# 【精品文档】32中英文双语外文文献翻译成品：连续箱梁中剪力滞产生的应力集中现象.doc

此文档是毕业设计外文翻译成品（ 含英文原文+中文翻译），无需调整复杂的格式！下载之后直接可用，方便快捷！本文价格不贵,也就几十块钱！一辈子也就一次的事！ 外文标题：Stress concentration due to shear lag in continuous box girders 外文作者：Jaturong Sa-nguanmanasak, , Taweep Chaisomphob, Eiki Yamaguchi 文献出处:《Engineering Structures》 , 2018 , 29 (7) :1414-1421(如觉得年份太老，可改为近2年，毕竟很多毕业生都这样做) 英文2869单词， 14798字符(字符就是印刷符)，中文4289汉字。 Stress concentration due to shear lag in continuous box girders Abstract Quite a few researches on shear lag effect in box girder have been reported in the past, and many of them employed the finite element method. The past researchers, however, do not seem to have paid much attention to the influence of the finite element mesh on the shear lag, although the shear lag effect in terms of stress concentration can be quite sensitive to the mesh employed in the finite element analysis. In addition, most of the researchers on the shear lag have focused on simply supported girders and cantilever girders, while continuous girders have been dealt with in very few researches. The present study investigates the shear lag effect in a continuous box girder by using the three-dimensional finite element method. The whole girder is modeled by shell elements, and an extensive parametric study with respect to the geometry of a box girder is carried out. The influence of finite element mesh on the shear lag is carefully treated by the multimesh extrapolation method. Based on the numerical results thus obtained, empirical formulas are proposed to compute stress concentration factors that include the shear lag effect. Keywords: Shear lag; Continuous box girders; Stress concentration; Three-dimensional finite element analysis Introduction Although normal stress in the longitudinal direction produced by bending deformation is assumed to be uniform across flange width in the elementary beam theory, it is not so in reality if the flange width is large. This phenomenon, known as the shear lag, has been studied for many years. A concise but excellent literature review of research on the shear lag is available in Tenchev [1]. Even in recent years, the subject has attracted many researchers and quite a few papers have been published [2–6]. Although much research has been done on the problem in the past, a discrepancy in numerical results is observed in the literature, an illustration of which is given by Lertsima et al. [6] for the case of simply supported girders. The discrepancy seems to be attributable to the factors that have considerable influence on the shear lag but have been overlooked. Lertsima et al. studied the shear lag of a simply supported box girder by the three-dimensional finite element analysis, using shell elements [6]. Loads were applied in multiple ways. Much attention was paid to finite element meshes as well: in short, the multimesh extrapolation method [7] was utilized so as to reduce discretization error and thus enhance accuracy of the results due to the finite element analysis. An extensive parametric study was then conducted and empirical formulas were proposed. Continuous girders are quite common structures in practice. Engineers dealing with ordinary box girders for highway bridges and buildings need not be daunted by the stress concentration due to shear lag. However, there are indeed some special cases of short stocky members, so that design codes provide formulas to account for the shear lag effect [8, 9]. Nevertheless, there appear to be very few research results available in the literature on the shear lag effect of continuous girders. Besides, Japan [8] and Eurocode 3 [9] yield very different shear lag effects, which will be shown later in this paper. Against the background of the above information, the three-dimensional finite element analysis of a continuous box girder by shell elements is carried out to investigate stress concentration due to the shear lag in the present study. With the multimesh extrapolation method [7], the analysis is performed to produce reliable numerical results. An extensive parametric study is conducted and empirical formulas are proposed to deal with the shear lag phenomenon in continuous box girders. In all the analyses, a well-known finite element program, MARC [10], is used Continuous box girder model Three-span continuous box girders under uniformly distributed load are analyzed. The symbols employed in the present study for describing the structural geometry are illus- trated in Fig. 1. For the design of a continuous girder, the stress distributions in the cross sections under large bending moment are important. Therefore, in the present study we focus on three cross sections of Sections A–C shown in Fig. 1(b): Section A is under the largest bending moment in the exterior span, Section B is at the interior support (under the largest negative bending moment) and Section C is at the center of the girder, which is under the largest bending moment in the interior