Calculation of seismic forces using CQC for all mode shapes

*Holo*BIM uses CQC to all stress resultants and displacements. All stress resultants are examined for both positive and negative signs (32 combinations), thus the results are satisfactory.

· The calculation of seismic accelerations a_{i,j} (j=x,y,z), at any point i along X, Y, Z directions, using CQC. The calculation takes into account the soil parameters of the earthquake, the seismic ground acceleration, the masses participating at the time of the earthquake at the point i and the available ductility of the building. The sign accelerations ai,j derives from the dominant mode (i.e. the mode with the highest modal participation factor).

· The calculation of seismic forces H_{i,j}=a_{i,j}×M_{i} at any point i, as the algebraic product of the seismic acceleration and the mass at this point.

· The calculation of seismic stresses in X, Y, Z direction for every seismic combination (e.g. earthquake in Y + 30%, earthquake in X + 20%, earthquake in Z), based of the seismic forces.

· In case the seismic combination includes accidental eccentricities, each mass M of a node i is placed at the position of the node i offset by the signed value (+ or –) of the eccentricities. In this way, all cases of nodes are resolved, whether they belong to the diaphragm or not. If all nodes of a floor belong to the diaphragm, the resultant loading is equivalent to the one that would result if the total mass of the floor was offsetted from the center of mass by the amount of the accidental eccentricities.

· Τhe stress resultants of each combination are signed according to the classic structural analysis.

Distribution of seismic accelerations – forces - shears