Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

Analysis of free vibration characteristic of steel-concrete composite box-girder considering shear lag and slip

Based on Hamilton principle,the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration of the shear lag effect meeting self equilibrated stress,shear deformation,slip,as well as rotational inertia were induced.Therefore,natural frequency equations were obtained for the boundary types,such as simple support,cantilever,continuous girder and fixed support at two ends.The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified,which also shows the correctness of longitudinal warping displacement functions.Some meaningful conclusions for engineering design were obtained.The decrease extent of each order natural frequency of the steel-concrete composite box-girder is great under action of the shear lag effect.The shear-lag effect of steel-concrete composite box girder increases when frequency order rises,and increases while span-width ratio decreases.The proposed approach provides theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder.

Theoretical and experimental study on shear lag effect of partially cable-stayed bridge

In order to resolve the traffic congestion problem, many cable-stayed bridges are designed with a large width to span ratio. This results in significant shear lag effect to cause nonuniform stress distribution along the flanges of the beam of bridge. This paper reports study on the shear lag effect of the Lanzhou Xiaoxihu Yellow River Bridge. A 3D finite element model of the bridge was developed and finite element analysis (FEA) was done to obtain the theoretical results. To evaluate the theoretical results, a scaled model was made to conduct static test in laboratory. The experiment results accorded with the results obtained by FEA. It is proved that FEA is an effective method to predict shear lag effect of bridges of this type.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

Strain transfer mechanism of passive wireless surface acoustic wave torque sensors using shear lag theory

A shear-lag theory was developed to investigate the strain transfer from the metal substrate to the surface acoustic wave （SAW） resonator through a bonding layer. A three-layer model of host structure-adhesive layer-resonator layer was established. The strain transfer was theoretically analyzed, and the main factors impacting the SAW sensor measurement were studied. The relationship between the sensor response and the individual effect of all these factors under static loads was discussed. Results showed that better accuracy could be achieved with increase in the adhesive stiffness or resonator length, or decrease in the adhesive thickness. The values of the strain transfer rate calculated from the analytical model agreed well with that from the available experiment data.

Experimental Study on Shear Lag Effect of Partial Cable-Stayed Bridge and Elasto-Plastic Seismic Analysis

The project of Xiaoxihu Yellow River Bridge in Lanzhou is chosen as partial cable-stayed bridge. To get the shear lag effect and anti-earthquake performance of the actual bridge under various loading conditions, organic glass scaled model was adopted to have an experiment and a theory research at one time. The experiment result is the basically same as the theory calculation which proves the FEA method can well calculate shear lag effect and dynamical performance. As a result, because the bridge is located in a seismic area of 8 degree, an elasto-plastic seismic checking is performed by customized FEA program in this paper.

A New Modification to Shear Lag Model as Applied to Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

A new modification for the shear lag model is given and the expressions for the stiffness and yield Strength of short fiber metal matri×composite are derived. These expressions are then compared with our experimental data in a SiCw/Al-Li T6 composite and the published experimental data on different SiCw/Al T6 composites and also compared with the previous shear lag models and the other theoretical models.

A theoretical model for investigating shear lag in composite cable-stayed bridges

The slab of the composite girder is usually very wide in composite cable-stayed bridges,and the main girder has an obvious shear lag.There is an axial force in the main girder due to cable forces,which changes the normal stress distribution of the composite girder and affects the shear lag.To investigate the shear lag in the twin I-shaped composite girder(TICG)of cable-stayed bridges,analytical solutions of TICGs under bending moment and axial force were derived by introducing the additional deflection into the longitudinal displacement function.A shear lag coefficient calculation method of the TICG based on additional deflection was proposed.Experiments with three load cases were conducted to simulate the main girder in cable-stayed bridges.And the stress,deflection,and shear lag coefficient obtained from the theoretical method considering additional deflection(TMAD)were verified by the experimental and finite element results.A generalized verification of a composite girder from existing references was made,indicating that the proposed method could provide more accurate results for the shear lag effect.

A new method based on the shear lag model for accurate determination of ice adhesion shear strength on solid surface

Accurate measurement of the interfacial shear strength between ice and solid surface has important reference significance for the design of anti-icing and de-icing functional surfaces.In this paper,a new method is proposed based on the shear lag model of a single fiber pulled out from matrix,in order to accurately determine the interfacial shear strength(ISS)between ice and metals.The maximum pull-out force at the initiation of interface debonding is well measured in the pull-out test of a metal fiber embedded in an ice matrix.A shear lag model similar to the pull-out test is established and a closed-form relation between the non-uniform interfacial shear stress and the pull-out force is achieved.When the pull-out force reaches its peak value,the ice/metal ISS can be consequently determined as the maximum interfacial shear stress.Such a method takes into account the stress concentration at the interface,which overcomes underestimation of ice/solid ISS based on the apparent strength in previous studies.The achieved ISS is proven to not only have good convergence,but also be independent of the size and embedded depth of metal fibers.Based on the present method,the enhancing effects of freezing temperature and surface roughness on the ice adhesion are further disclosed.The present research provides a simple and reliable approach to accurately calibrate the ice/solid ISS,which should be of important reference significance for the design and assessment of anti-icing functional surfaces.

