The modal response is determined by means of the following formula.

where:

n - Number of modes

e_{ ij } - Correlation coefficients

R_{ i }, R_{ j } - Spectral response to the modes i and j

The following types of quadratic combinations are available in the program.

For CQC method, the correlation coefficients are calculated based on the following formula.

where:

ζ_{ i }, ζ_{ j } - Damping coefficients for the modes i and j (relative values)

r = Min (T_{ i }/T_{ j }; T_{ j }/T_{ i }) ≤ 1

T_{ j }, T_{ i } - Vibration periods for the modes i and j.

The above formula is used when the Include damping in calculations option is selected in the dialog with modal analysis parameters. If this option is deselected, one damping value is applied to all modes and the formula above assumes the following form.

where R^{dir1} is the representative maximum value of a particular response of a given element to a given component of an earthquake, defined
as a dir1; R_{k}^{dir1} is a peak value of the element response due to the k-th mode.

where R^{dir1} is the representative maximum value of a particular response of a given element to a given component of an earthquake, defined
as a dir1; R_{k}^{dir1} is a peak value of the element response due to the k-th mode (k <-> s); N is a number of modes.

τ denotes duration of an earthquake

ξ_{k} is a damping coefficient for the k-th mode

ω_{k} is a pulsation for the k-th mode (k <-> s).