1.2design by elastic analysis

1.2.1 General Stability Requirements

Design by a second-order elastic analysis that includes the direct modeling of system and member imperfections is permitted for all structures subject to the limitations defined in this section. All requirements of Section C1 apply, along with the following additional requirements and exceptions. All load-dependent effects shall be calculated at a level of loading corresponding to LRFD load combinations.

The influence of torsion shall be considered, including its impact on member defor- mations and second-order effects.

The provisions of this method apply only to doubly symmetric members, including I-shapes, HSS, and box sections, unless evidence is provided that the method is applicable to other member types.

1.2.2 Calculation of Required Strengths

For design using a second-order elastic analysis that includes the direct modeling of system and member imperfections, the required strengths of components of the struc- ture shall be determined from an analysis conforming to Section C2, with additional requirements and exceptions as noted in the following.

1.2.2a General Analysis Requirements

The analysis of the structure shall also conform to the following requirements:

• (a) Torsional member deformations shall be considered in the analysis.
• (b) The analysis shall consider geometric nonlinearities, including P-∆, P-δ, and twisting effects as applicable to the structure. The use of the approximate proce- dures appearing in Appendix 8 is not permitted.

User Note: A rigorous second-order analysis of the structure is an important requirement for this method of design. Many analysis routines common in design offices are based on a more traditional second-order analysis approach that includes only $P-\Delta$ and $P-\delta$ effects without consideration of additional second-order effects related to member twist, which can be significant for some members with unbraced lengths near or exceeding $L_{r}$. The type of second-order analysis defined herein also includes the beneficial effects of additional member torsional strength and stiffness due to warping restraint, which can be conservatively neglected. Refer to the Commentary for additional information and guidance.

• (c) In all cases, the analysis shall directly model the effects of initial imperfections due to both points of intersection of members displaced from their nominal locations (system imperfections), and initial out-of-straightness or offsets of members along their length (member imperfections). The magnitude of the initial displacements shall be the maximum amount considered in the design; the pattern of initial displacements shall be such that it provides the greatest destabilizing effect for the load combination being considered. The use of notional loads to represent either type of imperfection is not permitted.

User Note: Initial displacements similar in configuration to both displacements due to loading and anticipated buckling modes should be considered in the modeling of imperfections. The magnitude of the initial points of intersection of members displaced from their nominal locations (system imperfections) should be based on permissible construction tolerances, as specified in the AISC Code of Standard Practice for Steel Buildings and Bridges or other governing requirements, or on actual imperfections, if known. When these displacements are due to erection tolerances, 1/500 is often considered based on the tolerance of the out-of-plumbness ratio specified in the Code of Standard Practice. For out-of-straightness of members (member imperfections), a 1/1,000 out-of-straightness ratio is often considered. Refer to the Commentary for additional guidance.

1.2.2b Adjustments to Stiffness

The analysis of the structure to determine the required strengths of components shall use reduced stiffnesses as defined in Section C2.3. Such stiffness reduction, including factors of 0.8 and $\tau_{b}$, shall be applied to all stiffnesses that are considered to contribute to the stability of the structure. The use of notional loads to represent $\tau_{b}$ is not permitted.

User Note: Stiffness reduction should be applied to all member properties including torsional properties ( $G J$ and $E C_{w}$ ) affecting twist of the member cross section. One practical method of including stiffness reduction is to reduce $E$ and $G$ by $0.8 \tau_{b}$, thereby leaving all cross-section geometric properties at their nominal value.

Applying this stiffness reduction to some members and not others can, in some cases, result in artificial distortion of the structure under load and thereby lead to an unintended redistribution of forces. This can be avoided by applying the reduction to all members, including those that do not contribute to the stability of the structure.

1.2.3 Calculation of Available Strengths

For design using a second-order elastic analysis that includes the direct modeling of system and member imperfections, the available strengths of members and connections shall be calculated in accordance with the provisions of Chapters D through K, as applicable, except as defined below, with no further consideration of overall structure stability.

The nominal compressive strength of members, $P_{n}$, may be taken as the cross-section compressive strength, $F_{y} A_{g}$, or as $F_{y} A_{e}$ for members with slender elements, where $A_{e}$ is as defined in Section E7.