Mechanics analysis of thin-walled box continuous girder with variable cross-sections in considering effect of large deflection and shear lag

In order to study the mechanics behavior of a thin-walled box continuous girder with variable crosssections,using potential variation theories,considering the effect of shear lag of flange’s stress and the nonlinear geometry of vertical displacement,and evolving five generalized displacements with the spline function,the large deflection problem of the thin-walled box continuous girder with variable cross-section was transformed to a nonlinear algebraic equation,which was solved using the Newton-Raphon iterative method.The results of the calculation show that different shear lag warp functions to the cantilever,top and bottom plate should be taken to analyze the mechanics behavior of the thin-walled box continuous girder reliably.The thin-walled box continuous girder with variable cross-sections has more reasonable stress state and is more adaptable for the longitudinal change of internal forces than that with equal crosssections.The effect of large deflection on the stress and displacement of the thin-walled box continuous girder with variable cross-sections depends on the values of the load.

Mechanical Characterisation of Interface for Steel/Polymer Composite Using Pull-out Test: Shear-Lag and Frictional Analysis

Fibre-matrix interface is known to have contribution to the mechanical performance of fibre-reinforced composite by its potential for load transfer between the fibre and the matrix. Such load transfer is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. In this study, a pull-out test was carried out to analyse the interfacial properties of a steel fibre embedded in a polyester and epoxy matrices. It was found that the fibre-matrix interface is debonded on the whole embedded length when the fibre stress reached the debonding stress. Then, the fibre stress fell down to the initial extraction stress required to pulling out the debonded fibre from the matrix. Both debonding stress and initial extraction stress initiated a linear increase with the implantation length after the debonding stress reached horizontal asymptotes. To analyse the fibre-matrix load transfer before debonding, an analytical shear-lag model was adopted to in this test conditions. Fitting the experimental results with the analytical model provided the interfacial shear strength. By considering the Coulomb friction at the fibre-matrix interface during the fibre extraction process, an analytical model which considers Poisson＇s effects on both fibre and matrix, was developed. In this model, knowledge of the initial extraction stress of the fibre provides the residual normal stress at the fibre-matrix interface.

An elastic-plastic analysis of short-leg shear wall structures during earthquakes

Short-leg shear wall structures are a new form of building structure that combine the merits of both frame and shear wall structures. Its architectural features, structure bearing and engineering cost are reasonable. To analyze the elastic-plastic response of a short-leg shear wall structure during an earthquake, this study modified the multiple-vertical-rod element model of the shear wall, considered the shear lag effect and proposed a multiple-vertical-rod element coupling beam model with a new local stiffness domain. Based on the principle of minimum potential energy and the variational principle, the stiffness matrixes of a short-leg shear wall and a coupling beam are derived in this study. Furthermore, the bending shear correlation for the analysis of different parameters to describe the structure, such as the beam height to span ratio, short-leg shear wall height to thickness ratio, and steel ratio are introduced. The results show that the height to span ratio directly affects the structural integrity; and the short-leg shear wall height to thickness ratio should be limited to a range of approximately 6.0 to 7.0. The design of short-leg shear walls should be in accordance with the ＂strong wall and weak beam＂ principle.

考虑加劲肋影响的钢箱梁剪滞效应研究

以剪滞效应引起的变形作为广义位移,将钢箱各翼缘板的加劲肋面积折算到相应板件上,运用能量法建立了考虑加劲肋影响的钢箱梁剪滞效应微分方程和边界条件。以简支和悬臂的边界约束条件为例,推导了在均布荷载作用下简支和悬臂钢箱梁的剪滞效应解析解,并分析了考虑加劲肋影响的钢箱梁剪滞系数和挠曲线分布规律。研究结果表明:在均布荷载作用下,考虑加劲肋影响的钢箱梁剪滞解析解与有限元数值解吻合较好,证明了研究方法的正确性;在简支和悬臂约束条件下,钢箱梁剪滞系数纵向分布规律较悬殊;与初等梁挠度相比,均布荷载作用下考虑剪滞影响的简支钢箱梁跨中截面的挠度差值比为4.18%,悬臂钢箱梁自由端的挠度差值比为3.16%。

Mechanism of Phase Lag Between Current Speed and Suspended Sediment: Combined Effect of Erosion, Deposition, and Advection

To retrieve and explain the phase lag between current speed and suspended sediment concentration(SSC), erosion, deposition, and advection were isolated as primary processes of sediment movement in a three-dimensional model. The response time was proved to be one of the reasons for the phase lag, as time is needed for suspension to diffuse from bottom to surface. A fitted Shields diagram was introduced into the model to reflect the relationship between SSC and shear stress, between shear stress and critical shear stress, as well as between SSC and critical shear stress for erosion. It takes some time for shear stress to increase to the critical value after high or low tide, and this was proved to be an important contributor to the phase lag. Overall, the variation of vertically integrated SSC is influenced by erosion mass flux, deposition mass flux, and advection flux. The phase pattern of erosion mass flux is consistent with the pattern of current if there was no wave action. However, phase difference is produced by the influence of deposition mass flux and advection. In this study, SSC peak/trough mostly occurred near the moment erosion mass flux approximately equaled deposition mass flux and would be impacted by advection. The time required for instantaneous variation of suspension to get to 0 after current peak/trough represents the phase lag between current speed and SSC.

