《桥梁工程》荷载横向分布计算(偏心压力法).ppt
,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,第五章 Chapter 5 Analysis of simple supported beam bridge 简支梁桥的计算,3）荷载横向分布系数计算方法杠杆原理法 偏心压力法 横向铰接梁（板）法横向刚接梁法比拟正交异性板法,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,3.偏心压力法 Method based on stiffness transverse connection,1）基本假设横梁刚性极大,刚性横梁的微小变形可以忽略不计,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,3.偏心压力法 Method based on stiffness transverse connection,2）基本假设的适用范围 Suitability of the assumption 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。,3.偏心压力法 Method based on stiffness transverse connection,3）原理 Theory,P,P,L,e,3.偏心压力法 Method based on stiffness transverse connection,3.偏心压力法 Method based on stiffness transverse connection,3）原理 Theory中心荷载作用Pointed load at the center P=1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=w5,3.偏心压力法 Method based on stiffness transverse connection,3.偏心压力法 Method based on stiffness transverse connection,P=1,w1,w2,R1,R2,R3,R4,R5,简支梁在集中荷载作用下的挠度：,3）原理 中心荷载作用 P=1Theory Pointed load at the center,w1,w2,R1,R2,R3,R4,R5,竖向静力平衡：,3）原理 Theory A.中心荷载作用 P=1,3.偏心压力法 Method based on stiffness transverse connection,3）原理Theory偏心力矩作用 M=Pe=e 各梁竖向挠度：,M=Pe=e,R1,R2,R4,R5,wi,ai,3.偏心压力法 Method based on stiffness transverse connection,M=Pe=e,R1,R2,R4,R5,wi,ai,3）原理Theory偏心力矩作用M=Pe=e 弯矩静力平衡：,3.偏心压力法 Method based on stiffness transverse connection,3）原理 Theory C.偏心荷载对各主梁的综合作用 当荷载作用于第k号梁(e=ak)：,R1k,R2k,R5k,（3）,R3k,R4k,R1,R2,R4,R5,ak,P,3.偏心压力法 Method based on stiffness transverse connection,a1,P,-a1,R11,R51,3）原理 TheoryC.偏心荷载对各主梁的综合作用 当荷载作用于第1号梁 如图所示 e=a1 and I1=I5,3.偏心压力法 Method based on stiffness transverse connection,3）原理 TheoryD.荷载横向影响线 当荷载P=1作用于第i号梁上时，各主梁的荷载分布：,a1,P=1,（5）,当各主梁截面尺寸相同时，,11,3.偏心压力法 Method based on stiffness transverse connection,（6）,4）偏心压力法的计算实例 Example,75,700,75,计算步骤判断采用何种方法计算,3.偏心压力法 Method based on stiffness transverse connection,4）偏心压力法的计算实例 Example,75,700,75,计算步骤判断采用何种方法计算绘制横向影响线,-0.200,0.600,480,30,3.偏心压力法 Method based on stiffness transverse connection,4）偏心压力法的计算实例 Example,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,-0.200,0.600,460,30,3.偏心压力法 Method based on stiffness transverse connection,4）偏心压力法的计算实例 Example,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,-0.200,460,30,3.偏心压力法 Method based on stiffness transverse connection,5）偏心压力法的计算实例 Example,75,700,75,横向影响线绘制的技巧1#梁影响线2#梁影响线3#梁影响线,-0.200,0.600,480,30,0.400,0.200,0.000,3.偏心压力法 Method based on stiffness transverse connection,5.3荷载横向分布计算,【例】一座计算跨径l=19.5m的简支梁，其横截面如图所示，纵断面布试求荷载位于跨中时1号边梁的荷载横向分布系数mcq(汽车荷载)和mcr(人群荷载)。,解此桥设有横隔梁，且承重结构的跨宽比为:,故可按偏心压力法来计算横向分布系数mc，其步骤如下:,1)求荷载横向分布影响线竖标本桥各根主梁的横截面均相等，梁数n=5，梁间距为1.6m，则:,5.3荷载横向分布计算,l号梁在两个边主梁处的横向影响线的竖标值为:,(2)绘出荷载横向分布影响线，并按最不利位置布载，如图2-3-16b)所示，其中:行道缘石至1号梁轴线的距离为:,=1.05-0.75=0.3m,5.3荷载横向分布计算,荷载横向分布影响线的零点至1号梁位的距离为x，可按比例关系求得:并据此计算出对应各荷载点的影响线竖标qi和r。,(3)计算荷载横向分布系数mc1号梁的活载横向分布系数分别计算如下:,汽车荷载,人群荷载,求得1号梁的各种荷载横向分布系数后，就可得到各类荷载分布至该梁的最大荷载值。,偏心压力法回顾Review on the Method based on stiffness transverse connection,P,P,L,e,偏心压力法回顾Review on the Method based on stiffness transverse connection,当荷载作用于第k号梁(e=ak)：When the load is applied on the k girder,R1k,R2k,R5k,R3k,R4k,ak,P,偏心压力法回顾Review on the Method based on stiffness transverse connection,R1k,R2k,R5k,R3k,R4k,ak,P,当荷载作用于第k号梁(e=ak)：When the load is applied on the k girder,4.修正偏心压力法 Modified method of the stiffness transverse connection,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,MT4,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,4.修正偏心压力法Modified method of the stiffness transverse connection,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,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,MT1,4.修正偏心压力法Modified method of the stiffness transverse connection,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,MT1,4.修正偏心压力法Modified method of the stiffness transverse connection,则：,代入：,4.修正偏心压力法Modified method of the stiffness transverse connection,则：,4.修正偏心压力法Modified method of the stiffness transverse connection,修正后的公式,4.修正偏心压力法Modified method of the stiffness transverse connection,4.修正偏心压力法 Modified method of the stiffness transverse connection,4）关于 值,当各主梁截面相同时：,4.修正偏心压力法Modified method of the stiffness transverse connection,5）关于IT 值,t1,4.修正偏心压力法Modified method of the stiffness transverse connection,4.偏心压力法小结 Summarization on the method,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,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,荷载横向分布系数计算方法回顾Review of the methods for computing coefficients of transverse distribution of loads 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,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,7.荷载横向分布系数沿桥跨的变化 The Variation of the Coefficients along the span 支点处 m0 Supported end跨中处mc Mid-span,端横隔板,中横隔板,1/4横隔板,l/4,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,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,m0,mc m0,边梁,中梁,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,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,m0,5.3荷载横向分布计算Computation of Coefficients of Transverse Distribution of Loads,5.4 主梁内力计算Computing the internal forces of the main girder,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,5.4 主梁内力计算Computing the internal forces of the main girder,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,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,5.4 主梁内力计算Computing the internal forces of the main girder,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,y2,5.4 主梁内力计算Computing the internal forces of the main girder,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,5.4 主梁内力计算Computing the internal forces of the main girder,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,5.4 主梁内力计算Computing the internal forces of the main girder,
