chapter4 concrete structure
英文原文来源：《土木工程英语》陈瑛 邵永波主编
4.2 shear and diagonal tension inreinforced concrete beam
shear failure of reinforced concrete,more properly called /diagonal failure,is more dangerous than flexural failure because of its catastrophic nature.if a beam without properly designed shear reinforcement is overloaded to failure,shear collapse is likely to occue suddenly,with no advance warning of distress.this is in strong contrast with the natural of flexural failure.for moderate reinforced beam,flexural failure is initiated by gradual yielding of the tension steel,acompanied by obvious cracking of the concrete and large deflection,giving ample warning and providing the opportunity to take corrective measures.because of these differences in behavior reinforced concrete beams are generally provided with special shear reinforcement to ensure the flexural failure would occur before shear failure if the member should be severly overloaded.
钢筋混凝土的剪切破坏，常常称为斜截面破坏，由于脆性特性比弯曲破坏更危险。如果一根没有合理设计抗剪钢筋的梁因超载破坏，剪切破坏有可能突然发生，没有任何破坏预兆。这与弯曲破坏形成明显的对比。对适筋梁，弯曲破坏以钢筋的逐步屈服为开始，并且混凝土明显开裂，有大的挠度。提供足够的预警并提供采取加固措施的机会。由于受力性能的不同，钢筋混凝土梁通常配置特殊的抗剪钢筋以确保当构件严重超载时发生弯曲破坏而不是剪切破坏。
4.2.1 formation of diagonal cracks due to shear
in the case of simply supported beam subjected to two-point loading,the moment and shear distribution is such that the moment is constant in the mid span and in two side spans,shear force is constant.these two side sapns are called "shear span".for the elastic beam,the flexure stress σ ,shear stress τ ,and the principal tensile stress σ1 are determined to the beam theory.since concrete material is weak in tension,the magnitude and direction of principal tensile stress are important.at the location of zero shear stress,i,e,the extreme tension fiber,the principal tensile stress takes the horizontal direction.at the point of zero normal stress,i,e,the neutral axis ,the principal tensile stress is euqal to shear stress,and its direction is 45 degrees with respect to the member axis.
在受两点荷载的简支梁中，弯矩和剪力的分配是在中间跨弯矩为常数，在两边跨剪力为常数。两边跨称为剪跨。对弹性梁，弯曲正应力σ，剪应力τ，以及主拉应力σ1根据梁理论确定。因为混凝土材料抗拉强度低，主拉应力的方向和大小很重要。在剪应力为零的区域，比如，梁受拉边缘，主拉应力的方向是水平的。在正应力为零的区域，比如，中性轴处，主拉应力等于切应力，应力方向与轴线呈45度。
as the principal tensile stress inncreases and exceeds the tensile strength of concrete,cracks occurs in the direction perpendicular to the direction of principal tensile stress.
当主拉应力增长并超过混凝土抗拉强度，裂缝形成在与主拉应力方向垂直的方向上。
4.2.2 reinforced concrete without shear reinforcement
for a reinforced concrete without shear reinforcement ,flexural crack is first formed in regions of large moments,and its direction is perpendicular to the member axis.the flexural tensile strength can be funished by the tension steel after the formation of tension cracks in the concrete.the longitudial tension reinforcement has been so calculated and placed that it is chiefly effective resisting longitudial tension near the tension face. it does not reinforce the tensionally weak concrete against the diagonal tension stresses that occur elsewhere,caused by shear alone or by the combined effect of shear and flexural.eventually ,these stresses attain magnitudes suffucuent to open additional tension caracks in a direcion perpendicular to the local tension stress.they are known as diagonal cracks ,in distinction to the vertical flexural cracks.diagonal cracks occur in regions in which the shear forces are high.
