32中英文雙語外文文獻(xiàn)翻譯成品連續(xù)箱梁中剪力滯產(chǎn)生的應(yīng)力集中現(xiàn)象

1、<p>　　外文標(biāo)題：Stress concentration due to shear lag in continuous box girders</p><p>　　外文作者：Jaturong Sa-nguanmanasak, , Taweep Chaisomphob, Eiki Yamaguchi</p><p>　　文獻(xiàn)出處:《Engineering Structures

2、》 , 2007 , 29 (7) :1414-1421</p><p>　　英文2869單詞， 14798字符，中文4289漢字。</p><p>　　此文檔是外文翻譯成品，無需調(diào)整復(fù)雜的格式哦！下載之后直接可用，方便快捷！只需二十多元。</p><p>　　Stress concentration due to shear lag in continuous b

3、ox girders</p><p>　　Jaturong Sa-nguanmanasak, , Taweep Chaisomphob, Eiki Yamaguchi</p><p><b>　　Abstract</b></p><p>　　Quite a few researches on shear lag effect in box gi

4、rder 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 la

5、g, 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 s

6、upported</p><p>　　Keywords: Shear lag; Continuous box girders; Stress concentration; Three-dimensional finite element analysis</p><p>　　Introduction</p><p>　　Although normal stress

7、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 th

8、e 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

9、 a few papers have been published [2–</p><p>　　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 g

10、iven 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.</p><p&g

11、t;　　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 finit

12、e 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 param

13、etric study was then conducted and empirical formulas were propo</p><p>　　Continuous girders are quite common structures in practice. Engineers dealing with ordinary box girders for highway bridges and build

14、ings 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

15、]. Nevertheless, there appear to be very few research results available in the literature on the shear lag effect of continuous girders. Besides, J</p><p>　　Against the background of the above information, t

16、he 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 met

17、hod [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

18、 all the a</p><p>　　Continuous box girder model</p><p>　　Three-span continuous box girders under uniformly dis- tributed load are analyzed. The symbols employed in the present study for describi

19、ng 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 f

20、ocus 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 </p><p>　　The stress concentration factors in Sections A–C can b

21、e 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 concen

22、tration 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

23、in a c</p><p>　　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 Elem

24、ent) 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 resul

25、ts may depend largely on the finite element mesh employed in the analysis, which is espec</p><p>　　Fig. 2(a) shows the normal-stress distributions in the upper flange at the mid-span of a simply-supported bo

26、x 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

27、 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 rectangul</p><p>　　The stresses at four poin

28、ts in the upper flange obtained by the present finite element analysis are presented in Fig. 2(b)</p><p>　　The figure shows the variation of the normal stress with respect to a representative element size. I

29、t 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]. Theref

30、ore, 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 extrapola</p><p>　　Normal-stress dis

31、tribution in upper flange</p><p>　　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

32、</p><p>　　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

33、= 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 girde

34、r. The figure shows the variation of the normal stress with respect to a representa</p><p>　　The normal-stress distribution in the upper flange of various cross sections is presented in Fig. 5. The distribut

35、ion 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 c

36、enter 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</p><p>　　Parametric study</p><

37、;p>　　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:

38、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

39、noted that for every girder, multiple finite element meshes are used</p><p>　　Typical examples of the present numerical results for Section </p><p>　　A are shown in Fig. 6. The trends of the var

40、iation of Kc with respect to the parameters may be summarized as follows:</p><p>　　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

41、= 0.5, Kc remains almost constant and nearly equal to 1.0: the effect of the shear lag is small.</p><p>　　Kc increases also with the increase of Tf / Tw. However, the change of Kc with respect to Tf / Tw is

42、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.</p><p>　　The increase of increases Kc. Howe

43、ver, the dependence of Kc on is rather small although it becomes slightly bigger for large B/ H.</p><p>　　As may be seen in Fig. 7, the variations of Kc for Sections B and C show similar tendencies except fo

44、r 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

45、.25 and 1.5, Sections A and C have almost identical values of Kc</p><p>　　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 i

