## Energy principles in theory of structures |

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### Contents

Introduction | 1 |

Further Examples of the Use of the StrainEnergy | 29 |

The Principle of Virtual Work | 38 |

Copyright | |

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6x6lxEI a2 cos a3 a2 sin a3 analysis applied approximate solutions assumed beam bending Castigliano's changes in length Chapter complementary-energy method conditions of equilibrium conservation of energy conservative systems considered cosa2 degrees of freedom derived dFBH dFDv due to unit elastic supports energy methods energy principles equation of virtual equations of equilibrium example flexibility coefficients follows force F Fv and FH geometrical gross distortion Hooke's law law of conservation line of action linear systems load Fv load-deflection characteristics obtained pin-jointed position of equilibrium potential energy potential-energy method principle of virtual quantities reciprocal theorem redundant member redundant system represent respectively self-straining shown in fig simultaneous equations sina2 small displacement specified spring stable equilibrium statically statically-determinate system stationary stiffness coefficients strain energy strain-energy method system of forces system shown T2 sin a2 tions University of Aberdeen vertical vertical deflection virtual displacements equal