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# A509.3.3.3 Bilinear Representation of the Capacity Spectrum

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A bilinear representation of the capacity spectrum curve obtained in Section A509.3.3.2 shall be used in estimating the appropriate reduction of spectral demand. The first segment of the bilinear representation of the capacity spectrum shall be a line from the origin at the initial stiffness of the building using the component initial stiffness specified in Table A508.1. The second segment of the bilinear representation of the capacity spectrum shall be a line back from the trial performance point,

*a*,

_{pi}*d*, at a slope that results in the area under the bilinear representation being approximately equal to the area under the actual capacity spectrum curve. The intersection of the two segments of the bilinear representation of the capacity spectrum shall determine the yield point

_{pi}*a*,

_{y}*d*.

_{y}### Related Code Sections

A509.3.3.3 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, Bilinear Representation of the Capacity Spectrum

A

*bilinear**representation*of the*capacity**spectrum*curve obtained in Section A509.3.3.2 shall be used in estimating the appropriate reduction ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.3 Capacity Spectrum Analysis Procedure > A509.3.3 Description of Analysis Procedures > A509.3.3.3 Bilinear Representation of the Capacity Spectrum

A509.3.3.5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, Calculation of the Performance Point

of intersection of the

*capacity**spectrum*defined in Section A509.3.3.2 and the demand*spectrum*defined in Section A509.3.3.4 is within 5 percent ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.3 Capacity Spectrum Analysis Procedure > A509.3.3 Description of Analysis Procedures > A509.3.3.5 Calculation of the Performance Point

A509.4.2 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings, Target Displacement (δ

_{t})
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*bilinear*relation (see Section ...
2010 Existing Building Code of NY > A5 Earthquake Hazard Reduction in Existing Concrete Buildings and Concrete With Masonry Infill Buildings > A509 Tier 3 Analysis Procedure > A509.4 Displacement Coefficient Analysis Procedure > A509.4.2 Target Displacement (δ

_{t})
25.4.8.3 Reinforcement Details,

obtained from the

*bilinear*relationship defined by Eq. (25.4.8.1) ...
Building Code Requirements for Structural Concrete of New York State > 25 Reinforcement Details > 25.4 Development of Reinforcement > 25.4.8

*Development of Pretensioned Seven-Wire Strands in Tension*> 25.4.8.3
24.2.3.9 Serviceability Requirements,

analysis. It shall be permitted to base deflection calculations on a

*bilinear*moment-deflection relationship or I e in accordance with Eq ...
Building Code Requirements for Structural Concrete of New York State > 24 Serviceability Requirements > 24.2 Deflections Due to Service-Level Gravity Loads > 24.2.3

*Calculation of Immediate Deflections*> 24.2.3.9