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Design for Stability
Gu = GL = Slenderness Ratio for non-sway Frames k =

Stiffness reduction factor ( t ) due to column inelasticity:

a).  Pf / Py <= 0.5 (elastic):     t =1.0
b).  Pf / Py > 0.5 (inelastic):    t = 4 (Pf / Py). ( 1 - Pf / Py)

  Py = Fy.Ag
  Pf - factored axial load on the column, Pf <= 0.85 Py

Methods for Stability Design

Direct Analysis:

  1). Use any second-order elastic analysis

  2). Consider notional load for out-of-plumbness (0.2% of total gravity load)

  3). Use a reduced flexural and axial stiffness to account for influence of inelasticity (EI* = 0.8 t EI, EA* = 0.8 EA)

  4). K = 1.0

Effective Length Method: (B2 = D2nd-order / D1st-order <= 1.5)

  1). Use any second-order elastic analysis (nominal geometry, stiffness)

  2). Consider notional load for out-of-plumbness (0.2% of total gravity load)

  3). Determine K from a sideway buckling analysis

Design for Stability 

Tool to Get Effective Length for Column with Various Sections under Axial Loads