1、Chapter4 Shear Capacity of Flexural Member,4.1 Introduction 4.2 Diagonal cracks（斜裂缝）, Shear span ratio（剪跨比） and failure modes of inclined section（斜截面的破坏形态） 4.3 Inclined-section shear mechanism of simple beam,4.4 Calculation of shear capacity 4.5 Detailing requirements satisfying inclined-sectional f
2、lexural capacity(保证斜截面受弯承载力的构造措施) 4.6 Some detailing requirements for beams and slabs,5.1 Introduction,4.2 Diagonal crack, shear span ratio and failure modes of inclined section,4.2.1 Web-shear cracks and flexural-shear cracks4.2.2 Shear span ratio 4.2.3 Three failure modes of inclined section,1. St
3、ress analysis of flexural member,4.2.1 Flexural-shear cracks and web-shear cracks,Principal tensile stress,Principle stress trajectory,2、Types of cracks,4.2.2 Shear span ratio(shear span-to-effective depth ratio),Generalized shear span ratio（广义剪跨比）：,Calculated shear span-to-effective depth ratio ：,4
4、.2.3 Three main failure modes of inclined section,1,（1）Diagonal compression failure：,1. Failure modes of inclined section of beam without web reinforcements(无腹筋梁的斜截面破坏形态),13,（2）Shear compression failure：,（3）Diagonal tension failure：,3,The shear capacity for the three failure modes： Diagonal compress
5、ion shear compression diagonal tension， They are all brittle failure,The amount of web reinforcement is appropriate,3 and the amount of reinforcement is inadequate,The amount of web reinforcement is too much,Avoid it by shear capacity design,2. Failure modes of inclined section of beam with web rein
6、forcements(有腹筋梁的斜截面破坏形态),Avoid it by stipulate the minimum amountof shear reinforcement,Avoid it by Check the section dimension,4.3 Mechanical mechanism of inclined section,4.3.1 Tied-arch structure,The forces in the inclined section ： (1)Tension force T in longitudinal reinforcement ； (2) Shear for
7、e Vc and compression force C in the residual concrete； (3)Interlock force of aggregate Va； (4) Dowel force Vd。,4.3.3 Truss model,C,Diagonal compression strut,Vertical tension strut,Tension chord,Compression chord,The forces in the inclined section ： (1)Tension force T in longitudinal reinforcement ；
8、 (2) Shear fore Vc and compression force C in the residual concrete； (3)Interlock force of aggregate Va； (4) Dowel force Vd。 (5) Tension force in stirrups Vsv,4.4.1 The main factors affecting shear capacity,4.Reinforcement ratio,1. Shear span ratio,2.Streength of concrete,4.4 Formulas for shear capa
9、city in inclined section,4.4.2 Formulas for shear capacity in inclined section,1. Fundamental assumption,Neglect the interlock force , dowel force.,The forces balancing the Vertical force： (1) Shear fore Vc in the residual concrete； (2) Vertical component force of interlock force of aggregate Va； (3
10、) Dowel force Vd。 (4) Tension force in stirrups Vsv 。 (5) Vertical component force of tension force Vb in bent-up bars,2. Calculation formulas for shear capacity,Only Stirrup,Stirrup and bent-up bars,Independent beams prominently subjected to concentrated loads,Other beams,4、Calculation formula for
11、Vsb,as,Angle bent-up bars with respect to the axis of beam. Generally 45 ， 60when the depth of section is more than 800 mm,5. Accommodated condition of formulas,When the dimension of member is not adequate compared to the higher shear force, the beam will fail in diagonal compression mode.,（1） The m
12、inimum dimension （upper limit ),hw- web Depth of section.,.,（2） The minimum amount of stirrup（Lower limit）,6. Conditions of selecting stirrup according to minimum stirrup ration and detailing requirements,Formulas for shear capacity,（1）Independent beams prominently subjected to concentrated loads,（1
13、）Other beams,4.4.3 Stirrup Design Procedure,（1）Determine the shear force values based on clear span,（2）Check the dimensionof section,（4）Calculate the stirrup required（area、spacing、legs）,（5）Check the stirrup reinforcement ratio,（3）Determine if stirrup are required,Calculation formula forshear capacit
14、y,Example,Calculation formula for shear capacity,Only Stirrup,Stirrup and bent-up bars,Independent beams prominently subjected to concentrated loads,Other beams,4.5 Detailing Requirement for Flexural Capacity of Inclined Section,4.5.1 Moment capacity diagram（正截面受弯承载力图-材料图）4.5.2 Bent-up of longitudin
15、al reinforcements(纵向钢筋的弯起)4.5.3 Cutoff of longitudinal reinforcements(纵向钢筋的截断),4.5.1 Moment capacity diagram （正截面受弯承载力图-材料图）,Definition,2.Method to plot Mu,Calculate the moment capacity of every longitudinal steel bars，and the method is as follows:,It is the diagram of moment capacity Mu in all sect
16、ions computed based on actual amount of longitudinal reinforcements (由实际配置的纵钢筋所确定的梁上各正截面能抵抗的弯矩图形。),4.5.2 Bend point of longitudinal bars (纵筋的弯起）,Bend position:,The bend position is not at the section where the steel bars are fully stressed.(不能在钢筋充分利用截面弯起）,Fig.3,The bend point is at the distance 0.5h
17、0 beyond the fully stressed section of bars(弯起点应距离充分利用截面不小于0.5h0),4.5.3 Cutoff of longitudinal reinforcements (纵筋的截断）,1. The principles for cutoff (截断的原则)：,(1)The negative bars resisting the negative moment may be cutoff.( 允许抵抗支座负弯矩的纵筋延长截断)；,(2) The positive bars resisting the positive moment within
18、 the span may not be cutoff. (一般不截断抵抗跨中正弯矩的纵筋),Bars are cutoff at a distance beyond its theoretical cutoff point or the fully-stressed point.(在离开理论断点或充分利用点以外一定距离截断）,Method,2. Method of cutoff(截断的方法)：,Chinese Code,Fig.5,Fig.1,Fig.2,Take the bar as an example,Assuming the bar is bent up at point a, th
19、e moment capacity Mu will less than the moment M.,Fig.3,Fig. 5,4.6 Detailing requirements for beams and slabs,4.6.1 Longitudinal stressed steel bars,4.6.2 Bent-up steel bars,4.6.3 Stirrup in beams,4.6.4 Erection steel bars and other longitudinal detailing steel bars,Anchorage of longitudinal steel b
20、ars in supports (纵向受力钢筋在支座中的锚固),1)Simply supported beams,2) Continuous beams,4.6.1 Longitudinal stressed steel bars,1. Anchorage,（2）Splice of longitudinal steel bars (纵向受力钢筋搭接),（3）Erection steel bars (stirrup-support bars),（4）Longitudinal detailing steel bars along the depth of beams,Lapped splice, mechanical splice, and welded splice,2、Bent-up steel bars,3、Stirrups,Minimum diameter，maximum spacing,Take bar as an example,Two-leg (double-leg) Stirrup,20d或h0,1,
