橋梁工程外文翻譯--鋼索和預(yù)應(yīng)力混凝土梁橋之間的三維關(guān)系協(xié)調(diào)（原文）

1、3D Coordinating Relations between Steel Cables and Concrete of Prestressed Concrete Beam BridgesXiong-jun He1; Li-chu Fan2; Hong-ming Zhu3; and Zhong-wu Ye4Abstract: Interaction between steel cables and concrete is compl

2、icated in prestressed concrete bridges, especially in curved prestressed concrete bridges. The most significant behavior of curved beam bridges under the loads is that, at the same time of vertical flexure, torsion occur

3、s on the cross section, which complicates the mechanical analysis to curved beam bridges. Based on coordinating relations of steel cables and concrete ?CRSC?, the grillage structure finite-element method was adopted to a

4、nalyze the spatial effect of curved beam bridges. This way, the effect of all prestressing procedures can be simulated properly, including the prestressing loss due to concrete shrinkage and creep, batch prestressing of

5、the cables, etc. Furthermore, it is effective to analyze the integrated behavior of the combined steel cables space out and concrete. The efficiency and reliability of the CRSC method is demonstrated by our analysis syst

6、em WXQ2.0 developed for curved-skew bridges.DOI: 10.1061/?ASCE?1084-0702?2009?14:4?279?CE Database subject headings: Bridges, box girder; Bridges, concrete; Beams; Prestressing; Structural models; Three-dimensional analy

7、sis.IntroductionWith the development of bridge structure technology and traffic technology, the prestressed concrete bridges have been widely applied, especially to curved prestressed concrete bridges. The structures hav

8、e serious curvature-twisting coupling, which com- plicates the interaction mechanism between steel cables and con- crete. In application of thin-walled box sections, all kinds of difficulties of thin-walled box section a

9、nalysis are encountered. Many scholars have made great achievements, such as profound theoretical research to torsion and bending of big curvature thin- walled box beams ?Li 1987?, shear lag effect of curved continu- ous

10、 beam bridges ?Peng and Wang 1998?. In order to study structural behaviors of internally bonded tendon, unbonded ten- don and externally prestressed concrete beam bridges, a tendon model that can be used in finite-elemen

11、t analyses of prestressed concrete structures with bonded tendons was studied based on the bond characteristics between a tendon and its surrounding con- crete ?Kwak and Kim 2006a,b?; The ultimate load of prestressed hig

12、h-strength concrete beam was analyzed with nonlinear mate- rial properties considered ?Liu and Yan 2006?; A modified bond reduction coefficient is studied for evaluation of the flexuralstrength of externally prestressed

13、beams based on strain compat- ibility and force equilibrium ?Ck 2003; Ck and Kh 2006a,b?. However, how to treat internal or external prestressing forces and to consider the interaction between steel cables and concrete t

14、o conduct linear or nonlinear analysis is still a problem worth studying. Since the beginning, internal prestressing forces have been traditionally treated as external loads in analysis ?Wu 1990; Sun 1995?. This is an ap

15、proximate equivalent method, which has some limitations as well as some errors in the results under com- plicated situations. In long-span bridges, as to the need of struc- tural forces, the prestressing cables with diff

16、erent working procedures are spatial curves with big curvatures in some direc- tions, the calculation would be very complicated. In this case, the error of the results would occur easily if the approximate stimu- lation

17、method of the external loads is adopted. In order to have a better understanding of the structural behav- ior of the prestressed concrete beam bridges ?including internally bonded tendons, unbonded tendon, and externally

18、 prestressed?, this paper proposes a finite-element analysis method based on coordinating relations of steel cables and concrete ?CRSC?, to improve the accuracy of the analysis, especially to the analysis of curved prest

19、ressed concrete bridges.Traditional Analysis Method of Prestressing Forces and Its ProblemsThe equivalent load method ?Wu 1990; Sun 1995? is applied in the traditional analysis of prestressing forces. The theory of this

20、method is to separate prestressing cables from the structures, equalize their effects as external loads, and then adding those loads into the structural calculation diagram as the external loads to evaluate the prestress

21、ing effect. Through the vector analysis, the three-dimensional forces pro- duced by prestressing cables at the gravity center on the end section is shown as Eq. ?1? and Fig. 11Professor, School of Communications, Wuhan U

22、niv. of Technology, Wuhan 430063, China ?corresponding author?. E-mail: hxjwhut@163. com 2Academician, Professor, Dept. of Bridge Engineering, Tongji Univ., Shanghai 200092, China. E-mail: lefan@#edu.cn 3Senior Eng

