房屋建筑毕业设计外文翻译---钢筋混凝土板的拉伸硬化过程分析.doc

毕业设计 (论文)外文翻译设计（论文）题目： 宁波天合家园某住宅楼 2号轴框架结构设计与建筑制图 学 院 名 称： 建筑工程学院 专 业： 土木工程 姓 名： 陈绍樑 学 号 09404010421 指 导 教 师： 马永政、陶海燕 2012 年 12 月 10 日宁波工程学院本科毕业设计（论文）外文翻译外文原稿1Tension Stiffening in Lightly Reinforced Concrete Slabs1R. Ian Gilbert1Abstract: The tensile capacity of concrete is usually neglected when calculating the strength of a reinforced concrete beam or slab, even though concrete 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 and it affects the members 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 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 in the ACI, European, and British codes are evaluated critically and predictions are compared with experimental observations. Finally, recommendations are included for modeling tension stiffening in the design of reinforced concrete floor slabs for deflection control.CE Database subject headings: Cracking; Creep; Deflection; Concrete, reinforced; Serviceability; Shrinkage; Concrete slabs.1Professor of Civil Engineering, School of Civil and EnvironmentalEngineering, Univ. of New South Wales, UNSW Sydney, 2052, Australia.Note. Associate Editor: Rob Y. H. Chai. Discussion open untilNovember 1, 2007. Separate discussions must be submitted for individualpapers. To extend the closing date by one month, a written request mustbe filed with the ASCE Managing Editor. The manuscript for this technicalnote was submitted for review and possible publication on May 22,2006; approved on December 28, 2006. This technical note is part of theJournal of Structural Engineering, Vol. 133, No. 6, June 1, 2007.11Professor of Civil Engineering, School of Civil and Environmental Engineering, Univ. of New South Wales, UNSW Sydney, 2052, Australia. 28宁波工程学院本科毕业设计（论文）外文翻译Journal of Structural Engineering, Vol. 133, No. 6, June 1, 2007. 1.Introduction The tensile capacity of concrete is usually neglected when calculatingthe strength of a reinforced concrete beam or slab, eventhough concrete continues to carry tensile stress between thecracks due to the transfer of forces from the tensile reinforcementto the concrete through bond. This contribution of the tensileconcrete is known as tension stiffening, and it affects the membersstiffness after cracking and hence its deflection and thewidth of the cracks. With the advent of high-strength steel reinforcement, reinforcedconcrete slabs usually contain relatively small quantities oftensile reinforcement, often close to the minimum amount permittedby the relevant building code. For such members, the flexuralstiffness of a fully cracked cross section is many times smallerthan that of an uncracked cross section, and tension stiffeningcontributes greatly to the stiffness after cracking. In design, deflectionand crack control at service-load levels are usually thegoverning considerations, and accurate modeling of the stiffnessafter cracking is required. The most commonly used approach in deflection calculationsinvolves determining an average effective moment of inertia Iefor a cracked member. Several different empirical equations areavailable for Ie, including the well-known equation developed byBranson 1965 and recommended in ACI 318 ACI 2005. Othermodels for tension stiffening are included in Eurocode 2 CEN1992 and the British Standard BS 8110 1985. Recently,Bischoff 2005 demonstrated that Bransons equation grossly overestimates thtie average sffness of reinforced concrete memberscontaining small quantities of steel reinforcement, and heproposed an alternative equation for Ie, which is essentially compatiblewith the Eurocode 2 approach. In this paper, the various approaches for including tensionstiffening in the design of concrete structures, including the ACI318, Eurocode 2, and BS8110 models, are evaluated critically andempirical predictions are compared with measured deflections.Finally, recommendations for modeling tension stiffening instructural design are included.2.Flexural Response after Cracking Consider the load-deflection response of a simply supported, reinforcedconcrete slab shown in Fig. 1. At loads