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Shih Toh Chang - One of the best experts on this subject based on the ideXlab platform.

  • Shear Lag Effect in simply supported prestressed concrete box girder
    Journal of Bridge Engineering, 2004
    Co-Authors: Shih Toh Chang
    Abstract:

    In this paper, derivation and computed formulas are provided for the Shear Lag coefficient in a simply supported prestressed concrete box girder under dead load. In the case of prestressed tendons having parabolic configurations, formulas to compute the Shear Lag Effect are also developed. The magnitude of upward loading intensity caused by prestress as well as the relationship between the height of the box girder and the sag of prestressed tendons have been fully treated. Conclusions are drawn that the Shear Lag Effect caused by dead load and prestress force is equivalent to dead load acting alone, provided that the prestressed tendon is set up with a parabolic profile. Shear Lag Effect caused by movable load is also analyzed according to the eccentricity of the load to the half-width ratio of the box girder. Charts were prepared to predict the Shear Lag coefficient for live load. Finally, having considered the Shear deformation of flanges, the deflection of box girders is studied for both uniformly distributed load and concentrated load. Examples are given for illustrative purpose.

  • Shear Lag Effect in simply supported prestressed concrete box girder
    Journal of Bridge Engineering, 2004
    Co-Authors: Shih Toh Chang
    Abstract:

    In this paper, derivation and computed formulas are provided for the Shear Lag coefficient in a simply supported prestressed concrete box girder under dead load. In the case of prestressed tendons having parabolic configurations, formulas to compute the Shear Lag Effect are also developed. The magnitude of upward loading intensity caused by prestress as well as the relationship between the height of the box girder and the sag of prestressed tendons have been fully treated. Conclusions are drawn that the Shear Lag Effect caused by dead load and prestress force is equivalent to dead load acting alone, provided that the prestressed tendon is set up with a parabolic profile. Shear Lag Effect caused by movable load is also analyzed according to the eccentricity of the load to the half-width ratio of the box girder. Charts were prepared to predict the Shear Lag coefficient for live load. Finally, having considered the Shear deformation of flanges, the deflection of box girders is studied for both uniformly distributed load and concentrated load. Examples are given for illustrative purpose.

  • PRESTRESS INFLUENCE ON Shear-Lag Effect IN CONTINUOUS BOX-GIRDER BRIDGE
    Journal of Structural Engineering-asce, 1992
    Co-Authors: Shih Toh Chang
    Abstract:

    The Shear-Lag Effect in a thin-walled box girder has been recognized and introduced in the technical literature. In contrast however, a discussion of Shear-Lag Effect caused by the combination of prestress force and self-weight of a box girder is limited. In this paper, the Shear-Lag Effect is treated by the principle of superposition by considering that the configuration of a prestressed tendon takes the form of a broken straight line. Two equal spans of a continuous box girder of constant depth with a Shear-Lag Effect are used as an illustrative example. If λ\N denotes actual stress due to bending under symmetrical loading over the stress computed by elementary beam theory, a compound parameter \IN\N\I\dy\Nθ\N/ω\N\IL\N is a measure of the Shear-Lag Effect in this particular example, where \IN\N\I\dy\N is Effective prestress force, θ\N is the inclined angle of tendon at support, ω\N is the intensity of uniformly distributed load, and \IL\N is the span length of bridge. On the \IN\N\I\dy\Nθ\N/ω\N\IL\N and λ\N diagram, an asymptote exists. Usually in engineering practice \IN\N\I\dy\Nθ\N/ω\N\IL\N is equal to or greater than unity. Based on this approach, some preliminary conclusions are presented for this study.

Lin Lixia - One of the best experts on this subject based on the ideXlab platform.

  • initial parameter method for analyzing Shear Lag Effect of thin walled box girders
    Engineering mechanics, 2013
    Co-Authors: Lin Lixia
    Abstract:

    The additional deflection induced by Shear Lag Effect is adopted as the generalized displacement of a thin-walled box girder.Based on the new generalized moment and warping displacement function defined,the Shear Lag deformation state is separated from the flexural deformation state of an elementary beam and analyzed as a fundamental deformation state.Two modification factors are introduced in the generalized warping displacement function to consider fully the self-equilibrium of Shear Lag warping stresses.A simple and convenient formula for Shear Lag warping stress is proposed,which has the same form as that of the bending stress of an elementary beam.The governing differential equation for Shear Lag is established by using energy calculus and its initial parameter solution is given,in which the generalized moment,generalized Shear force,additional deflection and its variation rate are chosen as the initial parameters.A two-span continuous box girder model is analyzed and the calculated results are in a good agreement with test results and those provided in other reference literatures.The Shear Lag Effect increases the mid-span deflection of a box girder under concentrated and uniformly distributed loads by 17% and 16%,respectively.

  • study on warping displacement function and generalized internal force in Shear Lag Effect analysis of box girder
    Chinese Journal of Computational Mechanics, 2012
    Co-Authors: Lin Lixia
    Abstract:

    Based on the flexural theory of thin-walled box girder,the curve of quadratic parabola is proved to be the reasonable form of the warping displacement function in the Shear Lag Effect analysis of a box girder through investigating the in-plane Shear deformation and the bending Shear flow distribution in the flanges.The additional deflection induced by Shear Lag Effect is adopted as the generalized displacement.The governing differential equations and the corresponding boundary conditions for Shear Lag Effect of box girder are established by the energy calculus of variations based on the principle of minimum potential energy.The new generalized internal force is defined rigorously,and a simple and convenient formula of stress for Shear Lag warping is presented which has the same form as the bending stress of elementary beam.A simply supported box girder model is analyzed and the calculated results are in good agreement with the test results,validating the method and formula presented.The generalized moment for Shear Lag differs from the bending moment in distribution and attenuates quickly.For the simply supported box girder example under concentrated load,Shear Lag Effect increases the mid-span deflection by 12%,which should be treated carefully in practice.

