外文翻译---钢筋混凝土板的拉伸硬化过程分析.doc

本 科 生 毕 业 设 计（论文）外文翻译园林艺术系题 目： 钢筋混凝土板的拉伸硬化过程分析 学生姓名： 胡 斌 学 号： 200708350209 专业班级： 土木工程072班 指导教师： 党改红 职称： 讲师 2011年 3 月 1 日钢筋混凝土板的拉伸硬化过程分析r. ian gilbert摘要：当计算一个钢筋混凝土梁或板的承载力时混凝土的抗拉能力通常被忽视,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，建议书包括建模系统紧张挠度控制的钢筋混凝土楼板设计变硬。分类号： 1061/asce0733-94452007133:6899关键词：开裂;蠕变挠度，混凝土，钢筋，适用性，收缩，混凝土砖。简介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。 随着高强度钢筋的到来，增强混凝土板通常包含相对少量的拉钢筋，经常接近相关建筑法规允许的最低含量。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，并在开裂后建模精确的刚度是必需的。挠度计算中最常用的方法包括确定为破解构件平均惯性（）有效时刻。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，布兰森的方程极高估含有少量的钢筋混凝土构件钢筋平均刚度，他提出了一个对于，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，在模拟张力加劲的建议结构设计均包括在内。开裂后弯曲响应考虑简支一个负载变形响应，钢筋混凝土板图1所示。在负载超过负荷少的开裂，该构件未开裂和行为均匀和弹性，以及挠度斜率是成正比的未开裂的转动惯量的转化节，。该构件在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有一个刚度突变，并立即出现裂纹。在包含破碎部分，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平均抗弯刚度在整个构件中减少。如果在梁的混凝土开裂区域进行拉没有压力，负载变形关系将遵循虚线acd，图1。如开裂后如果平均极端纤维拉伸在具体的压力维持在，将遵循虚线ae。事实上，实际的响应介于这两个极端，是如图1所示为实线ab型。之间的差异实际反映和零张力反应是张力加劲影响。随着负载的增加，平均拉应力混凝土随着越来越多的裂缝降低对实际的响应趋于零紧张的反应，至少要等到裂缝模式充分开发和裂缝的数量已趋于稳定。对于含有少量的拉钢筋砖（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。 张力加劲的效果随着时间负荷下降，可能是由于拉伸的综合影响蠕变，蠕变断裂，收缩开裂，而这必须占长期绕度计算。加劲的张力模型aci 318-2005梁或板在使用载重挠度可以瞬间从弹性论计算采用混凝土弹性模量ec和有效的惯性矩,例如，为构件是价值计算eq.1计算公式为在跨中简支构件和加权平均值计算在连续正，负弯矩区跨度 （1）为换算截面惯性裂的时刻；为目前的毛质心横截面有关惯性轴，但更应该是正确换算截面的未开裂的惯性力矩；为在构件的最大弯矩阶段挠度计算；为开裂时（=）；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紧张。 aci的方法的修改包括在澳大利亚标准as3600-2001(as2001)交代的事实，收缩引起的紧张局势可能会降低混凝土开裂时刻显着。开裂的时刻由公式决定，是最大收缩引起的拉在未开裂截面应力在极端的情况在该纤维发生开裂（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和光圆钢筋0.5；为单一的，短期负荷为1.0和重复或持续荷载为0.5；在加载应力造成的受拉钢筋首先开裂，计算混凝土紧张；是在考虑钢筋应力加载；在截面曲率而忽视具体的紧张；曲率的未开裂换算截面。 在纯弯板，如果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）对于受弯构件变形钢筋包含短期下载入中，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的计算bischoff(2005) (5)bs 8110-1985这种做法，目前已在英国已经取代了欧洲法规2的方法，还涉及到在特定的截面曲率的计算，然后结合取得的偏转。开裂后的曲率k计算假设1、平面为平截面；2、在压缩和钢筋混凝土被认为是线弹性；3、在紧张的混凝土应力分布是三角形的，曾在中性轴和一个值为零值在1.0 mpa的瞬间强度钢质心，减少至0.55mpa。与实验数据的比较为了测试aci 318，欧洲规范的适用性和bs 8110钢筋混凝土构件的轻轻的方法，测瞬间响应与偏转11简支，单钢筋单向拉伸板含钢量在范围进行比较和计算的答复，该板块（指定s1至s3，s8的，到ss2的ss4型，和z1到z4）都是柱状，矩形截面，850mm，并在一个有效深度载有纵向拉伸单层钢筋d(es=200000mpa和屈服应力=500mpa)。