Evaluation of the effect of local rotation and vertical displacements modes in the nonlinear seismic response of steel frames

Seismic analysis of buildings is normally based on a damping matrix derived from the Rayleigh Model (CR). However, it is accepted that the damping matrix (CS) derived from the superposition of modal damping matrices (SMDM) gives more accurate results. Another issue related to seismic analysis of structures consists in the overlooking of the contribution of the modes associated to local rotations (LR) and vertical displacements (VD). The main purposes of this paper are to illustrate the inconvenience of using the CR matrix and to evaluate the contribution of the LR and VD modes. To this aim, the nonlinear seismic responses of three steel building models idealized as complex 2D MDOF systems under de action of several seismic records are calculated. The major finding of the paper are: (a) The underestimation of axial loads and bending moments can be larger than 40% and 30%, respectively, if the matrix CR is used; (b) if only lateral displacements (LD) modes are used to generate CS, some damping should be given in LR and VD modes to avoid amplification of the response; (c) the combined contribution of the LR and VD modes to axial loads, bending moment can be, on an average basis, larger than 50 % and 17 %, respectively, while for interstory shears and drifts it can be larger than 20 %. In light of the findings of this study, it is strongly recommended to use the SMDM procedure to form the damping matrix and to consider the contributions of the LR and VD modes when calculating the seismic response. The presented study was limited to plane frames that are regular in-plan and elevation. Other aspects like irregularity and 3D models need to be considered to get more general conclusions.