This paper presents an efficient and simplified analytical method for the torsional-warping analysis of thin-walled beams with arbitrary asymmetric sections, such as single-cell or multi-cell boxes with varying wall thickness. A key innovation is the development of a general computational procedure, TCRP, which virtual disassembles the cross-section into individual plate elements. By enforcing deformation compatibility and internal force equilibrium at the junctions, the program accurately calculates the sectorial geometric properties for complex sections. Building upon these accurate properties, the proposed Torsional Simplified Method (TSM) incorporates the influence of secondary non-uniform shear deformation, enabling rapid prediction of warping stresses under eccentric loads without solving complex differential equations. Numerical examples, including cantilever and continuous box girders, demonstrate the method's effectiveness. The results show that the proposed TSM predicts warping stresses within a 10% error compared to 3D FEM results, offering a substantial efficiency gain for practical design. For realistic concrete box cross-sections with non-uniform thickness, the peak principal sectorial coordinate shifts inward from the web-flange junction, and the generalized static moment distribution becomes highly asymmetric in skewed cross-sections, with discrepancies of 20-60% compared to constant-thickness models. Furthermore, accurate prediction of stress distributions necessitates the consideration of both secondary shear deformation and thickness variation. The presented methodology provides a practical and reliable tool for the design of thin-walled girders.

To address the complex mechanical state arising from the nonuniform shear deformation in concrete flanges, the accordion effect of corrugated steel webs, and their coupled interaction during distortion of concrete composite box girders with corrugated steel webs (CCBG-CSWs), this paper proposes a new distortional analysis theory that adequately captures these deformation characteristics. The method virtually decomposes the composite box girder into multiple platebeams. Based on the actual deformation pattern of each platebeam and in conjunction with the deformation compatibility and internal force selfequilibrium conditions of the crosssection, a system of mechanical equations describing the interrelationship among the platebeam deformations is established. This leads to simplified expressions for the platebeam displacements under complex deformation states and ultimately yields the governing differential equation for this distortional mode. Building upon this theory, a distortional beamsegment finite element program system tailored to such composite box girders is developed. The proposed theory and program are systematically validated through a series of practical bridge examples with different crosssectional shapes and structural configurations. The results show that: the results from the beamsegment program agree well with those from threedimensional solid finite element analysis; at the midplane near the intersection of the steel web and the upper concrete flange, conventional distortional analysis underestimates the distortional warping stress by more than 30%; and the outofplane distortional warping stress in the concrete flange induced by the coupled accordion effect and shear deformation can reach a magnitude comparable to the midplane stress, which must be given due consideration in structural design.

This study proposes a method for the distortion analysis of thin-walled box girders considering the influence of non-uniform shear deformation of each box-wall slab. Firstly, the distribution pattern of distortion shear flow across the cross-section is derived using the principles of stress equilibrium in micro-elements and the torsional self-balancing condition of the box girder cross-section. Then, by introducing the generalized displacement of shear distortion, according to the deformation continuity and internal force self-balancing conditions of the box girder cross-section, a theoretically sound and practical distribution function for the distortion and warping displacement of thin-walled box girders, accounting for the impact of non-uniform shear deformation is proposed. The governing differential equation for distortion is established through the principle of minimum potential energy. A practical 1D beam-type finite element model for box girder distortion analysis is then proposed, employing the Hermite interpolation function. The reliability and accuracy of this model are verified through a series of numerical examples involving different types of box girders. The results demonstrate that the in-plane and out-of-plane distortion warping stresses of the box-wall slabs, when considering non-uniform shear deformation, align well with measured values and three-dimensional finite element results. Notably, shear deformation significantly impacts the distortion effect of the top flange in box girders. Ignoring the influence of nonuniform shear deformation may lead to an underestimating the distortion warping stresses at critical cross- sections of box girder bridges. The research findings provide an effective means for the improved analysis of box girder distortion.

