6TH International Congress on Technology - Engineering - Kuala Lumpur3 - Malaysia (2018-07-19)

The Role Of Mass Eccentricity On The Earthquake Induced Torsion In Buildings

This paper investigates the role of mass eccentricity on the earthquake induced torsion in buildings. It is now widely accepted that using the centers of rigidity (CR) as a reference system to assess the torsional response of buildings, poses a number of difficulties associated with the fact that the centers of rigidity are generally not located on the same vertical line and they are also load dependent ([1], [2]). An alternative reference system for implementing the torsional code provisions can be determined by locating an optimum torsional axis (OTA), for which any in-plane lateral load, the torsional distorsion on the structure is minimized ([1], [3], [4], [5]). It was demonstrated that in systems where the centers of mass of the various floors are located on the same vertical axis, their dynamic response is essentially translational, when the mass axis coincides with OTA . This axis may be either determined using the approximate method of the continuous medium ([6], [7]), where it is defined as the vertical axis passing through the center of rigidity (m-CR) of an equivalent (modal) single story system or using the discrete element approach (stiffness method), which is familiar to practicing engineers ([8]). In a recent paper it was shown that a structural configuration of practically translational response may be easily attained by a suitable arrangement of the lateral load resisting bents [9]. This paper examines how such an arrangement can also be achieved, when the centers of floor masses are shifted, in a random spatial way, from their nominal positions, but within the limits of the code ( ).The role of mass eccentricities on the torsional response of a building is investigated though an analytical (mathematical) approach and the analytical solution is then verified with a case study on a 9-story building (T3/B6) where the location of the accidental eccentricities is varied throughout the building height. The plan view of the analyzed building model T3/B6 is presented in Fig.1. T3/B6 is a setback building, which comprises a six floor base structure, with plan dimensions of 23x16m (shown by the exterior perimeter), and a three floor top structure with a reduced size of 18x12m (shown by the interior perimeter in Fig. 1). The lateral load resisting system along the y-direction consists of a wall, W, a coupled wall bent, CWy, and by two moment resisting frames, FR. A pair of coupled wall bents provides the resistance in the x-direction. Six different mass eccentric configurations were investigated. The configuration of the first three analyzed mass eccentric systems (+)A:T3/B6, (+)B:T3/B6 and (+)C:T3/B6) is shown in Fig 2. In all cases the centers of mass were shifted along the x-axis, while the mass polar moment if inertia remained unchanged (lumped masses). Since all the three analyzed mass eccentricities systems (+)A:T3/B6, (+)B:T3/B6 and (+)C:T3/B6) are structurally symmetric along the y-direction, all the aforementioned systems were also investigated for the reversed location of the various floor eccentricities (i.e.: their algebraic sign was reversed). The resulting eccentric systems were defined as (-)A:T3/B6, (-)B:T3/B6 and (-)C:T3/B6. The numerical analysis of the mass eccentricity configurations was performed with the structural analysis program SAP2000-V16, for a ground excitation along the y-direction, as defined by the acceleration spectrum of EC8-2004 (type 1, ground type B, soil factor 1, horizontal ground acceleration 0.40g). The normalized base torques, (where Vo is the base shear of the corresponding uncoupled building and rb is the radius of gyration of the base structure) and top rotations, ?, for the different locations (indicated by the normalized coordinate ) of the coupled wall bent CWy, are shown in Fig. 3. All the data were calculated on the basis of the first 12 peak modal values combined according to the CQC rule (the damping ratio in each mode of vibration was taken as 5%). The red lines show the response of the mass eccentric systems of Fig.2 ( (+)A:T3/B6, (+)B:T3/B6 and (+)C:T3/B6), the blue lines in Fig. 3 show the torsional response of the systems with reversed mass eccentricities ((-)A:T0/B9, (-)B:T0/B9 and (-)C:T0/B9), while the black lines show the response of these systems when no mass eccentricities are taken into account. The results show that the inverted peaks of the red and blue lines (either solid, which represent base torques, or dotted, which represent top rotations) are pointing to almost symmetrical locations with respect to those indicated by the black lines, whose inverted peaks indicate the optimum location of CWy where the torsional response is minimized. ?able 1 shows the locations of the CWy bent, which minimizes the torsional response of the six mass eccentricity configurations. as predicted by the analytical solution. The locations of the models without mass eccentricities, as derived in Georgoussis (2017), are also shown in this Table. The results suggest that the numerical modeling verifies the analytical solution with reasonable accuracy.
George Georgoussis, Anna Mamou