建筑结构(第2版)》-第三章 受弯构件承载力计算

1、.第三章受弯构件承载力计算【学习重点】受弯构件正截面承载力计算；受弯构件斜截面承载力计算；受弯构件裂缝宽度及变形的验算。【学习目标】了解受弯构件正截面的受力性能及构造要求；熟悉受弯构件正截面承载力计算依据及条件；掌握单筋矩形截面、双筋矩形截面、形截面受弯构件正截面承载力的计算方法；了解受弯构件斜截面的工作性能；掌握受弯构件斜截面受剪承载力计算；掌握构件裂缝宽度及变形的验算方法。第一节受弯构件正截面承载力计算在荷载作用下，同时承受弯矩和剪力作用的构件称为受弯构件。梁和板是典型的受弯构件，它们是工业与民用建筑中数量最多，使用面最广的一类构件。梁和板的区别在于：梁的截面高度一般大于其宽度，而板的截面

2、高度则远小于其宽度。受弯构件在建筑工程中最常见。仅在截面受拉区配置纵向受力钢筋的构件，称作单筋受弯构件；在截面受拉区和受压区都配置有受力钢筋的构件，称作双筋受弯构件。按构件的截面形式分为单筋矩形梁、双筋矩形梁、形梁、形梁、环形梁、空心板、槽形板等，如图3-1、图3-2所示。 图3-1 梁的截面形式 图3-2 板的截面形式（）单筋矩形梁；（）双筋矩形梁； （）空心板；（）槽形板（）形梁；（）形梁；（）环形梁一、受弯构件正截面的受力性能1.钢筋混凝土梁正截面工作的三个阶段钢筋混凝土受弯构件的破坏有两种情况：一种是由弯矩引起的，破坏截面与构件的纵轴线垂直（正交），称为沿正截面破坏；另一种是由弯矩及剪

3、力共同引起的，破坏截面是倾斜的，称为沿斜截面破坏，如图3-3所示。图3-3 受弯构件的破坏形态（）沿正截面破坏；（）沿斜截面破坏试验研究表明：钢筋混凝土受弯构件当具有足够的抗剪能力而且构造设计合理时，构件受力后将在弯矩较大的部位，或在图3-3中纯弯区段的正截面发生弯曲破坏。受弯构件自加载至破坏的过程中，随着荷载的增加及混凝土塑性变形的发展，对于正常配筋的梁，其正截面上的应力及其分布和应变发展过程可分为以下三个阶段。第阶段弹性工作阶段。开始增加荷载时，弯矩很小，截面应力及应变均很小，混凝土基本处于弹性工作阶段，截面应变变化符合平截面假定（图3-4），梁截面应力分布图形为三角形，中和轴以上受压，另

4、一侧受拉。随着<math display='block'> <semantics> <mi>M</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGe

5、aGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbaaaa3FEF</annotation> </semantics></math>的增大，由于混凝土抗拉能力远小于抗压能力，在受拉边缘处混凝土产生塑性变形，当弯矩增加到使受拉边缘的应变达到混凝土的极限拉应变时，相应的边缘拉应力达到混凝土的抗拉强度<math

6、display='block'> <semantics> <mrow> <msub> <mi>f</mi> <mi>t</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9w

7、DYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadshaaeqaaaaa412D</annotation> </semantics></math>，拉应力图形接近

8、矩形的曲线变化，压应力图形接近三角形，构件处于将裂未裂的极限状态，此即第阶段末，以a表示（图3-4a）；相应构件所能承受弯矩以<math display='block'> <semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>c</mi><mi>r</mi> </mrow> </msub> </mrow> <annotation encoding='Math

9、Type-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaci

10、GaaiaabeqaamaabaabauaakeaacaWGnbWaaSbaaSqaaiaadogacaWGYbaabeaaaaa41FA</annotation> </semantics></math>表示。第阶段带裂缝工作阶段。弯矩达到<math display='block'> <semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>c</mi><mi>r</mi>

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

12、Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbWaaSbaaSqaaiaadogacaWGYbaabeaaaaa41FA</annotation> </semantics></math>后，在纯弯段内混凝土抗拉强度最弱的截面上将出现第一批裂缝。开裂部分混凝土承受的拉力将传给钢筋，使开裂截面的钢筋应力突然增大，截面中和轴上移。随着弯矩增大，截面应变增大；但截面应变分布基本上符合平截面假定；而受压

13、区混凝土则逐渐表现出塑性变形的特征，压区的应力图形呈曲线形。当荷载增加到某一数值时，纵向受拉钢筋开始屈服，钢筋应力达到其屈服强度<math display='block'> <semantics> <mrow> <msub> <mi>f</mi> <mi>y</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2a

