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

ScopeThe 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.

Formula or tablePy = 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.

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

Free accessAISC 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.

What governsEstimate. AHJ and licensed professional govern.

API field namespr_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