Chapter 7 - Concentrically Loaded Compression Members
© 2006, 2008, 2011 T. Bartlett Quimby
Slenderness Limit State
Last Revised: 11/04/2014
The slenderness limit state is found in SCM E2. In actuality, slenderness is not a firm limit state. It is a suggestion, much like the slenderness limit state discussed in the tension member chapter.
Slender members are difficult to handle, in addition to being weak under compressive loads. This limit state, if adhered to, will result in the selection of members that are easier to handle during fabrication and erection.
The Limit State
The limit state simply recommends at the slenderness ratio, KL/r, not exceed 200. This is not a requirement. The user note in SCM E2 implies that the KL/r is the maximum KL/r for the member--this can either be in the member's final location in a structure or during construction. Mathematically this suggestion is stated as:
(KL/r)max < 200
(KL/r)max / 200 < 1
It is good to note that members with slenderness ratios as high as 200 have little compressive strength. This will become apparent in the following sections. Consequently, it is uncommon to find such slender compression members in a structure as they rarely have the needed strength to support the applied loads. The design process will lead to columns with smaller values of KL/r.
SCM E2 states that the effective length factor, K, using in this section "shall be determined in accordance with Chapter C or Appendix 7". SCM Chapter C is not particularly useful in computing K as it focuses on the Direct Analysis Method for which K is always equal to 1 when computing strengths to compare with demand resulting from a rigorous analysis which accounts for member stability. When considering this limit, no such analysis enters into the limit state, so the the provisions of SCM Appendix 7 appear to be more applicable here.
If this section is being used to consider the stiffness during construction handling, then it is appropriate to use K=1 in most cases.