How do the B1 and B2 factors differ from the P-Delta option in RAM Frame - Analysis mode?

The B1 and B2 factors are magnifiers that amplify the force results from a first-order analysis in order to approximate second order effects. The B1 factor accounts for second order effects caused by local displacement between the ends of a member (small P-delta effects). The B2 factor accounts for second order effects caused by relative displacement at member ends (large P-Delta).

The P-Delta analysis in RAM Frame – Analysis mode (option in Criteria – General) accounts for large P-Delta effects, but not small P-delta effects. The B2 factor should not be used simultaneously with the P-Delta option in Analysis mode.

In general, the P-Delta analysis is a more rigorous method for accounting for second order effects (large P-Delta) and is the preferred method over the B2 factor. However, the P-Delta analysis only applies to rigid and semirigid diaphragms and is problematic for some building configurations (see P-Delta tech note). For Flexible/None and Pseudo-Flexible Diaphragms or when the building configuration is the cause of an instability error, the B2 factor may be a better option.

How are the B1 and B2 factors calculated?

B1 factors are calculated using Eq. A-8-3 in Appendix 8 of AISC 360-10.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.

B2 factors are calculated using Eq. A-8-6 in Appendix 8 of AISC 360-10. This equation uses the first-order interstory drift. When semirigid or pseudo-flexible diaphragms are used in RAM Frame, the interstory drift is calculated as the average displacement at all nodes associated with the diaphragm. B2 factors are applied to the axial loads and moments from the lateral load cases.

There is not a way to override the calculated B1 and B2 factors at this time. However, this is a feature that we are considering for a future release.

Why does the Member Code Check identify a Pr > Pe1 error when the B1 factor is used or a Pnt > Pe2 error when the B2 factor is used?

Pe1 represents the elastic critical buckling resistance of the member in the plane of bending. When Pnt > Pe1, the axial force in the member exceeds the critical buckling load. This would result in the denominator of Eq. A-8-3 in Appendix 8 of AISC 360-10 to be negative, which would result in a negative B1 and affect the interaction values determined by the program.

Pe2 represents the elastic critical bucking resistance for the story. When Pnt > Pe2, the sum of the axial forces in sections attached to the diaphragm exceed the critical buckling load. This can occur when displacements are large, which results in a small Pe2 (see AISC 360-10 Eq A-8-7). In some cases, a Pnt>Pe2 error can occur even when the story displacement for each load combination is reasonable. This can occur when a load combination produces small displacements with small, non-zero diaphragm shears. In these cases, Pe2 is a small and the denominator of AISC 360-10 Eq A-8.6 becomes negative. In general, a buckling issue should not occur when the displacement and diaphragm shear are small. When a Pnt > Pe2 error occurs, we recommend the following:

1. Turn off B2 and make sure that all members have adequate strength.
2. Review story displacements and make sure they are reasonable.
3. If the story displacements are large, then the error indicates a stability issue and the lateral stiffness should be increased.
4. If the story displacements are reasonable, try unselecting load combinations that have small displacements and diaphragm shears and will not control the design on the member by inspection. Note that will unselected load combination would no longer be considered in the design of the member.
5. If the error still occurs and a P-Delta analysis cannot be used, then you may need to account for second order effects outside the program.

See Also

RAM Frame P-Delta

RAM Frame AISC360 Stability Analysis and Design

AISC 360 Direct Analysis Method in RAM Structural System

RAM SS Pseudo-Flexible Diaphragms FAQ