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# A509.4.2 Target Displacement (δ_{t})

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The target displacement of the control node (typically the center of mass of the building's roof) shall be determined using the following equation:

where:

where:

C_{0} = | Modification factor to relate spectral displacement to expected building roof displacement. Value of C_{0 }can be estimated using any one of the following: | |

1. | The first modal participation factor at the level of the control node. | |

2. | The modal participation factor at the level of the control node computed using a shape vector corresponding to the deflected shape of the building at the target displacement. | |

3. | The appropriate value from Table A509.4.2. |

TABLE A509.4.2 VALUES OF MODIFICATION FACTOR,

TABLE A509.4.2 VALUES OF MODIFICATION FACTOR,

*C*_{0} NUMBER OF STORIES | C_{0} |

1 | 1.0 |

2 | 1.2 |

3 | 1.3 |

5 | 1.4 |

10+ | 1.5 |

NOTE: Linear interpolation shall be used to calculate intermediate values. | |||||

C_{1} | = | Modification factor to relate expected maximum inelastic displacements to displacements for linear elastic response. C_{1} shall not be taken as less than 1.0. | |||

= | 1.0 for T_{e} ≥ T_{0} | ||||

= | [1.0 + (R - 1)T_{0}/T_{e}]/R for T_{e} < T_{0} | ||||

Where: | |||||

R | = | Strength ratio = | |||

V_{y} | = | Yield strength calculated using the results of static pushover analysis where the nonlinear base-shear roof-displacement curve of the building is characterized by a bilinear relation (see Section A509.4.5). | |||

T_{0} | = | Characteristic period of the response spectrum, defined as the period associated with the transition from the constant acceleration segment of the spectrum to the constant velocity segment of the spectrum. | |||

C_{2} | = | Modification factor to represent the effect of hysteresis shape on maximum displacement response. | |||

= | 1.3 where T > T_{0} | ||||

= | 1.1 where T ≥ T_{0} | ||||

Exception: Where the stiffness of the structural component in a lateral-force-resisting system, which resists no less than 30 percent of the story shear, does not deteriorate at the target displacement level, C_{2} may be assumed to be equal to 1.0. | |||||

S_{a} | = | Response spectral acceleration at the effective fundamental period and damping ratio of the building, g, in the direction under consideration. | |||

T_{e} | = | Effective fundamental period of the building in the direction under consideration, per Section A509.4.5. |