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Redundancy Coefficient

Posted Date: 30 May 2014

The intent of the redundancy coefficient is to encourage the design of more redundant structures, with a greater number of elements provided to resist lateral forces. Introduction of the redundancy coefficient into the building code was a direct reaction of the observation of structures damaged by the 1994 Northridge earthquake and the resulting conclusion that economic pressures had led many engineers to design structures with very little redundancy. This was particularly observed to be a problem for certain classes of moment-resisting steel frame and concrete shear wall buildings.

The basic premise of the redundancy provisions is that the most logical way to determine lack of redundancy is to check whether a component’s failure results in an unacceptable amount of story strength loss or in the introduction of extreme torsional irregularity. The redundancy factor, ρ, is equal to either 1.0 or 1.3, depending upon whether or not an individual element can be removed (deemed to have failed or lost its force-resisting capabilities) from the lateral force-resisting system without causing the remaining structure to suffer a reduction in story strength of more than 33 percent or creating an extreme torsional irregularity (Horizontal Structural Irregularity Type 1b in ASCE Table 12.3-1).

Braced frame, moment frame, shear wall, and cantilever column systems have to conform to redundancy requirements. Dual systems are included also, but in most cases are inherently redundant. Shear walls with a height-to-length ratio greater than 1.0 are included in redundancy considerations to help ensure that an adequate number of wall elements is included or that the proper redundancy factor is applied. Stories resisting more than 35% of the base shear only are considered.

The above way of determining ρ obviously involves a number – possibly a significant number – of structural analyses. There is an alternative way of determining ρ essentially by inspection. If a structure is regular in plan and there are at least 2 bays of seismic force-resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35% of the base shear, then ρ = 1. Significantly, the number of bays for a shear wall is to be calculated as the length of the shear wall divided by the story height or two times the length of shear wall divided by the story height for light-framed construction. Thus, the shear wall length plays a major role and light-framed construction is given an advantage.

ASCE 7 Section 12.3.4.1 includes a user-friendly feature of conveniently listing when ρ may be taken as 1.0 and reads as follows:

12.3.4.1 Conditions Where Value of ρ is 1.0. The value of ρ is permitted to equal 1.0 for the following:

  1. Structures assigned to Seismic Design Category B or C.
  2. Drift calculation and P-delta effects.
  3. Design of nonstructural components.
  4. Design of non-building structures that are not similar to buildings.
  5. Design of collector elements, splices, and their connections for which the load combinations with over strength factor of Section 12.4.3.2 are used.
  6. Design of members or connections where the load combinations with over strength of Section 12.4.3.2 are required for design.
  7. Diaphragm loads determined using Eq. 12.10-1.
  8. Structures with damping systems designed in accordance with Section 18.
  9. Design of structural walls for out-of-plane forces including their anchorage

The following figure is from the 2009 NEHRP Recommended Seismic Provisions Commentary and presents a flowchart for implementing the redundancy requirements:

Redundancy Coefficient