偏载作用下薄壁箱梁空间整体效应的综合分析

为了研究斜腹板箱梁在竖向偏心荷载作用下的受力性能,在合理构造各翘曲位移函数的基础上,用能量变分法建立全面反映竖向弯曲变形以及剪力滞、约束扭转、畸变等翘曲变形的控制微分方程,通过对既有文献中的模型梁进行计算分析,明确剪力滞、约束扭转及畸变翘曲应力在竖向弯曲应力中的占比情况,并揭示各翘曲广义内力的分布规律。结果表明:按文章解析法求得的模型梁应力理论值与实测值吻合良好,从而验证文章方法的合理性;在偏载作用下箱梁的约束扭转微分方程与畸变微分方程是相互耦联的,这在已有文献中往往被忽略;在剪力滞、约束扭转及畸变翘曲应力中,畸变翘曲应力占据主导地位,剪力滞和约束扭转翘曲应力相对较小,但仍不可忽略,在控制截面上因各种翘曲变形引起的应力放大系数达到1.362;偏心集中荷载引起的各翘曲广义内力均具有快速衰减的分布规律,剪力滞和约束扭转广义内力分布范围很小,而畸变广义内力分布范围广阔。建议在桥梁设计规范相关条文及实际箱梁桥设计中,对畸变效应给予充分重视。

基于翼板横向位移模式的箱梁剪力滞效应分析

以剪翘变形状态为分析对象,综合运用广义坐标法、剪翘变形协调条件和平衡微分方程,提出箱梁的翼板横向位移模式。基于最小势能驻值原理,推导考虑翼板横向位移影响的箱梁剪力滞解析解。引入翼板横向位移对剪力滞影响的差值比参数,详细分析截面参数及梁端约束条件对剪力滞差值比的影响。算例分析表明:翼板横向位移对剪力滞有一定的削弱作用,考虑横向位移的纵向应力与有限元解、实测值吻合更好;跨宽比、高宽比越大,剪力滞差值比越小;悬臂板宽度越大,剪力滞系数差值比越小;梁端约束条件越强,剪力滞差值比分布曲线越陡峭,约束条件较强时需考虑横向位移的影响。

RC框架梁端负弯矩纵筋部分置于梁侧楼板对性能的影响及构造问题分析

为适应建筑多功能、大跨度、重荷载、高抗震的发展要求,框架梁端部负弯矩纵筋配筋率通常较高,节点区钢筋过于密集,混凝土施工质量不易保证,对结构综合性能有不利影响。先对梁端负弯矩纵筋部分设置于梁侧楼板内(简称APNRFS)的布筋方式进行阐述,然后基于试验结果分析探讨了该配筋方式对结构性能带来的变化及相关构造问题。研究表明:梁端采用APNRFS布筋方式一般不会降低框架梁的承载力;梁端的弯曲变形能力和结构抗震性能有一定提高;移至板内的梁负筋布置宽度宜小于有效翼缘宽度范围;移至板内的梁端负筋宜同时兼作楼板负筋;横向分布筋参与受力,设计中应适当增配。

基于修正翘曲位移函数的单箱双室薄壁箱梁剪力滞效应分析

为完善单箱双室薄壁箱梁剪力滞效应理论研究,基于弯曲剪力流零点位置分布确定翼缘板宽度划分原则,考虑剪切变形对弯曲曲率的影响,引入内力平衡因子,利用纵向翘曲位移横向分布连续性条件,对翼缘板纵向翘曲位移函数进行修正。同时,考虑悬臂翼缘板端部自由状态,提出初始剪切转角的概念,以解释悬臂板端部理论应力高于真实应力的现象,并明确初始剪切转角对纵向翘曲位移函数的影响机理。采用无量纲法,统一翼缘板纵向翘曲位移滞后函数的关系,理论推导纵向翘曲位移横向分布函数的合理形式。基于能量变分原理,建立单箱双室薄壁箱梁剪力滞效应控制微分方程,并给出位移边界条件。以单箱双室薄壁简支箱梁满布均布荷载为例,采用本文提出的分析方法对算例进行理论求解,并利用ABAQUS有限元软件建立相应的力学模型,将本文理论解析解与有限元数值结果进行比较分析。研究结果表明:根据弯曲剪力流零点位置确定单箱双室薄壁箱梁剪力滞效应翼缘板宽度划分是合理可行的。本文理论分析方法(考虑初始剪切转角和翼缘板应力修正)计算的翼缘板应力和挠度值与有限元数值结果吻合良好,最大误差不超过2%,不仅验证了选用余弦函数作为纵向翘曲位移横向分布函数的合理性,还表明了理论分析方法和理论推导的正确性。