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A509.4.2 Target Displacement (δ_t)

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)

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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:

C₀ =	Modification factor to relate spectral displacement to expected building roof displacement. Value of C₀can 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 T_e ≥ T₀

		=	[1.0 + (R - 1)T₀/T_e]/R for T_e < T₀

	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).

	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.

	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.

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