006建筑结构(第2版)第六章 受拉构件承载力计算.doc

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1、第六章受拉构件承载力计算【学习重点】轴心受拉构件承载力计算；偏心受拉构件承载力计算。【学习目标】了解受拉构件的种类；熟悉轴心受拉构件计算的适用范围；掌握受拉构件承载力的计算方法；熟悉偏心受压构件的构造要求及计算适用范围；掌握偏心受拉构件承载力的计算方法。钢筋混凝土受拉构件按纵向拉力作用位置的不同分为轴心受拉和偏心受拉两种类型。当纵向拉力 N MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNC

2、HbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobaaaa3FF0 作用在截面形心时，称为轴心受拉构件，如钢筋混凝土屋架下弦杆、高压圆形水管及圆形水池等。当纵向拉力 N MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLb

3、vyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobaaaa3FF0 作用在偏离截面形心时，或截面上既作用有纵向拉力 N MathT

4、ypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaak

5、eaacaWGobaaaa3FF0 ，又作用有弯矩 M MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad

6、baqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbaaaa3FEF 的构件，称为偏心受拉构件，如钢筋混凝土矩形水池、工业厂房中双肢柱的肢杆等。第一节轴心受拉构件承载力计算一、轴心受拉构件的受力特点承受节点荷载的桁架或屋架的受拉弦杆和腹杆、刚架和拱的拉杆、受内压力作用的圆形储液池的环向池壁、承受内压力作用的环形截面管道的管壁等通常按轴心受拉构件计算。钢筋混凝土轴心受拉构件，开裂以前混凝土与钢筋共同负担拉力；开裂以后，开裂截面混凝土退出工作，全部拉力由钢筋承受。当钢筋应力达到其抗拉强度，截面到达受拉承载力极限状态。二、轴心受拉构件承载力计算根据承载力极限状态设计法

7、的基本原则及力的平衡条件，轴心受拉构件正截面承载力计算公式为： N MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr

8、=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobaaaa3FF0 N u = f y A s + f py A p MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm

9、0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobWaaSbaaSqaaiaadwhaaeqaaOGaeyypa0JaamOzamaaBaaaleaacaWG5baabeaakiaadgeadaWgaaWcbaGaam4CaaqabaGccqGHRaWkcaWGMbWaaSbaaSqaaiaadchacaWG5baabeaakiaadgeadaWgaaWcbaGaamiCaaqabaaaaa4C16 （6-1）式中 N MathTypeMTEF55+=f

10、eaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobaaa

11、a3FF0 轴向拉力设计值； N u MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGac

12、iGaaiaabeqaamaabaabauaakeaacaWGobWaaSbaaSqaaiaadwhaaeqaaaaa4116 轴心受拉构件正截面承载力设计值； f y MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqp

13、epm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhaaeqaaaaa4132 钢筋抗拉强度设计值， f y MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeH

14、bl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhaaeqaaaaa4132 大于300Nmm2时，按300Nmm2取值； f py MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTf

15、MBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadchacaWG5baabeaaaaa4227 预应力钢筋的抗拉强度设计值； A s MathTypeMTE

16、F55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaW

17、GbbWaaSbaaSqaaiaadohaaeqaaaaa4107 截面上全部纵向受拉钢筋的截面面积； A p MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9

18、pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadchaaeqaaaaa4104 截面上预应力钢筋的全部截面面积。由式（6-1）可知，轴心受拉构件正截面承载力只与纵向受拉钢筋有关，与构件的截面尺寸及混凝土的强度等级无关。三、轴心受拉构件构造要求（一）纵向受力钢筋轴心受拉构件的受力钢筋不得采用绑扎搭接；搭接而不加焊的受拉钢筋接头仅仅允许在圆形池壁或管中，其接头位置应错开，搭接长度应满足规范要求。为避免配筋过少引起的脆性破坏，按构件截面面积计算的全部受力钢筋的直径不宜小于12mm

19、，构件一侧受拉钢筋的最小配筋百分率不应小于0.2%和（45 f t MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr

20、=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadshaaeqaaaaa412D / f y MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqp

21、epm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhaaeqaaaaa4132 ）%的较大值，也不宜大于5%。受力钢筋沿截面周边均匀对称布置，净间距不应小于50mm，且不宜大于300mm。（二）箍筋在轴心受拉构件中，与纵向钢筋垂直放置的箍筋主要是与纵向钢筋形成骨架，固定纵向钢筋在截面中的位置，从受力角度而言并无要求。箍筋直径不应小于纵筋直径的1/4，且不应小于6mm，间距一般不应大于400mm及构件截面短边尺寸。【例

22、6-1】已知某钢筋混凝土屋架下弦，截面尺寸 b MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqa

23、aeGaciGaaiaabeqaamaabaabauaakeaacaWGIbaaaa4004 h MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0Firp

24、epeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGObaaaa400A 200mm150mm，其所受的轴向拉力设计值为300kN，钢筋为HRB335级，混凝土强度等级为C30，求纵向受拉钢筋截面面积 A s MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZ

25、LdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohaaeqaaaaa4107 并选配钢筋。 【解】由题意知此屋架下弦为轴心受拉构件，钢筋HRB335， f y MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov

26、2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhaaeqaaaaa4132 300Nmm2，C30混凝土， f t MathTypeM

27、TEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaac

28、aWGMbWaaSbaaSqaaiaadshaaeqaaaaa412D 1.43Nmm2，令 N MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0Firp

29、epeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobaaaa3FF0 N u MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9

30、pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobWaaSbaaSqaaiaadwhaaeqaaaaa4116 ，代入式（6-1），得 A s = N f y = 300000 300 =1000m m 2 MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbW

31、exLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohaaeqaaOGaeyypa0ZaaSaaaeaacaWGobaabaGaamOzamaaBaaaleaacaWG5baabeaaaaGccqGH9aqpdaWcaaqaaiaaiodacaaIWaG

32、aaGimaiaaicdacaaIWaGaaGimaaqaaiaaiodacaaIWaGaaGimaaaacqGH9aqpcaaIXaGaaGimaiaaicdacaaIWaGaamyBaiaad2gadaahaaWcbeqaaiaaikdaaaaaaa537B 纵向受拉钢筋的配筋率为： ρ= A s A = 1000 200×150 =3.3% MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaHbpGCcqGH9aqpdaWcaaqaaiaadgeadaWgaaWcbaGaam4CaaqabaaakeaacaW