(双语版)混凝土结构设计原.ppt

Concrete Structural Fundamentals,混凝土结构基本原理,主 讲：管 巧 艳,2010 - 10 - 11,CHARPTRE 5 SHEAR STRENGTH OF MEMBERS (构件的受剪承载力),5.1 Introduction (概述),受弯构件(a member under flexure)除承受弯矩(moment)外，往往还同时承受剪力(shear)。即使构件配置有足够的纵筋(longitudinal reinforcement)以抵抗正截面(perpendicular sections)的弯矩，构件仍有可能发生破坏，这是因为在弯矩和剪力的共同作用下斜截面(diagonal sections)强度不足引起的.,斜截面破坏带有脆性破坏的性质，缺乏明显的预兆，设计人员必须使设计的构件既能抵抗弯矩，也能抵抗剪力,For this purpose, transverse reinforcement(横向钢筋）, or the so called web reinforcement（腹筋）, must be designed to provide adequate ultimate strength for the diagonal sections. The web reinforcement may be composed of transverse ties or stirrups（箍筋） and inclined bars （斜筋）bent up from the surplus longitudinal reinforcing bars.,5.2 The Mechanism of Shear Resistance in Reinforced Concrete Beams without Web Reinforcement （无腹筋钢筋混凝土梁的受剪机理）,5.2.1 Stress State of Reinforced Concrete Beams without Web Reinforcement before Diagonal Cracks （无腹筋梁斜裂缝出现前的应力状态）,The normal stress and shear stress at any point in a cross section E-E of the beam can be expressed as,The principal tension stress and the principal compression stress can be expressed as,主拉应力的作用方向与梁纵轴的夹角,单元2位于中和轴处，该单元上只作用有剪应力(shear stress)，而无正应力(direct stress)，主拉应力与主压应力相互垂直与梁轴线成450角，主拉应力与主压应力的大小相等，均等于剪应力,分析图5.2有：,单元1在梁受压区内，单元作用有剪应力和压应力，由于压应力的存在，使得主拉应力小于主压应力，且主拉应力与梁轴线的夹角大于450,单元3在梁受拉区内，单元上作用有剪应力和拉应力，由于拉应力的存在，使得主拉应力大于主压应力，且主拉应力与梁轴线的夹角小于450,5.2.2 Stress State of Reinforced Concrete Beams without Web Reinforcement after Diagonal Cracks （无腹筋梁斜裂缝出现后的应力状态）,When the principal tensile stress exceeds the tensile strength of concrete, cracking is produced in a reinforced concrete beam, and the cracks are formed perpendicularly to the tensile stress trajectories.,In the regions of large bending moments, cracks develop almost perpendicularly to the axis of the beam. These cracks are called “flexural cracks”. （弯曲裂缝）,In regions of high shear due to the diagonal tension, the inclined cracks developed as an extension of the flexural cracks and are termed “flexural-shear cracks”. （弯剪裂缝）,Some diagonal cracks may develop near the neutral axis of beam, these cracks are also called “web-shear cracks”. （腹剪裂缝）,After cracking occurs, the shear resistance of a reinforced concrete beam without web reinforcement is provided by the following three components（裂缝出现后，无腹筋梁的剪力由以下三部分组成）:,（1）The shear strength on the residual concrete compression zone. （斜裂缝上端剪压区混凝土截面承担的剪力）,（2）The vertical component of the interlocking force between the aggregates on the two sides of the diagonal crack.（斜裂缝交界面骨料的咬合与磨擦作用传递的剪力）,（3）The dowel action of the longitudinal reinforcing bars crossing the diagonal crack（纵向钢筋的销栓作用传递的剪力）.,The total ultimate shear resistance of the diagonal section,三个剪力分量的大小随着梁的不同工作阶段而变化, At the initial stage of the diagonal crack,骨料的咬合力占了很大比例，但随着裂缝的开展，其所承担的剪力迅速减少,Because the dowel shear acting on the longitudinal reinforcing rods may develop tearing tensile stress in the concrete between the rods,（作用在纵筋的销栓力可能产生沿纵筋的劈裂裂缝，使销栓作用大大降低）,Consequently, the only reliable contribution to the shear resistance of a member without web reinforcement