A Beginner's Guide to the Steel Construction Manual, 15th ed.

Chapter 6 - Buckling Concepts

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Section 6.5.2

Example Problem 6.2

Last Revised: 04/19/2021

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 Fy 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 lr can be solved for Fy for given cross-sections. Doing so yields the value of Fy for which the section is slender. A similar approach can be made to determine the value of Fy 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 Fy.

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

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

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

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

In this case, the Fy for which the section will be considered to be slender is 22.5 ksi,

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, bf, and flange thickness, tf.

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

In this case, the Fy for which the section will be considered to be slender is 71.3 ksi,

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 lr equation and solved for Fy.

In this case, the Fy for which the section will be considered to be slender is 8.2 ksi,

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 lr. Note that for this case that there is NOT a square root in the equation for lr. The equation is then solved for Fy.

In this case, the Fy for which the section will be considered to be slender is 79.4 ksi,

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

In this case, the Fy for which the section will be considered to be slender is 64.2 ksi,

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 Fy 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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