在采用该法时，写出联立方程并求解位移的未知量，而不是力或弯矩作为未知量。它采用了简单的符号约定：所有与构件有关的变量如果是顺时针则为正。对MAB和MBA ,完整的转角位移方程为四个部分的叠加： A, B , 和荷载。因此
MAB = 4EI/L A +2EI/L B -6EI/L2 +FEMAB （5-3）
MBA = 2EI/L A +4EI/L B -6EI/L2 +FEMBA （5-4）
Where MAB and MBA are clockwise end moments
Aand B are clockwise end rotations is a relative linear displacement of ends A and
B that matches（符合）a clockwise rotation
of AB
FEM is referred to as fixed end moment. A和 B为顺时针的端部转角； 是端部A相对于B的线位移，符合 AB的 FEM 称为固定端弯矩。 这里， MAB和MBA为顺时针的端部弯矩； 顺时针转动；
Analysis by slope deflection begins with use of above equations to write separate expressions for the end moments at each end of each member. Equilibrium is then imposed（利用）using moment equilibrium at joints rotated an unknown and transverse force equilibrium on members with an unknown . A system of equations（方程组）is produced that has the end displacements as unknowns. When solved simultaneously（联立求解）, the resulting displacements（得到的位移）are substituted in（代入）the slope deflection equations, giving the end moments.
转角位移法的分析从采用上述方程分别写出每个构件在每一端的端部弯矩表达式着手。然后利用平衡，即采用节点转动未知量 时的弯矩平衡和构件有未知量 时的横向力平衡。形成以端部位移为未知量的方程组。当联立求解时，将求解得到的位移代入转角位移方程，得到端部弯矩。
The method of analyzing beams and frames using moment distribution was developed by Hardy Cross, a professor of civil engineering at the University of Illinois. At the time this method was first published（公布）in 1932, it attracted immediate attention, and it has been recognized as one of the most notable（显著的） advances in structural analysis during the twentieth century. Moment distribution is a method of successive approximations（逐次近似计算法）that may be carried out （实现）any desired degree of accuracy（精度）. Essentially（本质上）, the method begins by（首先）assuming each joint of structure is fixed. Then, by unlocking and locking（解开与锁住）each joint in succession（连续地）, the internal moments at the joints are “distributed”（分配）and balanced until the joints have rotated to their final or nearly final positions. 采用弯矩分配法分析梁和框架的方法由Illinois大学的土木工程教授Hardy Cross提出。该法于1932年首次公布时便立刻受到了注意，并被承认是20世纪结构分析中最显著的进步之一。弯矩分配法是一种逐次近似计算法，可以实现任何需要的精度。本质上来说，该法首先假定结构的每一个节点是固定的。然后连续地解开和锁住每个节点，节点的内部弯矩被分配和平衡，直到节点转至它们最终的或几乎最终的位置。
It will be found that this process of calculation is both repetitive（重复的）and easy to apply. Before explaining the techniques of moment distribution, however, certain definitions and concepts must be presented（介绍）. Clockwise moments that act on the member are considered positive, whereas counterclockwise（反时针的）moments are negative. The moments at the “walls”（墙壁）or fixed joints of a loaded member are called fixed-end moments（固端弯矩）. The member stiffness factor at A can be defined as the amount of moment M required to rotate the end A of the beam A=1 rad. If several members are fixed-connected to a joint, then by the principle of superposition, the total stiffness factor at the joint is the sum of the member stiffness factors at the joint, that is, KT= K.
发现该计算过程是重复的且容易运用。但是在解释弯矩分配法的技术之前，必须介绍某些定义和概念。作用在构件上的顺时针弯矩为正，而逆时针弯矩为负。“墙”上的弯矩或负荷构件上固定节点的弯矩称为固端弯矩。构件在A点的刚度系数可定义为使梁端A转动值 A=1弧度所需要的弯矩M的值。如果一些构件与一个节点固接，则根据叠加原理，该节点处总的刚度系数为该节点处的构件刚度系数的总和，即KT= K 。
This value represents the amount of moment needed to rotate the joint through an angle of 1 rad. If a moment M is applied to a fixed-connected joint, the connecting members will each supply a portion of（一部分）the resisting moment necessary to satisfy moment equilibrium at the joint. That fraction of（部分） the total resisting moment supplied by the member is called the distribution factor (DF)（分配系数）. The carry-over factor（传递系数）represents the fraction of M that