每个板块的详细情况见表1，包括有关的几何和材料特性。在每个板跨中挠度的预测结果与实测时，在跨中时刻等于1.1，1.2和1.3mcr列于表2。与瞬时变形响应的测量时刻的两跨中的砖。（ss2 and z3）进行比较和计算反应获得图2使用三个代码方式同时显示的反应，如果没有出现开裂，如果紧张僵硬被忽略。讨论结果很明显，这些轻轻钢筋砖，紧张硬化非常显着，提供了刚度大的比例。从表2，跨中挠度的比例得到了加劲对测量张力跨中挠度忽视（在mcr和1.3mcr范围）是在1.38-3.69范围取平均指2.12。也就是说，平均而言，紧张硬化超过50的一个刚性板钢筋在屈服荷载的瞬间开裂。对于每一个板，在aci 318的方法低估了瞬间变形开裂后，尤其如此轻率加强板块。此外，在这一时刻aci 318突然不模型，偏转方向改变最初的反应开裂，也没有预测的正确形状矩挠度曲线。在短期挠度低估使用的aci318模式是经化验报告在这里在表示实践中相当大的比。不同于eurocode 2和bs 8110，aci 318模型不承认或为在开裂的时刻，这将不可避免地减少在实践中出现的由于紧张引起的混凝土干燥收缩或热变形。对于许多砖，开裂会发生因提前铸造干燥或几周内温度变化，以及经常暴露之前，其板全方位服务的负荷。通过限制在拉伸的水平拉应力混凝土强化只为1.0 mpa，高估了bs 8110的方法测试的砖都低于并立即偏转以上开裂的时刻。有道理和损失的刚度，在实践中由于克制，早期收缩和热变形发生膨胀。不过，bs 8110提供了一个相对较差模型刚度，并错误地认为，平均拉力混凝土裂缝进行了实际调高m增大和中性轴的上升。因此，斜坡的sb 8110 时刻，挠度情节较陡测量所有板坡。这种方法使用比欧洲法规2或aci两种方式也比较繁琐。在所有情况下，欧洲法规2挠度计算eps.(3)-(5)是在更接近与实测挠度在整个负载范围内协议。可以看出在图2，载挠度曲线的形状获得使用欧洲规范2是一个比这更好的代表性实际曲线获得使用ep.(1)。考虑到具体的变异材料性能影响的砖，服务行为和对开裂的随机性，欧洲法规2之间的协议预测和对这种范围广泛的测试结果拉钢筋的比例是相当显着。随着图2（）0.80和1.39之间的值平均值为1.07，欧洲法规2的方法提供了aci318或bs8110更好地估计短期行为。结论 虽然紧张僵硬只对重钢筋梁挠度的影响相对较小，这是非常轻的比例在iuncr / icr的是高钢筋构件显着，例如作为最实用的钢筋混凝土楼板。加劲张力的模型纳入aci(2005)，欧洲法规2(cen1993)，和bs8110(1985) 已提交其适用性已轻轻钢筋混凝土楼板评估。计算模型的三个代码瞬时挠度进行了比较与来自11个实验室测试测量挠度在含有不同数量的钢筋砖。在欧洲法规2方案（ep.(5)已被证明是更准确地模拟了瞬时负载变形的加固构件轻轻响应的波形和aci 318(ep.(1)比更为可靠的方法。出自：journal of structural engineering asce / june 2007tension 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.doi: 10.1061/（asce）0733-9445（2007）133:6（899）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.asce, issn 0733-9445/2007/6-899903/$25.00.11professor of civil engineering, school of civil and environmental engineering, univ. of new south wales, unsw sydney, 2052, australia. journal of structural engineering, vol. 133, no. 6, june 1, 2007.asce, issn 0733-9445/2007/6-899903/$25.00.introductionthe 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.flexural response after crackingconsider 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.models for tension stiffeningaci 318-2005the 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)bs 8110-1985this 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.comparison with experimental datato 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.discussion of resultsit 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