Beam-Column Nonsway Moment Amplifier B1 (AISC 360 App. 8)

The second-order P-delta moment amplifier B1 for a steel beam-column.

Run the calculator

Example

You enter

Required axial compression Pr (kip) 400
In-plane moment of inertia I (in⁴) 272
Effective length in the plane K1 L (ft, K1 <= 1) 16
Transverse load between supports? yes
Design basis LRFD

You get

Moment amplifier B1 1.234
Pe1 (kip) 2112

Details, formula, and sources

AISC 360 Appendix 8.2.1: B1 = Cm / (1 - alpha Pr / Pe1) >= 1, with Cm = 0.6 - 0.4 (M1/M2) (or 1.0 with transverse load), Pe1 = pi^2 EI / (K1 L)^2 the in-plane elastic buckling load, alpha = 1.0 (LRFD) / 1.6 (ASD). A W10x49 carrying 400 kip over a 16 ft braced length with transverse load amplifies its moment 1.23x (LRFD), 1.43x on the ASD basis; when alpha Pr reaches Pe1 the member is unstable. Multiplies the first-order Mnt to the Mr the H1.1 check needs. In-plane only; the sidesway B2 is separate. A design aid, not the engineer of record's stamped design.

Pe1 = pi^2 E I / (K1 L)^2 (E = 29,000 ksi); Cm = 0.6 - 0.4 (M1/M2) or 1.0 (transverse load); alpha = 1.0 LRFD / 1.6 ASD; B1 = max(1, Cm / (1 - alpha Pr / Pe1)).

The AISC 360-22 Appendix 8.2.1 nonsway (braced) beam-column moment amplifier B1, with the Cm end-moment factor and the in-plane elastic buckling load Pe1, by name.

AISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); the Appendix 8 amplified first-order provisions are public. Pr, I, K1 L, and the end-moment ratio are the user's own analysis inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: pr_kip, i_in4, lc1_ft, transverse_load, method, b1, pe1_kip

Amplifier B1 = Cm / (1 - alpha Pr / Pe1) >= 1AISC 360-22 Eq. A-8-3
Buckling load Pe1 = pi^2 EI / (K1 L)^2, E = 29,000 ksi, K1 <= 1.0 braced (nominal EI; DAM uses 0.8 tau_b EI)AISC 360-22 Eq. A-8-5
End-moment factor Cm = 0.6 - 0.4 (M1/M2) (no transverse load) or 1.0 (transverse load); alpha = 1.0 LRFD / 1.6 ASDAISC 360-22 Eq. A-8-4