# Pushover Curve and Modal Capacity Curve (5B.2.5 , 5B.2.6)

*Modal Capacity Curve*is obtained automatically.

*After the Modal Capstie Curve*, the*impulse curve*is obtained automatically.

**ICONS**

* a _{1 }^{(X,k)}* = modal pseudo-acceleration of the first mode modal single degree of freedom system at the kth push step for the earthquake direction [m/s

^{ 2}]

*= (X) The modal displacement of the modal single degree of freedom system belonging to the first mode at the kth thrust step for the earthquake direction [m]*

**d**_{1 }^{(X,k)}*= (X) for the earthquake direction, which is determined in the first thrust step in the x-axis direction and remains unchanged throughout the thrust calculation.*

**m**_{tx1 }^{(X,1)}*modal effective mass of base shear*calculated according to

*constant mode shape*[t]

*= (X)*

**m**_{txk }^{(X,k)}*modal effective mass of the base shear force*calculated according to the

*constant mode shape*renewed with the free vibration calculation at the kth thrust step in the x-axis direction for the earthquake direction [t]

*= (X) for the earthquake direction The displacement [m]*

**u**_{ix1 }^{(X,k)}*= (X) calculated in the x-axis direction at the i-th floor at the k-th thrust step is the*

**Δa**_{1 }^{(X,k)}*modal pseudo-acceleration*of the modal single degree

*-of-*freedom system of the first mode at the k-th thrust step for the earthquake direction.

*increment*[m/s

^{2}]

*= (X) belonging to the first mode at the kth push step for earthquake*

**Δd**_{1 }^{(X,k)}*modal single degree of freedom system*'s

*modal displacement of*[m]

*= N th layer on the first push is determined at step and push account never changed during*

**Φ**_{Nx1 }^{(1) }*the fixed mode shape*"amplitude in the x direction

*= N-th floor The amplitude of the*

**Φ**_{Nx1 }^{(k) }*fixed mode shape*determined in the first thrust step and renewed with the free vibration calculation in the kth thrust step , in the x direction

*= (X)*

**Γ**_{1 }^{(X,1)}*fixed mode shape*determined in the first thrust step for the earthquake direction and never changed during the thrust calculation

*modal contribution multiplier*calculated according to

*=*

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

*mode shape*renewed with free vibration calculation at each k th thrust step for (X) earthquake direction

*= renewed at each k th thrust step first mode natural angular frequency [rad/s] found from free vibration calculation*

**ω**_{1 }^{(k) }**TDY 5B.2.5** 'in the manner described, k' th obtained in step push *modal displacement increments expressed as a dimensionless _{one }^{(X, k)}* using

**TDY Equation 5B.10**'calculated by the

*modal-called acceleration increment Δ A*, of the previous step

_{1 }^{(X, k)}**TDY**is obtained as in

**Equation 5B.11**by summing with the values obtained at the end .

Thus, in the *propulsion method with variable displacement distribution* , a *modal capacitance diagram* whose coordinates are *modal displacement – modal pseudo-acceleration* is obtained without the need to *plot the* thrust curve . In this diagram , the slope of the line segment, which represents the *step-by-step linear behavior* at the kth push step between two successive hinge formations *,* is equal to * ^{2}* (

*ω*according to

_{1 }^{(k)})**TDY Equation 5B.10**(

**Figure 5B.2a**).

To find the building performance point, a *modal capacitance diagram* whose coordinates are *modal displacement – modal pseudo-acceleration* is used so that the displacement demand can be obtained using the *Horizontal Elastic Design Spectrum* . Each k th step push **TDY Equation 5B.11** obtained by the *spectral displacement d _{1 }^{(X k)}* and

*modal so-called acceleration a*values

_{1 }^{(X, k)}**TDY Equation 5B.3**and

**TBDY Equation 5B.4**coordinates using

*base*is converted to a

*thrust curve*with

*shear force-peak displacement*.

However, since these equations ( **TDY Equation 5B.3** and **TDY Equation 5B.4** ) are written for the *Constant Single Mode Propulsion Method* , the terms in the equations must be written for the *Variable Single Mode Propulsion Method* .

Instead of the modal effective mass *m _{tx1 }^{(X,1)}* obtained in the first mode of the modal analysis performed in the initial step given in

**TDY Equation 5B.3**, the calculated mode shape is calculated according to the mode shape obtained from the free vibration calculation (modal analysis) made at each kth thrust step. The values of

*modal effective masses m*on the i th floor are used.

_{ix1 }^{(X,k)}**TDY Equation 5B.4** , the *modal analysis* made in the initial step given in the first mode (dominant mode) is the modal amplitude at the * _{Nth}* floor

*Φ*instead of the modal amplitude

_{Nx1 }^{(1),}*Φ*, taking into account the stiffness change caused by the plastic hinges in each kth thrust step. The mode amplitude

_{Nx1 }^{(1)}*Φ*the N 'th floor obtained in the first mode of the modal analysis (dominant mode) is used. Similarly, the

_{Nx1 }^{(k) in}*modal contribution factor*obtained as a result of the modal analysis performed in the initial step is replaced by the value

*Γ*The

_{1 }^{(X,1).}*modal contribution factor Γ*value calculated as a result of the modal analysis made by taking into account the change in stiffness caused by the plastic hinges in each kth pushing step is used.

_{1 }^{(X,k)}Obtaining the performance point described in detail inDetermination of Modal Displacement and Performance Point (5B.3).