Chapter 3 - Tension Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
Last Revised: 07/30/2011
The goal of the selection process is to find the section that best meets the objective function and still satisfies all the constraints.
For example, let us say that you are trying to find the lightest section to use for a tension member of length L with an applied factored force of Pu and a given type of steel.
The objective function then becomes:
The best solution will be the one with the least weight.
The constants in the problem are:
The design variables are those things that you have control over as a designer. In this case:
Another way to look at the design variables is that they are all the items that you need to choose in order to draw a complete picture of the structural element.
The constraints on the design include all or some the limit states that have been presented in this chapter, depending on the nature of the end connections:
Later we will add limit states for the strength of the bolts and welds which may have an impact on your selection as well.
So... the question is: How do you approach this problem?
Well, there are several methods that work.
Brute Force Method
This method involves applying the constraints to all available sections. Spreadsheets and the database provided by AISC make this method relatively easy. In the case of a member with bolted end connections this can be tedious as you may need to determine a new bolt layout in each case.
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, so the W8 sections, then determine the best section in that category. You then examine other subsets (W10, W12, W14, etc) 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 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 tensile yielding for a required Ag or slenderness for a required r (or both):
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 tensile rupture or block shear then you may need to select another section (one that still satisfies tensile yielding and slenderness) using the random selection method and try again.
If you have a welded connection, you can by pass the bolt bearing and block shear limit states, however, you do need to compute tensile rupture.