In this paper, we investigate the performance of reduced order modeling of dynamic structural systems based on the proper orthogonal decomposition (POD) technique. Singular value decomposition of the so-called snapshot matrix is adopted to generate the reduced space, onto which the system equations of motion are projected to speedup the computations. To get insights into the achievable speedup and the capability of POD to provide an input-independent reduced model, we consider the 39-story Pirelli tower in Milan-Italy. First, we assume that a shear model of the building is excited by the May 18-1940, M_w 7.1, El Centro earthquake, and generate the data ensemble necessary to build the reduced model. Second, we assess the local and global accuracies of the same reduced model in tracking the dynamics of the building, if excited by the May 6-1976, M_w 6.4, Friuli earthquake and by the January 17-1995, M_w 6.8, Kobe earthquake, which differ from the El Centro one in terms of excited vibration frequencies. We show that POD allows to attain a speedup approaching 250, when the reduced order model is asked to feature a high accuracy; moreover, POD tends to outperform a standard modal analysis at increasing number of modes retained in the model.