## Optimum design of structures |

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### Contents

An outline of existing design methods | 1 |

Mathematical optimisation | 17 |

Design of structures by matrix force method | 82 |

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area A2 axial beam becomes bending moment diagram boundary calculated column cost deflection at joint deflection constraints deflexion design problem dynamic programming equations 3.4 external loads feasible region final design force in member frame in Figure frame shown given by equation gives global optimum ground structure horizontal deflection hyperstatic structures inequality integer programming jointed plane frame last row linear programming problem Maximise member forces midspan minimum weight modulus modulus of elasticity non-linear programming problem obtained optimisation optimum design optimum solution overall stiffness matrix piecewise linearisation pin jointed structure pitched roof frame plastic hinge portal frame redundant forces redundant members removed sectional properties selected shape shown in Figure Similarly simplex method slack variables solved span statically determinate structure stiffness constraints stiffness equations stress constraints surplus variable theorems tion topology unit loads vertical deflection volume zero