Przemieniecki J.S. Theory of Matrix Structural Analysis

Dover Publications, 1985. — 480 pages.The matrix methods of structural analysis developed for use on modern digital computers, universally accepted in structural design, provide a means for rapid and accurate analysis of complex structures under both static and dynamic loading conditions.The matrix methods are based on the concept of replacing the actual continuous structure by an equivalent model made up from discrete structural elements having known elastic and inertial properties expressible in matrix form.The matrices representing these properties are considered as building blocks which, when fitted together in accordance with a set of rules derived from the theory of elasticity, provide the static and dynamic properties of the actual structure.In this text the general theory of matrix structural analysis is presented. The following fundamental principles and theorems and their applications to matrix theory are discussed: principles of virtual displacements and virtual forces, Castigliano's theorems, minimum-strain-energy theorem, minimum-comple-'mentary-strain-energy theorem, and the unit-displacement and unit-load theorems. The matrix displacement and force methods of analysis are presented together with the elastic, thermal, and inertial properties of the most commonly used structural elements. Matrix formulation of dynamic analysis of structures, calculation of vibration frequencies and modes, and dynamic response of undamped and damped structural systems are included. Furthermore, structural synthesis, nonlinear effects due to large deflections, inelasticity, creep, and buckling are also discussed.