The existing flexural analysis methods of corrugated steel web composite box girders are either inaccurate due to thoughtlessness of the influencing factors, or complicated due to excessive consideration of the influencing factors. In this study, a flexural displacement model of composite box girder considering both the accordion effect and shear deformation of web and the shear lag effect of flange is proposed. According to the internal force balance condition, the complex flexural models of a composite box girder are decoupled into three independent simple flexural states: Euler–Bernoulli beam flexure satisfying the quasi-plane assumption, flexure of equivalent web deformation, and flexure of shear lag of flange. Based on the flexural theory of the thin-walled beam, the generalized internal force system and beam-type finite element model was established corresponding to each flexural state. The results of numerical examples show that the proposed method has high solution accuracy and can directly obtain the displacement and internal force of each flexure deformation. The moment results show that the generalized moment has a peak value at the point of shear discontinuity, and increases or decays rapidly near it.

Shear warping deformation is an important part of the flexural and constrained torsion analysis of composite box girder with corrugated steel webs (CBG-CSWs), which is also the main reason for the complex force analysis of box girders. A new practical theory for analyzing shear warping deformations of CBG-CSWs is presented. By introducing shear warping deflection and corresponding internal forces, the flexural deformation of CBG-CSWs is decoupled to the Euler-Bernoulli beam (EBB) flexural deformation and the shear warping deflection. On this basis, a simplified method for solving shear warping deformation using the EBB theory is proposed. According to the similarity of the governing differential equations of constrained torsion and shear warping deflection, a convenient analysis method for the constrained torsion of CBG-CSWs is derived. Based on the decoupled deformation states, a beam segment element analytical model applicable to EBB flexural deformation, shear warping deflection, and constrained torsion deformation is proposed. A variable section beam segment analysis program considering the variation of section parameters is developed for CBG-CSWs. Numerical examples of constant and variable section continuous CBG-CSWs show that the stress and deformation results obtained by the proposed method are in good agreement with the 3D finite element results, verifying the effectiveness by the proposed method. Additionally, the shear warping deformation has a great influence on the cross-sections near the concentrated load and middle supports. This impact along the beam axis decays exponentially, and the decay rate is related to the shear warping coefficient of the cross-section.

为满足"新工科"人才能力需求,提升学生理论知识、实践与创新能力,从土力学实验的现状出发,梳理现实实验中的不足,提出改革的需求与达成目标.将基于颗粒力学模型的离散元数值技术引入土力学的理论与实验中,实现学生对土体在微观结构的不连续与宏观连续性的全方位理解,提升学生数值模拟水平.通过土力学实验的实体演练,结合线上虚拟仿真实验的自主训练,突破现实实验条件的制约,大幅提升学生动手实践能力.土力学实验的测试结果为离散元数值模拟提供必要的参数支撑,而数值仿真也可补充实验的不足.实验科学与计算科学相辅相成,相互印证,能够有效地深化学生的理论认知,激发学生创新与解决实际工程问题的能力.

为快速准确地获得薄壁梁的挠曲应力及位移,提出一种考虑各板剪切变形影响的薄壁梁挠曲分析方法.从薄壁板剪应变与位移关系出发,推导出具有明确力学机制的挠曲纵向位移函数;选取剪切变形引起的挠度作为广义位移,通过解耦挠曲性能提出剪切翘曲应力及挠度的一种简化分析方法;基于矩形板条的平面应力解,导出翼板翘曲应力修正系数的表达式;利用中支点的变形连续条件及简化分析理论,提出薄壁连续梁的剪切挠曲简化分析方法.数值算例结果表明,本文方法求得的应力结果与3D FEM结果最大误差在3％以内,挠度最大误差为6％以内,说明所提方法可靠且精度较高;参数分析表明,材料泊松比及板宽比对翼板的翘曲应力影响较大.

