《建筑结构(第版)》第四章受扭构件承载力计算

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

3、由混凝土开裂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<math display='block'> <semantics> <mrow> <msub> <mi>T</mi> <mi>u</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMT

4、EF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaaca

5、WGubWaaSbaaSqaaiaadwhaaeqaaaaa411C</annotation> </semantics></math>基本上等于开裂扭矩<math display='block'> <semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi><mi>r</mi> </mrow> </msub> </mrow> &l

6、t;annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0Firp

7、epeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGubWaaSbaaSqaaiaadogacaWGYbaabeaaaaa4201</annotation> </semantics></math>。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

8、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

9、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<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqt

10、ubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>的适合范围作出了限定。<math display='block'>

11、; <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrF

12、fpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>的取值按下式计算：<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding

13、='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad

14、baqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math><math display='block'> <semantics> <mrow> <mfrac> <mrow> <msub> <mi>f</mi> <mi>y</mi> </msub> <msub> <mi>A</m

15、i> <mrow> <mi>s</mi><mi>t</mi><mi>l</mi> </mrow> </msub> <mi>s</mi> </mrow> <mrow> <msub> <mi>f</mi> <mrow> <mi>y</mi><mi>v</mi> </mrow> </msub> <msub> &

16、lt;mi>A</mi> <mrow> <mi>s</mi><mi>t</mi><mn>1</mn> </mrow> </msub> <msub> <mi>u</mi> <mrow> <mi>c</mi><mi>o</mi><mi>r</mi> </mrow> </msub> </mrow> </mfrac&g

17、t; </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs

18、0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaadaWcaaqaaiaadAgadaWgaaWcbaGaamyEaaqabaGccaWGbbWaaSbaaSqaaiaadohacaWG0bGaamiBaaqabaGccaWGZbaabaGaamOzamaaBaaaleaacaWG5bGaamODaaqabaGccaWGbbWaaSbaaSqaaiaadohacaWG0bGaaGymaaqabaGccaWG1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaaaa

19、50DD</annotation> </semantics></math> （4-1）式中<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBa

20、erbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>受扭的纵向钢筋与箍筋的配筋强度比值；<m

21、ath display='block'> <semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>s</mi><mi>t</mi><mi>l</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev

22、2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaa

23、dohacaWG0bGaamiBaaqabaaaaa42F1</annotation> </semantics></math>受扭计算中取对称布置的全部纵向非预应力钢筋截面面积；<math display='block'> <semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>s</mi><mi>t</mi><mn>1</mn> </mrow

24、> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpe

25、pm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohacaWG0bGaaGymaaqabaaaaa42BB</annotation> </semantics></math>受扭计算中沿截面周边配置的箍筋单肢截面面积；<math display='block'> <semantics> <mrow> <msub> <

26、mi>u</mi> <mrow> <mi>c</mi><mi>o</mi><mi>r</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz

27、YbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWG1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4316</annotation> </semantics></math>

28、;截面核心部分的周长：<math display='block'> <semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>c</mi><mi>o</mi><mi>r</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF

29、55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWG

30、1bWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4316</annotation> </semantics></math>2（<math display='block'> <semantics> <mrow> <msub> <mi>b</mi> <mrow> <mi>c</mi><mi>o</mi><mi>r</mi> </mrow> <

31、;/msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9

32、pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGIbWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4303</annotation> </semantics></math><math display='block'> <semantics> <mrow> <msub> <mi>h</mi> <mrow>

33、; <mi>c</mi><mi>o</mi><mi>r</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbX

34、gBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGObWaaSbaaSqaaiaadogacaWGVbGaamOCaaqabaaaaa4309</annotation> </semantics></math>）；<math display='block

35、'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>y</mi><mi>v</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhi

36、ov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhacaWG2baabeaaaaa422D</annotation> &

37、lt;/semantics></math>箍筋抗拉强度设计值；<math display='block'> <semantics> <mi>s</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbW

38、exLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGZbaaaa4015</annotation> </semantics></math>箍筋间距。 对钢筋混凝土结构构件，其<math display='block'> <

39、;semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea

40、0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>值应符合0.6<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='M

41、athType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeG

42、aciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>1.7的要求，当<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyN

43、v2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics

44、></math>1.7时；取<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBb

45、XgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>1.7；对偏心矩<math display='block'> <semantics>

