混凝土设计基本原理第7章受扭构件的扭曲截面承载力学习教案

1、会计学1混凝土设计混凝土设计(shj)基本原理第基本原理第7章受扭构章受扭构件的扭曲截面承载力件的扭曲截面承载力第一页，共35页。Compatibility torsion (协调(xitio)扭矩)：statically indeterminate torsion（超静定扭矩）; secondary torsion无法根据静力平衡确定，与刚无法根据静力平衡确定，与刚度及变形度及变形(bin xng)相关相关It cannot be determined based on static equilibrium alone, and related to the torsional stiffn

2、ess and deformation of members .第1页/共35页第二页，共35页。7.2 Experiment of pure torsion1.（开裂前纯扭构件(gujin)受力分析） Mechanical analysis of pure torsion before crack主拉应力超过抗拉强度后，开裂，主拉应力超过抗拉强度后，开裂，并沿并沿45 45 斜向发展，和上下底面相斜向发展，和上下底面相交后进行发展，形成交后进行发展，形成(xngchng)(xngchng)螺旋形斜裂缝，构件破坏。螺旋形斜裂缝，构件破坏。When the principle stresses

3、When the principle stresses exceed the tensile strength, exceed the tensile strength, cracks form at the middle cracks form at the middle point of longer side and point of longer side and extend diagonally along extend diagonally along 4545line line toto the neighboring the neighboring faces. Finall

4、y, cracks are faces. Finally, cracks are spiral when the member reaches spiral when the member reaches its ultimate capacity.its ultimate capacity.Spiral cracks第2页/共35页第三页，共35页。2. Torsional reinforcements（受扭钢筋(gngjn)）StirrupsLongitudinal bars第3页/共35页第四页，共35页。2. 受扭破坏(phui)模式scarce-reinforced failure（

5、少筋破坏）（少筋破坏）Tension failureUnder-reinforced failure（适筋破坏）（适筋破坏）Bending failureUnder-reinforced member , scarce-reinforced member , Partially over-reinforced member , Over-reinforced member When member is adequately reinforced , the reinforcements yield before concrete crushes.Calculation of torsional

6、 strength（承载力计算(j sun)）When torsional reinforcements are inadequate , members fail as soon as cracks form.Minimum amount of torsional reinforcements（最小钢筋(gngjn)用量）第4页/共35页第五页，共35页。Partially over-reinforced failure（部分(b fen)超筋）Over-reinforced Failure（全部超筋（全部超筋）Compression failureWhen two types of tor

7、sional reinforcements are excessive , the reinforcements do not yield before concrete crushes.When one type of torsional reinforcements is excessive , the excessive reinforcements do not yield before concrete crushes.Check the minimum dimension of section（最小截面(jimin)尺寸验算）Control the ratio of longitu

8、dinal bars to stirrups （）第5页/共35页第六页，共35页。1、开裂(ki li)扭矩（Cracking torque) Tcr 45F1F2F3F4tttcrWfbhbfT)3(6.2ttcrWfT7 . 0tPrinciple stressIf concrete is ideal plastic material, member cracks when principle stresses at all points of section exceed tensile strength (若混凝土时理想塑性，则截面(jimin)上所有点的主拉应力达到抗拉强度构件才开

9、裂）第6页/共35页第七页，共35页。2、Torsional capacity of member with torsional reinforcements（配筋受扭构件（配筋受扭构件(gujin)承载力）承载力）(1) 力学模型(mxng)-空间桁架（space truss analogy）Longitudinal bars- tension chords（受拉弦杆）Stirrups-tension web members（受拉腹杆）concrete-compression diagonals （受压斜杆(xi n)）第7页/共35页第八页，共35页。cosDDsinD2dcorTqtA

10、cosFFD 13sincorDqb coscoscotsin13corcorqbFFDqb cotcorFFqh 12cotcot2corcorcorTuFquA1-3片片水平水平(shupng)力和竖向力平衡力和竖向力平衡3F1F箍筋第8页/共35页第九页，共35页。corNqb假设钢筋(gngjn)均屈服tan12styvcorTNAfsA cot2corstlycorTuFA fA tan11yvstcorystlf A uf A s T12yvstcoruf A As 1ystlyvstcorf A sfA u 1Ncorbcotcorb 3F1F箍筋/(cot/ )tantan12

