# Reduced Design Acceleration Spectra for Building Related Aspects

**Symbols**

* S_{DS} *= Short-period design spectral acceleration coefficient [dimensionless]

*= Design spectral acceleration coefficient for a period of 1.0 seconds [dimensionless]*

**S**_{D1}*=*

**S**_{S }*Short-period map spectral acceleration coefficient [dimensionless]*

*=*

**S**_{1}*Map spectral acceleration coefficient for a period of 1.0 seconds [ dimensionless]*

*= Natural vibration period [s]*

**T***=*

**T**_{A}*Horizontal elastic design acceleration spectrum corner period [s]*

*=*

**T**_{B}*Horizontal elastic design acceleration spectrum corner period [s]*

*= Transition period to constant displacement region in the horizontal elastic design spectrum [s]*

**T**_{L}*= Horizontal elastic design spectral acceleration [g]*

**S**_{ae}(T)*= Reduced horizontal elastic design spectral acceleration [g]*

**S**_{aR}(T)*= Structural system response coefficient*

**R***= Earthquake load reduction coefficient*

**R**_{a}(T)*= Strength excess coefficient*

**D***= Building importance coefficient*

**I**The excel file containing the calculations described below can be examined.

#### Reduced Design Spectrum for the Upper Part of the Building

Reduced design acceleration spectra are obtained by using R and D coefficients determined according to TBDY 2018 Table 4.1 and the (4/5)R and D coefficients at the end of the control of shearwall overturning moment.

In TBDY 2018 4.2.1.2 , the horizontal elastic design spectrum is reduced by the

*earthquake load reduction coefficient*R_{a}(T).

Using the Building Importance Factor, I = 1 for the upper part of the building and R = 4.8, D = 2.5 in the X and Y direction, a reduced horizontal elastic design spectrum for DD-2 in both directions is obtained.

In the following visuals , the calculation of R

_{a}(T) and the calculation of the reduced design spectrum with excel are included. The equations given above are used in this calculation.

The interval for T is taken as 0.005 s for precision calculation. Therefore, the entire spectrum cannot be shown in the image above. Graphically given below.

To achieve the reduced design acceleration spectrum that the program calculates for the upper section, simply type 'exportspectrum' in the lower toolbar command line and press enter. Program spectrum txt. file as Exp_spec.txt in the Computer: C: Program Files: ideCAD v10 folder. From here, you can take the txt file and compare the spectrum calculated by the program with manual calculation in excel.

In the graph above, it is seen that the reduced spectrum calculated manually and the reduced spectrum calculated by ideCAD overlap and the calculation is correct.

#### Reduced Design Spectrum for the Basements of the Building

In accordance with TBDY 2018 4.8.5.3, the Building Importance Factor for the lower part of the building is taken by taking I = 1, R = 2.5 and D = 1.5 and the horizontal elastic design spectrum reduced in both directions for the earthquake level DD-2 is determined.