Structural Mechanics and Dynamics - OSA &amp; Dynamics 2009-10

# Structural Mechanics and Dynamics - OSA & Dynamics 2009-10

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Structural Mechanics and Dynamics 2 nd Year Lecture Notes on Overall Structural Analysis and Structural Dynamics Dr Silvestre T Pinho (These notes are based on previous notes by D Hitchings) Thursday, 01 October 2009

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Contents i CONTENTS 1 Overall Structural Analysis . ............................................................. 3 1.1 Corresponding Forces and Displacements. .................................................... 3 1.2 The Stiffness and Flexibility Equations. ........................................................ 4 1.3 Forming the Stiffness Matrix. ........................................................................ 4 1.3.1 Example - Forming the Stiffness Matrix of a Pin-Jointed Frame. ......... 6 1.4 Alternative Member Form for Constructing a Stiffness Matrix . ................... 9 1.4.1 Inclusion of supports. ........................................................................... 13 1.5 Forming and Using the Flexibility Matrix. .................................................. 14 1.5.1 Example - The flexibility matrix of a Cantilever Beam. ....................... 16 1.5.2 Example - Flexibility Matrix of a Beam with One End Built in and the Other End Propped. ............................................................................................. 20 1.5.3 Example - Flexibility Matrix of a Beam with Both Ends Built In. ....... 22 1.5.4 A Physical Description of Finding the Redundancies . ........................ 23 1.6 The Flexibility Method for Statically Indeterminate Pin-Jointed Frameworks. ............................................................................................................. 24 1.6.1 Thermal Strains and Lack of Fit Loadings . ......................................... 26 1.7 Deflections of Redundant Structures . .......................................................... 27 1.8 Steps for Solving a Redundant Framework . ................................................ 28 2 Structural Dynamics. ....................................................................... 29 2.1 Introduction. ................................................................................................. 29 2.2 Degrees of Freedom. .................................................................................... 29 2.3 Free Vibrations. ............................................................................................ 30 2.4 Equations of Motion of a Two Degree of Freedom System . ....................... 34 2.4.1 Flexibility Form of the Equations of Motion . ...................................... 36 2.5 Solution of the Equations of motion. ........................................................... 37 2.5.1 No Forcing Function – Free Vibrations. ............................................. 37 2.6 Free Vibrations, Natural Frequencies and Mode Shapes. ............................ 37 2.6.1 Orthogonal Properties of the Eigenvectors. ........................................ 39 2.6.2 Normalisation of the Eigenvectors. ...................................................... 40
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## This note was uploaded on 03/24/2010 for the course AE A.213 taught by Professor S.pinhoandm.aliabadi during the Winter '09 term at Imperial College.

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Structural Mechanics and Dynamics - OSA & Dynamics 2009-10

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