影响线及其应用 Influence lines and their application.ppt

* Dd wwweecc 确定绝对最大弯矩要解决以下两个问题 2 problems need to be solved： （1）绝对最大弯矩发生在哪一截面；Identify the section at which the absolute maximum moment is reached （2）此截面发生最大弯矩时的荷载位置The positions on which the absolute maximum moment is reached . 对由集中荷载组成的移动荷载，问题可以简化,因为弯矩的最大值点必定是某个集中载的作用点：For a series of moving concentrated loads the problem may be simplified, because the section with maximum bending moment is one of the application points of loads FK 作用点处的弯矩Mx为 The moment at the section of application of FK is 式中MK 表示FK以左梁上荷载对于FK点处的力矩总和 Where MK is the sum of moments induced by all the loads in the left of FK about the application point of FK 支座反力为The reaction at support A is 极值条件为the condition for extreme value is 即当FK 与合力FR的位置对称于梁的中点时FK之下截面的弯矩达到最大值 I.e. when FK and FR are symmetrical with respect to the middle point of the beam the moment at the application section of FK reaches its maximum value 当FR 位于FK 的左边时 When FR is located at the left of FK we have 在荷载多时，上述方法非常烦杂。When there are many loads, the previous method is very complicated. 可以利用这样的事实：通常简支粱的绝对最大弯矩发生在粱的中点附近。But we can use the following fact: generally the maximum bending moment arises at the middle of the beam. 使粱中点截面发生最大弯矩的临界荷载通常也是发生最大弯矩的荷载。利用这一事实可得下列简化方法。 The critical loads that induce maximum bending moment at the middle of beam are loads that result in maximum bending moment. Using this fact we can obtain the following simplified method. 计算最大弯矩的基本方法(basic method for determination of maximum bending moment 1、首先确定使粱的中点发生最大弯矩的临界荷载 3、计算 作用处的弯矩，即为绝对最大弯矩。 2、计算合力 ，把 与 对称于梁的中点布置，这时要注意是否有力移出粱跨。如果有力移出粱跨，需要重新计算合力，重复上述步骤. At first determine the load that induces the maximum moment at the middle of the beam, and calculate the Calculate FR, and place FR and Fk symmetrically with respect to the middle of the beam, in this case need pay attention to whether there are loads outside the span, if there are, then calculate FR again, and repeat the above mentioned procedur