文档介绍：外文出处: Theory of structures Publisher:McGraw Hill
外文原文
Matrix methods in structural analysis
FORCE AND DEFORMATION METHODS
The various methods of analysis of statically indeterminate systems that have been used in preceding chapters fall into two distinct classifications. In the analysis of arches and frames, for example ,the procedure was as follows: First, all redundant constraints were removed and replaced by the corresponding redundant forces(or moments).The magnitudes of these forces were then found by using the theorem of least work based on a consideration of the strain energy in the structure. A similar procedure was used in the analysis of statically indeterminate trusses. This general approach is called the method of forces.
In the analysis of continuous beams and frames, a somewhat different procedure was used. In this case, we calculated first the angles of rotation of the joints (deformations) and considered the redundant forces only later. The three-angle equation used in the analysis of continuous beams represents again the kind of approach. Such procedure is called the method of deformation.
To illustrate, on the same example, the distinction between the two methods, let us consider the statically indeterminate plane truss shown in Fig . Here, a load P, defined by ponents Px and Py, is supported by five prismatic members hinged together at A and to a rigid foundation at their upper ends, Since the number of bars is greater than the number of equations of equilibrium for the joint A, the problem is evidently statically indeterminate . In general, if the hinge A is attached to the foundation by n bars, all in one plane, the number of redundant bars will be (n-2). Then, to determine the corresponding redundant forces X1,X2,X3,……,Xn-2 by a method of forces, we write the expression for the strain energy of the system as a function of these forces and, by using the theorem of least work, obtain the necessary equations: U/ X1 U/ X2 ……(a)
Each of