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1、BRIDGE ENGRGPART IIPart 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 CHEN3）荷载横向分布系数计算方法l杠杆原理法 Method based on mechanics of leveragel偏心压力法Method based on stiffness transverse connectionl横向铰接梁（板）法l横向
2、刚接梁法l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 stiff
3、ness 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 P/2P/2PPBLffff fSCHOOL 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 transv
4、erse connection偏心压力法2）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。P/2P/2PPBLSCHOOL 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PPLePPewPPewSCHOOL OF TRANSPORTATION, WUT PRODUCE
5、D BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法3. Method based on stiffness transverse connection偏心压力法3） Theory 原理A.Pointed load at the center P=1B. 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。P=1
6、w1w2R1R2R3R4R5w1= w2= w3= w4= w5SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法P=1w1w2R1R2R3R4R5or 或写为R1w1SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHENThe 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A.Point
7、ed load at the center P=1B. 中心荷载作用3. Method based on stiffness transverse connection偏心压力法P=1w1w2R1R2R3R4R5（1）SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHENStatic equilibrium equation in vertical 竖向静力平衡：3） Theory 原理A.Pointed load at the center P=1B. 中心荷载作用3. Method based on stiffness transverse c
8、onnection偏心压力法3） Theory 原理B.Moment caused by eccentric loadC. 偏心力矩作用M=Pe=eThe deflection of the girders各梁竖向挠度：M=Pe=eR1R2R4R5wiaiThe deflection-load relationship根据位移与荷载的关系，SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法M=Pe=eR1R2R4R5wiai（2）SCH
9、OOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3） Theory 原理B.Moment caused by eccentric loadC. 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)：R1kR2k
10、R5k（3）R3kR4kR1R2R4R5R1R2R3R4R5akPObtain 推出：（4）SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法a1P（5）-a1R11R51SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3） 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
11、 is applied on the first girder当荷载作用于第1号梁Note that e=a1 and I1=I53. Method based on stiffness transverse 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：a1P=1R11R51（6）Specially, when
12、 each girder has the same section当各主梁截面尺寸相同时，（6）1115SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法4）Example 偏心压力法的计算实例1601601601607570075 计算步骤l判断采用何种方法计算SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transvers
13、e connection偏心压力法4） Example 偏心压力法的计算实例1601601601607570075 计算步骤l判断采用何种方法计算l绘制横向影响线-0.2000.60048030SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法4） Example 偏心压力法的计算实例0.5751502807570075 计算步骤l判断采用何种方法计算l绘制横向影响线l按最不利位置布载 汽车布载180180130500.350-0.03
14、80.188-0.2000.60046030SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN3. Method based on stiffness transverse connection偏心压力法4） Example 偏心压力法的计算实例计算步骤l判断采用何种方法计算l绘制横向影响线l按最不利位置布载l计算相应的 荷载横向分布系数0.5751502807570075 180180130500.350-0.0380.188-0.20046030SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CH
15、EN3. Method based on stiffness transverse connection偏心压力法5） Example 偏心压力法的计算实例1601601601607570075 横向影响线绘制的技巧l1#梁影响线l2#梁影响线l3#梁影响线-0.2000.600480300.4000.2000.000SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHENReview on the Method based on stiffness transverse connection偏心压力法回顾PPLePPewPPewSCHOOL OF
16、TRANSPORTATION, WUT PRODUCED BY：X J CHENReview on the Method based on stiffness transverse connection偏心压力法回顾When the load is applied on the k girder当荷载作用于第k号梁(e=ak)：R1kR2kR5kR3kR4kakPSCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHENReview on the Method based on stiffness transverse connection偏心压力法回
17、顾R1kR2kR5kR3kR4kakP（5）SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHENWhen the load is applied 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 Pewl变形的实际过程l偏心压力
18、法带来的后果MT1MT2MT3MT4MT5SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN 4. Modified method 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PPewPPeSCHOOL 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
19、压力法原理偏心力矩M=Pe=e作用下， 弯矩静力平衡：M=Pe=eR1R2R4R5wiaiMT5MT4MT3MT2MT1SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN 4. Modified method of the stiffness transverse connection 修正偏心压力法l 材料力学关于简支梁跨中的 扭矩与扭转角的关系 又R1R2R4R5wiaiMT5MT4MT3MT2MT1l几何关系SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN 4. Modified met
20、hod of the stiffness transverse connection 修正偏心压力法则：代入：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：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
21、l修正后的公式SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN4. Modified method of the stiffness transverse 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： 主梁根数1.06741.04251.02861.0217SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN 4. Modified metho
22、d of the stiffness transverse connection 修正偏心压力法5）关于IT 值b3t3t2b2b1t1t/b10.90.80.70.60.50.40.30.20.1mcmcm0m0mcm0m0mc 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：mcm0m0mcm0m0mcm0m0mcm0m0Q0影响线
23、Mc影响线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1.恒载内力计算2. 结构自重3. 桥面铺装 4. 附属设施重量5.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m0mcPky1Mc影响
24、线荷载横向分布系数PkqkSCHOOL 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mckQ0影响线荷载横向分布系数m0mcPkqkay1y2SCHOOL 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 恒荷载恒荷载+1.4 汽车荷载汽车荷载+0.8 1.4 人群荷载人群荷载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n恒载内力计算 一期恒载、二期恒载集度 恒载内力n活载内力计算 跨中弯矩、剪力 支点剪力n内力组合 SCHOOL OF TRANSPORTATION, WUT PRODUCED BY：X J CHEN
