Modal Response Spectrum Analysis of Structures with Basement (4.3.6.2)

Owned by Hakan Şahin
Last updated: Sept 28, 2022 by Zeynep Aladağ
4 min read

  • In buildings where different R and D coefficients are used in the upper and lower sections , the calculation is made automatically according to the rules given in 4.3.6.2 .

  • According to the definition given in 3.3.1 , this rule can be applied in buildings with basements surrounded by rigid walls.

  • Equation 4.4-4.5-4.6 is used automatically in the calculation made by considering the upper + lower part .

Symbols

D

 Strength Excess Coefficient

D alt

 Strength Excess Coefficient applied to the lower part of the building

D üsy

 Strength Excess Coefficient applied to the lower part of the building

R

 Carrier System Behavior Coefficient

R alt

 Structural System Behavior Coefficient applied to the lower part of the building

(R a ) alt

 Earthquake Load Reduction Coefficient applied to the lower part of the building

(R a ) n, alt

Earthquake Load Reduction Coefficient  applied to the lower part of the building in nth vibration mode

R üst

 Structural System Behavior Coefficient applied to the lower part of the building

( R a ) üst

 Earthquake Load Reduction Coefficient applied to the upper part of the building

(R a ) n, üst

Earthquake Load Reduction Coefficient  applied to the upper part of the building in the nth vibration mode

T

 Natural vibration period

Tn

 Natural vibration period of the nth mode

Tp(X)

 (X) the dominant natural vibration period of the building in the direction of the earthquake

νn(X)

 The coefficient used in the calculation of the equivalent earthquake load reduction coefficient applied in the nth mode for the lower part of the building

ν alt (X)

 Coefficient used to calculate the reduced internal forces caused by the vibration of the lower part of the building itself

ν n, alt(X)

 Coefficient used to calculate the reduced internal forces from the vibration of the lower part of the building itself in the nth mode

νüst(X)

 Coefficient used to calculate the internal forces transferred from the upper to the lower part of the building

ν n, üst(X)

 Coefficient used to calculate the internal forces transferred from the upper to the lower part of the building in the nth mode

In buildings with basements where different R and D coefficients are used in the upper and lower sections, the earthquake calculation is made by considering the Modal Calculation Methods as mentioned in 4.3.6.2 . For each nth vibration mode and taking the relevant natural vibration period T n into consideration , the procedures in Equation (4.4) , Equation (4.5) and Equation (4.6) are applied.

Here , instead of the base shear ratio in Eq. (4.5b) , the ratio of the modal effective masses corresponding to these shear forces in the same mode mentioned in TBDY Section 4B.1.4 is used. According to TBDY Section 4B.1.4 for the (X) earthquake direction, the modal contribution factor Γ n (X) for the nth vibration mode and the base shear force modal effective mass of the building in the x-axis direction m txn (X) Eq. (4B) .1) .

When the option "Calculation method with single load case" is selected in rigid basement buildings with R bottom <R top , ν n, top (X) = 0 assumption is made according to 4.3.6.2 (b) . In this case, the following simplifications are applied in the nth mode for the subsection and D sub = 1.5 for the basements .

The "Calculation method with single loading status" option is selected from the "Analysis Settings" command as shown in the picture below.

Modal Response Spectrum Analysis of Structures with Basement Located under the heading.