Calculation and Control of Relative Story Displacements.

Owned by nurgül Kaya (Unlicensed)
Last updated: Nov 22, 2022 by Zeynep Aladağ
4 min read

Symbols

D = Strength coefficient
hi = ith floor height
I = Building importance factor
R = Bearing system response coefficient
Sae (T) = Horizontal elastic design spectral acceleration [g]
SaR (T) = Reduced design spectral acceleration [g]
SDS = Design spectral acceleration coefficient for short period [dimensionless]
SD1 = Design spectral acceleration coefficient for 1.0 second period [dimensionless]
T = Natural vibration period [s]
TA = Horizontal elastic design acceleration spectrum corner period [s]
TB = Horizontal elastic design acceleration spectrum corner period [s]
TL = Transition period to the constant displacement region in the horizontal elastic design spectrum [s]
ui = For any column or wall, Reduced displacement at i th floor
Δi = Displacement difference between two consecutive stories for any column or wall
δi = Effective relative storey drift for columns or walls at ith floor
δi,max = Effective relative storey drift for columns or shear walls on the ith floor of the building
λ = Empirical coefficient used to limit the relative storey drifts
κ = Differential coefficient used for reinforced concrete and steel load-bearing systems

Calculation of Lambda Coefficient

DD-2 default values

SDS =0.565

SD1 = 0.164

Ta = 0.2*SD1 /SDS = 0.2*0.164/0.565 =0.058

Tb = SD1 / SDS =0.389 / 1.112 =0.290

DD-3 default values

SDS=0.221

SD1=0.068

Ta = 0.2*SD1 /SDS = 0.2*0.068/0.221 =0.00615

Tb = SD1 / SDS =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 Sae (T) values

Calculation for X Direction

DD-2

T=1.08011 sn için

Ta= 0.058 < Tb= 0.29 < T=1.08011 -> Sae(T)=SD1/T = 0.152

DD-3

T=1.08011 sn için

Ta= 0.068 < Tb=0.307 < T=1.08011 ->  Sae(T)=SD1/T= 0.063

Lamda = 0.063/ 0.152=0.4145

Calculation for Y Direction

DD-2

T= 1.32680 sn için

T=0.058> Tb=0.29< T=1.32680 -> Sae(T)=SD1/T= 0.164/ 1.32680=0.1236

DD-3

T=1.32680 sn için

T=0.068> Tb=0.307< T=1.32680 ->  Sae(T)=SD1/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 Tb, the lambda coefficient is actually equal to the ratio of SD1 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.

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