A509.4.2 Target Displacement (δ_t)

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:

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.