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Home > User Area > CES Selector Documentation > Structural Section Case Studies Structural Section Case StudiesThe selection methodology used in CES Sections can be encapsulated by developing a case study. Here, we will use the design of a simple beam to illustrate the development of some selection criteria, we will apply them and plot them on some selection stages by using CES. The Design ProblemHere is a typical problem in selection for structural design: choose the cheapest beam (the objective), simply supported at both ends, which will support given load F safely (a strength constraint) without deflecting more than d (a stiffness constraint) and which is no deeper than D or wider than B (geometric constraints).We will also consider also the choice if the objective were to minimise mass, rather than cost.
Figure 1 A simply supported, uniformly loaded beam
Design Requirements
Table 1The SelectionThe selection requires 3 stages. The first, Figure 2, shows the maximum width B plotted against the maximum depth D of all sections in the database. The selection box isolates sections that are less than 100 mm deep and 100 mm wide.Figures 3 and 4 plot a constraint against an objective. The first shows the bending stiffness EImax plotted against mass/length of the section. The lower edge of the selection box is positioned at the required minimum stiffness EImax = 1.25 x 105 Nm2, corresponding to the stiffness constraint (this was calculated using the equation for d in Solutions to Standard Problems). The second shows the failure moment YZmax plotted against the mass/length m/L of that section. Here the lower edge of the selection box has been placed at YZmax = 2.5 x 103 Nm, corresponding to the constraint that the beam must not fail (see Figure A3). The three stages capture the constraints on B, D, EImax and YZmax ; only sections which meet or exceed these constraints pass and remain as viable candidates.
Figure 2 Structural Section selection chart of maximum width against maximum depth of section
Figure 3 Structural Section selection chart of bending stiffness EI about major axis as a function of mass/length of that sectionTwo alternative optimisations are now possible, allowing either mass or cost to be minimised. Mass is minimised by pushing the vertical edge of the box on Figure 3 as far to the left as possible while still retaining one or more viable candidates. Cost is minimised by pushing the vertical edge of the box on Figure 4 as far to the left as possible while still retaining one or more viable candidates.
Figure 4 Structural Section selection chart of failure moment YZ about major axis as a function of cost/length of that section
ResultsTables 2 and 3 list the results.Table 2 shows the selection when optimisation is based on mass (with the cost objective relaxed): these are the lightest beams which meet all the design constraints. Table 3 shows the selection when optimisation is based on cost (with the mass objective relaxed): these are the cheapest beams which meet all the design constraints.
Table 2 Selection results: Lightest beam meeting Design Requirements
Table 3 Selection results: Cheapest beam meeting Design Requirements |
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