  • influence of Shear Lag Effect on deflection of box girder
    Chinese Journal of Computational Mechanics, 2012
    Co-Authors: Zhang Yuanhai, Lin Lixia, Liu Yong
    Abstract:

    The warping displacement function for Shear Lag of twin-cell box girder is chosen upon the axial equilibrium of the relevant warping stress.Through defining the moment and product of inertia corresponding to the Shear Lag warping,the governing differential equations for Shear Lag analysis of thin-walled box girder are established by applying the energy variation method.The deflection formulas for simply supported and cantilever box girders under concentrated and uniform loads respectively and the finite segment element stiffness matrix are derived through solving the governing differential equations.Model test and ANSYS shell element results validate the formulas derived.The increase of deflection due to Shear Lag Effect of simply supported,cantilever,and continuous box girders is numerically studied.It is shown that,the increase of deflection for simply supported box girder due to Shear Lag is remarkable under both concentrated and uniform loads.The increase of deflection for continuous box girder can reach 14% under concentrated loads.For a simply supported box girder with span-width ratio 4.0~6.0,the mid-span deflection calculated by elementary beam theory can be multiplied by 1.05~1.11.The influence of Shear Lag Effect on the deflection of cantilever box girder can be generally ignored.

  • a method considering Shear Lag Effect for flexural torsional analysis of skewly supported continuous box girder
    Engineering mechanics, 2012
    Co-Authors: Lin Lixia
    Abstract:

    An element for thin-walled box beams is proposed for the flexural-torsional analysis of skewly supported continuous box girder considering the constraint condition in the supporting coordinate system.The element has ten degrees of freedom and can conveniently simulate Shear Lag Effect and torsional-warping deformation of skewly supported continuous box girder.The element stiffness matrix is derived by taking the homogeneous solutions of the governing differential equations for flexural Shear Lag and restraint torsion as the element displacement functions.The Shear Lag warping displacement function for the twin-cell box section is established through the axial equilibrium condition of the Shear Lag warping stress.General formulas for the geometrical properties of cross section concerning the Shear Lag warping are presented.The program SSCBA is developed and used to analyze a skewly supported three-span continuous box girder model with twin-cell cross section.The calculated results are in good agreement with the experimental results and the calculated results from shell element of ANSYS.It is shown that the warping deformations of Shear Lag and restraint torsion affect remarkably the stress distribution in a skewly supported continuous box girder under eccentric load at the mid-span.

Lizhong Jiang - One of the best experts on this subject based on the ideXlab platform.

  • analysis of free vibration characteristic of steel concrete composite box girder considering Shear Lag and slip
    Journal of Central South University, 2013
    Co-Authors: Wangbao Zhou, Lizhong Jiang
    Abstract:

    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.

  • closed form solution to thin walled box girders considering Effects of Shear deformation and Shear Lag
    Journal of Central South University, 2012
    Co-Authors: Wangbao Zhou, Lizhong Jiang, Zhijie Liu, Xiaojie Liu
    Abstract:

    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.

J Tang - One of the best experts on this subject based on the ideXlab platform.

  • Membrane forces acting on thin-walled box girders considering Shear Lag Effect
    Thin-walled Structures, 2004
    Co-Authors: J Tang, Qiusheng Li, J R Wu
    Abstract:

    Abstract A new method for the determination of membrane forces acting on box girder bridges considering Shear Lag Effect is proposed in this paper. A box girder is divided into four thin plate elements: top plate, bottom plate, cantilever and web. Using the equilibrium conditions of the plates, the membrane force equation for each plate element is established. The analytical formulas for calculating the membrane normal, transverse and Shear forces of each plate element considering Shear Lag Effect are derived. The proposed method is easy to implement in the design of thin-walled box girders considering Shear Lag Effect. Through examples using the high order finite strip element method and the experiment, the results obtained by the proposed method are examined and the accuracy of the proposed method is verified. The discussions on the Shear Lag Effect on the membrane forces acting on cantilever box girders are given considering the variations of span to width ratio, width to height ratio and various loading conditions.

  • negative Shear Lag Effect in box girders with varying depth
    Journal of Structural Engineering-asce, 2001
    Co-Authors: Q Z Luo, J Tang
    Abstract:

    A study on negative Shear Lag Effects in box girders with varying depth is performed using a modified finite segment method developed by the writers. Three types of structuressimply supported, cant...

Wangbao Zhou - One of the best experts on this subject based on the ideXlab platform.

  • analysis of free vibration characteristic of steel concrete composite box girder considering Shear Lag and slip
    Journal of Central South University, 2013
    Co-Authors: Wangbao Zhou, Lizhong Jiang
    Abstract:

    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.

  • closed form solution to thin walled box girders considering Effects of Shear deformation and Shear Lag
    Journal of Central South University, 2012
    Co-Authors: Wangbao Zhou, Lizhong Jiang, Zhijie Liu, Xiaojie Liu
    Abstract:

    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.