Effective length factor

Finds the effective length factor K of a column (k in ACI 318), solved from the equations behind the alignment charts, so no chart is read by eye. It also gives the idealized values of Commentary Table C-A-7.1 and K2 by the two story approaches. The result is a number to enter in a column calculation: nothing links them, so changing this calculation does not change that one.

Inputs of the effective length #

• Code: AISC 360-22 (G), or ACI 318-19 (ψ). The equations are the same. ACI 318-19 6.6.4.4.3 uses Ec and the inertias of 6.6.3.1.1, so the factor on I defaults to 0.70 for columns and 0.35 for beams; enter another factor where Table 6.6.3.1.1(a) or an analysis allows it.
• Way of finding K: alignment chart equations; idealized end conditions; K2 by story stiffness; K2 by story buckling. Story approaches are AISC only.
• Frame: sidesway uninhibited or inhibited. Which it is, is your call.
• Column: E, I about the axis perpendicular to the plane of buckling, unsupported length L.
• Column inelasticity τb (AISC): the Commentary replaces E I with τb E I for all columns in G, using Eq. C2-2 with the required strength Pr and Pns = Fy Ag, α = 1.0 for LRFD and 1.6 for ASD. On by default. It may be conservatively ignored, which gives a larger K. Pns is taken as Fy Ag: reduce the area for a slender section.
• Top and base: a joint with its members, or G entered. A base may be pinned (G = 10 prefilled, the Commentary's value unless it is a true frictionless pin) or rigidly attached to a footing (G = 1.0 prefilled; smaller if justified by analysis).
• Members at a joint: other columns and girders in the plane of buckling. The column under consideration counts already. For each girder:
  • Far end: as the chart assumes; rotation prevented (× 2 braced, × 2/3 sway); pinned (× 1.5 braced, × 1/2 sway); or MF/MN from a first-order lateral analysis, which sets Lg' = Lg (2 − MF/MN), Eq. C-A-7-4.
  • Q/Qcr: axial load in the girder over its in-plane buckling load at K = 1.0. Multiplies its E I / L by (1 − Q/Qcr).
  • Connection: a shear-only connection gives no restraint and is left out of G. Partially restrained connections: adjust the factor on I yourself from a documented moment-rotation response.
• Story (story approaches): Pstory for all columns of the story including gravity-only ones; Pmf, ΔH, H and Hcol for story stiffness; the sum of π²EI/(Kn2 L)² for the moment frame columns, and Kn2, for story buckling.

The design method only sets α in τb.

Checks performed #

The type reads Calculated. It has no pass or fail: a column calculation uses K. Pc from K2 may not exceed the sidesway inhibited value: compare it there.

Limitations #

• The charts assume elastic behavior, constant sections, rigid joints, and the curvature stated for each frame. These seldom hold exactly, and you judge where they do.
• MF/MN of 2 or more makes G negative: the type stops, since it solves the equations for positive G only. Solve it yourself and enter G.
• Under the direct analysis method (AISC 360-22 Chapter C) K = 1.0, and this type is not needed.
• ACI 318-19 gives no idealized table or K2: those ways stop for that code. For nonsway members ACI permits k = 1.0 and its commentary recommends it.
• The LeMessurier approach of the Commentary is not built.

Verification examples #

Verification status: 32 values compared in 26 examples (16 published, 10 hand calculations from the cited equations): 32 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.

No published value of Eq. C-A-7-5 or C-A-7-8 was found. Hand calculations from the Commentary's equations cover both story approaches and their lower limits, the chart equations' limits (0.5, 0.699, 1.0 braced; 1.0, 1.316, 2.0 sway), the girder adjustments and ACI's factors.