is the shear strength,（无腹筋构件剪力的三个组成部分中，只有斜裂缝上端截面承担的剪力最为稳定）,In order that the member not to be failed by shear, the following condition must be fulfilled,Take moment about the compression force of the concrete（对混凝土压力作用点取矩）, the moment acting on the diagonal section is resisted by,Again the only reliable resisting moment is due to the longitudinal reinforcement. In order that the member not to be failed by the moment on the diagonal section, the condition to be fulfilled is,构件的应力状态在斜裂缝出现后发生了以下变化,（1）斜裂缝出现前，剪力由梁全截面承担，但在斜裂缝出现后，剪力由斜裂缝上端剪压区的混凝土截面来承担，因而剪压区的剪应力显著增大；,（2）在斜裂缝出现前，在图5.3中截面E处纵筋拉力的拉应力由 决定，在斜裂缝出现后，E处的纵筋拉力由C处的弯矩 决定，由于 ，故斜裂缝出现后纵筋的拉应力将显著增大；,（3）纵筋应力突然增大，使斜裂缝的宽度加大，向上延伸到剪压区，使剪压区高度减小，混凝土的压应力突然增大；,（4）斜裂缝出现后，纵筋间的混凝土可能产生沿纵筋的撕裂裂缝 。,随着荷载的继续增加，剪压区混凝土承受的剪应力和压应力也 继续增加，混凝土处于剪压复合受力状态，当达到此种状态的极限 强度时，剪压区混凝土发生破坏，亦即发生斜截面破坏。,5.2.3 Modes of Failure of Diagonal Section of Beams without Web Reinforcement （无腹筋梁斜截面的破坏形态）,Diagonal Compression Failure（斜压破坏）,These beams have a small shear span/depth ratio of less than 1 for the case of concentrated loading, or have a small span/depth ratio of less than 3 for the case of distributed loading.,The concrete between the support and the concentrated load is crushed by the principle compression（支座与集中荷载之间的混凝土被斜向压酥而破坏）.,抗剪承载力取决于混凝土的抗压强度,2.Shear Compression Failure （剪压破坏）,The concrete at the tip of the crack is crushed by the principle compression（斜裂缝上端剪压区的混凝土被压碎而破坏）.,梁破坏时的荷载明显高于斜裂缝出现时的荷载，破坏前变形发展较充分,抗剪承载力主要取决于混凝土在复合应力下的抗压强度,3.Diagonal Splitting Failure（斜拉破坏）,斜裂缝迅速向上延伸并将构件斜向拉断为两部分，拉断面光滑。整个过程的发展非常快，破坏时的荷载等于或稍大于斜裂缝出现时的荷载，破坏前挠度很小。,抗剪承载力取决于混凝土的抗拉强度,受剪破坏均属于脆性破坏，其中斜拉破坏最明显，斜压破坏次之，剪压破坏稍好。,5.3 The Mechanism of Shear Resistance in Reinforced Concrete Beams with Web Reinforcement（有腹筋钢筋混凝土梁的受剪机理）,为了提高无腹筋钢筋混凝土梁的受剪承载力，防止梁沿斜截面发生脆性破坏。实际结构中常配有腹筋（stirrup and bend-up bar) 。,有腹筋梁斜裂缝出现前：腹筋的应力很小，腹筋作用不明显，其受力性能和无腹筋梁相近。,有腹筋梁斜裂缝出现后：形成了一种桁架-拱的受力模型，, 斜裂缝间齿状体混凝土有如斜压腹杆(diagonal compression) 箍筋的作用有如竖向拉杆 临界斜裂缝上部及受压区混凝土相当于受压弦杆 (compression chord) 纵筋相当于下弦拉杆(tension chord),1.与斜裂缝相交的腹筋可以通过以下的作用来延缓构件的破坏,The web reinforcement crossing the crack can take up part of the shear（与斜裂缝相交的腹筋可以承担部分剪力）.,(2)The presence of the web reinforcement restricts the extension of the diagonal crack and thus retains a deeper residual compression zone（腹筋能限制斜裂缝的开展和延伸，增大剪压区的面积）. The shear stress and compression stress are thereby lower.,(3)The presence of the web reinforcement restricts the widening of the diagonal cracks. Thus the aggregate interlocking force can no more be neglected in the evaluation of the ultimate shear resistance of the diagonal section（腹筋可以限制斜裂缝的宽度，因此可不再忽略骨料的咬合传递的剪力）.,（4）The transverse ties between the support and the diagonal crack effectively prevent the longitudinal rods from any vertical displacement, and the concrete in between the bars will not be torn by the dowel action of the longitudinal bars（箍筋可以有效地阻止纵筋发生垂直方向的位移，使纵筋之间的混凝土不会由于纵筋的销栓作用而被撕裂）. This effect of the ties is fully verified by experiments. So the dowel action of the longitudinal bars cannot be neglected in the evaluation of the ultimate resistance of the diagonal section（可不再忽略纵筋的销栓作用）.,2.