# Structural Behavior of Floor Systems Made by Floor Plates--Mechanical Model Based on Test Results
## 4 Discussion
### Yield and Failure Loads  
Basically, the observed failure mode should correspond to the proposed model assumed in the calculation. Even in combination with delamination during all the tests (except C05 and C06), it was the behavior of the reinforcement that governed the failure  
Figure 11: Observations from test C06: (**a**) typical crack pattern with formation of an overlap block and pull-out of the lattice girder before the end of the overlap reinforcement; (**b**) lower face of C06. mode. With the application of a rectangular stress distribution for the compression zone in the slab, a design model using Equations (3) and (4) is proposed:  
\[M_{calc}=A_{s}\sigma_{s}\bigg{(}h-h_{p}-c-\frac{\varnothing}{2}-\frac{A_{s} \sigma_{s}}{2f_{c}b}\bigg{)} \tag{3}\]  
\[M_{test}=g\bigg{(}\frac{L^{2}}{8}-\frac{\o^{2}}{2}\bigg{)}+a\bigg{(}\frac{F_{ test}}{2}+\frac{G}{2}\bigg{)} \tag{4}\]  
where:  
\(M_{calc}\) = estimated failure moment based on the design model, or test with abbreviation \"test\";  
\(A_{s}\) = cross-section area of the rebars;  
\(\sigma_{s}\) = reference strength of the rebars, which can be the yield, ultimate, or the one corresponding with slip;  
\(h\) = measured thickness of the slab at the joint location (midspan);  
\(h_{p}\) = thickness of the prefabricated floor plate;  
\(c\) = applied concrete cover, including effects of the roughness on the upper face of the floor plate--in case of an intended surface, an extra 5 mm was counted for the roughness;  
\(\O\) = diameter of the overlap bars;  
\(f_{c}\) = concrete strength at the time of the test, based on cylinder strength;  
\(b\) = width of the test specimen in the compression zone;  
\(g\) = own weight per meter of the test specimen;  
\(L\) = span in between the supports;  
\(o\) = overhang over the supports;  
\(a\) = distance between the support and the application of the concentrated load \(F_{test}/2\);  
\(F_{test}\) = test load when yielding failure or slipping of the reinforcement occurs--when after reaching a peak value, the capacity drops dramatically, the post-peak value is taken to satisfy ductility criteria;  
\(G\) = dead load coming from the steel profiles between the test specimen and the hydraulic jack. Differentiation must be made between nonsignificant and significant delamination. At the moment that nonsignificant delamination occurs, and this is the case for all solid slabs and slabs containing void formers but with a first lattice girder at 95 mm from the joint, the overlap length starts at the joint. However, for the opposite cases the overlap length starts only at the location of the center of the first lattice girder, see Figure 11a. Notice that this fits the guidelines of [16] and deviates from [8], there the starting point was set equal to the first horizontal bar of the lattice girder. When the maximum overlap length is not available, the steel stress \(\sigma_{s}\) will not reach the full capacity \(f_{y}\) and \(f_{u}\) of the rebars. A linear relationship between the available and the required overlap length defines the final steel stress in relation to \(f_{y}\) or \(f_{u}\). No real differences could be observed between the position of the rebar (on the floor plate or with a concrete cover) and only a slight one in post-peak behavior, depending on the roughness of this interface. Hence, it seems that for the concrete finishing and preparation used (which corresponds all to the guidelines from the product certificate [1]) no difference can be found between a rebar fully enveloped by concrete or one in the neighborhood of an interface. The resulting bond in the concrete matrix around a bar or the one partially enveloped plus the friction of the nonenveloped part seems to be equal, see Figure 12b,c. Considering the post-peak values for the A-series of tests and the full capacity for the B-, C-, and D-series, an excellent relation can be found between the tested and calculated values, see Table 4. An average value of \(\mu_{\theta}\) = 1.02 and a standard deviation \(\sigma_{\theta}\) of 0.06 are obtained.