less than thecracking load, Pcr, the member is uncracked and behaves homogeneouslyand elastically, and the slope of the load deflection plotis proportional to the moment of inertia of the uncracked transformedsection, Iuncr. The member first cracks at Pcr when theextreme fiber tensile stress in the concrete at the section of maximum 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 containing the crack, the flexural stiffness drops significantly, but much of the beam remains uncracked. As load increases, more cracks form and the average flexural stiffness of the entire member decreases. If the tensile concrete in the cracked regions of the beam carried 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 at fr after cracking, the loaddeflection relationship would follow the dashed the actual response lies between these two extremes and is shown in Fig. 1 as the solid line AB. The difference between the actual response and the zero tension response is the tension stiffening effect （ in Fig. 1）. As the load increases, the average tensile stress in the concrete reduces as more cracks develop and the actual response tends toward the zero tension response, at least until the crack pattern is fully developed and the number of cracks has stabilized. For slabscontaining small quantities of tensile reinforcement typicallytension stiffening may be responsible for morethan 50% of the stiffness of the cracked member at service loads and remains significant up to and beyond the point where the steel yields and the ultimate load is approached. The tension stiffening effect decreases with time under sustained loads, probably due to the combined effects of tensile creep, creep rupture, and shrinkage cracking, and this must be accounted for in long-term deflection calculations. 3.Models for Tension Stiffening The instantaneous deflection of beam or slab at service loads may be calculated from elastic theory using the elastic modulus of concrete Ec and an effective moment of inertia, Ie. The value of Ie for the member is the value calculated using Eq. 1 at midspan for a simply supported member and a weighted average value calculated in the positive and negative moment regions of a continuous span （1）where Icr=moment of inertia of the cracked transformed section;Ig=moment of inertia of the gross cross section about the centroidal axis but more correctly should be the moment of inertia of the uncracked transformed section, Iuncr; Ma=maximum moment in the member at the stage deflection is computed; Mcr=cracking moment =(frIg / yt); fr=modulus of rupture of concrete (=7.5 fc in psi and 0.6 fc in Mpa); and yt=distance from the centroidal axis of the gross section to the extreme fiber in tension. A modification of the ACI approach is included in the Australian Standard AS3600-2001 (AS 2001)to account for the fact that shrinkage-induced tension in the concrete may reduce the cracking moment significantly. The cracking moment is given by Mcr=(fr fcs)Ig / yt, where fcs is maximum shrinkage-induced tensile stress in the uncracked section at the extreme fibre at which cracking occurs（Gilbert 2003）. （2）where distribution coefficient accounting for moment level and degree of cracking and is given by （3）and 1=1.0 for deformed bars and 0.5 for plain bars; 2=1.0 for a single, short-term load and 0.5 for repeated or sustained loading; sr=stress in the tensile reinforcement at the loading causing first cracking (i.e., when the moment equals Mcr), calculated while ignoring concrete in tension; s is reinforcement stress at loading under consideration (i.e., when the in-service moment Ms is acting), calculated while ignoring concrete in tension; cr=curvature at the section while ignoring concrete in tension; and uncr=curvature on the uncracked transformed section. For slabs in pure flexure, if the compressive concrete and the reinforcement are both linear and elastic, the ratio sr /s in Eq.(3) is equal to the ratio Mcr /Ms. Using the notation of Eq.（1）, Eq.(2) can be reexpressed as （4） For a flexural member containing deformed bars under shortterm loading, Eq. (3) becomes =1（Mcr /Ms）2 and Eq.