# Modal Response Spectrum Analysis of Structures with Basement

**Symbols**

* D =* overstrength factor, amplification factor to account for overstrength of the seismic-force-resisting system

*overstrength factor applied to the lower part of the building*

**D**_{bottom}=*overstrength factor applied to the upper part of the building*

**D**_{top }=*building importance factor*

**I =***respose modification coefficient*

**R =***respose modification coefficient calculated depending on ductility and period*

**R**_{a }=*respose modification coefficient applied to the lower part of the building*

**R**_{bottom }=*respose modification coefficient applied to the upper part of the building*

**R**_{top}=**(**

*respose modification coefficient of lower part of the building calculated depending on ductility and period*

**R**_{a})_{bottom}=According to the definition given in **3.3.1** , the upper part of the building and the lower part with basement surrounded by rigid walls will be modeled together as a lateral force resistance system. In such buildings, one of the following two calculation methods can be used in the seismic analysis.

**(a)** The method described in **4.3.6.2** ,

**(b)** The method consisting * two steps* described in

**4.8.5.1**,

**4.8.5.2**and

**4.8.5.3**.

**4.8.5.1 -** In accordance with** 4.7.5.1**, the lower part with basement and the upper part of the building are modeled together as a single lateral force resistance system in the approximate *two load-steps calculation approach* that can be applied to *Modal Response Spectrum Analysis*. However,* The upper part *and the *lower part *vibrates in significantly different modes, the seismic analysis is applied in *two load-steps*:

**4.8.5.2** **-** In the first step of the seismic analysis, *Modal Response Spectrum Analysis* is performed by considering only *the* masses of the *upper part in *mathematical model of the whole structure. In this case, the sufficient number of vibration modes will be determined only by the *effective mass participation rates* calculated on the basis of the total mass of the *upper part*. When applying the *Modal Response Spectrum Analysis*, *respose modification coefficient of upper part of the building,* **(****R**** _{a})_{m,top}** is calculated by using

**R****and**

_{top}

**D****coefficients for each vibration mode in accordance with**

_{top}**Eq.(4.1).**

**R****and**

_{top}

**D****coefficients shall be selected in accordance with**

_{top}**Table (4.1).**At the end of the

*first step*, reduced internal forces with relevant

*respose modification coefficient*are obtained in both the upper part and the lower part of the structre.

**4.8.5.3 - **In the second step of the seismic analysis, *Modal Response Spectrum Analysis* is performed by considering only the masses of the lower part in mathematical model of the whole structure. In this case, the sufficient number of vibration modes will be determined only by the *effective mass participation rates* calculated on the basis of the total mass of the *lower part*. When applying the *Modal Response Spectrum Analysis*, *respose modification coefficient of lower part of the building,* **(****R**** _{a})_{n,bottom }**is calculated by using

**(**

**R****/**

_{bottom}**I) = 2.5**and

**(**

**D****coefficients for each vibration mode in accordance with**

_{bottom}=2.5)**Eq.(4.1).**

**4.8.5.4 - ***Design*** ***Internal forces *for* *structures with **basements** are defined in **4.10.1.**

**Related Topics**