Analysis of Shear Lag Effect of Box Beam under Dead Load Qi Wang 1, a, Hongsheng Qiu 2, b 1 School of transportation, Wuhan University of Technology, 430063, Wuhan Hubei China 2 School of transportation, Wuhan University of Technology, 430063, Wuhan Hubei China a Wqhome776@163.com, b qiuhhss@163.com Abstract. Simply supported box beam are widely used in bridge engineering, so in this paper, using the finite element analysis software ANSYS, to do the numerical anaysis of shear lag effect about a simply supported thin-walled box beam under the action of dead load,then calculate it.and at last compared with the shear lag effect through the result which can be obtained by variational method and test.according to result anaysis and comparison of data,we should consider the infulence of shear lag when we design a structure,so through this way it will be more safe. Keywords: Finite element; Box beam; Variational method; Shear lag effect 1. Introduction In recent years, with the rapid development of the transportation industry in our country, because of the box thin-walled beam has the excellent feature of bending resistance, torsional resistance, light weight and fast construction in the cantilever construction and casting, thus this structure is widely used in bridge structures. But the width of box section beam under the action of dead load or symmetrical load will produce flexure, because the shear deformation of wing plate shear flow along the beam width of the transverse transfer process with hysteresis, therefore the phenomenon is called shear lag effect. If we do not consider the influence of the shear lag effect, it will underestimate the actual stress status inside the box girder structure, the safety of engineering structures becomes low. The shear lag effect of box beam method for calculating the general has the following kinds: (1) based on the principle of minimum potential energy variational method; (2) the tuning function method, based on the theory of the elastic orthotropic plate method and the theory of folded plate method; (3) based on the numerical method of finite element method and limited legal persons, the finite difference method, finite segment method, and using the state space method of modern control theory and the plate of the box girder as a plate girder plate beam element method for space; (4) match rod; (5) test methods. This paper will use the cross section such as described in the literature [1], which is a simply supported box beam model, using the shell 63 units to establish the corresponding model, then analysis and calculate the model through the finite element software ANSYS, at least compare the numerical calculation results, the calculated value of literature, the calculated results from variation method and test data. 2. Construct Finite Element Model Using the organic glass model which is used in the literature [1], thin-walled box beam linear model, and analysis, shear lag effect of the simply supported box beam under constant load. Detailed numerical parameters are as follows: 1) Module dimension: width of top flange is 40cm; width of bottom flange is 20.8cm; thickness of the flange plate and web plate are 0.8cm; the depth of the beam is 8cm; box girder span is 80cm;do not set diaphragm plate box girder and simply supported beam end. The cross section and arrangement of measuring points is shown in figure 1. 101
Figure.1 Cross section and the arrangement of measuring points (cm) 2) The beam body material parameters: modulus of elasticity is 3000MPa; poisson's ratio is 0.385; exert a dead load that is concentrated symmetry and value is 0.2722kN. 3)Unit selection: the feature of shell63 unit is both bending and membrane forces, so it can withstand the plane load and normal load. This unit each node are six degrees of freedom: the node coordinates are X, Y, Z direction of translation and the node coordinates X, Y, Z axis of rotation. Players of stress and large deformation is considered in it. In the large deformation analysis (finite rotation) can use the same tangent stiffness matrix. With Shell63 box girder of three-dimensional finite element model is set up as shown in figure 2, there are 456 nodes and 432 unit cells. Here is an application Shell63 element to solve the problem of shear lag some matters needing attention: 1) The area of the unit cannot be 0, usually unit connection number is not correct will cause this phenomenon. The thickness of the unit to 0 or linear variations in thickness of unit 4 0 is not allowed. 2) The surface shell structure adopts flat shell element, can produce good results, but the plane shell element buckling curve must not be greater than 15 degrees. 3) Application Shell63 element analysis of shear lag post-treatment process, should choose: the Middle layer, or the process after the data is not the result of the board on the plate surface, will draw the wrong conclusions. Fig.2 Box beam finite element model 3. The calculation results and analysis Box girder structural formula of typical thin-walled structure, based on the theory of thin plate with a thin plate element of spatial finite element method in structure analysis is one of the common methods, analysis precision mainly depends on how to choose the suitable unit simulates form and structure, so that after the discrete structure 102
of the mechanical properties and actual structure to as much as possible. In order to improve the calculation accuracy, discrete structure and grid should try to follow these rules:(1)sheet unit should be corresponding parts and structure the center of gravity of the overlap;(2)bridge across the direction to consider all main control interface unit locations, in order to ensure sufficient accuracy at the same time, in a big stress, appropriate encryption meshing. Due to the constant load under the action of working stress of the concrete is lower, so the hypothesis in the elastic state, the concrete work doesn't consider the effect of concrete material nonlinearity., finite element calculation when using entity unit can output the stress of the up and down eight nodes, reflect the distribution of shear lag effect in the thickness direction. The numerical calculation results by ANSYS, numerical results in the literature [1], variational method, results and test data are as shown in table 1. Table. 