14、aatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadM

15、haaeqaaaaa4132</annotation> </semantics></math>，此即为第阶段末，以a表示（图3-4a）。第阶段屈服阶段。当荷载再继续增加时，钢筋将继续变形而应力保持<math display='block'> <semantics> <mrow> <msub> <mi>f</mi> <mi>y</mi> </msub> </mrow> <annotation encoding='

16、MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae

17、GaciGaaiaabeqaamaabaabauaakeaacaWGMbWaaSbaaSqaaiaadMhaaeqaaaaa4132</annotation> </semantics></math>数值不变。此时裂缝不断扩展且向上延伸，由于中和轴上升，压区高度很快减小，内力臂增大，截面弯矩仍然有所增长，但受压区混凝土的总压力<math display='block'> <semantics> <mi>D</mi> <annotation encoding='MathType-MTE

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

19、qaamaabaabauaakeaacaWGebaaaa3FE6</annotation> </semantics></math>始终保持不变，与钢筋总拉力<math display='block'> <semantics> <mi>T</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2

20、DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGubaaaa3FF6</annotation> </semantics></math>保持

21、平衡（<math display='block'> <semantics> <mrow> <mi>D</mi><mo>=</mo><mi>T</mi> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBa

22、erbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGebGaeyypa0Jaamivaaaa41C5</annotation> </semantics></math>）。此时受压混凝土边

23、缘应变迅速增长，受压区应力图形更趋丰满（图3-4）。图3-4 钢筋混凝土受弯构件工作的三个阶段当弯矩再增加至极限弯矩<math display='block'> <semantics> <mrow> <msub> <mi>M</mi> <mi>u</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvA

24、UfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbWaaSbaaSqaaiaadwhaaeqa

25、aaaa4115</annotation> </semantics></math>时，称为第阶段末，以 表示。此时，由于钢筋塑性变形的发展，截面中和轴不断上升，混凝土受压区高度不断减小。截面受压区边缘纤维应变增大到混凝土极限压应变<math display='block'> <semantics> <mrow> <msub> <mi>&#x03B5;</mi> <mrow> <mi>c</mi><mi>u</m

26、i> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0

27、xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaH1oqzdaWgaaWcbaGaam4yaiaadwhaaeqaaaaa42D2</annotation> </semantics></math>，构件即开始破坏。其后，在试验时虽然仍可继续变形，但所承受的弯矩将有所降低，最后受压区混凝土被压碎甚至崩落而导致构件完全破坏（图3-4a）。在以上三个阶段中：第阶段末（a）：构件所能承受的抗裂弯矩

28、<math display='block'> <semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>c</mi><mi>r</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZ

29、L2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbWaaSbaaSqaaiaadogacaWGYbaabeaaa

30、aa41FA</annotation> </semantics></math>，是作为抗裂度计算的依据。第阶段：构件在荷载标准值作用下所处的阶段，它是构件正常使用极限状态中变形及裂缝宽度验算的依据。第 阶段末（）：构件所能承受的破坏弯矩<math display='block'> <semantics> <mrow> <msub> <mi>M</mi> <mi>u</mi> </msub> </mrow> <annot

31、ation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr

32、0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGnbWaaSbaaSqaaiaadwhaaeqaaaaa4115</annotation> </semantics></math>，是作为承载力极限状态计算的依据。2.钢筋混凝土梁正截面的破坏特征在钢筋混凝土受弯构件中，钢筋用量的变化将影响构件的受力性能和破坏形态。钢筋用量的多少，通过受拉钢筋面积<math display='block'> <semantics> <mrow> <msub>

33、; <mi>A</mi> <mi>s</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je

34、9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohaaeqaaaaa4107</annotation> </semantics></math>与混凝土有效面积<math display='block'> <semantics> <mi>A<

35、/mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpep

36、ae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbaaaa3FE3</annotation> </semantics></math>的比值（即配筋率）来反映，即：<math display='block'> <semantics> <mrow> <mi>&#x03C1;</mi><mo>=</mo><mfrac> <mrow> <

37、;msub> <mi>A</mi> <mi>s</mi> </msub> </mrow> <mi>A</mi> </mfrac> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItL

38、Dharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaHbpGCcqGH9aqpdaWcaaqaaiaadgeadaWgaaWcbaGaam4CaaqabaaakeaacaWGbbaaaaaa44AD</annotation> </sema

39、ntics></math> （3-1）式中 <math display='block'> <semantics> <mrow> <msub> <mi>A</mi> <mi>s</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caer

40、buLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbWaaSbaaSqaaiaadohaaeqaaaaa4107</annotation>

41、 </semantics></math>纵向受拉钢筋截面面积；<math display='block'> <semantics> <mi>A</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNC

42、HbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbaaaa3FE3</annotation> </semantics></math>构件截面面积，对矩形截面，<math display='block'> <s