对没有抗剪钢筋的钢筋混凝土梁，弯曲裂缝形成在弯矩较大的区域，并且裂缝的方向与构建轴线的方向垂直。在混凝土中抗拉裂缝形成后抗拉钢筋将提供抗拉强度。纵向抗拉钢筋已经被计算并配置，主要抵抗受拉侧的拉力。纵向钢筋并没有增强抗拉强度低的混凝土抵抗随处可见的斜拉应力，斜拉应力是由剪力单独产生或者弯剪共同作用产生的。最终，这些应力达到足够大以在主拉应力垂直的方向上开展附加拉裂缝。这些裂缝称为斜裂缝，区别于竖向抗弯裂缝。斜裂缝在剪力大的区域开展。
three types of failure modes have been observed in many tests of reinfoeced beam without shear reinforcement .the mode of failure is influenced by the shear span to effective depth ratio given by λ=a/h0,where a is the distance between the support and the nearest concentrated load.
已经在众多没有腹筋的钢筋混凝土梁测试中观测到三种形式的破坏。破坏的形式受剪跨比λ=a/h0影响，其中a是支座与最近集中荷载之间的距离。
(1)diagonal tension failure.the diagonal crack,once formed,spreads either immediately or at only slightly higher load,traversing the entire beam from the tension reinforcement to the compression face,splitting it into two and failing the beam.this possess is sudden and without warning and occurs chiefly in the beams with sheat sapn to effective depth ration of about 3 or more.
（1）斜拉破坏。斜裂缝一旦形成，要么立刻开展，要么在稍微大一点的荷载作用下开展，从受拉钢筋到受压侧穿过整个梁，将梁劈裂为两半并使梁破坏。这一过程是突然地并且没有预兆，主要发生在剪跨比大于3的梁中。
(2)shear compression failure.the diagonal crack,once formed,spreads toward and partially into the compression zone but stops penetrating to the conpression face.in this case no sudden collapse occurs,and the failure load may be significantly higher than that at which the diagonal cracks first formed.the stress state becomes like a compression arch formed by diagonal cracks.in this case the beam fails when this arch crushes under diagonal compression.this behavior is chiefly observed in the beam with shear span to effevtive depth ratio ranging from 1to 3.
（2）剪压破坏。斜裂缝一旦形成，向上开展并且部分进入受压区但不会开展到受压侧。在这种情况下，不会发生突然破坏，并且破坏荷载可能远远大于斜裂缝首次形成时的荷载。此时应力状态像一个由斜裂缝形成的压拱。这种情况中，梁在拱在斜向压力下压碎时发生破坏。这种力学性能主要在剪跨比在1-3的梁中观测到。
(3)diagonal compression failure. for the beam of so-called deep beam,i,e,the shear span to effective depth ratio is very small(a/h0<1.0),the shear resisiting mechanism is formed as a compression strut joining the loading and support points.
斜压破坏。对所谓的深梁，比如，剪跨比非常小，抗剪机制是通过有荷载和支座点的压杆拱形成的。
since all of these failures are preceded by diagonal cracking of web concrete,so they are called as"shear failure".
由于这些破坏都是以腹板混凝土斜向开裂为先的，所以被称为剪切破坏。
figure 4.14 shows a portion of a beam in which a diagonal tension crack has formed. considering the part of the beam to the left of the crack,shown in solid line.there is a external upward shear force Vext acting on this portion.
图4.14所示，已经形成斜拉裂缝的梁的一部分。考虑裂缝左侧的梁部分，图中已实线表示。有一个外部竖向剪力Vext作用在这一部分。
once a crack is formed,no tension force perpendicular to the crack can be transmitted arcoss it.however,as long as the crack is narrow,it can still transmit force in its own plane through interlocking of the surface roughness.the aggregate interlock force ,Vi.amounts to one-third and more of the shear force. the other internal forces are those in the uncracked portion of the concrete,Vcz,and those across the longitudinal steel,acting as a dowel,Vd.
