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Caslli et al.way that will serve us to search the optimizedsolutions.Being based on the constraints, we define theanalytic relations that connect the functionrequirements (the load) with geometricparameter of the beam and the properties ofmaterial.A) Stiffness constraint is expressed:3Fl (3)C1EI3Flor EI (3’)C1Where, F is the load that applies upon thebeam (F = 13.2 kN), E – Young’s Modulus, I –Second Moment of Area (major) and constantC 1 , that accounting for equable disperse loadsand end conditions, in this case C 1 = 384/5 [1].From the equation (3’), by placing the values ofdecided parameters (so-called “solid”constraints), we display the condition that“free” parameters must fulfill, i.e. that whichmay be the optimizing object:EI 1.074 x 10 6 Nm 2 (4)In this way, by looking for the sectionoptimization according to product EI, wepractically concretize the idea for a combinematerial-shape selection (E – property ofmaterial, I – geometric parameter of sectionshape).B) The strength constraint is expressed:IyZYF C2 C2, (5)ymllIyhere ZY [Nm] (6)ymIt gives the moment of bending (major), theone that the section can confront withoutcausing any plastic deformation. Thisspecification, which will be called FailureMoment, emphasizes the influence of both thegeometry of the section (I dhe y m ) and of thematerial property ( y ). Referring to thisspecification, the strength constraint will be:FlZY (7)C 2Considering the studying scheme C 2 = 8 [2] andknowing the values of F and l, we can find thenumerical expression of strength constraint:ZY 0.825 x10 4 Nm (8)C) The geometric constraint is expressed: l= 5 mSuch a constraint is an independent constraintin itself, but it influences the other constraintssuch as A and B (geometric parameter l countsat their expressions).Based on analytic equations of A and Bconstraints (relation 3’ and 7) and theobjectives of design (Table 1), we candetermine the performance indexes, M:- Safety of stiffness with minimum mass:EIM1 (9)ml- Safety of strength with minimum mass:ZYM2 (10)ml- Safety of stiffness with minimum cost:EIM 3 (11)C- Safety of strength with minimum cost:ZYM 4 (12)Cwhere C is the cost for unit length (USD/m),while m l is linear mass (kg/m).5. THE ASHBY’S METHOD APPLICATION INCOMPUTERIZED SELECTION OF SECTIONSPreliminary selectionThe selection of sections is done by using theoptions of CES software and it starts by placingthe “solid” constraints (4) and (8). 385 “winner”sections, which are presented and visible in thebox selected, up right in figure 2, come out inthe first screening:5.1. Narrowing down of searching zoneThe narrowing of searching zone is done inaccordance with the two objectives of thedesign project: the minimization of mass andAKTET Vol. IV, Nr 2, 2011 203