to ease the process, a soft computing technique called artificial neural network (ANN), has been used to estimate the effective stiffness of columns sections. The statistical performances of the ANN model show that it can be used as an alternative tool to estimate the effective stiffness of RC column sections with good accuracy. Moreover, a model equation is presented based on the parameters of trained neural network which can be readily used to estimate effective stiffness ratios.

Seismic performance improvement of tension-only-braced frames with Energy-Dissipative Rocking Columns

Steel braced frames consisting of strong beams, weak columns, and tension-only braces (BTFs) have been extensively used in low-rise steel buildings, since it is prefabricated rapidly and is cost-efficient. However, BTFs are vulnerable to soft story failure due to the negligible post-yielding stiffness of tension-only braces. A novel device of Energy-Dissipative Rocking Column (EDRC) is proposed to improve the seismic performance of BTFs. An EDRC consists of dual hinge supported steel column branches and replaceable steel strip dampers between them. Firstly, the effectiveness of EDRCs were verified through nonlinear time history analyses on benchmark multi-story BTFs using a suite of far-field ground motion records. Secondly, systematic parametric studies are conducted to quantify the effect of key influencing factors such as stiffness ratio of EDRC to BTF and bending stiffness of column branches on the seismic performance improvement of BTF-EDRC systems. The results show that the maximum inter-story drift and inter-story drift concentration under earthquakes as well as the residual drift after earthquakes can be significantly mitigated by coupling with EDRC. It is found that the maximum inter-story drift ratio can be reduced by 50% when the stiffness ratio of EDRC to BTF reached 1.0. The most effective stiffness ratio of EDRC to BTF for mitigating the inter-story drift concentration and residual drift ratio falls in a range of no more than 0.2 and 0.4, respectively.

Evaluation of effective stiffness of RC column sections by support vector regression approach

Effective stiffness of reinforced concrete (RC) members has a very important role in the performance evaluation of RC frame buildings through nonlinear dynamic analyses. The beam effective stiffness can be readily computed using mechanics, but the evaluation of column stiffness is a complicated process and the use of support vector regression helps in this regard. Therefore, in this study, an attempt is made to predict the effective stiffness ratio of reinforced concrete columns using support vector regression (SVR) approach. A data set of 208 samples, which are collected through nonlinear dynamic analysis of reinforced concrete buildings using SAP2000 software, is utilized to develop the SVR model. The input parameters considered are reinforcement percentage, axial load and depth of the column section in both the perpendicular directions, and the output parameter is the effective stiffness ratio of columns. Three different kernel parameters are used, namely exponential radial basis function (ERBF), Gaussian radial basis function and polynomial function for SVR modelling, among which ERBF is found to be the most suitable one. The obtained results indicate that the statistical performance of the SVR-ERBF model is better than the models with other two kernels in predicting the effective stiffness ratio of reinforced concrete columns. Performance of the SVR model is compared with the results of multi-variable regression analysis. In addition to that, a sensitivity analysis is also performed to check the influence of each input parameter on output responses.

Tuning the wrinkling patterns of an interfacial/coating layer via a regulation interphase

In this investigation, the mechanical response of a tri-phase system subjected to far-field compression is explored. The system includes a stiffer interfacial/coating layer surrounded by an interphase/regulation layer, and both layers are embedded in an infinite softer matrix. Both theoretical and finite element (FE) mechanical models of the system are developed. From the results of these models, three wrinkling patterns are proved to exist: (I) single-layer wrinkling mode, (II) bi-layer wrinkling mode, and (III) the simultaneous nested-wrinkling mode. The wrinkling patterns are reported to be attributed to the instability of the system. The results of FE simulations show that the theoretical model can accurately predict the instability of the system. The influences of the geometry and material properties of all three phases on the transition between the three instability modes are quantified. It reveals that the regulation layer/interphase around the interfacial/coating layer is the key to tune the wrinkling patterns. The critical physical parameters to determine the characteristics of the three instability modes are the effective thickness ratio between the regulation layer and interfacial/coating layer, the effective stiffness ratio between the interfacial/coating layer and the regulation layer and that between the interfacial/coating layer and the matrix. As an example of the application of the theoretical model, a graded interfacial wrinkling pattern is designed and verified via FE simulations.

