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mi = total mass of the ith story
miθ = mass moment of inertia of the ith story
mixn (X) = (X) for the earthquake direction, the i'th story modal effective mass of the nth natural vibration mode of the building in the x-axis direction
miyn (X) = (X) for the earthquake direction i'th story modal effective mass
miθn (X) = (X) of the building's nth natural vibration around the z-axis for the earthquake direction i'th storey modal effective mass moment of inertia
mj (S) = Finite Element Analysis node j to effect individual masses
mtxn (X) = (X) earthquake direction for building the x-axis direction of the nth vibration mode of base shear modal effective mass
mtyne (Y) = (Y) earthquakes base shear in the building along the y axis for the direction of modal effective mass
rmax (X) = (X) earthquake direction for any behavior variables (displacements and relative story drift, strain component) corresponding to the coupled typically to the maximum modal behavior of size
rn (X) = Typical unit modal behavior magnitude corresponding to any action magnitude (displacement, relative floor displacement, internal force component) for the earthquake direction in the nth natural vibration mode (X),
rn,max (X) = nth natural vibration mode ( X) Typical largest modal behavior magnitude corresponding to any action magnitude (displacement, relative floor displacement, internal force component) for the earthquake direction
SaR (Tn ) = reduced design spectral acceleration for the nth vibration mode
Tn = nth mode natural vibration period
βmn = ratio of mth and nth natural vibration periods
Φi (X) n = nth natural vibration mode shape amplitude at i'th story (X) earthquake direction
Φixn =nth natural vibration mode shape amplitude ati'th story in x-axis direction
Φiyn = y-axis at i'th story nth natural vibration mode shape amplitude in the direction
θiθn = nth natural vibration mode shape amplitude as rotation around the z-axis at the ith story
Γx (X) = (X) for the earthquake direction, modal contribution of the nth vibration mode multiplier
ξn = modal damping ratio of the nth vibration mode
ωn = Natural vibration angular frequency of the nth vibration mode
ρmn = Cross-correlation coefficient of the mth and nth natural vibration modes in the Complete Quadratic Combination Rule
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Modal Response Analysis Method
In the modal response spectrum analysis this method, the structure is decomposed into a number of single degree-of-freedom systems, each having its own mode shape and natural period of vibrationmaximum internal forces and displacements are determined by the statistical combination of maximum contributions obtained from each of the sufficient number of natural vibration modes considered. The number of modes available is equal to the number of mass degrees of freedom of the structure, so the number of modes can be reduced by eliminating mass degrees of freedom.
For a given direction of loading, the displacement in each mode is determined .
The displacement and internal forces in each mode are calculated from the corresponding spectral acceleration, modal participation, and mode shape. Because the When the response spectrum curve is created, The sign (positive or negative) and the time of occurrence of the maximum acceleration are lost in creating a response spectrum, there is no way to recombine modal responses exactly. However, . Therefore, it is not possible to fully reassemble modal responses. However, displacements and component forces can be estimated closely by the statistical combination of modal responses produces reasonably accurate estimates of displacements and component forcesproduced. The loss of signs for computed quantities leads to causes problems in interpreting force results where seismic effects are combined with gravity effects, produce . Modal response analysis method produces forces that are not in equilibrium , and make it impossible to plot deflected shapes of the structure.
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