# 15.5.1

Linear performance analysis is the application of non-linear behavior with a linear calculation method, in which the SGDT approach is applied in the evaluation of the seismic performance of existing buildings. While applying linear performance analysis in existing buildings, Mode Combination Method is applied. Element damage types, application limits of linear performance analysis, strain and plastic rotation demands; determined using displaced axis rotations in columns, beams and shearwalls.

With the mode combination method, earthquake calculation is made automatically according to the carrier system elements and masses.

R

_{a}= 1 is taken in the earthquake calculation to be used in the evaluation of existing buildings .

Internal forces and capacities are automatically calculated based on the internal force directions obtained in the dominant mode.

**ICONS**

**S _{aR} (T) =** reduced design spectral acceleration of the nth vibration mode [g]

**S**earthquake ground motion level with 2% probability of exceedance in 50 years (recurrence period 2475 years)

_{ae}(T) =**R**Predicted ductility

_{a}(T) =*Earthquake Load Reduction Coefficient*depending on capacity and period

**T =**Natural vibration period [s]

**r**nth natural vibration mode (X) for any response magnitude (displacement, relative floor displacement, internal force component for the earthquake direction (X) ) corresponding typical largest modal behavior magnitude

_{n, max }^{(X)}_{ }=If the earthquake calculation of existing buildings within the scope of Assessment and Design Based on Shaping (ŞGDT) is made by linear method, the *Mode Combination Method* specified in **Section 4.8.2 of TBDY** is applied. Detailed explanation of mode combination method is given in **TBDY Section Annex 4B** .

The *Earthquake Load Reduction Coefficient* is taken as R _{a} (T) = 1 while applying the modal combination method within the scope of the evaluation of existing buildings . Thus, in the modal combination method, any behavior magnitude (displacement, relative floor displacement, internal force component) for a typical n th vibration mode is found with the following equation.

*S _{aR} (T)* The horizontal elastic design spectral acceleration obtained by using the

*horizontal elastic design spectrum*

*graph is obtained by dividing the value of S*

_{ae}(T) by the value of R

_{a}(T).

Since R _{a} (T) = 1 for each mode in performance analysis , the equation *S _{aR} (T)* =

*S*emerges. For this reason, while determining the performance of existing structures , the

_{ae}(T)*Carrier System Behavior Coefficient*R given in

**Table 4.1**is not used, only the horizontal elastic design spectrum is used.