Analysis of Pure Bending Vertical Deflection of Improved Composite Box Girders with Corrugated Steel Webs

Steel bottom plates are applied as replacements for the concrete bottom plates in order to reduce the dead weight of the composite box girders with corrugated steel webs and steel bottom plates (CSWSB). Due to the change in the material, the previous analytical calculation methods of vertical deflection of composite box girders with corrugated steel webs (CSWs) cannot be directly applied to the improved composite box girders. The shear lag warpage displacement function was derived based on the shear deformation laws of the upper flange and the bottom plates of the improved composite box girders. The equations for the calculation of the shear deformation and the additional deflection due to the shear lag of continuous and simply supported composite box girders with CSWSB under concentrated and uniformly distribution loads were derived by considering the double effects of the shear lag and the shear deformations of the top and the bottom plates with different elastic moduli. The analytical solutions of the vertical deflection of the improved composite box girders include the theory of the bending deflection of elementary beams, shear deformation of CSWs, and the additional deflection caused by the shear lag. Based on the theoretical derivation, an analytical solution method was established and the obtained vertical deflection analytical solutions were compared with the finite element method (FEM) calculation results and the experimental values. The analytical equations of vertical deflection under the two supporting conditions and the two load cases have verified the analyses and the comparisons. Further, the additional deflections due to the shear lag and the shear deformation are found to be less than 2% and 34% of the total deflection values, respectively. Moreover, under uniform distributed load conditions, the deflection value was found to be higher than that of the under concentrated load condition. It was also found that the ratio of the deflection caused by the shear lag or the shear deformation to the total deflection decreased gradually with the increase in the span width ratio. When the value of the span width ratio of a single box and single chamber composite box girder with CSWSB was equal to or greater than 8, the deflections caused by the shear lag and the shear deformation could be ignored.

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Shear Lag in Thin-Walled Box Girder with Variable Section

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.194-196.1165 ◽

2011 ◽

Vol 194-196 ◽

pp. 1165-1169

Author(s):

Yu Hong Zhang ◽

Zi Jiang Yang ◽

Shi Zhong Liu

Keyword(s):

Significant Influence ◽

Width Ratio ◽

Stiffness Ratio ◽

Shear Lag ◽

Box Girders ◽

Box Girder ◽

Lag Effects ◽

Variable Section ◽

Thin Walled ◽

Span Width

In this paper, a equivalent-section method of analyzing shear lag effects in box girders is presented. The effect of two major parameters on shear lag is investigated for cantilever and continuous box girders with variable section under two kinds of loads. It is shown that the span-width ratio, in addition to the flange stiffness to total stiffness ratio, has a significant influence on the shear lag. Finally, conclusions are drawn with regard to further study and research.

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Beam finite element for thin-walled box girders considering shear lag and shear deformation effects

Engineering Structures ◽

10.1016/j.engstruct.2021.111867 ◽

2021 ◽

Vol 233 ◽

pp. 111867

Author(s):

Xiayuan Li ◽

Shui Wan ◽

Yuanhai Zhang ◽

Maoding Zhou ◽

Yilung Mo

Keyword(s):

Finite Element ◽

Shear Deformation ◽

Shear Lag ◽

Box Girders ◽

Thin Walled

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A finite beam element for analyzing shear lag and shear deformation effects in composite-laminated box girders

Computers & Structures ◽

10.1016/j.compstruc.2004.02.007 ◽

2004 ◽

Vol 82 (9-10) ◽

pp. 763-771 ◽

Cited By ~ 18

Author(s):

Yaping Wu ◽

Yuanming Lai ◽

Xuefu Zhang ◽

Yuanlin Zhu

Keyword(s):

Shear Deformation ◽

Beam Element ◽

Shear Lag ◽

Box Girders

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Computation of Deflections for PC Box Girder Bridges with Corrugated Steel Webs considering the Effects of Shear Lag and Shear Deformation

Mathematical Problems in Engineering ◽

10.1155/2020/4282398 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Wei Ji ◽

Kui Luo ◽

Jingwei Zhang

Keyword(s):

Shear Deformation ◽

Prestressed Concrete ◽

Displacement Function ◽

Shear Lag ◽

Longitudinal Displacement ◽

Box Girders ◽

Element Analysis ◽

Box Girder ◽

Bridge Model ◽

Bridge Models

Prestressed concrete (PC) girders with corrugated steel webs (CSWs) have received considerable attention in the past two decades due to their light self-weight and high prestressing efficiency. Most previous studies were focused on the static behavior of CSWs and simple beams with CSWs. The calculation of deflection is an important part in the static analysis of structures. However, very few studies have been conducted to investigate the deflection of full PC girders or bridges with CSWs and no simple formulas are available for estimating their deflection under static loads. In addition, experimental work on full-scale bridges or scale bridge models with CSWs is very limited. In this paper, a formula for calculating the deflection of PC box girders with CSWs is derived. The longitudinal displacement function of PC box girders with CSWs, which can consider the shear lag effect and shear deformation of CSWs, is first derived. Based on the longitudinal displacement function, the formula for predicting the deflection of PC box girders with CSWs is derived using the variational principle method. The accuracy of the derived formula is verified against experimental results from a scaled bridge model and the finite element analysis results. Parametric studies are also performed, and the influences of shear lag and shear deformation on the deflection of the box girder with CSWs are investigated by considering different width-to-span ratios and different girder heights. The present study provides an effective and efficient tool for determining the deflection of PC box girders with CSWs.

