During the development of the analytical models, several issues are taken into consideration. An important topic at this stage is to evaluate easily the existence of the soft story behaviour in the structure. For this reason, two dimensional shear frame models for which the soft story behaviour can easily be recognized are selected for investigation. Another important point is the representation of the building stock of Turkey by the models that are considered. In order to take this into account, 3, 5 and 8 story frames with 2, 4 and 6 bays are modelled since most of the framed structures in Turkey have number of stories ranging between three to eight with two-to-six
The span length for the bays is chosen as 5m in all the models considered. The story height in the models is chosen as 3m for all the floors except the first floors. In order to carry out a parametric study to examine the soft story irregularity, the height of the first story (H1) of the models is kept as the selected variable. Three different heights that are considered for the first floor are: 3m, 4.5m and 6m. With these three different heights for the first floor the total number of analysed models reaches to 27.
In Figures 5.1, 5.2 and 5.3, the front views of the analytical models are given together with the dimensions of the beams and columns for each model.
Each model in this study is named according to the total number of stories, total number of spans and first story height of it. For example model name “5-4-1-4.5”
refers to the model with 5 stories having 4 spans according to the first two numbers in the model name and the last two numbers “1-4.5” indicate that the height of the first story is 4.5 m. The expression “HOM” used for the height of the first story means that this story has the same height with the other stories, which is 3m (ex. 3-2-HOM).
The vertical design loads of the two dimensional analytical models are calculated as three dimensional frames. The sum of the vertical loads from the slabs are calculated as a uniformly distributed load of 25 kN/m (except the beams’ self weights) for the normal story beams and uniformly distributed load of 20 kN/m for the roof floor beams (except beams’ self weights). These mentioned loads cover the dead and reduced live loads together. Beam self-weights are calculated and assigned to the beams as uniformly distributed dead loads for the related beams. Additionally, column self weights are calculated and assigned as joint loads on the columns. In Figure 5.4, the slab loads on the analytical models is shown.
Figure 5.2. The 4 span analytical models and member dimensions
Figure 5.4. Assigned slab loads on the analytical models
In addition to these, all of the analytical models are designed according to the requirements of the current Turkish Earthquake Code-2007 [39]. During this design phase Probina-V14 Structural Analysis Programme [46] is used, which has common usage in the design of reinforced concrete building structures in Turkey due to its practicality. The dimensions and the reinforcements of the members are calculated by this software and the other displacement requirements, which are defined in the Turkish Earthquake Code-2007, are taken into account. The parameters, which are used in the design of the models, are given in the Table 5.1.
Table 5.1. Parameters used in the design of the models
Effective Ground Acceleration Coefficient ( Ao ) 0.40g Building Importance Factor ( I ) 1.00
Local Site Class Z-4
Live Load Participation Factor ( n ) 0.3
Structural Behaviour Factor (R) 8
Concrete C-20
Steel S-420
From the chosen parameters and the geometries of the models, it can easily be stated that these analytical models represent the possible Turkish stock of building
structures. The column and beam dimensions and their reinforcements which are calculated with Probina-V14 Structural Analysis Programme are given in Tables 5.2.A and 5.2.B, respectively. Additionally, in Figure 5.5, the reinforcement details of a typical beam and column of the model 3-2-1-6 are given as an example. It should be noted that, the models are designed in order to meet the high level of ductility demands, which are defined and required by the Turkish Earthquake Code-2007.
After obtaining the dimensions and the reinforcements of the members, the nonlinear hinge properties are calculated and compared with the SAP2000 programme’s default hinge properties.
For determining the nonlinear hinge properties of a column, the axial force vs.
moment interaction diagram must be calculated and plotted. When an axial force and corresponding moment value of a loading is formed outside the plotted interaction diagram, this column exhibits nonlinear behaviour. The interaction diagrams calculated with both programmes are plotted on each other. Here, some deviation has been determined for high level of axial forces in the interaction diagrams, but the current Turkish Earthquake Code 2007 prohibits this axial force level, hence this variation does not affect the results.
For determining the nonlinear hinge properties of a beam, the moment capacity values must be calculated. When the moment value at that beam exceeds the calculated capacity moment, this beam exhibits nonlinear behaviour. The calculated capacity moment values are approximately the same for both of the programmes.
As an example, the interaction diagrams for columns of the model 3-2-1-6 determined by SAP2000 and Probina-V14 are given in Figure 5.6. and moment hinge values for beams are tabulated in Table 5.3 . As seen in the figure and the table, obtained results are quite similar.
Table 5.2.A. Dimensions and reinforcements of the columns used in the models
Table 5.2.B. Dimensions and reinforcements of the beams used in the models
42
-100 -50 0 50 100 150 200 250 300 350
0 2 4 6 8 10 12 14 16 18 20 22
Moment (t.m)
Axial Force (t)
Probina Sap2000
Figure 5.6. A typical column’s interaction diagram of the model 3-2-1-6
Table 5.3. A typical beam’s moment capacity values of the model 3-2-1-6 calculated by SAP2000 and Probina-V14 ( Msf = Moment Capacity Value)
SAP2000 DEFAULT PROBINA V14
Msf + (kNm) Msf - (kNm) Msf + (kNm) Msf - (kNm)
121.882 188.379 120.327 190.540