[雙語翻譯]--外文翻譯--估算鋼-混凝土組合梁在正常使用極限狀態(tài)的撓度（原文）

1、Evaluation of the deflection of steel-concrete composite beams at serviceability limit stateClaudio Amadio a,?, Massimo Fragiacomo b, Lorenzo Macorini ca Department of Civil and Environmental Engineering, University of T

2、rieste, Piazzale Europa 1, 34127, Italy b Department of Architecture, Design and Urban Planning, University of Sassari, Palazzo del Pou Salit, Piazza Duomo 6, 07041 Alghero, Italy c Department of Civil and Environmental

3、Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdoma b s t r a c t a r t i c l e i n f oArticle history:Received 14 December 2010Accepted 28 January 2012Available online xxxxKeyw

4、ords:Composite beamsConcreteCreepDeflectionFinite element methodTime dependenceServiceabilityShrinkageThe paper investigates the response of steel–concrete composite beams at serviceability limit state. Bothcases of prop

5、ped and unpropped steel beam during the pouring of the concrete slab were considered. Themaximum vertical displacements in the short- and long-term were evaluated for simply supported and con-tinuous composite beams usin

6、g accurate finite element models. The numerical results were compared withthe maximum displacements obtained using the simplified approach suggested by the Eurocode 4. This for-mulation which, in the case of continuous b

7、eams, accounts for the nonlinear behavior of the component ma-terials, was found to be often non-conservative. On the basis of the outcomes of an extensive parametricanalysis, a simple design criterion was proposed. This

8、 method is based on the limitation of stresses in thesteel profile below the yield limit, and on the use of a simple relationship to account for the connection flex-ibility. The proposed procedure to calculate maximum di

9、splacements of composite beams provides conserva-tive results, with a level of accuracy suitable for practical design.© 2012 Elsevier Ltd. All rights reserved.1. IntroductionModern codes of practice such as the Euro

10、code 4 [1], CNR 10016[2] and LFRD Specification [3] recommend checking serviceabilitylimit state of steel–concrete composite beams to ensure that func-tionality and durability will not be compromised during the serviceli

11、fe. The main quantity to consider in the design for serviceabilitylimit state is the maximum deflection. Such a quantity is influencedby several phenomena such as concrete cracking in tension zones,time-dependent behavio

12、r of concrete (creep and shrinkage), andyielding of reinforcing and construction steel. It should be notedthat the Eurocode 4 [1] does not prescribe any stress control of thesteel profile and, therefore, implicitly allow

13、s plasticization evenunder the service load. Steel yielding, hence, may significantly affectthe beam behavior, particularly for steel beams which are leftunpropped during the concrete placement [4,5]. Another importantpa

14、rameter to consider is the interlayer slip at the interface betweenthe concrete slab and the steel profile. Such a parameter is particular-ly important when the shear connection is partial, i.e. when the num-ber of conne

15、ctors is less than the minimum number required for a fullstrength shear connection. This case is fairly common for unproppedbeams as in many cases the design of the steel profile is governed bythe ultimate limit state of

16、 flexural strength before the steel beam isconnected to the concrete slab. Adopting a reduced number of con-nectors allows some cost saving but, at the same time, leads to reduc-tion in stiffness and strength of the comp

17、osite beam that should beconsidered in design.Due to the complexity of the problem, an accurate investigation ofthe behavior of steel-concrete composite beams at serviceability limitstate can be carried out only using ac

18、curate numerical models [6–11].The analysis is particularly demanding in the long-term, where creepand shrinkage of concrete increases the deflection and, for continuousbeams, causes concrete cracking and moment redistri

19、bution from theinterior supports to mid-spans. Nonlinear analysis is usually carriedout only for design of very demanding structures such as bridgegirders. Conversely, approximate methods can be used for beamswhich are p

20、art of composite frames in residential and office buildings.In this respect, current codes [1–3] suggest simplified procedureswhich accounts for material nonlinearity and shear connectiondeformability. However the latter

