# Structural Behavior of Floor Systems Made by Floor Plates--Mechanical Model Based on Test Results
## 3 Results
### Load-Deflection Curves  
For all longitudinal joints tested (A-, C-, and D-series), the load-deflections are given in Figure 5; different parameters can be found in the Table 2; Table 3, Sections 2.1.1 and 2.1.2. The transversal joints (B-series) are not represented as these diagrams are not valuable. The reinforcement ratio leads to almost the same resistance moment as the one of the uncracked concrete; in addition, these tests are also three-point bending tests. Nevertheless, other observations are discussed. The theoretical behavior of the slabs is simulated by the aid of mean values for the mechanical properties and the production formula from [4], based on the distribution coefficient \(\zeta\), depending on the ratio of the moment at the first crack (\(M_{cr}\)) and the one applied (\(M\)), see Equations (1) and (2). \[\delta_{tot}=\zeta\delta_{c}+(1-\zeta)\delta_{nc} \tag{1}\]  
\[\zeta=1-\beta\bigg{(}\frac{\sigma_{s,r}}{\sigma_{s,c}}\bigg{)}^{2}\approx 1- \beta\bigg{(}\frac{M_{cr}}{M}\bigg{)}^{2} \tag{2}\]  
where:  
\(\delta_{tot}=\) total vertical deflection = theoretical value indicated in Figure 5 (solid black lines);  
\(\delta_{c}=\) vertical deflection based on a cracked second moment of area of the section;  
\(\delta_{nc}=\) vertical deflection based on a noncracked second moment of area of the section;  
\(\beta=\) coefficient that takes into account the load duration or of repeated loading = 1 (short duration);  
\(\sigma_{s,r}=\) stress level of the rebars under the loading causing a first crack, belonging to \(M_{cr}\);  
\(\sigma_{s,c}=\) stress level of the rebars for a cracked section in the appropriate limit state, belonging to \(M\). Figure 5: _Cont._  
Further on, an approximation is made for the load-deflection curves based on an equivalent uniform load that causes a deviation of about 10% (underestimation of the stiffness), which is still acceptable for deformation estimations. To account for the presence of voiding elements, the weight was reduced to only 20 kN/m\({}^{3}\) instead of 25 kN/m\({}^{3}\) for solid slabs and the second moment of area, and the section modulus was adopted. The latter decreases the cracking moment \(M_{\sigma}\) for slabs containing voiding elements. From these figures, it is seen that the A-series do not reach the full capacity of the joint due to shorter overlap reinforcement and a shift of the starting point of the overlap. This was previously discussed in [28], and can be attributed to the location of the first lattice girder at 300 mm from the joint. Nevertheless, the slabs seem to react relatively close to the expected curve (abbreviated as Theoretical), only the solid slab reacts stiffer, which should be expected. The ratio between the measured to the calculated value (\(F_{test}/F_{calc,u}\)) and explanation of observed differences is postponed to Section 4. The retained value after a first peak seems to correspond reasonably well with the strength of the joint, based on the reduced overlap length. Results of the solid slab (A10) correspond to the one with bended up reinforcement (A06) and the one with anchor rods (A05). Overlap rebars were broken by none of the tests, which might be expected as the expected yielding \(F_{calc,y}\) and failure load \(F_{calc,u}\) were not reached. The C-series of solid slab tests perform all very well and react as can be expected, based on the theoretical model from [4]. The deviation of the slope of the load-deflection curve can be explained by the unfavorable approximation (uniform versus 4-point) made where the stiffness is underestimated. The C05 and C06 tests need some extra attention,  
Figure 5: Measured and estimated load–deflection curves: (**a**) A-series of Airdeck tests; (**b**) C-series of solid tests; and (**c**) D-series of U-Boot tests. which will be given later. Besides these tests, the failure mode was governed by the tensile strength of the overlap reinforcement, which was also the case in the B-series. It seems that the D-series reacts much stiffer as a solid slab.