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Draft DRAFT Lecture Notes in: MATRIX STRUCTURAL ANALYSIS with an Introduction to Finite Elements CVEN4525/5525 c VICTOR E. SAOUMA, Fall 1999 Dept. of Civil Environmental and Architectural Engineering University of Colorado, Boulder, CO 80309-0428 Draft 0–2 Blank page Victor Saouma Matrix Structural Analysis Draft Contents 1 INTRODUCTION 1.1 Why Matrix Structural Analysis? 1.2 Overview of Structural Analysis . 1.3 Structural Idealization . . . . . . 1.3.1 Structural Discretization . 1.3.2 Coordinate Systems . . . 1.3.3 Sign Convention . . . . . 1.4 Degrees of Freedom . . . . . . . . 1.5 Course Organization . . . . . . . I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Structural Analysis of Framed Structures 2 ELEMENT STIFFNESS MATRIX 2.1 Introduction . . . . . . . . . . . . . . . 2.2 Influence Coefficients . . . . . . . . . . 2.3 Flexibility Matrix (Review) . . . . . . 2.4 Stiffness Coefficients . . . . . . . . . . 2.5 Force-Displacement Relations . . . . . 2.5.1 Axial Deformations . . . . . . . 2.5.2 Flexural Deformation . . . . . 2.5.3 Torsional Deformations . . . . 2.5.4 Shear Deformation . . . . . . . 2.6 Putting it All Together, [k] . . . . . . 2.6.1 Truss Element .