The horizontal seismic loads, acting on a structure, are determined for each natural mode of vibration.

 If the natural vibration occur in one plane, the resultant of horizontal seismic loads (base shear force), corresponding to the ground motion direction and to the r^th  vibration mode, is determine using the following relation:

S_r = c_r ×G

S_r：base　shear

G – resultant of gravity loads for the whole building

C_r – overall seismic coefficient corresponding to the r^th vibration mode.

       

α – importance coefficient of the building

The “α” coefficient provide differences between buildings aseismic  protection level according to the classes of importance they belong to.

α = 1.4 for class Ⅰ importance buildings

α = 1.2 for class Ⅱ importance buildings

α = 1.0 for class Ⅲ importance buildings

α = 0.8 for class Ⅳ importance buildings

Class 1 – Buildings of vital social importance, whose functionality during and immediately after earthquake should be fully granted – hospitals, fire stations, ambulance services 

Class 2 – Very important buildings requiring a limitation of damage, keeping in view its potential consequences – schools, churches

Class 3 – Normal importance buildings (not falling into classes 1,2 or 4) – residential buildings, hotels

Class 4 – Reduced importance buildings – agrozootechnical structures of reduced importance

k_s = coefficient depending on the seismic zone

 The “k_s” coefficient represents the ratio between the peak ground acceleration of the seismic motion (with an average recurrence period of about 50 years),

Corresponding to the seismic zone, and the gravity acceleration.

 “k_s” coefficient values according to the seismic zone

Seismic zonation map of Romania – k_s coefficient

β_r = dynamic amplification coefficient

 The “β_r” coefficient depends on the site spectral composition of the seismic motion and is determined according to the natural oscillation periods (T_r) of the building and to the local seismic conditions, characterized by the corner periods (T_c) using the following relations.

                            β_r = 2.5                                    for T_r ≤ T_c

β_r = 2.5 – (T_r – T_c) ≥ 1           for T_r > T_c 

β_r – T_r”  diagram

Seismic zonation map of Romania – T_c corner period

ε_r – equivalence coefficient

ε_r – equivalence coefficient between the real system and a system with one degree of  

       freedom corresponding to the own mode of vibration „r”.

where:   u_kr – the component of „k” degree of freedom coresponding to the vector „r”

              G_k – the resultant of  gravitational loads corresponding for level „k”

Ψ – coefficient of reduction of seismic effects

The Ψ coefficient takes into account:

                u       Structural ductility,

u       Stresses re-distribution capacity,

u       Contribution of strength reserve not considered in the analysis,

u       Vibration damping effects.

 Ψmin = 0.15 for industrial one story reinforced concrete structures with stiff　beam-column joints;

Ψmax= 0.65 for steel latticed masts.