Direct Analysis Method

The Direct Analysis Method requires:

2^nd order analysis (either an iterative 2^nd order analysis of amplified 1^st order analysis), including both P-Δ and P-δ
Notional loads
Reduced flexural and axial stiffness

Second Order Analysis

The amplified 1^st order analysis is implemented and it involves the calculation of B₁ and B₂ factors by which the member forces are multiplied. The advantage to this method is that it does not require an iterative analysis and it would allow the analysis of individual load case, with the results combined in the load combinations (the principle of superposition).

Notional Loads

Notional loads are required to be applied. If the ratio of 2^nd order drift to 1^st order drift (i.e., B₂) is greater than 1.5, the notional loads must be applied in addition to the other lateral loads (wind and seismic); if the ratio is less than 1.5, it is permissible to apply the notional loads to the gravity-only combinations.

Note: The value 1.5 is based on a model with nominal member properties. Otherwise, it is 1.7 for models with reduced member stiffness properties.

The notional loads are defined as:

N_i = 0.002 Y_i

where

Y_i

the factored gravity load(for ASD, use a factor of 1.6 on both Dead and Live load)

Reduced Stiffness

A reduced flexural stiffness is to be used for columns and beams:

EI* = 0.8 τ_b EI

Eq. (A-7-2)

where

τ_b	=	1.0 when $α \frac{P_{r}}{P_{y}} \leq 0.5$ $4 [\frac{α P_{r}}{P_{y}} (1 - \frac{α P_{r}}{P_{y}})] w h e n α \frac{P_{r}}{P_{y}} > 0.5$
α	=	1.0 for LRFD and 1.6 for ASD
P_r	=	total axial load in the member (combined using the appropriate LRFD or ASD Load Combinations)
P_y	=	A_sF_y

Note: In the second case the analysis must be iterative since P_r is a function of τ_b and vice versa. In lieu of that, the Specification permits the application of an additional notional load equal to 0.001 Y_i

A reduced axial stiffness is also to be used:

EA* = 0.8 EA

Eq. (A-7-3)