1 Normal stress calculation result (MPa) Position Number Study results Literature results Variational method results Test results 1-0.21176-0.22583-0.24245-0.21224 Suspended panel 2-0.24158-0.24441-0.25728-0.24850 3-0.29357-0.28482-0.36103-0.32900 4-0.36072-0.38761-0.40740-5 -0.39072-0.38761-0.40740 - Top slab 6-0.32015-0.31256-0.36103-0.32004 7-0.28736-0.28315-0.25728-0.26040 8-0.27403-0.27462-0.24245-0.24500 11 0.62742 0.63967 0.66929 - Bottom slab 12 0.47238 0.48256 0.59313 0.57376 13 0.44127 0.43679 0.44267 0.39840 14 0.42060 0.42351 0.39832 0.38880 From table 1, numerical solution by using ANSYS compares with results which are obtained by the variational method, we can easily find that the result of ANSYS are very close to the real state between these data, the error of theoretical calculation value is within 19.8%, with the test data of error values are not more than 13.6%, the remaining points in 20%, especially in the bottom part of the roof and a border of web plate, this study calculated the literature [1] is more consistent, well verified the correctness of the numerical method in this study. In order to bring the study of the numerical calculation result tallies with the literature data and experimental data better, can draw out of the box girder cross section normal stress distribution curve, as shown in figure 3 and figure 4. Clearly calculated by using an ANSYS numerical solution closer to the actual data, therefore, higher precision and can better reflect the actual stress state in box girder cross-section. 103
Fig.3 Roof normal stress distribution Fig.4 Bottom plate normal stress distribution According to the definition of shear lag coefficient, firstly use elementary beam theory to calculate the cross section of the roof and floor of the stress value: MyT 54.44 0.028 0T 0.3026MPa 6 I 5.037 10 MyB 54.44 0.046 0B 0.4972MPa 6 I 5.037 10 Then put it into the calculation formula of the shear lag coefficient, we can draw a cross section of each node of the shear lag coefficient its distribution is shown in figure 5. Fig.5 Shear lag coefficient distribution in each node of the box girder cross section 104
From the figure 5, we can see clearly that the shear lag coefficient is the max in the junction of the web and flange, which shows that the stress is concentrated, to improve the bending moment value at design time, so that the structure of local is stability and security. 4. Conclusions Using ANSYS finite element software, establish a simply supported box beam under the action of dead load a space finite element model of beam of single box room such as a section of the shear lag coefficient is calculated. At the same time, the ANSYS calculating results with the results of variational method, the experimental results are compared and analyzed, it is concluded that the ANSYS calculation is more precise than others, the shear lag coefficient are maximum at the junction of web and flange. By the finite element solution and decomposition of contrast can be seen that the results are quite good; Normal stress distribution basic shows parabola, shows that the reliability of the finite element software to solve. ANSYS of solving the model and the numerical results by analyzing the above steps, can draw the following conclusion: 1) Using numerical method and variation method in section box girder, the results accord with those of theoretical calculation value and experimental data. One hand, the study has verified the correctness of the numerical calculation method; On the other hand, the shear lag effect for other similar model of numerical calculation to provide the related guidance. Straight box girder under the vertical load, the shear lag coefficient distribution along the cross section symmetry, so it may require that the reinforced should layout symmetrical. 2) Many engineering examples prove that the cracks of concrete box girder bridge in the process of construction and using main reason is considered that the shear lag coefficient during the design process is inconsiderable or completely ignores the influence of the shear lag effect of box girder. 3) During the bridge design in the future, the designer should realize the impact of the shear lag effect of the structure, the dead load on the cross section of shear lag effect is particularly important. So it is necessary to improve the bending moment of design value of dead load, but the concrete value is calculated by the shear lag coefficient. 5. References [1] XU F H, CAI W Sh. Numerical calculation of the shear lag effect of thin walled box girder [J]. Journal of ChangshaUniversity of Science and technology (Natural Science), 2009,6 (4). [2] Reissner E. Analysis of shear lag in box beam by the principle of minimum potential energy [J]. Quarterly of applied mathematics, 1946,5 (3): 268-278. [3] Zhang Sh D, Deng X H, Wang W Zh. Shear Lag of Thin Box Girder [M]. Beijing: People Communication Press, 1998. [4] Zhou, S J. Finite beam element considering the shear - lag effect in a box girder [J]. Journal of Engineering Mechanics, ASCE, 2010,136 (9): 1115-1122. [5] Chang, S T. Shear-lag Effect in Simply Supported Pre-stressed Concrete Box-girder Bridge [J]. Journal of Bridge Engineering, 2004,9 (2), 178-184. [6] SHEN G Sh, LIU Sh Zh. The application of ANSYS to analysis of shear lag effect of thin-wall box-girder [J]. Scientific and Technical Information of Gansu.2006 (35): 144-146. [7] LIAO Zh H. The application of ANSYS to analysis of shear lag effect of box-girder [J]. Henan Building Materials, 2009 (3): 68-69. [8] Evans. H.R, Ahmad M.K, Kristen V. Shear Lag in Composite Box Girders of Complex Cross Section [J]. Constructional Steal Researeh, 1993,24 (3). [9] JGJ100-98 (2009). Design Code for Garage [S]. Beijing: China Architecture & Building Press. [10] Building, structural load norms GB50009-2001.National standards of the People's Republic of China. [11] General Code for Design of Highway Bridges and Culverts G D60, 2004), the industry standard of the People's Republic of China. [12] Malcolm D J, Redwood R G. Shear lag in stiffened box girders [J]. Structure Div, ASCE, 1970, 96 (ST7): 1403-1415. [13] Bogdan O. Kazmanvic, H. Janes Graham. Shear Lag in Box Girders [J]. Journal of the Structural Division.1978, 107 (ST9): 1701-1710. [14] Chang, S T. Shear-lag Effect in Simply Supported Pre-stressed Concrete Box-girder Bridge [J]. Journal of Bridge Engineering, 2004,9 (2): 178-184. 105