# Equivalent Lateral Force Method

**Symbols**

* A _{t} =* Equivalent area used in the empirical natural vibration period calculation [m2]

*= Body cross-sectional area of the jth wall [m2]*

**A**_{wj}*Coefficient used in the empirical natural vibration period*

**C**_{t}=*Additional eccentricity amplification coefficient at the i'th floor*

**D**_{bi}=*(X) displacement consisting of the fictitious load imposed on the i'th floor in the calculation of the dominant natural vibration period of the building in the earthquake direction [m]*

**d**_{fi }^{(X)}=*(X) In the calculation of the dominant natural vibration period of the building in the direction of the earthquake, the fictitious load on the i'th floor [kN]*

**F**_{fi }^{(X)}=*(X) the equivalent earthquake load acting on the center of the i'th storey mass in the earthquake direction [kN]*

**F**_{iE }^{(X)}=*= Equivalent earthquake load acting on jth finite element node [kN]*

**f**_{jE }^{(S ) }*Gravitational acceleration [m / s2]*

**g =***= Total height of the upper part of the building above the basements [m]*

**H**_{N}*Curtain height [m]*

**H**_{w}=*= Height of the i'th floor [m]*

**h**_{i}*Building Importance Factor*

**I =***Length ofwall inplan [m]*

**l**_{wj}=*Total number of floors in the upper section above the basement floors of the building*

**N =***Reduced design spectral acceleration [g]*

**S**_{aR}(T) =*= Short period design spectral acceleration coefficient [dimensionless]*

**S**_{DS}*Natural vibration period [s]*

**T =***Dominant natural vibration period calculated empirically [s]*

**T**_{pA}=*(X) dominant natural vibration period of the building in the earthquake direction [s]*

**T**_{p }^{(X) }=*(X) additional equivalent earthquake load acting on the Nth storey (top) of the building in the earthquake direction [kN]*

**∆F**_{NE }^{(X)}=*torsional irregularity coefficient at i'th storey*

**η**_{bi}=*Equivalent Earthquake Load Method* will be applied separately for earthquakes affecting the building in vertical (X) and (Y) earthquake directions. The following equations (X) are given for the earthquake direction. In buildings with and without basement, **3.3.1** will be used for the definition of building base and building height .

**4.7.1. Determination of Total Equivalent Earthquake Load**

**4.7.1.1 - In** the (X) earthquake direction considered, the *total equivalent earthquake load* ( *base shear force* ) acting on the entire building , *V *_{tE }^{(X)}_{ }, **Eq. It will** be determined by **(4.19)** .

Wherein *S *_{ar} ( *T *_{p }^{(X)} ), considering the received (X) earthquake direction **4.7.3** 'to the natural vibration period judges the calculated building by *T *_{p }^{(X)} taking into account **Eq. (4.8)** from the calculated *reduced design spectral acceleration* ' shows ni. *S *_{DS} is the *design spectral acceleration coefficient* defined in **2.3.2.2** for a *short period* .

**4.7.1.2 - Eq. (4.19)** at the *m *_{t} building **Eq. (4.20)** and corresponds to the total mass calculated:

Where *m *_{i is the} total mass of the _{i} th floor slab.

**4.7.2. Determination of Equivalent Earthquake Loads on Floors**

**4.7.2.1 - The** total equivalent earthquake load calculated with **Equation (4.19 )** is expressed in **Equation (4.21)** as the sum of equivalent earthquake loads acting on the building floors :

**4.7.2.2 -** Construction *N* -th times (top) effect *addition the lateral force* Δ *F *_{NE }^{(X)} 'The value of **Eq. (4.22)** will be determined by.

**4.7.2.3 -** total equivalent seismic load Δ *F *_{NE }^{(X)} other than the remaining portion of *N* 'including th floor, building floors to **Eq. (4.23)** will be dealt with.

**4.7.2.4 - In case** floor slabs are modeled as *rigid diaphragm* according to **4.5.6.4** , the equivalent earthquake load *F *_{iE }^{(X)} calculated by **Equation (4.23)** will be impacted in the earthquake direction taken into account on the *main node point* on the i'th floor .

**4.7.2.5 -** The floors **4.5.6.2** according *plate* ( *membrane* ) in the case of modeling by finite elements, the i-th layer in the jth point of the lateral force acting on the node **Eq. (4.24)** will be calculated by:

Here *m *^{( }_{j }^{S)} is the singular mass ^{of the }_{jth} joint defined by **Equation (4.16)** .