Review on the macro-modeling alternatives and a proposal for modeling coupling beams in tall buildings

Coupling beams between shear walls are one of the key elements for energy dissipation in tall buildings. A representative mathematical model of coupling beam should represent flexure, shear and interface slip/extension mechanisms simultaneously. This goal can be achieved by using either detailed finite element models or by using macro models. This paper presents a review of various macro model alternatives for diagonally reinforced coupling beams in the literature. Three distinct methods have been reviewed in terms of their modeling techniques, the cyclic response overlap and the amount of cumulative plastic energy dissipated based on the results of previously performed tests. Through an analytical study, adequately accurate results can be captured by using macro models, although they are simpler in practice compared to sophisticated micro models. This study shows that, by modifying ultimate shear capacities where concrete material between diagonal bundles is adequately confined, it is possible to capture a more realistic result and a better approximation to the actual responses. It is also concluded that a simpler numerical model for diagonally reinforced coupling beams can be achieved by introducing linear part of slip/extension behavior into elastic part of the beam. It is observed, as a result of this study, that the ratio of effective stiffness to that of the gross cross-sectional one ranges from 0.04 to 0.14 in diagonally reinforced coupling beams depending on the aspect ratio and the beam strength parameters.

A case study of damage detection in four-bays steel structures using the HHT approach

This study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert-Huang transform (HHT) method. Two damage detection indices are proposed: the ratio of bandwidth (RB), and the ratio of effective stiffness (RES). The nonlinear four bays multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA earthquake data (Japan 311, Chi-Chi 921) are used as the excitations. Next, the damage detection indices obtained using the HHT and the fast Fourier transform (FFT) methods are evaluated based on the acceleration responses of the structures to earthquakes. Simulation results indicate that, the column of the 1st floor is the first yielding position and the RB value is changed when the RES<90% in all cases. Moreover, the RB value of the 1st floor changes more sensitive than those from the top floor. In addition, when the structural response is nonlinear (i.e., RES<100%), the RB and the RES curves indicate the incremental change in the HHT spectra. However, the same phenomenon can be found from FFT spectra only when the stiffness reduction is large enough. Therefore, the RB estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage.

Seismic behavior of slender reinforced concrete walls

Residential reinforced concrete buildings performed well during the 2010 Mw 8.8 Maule, Chile earthquake. However, brittle damage was observed in reinforced concrete structural walls. The most frequent observed damage in such walls was crushing of concrete due to flexural-compressive interaction, buckling and fracture of longitudinal reinforcement, and opening of the horizontal reinforcement. The main objective of this study is to understand the observed damage in slender walls after 2010 Maule earthquake and to reproduce and analyze experimentally the seismic behavior of such walls. The second objective is to provide recommendations to estimate the lateral displacement and the effective stiffness of slender walls. To achieve these objectives, six ½-scale slender reinforced concrete walls were tested using a conventional quasi-static cyclic incremental lateral displacement test protocol with a constant axial load. The test results are compared to a reference wall tested previously in the same research project. The variables analyzed in this study are: wall thickness, wall aspect ratio, use of uniformly distributed vertical reinforcement, detailing of 135-degree hooks for the horizontal reinforcement, addition of closed stirrups in the wall boundaries, and addition of transverse cross-ties. The observed damage in the tested walls was similar to that observed in walls of buildings damaged during the 2010 Maule earthquake. The behavior of the tested walls was dominated by bending due to their relatively large aspect ratio. The failure, determined by the loss of ability to carry axial load, occurred suddenly as a compression failure along the entire cross section at the base of the tested walls. Test results showed that a 25% reduction in wall thickness reduced the ultimate displacement capacity, ductility, and energy dissipation ability of the wall. Closed stirrups and cross-ties were effective in increasing displacement capacity and ductility, and closed stirrups were effective in preventing out-of-plane buckling of the wall after compression failure. The average effective stiffness ratio of the tested walls was 0.39, which is slightly larger than the ACI 318 suggestion of 0.35.

Pore pressures around tunnels in clay

The pore-pressure generation and dissipation around shallow tunnels excavated in both normally and overconsolidated clays are investigated. The influence of the diameter D, depth of cover to diameter ratio H/D, coefficient of earth pressure at rest K0, and strength and modulus variations with depth on pore-pressure generation are examined. The effects of immediate support on pore pressure are also studied by defining a quantity termed effective stiffness ratio (ESR). A two-dimensional, nonlinear finite element analysis is performed to obtain the pore-pressure generation behav-iour. Strength, modulus, initial stress field, and unloading due to excavation are reflected in this analysis. The pore-pressure dissipation behaviour is investigated by employing an uncoupled consolidation theory using finite elements. A dimensionless time factor is used to present the results of pore-pressure dissipation. These results are presented using nondimensional quantities and in normalized forms. The results are directly applicable to estimation of pore pressures for determining long-term stability of tunnels. Key words : clay, pore pressure, tunnels, uncoupled consolidation, finite elements, stress-strain.