混凝土的設(shè)計基本原理第7章受扭構(gòu)件的扭曲截面承載力ppt課件

1、第7章 受扭構(gòu)件承載力計算Chaper 7 Torsional strength of members7.1 （概述（概述Introduction7.2純扭構(gòu)件試驗研究）純扭構(gòu)件試驗研究） Experiment about pure torsion member7.3 （純扭構(gòu)件承載力（純扭構(gòu)件承載力Torsional capacity of members under pure torsion7.4 （彎、剪、扭構(gòu)件承載力（彎、剪、扭構(gòu)件承載力Torsional capacity of member under combined flexure, shear and torsion7.7構(gòu)造

2、要求）構(gòu)造要求） Detailing requirements7.1 Introduction概述）兩類扭矩Two types of torsion）Equilibrium torsion (平衡扭矩)：根據(jù)靜力平衡條件確定的扭矩、初始扭矩statically determinate torsion; primary torsion由靜力平衡確定，與剛由靜力平衡確定，與剛度無關(guān)度無關(guān)It is determined It is determined based on static based on static equilibrium, and not equilibrium, and not

3、 related to the related to the torsional stiffness.torsional stiffness.Compatibility torsion (協(xié)調(diào)扭矩)：statically indeterminate torsion超靜定扭矩）; secondary torsion無法根據(jù)靜力平衡確定，與無法根據(jù)靜力平衡確定，與剛度及變形相關(guān)剛度及變形相關(guān)It cannot be determined based on static equilibrium alone, and related to the torsional stiffness and def

4、ormation of members .7.2 Experiment of pure torsion1.（開裂前純扭構(gòu)件受力分析） Mechanical analysis of pure torsion before crack主拉應(yīng)力超過抗拉強度后，開裂，主拉應(yīng)力超過抗拉強度后，開裂，并沿并沿45 45 斜向發(fā)展，和上下底面斜向發(fā)展，和上下底面相交后進行發(fā)展，形成螺旋形斜相交后進行發(fā)展，形成螺旋形斜裂縫，構(gòu)件破壞。裂縫，構(gòu)件破壞。When the principle stresses When the principle stresses exceed the tensile streng

5、th, 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 to the neighboring line to the neighboring faces. Finally, cracks are faces. Finally, cracks are spiral when

6、 the member spiral when the member reaches its ultimate capacity.reaches its ultimate capacity.2. Torsional reinforcements受扭鋼筋）StirrupsLongitudinal bars2. 受扭破壞模式scarce-reinforced failure少筋破壞）Tension failureUnder-reinforced failure適筋破壞）Bending failureUnder-reinforced member , scarce-reinforced member

7、 , Partially over-reinforced member , Over-reinforced member When member is adequately reinforced , the reinforcements yield before concrete crushes.Calculation of torsional strength承載力計算）When torsional reinforcements are inadequate , members fail as soon as cracks form.Minimum amount of torsional r

8、einforcements最小鋼筋用量）Partially over-reinforced failure部分超筋）Over-reinforced Failure全部超筋）Compression failureWhen two types of torsional reinforcements are excessive , the reinforcements do not yield before concrete crushes.When one type of torsional reinforcements is excessive , the excessive reinforce

9、ments do not yield before concrete crushes.Check the minimum dimension of section最小截面尺寸驗算）Control the ratio of longitudinal bars to stirrups （）7.3 Torsional capacity of member under pure torsion （純扭構(gòu)件抗扭承載力）1、開裂扭矩Cracking torque) Tcr 45F1F2F3F4tttcrWfbhbfT)3(6.2ttcrWfT7 . 0tPrinciple stressIf concret

10、e is ideal plastic material, member cracks when principle stresses at all points of section exceed tensile strength (若混凝土?xí)r理想塑性，則截面上所有點的主拉應(yīng)力達到抗拉強度構(gòu)件才開裂）2、Torsional capacity of member with torsional reinforcements配筋受扭構(gòu)件承配筋受扭構(gòu)件承載力）載力）(1) 力學(xué)模型-空間桁架space truss analogy）Longitudinal bars- tension chords受拉弦

