Column Effective Length Factor K (Alignment Chart)

Using the Dumonteil closed-form fits to the AISC alignment charts: sway K = sqrt((1.6 GA GB + 4(GA+GB) + 7.5)/(GA+GB+7.5)) and a braced form. GA 1, GB 2 gives K 1.47 sway but 0.82 braced - a factor of 3.2 in buckling capacity, why bracing a frame is the cheapest way to shorten a column. Enter G (or 10 pinned / 1 fixed); within ~2% of the nomograph, no tau_b. A design aid, not the engineer of record's stamped design.

G = sum(EI/L)_columns / sum(EI/L)_beams; sway: K = sqrt((1.6 GA GB + 4(GA+GB) + 7.5)/(GA+GB+7.5)); braced: K = (3 GA GB + 1.4(GA+GB) + 0.64)/(3 GA GB + 2(GA+GB) + 1.28).

The AISC alignment-chart effective-length factor K from the joint stiffness ratios G, via the Dumonteil closed-form approximations to the sway and braced nomographs, by name.

The AISC alignment charts and the Dumonteil closed-form fits are public results in the AISC Commentary and the standard steel-design references.

Estimate. AHJ and licensed professional govern.

Field names used by the API: ga, gb, frame, k_factor

• Stiffness ratio G = sum(EI/L)_columns / sum(EI/L)_beams at each joint (10 pinned, 1 fixed)AISC Commentary alignment charts
• Closed-form K the Dumonteil sway/braced fits, within ~2% of the nomographDumonteil (1992)
• Chart assumptions elastic behavior, simultaneous column buckling, equal L/r; no tau_bAISC Commentary