Estimation of elastic seismic demands in TU structures using interactive relations between shear and torsion

The code static eccentricity model for elastic torsional design of structures has two critical shortcomings: (1) the negation of the inertial torsional moment at the center of mass (CM), particularly for torsionally-unbalanced (TU) building structures, and (2) the confusion caused by the discrepancy in the definition of the design eccentricity in codes and the resistance eccentricity commonly used by engineers such as in FEMA454. To overcome these shortcomings, using the resistance eccentricity model that can accommodate the inertial torsional moment at the CM, interactive relations between shear and torsion are proposed as follows: (1) elastic responses of structures at instants of peak edge-frame drifts are given as functions of resistance eccentricity, and (2) elastic hysteretic relationships between shear and torsion in forces and deformations are bounded by ellipsoids constructed using two adjacent dominant modes. Comparison of demands estimated using these two interactive relations with those from shake-table tests of two TU building structures (a 1:5-scale five-story reinforced concrete (RC) building model and a 1:12-scale 17-story RC building model) under the service level earthquake (SLE) show that these relations match experimental results of models reasonably well. Concepts proposed in this study enable engineers to not only visualize the overall picture of torsional behavior including the relationship between shear and torsion with the range of forces and deformations, but also pinpoint easily the information about critical responses of structures such as the maximum edge-frame drifts and the corresponding shear force and torsion moment with the eccentricity.