• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.507-518
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• 2005

In the shear-lag analysis of structures deterministic procedure is insufficient to provide complete information. Probabilistic analysis is a holistic approach for analyzing shear-lag effects considering uncertainties in structural parameters. This paper proposes an efficient and accurate algorithm to analyze shear-lag effects of structures with parameter uncertainties. The proposed algorithm integrated the advantages of the response surface method (RSM), finite element method (FEM) and Monte Carlo simulation (MCS). Uncertainties in the structural parameters can be taken into account in this algorithm. The algorithm is verified using independently generated finite element data. The proposed algorithm is then used to analyze the shear-lag effects of a simply supported beam with parameter uncertainties. The results show that the proposed algorithm based on the central composite design is the most promising one in view of its accuracy and efficiency. Finally, a parametric study was conducted to investigate the effect of each of the random variables on the statistical moment of structural stress response.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.351-360
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• 2000

A simple numerical modelling technique is proposed for estimating the shear lag effects of framed-tube system with multiple internal tubes. The tube(s)-in-tube structure is analysed by using an analogy approach in which each tube is individually modelled by a beam that can accounts for the flexural and shear deformations, as well as the shear lag effects. The numerical analysis is based on the minimum potential energy principle in conjunction with the variational approach. The shear lag phenomenon of such structures is studied with additional bending stresses. Structural parameters governing the shear lag behaviour in tube(s)-in-tube structures are also investigated through thirty-three numerical examples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.317-322
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• 2001

A mathematical modelling technique is proposed for estimating the additional bending stresses of tube(s)-in-tube structures due to tube-tube interaction, which has a significant effects on the shear-lag phenomenon. The proposed method simulates the framed-tube structures with multiple internal tubes as equivalent multiple tubes, each composed of four equivalent orthotropic plate panels. Hence, the tube(s)-in-tube structure can be analysed by using an analogy approach where each tube is individually modelled by a continuous beam that can account for the flexural and shear deformations as well as the shear-lag effects. The numerical analysis is applicable for the structural analysis of framed-tube structures with single and multiple internal tubes, as well as those without internal tubes. The shear-lag phenomenon of such structures is studied with additiona] bending stresses and shear-lag reversal points.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.493-502
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• 2022

Shear lag phenomenon has long been considered in numerous structural codes; however, the AISC provisions have now no longer proposed any unique equation to calculate the shear lag ratio in bolted connections for angles in general. It is noticeable that, however, codes used in this case are largely conservative and need to be amended. A parametric study consisting of 27 angle sections with equal legs and different with bolted connections was performed to investigate the effects of shear lag on the ultimate tensile capacity of angle members. The main parameters were: steel grade, connection length and eccentricity from the center of the plate, as well as the number of rows of bolts parallel to the applied force. The test results were compared with the predictions of the classical 1-x/l law proposed by Mons and Chesen to investigate its application to quantify the effect of shear lag. A parametric study was performed using valid FE models that cover a wide range of parameters. Finally, based on the numerical results, design considerations were proposed to quantify the effect of shear lag on the ultimate tensile capacity of the tensile members.

• Steel and Composite Structures
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• v.3 no.2
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• pp.111-122
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• 2003

The paper presents a model for analysing the shear-lag effect on the slab of twin-girder composite decks subjected to static actions, support settlements and concrete shrinkage, which are the main actions of interest in composite bridge design. The proposed model includes concrete creep behaviour and shear connection flexibility. The shear-lag in the slab is accounted for by means of a new warping function. The considered actions are then applied to a realistic bridge deck and their effects are discussed. The proposed method is utilised to determine the slab effective widths for three different width-length ratios of the deck. Finally, a comparison between the results obtained with the Eurocode EC4-2 and those obtained with the proposed model is performed.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.725-737
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• 2017

An analytical method considering axial equilibrium is proposed for the short- and long-term analyses of shear lag effect in reinforced concrete (RC) box girders. The axial equilibrium of box girders is taken into account by using an additional generalized displacement, referred to as the longitudinal displacement of the web. Three independent shear lag functions are introduced to describe different shear lag intensities of the top, bottom, and cantilever plates. The time-dependent material properties of the concrete are simulated by the age-adjusted effective modulus method (AEMM), while the reinforcement is assumed to behave in a linear-elastic fashion. The differential equations are derived based on the longitudinal displacement of the web, the vertical displacement of the cross section, and the shear lag functions of the flanges. The time-dependent expressions of the generalized displacements are then deduced for box girders subjected to uniformly distributed loads. The accuracy of the proposed method is validated against the finite element results regarding the short- and long-term responses of a simply-supported RC box girder. Furthermore, creep analyses considering and neglecting shrinkage are performed to quantify the time effects on the long-term behavior of a continuous RC box girder. The results show that the proposed method can well evaluate both the short- and long-term behavior of box girders, and that concrete shrinkage has a considerable impact on the concrete stresses and internal forces, while concrete creep can remarkably affect the long-term deflections.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.67-80
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• 2018

