Optimum Design of Structures |
Contents
An outline of existing design methods | 1 |
Mathematical optimisation | 17 |
Design of structures by matrix force method | 84 |
Copyright | |
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A₁ acting analysed beam becomes bending boundary calculated changes chapter column condition Consider constant constructed corresponding cost deflection constraints derived direction displacement element equal equation example express external loads factor feasible final follows forces frame given gives ground structure hand horizontal indicates inequality integer jointed structures kN/mm˛ limited linear linear programming linearised load material matrix Maximise method mm˛ moments necessary negative non-linear noticed objective function obtained Once optimum design permissible pin jointed plastic positive possible programming problem reduced redundant forces reference removed replaced respectively satisfy selected shape shown in Figure shows Similarly simplex simplex method solution solving span stage statically determinate stiffness stress constraints structure Substituting Table tion unit variables vector volume x₁ y₁ zero