裂缝一旦形成，没有垂直于裂缝的拉力可以穿过裂缝传递。但是，裂缝足够窄，裂缝仍然可以通过表面粗糙度的咬合在裂缝面上传递力。骨料咬合力，Vi，占剪力的1/3甚至更多。其余的内力是未开裂混凝土部分中的Vcz，纵筋销栓作用力Vd。
4.2.3 reinforced concrete with shear reinforcement
economy of design demands that a flexural member be capable of developing its full moment capacity rather than having its strength limited by premature shear failure.this is also desirable beacuse structures,if overloaded,should not fail in a sudden and explosive manner,but show adequate ductility and warining of impending distress. the latter is typical of flexural failure casued by the yielding of the longitudinal bars,which is preceded by gradual excessing large deflections and noticeable widening of cracks.therefore,special shear reinforcement,known as web reinforcement ,is used to increase this strength.
设计的经济性要求受弯构件能够充分发挥抗弯承载力而不是由于剪切破坏确定的强度。这也是合适的因为结构如果超载，不应该以突然、爆炸性的方式破坏，而是应该表现足够的延性并且破坏前的预警。后者通常是由纵筋屈服造成的受弯破坏，以逐渐变大的挠度以及裂缝明显的变宽为先。因此，特殊的抗剪钢筋，并称为腹筋，被用以提高这种强度。
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types of web reinforcement
typically,web reinforcement is provided in the form of vertical stirrups,spaced at varying intervals along the axis of the beam depending on the requirement,as shown in figure 4.15.multiple-leg stirrups suchs as shown in figure 4.15d are sometimes necessary.relatively small sized bars are used, generally 6 to 12 mm in diameters.stirrups are formed to fit around the main longitudinal bars at the bottom and hooked or bent around longitudinal bars at the top of the member to improve anchorage and provide support during construction.
通常情况下，腹筋以箍筋的形式配置，根据要求沿梁轴线按不同间隔分布，如图4.15所示。如图4.15d中的多肢箍在有些情况下是必要的。通常使用相对小尺寸的钢筋，直径为6-12mm。箍筋以绕过底部的主要的纵向钢筋并且绕过顶部钢筋形成钩形或者弯曲，以加强锚固并且为纵筋提供支撑。
alternatively,shear reinforcement may be provided by bending up a part of the longitudinal steel where it is no longer needed to resist flexural tension,as suggested in figure 4.15e.in continuous beams,these bent-up bars may also provide all or part of the necessary reinforcement for negative moment.the requirement of longitudinal flexural reinforcement often conflict with those for diagonal tension,and because the saving in steel resulting from the use of the capacity of bent bars as shear resistance is small,most designers prefer to include vertical stirrups to provide for all the shear reinforcement ,not counting on the bent part of the longitudinal bars,if bent bars are used,only to increase the overall safety against diagonal tension failure.
另外，抗剪钢筋可以由弯起一部分抗弯不需要位置处的钢筋配置，如图4.15e所示。在连续梁中，这些弯曲钢筋可能也作为部分或者全部抵抗负弯矩所必要的钢筋。纵向抗弯钢筋的需求经常与斜向拉力所需的钢筋矛盾，并且弯起钢筋节约的钢筋量很小，很多设计者更倾向于配置箍筋以提供全部的抗弯钢筋，不计入弯起的纵筋，如果使用弯起钢筋，仅仅提高抵抗斜拉破坏的整体安全性。
2.behavior of web reinforced concrete beams
web reinforcement has no noticeable effect prior to the formation of diagonal cracks.in fact,measurements show that the web steel is practically free of stress piror to crack formation.after diagonal cracks have been developed,web reinforcement augments the shear resisitance of a beam in four separate ways:
腹筋在斜裂缝形成之前没有明显的作用。事实上，试验数据说明腹筋在裂缝形成之前几乎是零应力。斜裂缝形成之后，腹筋从四个方面增强梁的抗剪强度
(1)part of the shear force is resisted by the bars that traverse a particular crack.
部分剪力由穿过裂缝的箍筋抵抗。
(2)the presence of these same bars restricts the growth of diagonal cracks and reduces their penetration into the compression zone.this leaves more uncracked concrete available at the end of the crack for resisting the combined action of shear and compression.