This study proposes a new analytical flexure theory that considers the shear deformation of the web and flange of a thin-walled box girder. Starting with the relationship between the strain and displacement of each slab, the flexural displacement function of thin-walled box girders considering the shear deformation effect is derived by using the deformation continuity condition. Compared with the traditional flexural displacement model, this function obtained by the theoretical analysis is more rigorous and can be transformed into the flexural displacement function of the traditional shear lag or Timoshenko beam by eliminating some parameters. Then, according to the balance conditions of axial force and bending moment, the shear deflection deformation state and Euler–Bernoulli beam deflection deformation state are decoupled. On this basis, a new convenient method for calculating the warping stress and shear deflection of thin-walled girders is proposed. Furthermore, a simplified analysis method for converting continuous box girders into simply supported beams is proposed on the basis of continuity condition of shear deflection at middle supports. Taking into account the shear deflection deformation state, a beam-type finite element model considering the shear deformations of each box wall is developed by using Hermite polynomials to analyze the complex variable cross-section box girder. Finally, numerical examples are used to verify the effectiveness of the simplified method and the beam-type finite element model. Numerical examples show that the flexural stress and deflection calculated by the proposed method agree well with the three-dimensional finite element model analysis results. The shear warping normal stress has a larger value at the shear force discontinuity point. In the control cross-section, the normal warping stress and shear deflection caused by shear deformation both exceed 75% and 38% of stress and deflection of the Euler–Bernoulli beam, respectively.

In this paper, a new formulation of beam finite element (B3S) is developed for predicting the performance of shear lag and shear deformation effects in thin-walled single-and multi-cell box girders. The longitudinal warping displacement of each wall of the cross-section is defined as the sum of five deformation modes, i.e., shear lag warping displacement mode, initial shear deformation mode, bending mode, axial mode, and correction mode. Based on the Minimum Potential Energy (MPE) principle with independent descriptions of the displacement fields, the governing differential equations in terms of two generalized displacements, normalized shear lag warping function U(x) and vertical displacement w(x), can be obtained. The proposed beam finite element is refined by selecting closed-form homogeneous solutions of the differential equations as interpolation functions. Besides the nodal Degree Of Freedoms (DOFs) of the conventional beam finite element, the normalized shear lag warping function has been considered as an additional DOF in each node at the element ends to account for the shear lag effect. Moreover, for comparison reasons, the one-dimensional beam finite elements developed based on the Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT) have been also introduced. Numerical examples are presented regarding single-or multi-cell box girders with constant or variable depth and the results obtained are compared with those retrieved from the pioneering work or calculated by using solid finite-element models to validate the proposed beam finite element and to demonstrate the wide range of applicability and convenience of using it.

为寻求考虑剪切变形影响的薄壁箱梁挠度计算简化方法,以单位力法为基础分析薄壁箱梁的挠曲变形.首先,通过对薄壁箱梁挠曲剪应力分布模式的分析获取组成箱梁各壁板的剪切影响系数表达式,基于该剪切影响系数,利用Timoshenko梁理论导出简单箱梁挠度的解析表达式;其次,利用卡式第二定律推导出箱梁的梁段单元分析模型,编制了求解变截面箱梁等复杂结构的电算程序;最后,对等截面及变截面箱梁的算例模型进行了分析.数值算例结果表明:程序计算的挠度与实测值及ANSYS空间有限元结果误差在3％以内;针对数值算例,剪切变形使箱梁挠度增大20％以上;随着宽高比的增大,翼板剪切产生的附加挠度会增大,而腹板情况与之相反.

为准确分析腹板手风琴效应、剪切变形与翼板剪力滞效应对波形钢腹板组合箱梁挠曲变形及应力的影响,利用截面变形连续条件建立了综合考虑腹板手风琴效应、剪切变形与剪力滞效应的挠曲位移模式.通过引入广义剪切位移和剪力滞位移,将该挠曲变形状态解耦为拟平截面的Euler梁挠曲、广义剪切变形引起的挠曲以及剪力滞效应引起的挠曲3种状态.依据广义位移与转角的关系,选用Hermite多项式作为位移形函数,推导出广义位移的单元刚度矩阵,提出了适合该组合箱梁的梁段分析方法.数值算例结果表明,基于该方法得到的应力及变形与三维空间有限元结果吻合良好.广义剪切变形对梁的挠曲变形与应力存在较大影响,集中荷载作用或中支点截面附近的应力放大系数甚至超过2.0.

