# Modal Characteristics and Lateral Load İncrement Determination (5B.1.1)

Modal Characteristics,

*Modal Additive Multiplier, Base Shear Modal Effective Mass and Mode Shape*given in**TDY APPENDIX 4B**are calculated automatically.

**ICONS**

* a _{first }^{(X, k)}* = (X) seismic line to kth pushing step in the first mode of modal single degree of freedom system modal pseudo-acceleration [m / s2]

*i 'th times the total mass*

**m**_{i}=*= (X)ith floor*

**m**_{ix1 }^{( X,1)}*modal effective mass*calculated accordingto the

*constant mode shape*determined in the first thrust step in the x-axis direction and never changed during the thrustcalculation[t]

* m _{tx1 }^{(X,1)}* = ( X)

*fixed mode shape*for the earthquake direction determined in the first thrust step in the x-axis direction and never changed during the thrust calculation

'ne calculated by

*base shear modal effective mass*[t]

*= (X) earthquake direction of the y-axis direction of the first propulsion determined at step and push account never changed during*

**m**_{iy1 }^{(X, 1)}*the fixed mode shape*' what i'th calculated floor

*modal effective mass*[t]

*= ith floor*

**m**_{iθ1 }^{(X,1)}*modal effective mass moment of inertia*calculated according to the

*constant mode shape*determined in the first thrust step around the z axis for the earthquake direction and never changed during the thrust calculation [tm2]

* Δa _{1 }^{(X,k)}* = (X)

*modal pseudo-acceleration increment of the*first mode modal single degree of freedom system at the kth thrust step for the earthquake direction [m/s

^{2}]

*= the kth for the (X) earthquake direction*

**Δf**_{ix1 }^{(X,k)}_{ }*Earthquake load increase*acting in the x-axis direction at the i th floor in the push step [kN]

*= (X)*

**Δf**_{iy1 }^{(X,k) }*earthquake load increase*acting in the y axis direction at the i th floor at the kth push step for the earthquake direction [kN]

*= Increment of*

**Δf**_{iθ1 }^{(X,k)}_{ }*earthquake load*acting in the z-axis direction at the i'th floor at the k'th push step for the (X) earthquake direction [kN]

*=*

**Φ**_{ix1 }^{(1)}_{ }*constant mode shape*in the x direction of the

*constant mode shape*determined in the first push step at the i'th floor and never changed during the push calculation

*= the*

**Φ**_{iy1 }^{(1)}_{ }*constant mode shape*determined in the first push step at the i'th floor and never changed during the push calculationAmplitude of ' in the y direction

*=Rotation amplitude about the z-axis of the*

**Φ**_{iθ1 }^{(1)}_{ }*constant mode shape*determined in the first thrust step at the i'th floor and never changed during the thrust calculation

*= (X) first for the earthquake direction determined in the push step and never changed during the push calculation.*

**Γ**_{1 }^{(X,1) }*modal contribution factor*calculated according to

*fixed mode shape*

*Constant Single Mode Pushover Analysis Method, earthquake load increments* acting on the floors at each push step in the direction of the considered earthquake , *non-linear increment* under *non-* earthquake loadings, determined in the first step after the *static calculation* (0 th step) and never changed during the thrust calculation. defined in proportion to the *fixed mode shape* . As a result of the thrust analysis, the *thrust curve* whose coordinates are the *base shear force-peak displacement* is obtained. Then, by applying coordinate transformation to this curve , a *modal capacitance diagram* whose coordinates are *modal displacement-modal pseudo-acceleration* is obtained. As a result of the *performance point* obtained using the *fashion capacity diagram* , the plastic deformations and internal forces at this performance point are compared with the limit values to determine the building performance.

**As** stated in **TDY Appendix 5B.1.1** , in the *Constant Single Mode Pushing Method* , internal forces and deformations, which take into account the second-order effects of non-earthquake loadings, are taken into account as the initial value (0 th step). K in the earthquake direction taken into consideration lactide floors of the seismic load increment in the pushing step, earthquake off after the first step of the installation *modal analysis methods are** *calculated by using the *mode shape* and *fold modal effective mass in* terms of **Equation 5B.1** expressed by.

Here, the terms Δf _{ix1 }^{(X,k)} , Δf _{iy1 }^{(X,k)} and Δf _{iθ1 }^{(X,k)} are the earthquake load increments acting on the floors at the kth push step for the earthquake direction ( X ) considered. The terms m _{ix1 }^{(X,1)} , m _{ix1 }^{(X,1)} and m _{iθ1 }^{(X,1)} are the first mode (dominant mode) equivalent of the floor effective masses calculated in the first step and are calculated using **Equation 5B.2** .

**In Equation 5B.2** , the terms Φ _{ix1 }^{(1)} , Φ _{iy1 }^{(1)} and Φ _{iθ1 }^{(1)} are the first (dominant) mode shape obtained by making the modal analysis of the deformed system in the initial step, considering the second-order effects consisting of non-earthquake loadings . This mode shape is expressed as the corresponding x, y, z axes, respectively. In the same equation ^{, the} value of Γ _{1 }^{(X,1)} is the *modal contribution factor* obtained as a result of the modal analysis performed in the initial step .

Mass Definition at Joints (5.4.6)

Calculation of Combined Response Parameters and Scaling Design Values of Combined Response (4.8.2.1)

The unknown magnitude at the k th thrust step defined between two successive hinge joint formations is the *modal pseudo acceleration increment* Δa _{1 }^{(X,k)} included in **Eq.(5B.1)** of the *modal single degree ***of freedom ***system* belonging to the first mode , and detailed explanation is available at Determination of Modal Pseudo-Acceleration, Modal Displacement Increment (5B.1.2 , 5B.1.3).