A Multi-Parameter Discrimination Method for Failure Modes of RC Beam-Column Joints Based on Fisher Transform and Bayes Classification Principle

doi:10.12141/j.issn.1000-565X.250203

Abstract

Abstract:

The various failure modes of reinforced concrete (RC) beam-column joints under lateral loading exert different impacts on the structural performance. Thus, accurately categorizing component failure modes is pivotal for determining the deformation performance limits in structural performance design. Existing research lacks clear boundaries between different failure modes of beam-column joints, and it remains difficult to distinguish intervals corresponding to distinct failure types using a single parameter. This paper proposes a more accurate and practical discriminant method for identifying failure modes in interior beam-column joints, incorporating multiple parameters based on the Fisher transform and Bayes classification principles. The method initially employs the Fisher discriminant analysis to identify projection spaces with maximum separation between classes, projecting original samples into these optimally separated spaces to obtain new samples more amenable to classification. Subsequently, Bayes classification principles are applied for discriminant analysis of the new samples. In studying interior joint failure mode classification, based on this method the corresponding multi-parameter classification discriminant equations are established using a combination of four parameters: axial compression ratio, shear compression ratio, concrete strength, and stirrup characteristic value. This approach effectively classifies failure modes of interior beam-column joints and clearly defines intervals corresponding to different failure types. Furthermore, through sensitivity analysis of influencing factors, the study determines that the shear compression ratio has the most significant influence on failure modes, followed by the stirrup characteristic value. Therefore, adjusting the shear compression ratio and the stirrup characteristic value is an effective means of preventing shear failure at this type of joint.

Key words: reinforced concrete, beam-column joints, Fisher transform, Bayes classification, failure mode

CLC Number:

TU375

WANG Suguo, FAN Cunxi, ZHENG Yi. A Multi-Parameter Discrimination Method for Failure Modes of RC Beam-Column Joints Based on Fisher Transform and Bayes Classification Principle[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(12): 107-116.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 1

Table 2

Fig.10

Table 3

Table 4

Table 5

References 16

[1]	GAO X L， LIN C ．Prediction model of the failure mode of beam-column joints using machine learning methods［J］．Engineering Failure Analysis，2021，120：105072/1-24.
[2]	NADERPOUR H， MIRRASHID M ．Classification of failure modes in ductile and non-ductile concrete joints［J］．Engineering Failure Analysis，2019，103（47）：361-375.
[3]	彭修宁，林焯铭，黄展业，等．双钢板混凝土剪力墙基于性能的变形指标限值研究［J］．地震工程与工程振动，2022，42（4）：80-91.
	PENG Xiuning， LIN Zhuoming， HUANG Zhanye，et al ．Study on the limit value of deformation index of double steel plate concrete shear wall based on seismic performance［J］．Earthquake Engineering and Engineering Dynamics，2022，42（4）：80-91.
[4]	崔济东，韩小雷，龚涣钧，等．钢筋混凝土柱变形性能指标限值及其试验验证［J］．同济大学学报（自然科学版），2018，46（5）：593-603.
	CUI Jidong， HAN Xiaolei， GONG Huanjun，et al ．Deformationlimits of reinforced concrete columns and their experimental verification［J］．Journal of Tongji University （Natural Science），2018，46（5）：593-603．
[5]	季静，刘寒，陈彬彬．基于试验的型钢混凝土柱抗震性能指标限值研究［J］．土木工程学报，2017，50（6）：1-10.
	JI Jing， LIU Han， CHEN Binbin ．Research on deformation limits of SRC columns based on experimental data［J］．China Civil Engineering Journal，2017，50（6）：1-10.
[6]	何晓群．多元统计分析［M］．北京：中国人民大学出版社，2004.
[7]	JOHNSON R A， WICHERN D W ．Applied multivariate statistical analysis［M］．Berlin，Heidelberg：Prentice Hall，2003.
[8]	PHAM-GIA T， TURKKAN N， BEKKER A ．Bounds for the Bayes error in classification：a Bayesian approach using discriminant analysis［J］．Statistical Methods and Applications，2007，16：7-26.
[9]	马健．配置HRB500E钢筋混凝土梁柱中节点试验及有限元研究［D］．武汉：华中科技大学，2015.
[10]	CAO Y， YANG Z ．Seismic damage evaluation of beam-column joints in monolithic precast concrete frame structures［J］．Materials，2022，15（17）：6038-6049.
[11]	GOMBOSUREN D， MAKI T ．Prediction of joint shear deformation index of RC beam-column joints［J］．Buildings，2020，10（10）：176-210.
[12]	范国玺，窦子琛，王德斌，等．不同加载速率和柱变轴力下钢筋混凝土梁柱边节点组合体受力性能研究［J］．建筑结构学报，2022，43（S1）：106-115.
	FAN Guoxi， DOU Zichen， WANG Debin，et al ．Study on mechanical performance of reinforced concrete exterior beam-column joint combination under different loading rates or variable column axial forces［J］．Journal of Building Structures，2022，43（S1）：106-115.
[13]	KIM J， LAFAVE J M ．Key influence parameters for the joint shear behaviour of reinforced concrete （RC） beam-column connections［J］．Steel Construction，2007，29（10）：2523-2539.
[14]	HWANG H J， PARK H G ．Requirements of shear strength and hoops for performance-based design of interior beam-column joints［J］．ACI Structural Journal，2019，116（2）：245-256.
[15]	MANGALATHU S， JEON J S ．Classification of failure mode and prediction of shear strength for reinforced concrete beam-column joints using machine learning techniques［J］．Engineering Structures，2018，160（8）：85-94.
[16]	苏佶智，刘伯权，马煜东．钢筋混凝土框架结构层间位移与构件变形关系研究［J］．建筑结构学报，2020，41（6）：149-160.
	SU Jizhi， LIU Boquan， MA Yudong ．Relationship between inter-story drift of RC frame structures and deformation of members［J］．Journal of Building Structures，2019，41（6）：149-160.

判别函数	系数项				常数项
判别函数	轴压比	剪压比	混凝土强度	配箍特征值	常数项
判别函数1	-3.153	26.760	0.059	-4.595	-4.808
判别函数2	-1.078	1.954	0.152	24.860	-13.215
判别函数3	4.883	3.467	0.070	-3.006	-5.080

判别函数	特征值	方差占比/%	累积占比/%	典型相关性
判别函数1	2.814	88.3	88.3	0.859
判别函数2	0.344	10.8	99.1	0.506
判别函数3	0.030	0.9	100.0	0.170

破坏形态分类函数	轴压比系数	剪压比系数	混凝土强度系数	配箍特征值系数	常量
y₁（梁端破坏）	-4.485	109.957	2.502	259.558	-86.687
y₂（剪切破坏）	-19.790	237.875	2.664	219.385	-101.955
y₃（梁端屈服剪切破坏）	-9.144	167.179	2.536	230.576	-87.742
y₄（柱端屈服剪切破坏）	-18.019	230.133	2.937	230.133	-121.565

有限元模型破坏形态判别数量		预测组模型破坏形态判别数量				判别正确数	判别准确率/%
有限元模型破坏形态判别数量		梁端破坏	剪切破坏	梁端屈服剪切破坏	柱端屈服剪切破坏	判别正确数	判别准确率/%
梁端破坏	56	50	0	6	0	50	89.3
剪切破坏	30	0	26	1	3	26	86.7
梁端屈服剪切破坏	96	10	7	77	2	77	80.2
柱端屈服剪切破坏	24	0	1	0	23	23	95.8