# Calculation and Control of Relative Story Displacements.

**Symbols**

**D = **Strength coefficient**h _{i} = **i

^{th}floor height

**I =**Building importance factor

**R =**Bearing system response coefficient

**S**Horizontal elastic design spectral acceleration [g]

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

_{aR}(T) =**S**Design spectral acceleration coefficient for short period [dimensionless]

_{DS}=**S**Design spectral acceleration coefficient for 1.0 second period [dimensionless]

_{D1}=**T =**Natural vibration period [s]

**T**Horizontal elastic design acceleration spectrum corner period [s]

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

_{B}=**T**Transition period to the constant displacement region in the horizontal elastic design spectrum [s]

_{L}=**u**For any column or wall, Reduced displacement at i th floor

_{i}=**Δ**Displacement difference between two consecutive stories for any column or wall

_{i}=**δ**Effective relative storey drift for columns or walls at i

_{i}=^{th}floor

**δ**Effective relative storey drift for columns or shear walls on the ith floor of the building

_{i,max}=**λ =**Empirical coefficient used to limit the relative storey drifts

**κ =**Differential coefficient used for reinforced concrete and steel load-bearing systems

For columns and shearwalls on any i

^{th}floor of the building in both horizontal earthquake directions, the maximum value of the effective relative storey drifts inside the storey δ_{i,max}must obey the conditions given in TBDY 4.9.1.3.The coefficient λ mentioned in TBDY 2018 4.9.1.3 is the ratio of DD-3 earthquake ground motion elastic design spectral acceleration to DD-2 earthquake ground motion elastic design spectral acceleration for the dominant vibration period in the earthquake direction of the building. The coefficient κ is taken as 0.5 for steel buildings.

Detailed information about the relative story drift calculation is located in Calculation and Control of Relative Story Displacements.

For the building, limitation has been selected in case of flexible joint or connection between the structural system and the walls. According to this selection, κ=0.5 is taken for steel and the limit value is calculated as 0.008.

#### Calculation of Lambda Coefficient

**DD-2 default values**

S_{DS} =0.565

S_{D1} = 0.164

T_{a }= 0.2*S_{D1} /S_{DS} = 0.2*0.164/0.565 =0.058

T_{b} = S_{D1} / S_{DS} =0.389 / 1.112 =0.290

**DD-3 default values**

S_{DS}=0.221

S_{D1}=0.068

T_{a} = 0.2*S_{D1} /S_{DS} = 0.2*0.068/0.221 =0.00615

T_{b} = S_{D1} / S_{DS} =0.155 / 0.475 =0.307

As a result of dynamic analysis, the dominant vibration period for X and Y direction is determined by choosing the largest modal participation rates compatible with the relevant direction.

Modal for x direction → T=1.08011 sec

Modal for y direction → T=1.32680 sec

### Calculation of S_{ae} (T) values

**Calculation for X Direction**

**DD-2**

T=1.08011 sn için

T_{a}= 0.058 < T_{b}= 0.29 < T=1.08011 -> S_{ae}(T)=S_{D1}/T = **0.152**

**DD-3**

T=1.08011 sn için

T_{a}= 0.068 < T_{b}=0.307 < T=1.08011 -> S_{ae}(T)=S_{D1}/T= **0.063**

**Lamda = 0.063/ 0.152=0.4145**

**Calculation for Y Direction**

**DD-2**

T= 1.32680 sn için

T=0.058> T_{b}=0.29< T=1.32680 -> S_{ae}(T)=S_{D1}/T= 0.164/ 1.32680=**0.1236**

**DD-3**

T=1.32680 sn için

T=0.068> T_{b}=0.307< T=1.32680 -> Sae(T)=S_{D1}/T= 0.068/ 1.32680=0.05125

**Lamda = 0.05125 / 0.124=0.0.4146**

**NOTE: **Since all T values in both directions are greater than T_{b}, the lambda coefficient is actually equal to the ratio of S_{D1} parameters of both ground motion levels.

The values calculated by the program are as follows:

First of all, it is necessary to determine the column with the highest horizontal displacement in EX loading for each floor. For doing this, please go to perspective screen - view analysis model - deformations - EX load. At each floor, X-direction displacement of the column-beam joint is read and the difference between them is checked. The largest value in the story is used in the calculation of the relative storey drift.

This value read is the raw value. According to TBDY 2018, the raw value should be increased according to the equivalent earthquake load increase coefficient.

Due to the large size of the building, this process was not carried out, and the relative storey drift calculation is summarized in the table below, using the ∆

_{i}value directly included in the earthquake code report. In the table below, only X + 5% is checked. The point to be considered here is that these results should be increased with Magnification factor.