（4）can be rearranged to give the following alternative expression for Ie for short-term deflection calculations recently proposed by Bischoff (2005): (5) This approach, which has now been superseded in the U.K. by the Eurocode 2 approach, also involves the calculation of the curvature at particular cross sections and then integrating to obtain the deflection. The curvature of a section after cracking is calculated by assuming that (1) plane sections remain plane; (2) the concrete in compression and the reinforcement are assumed to be linear elastic; and（3）the stress distribution for concrete in tension is triangular, having a value of zero at the neutral axis and a value at the centroid of the tensile steel of 1.0 MPa instantaneously, reducing to 0.55 MPa in the long term.4.Comparison with Experimental Data To test the applicability of the ACI 318, Eurocode 2, and BS 8110 approaches for lightly reinforced concrete members, the measured moment versus deflection response for 11 simply supported, singly reinforced one-way slabs containing tensile steel quantities in the range 0.00180.01 are compared with the calculated responses. The slabs (designated S1 to S3, S8, SS2 to SS4, and Z1 to Z4) were all prismatic, of rectangular section, 850 mm wide, and contained a single layer of longitudinal tensile steel reinforcement at an effective depth d (with Es=200,000 MPa and the nominal yield stress fsy=500 Mpa). Details of each slab are given in Table 1, including relevant geometric and material properties. The predicted and measured deflections at midspan for each slab when the moment at midspan equals 1.1, 1.2, and 1.3 Mcr are presented in Table 2. The measured moment versus instantaneousdeflection response at midspan of two of the slabs (SS2 and Z3) are compared with the calculated responses obtained using the three code approaches in Fig. 2. Also shown are the responses if cracking did not occur and if tension stiffening was ignored.5.Discussion of Results It is evident that for these lightly reinforced slabs, tension stiffening is very significant, providing a large proportion of the postcracking stiffness. From Table 2, the ratio of the midspan deflection obtained by ignoring tension stiffening to the measured midspan deflection (over the moment range Mcr to 1.3 Mcr)is in the range 1.383.69 with a mean value of 2.12. That is, on average, tension stiffening contributes more than 50% of the instantaneous stiffness of a lightly reinforced slab after cracking at service load. For every slab, the ACI 318 approach underestimates the instantaneous deflection after cracking, particularly so for lightly reinforced slabs. In addition, ACI 318 does not model the abrupt change in direction of the moment-deflection response at first cracking, nor does it predict the correct shape of the postcracking moment-deflection curve. The underestimation of short-term deflection using the ACI318 model is considerably greater in practice than that indicated by the laboratory tests reported here. Unlike the Eurocode 2 and BS 8110 approaches, the ACI 318 model does not recognize or account for the reduction in the cracking moment that will inevitably occur in practice due to tension induced in the concrete by drying shrinkage or thermal deformations. For many slabs, cracking will occur within weeks of casting due to early drying or temperature changes, often well before the slab is exposed to its full service loads. By limiting the concrete tensile stress at the level of the tensile reinforcement to just 1.0 MPa, the BS 8110 approach overestimates the deflection of the test slabs both below and immediately above the cracking moment. This is not unreasonable and accounts for the loss of stiffness that occurs in practice due to restraint to early shrinkage and thermal deformations. Nevertheless, the BS 8110 approach provides a relatively poor model of thepostcracking stiffness and incorrectly suggests that the average tensile force carried by the cracked concrete actually increases as M increases and the neutral axis rises. As a result, the slope of the BS 8110 postcracking moment-deflection plot is steeper than the measured slope for all slabs. The approach is also more tedious to use than either the ACI or Eurocode 2 approaches. In all cases, deflections calculated using Eurocode 2 Eqs.