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1、影响线的概念 the concept of influence line目的：解决移动荷载作用下结构的内力计算问题。 purpose: solve the problem of internal calculation under the function of load内容： content1）在移动荷载作用下结构内力变化规律和范围； internal force variation rule and scale under the function of movable load2）确定内力的最大值及相应的荷载位置最不利荷载 位置。confirm the maximum of intern
2、al force and relevant load position the most unfavorable load position当单位荷载（P=1）在结构上移动时，表示结构某一指定截面中某项内力变化规律的曲线，称为该项内力的影响线。 one curve that expresses variation rule of some internal force in an appointed section of structure when element load moves on the structure, called the influence line of the in
3、ternal force定义： definition1P=1xlAB11C ab11ba21、先按直接荷载作用画出内力影响线； draw influence line of internal force with direct load2、投影各结点与影响线相交，各交点间连以 直线。intersect the projection of various joint and influence line, line among jointsP=1l=4dABCDEI.L QD11I.L MD结点荷载作用下的影响线 the influence line under the function of
4、joint load37-5 机动法作影响线 influence line of kinematical method理论基础：虚位移原理。 theory base: virtual displacement principle 特 点：把作影响线的静力问题化为作位移图的几 何问题。 characteristic: change static problem with influence line to geometric problem with displacement picture优 点：不经计算可以得到影响线的形状。 merit: influence line shape witho
5、ut calculation4设体系上作用任意的平衡力系，又设体系发生符合约束的无限小刚体体系位移，则主动力在位移上所作的虚功总和恒等于零。Suppose it is arbitrary equilibrium force system, and system occurs infinitesimal rigid system displacement which accords to restriction, the summation of virtual work which principle power work on displacement is identical to zer
6、o.虚功原理:virtual principle5步 骤： step1、将与待求影响线的内力对应的约束拆除，代之以 内力；（原结构变成可变机构）remove the restriction which the internal force of ready solving influence line corresponds to with internal force (original structure change to alterable structure)2、令可变机构在内力正方向上发生单位位移，构造 符合约束条件的刚体体系位移；element displacement of a
7、lterable machine occurs in the positive direction of internal force, rigid system displacement of machine corresponds to restriction condition3、刚体体系位移即为待求的内力影响线。应用几何 关系求控制截面的影响线竖标。rigid system displacement as ready solving internal force influence line, solve influence line vertical mark of control
8、section with geometric relation67-6 影响线的应用 Application of influence line 一、求实际荷载作用的影响solve the influence of practical loadabCAB影响线面积代数和 Algebraic sum of area of i.l. 7二、求荷载的最不利位置the most unfavorable position of load如果荷载移到某一个位置，使某一指定内力达到最 大值（、），则此荷载所在位置称为最不利位置 。if load moves to a position to make one
9、 appointed internal force reach maximum, the position of load is called the most unfavorable position.我们可以利用影响线来确定最不利位置，对比较简单 的情况可以直观地判断最不利位置。we can use the influence line to confirm the most unfavorable position, it is intuitionistic to judge the most unfavorable position for simpler situation.8（）一
10、个集中荷载a concentrated load（）一组集中荷载 a group of concentrated loads（）任意分布荷载 arbitrary distributed load9三、临界位置的判定the judgment of critical position(1)求出使Z值达极值时荷载的位置,称临界位置。critical position (2)从各个临界位置中选出荷载的最不利位置。the most unfavorable position0+Z-Zx如何求临界位置呢？ How to find critical position?10ZxZx使Z成为极大值的临界位置 必须
11、满足的条件：(the critical position to make Z be maximum must satisfy:)使Z成为极小值的临界位置 必须满足的条件：(the critical position to make Z be minimum must satisfy:)11极值位置时只要荷载移动 就变号，它就是一个判别式。 It is a discriminant that the single changes when load moves on the extremum position 在什么情形下它才会变号呢？single changes in what situati
12、on?临界位置 critical position临界荷载 critical load极值位置时只要荷载移动 就变号。 the single changes when load moves on the extremum position小结summary121）选一个荷载置于影响线的某个顶点； select a load to a peak of influence line2）利用判别式，看是否变号； if single changes with discriminant3）求出每个临界位置对应的Z值； solve Z value corresponded to critical posi
13、tion4）比较各Z值，得出最大值。 compare various Z value, obtain maximum总结： summary: 1310 15520(kN) 3m 3.5m 4m1.8m3.36m1.6m设置于截面C处由判别式有：设置于截面d处由判别式有：3m6m14m4m8m3m5.6mcd此处不是临界位置10 15520(kN) 3m 3.5m 4m141.8m3.36m1.6m3m6m14m4m8m3m5.6mcd10 15520(kN) 3m 3.5m 4m设置于d截面处由判别式有：15影响线为三角形时的情形。 the situation that influence l
14、ine is triangleabc若存在情形： if the situation exists则是一临界位置 it is a critical position注意荷载移出影响线 范围以外的情形。 notice the situation that load moves outside of the influence line scale167-11 简支梁的包络图和绝对最大弯矩 envelope diagram and absolute maximal bending moment of simple beam设计时要求在实际荷载作用下各截面的最大和最小内力值。 maximal and
15、minimal value of every section under the function of practical load when designingP=1xlABC ab分别将各截面的最大和最小内力值连成的曲线称为内力包络图 。 The curve which is lined with maximal and minimal internal force value of every section is called internal force envelope diagram.170.090.160.210.240.251812mAB3.5m3.5m1.56.001.2
16、 2.412m21536646555957457821217915312794.365.041.725.316.48.20.0弯矩包络图（kNm） bending moment envelope diagram剪力包络图（kN） shearing force envelope diagram例：绘制简支梁在两台吊车作用下的弯矩包络图和剪力包络图。 draw the bending moment and shearing force envelope diagram of simple beam under the function of two cranes19求绝对最大弯矩,可以分为两个步骤：two steps1）它出现在那一个截面？ appear in which section? 2）在那一个集中荷载下面？ under which concentr