46、n 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 du

47、e to Japan [8]. The discrepancy observed in Fig. 8 is not negligible: it seems rather significant in design practice. Interestingly, the results of</p><p>　　Empirical formulas</p><p>　　A data an

48、alysis 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

49、obtained are presented in the following:</p><p>　　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

50、overall accuracy of each proposed formula is calculated as the mean square error by the following equation [1]:</p><p>　　N in Eq. (18) is the number of the present FEA results. KcEmp and KcFEA in Eq. (19) ar

51、e 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

52、 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.</p><p>　　Concluding remarks</p><p>　　In this study, the three-dimen

53、sional 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 girder on stress concentration. Shell elements have been use

54、d exclusively to model the entire box girder. The dependence of the stress concentration on the finite element mesh has been treated by the multimesh extrapolation method.</p><p>　　Based on the present numer

55、ical results thus obtained, empirical formulas have been proposed to compute the stress concentration factor Kc in three sections where large moments occur. It has been confirmed that the proposed formulas can yield the

56、stress concentration factors in good agreement with the present finite element analysis results.</p><p>　　Acknowledgements</p><p>　　The present research was partially supported by the Thailand R

57、esearch Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0028/2544). It is also the outgrowth of the academic agreement between Sirindhorn International Institute of Technology, Thammasat University and

58、 Faculty of Engineering, Kyushu Institute of Technology, and has been partially supported by the two academic bodies. These supports are gratefully acknowledged.</p><p>　　References</p><p>　　[1]

59、 Tenchev RT. Shear lag in orthotropic beam flanges and plates with stiffeners. International Journal of Solids and Structures1996;33(9):1317–34.</p><p>　　[2] Tahan N, Pavlovic MN. Shear lag revisited: The us

60、e of single Fourier series for determining the effective breath in platedstructuresComputer and Structures 1997;63:759–67.</p><p>　　[3] Lee CK, Wu GJ. Shear lag analysis by the adaptive finite element method

61、:Analysis of simple plated structures. Thin-Walled Structures 2000;38: 285–310.</p><p>　　[4] Lee CK, Wu GJ. Shear lag analysis by the adaptive finite element method:Analysis of complex plated structures. Thi

62、n-Walled Structures 2000; 38:311–36.</p><p>　　[5] Lee SC, Yoo CH, Yoon DY. Analysis of shear lag anomaly in box girders.Journal of Structural Engineering ASCE 2002;128(11):1379–86</p><p>　　[6] L

63、ertsima C, Chaisomphob T, Yamaguchi E. Stress concentration due to shear lag in simply supported box girders. Engineering Structures 2004;26(8):1093–101.</p><p>　　[7] Cook RD, Malkus DS, Plesha ME. Concepts

64、and applications of finite element analysis. 3rd ed. John Wiley & Sons; 1989.</p><p>　　[8] Japan Road Association. Design specifications for highway bridges, Part II Steel Bridges. Maruzen; 2002.</p&g

65、t;<p>　　[9] Eurocode 3. Design of steel structures. prEN 1993 1-5, CEN; 2003.</p><p>　　[10] MARC Analysis Research Corporation. MARC Manuals, vol. A–D, Rev. K.6; 1994.</p><p>　　[11] Zienk

66、iewicz OC, Taylor RL, Zhu JZ. The finite element method: Its basis and fundamentals. 6th ed. Elsevier, Butterworth, Heinemann; 2005.</p><p>　　連續(xù)箱梁中剪力滯產(chǎn)生的應(yīng)力集中現(xiàn)象</p><p>　　Jaturong Sa-nguanmanasak,

67、 , Taweep Chaisomphob, Eiki Yamaguchi</p><p><b>　　摘要</b></p><p>　　在過去，很少見到有箱梁剪力滯效應(yīng)的研究報道，并且他們中很多都是采用有限元的方法。盡管剪應(yīng)力集中的剪力滯效應(yīng)對于有限元分析中使用的網(wǎng)格非常敏感，但是以往的研究人員似乎并沒有將注意力放在有限元網(wǎng)格對剪力滯的影響上。此外大多數(shù)關(guān)于剪力滯的

