[雙語翻譯]外文翻譯--混凝土填充鋼管拱肋的幾何非線性和長期性能（英文）

1、Geometric Nonlinearity and Long-Term Behavior of Crown-Pinned CFST ArchesMark Andrew Bradford, Dist.M.ASCE1; and Yong-Lin Pi2Abstract: Concrete-filled steel tubular (CFST) arches are often used in engineering structures,

2、 particularly in bridge construction. In some instances, to expedite their construction and transport, curvilinear steel tube segments are fabricated and delivered to the construction site and then joined together at the

3、 crown to create a pin, so the arch becomes a crown-pinned arch. Wet concrete is then pumped into the steel tubes to form the concrete core after curing, which experiences time-dependent shrinkage and creep. This paper i

4、nvestigates the effects of geometric nonlinearity on the long-term in-plane behavior of crown-pinned circular CFST arches under a sustained central concentrated load, and derives analytical solutions for their nonlinear

5、response and buckling loads. It is found that the geometric nonlinearity influences the long-term behavior of crown-pinned CFST arches significantly. The long-term deformations predicted by the nonlinear analysis are lar

6、ger than those predicted by linear analysis, and they may be so large that the reserve of the serviceability limit state of crown-pinned CFSTarches may be reduced significantly. The nonlinear analysis also predicts signi

7、ficant long-term increases of the axial forces and bending moments in crown-pinned CFST arches, which is quite different from linear analysis that predicts no long-term changes of the axial force and bending moment for t

8、hee-pinned CFST arches and only small long-term changes for singly pinned CFST arches. It is also found that the nonlinear long-term in-plane buckling loads of crown-pinned CFST arches are smaller than their counterpart

9、values determined from linear analysis. Hence, the geometric nonlinearity together with the shrinkage and creep of the concrete core may reduce the reserve of the stability limit state of crown-pinned CFST arches in the

10、long term. To determine the long-term structural response and buckling of crown-pinned CFST arches correctly, nonlinear analysis is required. DOI: 10.1061/(ASCE)ST.1943-541X.0001163. © 2014 American Society of Civil

11、 Engineers.Author keywords: Arch; Buckling; Concrete core; Concrete-filled steel tube; Creep; Long-term; Nonlinear; Shrinkage; Time-dependent; Metal and composite structures.IntroductionBecause concrete-filled steel tubu

12、lar (CFST) sections have a number of merits, CFST arches are often used in engineering structures, par- ticularly in bridge construction (Pi et al. 2012). In some cases, CFST arches are fabricated as two separate curvili

13、near steel tube segments to reduce the size of the arch to meet transport requirements and then the two segments are joined together at the crown of the arch at the construction site. The wet concrete is then placed into

14、 the steel tubes by high pressure pumping and it forms the concrete core after curing. The crown joint is often significantly weaker compared to the CFST arch-rib, and so it can be simplified structurally as a pin. Becau

15、se of the pinned crown, such CFST arches are considered to be less sen- sitive to the detrimental effects of foundation settlement. It is known that the deformations of pin-ended and fixed CFST arches under a sustained l

16、oad continue to increase with time owing to shrinkage and creep of their core concrete (Bradford and Gilbert 2006; Bradford et al. 2007, 2011; Pi et al. 2011). Because of the pin at the crown, pin-ended and fixed CFST ar

17、ches become crown- pinned CFST arches (i.e., three-pinned and singly pinned CFSTarches). The pinned crown is able to transfer shear forces and nor- mal forces but is unable to resist bending moments, leading to free rota

18、tion of the arch segments about the pin. Because of this, the distributions of the bending moments along crown-pinned arches are much different from those of pin-ended and fixed arches, and the deformations of crown-pinn

19、ed CFST arches are larger than those of pin-ended and fixed CFST arches (Pi and Bradford 2013). As a result, the pin at the crown may make a crown-pinned CFST arch more susceptible to nonlinear deformations than pin-ende