为了方便研究考虑各板面内剪切影响的箱梁竖向纯弯曲自振频率,基于单位力法,结合箱梁弯曲剪应力的分布特点,推导出适用于箱梁各板面内的剪切影响系数表达式.以剪切影响系数为基础,利用哈密顿原理,导出考虑剪切及转动惯量影响的箱梁弯曲自振频率控制微分方程.采用分离变量法,结合边界条件给出了简支箱梁弯曲自振频率表达式.在该剪切影响系数的基础上,结合梁段单元刚度矩阵,编制了MATLAB程序用于分析考虑各板面内剪切影响的箱梁弯曲自振特性.数值算例表明:以本文程序计算的箱梁弯曲自振频率及振型与ANSYS空间有限元结果吻合较好;剪切变形对箱梁自振频率的影响随着频率阶数的增高而增大.参数分析表明,梁高对频率影响较大,当计入剪切影响时,转动惯量对箱梁弯曲自振频率的影响可忽略.

为了更精确地求解波形钢腹板组合箱梁的挠度,通过分析该组合箱梁挠曲剪应力分布特点,结合虚功原理,推导出考虑全截面剪切影响的剪切形式因子.基于能量变分原理,推导出该组合箱梁剪切附加挠度的控制微分方程,并给出一般荷载条件下简支箱梁剪切附加挠度的表达式.数值算例结果表明,考虑剪切变形影响计算的组合箱梁挠度与ANSYS空间有限元计算结果及实测值吻合良好,剪切变形对组合箱梁的挠度影响较大.参数分析结果表明:随着宽高比的增大,采用剪切系数方法计算所得的组合箱梁附加挠度也增大;随着跨高比的增大,波形钢腹板剪切变形产生的附加挠度不断减小,当跨高比大于40时,可忽略腹板剪切变形的影响.

从薄壁箱梁弯曲剪力流出发,分析箱梁的应力应变关系,并与初等梁理论相结合,导出适合薄壁箱梁的合理剪切参数,从而简化箱梁腹板剪切附加挠度的计算.采用对剪切附加曲率的积分及能量变分法,导出腹板剪切附加挠度和考虑全截面剪切变形的箱梁挠度计算公式.通过剪切附加挠度与弯曲挠度的对比,分析影响翼板和腹板剪切变形的主要因素.建立了ANSYS空间模型算例,结果表明,按本文的计算式所得挠度与ANSYS结果吻合良好;当宽跨比、高跨比较大时,均布荷载作用下的简支箱梁跨中因剪切变形产生的附加挠度将达弯曲挠度的22％以上,应予以重视.

In order to more accurately analysis of bending vibration frequency of simply-supported box girder, based on the bending theory of thin-walled box girder, the shear deformations of flange plate and web plate are both expressed by using a shear warping parameter. First, the expression of total bending potential energy is derived based on energy theory. Then, by using Hamilton principle, the control differential equations and the corresponding natural boundary conditions of bending vibration of the box girder with and without considering rotational kinetic energy are derived. In order to simplify the calculation and avoid solving high order differential equation, the natural boundary conditions of simply-supported box girder are analyzed, and the generalized displacement functions w( z,t) and g( z,t) which can satisfy the boundary conditions are calculated by using Galerkin method, thus the analytical formulas of bending vibration frequency of simply-supported box girder is easily derived. Taking a simply-supported vertical web box girder as a numerical example, the first 5 orders vertical bending vibration frequency are calculated by using the following 4 methods:(1) using beam189 of ANSYS to establish the finite element model which can consider the section shear effect of this simply-supported box girder; ( 2 ) using shell 63 of ANSYS to establish the spatial finite element model of this simply-supported box girder; ( 3 ) the derived 2 analytical formulas considering and unconsidering rotational kinetic energy. The correctness of the analytical formulas is verified by comparison and analysis the above 4 calculation results, and it is concluded that the natural bending vibration characteristics of the box girder are less affected by the rotational kinetic energy, which can be neglected. Finally, the influence of shear deformation on vertical bending vibration frequency of the box girder is analyzed. The result shows that ( 1 ) the influence of shear deformation of flange plate on the bending vibration frequency of the box girder is less than on the shear deformation of web plate; ( 2 ) the effect of shear deformation on the vertical bending vibration frequency of the box girder decreased with the increase of span-height ratio and increased with the increase of frequency order.