箍筋的配置限制了斜裂缝的开展并且减少向受压区延伸的趋势。这使得更多的未开裂混凝土用于在裂缝末端抵抗剪力和压力的共同作用。
(3)the stirrups also counteract the widening of the cracks ,so that the two crack faces stay in close contact,this makes for a significant and reliable interlock force.
箍筋也限制裂缝的变宽，因此两个裂缝面距离很近，这产生了一个重要可靠的骨料咬合力。
(4)the stirrups tie the longitudinal reinforcement into the main bulk of the concrete.this provides restraint against the splitting of concrete along the longitudinal reinforcement,and increases the shear of the shear force resisted by dowel action.
箍筋束缚混凝土主体内的纵筋。这提供了抵抗沿纵筋劈裂的抵抗力，并提高了销栓作用。
from this it is clear that failure will be imminent when the stirrups start yielding.this not only exhausts their own resistance but also permits a wider crack opening with consequent reduction of the beneficial restraining effects.point (2) to point (4),above.
从这可以清楚知道当箍筋开始屈服时破坏即将发生。这不仅耗尽了自身的抵抗能力而且允许更宽裂缝的开展，降低上述2-4条有力的约束作用。
the observed failure modes in reinforced beams with shear reinforcement are similar to that in beams without shear reinforcement.the modes of failure are influenced by shear span to effective depth ratio and stirrups ratio ρsv.
有腹筋梁的钢筋混凝土梁中观测到的破坏模式与无腹筋梁的破坏模式相似。破坏模式受剪跨比和配箍率影响。
3.shear capacity of reinforced concrete
since web reinforcemet is ineffective in the uncracked beam, the magnitude of the shear force or stress that causes cracking to occur is the same as that in a bram without web reinforcement.most frequently ,web reinforcement consists of vertical stirrups.the forces acting on the portion of such a beam between the crack and the nearby support are shown in figure 4.16.they are the same as those of figure 4.14,except that each stirrup traversing the crack exerts a force on the given portion of the beam.here Asv is the cross-section area of the stirrup (in the case of the U-shaped stirrup of figure 4.15b it is twice the area of one bar)and fyv is the tensile stress in the stirrup.
由于在未开裂梁中腹筋是不起作用的，使裂缝产生的剪力或者剪应力的大小与无腹筋梁中相同。大多数情况下，腹筋是由箍筋组成。作用于裂缝和最近支座部分的力如图4.16所示。他们与图4.14中的相同，除了穿过裂缝的每一根箍筋在给定梁部分上产生力。其中Asv 是箍筋截面积。（在U形箍筋中面积是单根钢筋截面积的两倍）并且Asv 是箍筋中的拉应力。
the sum of the first three internal shear components inequation is the shear strength contribution of the concrete (including the contribution from the uncracked concrete,aggregate interlock and dowel action) to the total shear resistance,and is devoted Vc.thus,the shear capacity of reinforced concrete beam with stirrups is V<=Vcs=Vc+Vsv
三种内部剪力组成的总和是混凝土抗剪强度对整体抗剪强度的贡献。（包括未开裂混凝土的贡献，骨料咬合力以及销栓作用）因此，配置箍筋的钢筋混凝土梁的抗剪承载力是 V<=Vcs=Vc+Vsv
for commom members with rectangular,T or I section subjected to shear and flexure,according to GB50010-2002 Vcs=0.7ftbh0+1.25fyv*Asv/s*h0. for isolated beam subjected to concentrated loads Vcs=1.75/(λ+1)*ftbh0+fyv*Asv/s*h0. where λ is shear span to effective depth ratio.λ is not to be taken greater than 3or less than 1.5.
对一般的承受剪力和受弯的矩形、T或者I形截面构件，根据GB50010-2002 ，Vcs=0.7ftbh0+1.25fyv*Asv/s*h0。对承受集中荷载的独立构件Vcs=1.75/(λ+1)*ftbh0+fyv*Asv/s*h0，其中 λ 是剪跨比。 λ 的范围是1.5-3.
in practice,shear design is carried out at only one or two critical loactions.the critical locations need be taken at the face of the support,at the section where web width changes,where tension reinforcement bends up ,or where stirrup spacing varies.