20、d and fixed CFST arches. Hence, the long-term interaction between the geometric nonlinearity and the creep and shrinkage of the con- crete core may be particularly important for the long-term structural response of crown

21、-pinned CFST arches, and nonlinear analysis may be required for correctly predicting the long-term response of crown-pinned CFST arches under sustained loading. Conventional linear long-term analysis (Gilbert and Ranzi 2

22、011) may not be able to determine the deformations and internal actions of crown-pinned CFST arches adequately, and so an investigation of how geometric nonlinearity influences the long-term analysis of crown-pinned CFST

23、 arches in determining their structural response is needed. The long-term buckling behavior of crown-pinned CFST arches may also be quite different from that of pin-ended and fixed CFST arches. Firstly, it has been shown

24、 that nonlinear long-term buckling dominates the in-plane instability of pin-ended shallow and fixed CFST arches, while linear long-term buckling analysis is adequate for pin-ended deep CFST arches (Bradford et al. 2011;

25、 Pi et al. 2011). However, because of the pinned crown, the very different distributions of the deformations and internal actions may make both shallow and deep crown-pinned CFST arches susceptible to nonlinear long-term

26、 buckling. Secondly, in the long-term, pin- ended and fixed CFST arches under sustained loading may buckle1Scientia Professor, Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineeri

27、ng, Univ. of New South Wales (UNSW), NSW 2052, Australia. E-mail: m.bradford@unsw.edu.au2Professor, Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, Univ. of New South Wale

28、s (UNSW), NSW 2052, Australia (corresponding author). E-mail: y.pi@unsw.edu.au Note. This manuscript was submitted on April 27, 2014; approved on August 5, 2014; published online on September 3, 2014. Discussion period o

29、pen until February 3, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineer- ing, © ASCE, ISSN 0733-9445/04014190(11)/$25.00.© ASCE 0401419

30、0-1 J. Struct. Eng.J. Struct. Eng. Downloaded from ascelibrary.org by Technische Universitat Munchen on 07/10/15. Copyright ASCE. For personal use only; all rights reserved.where the final creep coefficient ?u and final

31、aging coefficient χ?are given by?u ¼ 1.25t?0.118 0 ?∞;7 ð12Þandχ? ¼ k1t0 k2 þ t0 ð13Þwithk1 ¼ 0.78 þ 0.4e?1.33?∞;7; k2 ¼ 0.16 þ 0.8e?1.33?∞;7 ð14ÞBecause t

32、he core concrete is enclosed by the steel tube, moisture egress of the core concrete is prevented by the tube and the final creep coefficient of the concrete core is smaller than that of normal concrete. The value ?u

33、88; 2.4 obtained in the tests of Uy (2001) is adopted in this investigation. Solving Eqs. (1) and (2) simultaneously under the boundary conditions given by Eqs. (4)–(7) leads to the radial and axial displacements as~ v &

34、#188; Q4AE ½C1 cos θ þ C2θ sin θ þ HðθÞðC3θ cos θ þ C4 sin θÞþ C5? þ AcEec?sh AE?1 þ cos θ ? HðθÞ cot Θ2 sin θ?ð15Þ~ w ¼ Q4AE fHðθÞ

35、;½D1ðcos θ ? 1Þ þ D2θ sin θ? þ D3θ cos θþ D4 sin θ þ D5θgþ AcEec?sh AE?sin θ þ HðθÞ cot Θ2 ðcos θ ? 1Þ?ð16Þfor three-pinned arches, respectively,

36、 where the coefficients C1–C5 and D1–D5 are given in Appendix I; and~ v ¼ Q4AE ½C1 cos θ þ C2θ sin θ þ HðθÞðC3θ cos θ þ C4 sin θÞþ C5? þ ?shAcEec AE ½C6 cos θ &

