A Beginner's Guide to the Steel Construction Manual, 16^th ed.

Chapter 6 - Buckling Concepts

© 2006, 2008, 2011, 2017, 2023 T. Bartlett Quimby

Section 6.4

Stability Analysis Methods

Last Revised: 06/24/2023

SCM C1 (SCM page 16.1-26) puts forth the stability requirements for structures and their elements. These requirements are reflected in different ways within the available stability analysis methods. The requirements include:

• "flexural, shear, and axial member deformations, and all other deformations that contribute to displacements in the structure,
• second-order effects (both P-D and P-d effects),
• geometric imperfections,
• stiffness reductions due to inelasticity, including the effect of partial yielding of the cross-section which may accentuated by the presence of residential stresses, and
• uncertainty in system, member, and connection strength and stiffness."

The addition of the latter three requirements appeared in the 13^th edition and were a driving force towards the development of the "Direct Analysis Method" recommended by the specification.

With the 14^th edition of the SCM and the included ANSI/AISC 360-10 specification there is a shift from traditional column "Effective Length" stability analysis and design involving effective length coefficients, K, to the more recent "Direct Analysis" method (first introduced in the 2005 specification as an appendix) which uses K equal to one for all compression members. The older procedures have been moved from SCM Chapter C to SCM Appendix 7.

In general, the specification focuses on determining the capacity side of the design inequality, leaving the required strength determination method to the engineer to determine using recognized or defendable methods of structural analysis. The exception to this being the specification of load combinations according to the requirements of ASCE 7--even then it does not specify the analysis method. With the introduction of the 2005 specification, AISC now has something to say about how engineers are to do their analysis when designing steel structures.

The other exception is now in the area of stability analysis. Stability analysis has always been problematic--often requiring the engineer to make conservative approximations where there are holes in the available stability computational methods. This is particularly true in moment frames where the means for accurately determining the effective length coefficients is limited as the theory does not address all cases where rotational resistance of joints is provided by the structure. It has been determined that specifying the means of structural analysis can reduce some of the uncertainties associated with determining strength where stability is an issue.

Because of the problems inherent in effective length determination, efforts have been made to remove effective length from the process of determining member capacity and instead make changes to the analysis methods so that the computed member forces account for member stability. Consequently, if you wish to ignore effective length, then you need to use a modified structural analysis that considers member stability to determine member forces. The accepted method for doing this is the Direct Analysis method.

You should take the time to read the discussion on "Required Strength, Stability, Effective Length, and Second-Order Effects" on starting on SCM page 2-14.

There are three methods which can be employed to address the problems related to stability and strength design:

• The Direct Analysis Method
• The Effective Length Method
• The First-order Analysis Method

There are situations where each of the methods is advantageous. SCM Table 2-1 (SCM page 2-54) provides a summary of the methods, any limitations on their use, and relevant features of the various methods. The choice of methods will impact the structural analysis of the structure and the determination of member capacity.

Historically, steel design texts have spent little time on the analysis methods as the structural analysis has used methods presented in structural analysis courses. With the introduction of the Direct Analysis method there is a need to provide specific training in its use. After the release of the 15th edition, short courses devoted to teaching the method appeared in both academia and industry. The industry leading structural analysis software packages have implemented the procedure and providing training and reference materials on its use.

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