Recently, U-section decks have been more and more used in metro and light rail bridges as an innovative concept in bridge deck design and a successful alternative to conventional box girders because of their potential advantages. U-section may be viewed as a single vent box girder eliminating the top slab connecting the webs, with the moving vehicles travelling on the lower deck. U-section bridges thus solve many problems like limited vertical clearance underneath the bridge lowest point, besides providing built-in noise barriers. Beam theory in mechanics assumes that plane section remains plane after bending, but it was found that shearing forces produce shear deformations and the plane section does not remain plane. This phenomenon leads to distortion of the cross section. For a box or a U section, this distortion makes the central part of the slab lagging behind those parts closer to the webs and this is known as shear lag effect. A sample real-world double-track U-section metro bridge is modelled in this paper using a commercial finite element analysis program and is analysed under various loading conditions and for different geometric variations. The three-dimensional finite element analysis is used to demonstrate variations in the transverse bending moments in the deck as well as variations in the longitudinal normal stresses induced in the cross section along the U-girder's span thus capturing warping and shear lag effects which are then compared to the stresses calculated using conventional beam theory. This comparison is performed not only to locate the distortion, warping and shear lag effects typically induced in U-section bridges but also to assess the main parameters influencing them the most.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.369-383
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• 1997

The classical theory of thin-walled members is unable to reflect the shear lag phenomenon since it is based on the assumption of no shearing strains in the middle surface of the walls. In this paper, an energy equation for the lateral buckling of thin-walled members has been derived which includes the effects of torsion, warping and, especially, the shearing strains which reflect the shear lag phenomenon. A numerical analysis for the lateral buckling of thin-walled members with openings by using Galerkin's method of weighted residuals has been presented. The proposed numerical values and the predictions by experiment for the lateral buckling loads are to agree closely in the paper. The results from these comparisons show that the proposed method here is capable of predicting the lateral buckling of thin-walled members with openings. The fast convergence of the results indicates the numerical stability of the method. By the study, a very complex practical eigenvalue problem is transformed into a very simple one of solving only a linear equation with one variable.

• Steel and Composite Structures
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• v.32 no.5
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• pp.657-670
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• 2019

This paper proposes a one-dimensional fiber beam element model taking account of materially non-linear behavior, benefiting the highly efficient elastic-plastic analysis of girders with shear-lag effects. Based on the displacement-based fiber beam-column element, two additional degrees of freedom (DOFs) are added into the proposed model to consider the shear-lag warping deformations of the slabs. The new finite element (FE) formulations of the tangent stiffness matrix and resisting force vector are deduced with the variational principle of the minimum potential energy. Then the proposed element is implemented in the OpenSees computational framework as a newly developed element, and the full Newton iteration method is adopted for an iterative solution. The typical materially non-linear behaviors, including the cracking and crushing of concrete, as well as the plasticity of the reinforcement and steel girder, are all considered in the model. The proposed model is applied to several test cases under elastic or plastic loading states and compared with the solutions of theoretical models, tests, and shell/solid refined FE models. The results of these comparisons indicate the accuracy and applicability of the proposed model for the analysis of both concrete box girders and steel-concrete composite girders, under either elastic or plastic states.

• Steel and Composite Structures
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• v.24 no.5
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• pp.549-559
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• 2017

As few multi-tower single-box multi-cell cable-stayed bridges with corrugated steel webs have been built, analysis is mostly achieved by combining single-girder model, beam grillage model and solid model in support of the design. However, such analysis methods usually suffer from major limitations in terms of the engineering applications: single-girder model fails to account for spatial effect such as shear lag effect of the box girder and the relevant effective girder width and eccentric load coefficient; owing to the approximation in the principle equivalence, the plane grillage model cannot accurately capture shear stress distribution and local stress state in both top and bottom flange of composite box girder; and solid model is difficult to be practically combined with the overall calculation. The usual effective width method fails to provide a uniform and accurate "effective length" (and the codes fail to provide a unified design approach at those circumstance) considering different shear lag effects resulting from dead load, prestress and cable tension in the construction. Therefore, a novel spatial grid model has been developed to account for shear lag effect. The theoretical principle of the proposed spatial grid model has been elaborated along with the relevant illustrations of modeling parameters of composite box girder with corrugated steel webs. Then typical transverse and longitudinal shear lag coefficient distribution pattern at the side-span and mid-span key cross sections have been analyzed and summarized to provide reference for similar bridges. The effectiveness and accuracy of spatial grid analysis methods has been finally validated through a practical cable-stayed bridge.