11、corcorcorTNN nqbbsqssA第9页/共35页第十页，共35页。(2) Torsional capacity of rectangular member under pure torsion（矩形截面(jimin)纯扭构件受扭承载力）corstyvttscuAsAfWfTTT12 . 135. 0yvycorststlffuAsA1第10页/共35页第十一页，共35页。TWWTWebttww.TWWTflangeecompressivttff. TWWTflangeTensilettff. )3(62bhbWw)(22 bbhWfftf)(22bbhWfftftftftwtWWW

12、W第11页/共35页第十二页，共35页。1、Experiment and failure modesFlexure-typed failure（弯型破坏）弯型破坏）Torsion-typed failure（扭型扭型破坏）破坏）Torsion and shear-typed failure（扭剪型破坏）7.4 Torsional capacity of member under combined flexure, shear and torsion（弯、剪、扭构件(gujin)承载力）Flexure is dominant.（弯矩占（弯矩占优势）优势）Concrete at the botto

13、m cracks, then extending to the neighboring sides. Finally, concrete at the top crushes.（底部先开裂，向相邻面延伸(ynshn)，顶部混凝土压碎）Torsion is dominant, at the same time the amount of reinforcements at the top is little.（扭矩占优势，同时顶部(dn b)钢筋很少）Concrete in the longer side cracks, then extending to the neighboring sid

14、e. Finally, concrete at the bottom crushes.（长边先开裂，延伸到相邻面，底（长边先开裂，延伸到相邻面，底部混凝土压碎）部混凝土压碎）Torsion and shear are dominant（扭、（扭、剪占优势）剪占优势）Concrete in the longer side cracks, then extending to the neighboring side top. Finally, concrete in the opposite side crushes.（长边开裂，延伸到相邻面，长边开裂，延伸到相邻面，对边混凝土压碎）对边混凝土压碎

15、）第12页/共35页第十三页，共35页。2、Torsional capacity of member under combined flexure, shear and torsion （弯、剪、扭构件(gujin)承载力）TVBecause of torsion, the shear strength of member will lower than that of pure shear （扭矩的存在（扭矩的存在(cnzi)会降低混凝土抗剪承载力）会降低混凝土抗剪承载力）.(1.5- t)(1) Correlative relationship between shear and tors

16、ion剪、扭相关性剪、扭相关性 t -Reduction coefficient of torsional capacity（抗扭承载（抗扭承载(chngzi)了降低系数）了降低系数）Because of shear, the torsion strength of member will lower than that of pure torsion.（剪力的存在会降低混凝土抗扭承载力）（剪力的存在会降低混凝土抗扭承载力）第13页/共35页第十四页，共35页。5 . 100ccccVVTT受扭承载力降低系数0tccTT受剪承载力降低系数510tccVV.抗扭承载力降低抗扭承载力降低(jing

17、d)系数系数. 0 5. 0 5抗剪承载力降低抗剪承载力降低(jingd)系数系数第14页/共35页第十五页，共35页。Calculation formulas of torsion and shear010)5 . 1 (7 . 0hsnAfbhfVsvyvtt010)5 . 1 (175. 1hsnAfbhfVsvyvttcorstyvtttAsAfWfT12 . 135. 005.015.1TbhVWttFormulas of pure torsion and shear0)1(2.015.1TbhVWtt第15页/共35页第十六页，共35页。3、Design methods of me

18、mber under combined flexure, shear and torsion（弯矩扭构件设计(shj)方法）MVT受扭纵筋AstL受扭箍筋Ast1/st纵筋As或者As，As受剪箍筋Asv1/sv全部(qunb)箍筋第16页/共35页第十七页，共35页。7.7 Detailing requirements（构（构造造(guzo)）1、受扭纵筋最小配筋率ytstltlffVbTbhA6 . 0min,min,2、剪扭箍筋配箍率yvtsvsvff /28. 0min,cctfWTbhV25. 08 . 003、最小截面(jimin)尺寸第17页/共35页第十八页，共35页。4、构造