在工程设计中，抗剪设计仅在一到两个重要位置验证。重要的结构未知有支座截面、腹板宽度变化位置、抗弯钢筋弯起处，或者箍筋间距变化处。
4.limitation on cross-section dimension
when beam is heavily reinforced with shear stirrups,failure is due to local crushing of concrete in the compression strut prior to yielding of the shear reinforcement.to prevent the britte diagonal compression failure,the cross-section dimension of reinforced concrete beam subjected to shear and moment is limited to V<=0.25βcfcbh0 when hw/b<=4 or V<=0.20βcfcbh0 when hw/b<=4and the linear interpolation method shall be adopted when 4<hw/b<6. where βc=strength reduction factor for high strength concrete.
当梁配置过多的抗剪箍筋，破坏是由于受压杆中局部混凝土压碎而不是抗剪钢筋的屈服。为防止脆性斜压破坏，承受剪力和弯矩的钢筋混凝土梁，当hw/b<=4，横截面尺寸限定为 V<=0.25βcfcbh0；当hw/b<=4，横截面尺寸限定为V<=0.20βcfcbh0；当4<hw/b<6，采用插值法。其中βc是高强度混凝土的强度折减系数。
5.minimum web reinforcement
when stirrup in a beam are not adequate to constrain cracks,diagonal tension failure occurs on the formation of first diagonal tension cracking and stirrups yield.a minimum stirrup ratio should apply in the beam where V>0.7ftbh0
当梁中配置的箍筋不足以限制裂缝，斜拉破坏发生在首条斜拉裂缝开裂过程中并且箍筋屈服。在梁中最小配箍率限定为V>0.7ftbh0
6.detailing of transverse reinforcement
stirrrups are unable to resist shear unless they are crossed by an inclined crack.it is possible for a 45du crack to cross the web without intersecting a stirrup if the stirrup spacing exceeds beam depth.to ensure that a diagonal tension crack will be crossed by at least one stirrup and to reduce diagonal tension crack widths when V>0.7ftbh0,the maximum spacing and minimum diameter of stirrups are limited.
箍筋不能抗剪，除非箍筋被斜裂缝穿过。当箍筋间距超过梁的高度，有可能有未穿过箍筋的45度裂缝穿过腹板。当V>0.7ftbh0，为确保斜拉裂缝至少被一根箍筋穿过并且减小斜拉裂缝的宽度，箍筋的最大间距和最小直径被限定。
if the shear force is no greater than Vc,then theoretically no web reinforcement is required.even in such a case,to ensure that the sudden failure doesn't occur on the formation of a diagonal tension crack caused by an unecpected ovweload，GB50010-2002 specifies that the reuqired maximum spacing and the minimum diameter of stirrups when V<=0.7ftbh0.
当剪力不超过Vc，那么理论上不需要抗剪钢筋。甚至在这种情况下，为确保在由于超载造成的斜拉裂缝形成过程中不会发生突然地破坏。GB50010-2002 规定，当V<=0.7ftbh0时箍筋的最大间距和最小直径。
| diagonal tension failure |
斜拉破坏 |
| shear compression failure |
剪压破坏 |
| diagonal compression failure |
斜压破坏 |
| shear span |
剪跨 |
| shear span to effective depth ratio |
剪跨比 |
| contribution from the uncracked concrete |
未开裂混凝土贡献 |
| aggregate interlock force |
骨料咬合力 |
| dowel action |
销栓作用 |
| web reinforcement |
腹筋 |
| multiple-leg stirrup |
多肢箍 |
| stirrup ratio |
配箍率 |
| principal tensile stress |
主拉应力 |
| neutral axis |
中性轴 |
| imminent |
即将发生的 |
| linear interpolation |
线性内插法 |
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