有腹筋梁沿斜截面破坏的形态,腹筋虽然不能防止斜裂缝的出现，但却能限制斜裂缝的开展和延伸。因此，腹筋的数量对斜截面的破坏形态和受剪承载力有很大影响。,5.4 Factors affecting the strength of diagonal section（影响斜截面受剪承载力的主要因素）,5.4.1 Shear Span Ratio （剪跨比）,集中荷载作用时,均布荷载或复杂荷载作用时,“generalized shear span ratio”（广义剪跨比）,“calculated shear span ratio”（计算剪跨比）,5.4.2 Strength of Concrete（混凝土强度）,5.4.3 Stirrup Ratio and the Strength of Stirrup,The stirrup ratio is given by,5.4.4 Longitudinal Steel Ratio（纵筋配筋率）,纵筋可以抑制斜裂缝的扩展，从而可间接地提高构件的受剪承载力，随着纵筋率的增加，构件受剪承载力也稍有增加，大致呈线性关系 。但目前我国规范中的抗剪计算公式并未考虑这一影响。,5.5 Strength Calculation of Members under Shear（构件的受剪承载力计算）,5.5.1 Basic Assumption（基本假定）,The objective of shear design is to prevent shear failure prior to a ductile flexural failure.,The approach adopted by the Chinese Code GB50010-2002 is semi-rational and semi-empirical.,the strength calculation of beams under shear is based on the failure mode of shear compression failure. The diagonal compression failure and the diagonal tension failure are prevented by the art of detailing,(2)The web reinforcement intersecting with a critical diagonal section yields when the beam fails in shear,(3)The contributions from aggregate interlock and steel dowel action to shear resistance are neglected（忽略骨料的咬合作用和纵筋的销栓作用）.,The ultimate shear strength is composed of three components.,5.5.2 Design Equations for Shear Strength of Members（构件的受剪承载力计算公式）,(1) Design Equations for Shear Strength of Members without Web Reinforcement（无腹筋构件的受剪承载力计算公式）, 对无腹筋梁以及不配置箍筋和弯起钢筋的一般板类受弯构件， 其斜截面受剪承载力应按下列公式计算：,上公式未考虑剪跨比的影响，而实际上剪跨比的影响是必须考虑的,对于集中荷载作用下的独立梁，（包括作用有多种荷载，且其中集中荷载对支座截面所产生的剪力值占总剪力值的75%或75%以上的情况）,虽然给出了无腹筋梁的受剪承载力计算公式，但并不表示允许在设计中梁不配置腹筋。考虑到剪切破坏的脆性，无腹筋梁受剪承载力相对较低及正截面强度充分发展之前即由于斜截面的强度不足而发生破坏等。除非有专门规定，一般无腹筋梁应按构造要求配置箍筋。,(2) Design Equations for Shear Strength of Members with Stirrups（只配置箍筋构件的受剪承载力计算公式）,对于矩形、T形和工形截面的一般受弯构件，当仅配箍筋时,对于集中荷载作用下的独立梁（包括作用有多种荷载，且其中集中荷载对支座截面所产生的剪力值占总剪力值的75%或75%以上的情况 ），改按下式计算,(3) Design Equations for Shear Strength of Members with Both Stirrups and Bent-up Bars（配置箍筋和弯起钢筋构件的受剪承载力计算公式）,弯起钢筋所承担的剪力为弯起钢筋的总拉力在垂直于梁轴方 向的分力，按下式确定：,The design shear strength for members with both stirrups and bent-up bars is given by the equation,对于矩形、T形和工形截面的一般受弯构件，,对于集中荷载作用下的独立梁，（包括作用有多种荷载，且其中集中荷载对支座截面所产生的剪力值占总剪力值的75%或75%以上的情况 ）,V配置弯起钢筋处截面剪力设计值，当计算第一排（对支座而言）弯起钢筋时，取用支座边缘处的剪力值；当计算第二排弯起钢筋时，取前一排（对支座而言）弯起钢筋弯起点处的剪力值。,5.5.3 Bounds of Shear Strength of Beams（公式的适用范围）,(1) Upper Bound of Shear Strength（上限值）,从上面的计算公式可知，随着箍筋、弯起钢筋配置数量的增加，斜截面受剪承载力提高，但斜截面的受剪承载力存在着一个上限值。 当梁的截面尺寸确定之后，增加配箍率到一定程度后，梁的受剪承载力几乎不再增加，腹筋的应力达不到屈服强度而发生斜压破坏。此时梁的受剪承载力取决于混凝土的强度和梁的截面尺寸。 为了防止这种情况发生，规范规定对于矩形、T形和工形截面的一般受弯构件,When,When,When,the upper bound value is determined by interpolation,上限值是为了防止斜压破坏，限制梁所必须具有的最小截面 尺寸，在只配箍筋的情况下也限制了最大配箍率。,如果上述条件不能满足，则应加大梁截面尺寸或提高混凝土强度等级,2. Lower Bound of Shear Strength（下限值）,如果箍筋配量过少，则斜裂缝一出现，箍筋就很快达到了 屈服强度发生斜拉破坏，为了防止这种情况发生，规范规 定的最小配箍率为,当低于最小配箍率时，按无腹筋梁计算,如果箍筋选得较粗而配置较稀，则可能出现不与箍筋相交的斜裂缝，使箍筋无法发挥作用 。为此规范规定了箍筋和弯起钢筋的最大间距。