Issue 35

N. Oudni et alii, Frattura ed Integrità Strutturale, 35 (2016) 278-284; DOI: 10.3221/IGF-ESIS.35.32 281 D YNAMIC EQUATIONS OF MOTION ynamic analysis of structures exhibiting non linear behavior is performed by using direct integration, to trace the response in the time domain. The nonlinear dynamic equilibrium equation can be written as n n n n M Cu p f u      (14) where M and C are the global mass and damping matrices respectively, n p is the global vector of internal resisting nodal forces, n f is the vector of consistent nodal forces for the applied body and surfaces traction forces grouped together, the body force term ( g MIu   ) due to seismic excitation, is included in the body forces which are taken into account in n f , n u  is the global vector of nodal accelerations and n u  is the global vector of nodal velocities [7]. Figure 2 : Uniaxial response of the model in (a) tension and (b) compression [5] When the structure is subjected to seismic excitation, the external applied body forces is n g f MIu    (15) Where g u  is ground acceleration and I is a vector indicating the direction of the earthquake excitation. Figure 3 : Koyna accelerograms a) Transverse component b) Vertical component [8]. D