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# 1617.2 Redundancy

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The provisions given in Section 9.5.2.4 of ASCE 7 shall be used.

**Exception**: Structures designed using the simplified analysis procedure in Section 1617.5 shall use the redundancy provisions in Sections 1617.2.2.

Modify Section 9.5.2.4.2 as follows:

9.5.2.4.2 Seismic Design Category D: For structures inSeismic Design Category D, ñ shall be taken as the largest of the values of x calculated at each story "x" of the structure in accordance with Equation 9.5.2.4.2-1 as follows:

where:

Calculation of

For a story with a flexible diaphragm immediately above,

The value of need not exceed 1.5, which is permitted used for any structure. The value of shall not be taken as less than 1.0.

The metric equivalent of Equation 9.5.2.4.2-1 is:

Where:

The value ρ shall be permitted to be taken equal to 1.0 in the following circumstances:

For structures with vertical combinations of seismic-force-resisting systems, the value of ñ shall be determined independently for each seismic-force-resisting system. The redundancy coefficient of the lower portion shall not be less than the following:

where:

ρ

R

P

R

9.5.2.4.2 Seismic Design Category D: For structures inSeismic Design Category D, ñ shall be taken as the largest of the values of x calculated at each story "x" of the structure in accordance with Equation 9.5.2.4.2-1 as follows:

ρ = 2 —20/ (

*r*√_{maxx}*A*)_{x}where:

*r*= The ratio of the design story shear resisted by the single element carrying the most shear force in the story to the total story shear, for a given direction of loading. For braced frames, the value of_{maxx}*r*is equal to the lateral force component in the most heavily loaded brace element divided by the story shear. For moment frames,_{maxx}*r*shall be taken as the maximum of the sum of the shears in any two adjacent columns in the plane of a moment frame divided by the story shear. For columns common to two bays with moment-resisting connections on opposite sides at the level under consideration, 70 percent of the shear in that column is permitted to be used in the column shear summation. For shear walls,_{maxx}*r*shall be taken equal to shear in the most heavily loaded wall or wall pier multiplied by 10/_{maxx}*l*(the metric coefficient is3.3/_{w}*l*), divided by the story shear, where_{w}*l*is the wall or wall pier length in feet (m). The value of the ratio of 10/_{w}*l*need not to be greater than 1.0 for buildings of light-framed construction. For dual systems,_{w}*r*shall be taken as the maximum value defined above, considering all lateral-load-resisting elements in the story. The lateral loads shall be distributed to elements based on relative rigidities considering the interaction of the dual system. For dual systems, the value of ñ need not exceed 80 percent of the value calculated above._{maxx}*A*= The floor area in square feet of the diaphragm level immediately above the story._{x}Calculation of

*r*need not consider the effects of accidental torsion and any dynamic amplification of torsion required by Section 9.5.5.5.2._{maxx}For a story with a flexible diaphragm immediately above,

*r*shall be permitted to be calculated from an analysis that assumes rigid diaphragm behavior and x, need not exceed 1.25._{maxx}The value of need not exceed 1.5, which is permitted used for any structure. The value of shall not be taken as less than 1.0.

**Exception**: For structures with seismic-force-resisting systems in any direction comprised solely of special moment frames, the seismic-force-resisting system shall be configured such that the value of calculated in accordance with this section does not exceed 1.25. The calculated value of is permitted to exceed this limit when the design story drift, Δ, as determined in Section 9.5.5.7, does not exceed Δa/ρfor any story where a is the allowable story drift from Table 9.5.2.8.

The metric equivalent of Equation 9.5.2.4.2-1 is:

ρ

*= 2 — 6.1/ (*_{x}*r*√_{maxx}*A*)_{x}Where:

*A*is in square meters._{x}The value ρ shall be permitted to be taken equal to 1.0 in the following circumstances:

- When calculating displacements for dynamic amplification of torsion in Section 9.5.5.5.2.
- When calculating deflections, drifts and seismic shear forces related to Sections 9.5.5.7.1 and 9.5.5.7.2.
- For design calculations required b y Section 9.5.2.6, 9.6 or 9.14.

For structures with vertical combinations of seismic-force-resisting systems, the value of ñ shall be determined independently for each seismic-force-resisting system. The redundancy coefficient of the lower portion shall not be less than the following:

ρ

*=*_{L}*R*/_{L}ρ_{u}*R*_{u}where:

ρ

*= r of lower portion.*_{L}R

*= R of lower portion.*_{L}P

*= r of upper portion.*_{u}R

*= R of upper portion.*_{u}A redundancy coefficient, ρ, shall be assigned to each structure designed using the simplified analysis procedure in Section 1617.5 in accordance with this section. Buildings shall not exceed the limitations of Section 1616.6.1.

