comes from（来自于）the similarity（相似性）between both dV/dx = - and d2M/dx2 = - , which relate a beam’s internal shear and moment to its applied loading, and d /dx = M/EI and d2y/dx2 = M/EI, which relate the slope and deflection of its elastic curve to the internal moment.
共轭梁法首先在1860年由Otto Mohr提出。本质上说，它与弯矩图面积定理一样在确定梁的转角或挠度上需要相同的计算量；但是这种方法只依赖于静力学的原理，因此，它的应用更常见。该法的基础来自于dV/dx=- 和d2M/dx2=- 之间的相似性，它将梁的内部剪力和弯矩与它施加的荷载联系起来，而d /dx = M/EI和d2y/dx2 = M/EI将弹性曲线的转角和挠度与内部弯矩联系起来。
Note that the shear V compares with（与..对应）the slope , the moment M compares with the displacement y and the intensity of the external load compares with the area under the M/EI diagram. To make use of this comparison we will consider a beam having the same length as the real beam, but referred to here as the “conjugate beam”.
注意剪力V与转角 相对应，弯矩M与位移y相对应，而外力的强度 与M/EI图下的面积相对应。为了利用这些对应，我们将考虑一根与实际梁一样长的梁。但是这里称为共轭梁。
In general, though（然而）, remember that if the real support allows a slope, the conjugate support must develop（产生）a shear; and if the real support allows a displacement, the conjugate support must develop a moment, note that the conjugate beam is “loaded” with the M/EI diagram, in order to conform to（与..一致）the load on the real beam. We can therefore state（陈述）two theorems related to the conjugate beam, namely（即）, Theorem 1: The slope at a point in the real beam is equal to the shear at the corresponding point（相应点）in conjugate beam. Theorem 2: The displacement of a point in the real beam is equal to the moment at the corresponding point in the conjugate beam.
然而通常要记住如果实际的支座允许一个转角，共轭的支座必须产生一个剪力；如果实际的支座允许一个位移，共轭的支座必须产生一个弯矩，注意共轭梁用M/EI图来加荷，以便与实际梁上的荷载一致。因此，我们可以陈述与共轭梁相关的两种定理，即，定理1：实际梁上某一点的转角等于共轭梁上相应点的剪力。定理2：实际梁上某一点的位移等于共轭梁上相应点的弯矩。
For more complicated loadings or for structures such as trusses and frame, it is suggested（建议）that energy methods be used for the computation. All energy methods are based on the conservation of energy principle（能量守恒原则）, which states（规定）that the work（功）done by all the external forces acting on a structure, Ue, is transformed into（转化为）internal work or strain energy（应变能）UI, which is developed（形成）when the structure deforms（变形）.
对于较复杂的荷载或结构如桁架和框架，建议应该采用能量法来计算。所有的能量法是基于能量守恒原则，它规定了作用在结构上的所有外力作的功Ue转化成内部功或结构变形时形成的应变能UI 。
The principle of virtual work was developed by John Bernoulli in 1717 and is sometimes referred to as the unit-load method（单位荷载法）. It provides a general means（一般方法）of obtaining the displacement and slope at a point on a structure, be it（无论是）a beam, frame, or truss. Before developing the principle of virtual work, it is necessary to make some general statements（一般规定）regarding the principle of work and energy.
虚功原理在1717年由John Bernoulli提出，有时称为单位荷载法。它提供了获得结构上某一点的位移和转角的一般的方法，不管该结构是梁、框架还是桁架。在提出虚功原理之前，关于功和能量的原理有必要作些一般规定。
If we take（取）a deformable（可变形）structure of any shape or size and apply a series of external loads P to it, it will cause internal loads u at points throughout the structure. It is necessary that the external and internal loads be related by the equation of equilibrium. As a consequence of（通过）these loadings, external displacement will occur at the P loads and internal displacement will occur at each point of internal load u.
如果我们取一个任何形状或尺寸的可变形结构，并对它施加一组外力P，它将导致整个结构上的点产生内力u。有必要通过平衡方程将内外力联系起来。通过这些荷载，外部的位移 发生在荷载P作用处，而内部位移 发生在内力u所处的每个点。
In general, these displacements do not have to be elastic, and they may not be related to（与..有关）the loads; however, the external and internal displacements must be related by the compatibility of the displacements. In other words, if the external displacements are known, the corresponding internal displacements are uniquely defined（唯一确定）. In general, then, the principle of work and energy states（表述）:
P = u （5-1）
Work of External Loads = Work of Internal Loads
一般来说，这些位移不必是弹性的，它们可能与荷载无关。但是外部位移与内部位移必须通过位移协调联系起来。换句话说，如果已知外部位移，则相应的内部位移可惟一的确定。通常，功和能量原理表述为
P = u （5-1）
外力功=内力功