Q2 Strength and stiffness constraints in a cantilever beam Design problem: A square section cantilever beam of length L must meet, simultaneously, targets for strength (ability to support an end load F without failing by plastic yielding) and stiffness S (end deflection must be less than 5) and it must do this at a minimum weight. The requirements are Function: cantilever beam Constraints: must not fail by yielding under end load F; end deflection must be less than 8; minimum fracture toughness is 7 MPa m¹/2; length L and load F are specified Objective: minimize mass, m Free variables: section area A and choice of materials Hypothetical values to fix the coupling lines (one & imposes a rather fiercer stiffness constraint, the other is more relax) Parameter Value 10 KN 1.5m 0.002m 0.1m F L $₁ $2 ܢܢܢܢܢܢܢܢܢ

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