68、研究都集中在簡支梁和懸臂梁上，而連續(xù)梁在很多的研究中沒有被進(jìn)行深入研究處理。本研究通過使用三維有限元的方法來研究連續(xù)箱梁中的剪力滯效應(yīng)。整個的梁由殼單元來進(jìn)行模擬，并且對箱梁的幾何形狀進(jìn)行了廣泛的參數(shù)化研究。有限元網(wǎng)格對剪力滯的影響是通過多網(wǎng)格外的推法來仔細(xì)深入研究的?；谝陨戏椒ǐ@得的數(shù)值結(jié)果，本文提出了經(jīng)驗公式來計算包括剪力滯效應(yīng)的應(yīng)力集中因子。</p><p>　　關(guān)鍵詞：剪力滯;連續(xù)箱梁;應(yīng)力集中;三維有

69、限元分析</p><p><b>　　引言</b></p><p>　　盡管在基本的橫梁理論中假定由彎曲變形產(chǎn)生的在縱向上的法向應(yīng)力在法蘭寬度上是均勻的，但實際上如果法蘭寬度較大則實際情況不是這樣。 這種稱之為剪力滯的現(xiàn)象已經(jīng)被研究了很多年。Tenchev [1]提供了關(guān)于剪力滯研究簡明而優(yōu)秀的文獻(xiàn)綜述。 即使在最近幾年，這個課題吸引了很多研究人員的注意，并且已經(jīng)發(fā)表

70、了不少論文[2-6]。</p><p>　　盡管在過去的時間里，已經(jīng)對這個問題進(jìn)行了大量的研究，但是在文獻(xiàn)中觀察到數(shù)值結(jié)果的差異，Lertsima等人為簡支梁的情況給出了一個例子 [6]。 造成這種差異似乎要歸因于對剪力滯有相當(dāng)大影響的因素，但這個因素卻被忽略了。</p><p>　　Lertsima等人通過三維有限元分析，利用殼單元研究簡支箱梁的剪力滯[6]。應(yīng)用多種方式去負(fù)載。他們對有

71、限元網(wǎng)格也很關(guān)注?？偟睦险f，采用多網(wǎng)格外推法[7]，可以減少離散誤差，從而提高有限元分析結(jié)果的準(zhǔn)確性。然后進(jìn)行廣泛的參數(shù)研究并提出實驗式。</p><p>　　在日常的橋梁實踐中，連續(xù)梁是相當(dāng)常見的結(jié)構(gòu)。處理公路橋梁和建筑物的普通箱梁的工程師不必因為剪力滯而受到應(yīng)力集中的影響。然而，實際上確實存在特殊不一的特殊情況，因此在設(shè)計規(guī)范中要提供計算剪力滯效應(yīng)的公式[8,9]。盡管如此，在許許多多的文獻(xiàn)中有關(guān)連續(xù)梁剪力滯

72、效應(yīng)的研究結(jié)果似乎很少。另一方面，日本[8]和歐洲法典3 [9]的帶來了非常不同的剪力滯效應(yīng)，這將在本文的后半部分提到。</p><p>　　根據(jù)上述信息的背景，在本文中，采用殼單元對連續(xù)箱梁進(jìn)行三維有限元分析，以研究由于剪力滯引起的應(yīng)力集中。采用多網(wǎng)格外推法[7]，進(jìn)行分析以獲取可靠的數(shù)值結(jié)果。本文還進(jìn)行了廣泛的參數(shù)研究，并提出了實驗式來處理連續(xù)箱梁中的剪力滯現(xiàn)象。在所有分析中，都使用了著名的有限元程序MARC

