The B₁ factor is a moment amplifier to account for the P-δ effects (small P-delta, second order effects caused by displacement of the member between brace points).

The B₁ factor is to be calculated for each member individually, and differs for each combination. B₁ is calculated for each axis of the member:

where

Cm	=	form members with no transverse loading between supports in the plane of bending: 0.6 - 0.4(M1/M2)Eq.(C2-4) for members with transverse loading between supports in the plane of bending: Cm = 1.0
α	=	1.0 for LRFD 1.6 for ASD
Pr	=	total axial load in the member (combined using the appropriate LRFD or ASD Load Combinations)
Pe1	=	is the "elastic critical buckling resistance for the member in the plane of bending":

where

I	=	Ix or Iy, of the axis for which B1 is being calculated
K1	=	1.0
L	=	the unbraced length, in the axis for which B1 is being calculated

The B₁ factor is applied to moments from the gravity load cases (this is based on the assumption that all of the non-translational moments are due to gravity loads). The B₁ factor is calculated for both the local X- and Y-axes.

Note that it is not required to apply the B₁ factors for a given load combination if the following limit is met for all members whose flexural stiffness is considered to contribute to the stability of the structure:

αPr < 0.15 PeL

Eq. (A-7-1)

where

Pr	=	the required axial compressive strength under LRFD or ASD load combinations
PeL	=	π2EI/L2, evaluated in the plane of bending
α	=	1.0 for LRFD 1.6 for ASD

The program applies B₁ based on the criteria that the engineer has specified, not based on this exception, although this exception is checked and reported as part of the "AISC 360 Direct Analysis Validation" report.