Detailed Explanation of Redundancy Factor

SYMBOLS

ρ = Redundancy factor

Redundancy is an important property for structures designed with the expectation that damage will occur. Redundant structures have alternative load paths so that if some elements are severely damaged and lose load carrying capacity, other elements will be able to continue to provide a safe load path. Adequate redundancy is ensured when a large number of plastic hinges must form throughout the structure in a progressive manner before formation of a mechanism and when no one element is required to provide the full seismic resistance of the structure.

C12.3.4 Redundancy

The standard introduces a revised redundancy factor, ρ, for structures assigned to Seismic Design Category D, E, or F to quantify redundancy. The value of this factor is either 1.0 or 1.3.This factor has the effect of reducing the response modification coefficient, R, for less redundant structures, thereby increasing the seismic demand. The factor is specified irecognition of the need to address the issue of redundancy in the design.
The desirability of redundancy, or multiple lateral force-resisting load paths, has long been recognized. The redundancy provisions of this section reflect the belief that an excessive loss of story shear strength or development of an extreme torsional irregularity (Type 1b) may lead to structural failure. The value of ρ determined for each direction may differ.

C12.3.4.1 Conditions Where Value of ρ is 1.0

This section provides a convenient list of conditions where ρ is 1.0. C12.3.4.2 Redundancy Factor, ρ, for Seismic Design Categories D through F. There are two approaches to establishing a redundancy factor, ρ, of 1.0. Where neither condition is satisfied, ρ is taken as equal to 1.3. It is permitted to take ρ equal to 1.3 without checking either condition. A reduction in the value of ρ from 1.3 is not permitted for structures assigned to Seismic Design Category D that have an extreme torsional irregularity (Type 1b). Seismic Design Categories E and F are not also specified because extreme torsional irregularities are prohibited (see Section 12.3.3.1).
The first approach is a check of the elements outlined in Table 12.3-3 for caseswhere the seismic design story shear exceeds 35% of the base shear. Parametric studies (conducted by Building Seismic Safety Council Technical Subcommittee 2 but unpublished) were used to select the 35% value. Those studies indicated that stories with story shears of at least 35%of the base shear include all stories of low-rise buildings (buildings up to five to six stories) and about 87%of the stories of tall buildings. The intent of this limit is to exclude penthouses ofmost buildings and the uppermost stories of tall buildings from the redundancy requirements. This approach requires the removal (or loss of moment resistance) of an individual lateral force-resisting element to determine its effect on the remaining structure. If the removal of elements, one by one, does not result in more than a 33% reduction in story strength or an extreme torsional irregularity, ρ may be taken as 1.0.
For this evaluation, the determination of story strength requires an in-depth calculation. The intent of the check is to use a simple measure (elastic or plastic) to determine whether an individual member has a significant effect on the overall system. If the original structure has an extreme torsional irregularity to begin with, the resulting ρ is 1.3. Fig. C12.3-6 presents a flowchart for implementing the redundancy requirements. As indicated in Table 12.3-3, braced frame, moment frame, shear wall, and cantilever column systems must conform to redundancy requirements. Dual systems also are included but, in most cases, are inherently redundant. Shear walls or wall piers with a height-to-length aspect ratio greater than 1.0 within any story have been included; however, the required design of collector elements and their connections for Ω0 times the design force may address the key issues. To satisfy the collector force requirements, a reasonable number of shear walls usually is required. Regardless, shear wall systems are addressed in this section so that either an adequate number of wall elements is included or the proper redundancy factor is applied. For wall piers, the height is taken as the height of the adjacent opening and generally is less than the story height. The second approach is a deemed-to-comply condition wherein the structure is regular and has a specified arrangement of seismic force-resisting elements to qualify for a ρ of 1.0. As part of the parametric study, simplified braced frame and moment frame systems were investigated to determine their sensitivity to the analytical redundancy criteria. This simple deemed-to-comply condition is consistent with the results of the study.