# Structural Behavior of Floor Systems Made by Floor Plates--Mechanical Model Based on Test Results
## 4 Discussion
### Interface
#### 4.3.2 Vierendeel Effect of Lattice Girders  
Figure 11 makes clear that at the end of the overlap block, a compression zone is active at the top of the block. Due to horizontal equilibrium, this is only possible by the transfer of horizontal forces from the overlap block into the floor plate. Without the excluded mechanism (with the Plexi) this can only be realized by the mean of the cosines-part of the force that can be developed in the diagonal and the dowel effect of this diagonal, reacting as a Vierendeel beam. Translation and rotation after failure is shown in Figure 15a, and in a schematic way, the transfer of forces is represented in Figure 15b. Only two well-equipped tests are available, so no statistical analysis can be performed, but the methodology from annex J of [2] can be applied. Correspondence between the maximum measured values before failure and the calculated values based on Equations (9) and (10) delivers a \(F_{test}/F_{calc,inter}\) value of 0.96 and 1.14, thus both are above 0.95 with an average value above 1, which proves that the model fits well with the observations. In Equation (10), a constant factor of 0.4 mm is introduced to account for the effect that in each test at the location of the lattice girder an opening appeared during the test; see Figure 15a after the test and Figure 11a during the test.  
\[H_{R}=F_{pl,dia}+F_{pl,rod}+\frac{n}{2}A_{dia}\sigma_{s}cos(\alpha)=n\frac{ \varnothing_{dia}^{3}}{6}\sigma_{s}+2\frac{\varnothing_{rod}^{3}}{6}\sigma_{s, rod}+\frac{n}{2}\frac{\pi\varnothing_{dia}^{2}}{4}\sigma_{s}cos(\alpha) \tag{9}\]  
\[M_{calc}=H_{R}\bigg{(}h-h_{p}-\frac{Plexi+0.4}{2}\bigg{)} \tag{10}\]  
where:  
Figure 14: Evolution of the last (reinforcement) term from Equations (7) and (8), and their combination.  
\(H_{R}\) = horizontal resistance force that can be developed at the interface;  
\(F_{p|dia}\) = plastic capacity that can be developed in bending by the diagonals;  
\(F_{p|rod}\) = plastic capacity that can be developed in bending by the rods;  
\(\sigma_{s}\) = reference strength of the rebars, abbreviation s for the diagonal bars and \"s,rod\" for the rods;  
\(\O\) = diameter of the diagonals or throat diameter of the rod;  
_Plexi_ = thickness of the Plexi plate in mm, as 0.4 is the additional crack width in mm, all other thickness dimensions should also be written in mm;  
\(n\) = number of diagonals for a double-leg lattice girder;  
and other symbols already defined for Equations (3) and (4).  
It should be noted that the proposed failure mechanism will only be observed by the elimination of adhesion, mechanical interlock, and friction. In practice, this will only occur where severe execution errors will be observed, such as concrete top casting on a significant dust or ice layer, for example. In the case of more moderate conditions, a sensitivity check was performed. It follows that only starting from a horizontal opening between the floor plate and concrete topping of 2.4 mm will the Vierendeel effect govern the design. Below 2.4 mm, this will be dowel action with an upper bound equal to the shear capacity of the lattice girders. However, this is not yet thoroughly investigated.