Performance-based seismic evaluation aims to provide information on expected seismic performance of structures in measurable and meaningful terms for decision makers (performance objectives). The Pacific Earthquake Engineering Research (PEER) Center utilized the performance-based earthquake engineering (PBEE) framework by linking the earthquake scenarios, design ground motions, structural demand, and performance variables. PBEE procedure may be simplified by decoupling the evaluation of the design ground motion levels (probabilistic seismic hazard assessment, PSHA) and that of the structural demand due to design ground motions (probabilistic seismic demand assessment, PSDA). The objective of this chapter is to present the vector-valued implementation of PEER PBEE approach. Key points of PSDA methodology such as selection of engineering demand parameters along with the intensity measures, effects of ground motion record scaling, and construction of probabilistic seismic demand models are discussed. Integration of vector-valued intensity measures into these models is explained in detail. Results of a recent study investigating the effect of vertical ground motions on ordinary highway bridges is used to demonstrate the application of PEER PBEE framework for a particular class of structures.