桥梁工程课件 第2篇第3章 简支梁桥的计算3荷载横向分布计算(偏心压力法)A.ppt

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1、,BRIDGE ENGRGPART II,Part 2 RC&PC beam bridge第二篇 钢筋混凝土和预应力混凝土梁式桥,Chapter 3 第三章 Analysis of simple supported beam bridge 简支梁桥的计算,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3）荷载横向分布系数计算方法杠杆原理法 Method based on mechanics of leverage偏心压力法Method based on stiffness transverse connection横向铰接梁（板）法横向刚接

2、梁法比拟正交异性板法,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,3.Method based on stiffness transverse connection偏心压力法,1）Assumption 基本假设 The stiffnes

3、s of the transverse connection is very strong,the deformation of the connection is negligible.横梁刚性极大,刚性横梁的微小变形可以忽略不计,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,3.Method based on stiffness transverse connection偏心压力法,2

4、）Suitability of the assumption 基本假设的适用范围 试验证明，当B/L0.5(称为窄桥)及具有多道横隔梁时，刚性横隔梁假设是成立的。,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,3）Theory 原理,P,P,L,e,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on sti

5、ffness transverse connection偏心压力法,3.Method based on stiffness transverse connection偏心压力法,3）Theory 原理Pointed load at the center P=1 中心荷载作用 Based on the assumption,the deflections of each girder will be the same under the centric load 由刚性横梁假设，中心荷载作用下，各梁的挠度相等。,w1,w2,R1,R2,R3,R4,R5,w1=w2=w3=w4=w5,SCHOOL

6、 OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness transverse connection偏心压力法,P=1,w1,w2,R1,R2,R3,R4,R5,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,The relation between deflection and the centric load简支梁在集中荷载作用下的挠度：,3）Theory 原理Pointed load at the center P=1 中心荷载作用,3.Method

7、based on stiffness transverse connection偏心压力法,w1,w2,R1,R2,R3,R4,R5,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,Static equilibrium equation in vertical 竖向静力平衡：,3）Theory 原理Pointed load at the center P=1 中心荷载作用,3.Method based on stiffness transverse connection偏心压力法,3）Theory 原理Moment caused by ecc

8、entric load 偏心力矩作用M=Pe=eThe deflection of the girders各梁竖向挠度：,M=Pe=e,R1,R2,R4,R5,wi,ai,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness transverse connection偏心压力法,M=Pe=e,R1,R2,R4,R5,wi,ai,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3）Theory 原理Moment caused by eccent

9、ric load 偏心力矩作用M=Pe=eStatic equilibrium equation about the moment弯矩静力平衡：,3.偏心压力法,3）Theory 原理C.Total action of the eccentric pointed load 偏心荷载对各主梁的综合作用When the load is applied on the k girder当荷载作用于第k号梁(e=ak)：,R1k,R2k,R5k,（3）,R3k,R4k,R1,R2,R4,R5,ak,P,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3

10、.Method based on stiffness transverse connection偏心压力法,a1,P,-a1,R11,R51,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3）Theory 原理C.Total action of the eccentric pointed load 偏心荷载对各主梁的综合作用When the load is applied on the first girder当荷载作用于第1号梁Note that e=a1 and I1=I5,3.Method based on stiffness tra

11、nsverse connection偏心压力法,3）Theory 原理D.Transverse influence line of loads荷载横向影响线 The load distribution on the girders when load is applied on the k girder当荷载作用于第i号梁上时，各主梁的荷载分布：,a1,P=1,（6）,Specially,when each girder has the same section当各主梁截面尺寸相同时，,（6）,11,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CH

12、EN,3.Method based on stiffness transverse connection偏心压力法,4）Example 偏心压力法的计算实例,75,700,75,计算步骤判断采用何种方法计算,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness transverse connection偏心压力法,4）Example 偏心压力法的计算实例,75,700,75,计算步骤判断采用何种方法计算绘制横向影响线,-0.200,0.600,480,30,SCHOOL OF TRANSPOR

13、TATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness transverse connection偏心压力法,4）Example 偏心压力法的计算实例,0.575,150,75,700,75,计算步骤判断采用何种方法计算绘制横向影响线按最不利位置布载 汽车布载,180,180,130,50,0.350,-0.038,0.188,-0.200,0.600,460,30,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness trans

14、verse connection偏心压力法,4）Example 偏心压力法的计算实例,计算步骤判断采用何种方法计算绘制横向影响线按最不利位置布载计算相应的 荷载横向分布系数,0.575,150,75,700,75,180,180,130,50,0.350,-0.038,0.188,-0.200,460,30,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.Method based on stiffness transverse connection偏心压力法,5）Example 偏心压力法的计算实例,75,700,75,横向影响线绘制的技

