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1、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 IISCHOOL 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 Reinforcem
2、ent配筋计算 Drawing绘制施工图 3.1 Review on the design procedure 设计过程回顾桥梁工程结构设计原理桥梁工程Roadway,girder,transverse connection桥面板、主梁、横隔板计算SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN 3.2 Slab design for the roadway 行车道板计算SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN 3.2 Slab design for the roadway 行车道板计算
3、1.Types of connection detail 行车道板的类型nHinge connection between the wings of the girdern主梁翼板铰接构造 a)、b)nRigid connection between the wings of the girdern主梁翼板刚接构造 c)、d)a)b)c)d)SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN1.Structural Models of the roadway 行车道板的计算简图nSpan 计算跨径?nLoad distribution荷载分布？n
4、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ll0l0SCHOOL 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a)The contacted surface between the
5、 tyres and the pavementb)轮胎与桥面的接触面b)Consideration of the pavement effect桥面铺装的影响nLongitudinal 纵向 a1=a2+2HnTransverse 横向 b1=b2+2HnLocal distribution局部分布荷载 p=P2a1b1Ab1b245 oa1a2HHSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHENP/2P/2 3.2 Slab design for the roadway 行车道板计算3.Slab width participated for
6、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。lm2lm1bbSCHOOL 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lb1a1amxmaxBent mom
7、ent on the mid-section跨中截面弯矩图mxmaxxySCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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lb1a1amxmaxConclusion: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：nCondition of the support支撑条件nLoad distribution荷载分布性质nLocation of the lo
8、ad荷载位置SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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/3l：computed span 板的计算跨径，for calculation of the moment计算弯矩时
9、 l=l0+t and l0+b for the calculation of the shear计算剪力时 l=l0l0b1a1labtSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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
10、/3l0b1dlaSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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/3l0a1alSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.Slab width
11、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+2xl0a1alaxb1xSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.Slab width participated for the load carrying板的有效工作宽度 3.2 Slab design for the roadway 行车
12、道板计算nList of the slab width of participation 单向板有效工作宽度汇总l0la=a 1+l/3=a 2+2H+l/3 且 2l/3 ax=a+2x a=a 1+t=a+t且 l/3aaaxSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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nThe application of the slab width of part
13、icipationn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 CHEN3.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aaax如图所示：nApplication on the 单向板有效工作宽度的应用q1q
14、2qxSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.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l0mxmaxbSCHOOL OF TRANSPORTATION,WUT PR
15、ODUCED BY：X J CHEN3.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+2bb为荷载外边缘至悬臂跟部的距离 ba1a=a1+2bHb145SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN3.Slab width participated for the load carrying板的有效工作宽度 3.2
16、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 ththSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN1）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）n跨中弯矩 M中=+0.5M0n支点弯矩 M支=-0.7M0当t/h 1/4时（主梁抗扭能力较小）n跨中弯矩 M中=+0.7M0n支点弯矩 M支=-0.7M0t/h代表了板和梁的刚度之比M0代
17、为按简支梁计算的跨中弯矩值。ththSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN4.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：l0l(a-a)/2b1taaaxpgSCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN4.Internal force computation of the roadway行车道板的内力计算行车道板的内力计算1）多跨连续单向板支点剪力：l0l(a
18、-a)/2taaaxb1pgPy2y1A1A2SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN4.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：b1l0P/24.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铰接悬臂板l恒载及其内力计算l车辆荷载下的内力计算l荷载组合 b1l0P/2SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHENCombination of the loads 荷载组合 承载能力极限状态：正常使用极限状态：SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHENExample 行车道板的内力计算实例