Optimum Design of Structures |
Contents
An outline of existing design methods | 11 |
Mathematical optimisation | 17 |
Design of structures by matrix force method | 82 |
Copyright | |
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A₁ A₂ area A2 axial beam becomes bending moment boundary calculated column cos² deflection at joint deflection constraints deflexion design problem dynamic programming equations 3.4 example external loads feasible region final design frame shown given by equation gives ground structure horizontal deflection hyperstatic structures inequality integer programming jointed plane frame kN/mm² last row linear programming problem local optimum member forces minimum weight mm² mm³ modulus non-linear programming problem objective function obtained optimisation optimum design optimum solution piecewise linearisation pin jointed plane pin jointed structures 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 x₁ y₁ zero