C-C1C1 General stability requirements

There are many parameters and behavioral effects that influence the stability of steelframed structures (Birnstiel and Iffland, 1980; McGuire, 1992; White and Chen, 1993; ASCE, 1997; Ziemian, 2010). The stability of structures and individual elements must be considered from the standpoint of the structure as a whole, including not only compression members, but also beams, bracing systems, and connections.

Many building codes include stiffness requirements for control of seismic drift, which act as an indirect limit on sidesway amplification. ASCE/SEI 7, Minimum Design Loads and Associated Criteria for Buildings and Other Structures (ASCE, 2022), directly limits a stability coefficient, $\theta$, (approximately equal to $1-1 / B_{2}$ ) to 0.25 for seismic design of buildings, effectively requiring that $\Delta_{2 n d \text {-order }} / \Delta_{1 s t \text {-order }}$, calculated with nominal stiffness, not exceed a value of 1.33 if $P_{m f}=0$ nor 1.44 if $P_{m f}=P_{\text {story }}$ (Sabelli and Griffis, 2021). This limit is well within the more general recommendation that sidesway amplification, calculated with reduced stiffness, should be equal to or less than 2.5 . The latter recommendation is made because at larger levels of amplification, small changes in gravity loads and/or structural stiffness can result in relatively larger changes in sidesway deflections and second-order effects, due to large geometric nonlinearities.

Table C-C1.1 shows how the five general requirements, provided in Section C1, are addressed in the direct analysis method (Sections C2 and C3) and the effective length method (Appendix 7, Section 7.2). The first-order analysis method (Appendix 7,

TABLE C-C1.1 Comparison of Basic Stability Requirements with Specific Provisions

[a]In typical building structures, the "joint-position imperfections" refers to column out-of-plumbness. [b]Second-order effects may be considered either by a computational P-Δ and P-δ analysis or by the approximate method (using B₁ and B₂ multipliers) specified in Appendix 8.

Section 7.3) is not included in Table C-C1.1 because it addresses these requirements in an indirect manner using a mathematical manipulation of the direct analysis method. The additional lateral load required in Appendix 7, Section 7.3.2(a), is calibrated to achieve roughly the same result as the collective effects of notional loads required in Section C2.2b, $P-\Delta$ effects required in Section C2.1(b), and the stiffness reduction required in Section C2.3. Additionally, a $B_{1}$ multiplier addresses $P-\delta$ effects as defined in Appendix 8, Section 8.1.2.

In the 2010 AISC Specification (AISC, 2010), uncertainties in stiffness and strength was added to the list of effects that should be considered when designing for stability.

Although all methods detailed in this Specification, including the direct analysis method, the effective length method, and the first-order elastic method, satisfy this requirement, the effect is listed so that it is clear that it is to be included, along with the original four other effects, when any other rational method of designing for stability is employed.