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Vertical Deflection of Simply Supported Box Beam with Corrugated Steel Webs Including Effects of Shear Lag and Shear Deformation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.1012 ◽

2012 ◽

Vol 204-208 ◽

pp. 1012-1016 ◽

Cited By ~ 1

Author(s):

Wei Ji ◽

Shi Zhong Liu

Keyword(s):

Finite Element Method ◽

Shear Deformation ◽

Comprehensive Analysis ◽

Shear Lag ◽

The Finite Element Method ◽

Vertical Deflection ◽

Simply Supported ◽

Box Beam ◽

Box Beams ◽

Good Agreement

This paper presents an method to solve the vertical deflection of the box beams with corrugated steel webs, considering both the shear lag and shear deformation of corrugated steel webs. The method is deduced by means of the variational principle. The formulas given by this method is simple and practical. Then, a comprehensive analysis on the effects of shear lag and shear deformation of corrugated steel webs is given for a simply supported box beam with corrugated steel webs under uniformly distributed. The results of vertical deflection obtained by this paper are in good agreement with those obtained by the finite element method (FEM) and the model test, respectively.

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Study of Free Vibration Characteristic of Continuous Box-Girder Based on Hamilton Principle

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.351-352.476 ◽

2013 ◽

Vol 351-352 ◽

pp. 476-482 ◽

Cited By ~ 1

Author(s):

Wang Bao Zhou ◽

Li Zhong Jiang ◽

Zhi Huang

Keyword(s):

Free Vibration ◽

Natural Frequency ◽

Width Ratio ◽

Rotational Inertia ◽

Shear Lag ◽

Shear Lag Effect ◽

Box Girder ◽

Hamilton Principle ◽

Lag Effect ◽

Span Width

Based on Hamilton principle, the differential equation of free vibration and the corresponding boundary conditions of continuous box girder with consideration for the shear lag effect meeting self-equilibrated stress, shear deformation as well as rotational inertia were induced. The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified. The obtained formulas developed the shear lag theory. Some meaningful conclusions for engineering design were obtained. The contribution of the shear lag effect decreases each order natural frequency of the continuous box-girder, at the same time the higher the order natural frequency is, the greater the influence of shear lag effect on natural frequency of continuous box-girder is. The shear-lag effect of continuous box girder increases when frequency order rises, and increases while span-width ratio decreases.

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Improved method for shear lag analysis of thin-walled box girders considering axial equilibrium and shear deformation

Thin-Walled Structures ◽

10.1016/j.tws.2020.106732 ◽

2020 ◽

Vol 151 ◽

pp. 106732

Author(s):

Xiaoyang He ◽

Yiqiang Xiang ◽

Zhengyang Chen

Keyword(s):

Shear Deformation ◽

Shear Lag ◽

Improved Method ◽

Box Girders ◽

Thin Walled

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Elastic Bending Theory of Composite Bridge with Corrugated Steel Web Considering Shear Deformation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.400-402.575 ◽

2008 ◽

Vol 400-402 ◽

pp. 575-580 ◽

Cited By ~ 1

Author(s):

Jun He ◽

Yu Qing Liu ◽

Ai Rong Chen

Keyword(s):

Shear Deformation ◽

Load Condition ◽

Internal Force ◽

Equilibrium Equations ◽

Element Analysis ◽

Concentrated Load ◽

Elastic Bending ◽

Limit Value ◽

Composite Bridge ◽

Corrugated Steel Web

The classical Euler-Bernoulli girder theory is not applicable due to shear deformation of corrugated steel web, elastic bending theory considering shear deformation is presented to analyze deflection and mechanical property. Differential equation is derived based on displacement field assumption, internal force equilibrium equations, deformation compatibility condition and relation of deformation and internal force, and solutions are obtained according to boundary and load condition. Simply supported I and box girder bridges with corrugated steel web are analyzed with elastic bending theory considering shear deformation, their predicted results are found in good agreement with those by 3D finite element analysis and test. A limit value of depth-span ratio is suggested for considering influence of shear deformation or not, the simplified formula of deflection in middle span is presented to guide deflection design. Corrugated web accounts for more than 80% of total shear force in the whole span under uniform load while one third apart from bearing under concentrated load in mid-span. The elastic bending theory considering shear deformation makes a reference for designing composite bridge with corrugated steel web.

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Influence of Shear Lag and Shear Deformation Effects on Deflection of Composite Box Girder with Corrugated Steel Webs

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.671-674.985 ◽

2013 ◽

Vol 671-674 ◽

pp. 985-990 ◽

Cited By ~ 2

Author(s):

Peng Qiao

Keyword(s):

Shear Deformation ◽

Parametric Analysis ◽

Shear Lag ◽

Shear Lag Effect ◽

Deformation Effect ◽

Box Girder ◽

Composite Girder ◽

Deflection Coefficient ◽

Lag Effect ◽

Span Width

The shear lag and shear deformation effects on deflection of composite girder with corrugated steel webs (CGCSW) was studied. The influence of shear lag and shear deformation effect was expressed by deflection coefficient δ1 and δ2. Parametric analysis within a scope of dimensions of built-in girders was performed, including girder span, width, height, thickness of concrete flange and thickness of steel web. The results show that the deflection coefficient of shear lag effect is approximately directly proportional to square of width-span ratio, while the deflection coefficient of shear deformation effect is related to all parameters. It’s suggested that shear lag effect on CGCSW’s deflection be neglected when width-span ratio is smaller than 1/9, and shear deformation effect should always be considered.

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