for constructing an influence line is rather basic（基本的）, one should clearly be aware of the difference between constructing an influence line and constructing a shear or moment diagram. Influence lines represent the effect of a moving load only at a specified point on a member, whereas shear and moment diagrams represent the effect of fixed loads at all points along the axis of the member.
影响线在设计抵抗大量活荷载的结构时有着重要的应用。一根影响线代表着当集中力在构件上移动时构件上一个特定点的反力、剪力、弯矩或挠度的变化。一旦画出这根线，任何人一眼便知活荷载应该置于结构的哪个位置才能对这个特定的点引起最大的影响。而且，这点上相关的反力、剪力、弯矩或挠度可从影响线图的纵坐标上计算出来。因此，影响线在桥梁、工业吊车轨道、输送机和其它有荷载在整个结构长度上移动的结构设计中扮演着重要的角色。虽然画出一条影响线的步骤是相当基本的，但任何人应该清楚地意识到画一条影响线与画一条剪力或弯矩图的区别。影响线只代表着移动荷载对构件上特定点的影响，而剪力和弯矩图代表固定荷载对沿着构件轴线的所有点的影响。
Deflections of structures can occur from various sources（原因）, such as loads, temperature, fabrication errors, or settlement. In design, deflections must be limited in order to prevent cracking of attached（附属的） brittle materials such as concrete or plaster (石膏) . Furthermore, a structure must not vibrate or deflect（变位）severely in order to “appear” safe for its occupants（居住者）. More important, though（然而）, deflections at specified points in a structure must be computed if one is to analyze statically indeterminate structures. We often determine the elastic deflections of a structure using both geometrical and energy methods. Also, the methods of double integration（双重积分）are used. The geometrical methods include the moment-area theorems（弯矩图面积定理）and the conjugate-beam method（共轭梁法）, and the energy methods to be considered are based on virtual work（虚功）and Castigliano’s theorem（卡氏最小功定理）. Each of these methods has particular advantages or disadvantages.
结构的挠度可以因不同的原因而发生，如荷载、温度、制造错误或沉降。设计中，挠度必须加以限制以阻止附属的脆性材料如混凝土或石膏的开裂。而且，为了向居住者显示安全性，结构不能严重地振动或变位。而更重要的是如果有人要分析超静定结构，必须计算出结构中规定点的挠度。我们通常采用几何法和能量法来确定结构的弹性挠度。也采用双重积分法。几何法包括弯矩图面积定理和共轭梁法，而考虑的能量法是基于虚功定理和卡式最小功定理。每一种方法都有其特别的优缺点。
We can determine the equation of the elastic curve by integration of equation d2v / dx2 = M / EI. Solution of this equation requires two successive（连续的）integrations to obtain the deflection v of the elastic curve. For each integration, it is necessary to introduce（引入）a “constant of integration”（积分常数）, and then solve for the constants to obtain a unique solution（唯一解）for a particular（特定的）problem. It should be realized that the method of double integration is suitable only for elastic deflections（变位）such that the beam’s slope is very small. Furthermore, the method considers only deflections due to bending.
我们可以通过对方程d2v / dx2 = M / EI的积分来确定弹性曲线的方程。该方程的求解需要两个连续的积分，以获得弹性曲线的挠度v。对每次积分，有必要引入积分常数，求出该常数以获得一个特定问题的唯一解。应该了解到双重积分法只适合于弹性变位，因而梁的转角是非常小的。而且，该法只考虑了由于弯曲引起的挠度。
The initial ideas（最初的概念）for the two moment-area theorems were developed（提出）by Otto Mohr and later stated formally（正式确定）by Charles E. Greene in 1872. These theorems provide a semi-graphical （半图解）technique for determining the slope of the elastic curve and its deflection due to bending. They are particularly advantageous（有利）when used to solve problems involving beams especially those subjected to a series of concentrated loadings or having segments（段）with different moment of inertia（惯性矩）. Theorem 1: The change in slope（转角变化）between any two points on the elastic curve equals the area of the M / EI diagram between these two points. Theorem 2: The deviation（偏差）of the tangent（正切）at point B on the elastic curve with respect to（相对于）the tangent at point A equals the “moment” of the M / EI diagram between the two points A and B computed about point A (the point on the elastic curve), where（这里）the deviation tA/B is to be determined.
最初的关于两个弯矩图面积定理的概念是由Otto Mohr提出，后来由Charles E. Greene在1872年正式加以确定。这些定理为确定弹性曲线由于弯曲引起的转角和挠度提供了半图解的方法。当用以解决包括梁在内的问题，特别是那些承受一组集中加载的梁或有着不同惯性矩的梁段时，它们（指弯矩图面积定理）是特别得有利。定理1：弹性曲线上任何两点之间转角的变化等于这两点之间的M / EI图的面积。定理2：弹性曲线上B点的正切相对于A点的正切的偏差等于点A与点B之间的M / EI图对A点（该点在弹性曲线上）的矩，这里偏差tA/B将被确定。
The conjugate-beam method was first presented（提出）by Otto Mohr in 1860. Essentially（本质上）, it requires the same amount of computation（计算量）as the moment-area theorems to determine a beam’s slope or deflection; however, this method relies only on the principles of statics and hence its application will be more familiar（常见）. The basis for the method