23、ineer, Road-bridge Ltd. Co. of Hubei Province, Wuhan 430056, China. E-mail: leaf510@163.com 4Senior Engineer, Road-bridge Ltd. Co. of Hubei Province, Wuhan 430056, China. E-mail: leaf510@163.com Note. This manuscript was

24、 submitted on August 28, 2006; approved on December 12, 2008; published online on June 15, 2009. Discussion period open until December 1, 2009; separate discussions must be sub- mitted for individual papers. This paper i

25、s part of the Journal of Bridge Engineering, Vol. 14, No. 4, July 1, 2009. ©ASCE, ISSN 1084-0702/ 2009/4-279–284/$25.00.JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2009 / 279J. Bridge Eng. 2009.14:279-28

26、4.Downloaded from ascelibrary.org by Changsha University of Science and Technology on 02/26/14. Copyright ASCE. For personal use only; all rights reserved.in normal temperature is called the heterogeneous material com- b

27、ined component. The combined component concept proposed here is mainly considered from the function aspect. Combined from steel cables and concrete, the component possesses some functions, such as antipressure and antibe

28、nding. There are not only independences between them but also coordinating relations. The master-slavery relations are called coordinating relations be- tween steel cables and concrete. He ?2002a,b, 2004? had a re- searc

29、h on the two-dimensional ?2D? coordinating relations between steel cables and concrete, and further research on the three-dimensional ?3D? coordinating relations between concrete and steel cables is given here.3D Coordin

30、ating Relations between Steel Cables and ConcreteIt is just as well we take an internally bonded prestressed concrete beam bridge as an example to do the analysis; where the analysis figure is shown in Fig. 3. Node 2 on

31、steel cable is driven by Node 1 on a concrete beam, the coordinate of Point 1 is ?x,y,z?, the coordinate of Point 2 is ?x?,y?,z??, the spatial distance between Node 1 and 2 is d, and the projection of the spatial distanc

32、e d is dx, dy, dz, thendx = x ? x?dy = y ? y?dz = z ? z?Suppose the projections of the distance between 1 and 2 on the plane xoy, yoz, and zox are d1, d2, d3 respectively; and the angles between projection of the beam ax

33、es in the plane xoy, yoz, zox, and coordinate axes x, y, z are ?1, ?2, and ?3, respectively. ?x, ?y, ?z are corners circling around coordinate axes x, y, z, respectively, and anticlockwise direction is set as a positive

34、direction. So, if we set ???=?u,?,?,?x,?y,?z? as displacement of Point 1, ????=?u?,??,w?? ?no angle displacement? as displacement of Point 2, and getu? = u + dy?z ? dz?y?? = ? + dz?x ? dx?z?? = ? + dx?y ? dy?x ?4?Formula

35、 ?4? shows the relations between displacement ???? =?u?,??,w?? of Point 2 on the steel cable and displacement ??? =?u,?,?,?x,?y,?z? of Point 1 on the concrete shape center in one section. Through the analysis on coordina

36、ting relations between steel cables and concrete, it is very convenient to consider boththe effect of steel cables on shrink and creep of concrete and the effect of shrink and creep of concrete on steel cable forces, etc

37、. Furthermore, all of them are easily solved by the process of so- lution of the FEM equilibrium equations.Individual Parameters to Reflect Circumstances of Internally Bonded Tendon, Unbonded Tendon, and Externally Prest

38、ressed ConcreteIn order to explain the individual parameters in Eq. ?4?, a simple two-dimensional level prestressed concrete beam is shown in Fig. 4. Suppose that d is the distance from Point 2 on the cable to Point 1 on

39、 the gravity center of the beam, the displacements of Point 1 and Point 2 are ?u,?,?? and ?u?,???, respectively. Hence, Eq. ?4? becomes as Eq. ?5? under internally bonded tendonu? = u + d · ??? = ? ?5?While Eq. ?4?

40、becomes as Eq. ?6? under internally unbonded tendon?? = ? ?6?Fig. 5 describes a beam of externally prestressed concrete. Eq. ?5? fits bonded tendon of externally prestressed concrete, and Eq. ?6? fits an unbonded tendon

41、of externally prestressed concrete. It is emphasized that Eq. ?5? or Eq. ?6? is only aimed at to the nodes on deviation blocks. From what has been discussed above, the meanings of all pa- rameters in Eq. ?4? are easily u

42、nderstood. Furthermore, it also demonstrates the applications in internally bonded tendons, un- bonded tendons, and externally prestressed concrete.ozyx21dzdydxFig. 3. Spatial geometry relationship of master-slavery node

43、s21 beam axiscable element d dFig. 4. Simple two-dimensional level prestressed concrete beamFig. 5. Beam of externally prestressed concreteJOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2009 / 281J. Bridge Eng.