21、 contribution is usually consideredonly in the case of partial shear connection, thus often leading tonon-conservative results for beams designed with full strengthshear connection [6,12,13]. Creep and shrinkage of concr

22、ete werefound to markedly increase the deflection of composite beams inthe long-term [14]. Simplified methods such as the ‘effective modulusmethod’, the ‘mean stress method’, and the ‘a(chǎn)ge-adjusted effectivemodulus method

23、’ were recommended, respectively, in [1,15], and[12] in order to account for those time-dependent phenomena.Journal of Constructional Steel Research xxx (2012) xxx–xxx? Corresponding author. Tel.: +39 3393901026.E-mail a

24、ddresses: amadio@univ.trieste.it (C. Amadio), fragiacomo@uniss.itt(M. Fragiacomo), l.macorini@imperial.ac.uk (L. Macorini).JCSR-03469; No of Pages 100143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights res

25、erved.doi:10.1016/j.jcsr.2012.01.009Contents lists available at SciVerse ScienceDirectJournal of Constructional Steel ResearchPlease cite this article as: Amadio C, et al, Evaluation of the deflection of steel-concrete c

26、omposite beams at serviceability limit state, J Constr Steel Res (2012), doi:10.1016/j.jcsr.2012.01.009may be affected also by the mechanical non-linearity of the compo-nent materials. Because of the many parameters invo

27、lved, in thiscase it is not possible to draw a simplified approach leading to deflec-tion values close to those computed with a numerical algorithm.2.2. Influence of the mechanical nonlinearity and time-dependentbehavior

28、The Eurocode 4 [1] allows, in a simplified way, for both nonlinearmechanical phenomena affecting the behavior of the composite beamat serviceability limit state, and the time-dependent phenomena ofconcrete, which affect

29、the behavior in the long-term. For continuouscomposite beams, the reduction in stiffness caused by cracking ofthe concrete slab is evaluated with two alternative approaches. Thebetter approximation can be achieved neglec

30、ting the concrete stiff-ness above the interior supports for 15% of the span length on bothsides (cracked analysis). Another possibility is to reduce the hoggingbending moment on the interior supports depending on the ra

31、tio be-tween the stiffness of the fully cracked and fully uncracked compositesection, with an upper limit of 40%.Further moment reduction at internal supports must be consideredfor unpropped, continuous composite beams i

32、n order to allow for theplasticization of the steel beam. The hogging bending moment mustbe reduced using a 0.5 coefficient if the yielding of the steel profile isattained before the concrete curing, and a 0.7 coefficien

33、t if the profileplasticization occurs after the concrete slab and the steel profiles havebeen interconnected. Conversely, no allowance for yielding of the steelprofile is made for unpropped simply supported composite bea

34、ms.Eurocode 4 accounts for the time-dependent phenomena of con-crete (creep and shrinkage) using the same simplified formulationrecommended by the European regulation for concrete structures,the Eurocode 2 [27]. Such a f

35、ormulation is based on the effective mod-ulus method, where the creep of concrete is considered by dividingthe modulus of elasticity of concrete by one plus the creep coefficientof concrete at the end of the service life

36、. Concrete shrinkage is consid-ered as an additional inelastic strain, usually by neglecting thedeformability of the connection system and the interaction betweencreep and shrinkage.3. Numerical analysesSome short- and l

37、ong-term numerical analyses have been carriedout on simply supported and two-bay, symmetric, continuous com-posite beams varying the degree of connection. The compositebeams geometrical characteristics have selected cons

38、idering the var-iation of typical dimensions for steel beam, concrete slab and amountof steel reinforcement for composite beams in buildings. Details of theaccurate finite element numerical model used in the analyses, wh

39、ichaccount for material nonlinearity and shear connection nonlinear be-havior, can be found in [7,8].As pointed out in the previous sections, at serviceability limitstate, even the behavior of simply-supported composite

40、beams maybe nonlinear. The load level, therefore, markedly affects the structuralresponse. In order to investigate to what extent material nonlinearityaffects the performance of the composite beam, the maximum designload

