Reduced Stiffness

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

EI* = 0.8τ_bEI

Eq. (A-7-2)

where

τ_b	=	1.0 if $α \frac{P_{r}}{P_{y}} \leq 0.5$ $4 [\frac{α P_{r}}{P_{y}} (1 - \frac{α P_{r}}{P_{y}})]$ if $α \frac{P_{r}}{P_{y}} > 0.5$
α	=	1.0 for LRFD 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 that in the second equation given for τb 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 0.001Yi. The program does not perform any iterations on τ_b, the user has the option of conservatively specifying a value of τ_b to use in all cases (using the Criteria – General command in the RAM Frame Analysis mode) or to use τ_b = 1.0 and specify the larger notional load. Note that if a value of τ_b is specified it is used for all members for all combinations, even though in many cases a smaller value may be permissible for some members for some combinations; this feature is just offered as a simplification, as an alternative to applying the larger notional load. Although technically τ_b is distinct for each load combination for each member, the program uses the specified value for all members. The program does not provide an Assign command to assign different τ_b values to different members, nor will it use a different stiffness for each different load combination.

A reduced axial stiffness is also to be used:

EA* = 0.8EA

Eq. (A-7-3)

The option to Use Reduced Stiffness should be selected prior to analysis using the Criteria – General command in the RAM Frame Analysis mode.

Note that the program uses the reduced stiffness for all load cases. It is not clear from the Specification whether the reduced stiffness is required to be used for the drift analysis. Thus, it is up to the engineer to decide whether or not to run the analysis twice: once for drift with the full stiffness and once for member design with the reduced stiffness, or once for both drift and member design with the reduced stiffness.

The reduced flexural stiffness is applied to members "whose flexural stiffness is considered to contribute to the lateral stability of the structure". Thus, it is not applied to members that are pinned at both ends.

The reduced axial stiffness is applied to members "whose axial stiffness is considered to contribute to the lateral stability of the structure". All lateral beams, columns and braces are reduced for their axial stiffness.