37、#254; C7θ sin θ þ HðθÞC8 sin θ þ C9?ð17Þ~ w ¼ Q4AE fHðθÞ½D1ðcos θ ? 1Þ þ D2θ sin θ? þ D3θ cos θþ D4 sin θ þ D5θgþ ?shAcEec AE f½H&

38、#240;θÞD6ðcos θ ? 1Þ þ D7θ? þ D8θ cos θþ D9 sin θg: ð18Þfor singly pinned arches, respectively, where the coefficients C1–C9 and D1–D9 are given in Appendix II. In Eqs. (15)–(18),

39、HðθÞ is a step function defined byHðθÞ ¼? 1 θ > 0 ?1 θ < 0 ð19ÞThe distributions of the linear long-term radial displacements given by Eqs. (15) and (17) along the arch length are

40、 shown in Fig. 2 for a CFST arch with a rise-to-span ratio f=L ¼ 1=3, where the Young’s modulus of the steel tube and core concrete are Es ¼ 200 GPa and Ec ¼ 30 GPa. A central concentrated load Q ¼ 0.

41、2NE2 was applied, with NE2 being the second mode short-term flexural-buckling load of a pin-ended column under uniform axialcompression with the same length as that of the arch. It can be seen that the linear analysis pr

42、edicts long-term increases of the radial displacements for both three-pinned and singly pinned CFST arches. Under the same load Q ¼ 0.2NE2, the short-term and long-term radial displacements of three-pinned arches ar

43、e larger than those of singly pinned arches. The axial compressive force and bending moment can be obtained by substituting Eqs. (15)–(18) asN ¼ ?AEð ~ w 0 ? ~ vÞ ? ?shAcEec ¼ Q2?cot Θ2 cos θ þ H

44、ðθÞ sin θ?ð20ÞM ¼ ? EIR ð~ v 0 0 þ ~ w 0Þ ¼ QR2?cot Θ2 ð1 ? cos θÞ ? HðθÞ sin θ?ð21Þfor three-pinned arches, andN ¼ Q½R2ð1 ? cos Θ

45、Þ2 ? r2 esin2Θ? cos θ2Φ1 þ QHðθÞ sin θ2? 2AcEecr2 e?sh sin Θ cos θΦ1 ð22ÞM ¼ ? QRðcos θ ? 1Þ½R2ð1 ? cos ΘÞ2 ? r2 esin2Θ?2Φ1? QRHðθÞ sin θ2 þ 2AcE

46、ecr2 e?shR sin Θðcos θ ? 1ÞΦ1 ð23Þfor singly pinned arches, where Φ1 is given in Appendix II. Because a three-pinned CFST arch is statically determinate, linear analysis does not predict long-term cha

47、nges of the axial force and bending moment as shown by Eqs. (20) and (21), although linear analysis predicts long-term changes of the displacements as shown by Eqs. (15) and (16) and in Fig. 2. In deference to three-pinn

48、ed arches, singly pinned arches are statically indetermi- nate and linear analysis predicts long-term changes of the axial force and bending moment as shown by Eqs. (22) and (23). How- ever, because of the relaxation pro

49、vided by the pin at the crown, the effects of creep and shrinkage of the concrete core on the long-term bending moments of singly pinned CFST arches are very small as?1 ?0.8 ?0.6 ?0.4 ?0.2 0 0.2 0.4 0.6 0.8 1 0.10.080.06

50、0.040.020?0.02?0.04Three?pinned arch at t = 15 daysThree?pinned arch at t = 200 daysOne?pinned arch at t = 15 daysOne?pinned arch at t = 200 daysro=250mm, ri=240mm, φ∞,7=2.27, ε*sh=340×10?6, L=15m, f/L=1/3θ/ΘDimensi

51、onless radial displacement v/fFig. 2. Distributions of linear long-term radial displacements along arch length© ASCE 04014190-3 J. Struct. Eng.J. Struct. Eng. Downloaded from ascelibrary.org by Technische Universita