# An Effective Beam Width Model of Slab in Thick Wall-Thick Slab Joints Subjected to Lateral Forces
## 4 Results
### Modeling Procedure
#### 4.3.2 Model Processing Using Experimental Tests Results  
Four 1/2-scaled specimens of thick wall-thick slab joints were tested in [PERSON] et al. 's experimental tests [6,7], from which three specimens are selected for the modeling processing in this work. Specim 1 and 2 have slabs on both sides while Specim 3 only has an individual slab on one side as shown in Figures 8 and 9, respectively. The specimens have a uniform dimension for bearing wall (500 mm length, 1500 mm height, and 175 mm depth), flat slab (span length of 1500 mm and slab thickness of 175 mm), and the invisible beams that are concealed in the flat slab (length of 1500 mm equal to that of the slab, width of 350 mm, and depth of 175 mm). It is noticed that in their work, the bearing wall is not arranged symmetrically in the north-south direction, which is caused by the design consideration for the interior and exterior spaces (such as different reinforcement distribution for the indoor space and the balcony space). However, it is not affecting the flexural stiffness of solid components so that the discrepancy of the invisible beam component can be ignored for the stiffness calculation. Additionally, the properties and test results for concrete and steel materials in their test are summarized in Table 1.  
The fixity condition and test setup are shown in Figure 10. The bottom of the bearing wall was pin-supported on the strong ground to restrain the horizontal and vertical movements of the base, the top of the bearing wall was free where cyclic lateral loadings were \begin{table}
\begin{tabular}{c c c} \hline \hline
**Specimen** & **Compressive Strength (N/mm2)** & **Young’s Modulus (N/mm2)** \\ \hline
1 & 38.50 & 31.90 \\
2 & 36.80 & 32.20 \\
3 & 37.50 & 31.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material test results of concrete [6,7]. Figure 8: Design details for both-slab specimen (dimensions in mm) [6,7]. Figure 9: Design details for one-slab specimen (dimensions in mm) [6,7]. applied, and both ends of the slab were roller-supported and restrained only in the vertical direction to simulate points of inflection. Considering that the initial stiffness was defined as the secant stiffness at 0.05% inter-story drift ratio, the results from their experimental test of the lateral force at 0.05% drift ratio are defined as criterion values of the input lateral force \(Q_{0}\), in which the subscript \"0\" represents the criterion value. Additionally, the specimen and material properties from their experimental test are as well considered as criterion values for further model processing, such as \(A_{w0}\) for the wall cross-sectional area, \(l_{w0}\) for the wall length, \(t_{w0}\) for the wall thickness, and so on. Moreover, the initial stiffness \(K_{b0}\) using Equation (1) and the effective beam width \(b_{e0}\) using Equation (18) can be obtained as summarized in Table 2. It can be noted that for wall-slab joints with only one-side slabs, the effective beam is 2.60 times the uniform thickness while for joints with both-side slabs, it should be taken by 3.20 times. Thus, these values obtained from [PERSON] et al. 's results can be used to estimate the lateral force for the effective beam width model at the initial stage. To estimate the lateral force \(Q\) in Equation (18) using the criterion value \(Q_{0}\), a correction coefficient that represents the relationship between the target value \(Q\) and \(Q_{0}\) is established in the following section. First of all, \(\widetilde{\tau}_{0}\) representing the criterion value of the average shear stress distributed over the cross-sectional plane of the bearing wall at the 0.05% inter-story drift ratio is defined and it can be obtained using the criterion lateral force \(Q_{0}\) divided by the total cross-sectional area of the bearing wall. Based on the measured results from [PERSON] et al. 's experimental tests, \(\widetilde{\tau}_{0}\) equals 0.28 \(N/mm^{2}\) for both-slab joints while 0.21 \(N/mm^{2}\) for one