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Created on Feb 26, 2025

Add possibility to include B1 factor in Code checking Parameters with AISC 360 First Order Method

As per actual possibility provided by AISC 360, it is possible to perform design with Direct Analysis Method but also Effective Length Method and First Order method. In some case it is useful to do analysis with First order method (Dynamic Seismic Analysis). But to perform properly first order analysis we should include the B1 factor (refer appendix 7 and 8 of AISC 360-16) in the code checking to magnify the moment and take properly into account the small delta effect.



Appendix 7 ALTERNATIVE METHODS OF DESIGN FOR STABILITY

Appendix 7.3 FIRST-ORDER ANALYSIS METHOD

2. Required Strengths

(b) The nonsway amplification of beam-column moments shall be included by applying the B1 amplifier of Appendix 8 to the total member moments.

User Note: Since there is no second-order analysis involved in the first-order analysis method for design by ASD, it is not necessary to amplify ASD load combinations by 1.6 before performing the analysis, as required in the direct analysis method and the effective length method.


Appendix 8 APPROXIMATE SECOND-ORDER ANALYSIS

8.2. CALCULATION PROCEDURE

1. Multiplier B1 for P-δ Effects

The B1 multiplier for each member subject to compression and each direction of bending of the member is calculated as:

B1 = Cm/(1-α Pr/Pe)

where

α =1.0 (LRFD); α = 1.6 (ASD)

Cm = equivalent uniform moment factor, assuming no relative translation of the member ends, determined as follows:

(a) For beam-columns not subject to transverse loading between supports in the plane of bending

Cm = 0.6 − 0.4(M1 /M2) (A-8-4)

where M1 and M2, calculated from a first-order analysis, are the smaller and larger moments, respectively, at the ends of that portion of the member unbraced in the plane of bending under consideration. M1 /M2 is positive when the member is bent in reverse curvature and negative when bent in single curvature.

(b) For beam-columns subject to transverse loading between supports, the value of Cm shall be determined either by analysis or conservatively taken as 1.0 for all cases.

Pe1 = elastic critical buckling strength of the member in the plane of bending, calculated based on the assumption of no lateral translation at the member ends, kips (N)

= π^2 EI*/Lcl^2 (A-8-5)

where

EI* = flexural rigidity required to be used in the analysis (= 0.8τbEI when used in the direct analysis method, where τb is as defined in Chapter C; = EI for the effective length and first-order analysis methods)

E = modulus of elasticity of steel = 29,000 ksi (200 000 MPa)

I = moment of inertia in the plane of bending, in.4 (mm4)

Lc1 = effective length in the plane of bending, calculated based on the assumption of no lateral translation at the member ends, set equal to the laterally unbraced length of the member unless analysis justifies a smaller value, in. (mm)


So I suggest Bentley to add this possibility in the Design Parameters. SACS is allowing to do it.


You could also take the opportunity to add the checking mention below that is only applicable to First order analysis


Appendix 7 ALTERNATIVE METHODS OF DESIGN FOR STABILITY

Appendix 7.3 FIRST-ORDER ANALYSIS METHOD

1. Limitations

The required axial compressive strengths of all members whose flexural stiffnesses

are considered to contribute to the lateral stability of the structure satisfy

the limitation:

αPr ≤ 0.5Pns

where

α =1.0 (LRFD); α = 1.6 (ASD)

Pr = required axial compressive strength under LRFD or ASD load combinations, kips (N)

Pns = cross-section compressive strength; for non slender-element sections, Pns = FyAg, and for slender-element sections, Pns = FyAe, where Ae is as

defined in Section E7, kips (N)