span. Following Lertsima et al. [6], a uniformly distributed load is applied as a line load along the centerline of the web as shown in Fig. 1(c). Due to symmetry, only a quarter of the girder (a half of the cross section and a half of the girder length) need be analyzed. Therefore, the symmetric conditions, i.e., no displacement in y-axis and no rotations about x- and z-axes, are imposed on Section C, while only the displacement in z-axis is suppressed at the end of the girder and Section B. The material property is assumed to be isotropic linear elastic with Young’s modulus 206 GPa and Poisson’s ratio 0.3 The stress concentration factors in Sections A–C can be evaluated by the formula given in the design codes [8,9]. For a box girder with B/ H = 2.0, H/ L = 0.2, Tf / Tw = 1.0 and = 1.0, those values are computed and presented in Table 1, where Kc stands for the stress concentration factor defined by the ratio of the maximum normal stress in the flange to that of the elementary beam theory. Significant discrepancy is recognized, suggesting the necessity of the further study of the shear lag in a continuous girder. In the present study, the continuous box girders are analyzed by the three-dimensional finite element method, using 4-node shell elements. In particular, Element 75 (Bilinear Thick Shell Element) is used, and the nodal stress is evaluated as an average of the stresses in the elements sharing the node [10]. Although the finite element method is very versatile and powerful, caution must be used since the results may depend largely on the finite element mesh employed in the analysis, which is especially so when stress concentration is dealt with. The dependency on the finite element mesh is attributable to the discretization error. In Lertsima et al. [6], this issue was looked into numerically, and the multimesh extrapolation method was employed to reduce the discretization error in the evaluation of the stress concentration due to shear lag. It is noted that the stress concentration factors thus obtained are very close to those obtained by the adaptive finite element method [6]. The multimesh extrapolation method is also used herein, and the numerical procedure is briefly explained in what follows Fig. 2(a) shows the normal-stress distributions in the upper flange at the mid-span of a simply-supported box girder (B/ H = 1.0, H/ L = 0.2, Tf / Tw = 1.0) that was dealt with in Lertsima et al. [6]. In this figure, is the normal stress obtained by the three-dimensional finite element analysis, where beam is the normal stress due to the elementary beamwidth. Using the 4-node shell elements, four finite element meshes of Meshes A–D are employed herein. All the elements in each mesh are rectangular and every element in the box girder is made a quarter in the process of refining the mesh from Meshes A–D: an illustration of Meshes A–D is presented in Fig. 3. The total numbers of elements are 1920, 7680, 30,720 and 122,880 for Meshes A–D, respectively. Fig. 2(a) illustrates not only the shear lag phenomenon but also the dependence of the stress distribution on the finite element mesh. As expected, the dependence is stronger at the edge of the flange where the largest stress concentration takes place. At the same time, the tendency of stress convergence is observed, as the size of the finite element becomes smaller. The stresses at four points in the upper flange obtained by the present finite element analysis are presented in Fig. 2(b The figure shows the variation of the normal stress with respect to a representative element size. It is observed that the four lines in Fig. 2(b) become almost straight for small. This is in good agreement with the theory that the error in stress is of the p) where p is equal to 1 for a bilinear element [7,11]. Therefore, the linear extrapolation illustrated by the dotted lines in Fig. 2(b) can be used to estimate the converged stress. This extrapolation method is called the multimesh extrapolation method by Cook et al. [7] and is applied to the present study. The stress ratio / beam at the edge of the flange thus obtained, (b)Variation of normal stress with respect to representative element size. Fig. 2. Dependence of normal stress on finite element mesh. i.e., the point indicated by an arrow in Fig. 2(b), is the value of Kc that the authors seek in the present numerical study. Normal-stress distribution in upper flange Fig. 4 shows two variations of the normal stress at the edge of the upper flange along the length of the girder with B/ H = 2.0, H/ L = 0.2, = 1.5 and Tf / Tw = 2.0: one is obtained by the elementary beam theory and the other by the finite element analysis (FEA). Due to symmetry, only the stress distribution along a half of the girder (y/ L = 0.0 1.75) is given: y/ L = 1.75 corresponds to the location of Section C. Note that0 is the stress due to the beam theory at the internal (a) Mesh A. (b) Mesh B. (c)Mesh C. (d) Mesh D. Fig. 3. Finite