# An Effective Beam Width Model of Slab in Thick Wall-Thick Slab Joints Subjected to Lateral Forces
## 4 Results
### Modeling Procedure
#### 4.3.3 Discussions on Influencing Factors  
In the proposed model of the effective beam width for the initial stiffness, various features of the joint including the configuration dimensions and material properties, such as the concrete elastic modulus \(E\), the thickness of the slab \(D\), half of the wall height \(H\), half of the wall height \(L_{1}\), half of the slab span length \(L_{s}\), and the flexural length of the slab \(L_{2}\), has been considered. The influence of two main factors, the wall height \"\(H\)\", the wall length \"\(L_{1}\)\", and the slab span length of \"\(L_{s}\)\" on the effective beam width prediction is discussed in this section.  
Considering a situation in which except for the parameter of \"\(H\)\", other features of the wall-slab joints are kept identical to discuss the influence of \"\(H\)\", due to the strong bearing wall being assumed as a rigid body, the rotational angles generated for the slab ends are usually equaling to the value at an identical deformation angle occurring around the bearing wall footing at the initial stage. In other words, the input moment transferred over the effective beam is identical for cases with different values of \(H\). Thus, the value of \"\(QH\)\" is consequently considered unchanged for different wall-slab joint models with different \"\(H\)\". As a result, it can be known that if only the value of \"\(H\)\" is changing while other variables are kept identical, the value of \(b_{e}\) predicted using Equation (18) is a constant. However, it should be noticed that the model was developed by assuming the bearing wall was a rigid body, which was reasonable considering calculation simplification but not completely true in reality. In actual structures, initial and growing cracks, shrinkage, creeps, or other damages occur in the bearing wall, which could make the stiffness of the bearing wall reduce, can bring slight influences on the value of \"\(QH\)\" and leads to the value of \"\(QH\)\" not keeping a constant and showing a slight change. As a result, in the situation that only \"\(H\)\" changes, it can be considered that the effective beam width is predicted identical at the initial stage with sufficiently small deformation, based on which slight influences can be ignored.  
Due to \(L_{2}\) equals to \"\(L_{s}-L_{1}\)\", Equation (18) can also be expressed by Equation (34).  
\[b_{e}=\frac{4}{ED^{3}}\times\frac{\left(L_{s}-L_{1}\right)^{3}}{L_{s}L_{1}} \times 2000\cdot QH \tag{34}\]  
It can be known that \(b_{e}\) is disproportionate to the thickness of the slab \"\(D\)\", while for the group of \"\(\frac{\left(L_{s}-L_{1}\right)^{3}}{L_{s}L_{1}}\)\", more discussions are needed to figure out how these two parameters, \(L_{s}\) and \(L_{1}\), influence the value of \(b_{e}\). In the group \"\(\frac{\left(L_{s}-L_{1}\right)^{3}}{L_{s}L_{1}}\)\", as the value of wall length \(L_{1}\) increases, the part of \"\(L_{s}-L_{1}\)\" representing the flexural length of the effective beam decreases, which leads to a reduction of the calculation value of \(b_{e}\). Thus, it can be indicated that the length of the bearing wall is as well disproportionate to the value of \(b_{e}\). On the other hand, in the situation that the slab span length \(L_{s}\) increases, both of \"\(L_{s}-L_{1}\)\" as well as \"\(L_{s}L_{1}\)\" increases, which is not clear to determine whether the value of \"\(\frac{\left(L_{s}-L_{1}\right)^{3}}{L_{s}L_{1}}\)\" increases or decreases. Therefore, for the parameter of the span length of the slab \(L_{s}\), further investigations are needed in future work.