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1、第四章受扭构件承载力计算【学习重点】纯扭构件承载力计算；弯剪扭构件承载力计算。【学习目标】了解混凝土构件受到扭转的种类；熟悉钢筋混凝土矩形截面受扭构件的破坏形态；掌握弯剪扭构件承载力的计算方法。第一节纯扭构件承载力计算一、混凝土构件受到扭转的种类混凝土结构构件，除承受弯矩、轴力、剪力外，还可能承受扭矩的作用。工程中，混凝土构件受到的扭转有两类：一类是由外荷载直接作用产生的扭转，其扭矩可由静力平衡条件求得，与构件的抗扭刚度无关，一般也称为平衡扭转。图4-1（a）、（b）中的受檐口竖向荷载作用的挑檐梁，受水平制动力作用的起重机梁，截面上承受有扭矩，都是这一类扭转。图4-1 工程中常见的受扭构件（）
2、挑檐梁；（）起重机梁；（）现浇框架的边梁 另一类是超静定结构中由于变形的协调使截面产生的扭转，称为协调扭转。如图4-1 （c）中的现浇框架的边梁，由于次梁梁端的弯曲转动变形使得边梁产生扭转，截面承受扭矩。但在边梁受扭开裂后，其抗扭刚度迅速降低，从而截面所承受的扭矩也会随之而减少。二、钢筋混凝土矩形截面受扭构件的破坏形态试验表明，对于钢筋混凝土矩形截面受扭构件，其破坏形态与配置钢筋的数量多少有关，可以分为三类：少筋破坏。当配筋（垂直纵轴的箍筋和沿周边的纵向钢筋）过少或配筋间距过大时，在扭矩作用下，先在构件截面的长边最薄弱处产生一条与纵轴成45左右的斜裂缝，构件一旦开裂，钢筋不足以承担由混凝土开裂
3、后转移给钢筋承担的拉力，裂缝就迅速向相邻两侧面呈螺旋形延伸，形成三面开裂、一面受压的空间扭曲裂面，构件随即破坏。破坏过程急速而突然，属于脆性破坏。其破坏扭矩 T u MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpep
4、m0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGubWaaSbaaSqaaiaadwhaaeqaaaaa411C 基本上等于开裂扭矩 T cr MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl
5、7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGubWaaSbaaSqaaiaadogacaWGYbaabeaaaaa4201 。这种破坏形态称为“少筋破坏”。为防止发生这类脆性破坏，混凝土结构设计规范对受扭构件提出了抗扭箍筋及抗扭纵筋的下限（最小配筋率）及箍筋最大间距等作出了严格的规定。适筋破坏。配筋适量时，在扭矩作用下，首条斜裂缝出
6、现后并不立即破坏。随着扭矩的增加，将陆续出现多条大体平行的连续的螺旋形裂缝。与斜裂缝相交的纵筋和箍筋先后达到屈服，斜裂缝进一步展开，最后受压面上的混凝土也被压碎，构件随之破坏。这种破坏称为“适筋破坏”，属于具有一定延性的破坏。下面列出的受扭承载力公式所计算的也就是这一类破坏形态。超筋破坏。若配筋量过大，则在纵筋和箍筋尚未达到屈服时，混凝土就因受压而被压碎，构件立告破坏。这种破坏称为“超筋破坏”，属于无预兆的脆性破坏。在设计中，应力求避免发生超筋破坏，因此在规范中就规定了配筋的上限，也就是规定了最小的截面尺寸条件。 如果抗扭纵筋和抗扭箍筋的配筋强度（配筋量及钢筋强度值）的比例失调，破坏时会发生一
7、种钢筋达到屈服而另一种则没有达到，这种破坏形态称为“部分超筋破坏”。它虽也有一定延性，但比适筋破坏时的延性小。为防止出现这种破坏，规范对抗扭纵筋和抗扭箍筋的配筋强度比值 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq
8、=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 的适合范围作出了限定。 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZL
9、dGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 的取值按下式计算： ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharq
10、qtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA f y A stl s f yv A st1 u cor MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbu
11、LwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaadaWcaaqaaiaadAgadaWgaaWcbaGaamyEaaqabaGccaWGbbWaaSbaaSqaa
12、iaadohacaWG0bGaamiBaaqabaGccaWGZbaabaGaamOzamaaBaaaleaacaWG5bGaamODaaqabaGccaWGbbWaaSbaaSqaaiaadohacaWG0bGaaGymaaqabaGccaWG1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaaaa50DD （4-1）式中 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbI
13、tLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 受扭的纵向钢筋与箍筋的配筋强度比值； A stl MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Cae
14、rbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohacaWG0bGaamiBaaqabaaaaa42F1 受扭计
15、算中取对称布置的全部纵向非预应力钢筋截面面积； A st1 MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9
16、adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohacaWG0bGaaGymaaqabaaaaa42BB 受扭计算中沿截面周边配置的箍筋单肢截面面积； u cor MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC
17、0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWG1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4316 截面核心部分的周长： u cor MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYL
18、wzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWG1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4316 2（ b cor MathTypeMTEF55+=feaaguart1ev2aaatCvAUf
19、eBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGIbWaaSbaaSqaaiaadogacaWGVb
20、GaamOCaaqabaaaaa4303 h cor MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adb
21、aqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGObWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4309 ）； f yv MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq
22、=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhacaWG2baabeaaaaa422D 箍筋抗拉强度设计值； s MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd
23、9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGZbaaaa4015 箍筋间距。 对钢筋混凝土结构构件，其 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatL
24、xBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 值应符合0.6 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd
25、9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 1.7的要求，当 ζ MathTyp
26、eMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakea
27、acqaH2oGEaaa40DA 1.7时；取 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=
28、xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 1.7；对偏心矩 e p0 MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q
29、8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGLbWaaSbaaSqaaiaadchacaaIWaaabeaaaaa41E2 h/6 MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je
30、9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGObGaai4laiaaiAdaaaa417D 的预应力混凝土纯扭构件，当符合 ζ MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbIt
31、LDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA 1.7时，可在式（4-1）的右边增加预应力影响项0.05 N P0 A 0 W t MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL
32、2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaadaWcaaqaaiaad6eadaWgaaWcbaGaamiuaiaaicdaaeqaaaGcbaGaamyqamaaBaaaleaacaaIWaaabeaaaaGccaWGxbWaaSbaaSqaaiaadshaaeqaaaaa457C ，此处， N p0 annotation encoding=MathType-MTE
