A Transfer Matrix Method for Analyzing the Shear Lag Effect of Groove Beam with Different Tensile and Compressive Modulus.
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| Title: | A Transfer Matrix Method for Analyzing the Shear Lag Effect of Groove Beam with Different Tensile and Compressive Modulus. |
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| Authors: | Li, Bin1 12007030@hnist.edu.cn, Xing, Xuebin2 232174471@qq.com, Zeng, Yongqing3 yqzeng@hnist.edu.cn, Zhou, Xinheng4 751796632@qq.com, Lou, Hua1 12015024@hnist.edu.cn, She, Qingcong1 22017036@hnist.edu.cn |
| Source: | IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2265-2281. 17p. |
| Subjects: | Transfer matrix, Elastic modulus, Thin-walled structures, Structural analysis (Engineering), Finite element method, Shear (Mechanics) |
| Abstract: | Based on the transfer matrix theory, this paper proposes a transfer matrix method for analyzing the shear lag effect in thin-walled groove beams. Considering the influence of materials with different elastic moduli in tension and compression, the governing differential equations and natural boundary conditions for the groove beam are established. The equilibrium conditions of the tension and compression zones are also been taken into account, and the positions of these zones are derived. The general solutions and initial parameter solutions of the differential equation under four boundary conditions, namely simply supported, fixed, free, and directionally supported, are obtained. The corresponding field matrices and point matrices are derived, enabling a more accurate analysis of stress and displacement distributions in the groove beam. Using the transfer matrix method and ANSYS finite element software, a variable-cross-section cantilever groove beam under a uniformly distributed load across the full span is analyzed; the percentage error in normal stress and deflection results for the variable-cross-section groove beam under different elastic modulus ratios is calculated. Similarly, a three-span constant-cross-section continuous groove beam under a uniformly distributed load across the full span is analyzed; the percentage error in normal stress results for the three-span constant-cross-section continuous groove beam under different elastic modulus ratios is obtained. The transfer matrix method shows good agreement with the results from finite element simulations, further validating the correctness of the method. The proposed transfer matrix method is characterized by convenient calculation, good stability, and high accuracy, which can significantly reduce the computational workload and simultaneously provide the values Manuscript received December 9, 2025; revised May 5, 2026. The study was supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2025JJ70253, Grant No. 2025JJ70276, and Grant No. 2026JJ80250), the Key Scientific Program of Hunan Education Department, China (Grant No. 23A0496, and Grant No. 23B06245), the Ministry of Education's Collaborative Education and Training Program for Industry-Academia Cooperation (Grant No. 250901094234014, and Grant No. 250901094225658). Bin Li is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 12007030@hnist.edu.cn). Xuebin Xing is a senior engineer of Jiangsu Shengshi Railway Equipment Co., Ltd., Changshu, 215500 China (e-mail: 232174471@qq.com). Yongqing Zeng is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (corresponding author to provide e-mail: yqzeng@hnist.edu.cn). Xinheng Zhou is an undergraduate student of College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 751796632@qq.com). Hua Lou is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 12015024 @hnist.edu.cn). Qingcong She is a lecturer in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 22017036@hnist.edu.cn). of internal forces, bending moments, displacement, and stress on any cross-section. It offers an effective computational approach for solving the shear lag effect in beam structures such as variable-section thin-walled groove beams and continuous groove beams, and provides important reference and basis for the design of bridge structures. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
| Abstract: | Based on the transfer matrix theory, this paper proposes a transfer matrix method for analyzing the shear lag effect in thin-walled groove beams. Considering the influence of materials with different elastic moduli in tension and compression, the governing differential equations and natural boundary conditions for the groove beam are established. The equilibrium conditions of the tension and compression zones are also been taken into account, and the positions of these zones are derived. The general solutions and initial parameter solutions of the differential equation under four boundary conditions, namely simply supported, fixed, free, and directionally supported, are obtained. The corresponding field matrices and point matrices are derived, enabling a more accurate analysis of stress and displacement distributions in the groove beam. Using the transfer matrix method and ANSYS finite element software, a variable-cross-section cantilever groove beam under a uniformly distributed load across the full span is analyzed; the percentage error in normal stress and deflection results for the variable-cross-section groove beam under different elastic modulus ratios is calculated. Similarly, a three-span constant-cross-section continuous groove beam under a uniformly distributed load across the full span is analyzed; the percentage error in normal stress results for the three-span constant-cross-section continuous groove beam under different elastic modulus ratios is obtained. The transfer matrix method shows good agreement with the results from finite element simulations, further validating the correctness of the method. The proposed transfer matrix method is characterized by convenient calculation, good stability, and high accuracy, which can significantly reduce the computational workload and simultaneously provide the values Manuscript received December 9, 2025; revised May 5, 2026. The study was supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2025JJ70253, Grant No. 2025JJ70276, and Grant No. 2026JJ80250), the Key Scientific Program of Hunan Education Department, China (Grant No. 23A0496, and Grant No. 23B06245), the Ministry of Education's Collaborative Education and Training Program for Industry-Academia Cooperation (Grant No. 250901094234014, and Grant No. 250901094225658). Bin Li is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 12007030@hnist.edu.cn). Xuebin Xing is a senior engineer of Jiangsu Shengshi Railway Equipment Co., Ltd., Changshu, 215500 China (e-mail: 232174471@qq.com). Yongqing Zeng is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (corresponding author to provide e-mail: yqzeng@hnist.edu.cn). Xinheng Zhou is an undergraduate student of College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 751796632@qq.com). Hua Lou is an associate professor in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 12015024 @hnist.edu.cn). Qingcong She is a lecturer in College of Civil Engineering and Architecture, Hunan Institute of Science and Technology, Yueyang, 414000 China (e-mail: 22017036@hnist.edu.cn). of internal forces, bending moments, displacement, and stress on any cross-section. It offers an effective computational approach for solving the shear lag effect in beam structures such as variable-section thin-walled groove beams and continuous groove beams, and provides important reference and basis for the design of bridge structures. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 19929978 |
