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:
TABLE A509.4.2 VALUES OF MODIFICATION FACTOR, C0
where:
| C0 = | Modification factor to relate spectral displacement to expected building roof displacement. Value of C0 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, C0
| NUMBER OF STORIES | C0 |
| 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. | |||||
| C1 | = | Modification factor to relate expected maximum inelastic displacements to displacements for linear elastic response. C1 shall not be taken as less than 1.0. | |||
| = | 1.0 for Te ≥ T0 | ||||
| = | [1.0 + (R - 1)T0/Te]/R for Te < T0 | ||||
| Where: | |||||
| R | = | Strength ratio = |  | ||
| Vy | = | 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). | |||
| T0 | = | 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. | |||
| C2 | = | Modification factor to represent the effect of hysteresis shape on maximum displacement response. | |||
| = | 1.3 where T > T0 | ||||
| = | 1.1 where T ≥ T0 | ||||
| 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, C2 may be assumed to be equal to 1.0. | |||||
| Sa | = | Response spectral acceleration at the effective fundamental period and damping ratio of the building, g, in the direction under consideration. | |||
| Te | = | Effective fundamental period of the building in the direction under consideration, per Section A509.4.5. | |||