Making Calculations with Mode Combining Method
The Mod Combination Method was chosen for the building as a result of the necessity to be analyzed with the modal analysis method in accordance with Table 4.4 of TBDY 2018 .
Since the building is a basement structure, it is difficult to provide sufficient mode numbers, the mass participation rate of 95%, to be taken into account in the Mod Combination Method for the entire upper section above the rigid basement walls and the lower section containing the basement floors. For this reason, in TBDY 2018 4.8.5.1, two loading status calculations are made in the calculation of basement buildings using modal calculation methods.
In this method, the upper part of the building and the lower part with basement are modeled together as a common carrier system and two loading cases are calculated. In both loading cases, a mass participation rate of 95% should be achieved.
There are two stages in the analysis of the upper section and the basement floors, as the building consists of a carrier system with no beams. The first stage is the hinged modeling of the frame columns from the lower and upper ends, and the second stage is the monolithic modeling of the elements.
In addition, due to the dynamic method of solving the Extra- Eccentricity Effect in the program, 4 modal analyzes are made for each stage.
In accordance with TBDY 2018 4.5.10.4 clause, it is applied in a full rigid solution to determine the extra-eccentricity effect in floors with semi-rigid diaphragm adopted as a shell.
Due to all the earthquake code requirements listed above, a total of 20 modal analyzes were made for this building and the internal forces to be used for the design were determined.
Top Section Analysis (First Loading Status)
In the first loading model, a common carrier system model is established, that is, the entire structure is modeled. The masses of the basements are taken as '0' and their stiffness is used in the mathematical model, while both the mass and stiffness of the basement floors are included in the mathematical model. As a result of this analysis, internal forces are obtained in both the upper section and the basement floor elements.
First of all, the item summaries of the analyzes made with the symbols used by the program are explained in the table below.
The following table summarizes the dynamic analysis results for the upper section obtained from the monolithic model of frame columns.
Scaling of the Calculation Made with Mode Combination Method According to Equivalent Earthquake Load Method
According to TBDY 4.8.4, the total earthquake load obtained by modal combination method in any direction cannot be less than the total equivalent earthquake load calculated by the equivalent earthquake load method. If it is less, the equivalent base shear force is increased by the magnification factor.
For this calculation, first of all, the maximum value of the dominant vibration period T p obtained from the mathematical model can not be more than 1.4 times the T pA determined by TBDY 2018 Equation 4.27 .
In buildings where all earthquake effects are covered by reinforced concrete walls, C t is calculated with the following equation. Curtain net areas are used in this account.
The calculation below has been made manually for the X direction and compared with the program outputs for the sake of example.
The manual calculation above is done automatically by the program and the dynamic analysis report is detailed in the entry section. The table below is obtained from the dynamic analysis report for the X direction.
The base shear force of the structure is determined after the period to be used in determining the equivalent earthquake load is calculated. How the equivalent earthquake load is determined is described in TBDY 2018 4.7.2. The base shear force obtained using the equations here is compared with the modal total earthquake load obtained by the program and the coefficient of increase is calculated according to the following equation.
The E coefficient was used as 0.80 due to the absence of irregularities in the building.
Second Loading Condition (Sub Section - Analysis of Basement Floors)
In the second loading case of the calculation, only the masses of the sub-section are taken into account in the common single carrier system model. The stiffness of both the upper and lower section is included in the mathematical model. As a result of this analysis, the minimum mass participation rate of 95% must be achieved.
At this stage, analysis consisting of two stages is carried out in which the columns are hinged and monolithic models due to the carrier system with no beams.
Comparison with equivalent earthquake load method in basement floors is not made in accordance with the regulation.