[雙語翻譯]--橋梁外文翻譯-預(yù)應(yīng)力鋼梁的性能（英文）

1、Behavior of Prestressed Steel BeamsB. Belletti1 and A. Gasperi2Abstract: This paper reports on the behavior of simply supported ?I-shaped cross section? steel beams prestressed by tendons. It is well known that this typo

2、logy of beams has successfully been used mainly in the past. Prestressed steel beams are lighter than traditional ones that have the same length and vertical load capacity; this aspect could make them economically advant

3、ageous and a viable solution in many practical situations. This paper analyzes prestressed steel beams having a medium span ranging from 35 to 45 m and which are to be used as roof structural elements. This study focuses

4、 on two parameters that are considered two of the fundamental items for the design: the number of deviators and the value of the prestressing force. This study has been carried out with nonlinear finite-element analyses

5、that take into account both mechanical and geometrical nonlinearities. In particular, the behavior of these beams has been investigated up to failure during tensioning and during loading ?after tensioning?. The effect on

6、 the structural response of bracing, which can be only at the top flange of the beams or at the top and bottom flanges of the beams, also has been considered.DOI: 10.1061/?ASCE?ST.1943-541X.0000208CE Database subject hea

7、dings: Prestressing; Steel beams; Tendons; Bracing; Finite element method.Author keywords: Prestressed steel beams; Tendons; Deviators; Bracing; Nonlinear finite element method.IntroductionPrestressing techniques for ste

8、el beams were developed many years ago, both for the construction of new structures and for the rehabilitation of existing structures. Although tensioning prin- ciples were initially formulated and developed for reinforc

9、ed con- crete structures, the prestressing technology began to be applied also to steel beams by Dischinger and Magnel and by other engi- neers. A number of prestressed steel structures in the following years have been b

10、uilt throughout the world, especially in the U.S.A., Russia, and Germany, which demonstrates that pre- stressed steel beams can present both structural and economical advantages when compared with nonprestressed ?traditi

11、onal? beams. The prestressed steel technique has been adopted mainly for bridges and rarely for roof structures. Available literature con- cerning prestressed steel beams in specific reference to the topic of this paper

12、consists only of a few documents such as Belenya ?1977?, Troitsky ?1990?, the final report by Subcommittee 3 on Prestressed Steel of Joint ASCE-AASHO ?1968?, and Nunziata ?2004?. Furthermore, Bradford ?1991? proposed the

13、 use of design charts to evaluate the elastic buckling load induced by prestress- ing tendons in ?I-shaped cross section? steel beams with straight tendons. This paper analyzes the behavior of I-shaped prestressed steel

14、beams having a medium span ?i.e., a span in the range 35–45 m?for use as roof elements for buildings. In particular, the effects on the beams’ response, of the number of deviators ?which impose the shape of the tendons b

15、y fixing the distance between tendons and beam? and of the prestressing force value, are thoroughly investigated. Indeed, an accurate choice of these latter parameters is thought to be one of the main tasks for a thoroug

16、h design of these structures. In this paper, nonlinear finite-element analyses have been car- ried out to investigate the behavior up to failure of prestressed beams in correspondence of two different loading phases, ten

17、sion- ing and loading after tensioning. In the first loading phase ?ten- sioning?, when the self-weight is the only vertical load on the beam, the prestressing force is increased to the maximum value. The prestressing fo

18、rce value, corresponding to the failure during tensioning, is called in this paper “maximum” prestressing force value. In the second loading phase ?loading after tensioning?, for a given prestressing force value, vertica

19、l loads are increased up to the point at which the vertical load capacity of the beam has been reached. The number of deviators, that is one of the main items to be chosen in the design, is strictly connected to the cost

20、 of the beam. The advantages of using few ?less than three? deviators certainly consist in the simplicity of the structure, which allows reduction of the total cost of the beam. This solution, with few deviators, also in

21、cludes some disadvantages: first of all, to avoid instability problems, low values of prestressing force can be applied, and second, the shape of the tendons does not efficiently fit the dia- gram of the bending moment o

22、f the beam from vertical loads. On the other hand, the first advantage of using several deviators is the ability for applying high values of prestressing force; indeed, in- stability effects are reduced, thanks to the sh

23、ort spacing between deviators. The second advantage is that the shape of the tendons can efficiently fit the diagram of the bending moment of the beam from vertical loads. The main disadvantage of this solution, with sev

24、eral deviators, concerns the greater complexity in the construc- tion combined with high production costs.1Dept. of Civil and Environmental Engineering and Architecture, Univ. of Parma, via Usberti, 181/A, 43100 Parma, I

25、taly. 2Consulting Engineer, via Zodiaco, 72/1, 41126 Modena, Italy. Note. This manuscript was submitted on August 20, 2008; approved on February 17, 2010; published online on February 19, 2010. Discussion period open unt

26、il February 1, 2011; separate discussions must be submit- ted for individual papers. This paper is part of the Journal of Structural Engineering, Vol. 136, No. 9, September 1, 2010. ©ASCE, ISSN 0733- 9445/2010/9-113

27、1–1139/$25.00.JOURNAL OF STRUCTURAL ENGINEERING © ASCE / SEPTEMBER 2010 / 1131Downloaded 17 Mar 2011 to 111.8.34.170. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org1000” is a b

28、eam with two deviators and a total axial force of Np=1,000 kN. Even though this paper is focused on providing remarks on the response of prestressing steel beams that depend on the number of deviators and the prestressin

29、g force value, nominal values of ac- tions and load combinations have been defined, referring to an example of actual roof structures composed of beams having a spacing of 12 m. So self-weight ?g1k=3.62 kN/m?, permanent