15、巧1#梁影响线2#梁影响线3#梁影响线,-0.200,0.600,480,30,0.400,0.200,0.000,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,Review on the Method based on stiffness transverse connection偏心压力法回顾,P,P,L,e,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,Review on the Method based on stiffness transverse connection偏心压力

16、法回顾,When the load is applied on the k girder当荷载作用于第k号梁(e=ak)：,R1k,R2k,R5k,R3k,R4k,ak,P,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,Review on the Method based on stiffness transverse connection偏心压力法回顾,R1k,R2k,R5k,R3k,R4k,ak,P,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,When the load is ap

17、plied on the k girder当荷载作用于第k号梁(e=ak)：,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,4.Modified method of the stiffness transverse connection修正偏心压力法,1）偏心压力法中存在的问题,P,e,变形的实际过程,偏心压力法带来的后果,MT1,MT2,MT3,MT4,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,4.Modified method

18、 of the stiffness transverse connection 修正偏心压力法,2）对偏心压力法进行修正的思考方法,说明只需要对上式中的第二项进行修正,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,4.Modified method of the stiffness transverse connection 修正偏心压力法,3）修正偏心压力法原理,偏心力矩M=Pe=e作用下，弯矩静力平衡：,M=Pe=e,R1,R2,R4,R5,wi,ai,MT2,MT1,SCHOOL OF TRANSPORTATION,WUT PRODU

19、CED BY：X J CHEN,4.Modified method of the stiffness transverse connection 修正偏心压力法,材料力学关于简支梁跨中的 扭矩与扭转角的关系,R1,R2,R4,R5,wi,ai,MT2,MT1,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,4.Modified method of the stiffness transverse connection 修正偏心压力法,则：,代入：,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHE

20、N,4.Modified method of the stiffness transverse connection 修正偏心压力法,则：,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,修正后的公式,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,4.Modified method of the stiffness transverse

21、connection修正偏心压力法,4.Modified method of the stiffness transverse connection 修正偏心压力法,4）关于 值,当各主梁截面相同时：,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,4.Modified method of the stiffness transverse connection 修正偏心压力法,5）关于IT 值,t1,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coe

22、fficients of Transverse Distribution of Loads 荷载横向分布计算,4.Summarization on the method 偏心压力法小结,1）基本假设及适用范围2）原理及公式推导3）横向影响线的求法4）荷载布置及横向分布系数计算5）偏心压力法的修正,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,Review of the methods fo

23、r computing coefficients of transverse distribution of loads 荷载横向分布系数计算方法回顾杠杆原理法 适宜于支点截面处偏心压力法 适宜于跨中截面处,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,7.The Variation of the Coefficients along the span 荷载横向分布系数沿桥跨的变化Supp

24、orted end 支点处 m0Mid-span 跨中处mc,端横隔板,中横隔板,1/4横隔板,l/4,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,7.The Coefficient Variation along the span荷载横向分布系数沿桥跨的变化荷载横向分布系数沿桥跨的变化的几种情况：,mc,m0,m0,l/4,mc,m0,m0,m0 mc,mc,m0,m0,mc,m0,m

25、0,mc m0,边梁,中梁,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.3 Computation of Coefficients of Transverse Distribution of Loads 荷载横向分布计算,荷载横向分布系数沿桥跨的变化的几种情况：,mc,m0,m0,mc,m0,m0,mc,m0,m0,mc,m0,m0,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.4 Computing the internal forces of the main girder

26、 主梁内力计算,恒载内力计算 结构自重 桥面铺装 附属设施重量根据施工的过程决定分别计算不同阶段的恒载,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.4 Computing the internal forces of the main girder 主梁内力计算,2.活载内力计算,m0,mc,Pk,y1,Mc影响线,荷载横向分布系数,Pk,qk,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.4 Computing the internal forces of the main

27、girder 主梁内力计算,2.活载内力计算,mck,Q0影响线,荷载横向分布系数,m0,mc,Pk,qk,a,y1,y2,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.4 Computing the internal forces of the main girder 主梁内力计算,3.内力组合,对于简支梁，最不利组合：,1.2 恒荷载+1.4 汽车荷载+0.8 1.4 人群荷载,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,3.4 Computing the internal forces of the main girder 主梁内力计算,4.主梁内力计算实例,恒载内力计算 一期恒载、二期恒载集度 恒载内力,活载内力计算 跨中弯矩、剪力 支点剪力,内力组合,SCHOOL OF TRANSPORTATION,WUT PRODUCED BY：X J CHEN,