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A Beginner's Guide to the Steel Construction Manual, 14th ed. Chapter 7 - Concentrically Loaded Compression Members © 2006, 2008, 2011 T. Bartlett Quimby |
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Section 7.8 Example Problem 7.3 Last Revised: 11/04/2014 The example problems presented in this section have a spreadsheet solution. You will need this file to follow along with the presented solutions. You can click on the following link to get the file: Chapter 7: Excel Spreadsheet Solutions This problem does not lend itself to a hand solution, so one is not provided. Given: A column as effective lengths (KL)x and (KL)y of 30 ft and 6 ft, respectively. The load are such that the minimum required nominal axial strength for the column is 800 kips. Use ASTM A992 steel. Wanted: Select the lightest W section that will support the given load. Solution: The general steps required to determine the axial capacity of a member were outline previously in the text and in example problem 7.1. The approach taken here is to apply the steps to ALL W sections, sort the sections by area, then find the lightest one that provides the specified capacity. As you examine the spreadsheet in the provided solution, you will notice that each row of the table computes the capacity of a single section. First the necessary section properties are obtained, then the section is designated as being either slender or not slender based on SCM Table B4.1a criteria. The controlling member slenderness (KL/r) is then determined. Note that since KL is provided, it may have come from any of the acceptable analysis methods. The values of Qs and Qa are determined. If the associated cross sectional elements are not slender then these values are equal to 1. From these, the value of Q is determined. The equations of SCM E7 are used to compute Fcr since E3 is the same as E7 with Q=1. With Fcr computed, the nominal capacity Pn can be computed and compared against the required Pn. The spreadsheet uses color formatting to readily identify which sections are adequate and which are not. Since the table is sorted from smallest to largest (by area), the best solution is the first one encountered that meets the criteria. It is important to note that there are, quite frequently, sections larger than the best choice that do not meet the criteria. This is a problem when searching by hand as we did in example 7.2. There is a chance that manual search will not arrive at the best solution depending on where you enter the table. This technique is sometimes known as the "brute force" method. It is computationally intensive but will always yield the best solution. It is not a good method for "hand" solution! |