For structures assigned to Seismic Design Category B or C (see Section 1616), the value of the redundancy coefficient is 1.0.

For structures in Seismic Design Category D (see Section 1616), the redundancy coefficient, shall be taken as the largest of the values of, ρ

where:

For a story with a flexible diaphragm immediately above,

The value, ρ, shall not be less than 1.0, and need not exceed 1.5.

Calculation of

For structures with seismic-force-resisting systems in any direction comprised solely of special moment frames, the seismic-force-resisting system shall be configured such that the value of calculated in accordance with this section does not exceed 1.25 for structures assigned to Seismic Design Category D, and does not exceed 1.1 for structures assigned to Seismic Design Category E or F.

The value ρ shall be permitted to be taken equal to 1.0 in the following circumstances:

For structures with vertical combinations of seismic-force-resisting systems, the value, ρ, shall be determined independently for each seismic-force-resisting system. The redundancy coefficient of the lower portion shall not be less than the following:

R

R

*, calculated at each story*_{i}*"i"*of the structure in accordance with Equation 16-54, as follows:
ρ

*= 2 — 20/ (*_{i}*r*√_{maxi}*A*)_{i}**(Equation 16-54)**where:

ρ

*= 2 — 6.1/ (*_{i}*r*√_{maxi}*A*)_{i}*r*= The ratio of the design story shear resisted by the most heavily loaded single element in the story to the total story shear, for a given direction of loading._{maxi}*r*= For braced frames, the value_{maxi}*r*, is equal to the horizontal force component in the most heavily loaded brace element divided by the story shear._{maxi}*r*= For moment frames,_{maxi}*r*shall be taken as the maximum of the sum of the shears in any two adjacent columns in a moment frame divided by the story shear. For columns common to two bays with moment-resisting connections on opposite sides at the level under consideration, it is permitted to use 70 percent of the shear in that column in the column shear summation._{maxi}*r*= For shear walls,_{maxi}*r*, shall be taken as the maximum value of the product of the shear in the wall or wall pier and 10/_{maxi}*l*(3.3/_{w}*l*for SI), divided by the story shear, where_{w}*l*is the length of the wall or wall pier in feet (m). In light-framed construction, the value of the ratio of 10/lw need not be greater than 1.0._{w}*r*= For dual systems,_{maxi}*r*, shall be taken as the maximum value defined above, considering all lateral-load-resisting elements in the story. The lateral loads shall be distributed to elements based on relative rigidities considering the inter-action of the dual system. For dual systems, the value of need not exceed 80 percent of the value calculated above._{maxi}*A*= The floor area in square feet of the diaphragm level immediately above the story._{i}For a story with a flexible diaphragm immediately above,

*r*shall be permitted to be calculated from an analysis that assumes rigid diaphragm behavior and need not exceed 1.25_{maxi}The value, ρ, shall not be less than 1.0, and need not exceed 1.5.

Calculation of

*r*need not consider the effects of accidental torsion and any dynamic amplification of torsion required by Section 9.5.5.5.2 of ASCE 7._{maxi}For structures with seismic-force-resisting systems in any direction comprised solely of special moment frames, the seismic-force-resisting system shall be configured such that the value of calculated in accordance with this section does not exceed 1.25 for structures assigned to Seismic Design Category D, and does not exceed 1.1 for structures assigned to Seismic Design Category E or F.

**Exception**: The calculated value of ρ is permitted to exceed these limits when the design story drift, Δ, as determined in Section 1617.5.4, does not exceed Δa/ρ for any story where a is the allowable story drift from Table 1617.3.1.

The value ρ shall be permitted to be taken equal to 1.0 in the following circumstances:

- When calculating displacements for dynamic amplification of torsion in Section 9.5.5.5.2 of ASCE 7.
- When calculating deflections, drifts and seismic shear forces related to Sections 9.5.5.7.1 and 9.5.5.7.2 of ASCE 7.
- For design calculations required by Section 1620, 1621 or 1622.

For structures with vertical combinations of seismic-force-resisting systems, the value, ρ, shall be determined independently for each seismic-force-resisting system. The redundancy coefficient of the lower portion shall not be less than the following:

ρL =

*R*/_{L}ρ_{u}*R*_{u}*r*= r of lower portion._{L}R

*= R of lower portion.*_{L}*r*= r of upper portion._{u}R

*= R of upper portion.*_{u}