30、load ?g2k=0.7 kN/m2?, and snow load ?qk=1.3 kN/m2? have been considered nominal values for actions. The load multipliers, referring to the loading steps considered in the analyses, are re- ported in Table 2. The design l

31、oad combinations for serviceability limit state and for ultimate limit state are also indicated in Table 2. In this paper, the actual loading effect has been assumed to be equivalent to the effect of a uniformly distribu

32、ted load because the spacing of secondary elements ?i.e., the secondary beams, which are supported by prestressed beams? is, as a rule, really less than the span of the prestressed steel beams. No lateral restraints are

33、imposed during in situ pretensioning, Step b, except for the case of “delayed tensioning” ?see below?. In Steps c–f, bracing at the top and at the bottom flanges are usually connected to the beam, providing lateral stabi

34、lity. In Table 2, the italicized data indicate load steps without bracing, whereas the rests indicate load steps with bracing. As previously stated, NLFE analyses are carried out by assuming bracing both at the top and b

35、ottom flanges except for some analyses which were performed with top flange bracing only. These analyses are identified with the letters “-BTS.” For example, “T2-1000-BTS” is a beam with two deviators, prestressed with a

36、xial force Np=1,000 kN and with top flange bracing only. Furthermore, the beams identified with the letters “-NI” were analyzed without taking into account geometrical imperfections and with bracing at the top and bottom

37、 flanges, except beams identified with letter “-NI-BTS” which have the bracing only at the top flange.In the analyses with delayed tensioning, bracing at the top and bottom flanges are present in Step b also when the pre

38、stressing force is introduced ?see Table 2?. Stress losses in tendons are not considered because friction losses are negligible for unbonded tendons and relaxation losses are negligible.Finite-Element Analyses of the Ana

39、lyzed Prestressed Steel BeamsBuckling and nonlinear finite element analyses ?with both me- chanical and geometrical nonlinearities? were carried out with the ABAQUS code. Four-node shell elements ?S4? were employed for b

40、eam and stiffening ribs, three-dimensional pipe elements ?B31? for deviators having a radius of 70 mm and a thickness of 12 mm, and tube-tube contact elements ?ITT31? for modeling the finite-sliding interaction where ten

41、dons are inside the deviators. Fixed boundary conditions were imposed to simulate supports and lateral restraint resulting from the bracing. A plasticity model with isotropic hardening behavior was used to define the mec

42、hanical properties of the steel for the beam. Geometrical imperfections of the unloaded beam have been im- posed as an initial condition. To this end, the assumed shape of the beam and the assumed nodal coordinates for t

43、he NLFE analy- ses were derived from the shape of the elastic buckling mode, corresponding to the minimum positive eigenvalue, properly am- plified ?maximum amplitude of initial bow imperfection was as- sumed to be 50 mm

44、?. Buckling analyses were performed on beams subjected to a uniformly distributed vertical load. NLFE analyses were carried out in load control by adopting Newton’s method as convergence criteria. This means that the bea

45、m capacity was identified in correspondence of the peak value of the applied load corresponding to the last converging solution. It is well known that by standard load-control iterative proce- dures, it is not possible t

46、o describe softening branch or to detect bifurcation phenomena, etc. in the structural response. However, in the section titled “Remarks concerning the results of NLFE analyses,” it is shown that convergence fails after

47、the yielding of the steel, in correspondence with high levels of deformation. Even if higher values of displacement could be achieved with more refined solution techniques, no significant increase in applied loads can be

48、 obtained; in addition, higher values of deformation are not germane to this study because they cannot be accepted in practice.Failure during TensioningThe beam behavior during tensioning was analyzed in order to evaluat

49、e the maximum prestressing force that can be applied. The maximum prestressing force during tensioning was evaluated by applying the self-weight load and by increasing the prestressing until failure occurred. Fig. 3 depi

50、cts the top flange horizontal displacement ?z direction? at the midspan versus the prestressing force value for beams T2, T5, and T11; the initial horizontal dis- placement is not zero because of the imposed geometrical

51、imper- fection and self-weight. Deformed shapes at failure are shown in Fig. 4 for beams T2 and T11. Geometrical imperfection generate for T2 beam ?with the greatest spacing between deviators ?13.333 m?? the largest hori

52、- zontal displacements at midspan; these horizontal displacements reach, in correspondence with the maximum prestressing force ?1,559 kN?, a value of 375 mm. For the T11 beam, the maximum value of the prestressing force

53、?3,291 kN? is much higher than theTable 1. Geometrical Features of the Analyzed BeamsBeam name Number of deviatorsSpacing between deviators ?m?Number of tendonsNumber of strand per tendonaTotal area per tendon ?mm2?T2? 2

54、 13.333 2 4 600T5? 5 6.667 2 4 600T5 5 6.667 2 12 1,800T11? 11 3.333 2 4 600T11 11 3.333 2 12 1,800aArea of 0.6 inch diameter strands equal to 150 mm2.Table 2. Load Multipliers, Referring to the Steps and the Load Combi-

55、 nations Considered in the AnalysesSteps Self-weight Prestressing force Permanent load Snow loadStep a 1 0 0 0Step b 1 1 0 0Step c 1 1 1 0Step d ?SLS? 1 1 1 1Step e ?ULS? 1.4 1 1.4 1.5Step f 1.4 1 1.4 xNote: x means the

56、value till failure. Italicized data indicate steps without bracing. The rest refer to steps with bracing. Step b is with bracing for “delayed tensioning.”JOURNAL OF STRUCTURAL ENGINEERING © ASCE / SEPTEMBER 2010 / 1