P-Delta effects in the torsional response of structures

Abstract

Nonlinear dynamic analysis is an accepted procedure to assess the performance of building structures during earthquakes. Several documents have emerged to provide guidance in terms of mathematical modeling, ground motion selection and scaling, and acceptability of results. Due to computational advances, one of the newer requirements provided by these standards is to perform a three dimensional analysis and to include P-Delta effects. Unfortunately, the same provisions do not provide details on methods for incorporating P-Delta effects into the mathematical model, and as a result important response characteristics, including the potential for global torsional collapse may be overlooked. The issue at hand is the potential for not including or improperly modeling the P-Theta effect, which is an amplification of rotations about the vertical axis due to gravity loads. In this paper, the P-Theta effect is investigated for a torsionally irregular nine-story buckling restrained braced frame system. Three methods for incorporating the P-Delta and P-Theta effects are illustrated. The first method, which uses a single leaning column at the building’s center of mass, properly includes P-Delta effects but does not capture P-Theta effects. The second method uses four leaning columns, each located at the centroid of a quadrant of the buildings. This method captures P-Delta effects and P-Theta effects, although the influence of P-Theta effects is underestimated. Finally, each column of the structure, including gravity columns, is explicitly modeled, and geometric stiffness is assigned to the column based on its tributary gravity load. This method is deemed the most accurate, and captures detrimental behavior, including collapses, that the other methods miss.