简支梁桥的计算

Chapter 3 第三章 Analysis of simple supported beam bridge 简支梁桥的计算,Part 2 RC & PC beam bridge第二篇 钢筋混凝土和预应力混凝土梁式桥,BRIDGE ENGRGPART II,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,Chapter 3 Analysis of simple supported beam bridge 第三章 简支梁桥的计算,简支装配式RC、PC梁桥的设计 Dimension 拟定尺寸 Load荷载计算 Analysis内力分析 Reinforcement配筋计算 Drawing绘制施工图,3.1 Review on the design procedure 设计过程回顾,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3.2 Slab design for the roadway 行车道板计算,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3.2 Slab design for the roadway 行车道板计算,1.Types of connection detail 行车道板的类型,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,1. Structural Models of the roadway 行车道板的计算简图,Span 计算跨径? Load distribution荷载分布？ Width 板带宽度?,a) Simple supported slab单向板,b) Cantilever with hinge铰接悬臂板,c) Cantilever 悬臂板,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3.2 Slab design for the roadway 行车道板计算,3.2 Slab design for the roadway 行车道板计算,2. Distribution of the wheel on the roadway车轮荷载在板上的分布,The contacted surface between the tyres and the pavement 轮胎与桥面的接触面,b) Consideration of the pavement effect桥面铺装的影响,A,b1,b2,45 o,a2,H,H,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,P/2,P/2,3.2 Slab design for the roadway 行车道板计算,3. Slab width participated for the load carrying板的有效工作宽度,The problem is presented out 问题的提出： When the local load applied on the slab, how much width will partici- pate carrying the load? 局部荷载作用，板在多大范围内参与受力。,l,m2,l,m1,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3.2 Slab design for the roadway 行车道板计算,单向板的例子 有效工作宽度的概念,l,a,mxmax,Bent moment on the mid-section 跨中截面弯矩图,mxmax,x,y,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,l,a,mxmax,Conclusion: 数值计算结果表明，板的有效工作宽度主要与三个因素有关： Condition of the support支撑条件 Load distribution荷载分布性质 Location of the load荷载位置,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,1）单向板 When single load applied near the mid-span area 当单个荷载作用于板跨中附近时 a = a1+l/3 =a2 +2H+l/3 and 2l/3 l ：computed span 板的计算跨径， for calculation of the moment计算弯矩时 l= l0+t and l0+b for the calculation of the shear计算剪力时 l= l0,l0,l,a,b,t,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,1）单向板 When multi-load applied near the mid-span area 当多个荷载重叠作用于板跨中附近时： a = a1+d+l/3 =a2 +2H+d+l/3,l0,l,a,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,1）单向板 When loads applied on the supported area 当荷载作用于板支撑处时 a = a1+t =a2 +2H+t and l/3,l0,a,l,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,1）单向板 When loads applied near the supported edges 当荷载作用于靠近板支撑处时 ax = a +2x,l0,a1,a,l,ax,x,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,List of the slab width of participation 单向板有效工作宽度汇总,l0,l,a = a 1+l/3 = a 2+2H+l/3 且 2l/3, ax = a +2x, a = a 1+t = a +t且 l/3,a,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,The application of the slab width of participation 单向板有效工作宽度的应用,车轮荷载作用下，有效工作宽度内的板将共同工作，并承受相同大小的内力（弯矩），根据有效工作宽度的定义，有：,因此，只需要将车轮荷载平分到有效工作宽度a（沿纵向）和b1（沿横向）内，即可。,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,a,a,ax,如图所示： ,Application on the 单向板有效工作宽度的应用,q1,q2,qx,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,2）Cantilever slab 悬臂板 悬臂板的有效工作宽度定义与简支板同。 mxmax is the maximum moment on the root section of the cantilever 悬臂根部截面的最大弯矩,l0,mxmax,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,2） Cantilever slab 悬臂板 悬臂板的有效工作宽度接近于2倍悬臂长度 a = a1+2b b为荷载外边缘至悬臂跟部的距离,b,a=a1+2b,H,45,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,3. Slab width participated for the load carrying板的有效工作宽度,3.2 Slab design for the roadway 行车道板计算,4. Internal force computation of the roadway行车道板的内力计算,1）多跨连续单向板 主梁和板之间的作用 两种极端情况,t,h,t,h,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,1）多跨连续单向板 考虑梁的约束时的简便计算法 当t/h1/4时（主梁抗扭能力较大） 跨中弯矩 M中 = + 0.5M0 支点弯矩 M支 = - 0.7M0 当t/h 1/4时（主梁抗扭能力较小） 跨中弯矩 M中 = + 0.7M0 支点弯矩 M支 = - 0.7M0 t/h代表了板和梁的刚度之比 M0代为按简支梁计算的跨中弯矩值。,t,h,t,h,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,4. Internal force computation of the roadway行车道板的内力计算,1）多跨连续单向板 M0 =1.2 M0g +1.4 M0p 活载弯矩：,l0,(a-a)/2,a,a,ax,p,g,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,4. Internal force computation of the roadway行车道板的内力计算,1）多跨连续单向板 支点剪力：,l0,(a-a)/2,t,a,a,ax,p,g,P,y2,y1,A1,A2,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,4. Internal force computation of the roadway行车道板的内力计算,2）铰接悬臂板 活载弯矩：,b1,l0,P/2,4. Internal force computation of the roadway行车道板的内力计算,Example 行车道板的内力计算实例,铰接悬臂板 恒载及其内力计算 车辆荷载下的内力计算 荷载组合,b1,l0,P/2,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,Combination of the loads 荷载组合,SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN,Example 行车道板的内力计算实例,