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lecmat - Draft DRAFT Lecture Notes in: FINITE ELEMENT I...

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Draft DRAFT Lecture Notes in: FINITE ELEMENT I Framed Structures Victor E. Saouma Dept. of Civil Environmental and Architectural Engineering University of Colorado, Boulder, CO 80309-0428
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Draft Contents 1 INTRODUCTION 17 1.1 Why Matrix Structural Analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2 Overview of Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3 Structural Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Structural Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.2 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.3.3 Sign Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 Course Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 I Matrix Structural Analysis of Framed Structures 27 2 ELEMENT STIFFNESS MATRIX 29 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 In±uence Coe²cients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Flexibility Matrix (Review) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4 Sti³ness Coe²cients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5 Force-Displacement Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.1 Axial Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.2 Flexural Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.3 Torsional Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5.4 Shear Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Putting it All Together, [ k ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6.1 Truss Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6.2 Beam Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6.2.1 Euler-Bernoulli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6.2.2 Timoshenko Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6.3 2D Frame Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6.4 Grid Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6.5 3D Frame Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.7 Remarks on Element Sti³ness Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.8 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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This note was uploaded on 01/19/2012 for the course ENG 04 taught by Professor 045 during the Spring '11 term at UCLA.

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lecmat - Draft DRAFT Lecture Notes in: FINITE ELEMENT I...

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