The beam-column joint is a critical component of structural systems, vital to maintaining structural integrity. During seismic events, these joints undergo significant deformations, reducing their capacity to carry lateral and gravitational loads. This often results in damage or even collapse of the structure. Such failures have been observed, particularly in non-ductile reinforced concrete (RC) frames, even when adequate design details have been implemented.
The inelastic response of beam-column joints is fundamental to the overall performance of the structure. Therefore, accurate simulation of this behaviour in numerical models is essential for evaluating existing structures and designing new ones. Reliable assessments necessitate the precise prediction of failure modes and capacities of beam-column connections. However, current models for probabilistic assessment often overlook these failure modes. Developing a comprehensive model that accounts for these modes is a complex and computationally intensive task, primarily due to the reliance on finite element methods.
A study conducted by Sujith Mangalathu et al., from the Department of Civil and Environmental Engineering at the University of California, Los Angeles, focuses on predicting the shear strength of reinforced concrete beam-column joints through the application of various machine learning techniques. The methods employed include logistic regression, lasso logistic regression, discriminant analysis, k-nearest neighbors, support vector machines, decision trees, and random forests.
The authors utilized a dataset comprising 536 samples, which included 12 input parameters: concrete compressive strength, joint transverse reinforcement, design joint shear stress, in-plane joint geometry, out-of-plane joint geometry, the ratio of beam depth to column depth, joint eccentricity parameter, the ratio of beam width to column width, column axial load ratio, beam-bar bond parameter, column-to-beam flexural moment strength ratio, and column intermediate longitudinal reinforcement factor.
The output of the study classifies failure modes as either J or BJ. J failure is characterized by a response of the joint that leads to an abrupt loss of lateral load-carrying capacity, resulting in brittle failure. In contrast, the behaviour of sub-assemblages exhibiting BJ failure is primarily influenced by beam yielding, indicative of ductile failure. The dataset was systematically divided into 70% for training purposes and 30% for testing to ensure robust model development and evaluation.
The study aimed to (1) compare the effectiveness of different machine learning techniques in identifying the failure mode (ductile or nonductile) and shear strength of beam-column joints with transverse reinforcement, (2) propose a simple equation for determining failure mode and shear strength based on geometric, material, and structural properties, and (3) assess the significance of various uncertain input
parameters on the shear strength of beam-column joints.
To assess the failure modes of reinforced concrete beam-column joints, a variety of machine learning techniques were employed. Analysis of the misclassification data indicated that k-nearest neighbors, lasso regression, and extreme learning machines demonstrated superior performance, particularly in relation to the BJ failure mode. While extreme learning machines and k-nearest neighbors provide robust results, they lack interpretability and do not yield a definitive equation. In contrast, logistic regression and lasso logistic regression present a cohesive classification framework. From an engineering perspective, logistic regression may exhibit low bias; however, it is prone to high variance, which positions lasso regression as the preferred methodology for this study. Lasso regression is particularly advantageous as it systematically excludes non-significant variables from the analysis, assigning a coefficient of zero to these variables. Consequently, a comprehensive equation for classification has been established.
This study also aims to establish a predictive equation for estimating the shear strength of beam-column joints based on their failure modes. To achieve this, regression analyses were performed utilizing various machine learning techniques. The analysis identified several key variables that significantly influence joint shear strength, including concrete compressive strength, joint transverse reinforcement, design joint shear stress, plane joint geometry, out-of-plane joint geometry, and the ratio of beam depth to column depth.
For the J failure mode, stepwise, ridge, and lasso regression analyses revealed that the beam-bar bond parameter has a minimal impact on joint shear strength. Conversely, in the case of the BJ failure mode, three regression techniques consistently indicated that the column-to-beam
flexural moment strength ratio has a reduced effect on joint shear strength. In this study, lasso regression has been selected as the predictive equation.
The relative importance of input variables on joint shear strength can be more effectively assessed through lasso regression analysis. The design shear stress is identified as the most influential factor affecting the joint shear strength for both J and BJ failure modes. Additionally, the significance of in-plane joint geometry and concrete compressive strength is greater for the BJ mode compared to the J mode. Conversely, the input variables, including the ratio of beam width to column width, beam-bar bond parameter, joint eccentricity parameter, and the column-to-beam flexural moment strength ratio, have a lesser impact on joint shear strength.
The predictive equation proposed in this research effectively enables the evaluation of failure modes and joint shear strength without the necessity for costly and intricate finite element models. This equation, which takes into account various influential input variables, serves as a valuable tool for engineers in design offices, allowing for a swift assessment of beam-column joints and facilitating informed decisions regarding optimal retrofitting strategies.
The expression utilized for classification is:
ln (p/1-p) = -5.99 – 1.12 ln(concrete compressive strength) – 0.51 ln(joint transverse reinforcement) + 2.62 ln(design joint shear stress) – 6.07 ln(in-plane joint geometry) – 3.94 ln(out-plane joint geometry) + 0.3 ln(ration of beam depth to column depth) + 0.32 ln(column axial load ratio) – 2.86 ln(beam-bar bond parameter) – 0.32 ln(column-to-beam flexural moment strength ratio.
Reference
Mangalathu, S., & Jeon, J. S. (2018). Clsssification of failure mode and prediction of shear strength for reinforced concrete beam-column joints using machine learning techniques. Engineering Structures, 160, 85-94.