A Beginner's Guide to the Steel Construction Manual, 14^th ed.

Chapter 6 - Buckling Concepts

© 2006, 2008, 2011 T. Bartlett Quimby

Section 6.5

Example Problem 6.2

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 6:  Excel Spreadsheet Solutions

In addition to the spreadsheet solution this problem also has a downloadable hand solution:  BGSCMExample6_2.pdf

Given: The sections listed below are to be concentrically loaded in compression.

Wanted: Determine the F_y for which each of the sections will be considered slender.

a) W18x35; b) C9x13.4; c) HSS 10x4x1/8; d) HSS 7.5x0.188; e) M4x6

Solution:

The equations for l_r can be solved for F_y for given cross sections.  Doing so yields the value of F_y for which the section is slender.  A similar approach can be made to determine the value of F_y for which a section is compact or non-compact, however, in the case of members subjected to concentric axial compression, the only real concern is determining if the section is slender or non-slender.

To solve this problem, the initial challenge is to determine the applicable cases in SCM Table B4.1a (SCM pg 16.1-16).  Then, the appropriate section properties for the member are found in the section property tables or computed from the section properties.  Using the criteria from SCM Table B4.1a and the section properties, we can then determine F_y.

a)  W18x35:  This section has both unstiffened and stiffened elements. 

The unstiffened element (1/2 a flange) has a tabulated width/thickness ratio (b_f/2t_f) in the tables.  This value is set equal to the Table B4.1a case 1 l_r equation then the equation is solved for F_y.

The stiffened element (the web) has a tabulated width/thickness ratio (h/t_w) in the tables.  This value is set equal to the case 5 l_r equation then the equation is solved for F_y.

The value of F_y that is the least is the controlling value for the problem.  It is the value for which the member first becomes slender.

b) C9x13.4:  This member is essentially the same as for the W section.  The same SCM Table B4.1a cases apply.

In this case, the unstiffened element is the whole flange.  The width/thickness ratio for the unstiffened element is not tabulated in the tables, so it is computed from the tabulated values for the flange width, b_f, and flange thickness, t_f.

The width/thickness ratio is for the unstiffened element is not tabulated, so it is computed from the tabulated values for "T" and t_w.

c) HSS 10x4x1/8:  This member only has stiffened elements.

SCM Table B4.1a case 6 is applicable in this case. As the section has two different size "plates", you want the larger of the tabulated values for b/t and h/t.

Once you select the appropriate width/thickness ratio, this is equated to the correct l_r equation and solved for F_y.

d) HSS 7.5x0.188:  This is a round section that has no plate members in the cross section.

For this member, SCM Table B4.1a case 9 applies.  For this case we need the D/t ratio for the member and the equation for l_r.  Note that for this case that there is NOT a square root in the equation for l_r.  The equation is then solved for F_y.

e) M4x6:  This is a small "I" shaped member and is solved exactly as the W18x35 was above.

Observations:

• Neither the W18x35 nor the HSS 10x4x1/8 make good sections for use as columns as both are slender and will have low compressive strength values.  They are probably best used in flexure applications.
• This approach can be applied to all sections in the database to find the value of F_y for which the member is considered to be compact, non-compact, or slender for concentric axial compression and/or pure bending (the values for each member a different in each case)
• A similar exercise can be performed using SCM Table B4.1b to determine the classification of the same sections in flexure.

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