Chapter 3 - Tension Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
Last Revised: 11/04/2014
SCM D1 states that there is no official limit on slenderness in tension members, however, there is a strong suggestion about limiting slenderness. The suggested limit is a good idea, not a requirement. Slenderness is a serviceability limit state, not a strength limit state, so failure to adhere to the suggestion is unlikely to cause an unsafe condition.
It turns out that very slender members are difficult to handle without inadvertent bending during fabrication, transportation, and erection. Experience has shown that if you limit the slenderness (L/r) to 300 or less, then you are less likely to have problems handling the member.
Also, recalling that this is not a strength based limit state, the limit state is the same for both LRFD and ASD.
Slenderness, as you will recall from your mechanics course, relates the overall length of a member, "L", to its radius of gyration, "r".
The limit state is written as:
L/r < 300 or L/(300r) < 1.00
Where "r" is the least radius of gyration. "r" is a section property that equals the square root of the moment of inertia divided by the cross section area. Every member has an "r" for each of the of the principle axes.
Warning: Probably the most frequent error made by engineers and students alike is in unit conversions! Make sure that your "L" and "r" have the same units!
All AISC equations assume consistent units. So when computing L/r, make sure that L and r (both have length units) are both in the same units. If consistent units are used, then L/r becomes a unitless number.
Example 3.1 shows an application of this limit state.