43、emantics> <mrow> <mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqt

44、ubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbGaeyypa0JaamOyaiaadIgaaaa42BD</annotation> </semantics></math>；对倒形截面，<math display=&#

45、39;block'> <semantics> <mrow> <mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi><mo>+</mo><mo stretchy='false'>(</mo><msub> <mi>b</mi> <mi>f</mi> </msub> <mo>&#x2212

46、;</mo><mi>b</mi><mo stretchy='false'>)</mo><msub> <mi>h</mi> <mi>f</mi> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BT

47、fMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbGaeyypa0JaamOyaiaadIgacqGHRaWkcaGGOaGaamOyamaaBaaaleaacaWGMbaabeaak

48、iabgkHiTiaadkgacaGGPaGaamiAamaaBaaaleaacaWGMbaabeaaaaa4AD8</annotation> </semantics></math>。少筋梁的破坏特征。配筋率低于<math display='block'> <semantics> <mrow> <msub> <mi>&#x03C1;</mi> <mrow> <mi>min</mi> </mrow> </msub

49、> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8

50、fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaHbpGCdaWgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa43DB</annotation> </semantics></math>的梁称为少筋梁。这种梁受拉区混凝土一旦出现裂缝，受拉钢筋立即达到屈服强度，并可能进入强化阶段而破坏图3-5（a），这种少筋梁在破坏时裂缝开展较宽，挠度增长也较大，如图3-6中<math display='block'&

51、gt; <semantics> <mi>A</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9

52、Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGbbaaaa3FE3</annotation> </semantics></math>曲线所示。少筋梁破坏属脆性破坏，而且梁的承载力很低，所以设计时应避免采用。 图3-5 梁的破坏形式 图3-6不同破坏形态梁的<math display='block'> <semantics> <mi>p<

53、;/mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpe

54、pae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGWbaaaa4012</annotation> </semantics></math><math display='block'> <semantics> <mi>f</mi> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUf

55、eBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGMbaaaa4008</annotation&

56、gt; </semantics></math>曲线（）少筋梁；（）适筋梁；（）超筋梁适筋梁的破坏特征。适筋梁的破坏特点是受拉区钢筋首先进入屈服阶段，再继续增加荷载后，受压区最外边缘混凝土被压碎（达到其抗压极限强度），梁宣告破坏，其破坏形态如图3-5（b）所示，在压坏前，构件有显著的裂缝和挠度，即有明显的破坏预兆，这种破坏属于塑性破坏，在整个破坏过程中，挠度的增长相当大，如图3-6中<math display='block'> <semantics> <mi>B</mi> <annotation enc

57、oding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=

58、xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacaWGcbaaaa3FE4</annotation> </semantics></math>曲线所示，此时钢筋和混凝土两种材料性能基本上都得到充分利用，因而设计中一般采用这种设计方式。超筋梁的破坏特征。配筋率过高的梁称为“超筋梁”，即配筋率高于<math display='block'> <semantics> <mrow> <msub> <mi>&#x03C1;</mi> <

59、;mrow> <mi>max</mi> </mrow> </msub> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0J

60、e9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaacqaHbpGCdaWgaaWcbaGaciyBaiaacggacaGG4baabeaaaaa43DD</annotation> </semantics></math><math display='block'> <semantics> <mro

61、w> <mrow><mo>(</mo> <mrow> <msub> <mi>&#x03C1;</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>=</mo><msub> <mi>&#x03BE;</mi> <mi>b</mi> </msub> <msub> <mi>&

62、;#x03B1;</mi> <mn>1</mn> </msub> <mfrac> <mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> </mrow> <mrow> <msub> <mi>f</mi> <mi>y</mi> </msub> </mrow> </mfrac> </mrow>

63、<mo>)</mo></mrow> </mrow> <annotation encoding='MathType-MTEF'>MathTypeMTEF55+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpee

64、a0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabauaakeaadaqadaqaaiabeg8aYnaaBaaaleaaciGGTbGaaiyyaiaacIhaaeqaaOGaeyypa0JaeqOVdG3aaSbaaSqaaiaadkgaaeqaaOGaeqySde2aaSbaaSqaaiaaigdaaeqaaOWaaSaaaeaacaWGMbWaaSbaaSqaaiaadogaaeqaaaGcbaGaamOzamaaBaaaleaacaWG5baabeaaaaaakiaawIcacaGLPaaaaaa501E</annotation> </semantics></math>的梁称为“超筋梁”。若配筋率过高，加载后受拉钢筋应力尚未达到屈服强度前，受压混凝土却先达到极限压应变而被压坏，致使构件突然破坏图3-5（c），破坏前没有明显预兆，如图3-6中<math display='block'> <semantics> <mi>C</mi> <annotation e