外文翻譯---鋼筋混凝土板的拉伸硬化過(guò)程分析（英文）

1、Tension Stiffening in Lightly Reinforced Concrete SlabsR. Ian Gilbert1Abstract: The tensile capacity of concrete is usually neglected when calculating the strength of a reinforced concrete beam or slab, even though concr

2、ete continues to carry tensile stress between the cracks due to the transfer of forces from the tensile reinforcement to the concrete through bond. This contribution of the tensile concrete is known as tension stiffening

3、 and it affects the member’s stiffness after cracking and hence the deflection of the member and the width of the cracks under service loads. For lightly reinforced members, such as floor slabs, the flexural stiffness of

4、 a fully cracked section is many times smaller than that of an uncracked section, and tension stiffening contributes greatly to the postcracking stiffness. In this paper, the approaches to account for tension stiffening

5、in the ACI, European, and British codes are evaluated critically and predictions are compared with experimental observations. Finally, recommenda- tions are included for modeling tension stiffening in the design of reinf

6、orced concrete floor slabs for deflection control.DOI: 10.1061/?ASCE?0733-9445?2007?133:6?899?CE Database subject headings: Cracking; Creep; Deflection; Concrete, reinforced; Serviceability; Shrinkage; Concrete slabs.Int

7、roductionThe tensile capacity of concrete is usually neglected when calcu- lating the strength of a reinforced concrete beam or slab, even though concrete continues to carry tensile stress between the cracks due to the t

8、ransfer of forces from the tensile reinforcement to the concrete through bond. This contribution of the tensile concrete is known as tension stiffening, and it affects the mem- ber’s stiffness after cracking and hence it

9、s deflection and the width of the cracks. With the advent of high-strength steel reinforcement, rein- forced concrete slabs usually contain relatively small quantities of tensile reinforcement, often close to the minimum

10、 amount permit- ted by the relevant building code. For such members, the flexural stiffness of a fully cracked cross section is many times smaller than that of an uncracked cross section, and tension stiffening contribut

11、es greatly to the stiffness after cracking. In design, de- flection and crack control at service-load levels are usually the governing considerations, and accurate modeling of the stiffness after cracking is required. Th

12、e most commonly used approach in deflection calculations involves determining an average effective moment of inertia ?Ie? for a cracked member. Several different empirical equations are available for Ie, including the we

13、ll-known equation developed by Branson ?1965? and recommended in ACI 318 ?ACI 2005?. Other models for tension stiffening are included in Eurocode 2 ?CEN 1992? and the ?British Standard BS 8110 1985?. Recently, Bischoff ?

14、2005? demonstrated that Branson’s equation grossly overestimates the average stiffness of reinforced concrete mem-bers containing small quantities of steel reinforcement, and he proposed an alternative equation for Ie, w

15、hich is essentially com- patible with the Eurocode 2 approach. In this paper, the various approaches for including tension stiffening in the design of concrete structures, including the ACI 318, Eurocode 2, and BS8110 mo

16、dels, are evaluated critically and empirical predictions are compared with measured deflections. Finally, recommendations for modeling tension stiffening in structural design are included.Flexural Response after Cracking

17、Consider the load-deflection response of a simply supported, re- inforced concrete slab shown in Fig. 1. At loads less than the cracking load, Pcr, the member is uncracked and behaves homo- geneously and elastically, and

18、 the slope of the load deflection plot is proportional to the moment of inertia of the uncracked trans- formed section, Iuncr. The member first cracks at Pcr when the extreme fiber tensile stress in the concrete at the s

19、ection of maxi- mum moment reaches the flexural tensile strength of the concrete or modulus of rupture, fr. There is a sudden change in the local stiffness at and immediately adjacent to this first crack. On the section

20、containing the crack, the flexural stiffness drops signifi- cantly, but much of the beam remains uncracked. As load in- creases, more cracks form and the average flexural stiffness of the entire member decreases. If the

21、tensile concrete in the cracked regions of the beam car- ried no stress, the load-deflection relationship would follow the dashed line ACD in Fig. 1. If the average extreme fiber tensile stress in the concrete remained a

22、t fr after cracking, the load- deflection relationship would follow the dashed line AE. In real- ity, the actual response lies between these two extremes and is shown in Fig. 1 as the solid line AB. The difference betwee

23、n the actual response and the zero tension response is the tension stiff- ening effect ??? in Fig. 1?. As the load increases, the average tensile stress in the concrete reduces as more cracks develop and the actual respo

24、nse tends toward the zero tension response, at least until the crack pattern is fully developed and the number of cracks has stabilized. For slabs1Professor of Civil Engineering, School of Civil and Environmental Enginee

25、ring, Univ. of New South Wales, UNSW Sydney, 2052, Australia. Note. Associate Editor: Rob Y. H. Chai. Discussion open until November 1, 2007. Separate discussions must be submitted for individual papers. To extend the cl

26、osing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this techni- cal note was submitted for review and possible publication on May 22, 2006; approved on December 28,

27、 2006. This technical note is part of the Journal of Structural Engineering, Vol. 133, No. 6, June 1, 2007. ©ASCE, ISSN 0733-9445/2007/6-899–903/$25.00.JOURNAL OF STRUCTURAL ENGINEERING © ASCE / JUNE 2007 / 899

28、J. Struct. Eng. 2007.133:899-903.Downloaded from ascelibrary.org by University of Liverpool on 04/19/15. Copyright ASCE. For personal use only; all rights reserved.Table 1. Designation and Details of Slab SpecimensSlabSl

29、ab depth ?mm?Span L ?mm?Effective depth d ?mm?Steel area Ast ?mm2? ?=As/bd fc ? ?MPa? Ec ?MPa?Tensile strength ?MPa?S1 110 3,500 92 141 0.00180 37.3 26,800 3.39S2 110 3,500 91 227 0.00293 37.3 26,800 3.39S3 110 3,500 90