element meshes for a quarter of the box girder. The figure shows the variation of the normal stress with respect to a representative element size . It is observed that the four lines in Fig. 2(b) become almost straight for small . This is in good agreement with the theory that the error in stress is of the p) where p is equal to 1 for a bilinear element [7, 11]. Therefore, the linear extrapolation illustrated by the dotted lines in Fig. 2(b) can be used to estimate the converged stress. This extrapolation method is called the multimesh extrapolation support (Section B). The significant difference between the two normal-stress distributions confirms the importance of the shear lag in a continuous box girder. The normal-stress distribution in the upper flange of various cross sections is presented in Fig. 5. The distribution varies considerably from section to section. It may be noteworthy that as can be seen typically in Fig. 5(a) and (f), near the mid- span in the exterior span the magnitude of the normal stress decreases towards the center of the flange and the smallest value is nearly equal to zero, while the smallest value is rather close to the normal stress of the beam theory near the mid-span in the interior span. The normal-stress distribution in a simply- supported box girder has been found to be similar to that of the exterior span of the continuous box girder [6]. Parametric study Three-dimensional finite element analysis is conducted so as to reveal the influence of the parameters that characterize the geometry of a continuous box girder. To this end, the following values are considered: B/ H = 0.5, 1.0, 1.5, 2.0; H/ L =0.025, 0.05, 0.10, 0.15, 0.20; Tf / Tw = 0.5, 1.0, 1.5, 2.0; = 1.0, 1.25, 1.5. The combination of all these values results in 240 box girders different from each other in geometry. It is noted that for every girder, multiple finite element meshes are used to reduce discretization error by the multimesh extrapolation method Typical examples of the present numerical results for Section A are shown in Fig. 6. The trends of the variation of Kc with respect to the parameters may be summarized as follows: Kc tends to increase significantly in general with the increase of B/ H or H/ L. However, for H/ L = 0.025 and 0.05 or B/ H = 0.5, Kc remains almost constant and nearly equal to 1.0: the effect of the shear lag is small. Kc increases also with the increase of Tf / Tw. However, the change of Kc with respect to Tf / Tw is small. Unlike the cases of B/ H and H/ L, the Kc–Tf / Tw curves are close to straight lines and the slopes of those curves are almost identical regardless of B/ H. The increase of increases Kc. However, the dependence of Kc on is rather small although it becomes slightly bigger for large B/ H. As may be seen in Fig. 7, the variations of Kc for Sections B and C show similar tendencies except for the influence of : unlike in Section A, Kc decreases as increases. It is also observed that Kc in Section B is the largest in general. However, the difference between Kc values in the three sections varies with. At = 1.25 and 1.5, Sections A and C have almost identical values of Kc Fig. 8 shows Kc values due to the two design codes [8,9] together with the present FEA results. The influence of B/ H is focused on in particular herein. For Sections A and C, Japan [8] yields the largest value while Eurocode 3 [9] gives the smallest. For Section B, the tendency is reversed: Kc due to Eurocode 3 [9] is consistently larger than that due to Japan [8]. The discrepancy observed in Fig. 8 is not negligible: it seems rather significant in design practice. Interestingly, the results of the present FEA tend to lie between the two sets of the Kc values due to the two design codes. Empirical formulas A data analysis program, Statistica of StatSoft, Inc., is used to conduct a regression analysis of the present FEA results, yielding the empirical formulas for Kc in the three sections of Section A–C. The empirical formulas thus obtained are presented in the following: Fig. 9 illustrates some comparisons between the Kc values due to the empirical formulas and the present FEA. Good agreement is obvious in these figures. The overall accuracy of each proposed formula is calculated as the mean square error by the following equation [1]: N in Eq. (18) is the number of the present FEA results. KcEmp and KcFEA in Eq. (19) are the Kc values obtained from the proposed empirical formula and the present FEA, respectively. Since, in the present study, the combination of the geometrical parameters has required 240 box girders to be analyzed, N is equal to 240. Using Eq. (18), the mean square error is found to be 3.0%, 2.9% and 4.2% for Sections A, B and C, respectively. Concluding remarks In this study, the three-dimensional finite element analysis of continuous box girders of various geometries has been performed so as to determine the shear lag effect in the continuous box gird