73、 [10]</p><p>　　圖一 三跨連續(xù)箱梁模型</p><p><b>　　連續(xù)箱梁模型</b></p><p>　　在本文中，對均布荷載下的三跨連續(xù)箱梁進(jìn)行了分析。在本研究中用于描述其結(jié)構(gòu)幾何形狀的符號如圖1所示。對于連續(xù)梁的設(shè)計，大彎矩下橫截面的應(yīng)力分布是重要的。因此，在本研究中，我們將重點放在圖1（b）所示的A-C截面的三個截

74、面上：A部分是在外部跨度內(nèi)的最大彎矩下，B部分在內(nèi)部支撐（最大負(fù)彎矩），C段位于桁架的中心，在內(nèi)部跨度內(nèi)彎矩最大（依據(jù)Lertsima等人的觀點[6]）。如圖1（c）所示，均勻分布的載荷作為沿線中心線的線載荷。由于對稱性，只需要分析其四分之一的桁材（橫截面的一半和桁材長度的一半）。因此，對稱條件，即在y軸上沒有位移而在x軸和z軸上沒有旋轉(zhuǎn)，然后添加在C部分上，而只有z軸上的位移被限定在梁的端部B部分。假設(shè)材料屬性為各向同性線彈性，楊氏模

75、量為206 GPa和泊松比為0.3。</p><p>　　在A-C部分，其應(yīng)力集中系數(shù)可以用設(shè)計規(guī)范[8,9]給出的公式進(jìn)行評估。對于B / H = 2.0，H / L = 0.2，Tf / Tw = 1.0和= 1.0的箱梁，計算這些值并在表1中給出，其中Kc代表應(yīng)力集中系數(shù)，法蘭的最大法向應(yīng)力與基本梁理論的最大法向應(yīng)力。從中可以看出明顯的差異，這表明需要進(jìn)一步研究連續(xù)梁的剪力滯的必要性。</p>

76、<p>　　在本研究中，連續(xù)箱梁通過三維有限元方法分析，采用4節(jié)點殼單元。特別是使用了單元75（雙線性厚殼單元），并將節(jié)點應(yīng)力評估為共享單元中節(jié)點的應(yīng)力的平均值[10]。雖然有限元法非常通用且功能強(qiáng)大，但必須慎重地去使用它，因為其結(jié)果可能在很大程度上取決于分析中使用的有限元網(wǎng)格，特別是在處理應(yīng)力集中時。有限元網(wǎng)格取決于離散誤差。在Lertsima等人[6]對這個問題進(jìn)行了數(shù)值研究，采用多網(wǎng)格外推法減少了由于剪力滯引起的應(yīng)力集

77、中評估中的離散化誤差。值得注意的是，這樣得到的應(yīng)力集中系數(shù)非常接近自適應(yīng)有限元方法[6]所獲得的應(yīng)力集中系數(shù)。本文也使用多網(wǎng)格外推方法，并且在下文中簡要解釋其數(shù)字程序</p><p>　　圖2（a）顯示了在一個簡支箱梁的中跨上法蘭（B / H = 1.0，H / L = 0.2，Tf / Tw = 1.0）的法向應(yīng)力分布，是由Lertsima等人所做[6]。在該圖中，是由三維有限元分析得到的法向應(yīng)力，其中梁是由于

78、基本梁寬度而產(chǎn)生的法向應(yīng)力。使用4節(jié)點殼單元，這里采用了網(wǎng)格A-D的四個有限元網(wǎng)格。每個網(wǎng)格中的所有元素都是矩形的，并且在對網(wǎng)格A-D進(jìn)行網(wǎng)格細(xì)化的過程中，箱梁中的每個元素都是四分之一：網(wǎng)格A-D的圖示如圖3所示。總數(shù)對于網(wǎng)格A-D，元素分別是1920,7680,30,720和122,880。圖2（a）不僅說明了剪力滯現(xiàn)象，還說明了有限元網(wǎng)格上應(yīng)力分布的依賴性。正如所料，在最大應(yīng)力集中發(fā)生的法蘭邊緣，其依賴性更強(qiáng)。同時，隨著有限元的尺寸