30、354 0.00463 37.3 26,800 3.39S8 110 3,500 89 339 0.00448 52.2 30,700 4.16SS2 102 2,000 81.7 227 0.00327 38.0 27,470 4.42SS3 106.6 2,000 85.9 354 0.00485 38.0 27,470 4.42SS4 106.2 2,000 83.2 339 0.00480 38.0 27,470 4.42Z1

31、100 2,000 82 141 0.00203 38.4 27,390 3.60Z2 100 2,000 81 227 0.00329 38.4 27,390 3.60Z3 100 2,000 80 354 0.00521 38.4 27,390 3.60Z4 100 2,000 79 565 0.00842 48.4 30,500 4.04Table 2. Measured and Predicted Midspan Deflect

32、ions ??? for Test SlabsSlab Mcr ?kN.m? M ?s ?MPa?Experimental ?exp ?mm?ACI 318 Eurocode 2 BS 8110 No-tension stiffening?ACI ?mm? ?ACI/?exp?Euro ?mm? ?Euro/?exp?BS ?mm? ?BS/?exp?nts ?mm? ?nts/?expS1 5.93 1.1 Mcr 528 8.31

33、3.82 0.46 9.21 1.11 20.3 2.44 24.5 2.951.2 Mcr 576 13.2 5.22 0.40 15.1 1.14 23.7 1.80 29.8 2.261.3 Mcr 624 17.5 6.89 0.39 20.5 1.17 26.9 1.54 35.1 2.01S2 5.99 1.1 Mcr 341 6.37 3.79 0.59 7.08 1.11 14.5 2.28 17.2 2.701.2 M

34、cr 372 8.23 5.11 0.62 11.0 1.34 16.7 2.03 20.7 2.521.3 Mcr 403 10.8 6.66 0.62 14.7 1.36 19.0 1.76 24.3 2.25S3 6.07 1.1 Mcr 227 4.78 3.74 0.78 5.72 1.20 10.9 2.28 12.1 2.531.2 Mcr 248 6.09 4.94 0.81 8.42 1.38 12.4 2.04 15

35、.2 2.501.3 Mcr 268 9.03 6.34 0.70 11.0 1.21 14.0 1.55 17.4 1.93S8 7.38 1.1 Mcr 291 6.45 4.00 0.62 6.30 0.98 14.1 2.19 13.2 2.051.2 Mcr 317 8.48 5.28 0.62 10.1 1.19 16.0 1.89 17.8 2.101.3 Mcr 344 11.04 6.84 0.62 13.2 1.20

36、 17.9 1.62 21.1 1.91SS2 6.70 1.1 Mcr 4.26 3.45 1.59 0.46 3.00 0.87 7.21 2.09 5.91 1.711.2 Mcr 465 5.13 2.15 0.42 4.71 0.92 8.72 1.70 7.45 1.451.3 Mcr 503 6.71 2.82 0.42 6.31 0.94 9.16 1.37 9.80 1.46SS3 7.40 1.1 Mcr 290 2

37、.16 1.49 0.69 2.30 1.06 5.09 2.36 4.25 1.971.2 Mcr 316 3.49 1.98 0.57 3.43 0.98 5.76 1.65 5.20 1.491.3 Mcr 343 4.50 2.56 0.57 4.49 1.00 6.44 1.43 6.74 1.50SS4 7.30 1.1 Mcr 309 2.90 1.50 0.52 2.44 0.84 5.42 1.87 4.01 1.38

38、1.2 Mcr 337 3.83 2.01 0.52 3.70 0.97 6.16 1.61 5.68 1.481.3 Mcr 365 4.78 2.61 0.55 4.87 1.02 6.89 1.44 7.38 1.54Z1 5.20 1.1 Mcr 521 3.86 1.61 0.42 3.70 0.96 7.08 1.83 13.8 3.581.2 Mcr 568 6.18 2.18 0.35 6.21 1.01 8.21 1.

39、33 15.1 2.441.3 Mcr 616 9.49 2.94 0.31 8.66 0.91 9.35 0.98 16.2 1.71Z2 5.25 1.1 Mcr 337 2.20 1.59 0.72 2.98 1.35 5.04 2.29 8.11 3.691.2 Mcr 368 3.21 2.05 0.64 4.47 1.39 5.82 1.81 10.3 3.211.3 Mcr 398 4.55 2.84 0.62 6.16

40、1.35 6.62 1.45 11.3 2.48Z3 5.32 1.1 Mcr 225 3.04 1.59 0.52 2.43 0.80 3.78 1.24 6.45 2.121.2 Mcr 245 4.03 2.10 0.52 3.55 0.88 4.34 1.08 7.48 1.861.3 Mcr 266 5.09 2.72 0.53 4.65 0.91 4.91 0.96 7.92 1.56Z4 6.05 1.1 Mcr 166

41、2.38 1.59 0.67 2.15 0.90 3.39 1.42 5.38 2.261.2 Mcr 181 3.45 2.07 0.60 3.13 0.91 3.84 1.11 5.91 1.711.3 Mcr 196 4.15 2.63 0.63 3.85 0.93 4.29 1.03 6.46 1.56??predicted/?exp? Range 0.31–0.81 0.80–1.39 0.96–2.44 1.38–3.69M

42、ean 0.56 1.07 1.68 2.12JOURNAL OF STRUCTURAL ENGINEERING © ASCE / JUNE 2007 / 901J. Struct. Eng. 2007.133:899-903.Downloaded from ascelibrary.org by University of Liverpool on 04/19/15. Copyright ASCE. For personal