To analyze the bending natural vibration frequency of thin-walled box girders considering the shear deformation effect influence,a function expression is used to express the longitudinal dis-placement of the flanges and webs considering the shear deformation effect influence.Based on this expression and the Hamilton principle, the differential equations to solve the bending vibration fre-quency are established by using the energy variation method.The bending vibration frequency con-sidering the shear deformation effect influence of the simply supported beam is obtained according to the boundary conditions.Furthermore,the bending vibration frequency expression of the equal-sec-tion continuous box girder is derived by using the three-moment method.The numerical example re-sults show that, the bending vibration frequency obtained from the calculation formula considering the shear effect of the continuous box girder is in good agreement with the calculation results from ANSYS software with shell elements and those from the beam element model considering the shear effect.The bending vibration frequency of the box girder decreases when considering the shear de-formation effect influence.The higher the frequency order, the greater the shear deformation effect influence.Therefore,the influence of the shear deformation should not be neglected when solving the high order bending natural vibration frequency of the thin-walled box girder.

In order to analyze the influence of shear effect on curved box girder,the shear deformation of flange plates and web plates is expressed by using only one shear warping parameter based on the bending theory of thin-walled box girder.By using energy variation principle,the bending-torsion deflection governing differential equations are deduced considering the shear effect and restrained torsion.By analyzing the boundary conditions and using Galerkin method,the differential equations are solved and the stress expression of bending-torsion deflection of curved box girder is obtained.The numerical example results show that the bending-torsion stress of curved box girder calculated from the calculation formula is in good agreement with the measured value,and the shear deformation of web has less influence on shear-warping stress of box girder which can be ignored.By analyzing the component of the whole stress of simply supported box girders under the vertical uniform loading,it shows that the shear-warping stress accounts for 15%~20% of the whole stress,and the torsion-warping stress accounts for about 6%,which is relatively small.

在对梯形截面箱梁的畸变角给出一般定义的基础上,提出一种与薄壁箱梁约束扭转分析相似的薄壁箱梁畸变效应分析方法,推导梯形箱梁畸变效应分析的一般公式.应用基于势能驻值原理的能量变分法,建立以所定义的畸变角为未知量的控制微分方程,并给出其初参数解.对1个简支箱梁模型的畸变翘曲应力计算值与相关文献中的有限梁段单元计算值吻合良好,验证分析方法和所推导公式的正确性.研究结果表明:按本文方法揭示的梯形箱梁畸变内力及位移的分布规律与相关文献中的一致,但本文畸变双力矩和畸变矩均大于相关文献中的相应内力,而畸变角和畸变翘曲均小于相关文献中的相应位移.在跨中畸变矩荷载作用下,梯形箱梁腹板与顶板交点处的畸变翘曲应力和横向弯矩绝对值都小于腹板与底板交点处的对应值.

On the basis of the bending theory of thin-walled box girders, and in combination with the hypothesis for solving plane stress problems in elasticity theory, bending longitudinal displacement function considering each plate in-plane shear effect of thin-walled box girders was derived. At the same time, the shear lag warping displacement function was derived theoretically. The displacement mode considering in-plane shear effect of all plates was simplified and solved by using the principle of energy variation and Timoshenko hypothesis of deep beam theory, and the numerical example was given. The results show that the calculated stresses at mid-span cross section of a simply supported box girder by using the displacement mode with shear effect are in a good agreement with the measured values and the finite element analysis results. There are large differences between the calculated shear stresses which considering all plates’ shear effect and the traditional calculation results. Compared with previous methods, the shear stress and deflection calculated in this research are more accurate; what’s more, the shear stress of webs and deflection of the box girder increases, the biggest growth reaches 21%.