11、桿）Stirrups-tension web members受拉腹桿）concrete-compression diagonals （受壓斜桿）cosDDsinD2dcorTqtA cosFFD 13sincorDqb coscoscotsin13corcorqbFFDqb cotcorFFqh 12cotcot2corcorcorTuFquA1-3片片水平力和豎向力平衡水平力和豎向力平衡3F1F箍筋corNqb假設(shè)鋼筋均屈服tan12styvcorTNAfsA cot2corstlycorTuFA fA tan11yvstcorystlf A uf A s T12yvstcorufA As

12、1ystlyvstcorf A sf A u 1Ncorbcotcorb 3F1F箍筋/(cot/ )tantan12corcorcorTNN nqbbsqssA(2) Torsional capacity of rectangular member under pure torsion矩形截面純扭構(gòu)件受扭承載力）corstyvttscuAsAfWfTTT12 . 135. 0yvycorststlffuAsA1T member and -shaped member under pure torsionT形和工形截面構(gòu)件純扭）nThe section is divided into sever

13、al rectangular section.（截面分割成幾個矩形部分）TWWTWebttww.TWWTflangeecompressivttff. TWWTflangeTensilettff. )3(62bhbWw)(22 bbhWfftf)(22bbhWfftftftftwtWWWW1、Experiment and failure modesFlexure-typed failure彎型破壞）Torsion-typed failure扭型破壞）Torsion and shear-typed failure扭剪型破壞）7.4 Torsional capacity of member unde

14、r combined flexure, shear and torsion彎、剪、扭構(gòu)件承載力）Flexure is dominant.（彎矩占優(yōu)勢）Concrete at the bottom cracks, then extending to the neighboring sides. Finally, concrete at the top crushes.（底部先開裂，向相鄰面延伸，頂部混凝土壓碎）Torsion is dominant, at the same time the amount of reinforcements at the top is little.（扭矩占優(yōu)勢

15、，同時頂部鋼筋很少）Concrete in the longer side cracks, then extending to the neighboring side. Finally, concrete at the bottom crushes.（長邊先開裂，延伸到相鄰面，底部混凝土壓碎）Torsion and shear are dominant扭、剪占優(yōu)勢）Concrete in the longer side cracks, then extending to the neighboring side top. Finally, concrete in the opposite s

16、ide crushes.（長邊開裂，延伸到相鄰面，對邊混凝土壓碎）2、Torsional capacity of member under combined flexure, shear and torsion （彎、剪、扭構(gòu)件承載力）TVBecause of torsion, the shear strength of member will lower than that of pure shear （扭矩的存在會降低混凝土抗剪承載力）（扭矩的存在會降低混凝土抗剪承載力）.(1.5- t)Correlative relationship between shear and torsion剪

17、、扭相關(guān)性剪、扭相關(guān)性 t -Reduction coefficient of torsional capacity抗扭承載了降低系數(shù)）抗扭承載了降低系數(shù)）Because of shear, the torsion strength of member will lower than that of pure torsion.（剪力的存在會降低混凝土抗扭承載力）（剪力的存在會降低混凝土抗扭承載力）5 . 100ccccVVTT受扭承載力降低系數(shù)0tccTT受剪承載力降低系數(shù)510tccVV.抗扭承載力抗扭承載力降低系數(shù)降低系數(shù). 0 5. 0 5抗剪承載力抗剪承載力降低系數(shù)降低系數(shù)Calcul

18、ation formulas of torsion and shear010)5 . 1 (7 . 0hsnAfbhfVsvyvtt010)5 . 1 (175. 1hsnAfbhfVsvyvttcorstyvtttAsAfWfT12 . 135. 005.015.1TbhVWtt0)1(2.015.1TbhVWtt3、Design methods of member under combined flexure, shear and torsion彎矩扭構(gòu)件設(shè)計方法）受扭縱筋A(yù)stL受扭箍筋A(yù)st1/st縱筋A(yù)s或者As，As受剪箍筋A(yù)sv1/sv全部箍筋7.7 Detailing requ

