Chapter 8 - Bending Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
Last Revised: 07/30/2011
The objective of the selection process is, generally, to select the least cost (this is also frequently the lightest) member that satisfies the design criteria. For beams, there are multiple limit states to consider. Generally, only one limit state will control a particular selection.
The selection criteria can be stated as:
Experience with the selection process shows that
This is useful to know when making your initial selection. If you suspect that a particular limit state is likely to control, you can solve the limit state for the associated section property, then search the section tables for the most likely section to try. Before you are through, however, you must show that ALL limit states are satisfied with your final selection.
There are several different methods that can be used in the search for the optimum method. The method you use is not important as long as you find the right member. The chosen method will depend on the computational tools that you have available to you and what your feel comfortable with.
Using Sorted Section Property Tables
When plastic behavior controls the shear and flexure limit states, you can solve the limit state inequalities for the required related section properties, shear area and plastic section modulus. For deflection limit states you can always solve for required moments of inertia.
When plastic behavior controls for shear and flexure, or when selecting members based on deflection, the process can be enhanced by using sorted section property tables. The section property tables can be sorted by shear area (Aw), plastic section modulus (Zx and Zy), and moment of inertia (Ix and Iy) so that you can quickly find the most likely sections for your application. This is easily done with the shapes database available from AISC. Additionally the SCM has tables where the sections have been sorted by selected section properties. See SCM Tables 3-2, 3-3, 3-4, and 3-5 starting on SCM page 3-19. In addition to sec`tion properties, some of the tables include additional section related data. For example, the Z tables include compact criteria and moment capacities that are based on an Fy of 50 ksi. Only the first two columns can be used when using a material with an Fy other than 50 ksi.
When searching the tables for these section properties, be aware that resulting table is NOT sorted by LEAST WEIGHT! This means that the section with properties closest to the value you are searching for may not be the lightest section to meet the criteria. For example, look at SCM Table on SCM page 3-19. If you are looking for the lightest section that has a Zx that is greater than or equal to 1500 in3, the best choice is not the one (W36x361) that has the closest Zx that meets the criteria. Notice that the W44x335 also meets the criteria for Zx but is lighter than the W36x361, making it a better choice. It also has reserve capacity, which is a bonus.
The table identifies the lightest choice with bold font and a space between it and the next range. Note that the bolded section is always lighter than the ones on either side of it in the table. Using this observation, you can create your own tables in a spreadsheet by using the shapes database on the AISC website. To do this, sort the section tables by the section property of interest then use an "if" statement in an adjacent column to identify if the current section is lighter than both the one before and the one after.
Once a section is chosen, then all the limit states are computed to show that it satisfies all the applicable limit states. If it does not, a new member is selected based on the controlling limit state.
The "Hunt & Peck" Method
The Hunt & Peck method can always be used, regardless of the controlling flexural or shear limit state. This method involves searching through the section table using some means (i.e. algorithm) for determining the next section to try.
Once a selection is chosen, then all the limit states are computed to show that it satisfies all the applicable limit states. If it does not, a new member is selected based on the controlling limit state.
One way of implementing this method, is to search through a given size category (say the W18s) for the lightest section that works, then move to the other size categories. As each size category is investigated, only sections with weights less than the current best choice are considered.
The "Brute Force" Method
This method always works regardless of the controlling limit state and is best done with a spreadsheet or computer program.
In this method, a table is made that has all the sections you wish to consider (such as all the I shapes, all the rectangular HSS shapes, etc) and their section properties needed to compute the limit states. Additional columns are then added to compute the various limit states. Once all the limit states have been computed, the sections with violated limit states are deleted and the remaining table sorted by weight.
Conceivably, you can create a big table for beam design for all the sections of a particular type then just copy this over and do the eliminations and sorts for a given problem.
This method is computationally intensive but very easily done in a spreadsheet. It will always get the best result, after all the programming is debugged!