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Fundamentals of Structural Analysis Episode 2 Part 1

Tham khảo tài liệu 'fundamentals of structural analysis episode 2 part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beam and Frame Analysis Displacement Method Part I 1. Introduction The basic concept of the displacement method for beam and frame analysis is that the state of a member is completely defined by the displacements of its nodes. Once we know the nodal displacements the rest of the unknowns such as member forces can be obtained easily. For the whole structure its state of member force is completely defined by the displacements of its nodes. Once we know all the nodal displacements of the structure the nodal displacements of each member is obtained and member forces are then computed. Defining a node in most cases is easy it either appears as a joining point of a beam and a column or it is at a location where there is a support. In other cases it is a matter of preference of the analyzer who may decide to define a node anywhere in a structure to facilitate the analysis. We will introduce the displacement method in three stages The moment distribution method is introduced as an iterative solution method which does not explicitly formulate the governing equations. The slope-deflection method is then introduced to formulate the governing equations. Both are identical in their assumptions and concepts. The matrix displacement method is then introduced as a generalization of the moment distribution and slope-deflection methods. 2. Moment Distribution Method The moment distribution method is a unique method of structural analysis in which solution is obtained iteratively without ever formulating the equations for the unknowns. It was invented in an era out of necessity when the best computing tool was a slide rule to solve frame problems that normally require the solution of simultaneous algebraic equations. Its relevance today in the era of personal computer is in its insight on how a beam and frame reacts to applied loads by rotating its nodes and thus distributing the loads in the form of member-end moments. Such an insight is the foundation of the modern displacement .