41、 that the beam can resist at serviceability limit state was prelim-inarily evaluated for each type of composite beam analyzed. The max-imum load calculations have been carried out according to Eurocode4 [1]. This allowed

42、 a direct comparison between deflections deter-mined according to the Eurocode provisions and the values calculatedusing the advanced numerical model.3.1. Evaluation of the maximum design service loadThe maximum design s

43、ervice load qs,max was evaluated based onthe maximum tributary width Lmax that the composite beam canwithstand. Once the tributary width Lmax is known, the maximum de-sign service load is calculated using the equation:qs

44、; max ¼ L max? Gk þ ψk?Qk ð Þ ð10Þwhere symbols Gk and Qk denote the characteristic values of the per-manent and imposed loads, respectively. According to current regula-tions such as the Eu

45、rocode 2 [26], the combination factor ψk assumesdifferent values in the short- and long-term. In the former case, thecharacteristic load combination is considered, with ψk=ψ0, whereasin the latter case reference to the q

46、uasi-permanent load combinationis made, with ψk=ψ2. In all analyses, reference to an office buildingwas made, for which, according to the Eurocode [28], an imposedload Qk=3 kN/m2, a combination factor ψ0=0.7, and a combi

47、nationfactor ψ2=0.3 were assumed. The maximum tributary width is obvi-ously the lesser between the tributary width Lu satisfying the ultimatelimit state of bending strength, and the tributary width Ls satisfyingthe servi

48、ceability limit state of deflection control. Only class I steelprofiles according to the Eurocode 3 [29] were considered for contin-uous beams, whereas also class II steel profiles were considered forsimply supported bea

49、ms. The former profiles are compact sectionscharacterized by the possibility to redistribute the bending momentfrom hogging to sagging bending regions, whilst the latter profilesonly allows a full plasticization over the

50、 cross-section but no redistri-bution of bending moments along the beam length can occur. Thetributary widths Lu and Ls depend (Eqs. (11) and (12)) on the loadqu leading the composite structure to the attainment of the u

51、ltimatelimit state of flexural strength and on the load qs leading to the attain-ment of the maximum deflection allowed at serviceability limit state:Lu ¼ qu γG?Gk þ γQ?ψk?Qk ? ? ð11ÞLs ¼ qe Gk &

52、#254; ψk?Q k ð Þ ð12Þwhere γG, γQ signify the partial load safety factors, assumed equal to1.35 and 1.5, respectively, according to the Eurocode [28]. The ulti-mate load qu is evaluated using an elast

53、o-plastic analysis, where theinfluence of the shear on the bending strength capacity is neglected.For simply supported beams, qu is calculated using Eq. (13), whereasEq. (14) is used for continuous beams:qu ¼ 8?Mpl;

54、RdþL2 ð13Þqu ¼?2? Mpl;Rd??2?Mpl;Rdþ? ? þ 4?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

55、ffiffiffiffiffiffiffiffi ffiMpl;Rdþ? Mpl;Rdþ?Mpl;Rd?? ? rL2 ð14Þwhere Mpl,Rd+ and Mpl,Rd? signify, respectively, the sagging and hog-ging design flexural strength capacity, and L is the span length. T

56、hedesign flexural strength capacity is calculated in accordance withthe Eurocode 4 [1] provisions, depending upon the degree of connec-tion N/Nf, using Eq. (15):Mpl;RdNNf!¼ Mapl;Rd þ Mpl;Rd;f ?Mapl;Rd? ? ? 1? N

57、Nf!ð15Þwhere Mpl,Rd,f is the design flexural strength capacity of the compositesection in the case of complete connection, and Mapl,Rd is the designflexural strength capacity of the steel profile only.The tribu

58、tary width Le is calculated so as to satisfy the deflectioncontrol in the short- and long-term at serviceability limit state. Twoconditions were checked: (i) a total deflection in the long-termδmax≤L/250; and (ii) an ins

59、tantaneous (short-term) deflection dueonly to the imposed load δimp≤L/300, where L is the span length.3 C. Amadio et al. / Journal of Constructional Steel Research xxx (2012) xxx–xxxPlease cite this article as: Amadio C,