Finite Element Analysis of Restrained Torsion and New Algorithm of Flexural-torsional Moment for Thin-walled Box Girder

XIA Guiyun, LI Chuanxi, YANG Meiliang


  Using initial parameter solutions and transfer matrix method,the finite element formulation for restrained torsion of a thin-walled box girder was presented. The equivalent nodal forces of distributing torque and bimoment acted on an element were also derived. Based on the displacement solutions of the finite element method for restrained torsion, a new algorithm for calculating the flexural-torsional moment was developed. The relevant stiffness matrix and fixed-end forces for distributing torque and bimoment acted on the element were established. It facilitated the calculation of normal stress and shear stress. The examples show that the calculation results of the proposed method agree well with the theoretical solutions, which proves that the stiffnesses for restrained torsion, equivalent nodal forces for distributing torque and bimoment acted on element as well as new algorithm for flexural-torsional moment are exact.


Keywords: thin walled structures,  restrained torsion,  finite element analysis,  bimoment,  rate of twist,  new algorithm

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GENDY A S. Generalized thin –walled beam models for flexural torsional analysis [J]. computers & Structures, 1992, 12(4):531— 550.

GUO J Q, FANG Z Z, ZHENG Z. Design theory of box girder[M]. 2nd ed.Beijing:Сhina Сommunicationc Press,2008:9—10,78—84. (In Chinese)

BAO S H, ZHOU J. Structural mechanics of thin–walled bar[M]. Beijing:Сhina Architecture and Building Press,2006:38—161 (In Chinese)

XU X. Research of spacial effects of concrete box girder structure with long span [D]. Сhengdu:School of Сivil Engineering, South– west Jiaotong University, 2009:15—37 (In Chinese)

NIE G J, QIAN R J. Element stiffness matrix of thin–walled beam considering restrained torsion [J].Chinese Journal of computational Mechanics, 2002, 19 (3):344—348 (In Chinese)

YANG L F, REN X J, СHEN J F. Torsional analysis and application of thin walled bar with slosed profile [J]. Journal of Guangxi University (Natural Science Edition), 2008, 33(1):1—4 (In Chinese)

SU X F. Stress analyis and program design for torsion and distortion of box girder bridge [D]. Xiangtan:School of Сivil Engineering, Hunan University of Science and Technology, 2011:47—49 (In Chinese)

XIE X, HUANG J Y. Tkree dimensional analyses for warping, distortion and shear lag effect of thin walled box girder under restrained torsion [J]. Сhina Сivil Engineering Journal, 1995, 28 (4): 3—14(. In Chinese)

ZHU D R, ZHANG Y H, LIN L X. Restraint torsion analyses of continuous box girder bridge with special supports [J]. Journal of Сentral South University (Science and Technology), 2016, 47 (4): 1312—1318 (In Chinese)

HUA X G, YANG D, СHEN Z Q. A simplified method for calculating mass moment of inertia of stiffening truss in suspendion bridges [J]. Journal of Hunan University (Natural Sciences), 2017, 44 (3): 1—7 (In Chinese)

BU С Q, ZHANG Z T. Refined analyses of finite element for torsional divergence of suspension bridges [J]. Journal of Hunan University (Natural Sciences), 2016, 43 (9):88—97 (In Chinese)

XIANG H F. Advanced theory of bridge structures [M]. 2nd ed. Beijing: Сhina communication Press, 2013:24—35 (In Chinese)


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