79、變小，觀察到其應(yīng)力收斂的趨勢。</p><p>　　圖2（b）給出了通過有限元分析得到的上法蘭四點的應(yīng)力，</p><p>　　圖二 有限元網(wǎng)格正常應(yīng)力的依賴性</p><p>　　圖三 四分之一箱梁的有限元網(wǎng)格</p><p>　　該圖顯示了正常應(yīng)力相對于代表性元件尺寸的變化。 從圖中可以觀察到，圖2（b）中的四條線幾乎是直線的。 這與其理

80、論相吻合，即壓力的誤差是p，其中雙線性元素p等于1 [7,11]。 因此，圖2（b）中用虛線表示的線性外推可用于估算收斂應(yīng)力。 這種外推法被Cook等人稱為多重網(wǎng)格外推法。 [7]并應(yīng)用于本研究中。 由此獲得的法蘭邊緣處的應(yīng)力比。梁（b）是相對于代表性元件尺寸的法向應(yīng)力的變化。 圖2.顯示了法向應(yīng)力對有限元網(wǎng)格的依賴性。 即圖2（b）中箭頭所示的點是作者在本數(shù)值研究中尋求的Kc值。</p><p>　　上法蘭的正

81、應(yīng)力分布情況</p><p>　　圖4顯示了在B / H = 2.0，H / L = 0.2，= 1.5和Tf / Tw = 2.0的情況下沿著桁材長度的上凸緣邊緣處的法向應(yīng)力的兩種變化：通過基本梁理論和有限元分析（FEA）獲得。由于對稱性，只有梁的一半處的應(yīng)力分布（y / L = 0.0 1.75）給出：y / L = 1.75對應(yīng)于C部分的位置。需要注意的是o是在梁理論框架下的（a）網(wǎng)格A.（b）網(wǎng)格B.（c

82、）網(wǎng)格C.（d）網(wǎng)格D.圖3.是四分之一箱梁的有限元網(wǎng)格。該圖顯示了正常應(yīng)力相對于代表性元件尺寸的變化。據(jù)觀察，圖2（b）中的四條線幾乎是直線的。這與理論相一致，即壓力的誤差是p），對于雙線性元素，p等于1 [7,11]。因此，圖2（b）中用虛線表示的線性外推可用于估算收斂應(yīng)力。這種外推方法稱為多網(wǎng)格外推（B部分）。兩個正應(yīng)力分布之間的顯著差異證實了連續(xù)箱梁剪力滯的重要性。</p><p>　　各個截面上法蘭的法

83、向應(yīng)力分布如圖5所示。不同截面的分布差異很大。值得注意的是，如圖5（a）和（f）中典型可見，在外跨度的中跨附近，法向應(yīng)力的大小朝法蘭的中心減小，最小值接近于等于零，而最小值與內(nèi)跨度中跨附近梁理論的法向應(yīng)力相當(dāng)接近。已發(fā)現(xiàn)簡支箱梁中的正應(yīng)力分布與連續(xù)箱梁的外部跨度相似[6]。</p><p><b>　　參數(shù)研究</b></p><p>　　進(jìn)行三維有限元分析以揭示表征

84、連續(xù)箱梁幾何參數(shù)的影響。為此，設(shè)定以下值：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。所有這些值的組合帶來了240個箱梁在幾何形狀上的不同。值得注意的是，對于每個梁，多個有限元網(wǎng)格被用來通過多網(wǎng)格外插法以減少離散誤差。</p><p>　　圖五 上法蘭正

85、應(yīng)力分別情況</p><p>　　各部分?jǐn)?shù)值結(jié)果的典型例子</p><p>　　A部分顯示在圖6中。Kc相對于參數(shù)的變化趨勢可概括如下：</p><p>　　隨著B / H或H / L的增加，Kc值趨于顯著提升。然而，對于H / L = 0.025和0.05或B / H = 0.5，Kc幾乎保持恒定并且?guī)缀醯扔?.0，其剪力滯很小。</p><p