19、irements構(gòu)構(gòu)造）造）1、受扭縱筋最小配筋率ytstltlffVbTbhA6 . 0min,min,2、剪扭箍筋配箍率yvtsvsvff /28. 0min,cctfWTbhV25. 08 . 003、最小截面尺寸4、構(gòu)造配置剪扭箍筋的條件ttfWTbhV7 . 005、不考慮剪力或者扭矩的情形Shear cannot be considered (V0)035. 0bhfVt01875. 0 bhfVorcttWfT175. 0Torsion cannot be considered (T0)例題n雨篷剖面見圖7-16。雨篷板上承受均布荷載已包括板的自身重力q=3.6kN/m2設(shè)計值）

20、，在雨篷自由端沿板寬方向每米承受活荷載p=1.4kN/m設(shè)計值）。雨篷梁截面240mmX240mm，計算跨度2.5m，采用C30混凝土，箍筋采用HPB300，縱向鋼筋采用HRB400，環(huán)境類別為二類a。經(jīng)計算知，雨篷梁彎矩設(shè)計值M=14kN.m，剪力設(shè)計值V=30kN。確定雨篷梁的配筋數(shù)量。例題圖1、計算簡圖及內(nèi)力kNt5916. 5)12. 03 . 1 (4 . 1)12. 02/3 . 1 (3 . 16 . 3mkNl tT.725 . 25916. 52.mkNTkNVmkNM.7,30,.14內(nèi)力：2、幾何參數(shù)36210608. 44608000)3(6mmbhbWt220/43.

21、 1/3 .14 19545240 ,25mmNfmmNfmmhmmCtc，mmhbcorcor170352240例題圖3、驗算截面尺寸575. 325. 054. 246080008 . 0100000071952401000308 . 00ctfWTbhV4、是否可按構(gòu)造配置剪扭鋼筋001. 17 . 016. 24608000100000071952401000300ttfWTbhV需計算配置剪扭鋼筋5、驗算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. 0

22、0不能忽略剪力構(gòu)造要求6、受彎縱筋計算2min,211152113602 .222403 .14mmAmmfbxfAsycs2102(1 0.5)14.3 240 1950.518 (1 0.5 0.518)50.14.ucbbMf bhkN mMkN m因而，改梁可以設(shè)計成單筋截面（1驗算改梁是否可以設(shè)計成單筋截面（2配筋計算bfMhhxc12002mmx2 .222403 .140 . 110142195195627、受剪計算0 . 124. 119524010608. 4.10710305 . 015 . 15 . 015 . 16630bhWTVtt0 . 1t010)5 . 1 (

23、7 . 0hsnAfbhfVvyvttkNbhftt42.2319524043. 15 . 07 . 0)5 . 1 (7 . 00062. 02195270100042.231000301vvsA計算公式8、受扭計算2 . 1取46.01702702.12.110608.443.135.01072661tstsAyvycorststlffuAsA121280360270340246.02.1mmffsuAAyyvcorststl計算公式2972.0240103010736VbTytstlstffVbTbhA.6.0min,min,率要求受扭縱筋滿足最小配筋%,235. 036043. 197

24、2. 06 . 0min,st%15. 028. 0yvtsvff要求：受剪扭箍筋最小配筋率9、受剪扭鋼筋最小配筋率驗算522.046.0062.011tstvsvsAsA筋率要求滿足受剪扭箍筋最小配構(gòu)造要求10、配筋522.011tstvsvsAsA2280 mmAstl2211mmAsmm1500.52278.5s 10，箍筋采用223042113280933280mmmm底層：中間層層縱筋采用三層布置，頂mmHRBmmHRB14,400210,4002直徑根底層：直徑根中間層頂層Design Procedure設(shè)計過程） 1、Check the minimum dimension of

25、section；（檢查截面尺寸）2、Check if shear and torsion reinforcements can be arranged according to detailing requirements；（是否可以構(gòu)造配置剪扭鋼筋）3、Check whether shear or torsion can be neglected. （是否可忽略V或T）4、Compute the flexural strength to determine the flexural reinforcements.（計算抗彎鋼筋）5、Compute torsion strength to determine the torsional stirrups and longitudinal bars.（計算抗扭鋼筋