19、(guzo)配置剪扭箍筋的条件ttfWTbhV7 . 005、不考虑(kol)剪力或者扭矩的情形Shear cannot be considered (V0)035. 0bhfVt01875. 0 bhfVorcttWfT175. 0Torsion cannot be considered (T0)第18页/共35页第十九页，共35页。例题(lt)图第19页/共35页第二十页，共35页。1、计算(j sun)简图及内力kNt5916. 5)12. 03 . 1 (4 . 1)12. 02/3 . 1 (3 . 16 . 3mkNl tT.725 . 25916. 52.mkNTkNVmkNM.

20、7,30,.14内力：2、几何(j h)参数36210608. 44608000)3(6mmbhbWt220/43. 1/3 .14 19545240 ,25mmNfmmNfmmhmmCtc，mmhbcorcor170352240例题(lt)图第20页/共35页第二十一页，共35页。3、验算截面(jimin)尺寸575. 325. 054. 246080008 . 0100000071952401000308 . 00ctfWTbhV4、是否可按构造配置(pizh)剪扭钢筋001. 17 . 016. 24608000100000071952401000300ttfWTbhV需计算配置剪扭钢筋

21、5、验算(yn sun)是否可忽略剪力或者扭矩TmkNwftt.153. 110608. 443. 1175. 0175. 06不能忽略扭矩VkNbhft42.2319524043. 135. 035. 00不能忽略剪力构造要求第21页/共35页第二十二页，共35页。6、受弯纵筋计算(j sun)2min,211152113602 .222403 .14mmAmmfbxfAsycs2102(1 0.5)14.3 240 1950.518 (1 0.5 0.518)50.14.ucbbMf bhkN mMkN m因此，改梁可以设计成单(chn dn)筋截面（1）验算改梁是否(sh fu)可以设计

22、成单筋截面（2）配筋计算bfMhhxc12002mmx2 .222403 .140 . 11014219519562第22页/共35页第二十三页，共35页。7、受剪计算(j sun)0 . 124. 119524010608. 4.10710305 . 015 . 15 . 015 . 16630bhWTVtt0 . 1t010)5 . 1 ( 7 . 0hsnAfbhfVvyvttkNbhftt42.2319524043. 15 . 07 . 0)5 . 1 (7 . 00062. 02195270100042.231000301vvsA计算公式第23页/共35页第二十四页，共35页。8、受

23、扭计算(j sun)2 . 1取46.01702702.12.110608.443.135.01072661tstsAyvycorststlffuAsA121280360270340246.02 .1mmffsuAAyyvcorststl计算公式第24页/共35页第二十五页，共35页。2972.0240103010736VbTytstlstffVbTbhA.6 .0min,min,率要求受扭纵筋满足最小配筋%,235. 036043. 1972. 06 . 0min,st%15. 028. 0yvtsvff要求：受剪扭箍筋最小配筋率9、受剪扭钢筋(gngjn)最小配筋率验算522.046.00

24、62.011tstvsvsAsA筋率要求满足受剪扭箍筋最小配构造(guzo)要求第25页/共35页第二十六页，共35页。10、配筋522.011tstvsvsAsA2280 mmAstl2211mmAsmm1500.52278.5s 10，箍筋采用223042113280933280mmmm底层：中间层层纵筋采用三层布置，顶mmHRBmmHRB14,400210,4002直径根底层：直径根中间层顶层第26页/共35页第二十七页，共35页。1、Check the minimum dimension of section；（检查截面尺寸）2、Check if shear and torsion r

25、einforcements can be arranged according to detailing requirements；（是否可以构造配置剪扭钢筋）3、Check whether shear or torsion can be neglected. （是否可忽略(hl)V或T）4、Compute the flexural strength to determine the flexural reinforcements.（计算抗弯钢筋）5、Compute torsion strength to determine the torsional stirrups and longitudinal bars.（计算抗扭钢筋）6、 Compute the shear strength to determine the shear stirrups. （计算抗剪箍筋）7、Add the amount of the same type of reinforcements and select reinforcements（配筋）8、Sketch