Direct-Analysis Stiffness Reduction tau_b (AISC 360 C2.3)

The AISC 360 direct analysis method reduces every member stiffness by a flat 0.8 (EA and EI) and the flexural EI of stability members by a further tau_b: tau_b = 1.0 for alpha Pr / Py <= 0.5, else 4 (alpha Pr/Py)(1 - alpha Pr/Py), where Py = Fy Ag and alpha = 1.0 (LRFD) / 1.6 (ASD). A W10x49 (Ag 14.4 in^2, Fy 50, Py 720 kip) at Pr 400 kip (LRFD) is at ratio 0.556, so tau_b 0.988 and the reduced flexural stiffness is 0.79 EI; below half of yield (Pr 300) tau_b stays 1.0 and the reduction is the flat 0.8. tau_b drops toward 0 as the axial load nears Py. Enter Pr, Fy, and Ag; an analysis stiffness input, not a strength check. AISC also allows tau_b = 1.0 for all members with an added 0.001 alpha Yi notional load. A design aid, not the engineer of record's stamped design.

Py = Fy Ag; ratio = alpha Pr / Py (alpha = 1.0 LRFD / 1.6 ASD); tau_b = 1.0 for ratio <= 0.5 else 4 ratio (1 - ratio); reduced flexural stiffness EI* = 0.8 tau_b EI.

The AISC 360-22 Section C2.3 direct-analysis-method inelastic stiffness-reduction factor tau_b, with the flat 0.8 stiffness factor, by name.

AISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); the C2.3 stiffness-reduction provision is in the published specification. Pr, Fy, and Ag are the user's own demand and section data.

Estimate. AHJ and licensed professional govern.

Field names used by the API: pr_kip, fy_ksi, ag_in2, method, tau_b, flexural_stiffness_factor, ratio

• tau_b 1.0 for alpha Pr/Py <= 0.5, else 4(alpha Pr/Py)(1 - alpha Pr/Py)AISC 360-22 Eq. C2-2
• Stiffness reduction flat 0.8 on EA and EI, plus tau_b on the flexural EI; EI* = 0.8 tau_b EIAISC 360-22 C2.3
• alpha 1.0 (LRFD) / 1.6 (ASD); Py = Fy AgAISC 360-22 C2.3
• Feeds supplies 0.8 tau_b EI to the B1, K, and G stability tilesscope of this tile