# Unit Modal Behavior and Maximum Modal Behavior Sizes

#### ICONS

r max (X) = (X) combined typical largest modal response magnitude   corresponding to any response magnitude (displacement, relative story drift, internal force component) for the earthquake direction
r' n (X)   = nth natural vibration mode (X ) typical unit modal response magnitude

r n,max (X)   = any response magnitude for earthquake direction in the nth natural vibration mode (X)corresponding to any response magnitude (displacement, relative story drift, internal force component) for the(displacement, relative story translation, internal force component) corresponding typical largest modal response magnitude
S aR (Tn )   = reduced design spectral acceleration of the nth vibration mode
T n   = natural vibration period of the nth mode

Unit Modal Behavior Size specified in TBDY 4B.1.6  For a given earthquake direction (X), it is the magnitude corresponding to any behavior magnitude (displacement, relative story drift, internal force component) in the typical n'th vibration mode. In other words, Modal Calculation Parameters calculation such as modal shapes, modal vibration periods, Unit Modal Behavior Size for each mode , and  TBDY is obtained by a static calculation in which the modal effective masses  defined in  Equation 4B.2 are acted as loads in their own directions. All 6 degrees of freedom together with the (X) direction are used for modal analysis in three-dimensional systems. For this reason , (Y), (Z), (RX), (RY) and (RZ) values ​​are also calculated for the (X) terms defined in TBDY Equation 4B.2 .

According to TBDY 4B.2.3 In a typical nth vibration mode for a given earthquake direction (X), the typical largest modal response magnitude r n,max (X ) corresponding to any response magnitude (displacement, relative story translation, internal force component) ) is calculated by Equation (4B.3) .

Here It represents the typical unit modal response magnitude defined in 4B.1.6 , and S aR ( Tn ) represents the reduced design spectral acceleration obtained from Eq.(4.8) for the typical n'th natural vibration period Tn .

Equation (4B.3) shows that all calculations made in TBDY 4B.1 are values ​​obtained from vibration calculations only, independent of earthquake effects. For this reason , Mode Shapes, Modal Vibration Periods , Modal Additive Multiplier, Base Shear Force Modal Effective Mass , Modal Effective Masses and Modal Mass Participation Ratios are results that depend only on the mass and stiffness of the structure.

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