46、<mrow> <msub> <mi>e</mi> <mrow> <mi>p</mi><mn>0</mn> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerb

47、d9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGLbWaaSbaaSqaaiaadchacaaIWaaabeaaaaa41E2</annotation> </semantics></math&g

48、t;<math display='block'> <semantics> <mrow> <mi>h</mi><mo>/</mo><mn>6</mn> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBae

49、rbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGObGaai4laiaaiAdaaaa417D</annotation> </semantics></math>的预应力混凝土纯扭构件，

50、当符合<math display='block'> <semantics> <mi>&#x03B6;</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl

51、7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH2oGEaaa40DA</annotation> </semantics></math>1.7时，可在式（4-1）的右边增加预应力影响项0.05<math display='block'> <semantics>

52、<mrow> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mi>P</mi><mn>0</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>A</mi> <mn>0</mn> </msub> </mrow> </mfrac> <msub&

53、gt; <mi>W</mi> <mi>t</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0

54、Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaadaWcaaqaaiaad6eadaWgaaWcbaGaamiuaiaaicdaaeqaaaGcbaGaamyqamaaBaaaleaacaaIWaaabeaaaaGccaWGxbWaaSbaaSqaaiaadshaaeqaaaaa457C</annotation> </semantics></

55、math>，此处，<math display='block'> <semantics> <mrow> <msub> <mi>N</mi> <mrow> <mi>p</mi><mn>0</mn> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaat

56、CvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGobWaaSbaaSqaaiaadchac

57、aaIWaaabeaaaaa41CB</annotation> </semantics></math>为计算截面上混凝土法向预应力等于零时的纵向预应力筋及非预应力筋的合力，<math display='block'> <semantics> <mrow> <msub> <mi>A</mi> <mn>0</mn> </msub> </mrow> <annotation encoding='MathType-MTE

58、F'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabe

59、qaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaaicdaaeqaaaaa40C9</annotation> </semantics></math>为构件的换算截面面积。三、受扭钢筋的形式在混凝土构件中配置适当的抗扭钢筋，当混凝土开裂后，可由钢筋继续承担拉力，这对提高构件的抗扭承载力有很大的作用。根据弹性分析结果，扭矩在构件中引起的主拉应力轨迹线为一组与构件纵轴大致成45°角，并绕四周面连续的螺旋线。因此，最合理的配筋方式是在构件靠近表面处设置成45°走向的螺旋形钢筋。但这种配筋方式不仅不便于施工，而且在实际工程

60、中，扭矩在构件全长上常常要改变方向。扭矩方向一改变，螺旋筋的旋角方向也要相应地加以改变，这在配筋构造措施上就会造成很大的困难，而且当扭矩改变方向后则将完全失去效应。因此，在实际工程中，一般是采用由靠近构件表面设置的横向箍筋和沿构件周边均匀对称布置的纵向钢筋共同组成的抗扭钢筋骨架。它恰好与构件中抗弯钢筋和抗剪钢筋的配筋方式相协调。所以，在实际工程结构中都采用垂直构件纵轴的箍筋和沿截面周边布置的纵向钢筋组成的空间钢筋骨架来承担扭矩。四、矩形截面纯扭构件承载力计算矩形截面纯扭构件承载力按下式计算： <math display='block'> <semantics&

61、gt; <mi>T</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbb

62、a9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGubaaaa3FF6</annotation> </semantics></math>0.35<math display='block'> <semantics> <mrow> <msub> <mi>f</mi> <mi>t</mi> </msub> <

63、msub> <mi>W</mi> <mi>t</mi> </msub> <mo>+</mo><mn>1.2</mn><msqrt> <mi>&#x03B6;</mi> </msqrt> <mfrac> <mrow> <msub> <mi>f</mi> <mrow> <mi>y</mi><mi>v</mi> &

64、lt;/mrow> </msub> <msub> <mi>A</mi> <mrow> <mi>s</mi><mi>t</mi><mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow> <mi>c</mi><mi>o</mi><mi>r</mi> </mrow>

65、 </msub> </mrow> <mi>s</mi> </mfrac> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadshaaeqaaOGaam4vamaaBaaaleaacaWG0baabeaakiabgUcaRiaaigdacaGGUaGaaGOmam