**4.7.2.6 -** The total overturning moment occurring at the base of the building from earthquake loads is calculated with **Equation (4.25)** :

**4.7.3. Determination of the Building's Dominant Natural Vibration Period**

**4.7.3.1 - ***lateral force method* 'in all buildings to the application of **Eq. (4.19)** , located in and considering the received (X) earthquake direction building dominant fundamental period expressing *T *_{p }^{(X)} , a more accurate calculation is performed, **Eq It will** be calculated by **. (4.26)** .

Here, *F *_{fi }^{(X)} , which shows the fictitious load acting on the i'th floor , will be obtained by substituting any value ( *for example 100* ) instead of ( *V *_{tE }^{(X) }_{-} ∆ *F *_{NE }^{(X)} ) in **Equation (4.23)** .

**4.7.3.2 -** The maximum value of the dominant natural vibration period *T *_{p }^{(X) of the} building calculated with **Equation (4.26)** to be taken into account in the earthquake calculation shall not be more than 1.4 times the period *T *_{pA} given in **4.7.3.4** .

**4.7.3.3 -** DTS = 1, 1A, 2, 2A and IMS _{≥} are 6 buildings and DTS = 3, 3a, 4a, the natural vibration period prevails in all buildings 4, **4.7.3.1** from the without calculating the direct **4.7.3.4** 'in The given empirical *T *_{pA} can be taken as the period ( *T *_{p }^{(X)} ≅ *T *_{pA} ).

**4.7.3.4 -** Empirical dominant natural vibration period will be calculated with **Equation (4.27)** :

**(a) **delivery system only in buildings with reinforced concrete frame *C *_{t} = 0.1, or from steel braced frame in buildings with steel frame *C *_{t} = 0.08, all other buildings *C *_{t} = will be 0.07.

**(b) In **buildings where all earthquake effects are covered by reinforced concrete walls, the *C *_{t} coefficient will be calculated by Equation (4.28a):

The equivalent area of *A *_{t in} this relation is given in **Equation (4.28b)** :

**4.7.4. Torsion Calculation in Equivalent Earthquake Load Method**

Any i'th storey floor **Table 3.6** at defined **A1** event type and are irregularities, 1.2 <η _{b is} with ≤ 2.0 is condition, **4.5.10.2** according exerted on the floor ± 5% additional eccentricity both earthquake to the direction of **Eq. It** will be enlarged by multiplying the *D *_{bi} coefficient given in **(4.29)** .

**4.7.5. Calculation of Basement Buildings Using Equivalent Earthquake Load Method **

According to the definition given in **3.3.1** , in buildings with basements surrounded by rigid walls, the upper part of the building and the lower part with basement *will* be modeled together *as a single structural system* . One of the following two methods can be used in the earthquake calculation of such buildings:

**(a)** The calculation method described in **4.3.6.1** ,

**(b)** Calculation method with *two load ***cases** described in **4.7.5.1** , **4.7.5.2** and **4.7.5.3**

**4.7.5.1 - In** buildings with basements , the *lower section* (basement floors), which is relatively rigid in terms of horizontal rigidity with the *upper section* , have very different properties in terms of dynamic behavior and strength. In the *two-load-state calculation approach* , which can be applied for linear earthquake calculation with modal calculation methods of such buildings , the upper part of the building and the lower part with basement are modeled together as a single carrier system, but *the* reason for the vibrations of the *upper part* and the *lower part in* very distant modes. Earthquake calculation is done separately in two loading cases with:

**4.7.5.2 -** In case of initial loading, equivalent earthquake loads calculated according to **4.7.2.3** or **4.7.2.5 in** the *common single carrier system* model are **affected** only on the *upper section* ( **Figure 4.2b** ). To the upper portion of accounts **table (4.1)** from the selected *R *_{top} and the *D *_{top} coefficients and the earthquake direction *T *_{p }^{(X)} according to the characteristic periods **in Eq. (4.1)** from the calculated *seismic load reduction factor*

( *R *_{a top} ) will be used. As a result of the calculations made for a first load condition, and *the upper portion* from both *the bottom portion* from *the reduced internal forces* are obtained.

**4.7.5.3 -** case of the second installation still *common single carrier system* model, only *the lower portion* wherein the mass of basements, **Eq. (4.8)** from *T* = 0 placing the resulting reduced spectral acceleration *S *_{R} (0) by multiplying the effects of these layers being equivalent earthquake loads are calculated ( **Figure 4.2c** ). In the calculation, the *earthquake load reduction coefficient* ( *R *_{a} ) _{sub} = *D *_{sub} = 1.5 calculated from **Equation (4.1** ) for the *subsection* (basement) will be used. As a result of the calculation made for the second loading situation,*Reduced internal forces* in the *lower section* are achieved.

**4.7.5.4 - ***Internal forces essential to the design in* buildings with **basements** are defined in **4.10.1** .