,5.5.4 Position of critical section（计算截面的位置）,Section at the edge of support (section 1-1)（支座边缘处的截面）,(2)Section at the bent-up point of bent-up bars (section 2-2 and 3-3)（受拉区弯起钢筋弯起点处的截面）;,(3)Section at the position where there is a change in the spacing of stirrups (section 4-4)（箍筋直径或间距改变的截面）;,(4)Section at the position where there is a change in the width of the web section（腹板宽度改变处的截面）.,5.6 Shear Reinforcement Design Procedures（斜截面承载力的计算步骤）,5.6.1 Design of Web reinforcement for a Diagonal Section（截面设计）,(1)Determine the Critical Section and Calculate the Design Value of the Shear Force （确定计算截面的位置，计算剪力设计值）V,(2)Check whether（检验截面尺寸）,for,or,for,If this condition is not satisfied, the cross section has to be enlarged, or use a higher grade of concrete.,（3）Check whether（检验是否需要按计算配置腹筋）,If this condition is satisfied, the required web reinforcement can be decided according to construction requirements.,or,If this condition is not satisfied, the required web reinforcement must be decided shear strength by calculations.（如果不满足上述条件，则应按计算配置腹筋）,(4)Calculating of the Required Web Reinforcement.,a) For members with stirrups only,From equation (5-17) we have,for isolate beams under concentrated loads,b) For members with both stirrups and bent-up bars,From equation (5-20),from equation (5-21) we have,Provide that the section dimensions, the material property and the web reinforcement have been decided and also that the spacing and the thickness of transverse stirrups and bent-up bars satisfy the specified construction requirements, the ultimate shear resistance can be calculated from equations (5-17) or (5-18), and (5-20) or (5-21).（只要将各已知数据代入相关公式，即可求得解答，但应注意满足构造要求）,5.6.2 Check Web Reinforcement of Diagonal Section（截面校核）,a simply supported reinforced concrete beam with a clear span,Example 5-1,=3.56m,The section of the beam is rectangular with mm,The characteristic uniformly distributed permanent load,=25kN/m,the characteristic uniformly distributed variable load,=50kN/m,Calculation:,(1)已知条件（data),(2)计算剪力设计值（calculate the design value of shear force）,The critical section is at the edge of support, the design value of shear force V is,（3）验算梁截面尺寸（Check for adequacy of concrete section for shear）,=332475N=332.475kNV=178kN,Hence the concrete section is adequate.,（4）判别是否需要按计算配置腹筋（Check whether web reinforcement must be decided by calculation）,=93093N=93.093kNV=178kN,Hence the web reinforcement must be decided by calculation,（5）计算腹筋用量(Calculate the web reinforcement),a) With stirrups only,Try two-legged8 stirrups,Then,From the above equation we have s=137mm, and set s =130mm.,b) With both stirrups and bent-up bars,Preset two-legged8 stirrups, and spacing of stirrups =200mm according to the construction requirements.,At the diagonal section of the bent-up point of the bent-up bar (diagonal section C-J in Fig.5-15), the design value of shear force,Diagonal section C-J is required with stirrups only. The ultimate shear strength is,=154490N=154.49kN,=130kN,1.What are the major failure modes of diagonal section? In which case can they appear respectively?,Problems for discussion (思考题),2.What are the major factors affecting the diagonal ultimate strength? Please explain the influence.,3.What is the shear span ratio? Why is it one of the most important factors