A Beginner's Guide to the Structural Engineering Basic Design Concepts © 2006,2008 T. Bartlett Quimby 

Section DC.4 Searching for the Best Design Last Revised: 11/04/2014 After defining the problem with an objective function and constraints, the problem now becomes to find the set of design variables that result in the best objective function value while still satisfying the constraints. There has been and will be a lot of research done on optimization theory. It is not the intent of this text to give a thorough review of the available techniques. The effort here is focused on strategies that an entry level engineer can use to find the best solution to structural component design. In most civil engineering structures, members are selected from a set of available shapes. This is certainly true for steel, timber, and masonry structures. To a less extent, it is true for concrete structures as standard multiples of dimensions are frequently used. This fixed set of available choices is convenient because it limits the extent of the search for the best solution. It appears that search strategies used by practicing engineers fall into several broad categories. Brute Force Method This method involves applying the constraints to all available sections. Spreadsheets and a database of available shapes make this relatively easy. The method can get tedious of member connections are considered in the selection as often a different connector arrangement must be considered for each choice. Random Initial Selection Method In this method, you randomly select a member, design the end connection and compute the constraints. From examining the results of the constraints, you choose a new member that has hope of satisfying the constraints and resulting in a section that is better than the last. You never consider a section that would result in a worse objective than your current best feasible choice, thus paring down the list of possible selections. One variation on this method is to pick a subset of the available shapes then determine the best section in that category. You then examine other subsets in turn to see if there is a better choice in those subsets. The best solution is the one that returns the section with the best objective function value. Rational Use of Constraints This is generally the best method to use for hand solutions. It this case, you guess which constraint is likely to control then solve that constraint for a section property that you can use to search the section tables. For example, with a tension member you could solve either the limit state of tensile strength for a required A_{g} or slenderness for a required r (or both):
Using these two section properties the section database can be searched for sections that satisfy these criteria. Once you select a section that satisfies these criteria, if you have a bolted end connection then:
If you cannot determine a layout that satisfies fastener based limitations then you may need to select another section (one that still satisfies tensile strength and slenderness) using the random selection method and try again. In selecting design variables it is helpful to look at the limiting equations that use the variables to decided which variables are the most sensitive and focus on changing those.