(3)(5) are in much closer agreement with the measured deflection over the entire postcracking load range. As can be seen in Fig. 2, the shape of the load-deflection curve obtained using Eurocode 2 is a far better representation of the actual curve than that obtained using Eq. (1). Considering the variability of the concrete material properties that affect the in-service behavior of slabs and the random nature of cracking, the agreement between the Eurocode 2 predictions and the test results over such a wide range of tensile reinforcement ratios is quite remarkable. With the ratio of () in Table 2 varying between 0.80 and 1.39 with a mean value of 1.07, the Eurocode 2 approach certainly provides a better estimate of short-term behavior than either ACI 318 or BS8110.6.Conclusions Although tension stiffening has only a relatively minor effect on the deflection of heavily reinforced beams, it is very significant in lightly reinforced members where the ratio Iuncr / Icr is high, such as most practical reinforced concrete floor slabs. The models for tension stiffening incorporated in ACI （2005）, Eurocode 2 (CEN 1992), and BS 8110 （1985） have been presented and their applicability has been assessed for lightly reinforced concrete slabs.Instantaneous deflections calculated using the three code models have been compared with measured deflections from 11 laboratory tests on slabs containing varying quantities of steel reinforcement. The Eurocode 2 approach （Eq.（5） has been shown to more accurately model the shape of the instantaneous load-deformation response for lightly reinforced members and be far more reliable than the ACI 318 approach （Eq.（1）.中文翻译1钢筋混凝土板的拉伸硬化过程分析R. Ian Gilbert摘 要：混凝土的抗拉能力在计算钢筋混凝土梁或板的强度时通常被忽视,尽管具体的拉应力继续进行，由于拉钢筋到混凝土之间裂缝的转换力量。这一种混凝土的拉力被称为混凝土的张力硬化。在开裂后它会影响钢筋混凝土的刚度，因此它的挠度和裂缝宽度必须根据屈服强度负载。对轻混凝土，例如楼板，全部裂缝的弯曲刚度比没有裂缝部分的要小很多，张力加劲有助于刚度。在本文中，ACI方法必须考虑到紧张加劲，欧洲和英国的方法是严格评估和预测与实验结果进行比较。最后，建议依据钢筋混凝土楼板的建模张力加劲设计控制偏转。关键词：开裂，蠕变挠度，混凝土，钢筋，适用性，收缩，混凝土砖。1.引言由于拉钢筋到混凝土之间裂缝的转换力量，拉伸能力在计算时通常忽略钢筋混凝土梁或板的强度,尽管具体的拉应力将持续。这一种混凝土的拉力被称为张力硬化,它会影响各部分的刚度，因此必须考虑其挠度和裂缝宽度。 随着高强度钢筋的运用，增强混凝土板通常使用相对少量的拉钢筋，经常接近相关建筑法规允许的最低允许值。对于这样的构件，弯曲完全开裂的一个截面刚度比未开裂的截面小许多倍，张力加劲大大促进了开裂后构件的刚度。在设计中，挠度和裂缝的控制通常是在屈服水平调整考虑的，并在开裂后刚度的建模精确是必需的。挠度计算中最常用的方法包括确定破解构件平均有效的转动惯量（）。几种不同的经验公式可用于，包括著名的方程开发Branson（1965）和ACI 318（ACI 2005）。其他的张力硬化模式包括在Eurocode 2（CEN1992)和（British Standard BS 8110 1985），最近，Bischoff（2005）表明，布兰森的方程对含有少量的钢筋混凝土构件钢筋平均刚度评估过高，他提出了一个对于的替代方程，这基本上是与Eurocode 2方案兼容。在本文中，包括张力加劲在内的各种方法在混凝土结构设计，包括在Eurocode 2，ACI 318，BS8110模式，批判性进行评估经验预测与实测挠度进行了比较。最后，模拟张力加劲的建议结构设计均被包括在内。2.开裂后弯曲响应考虑一个简支负载的变形响应，钢筋混凝土板如图1所示。在负载小于开裂负载的情况下，该构件未开裂和表现均匀的弹性，以及挠度斜率是成正比的未开裂的转动惯量的换算界面，。该构件的第一裂缝在当极端纤维在混凝土拉应力的最大部分到达混凝土弯拉强度破裂或时。有一个刚度突变，并立即出现裂纹。在包含了破碎的部分，抗弯刚度显着下降，但大部分仍然未开裂的梁，随着负载的增加，出现更多的裂缝形式和整个构件的平均抗弯构件减少。 如果在梁的混凝土开裂区域内施加拉力而没有压力，负载变形关系将遵循虚线ACD，如图1。如果平均极端纤维拉伸应力在混凝土开裂后留在fr，将遵循虚线AE。事实上，实际的反应是介于这两个极端自建，如图1所示为实线AB型。实际反应之间的区别和零张力反应的张力是加强效应。随着越来越多的裂缝发展和实际响应趋向于零紧张反应，一般的拉应力混凝土减少，至少要等到裂缝模式充分开发和裂缝的数量趋于稳定。对于含有少量的拉结钢筋砖（通常= As/bd0.003），紧张硬化可能超过50的钢筋混凝土的刚度破坏屈服加载而且仍然要达到和超过的钢产量和负荷接近极限地步。依据在长期挠度的计算下，可能是由于综合作用的拉伸蠕变、蠕变断裂,收缩开裂，在持续负载下张力加劲效应随着时间而减少。3.加劲的张力模型梁的弯曲或板在使用载重挠度可以瞬间从弹性论计算通过混凝土弹性模量Ec和有效的惯性矩。的价值对于构件是计算使用Eq.1计算公式为一个在跨中简支构件和加权平均计算价值在正，负弯矩区的一个连续的跨度。 （1）为破碎的换算截面的惯性矩；为总截面的质心轴的惯性矩，但更正确的应该是换算截面的未开裂的惯性矩；为在构件的最大弯矩阶段的计算挠度；为开裂力矩（=）；为混凝土断裂模数；为从质心的距离轴的毛截面的纤维在极端的张力。 ACI方法的修改包括在澳大利亚标准AS3600-2001(AS2001)解释的收缩引起的张力可能会显著的降低混凝土的开裂构件这个事实。开裂的构件由公式决定，是纤维在最大收缩引起的拉在未开裂截面应力在极端的情况发生开裂（Gilbert 2003）。Eurocode 2（1994） 这种方法涉及到在特定的曲率计算交叉部分，然后结合取得的挠度。开裂后曲率K的计算为 (2)为分配系数占目前水平和打击的程度，并给出 （3）为变形钢筋=1.0，光圆钢筋=0.5；为单一的，短期负荷为1.0，重复或持续荷载为0.5；在应力加载造成的受拉钢筋首先开裂，计算混凝土张力；是考虑钢筋的加载应力；为忽略应力混凝土的曲率部分；曲率的未开裂换算截面。 在纯弯曲的板，如果抗压混凝土和钢筋都是线性和弹性， 等于 ，结合公式1和2能得 （4）对于一个包含变形钢筋受弯构件在短期的加载，公式3和公式4可以重新安排，以提供下列替代表达式短期挠度最近提出Bischoff(2005) (5)这种做法，目前在英国已经取代了Eurocode 2的方法，还涉及到在特定的截面曲率的计算，然后结合获得的挠度。开裂后的曲率K计算假设（1）、平面为平截面；（2）、压缩的钢筋