Slender Column Moment Magnifier, Nonsway (ACI 318-19 6.6.4)
The nonsway P-delta moment magnifier and magnified design moment for a slender column.
Example
You enter
- Factored axial load Pu (kip) 200
- Larger end moment M2 (kip-ft) 80
- Smaller end moment M1 (kip-ft; negative for single curvature, ACI 318-19) -50
- Unbraced length lu (ft) 14
- Effective-length factor k 1
- Effective stiffness EI (kip-in²) 1500000
- Column dimension h (in) 16
You get
- Cm 0.850
- Critical buckling load Pc 524.5 kip
- Moment magnifier delta_ns 1.73
- Mc kft 138.3
Checked against published worked examples from: ACI 318-19 Section 6.6.4.5 (nonsway moment magnifier).
Details, formula, and sources
ScopeThe ACI 318-19 6.6.4.5 nonsway P-delta moment magnifier delta_ns = Cm/(1 - Pu/(0.75 Pc)) and the magnified design moment Mc a slender braced reinforced-concrete column picks up. A column just over the slenderness limit gains a 1.3-1.7x amplifier the flexure check never applies; floored at M2,min.
Formula or tableCm = 0.6 - 0.4 M1/M2 (ACI 318-19 Eq. 6.6.4.5.3a; M1/M2 negative for single curvature, positive for double, no lower bound); Pc = pi^2 EI / (k lu)^2; delta_ns = max(Cm/(1 - Pu/(0.75 Pc)), 1.0); Mc = delta_ns x max(M2, M2,min) (6.6.4.5.4: the floor applies to M2 before it is magnified), M2,min = Pu(0.6 + 0.03 h).
Source and editionThe ACI 318-19 Section 6.6.4.5 nonsway (braced) slender-column moment magnifier, by name.
Free accessACI 318 is readable free through the ACI online reading room at concrete.org; the Section 6.6.4 slenderness provisions are in the published code.
What governsEstimate. AHJ and licensed professional govern.
API field namesfactored_axial_kip, end_moment_m2_kft, end_moment_m1_kft, unbraced_len_ft, eff_length_k, eff_stiffness_ei, column_dim_h_in, cm, pc_kip, delta_ns, mc_kft
- Nonsway frame braced (nonsway) 6.6.4.5 magnifier; a sway frame uses the 6.6.4.6 delta_s procedureACI 318-19 6.6.4.5
- 0.75 stiffness factor Pc appears as 0.75 Pc in the denominator (the stiffness-reduction factor)ACI 318-19 6.6.4.5.2