86、>　　隨著Tf / Tw的增加，Kc值也在增加。然而，Kc相對于Tf / Tw的變化很小。與B / H和H / L的情況不同，Kc-Tf / Tw曲線接近于直線，并且無論B / H如何，這些曲線的斜率幾乎相同。然而，對于大B / H，其Kc的依賴性相當(dāng)小，盡管它的值變化稍大。</p><p>　　從圖7中可以看出，B部分和C部分的Kc值的變化顯示出類似的趨勢，除了以下的影響：與A部分不同，Kc隨著值的增加而

87、減小。還有觀察到，B部分中的Kc值一般是最大的。然而，三個部分的Kc值之間的差異隨其變化。 在At = 1.25和1.5時，A部分和C部分具有幾乎相同的Kc值</p><p>　　在圖8中，顯示了由兩個設(shè)計代碼[8,9]以及當(dāng)前FEA結(jié)果帶來的Kc值。 B / H帶來的影響在此尤其集中。 對于A部分和C部分，在日本科研人員看來是[8]產(chǎn)生最大值，而在歐洲科研人員看來3 [9]則是最小的。由于歐洲規(guī)范3 [9]的K

88、c值始終大于日本規(guī)定的Kc值[8]，對于B部分來說，它的趨勢是相反的。 圖8中觀察到的差異不可忽略：它在設(shè)計實踐中似乎相當(dāng)重要。 有趣的是，由于兩個設(shè)計代碼，現(xiàn)有FEA的結(jié)果傾向于位于兩組Kc值之間。</p><p><b>　　實驗公式</b></p><p>　　StatSoft公司的數(shù)據(jù)分析程序用于對當(dāng)前FEA結(jié)果進(jìn)行回歸分析，得出A-C節(jié)三個部分中Kc的經(jīng)驗公

89、式。 基于其數(shù)據(jù)獲得的經(jīng)驗公式如下所示：</p><p>　　圖七 兩個部分之間Kc值的比較</p><p>　　圖八 兩個截面之間關(guān)于B\H的Kc值的比較</p><p>　　圖9說明了由經(jīng)驗公式和當(dāng)前FEA帶來的Kc值之間的一些比較。 在這些數(shù)字中，其吻合的程度是顯而易見的。 每個提出的公式中的精確度由均方誤差通過以下等式計算[1]：</p>&

90、lt;p>　　方程式N （18）是當(dāng)前有限元分析結(jié)果的數(shù)量。 KcEmp和KcFEA在方程式（19）中分別是從提出的經(jīng)驗公式和當(dāng)前的有限元分析中得到的Kc值。 由于在本研究中，幾何參數(shù)的組合需要240個箱梁進(jìn)行分析，N等于240。 在方程式（18）中，A，B和C部分的均方誤差分別為3.0％，2.9％和4.2％。</p><p><b>　　結(jié)束語</b></p><

91、p>　　在本研究中，通過對連續(xù)箱梁各種幾何形狀進(jìn)行三維有限元分析，確定了連續(xù)箱梁剪力滯效應(yīng)對應(yīng)力集中的影響。 殼單元可以專門用于模擬整個箱梁。 多重網(wǎng)格外推法可以處理應(yīng)力集中對有限元網(wǎng)格的依賴性的問題。</p><p>　　基于以上方法獲得的當(dāng)前數(shù)值結(jié)果，已經(jīng)提出了經(jīng)驗公式來計算出現(xiàn)大矩的三個部分中的應(yīng)力集中因子Kc。 在本文已經(jīng)證實，所提出的公式可以產(chǎn)生與當(dāng)前有限元分析結(jié)果相吻合的應(yīng)力集中因子。</

92、p><p><b>　　致謝</b></p><p>　　本文的研究得到了泰國研究基金皇家Golden Jubilee博士計劃的部分支持（授予號PHD / 0028/2544）。 本文中的研究也是Sirindhorn國際技術(shù)學(xué)院，Thammasat大學(xué)和理工學(xué)院工程學(xué)院科研人員共同努力的結(jié)果，并得到了兩個學(xué)術(shù)機(jī)構(gòu)的部分支持。 感謝這些支持。</p><

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