# Flexural Strength and Stiffness of Donut-Type Voided Slab
## 2 Optimization of Void Shape
### Determination of the Optimal Void Shape  
Based on above FE analysis results, it was deduced that the self-weight reduction of a slab was mainly decided by the base shape of void. Thus, the choice of base shape is important to decide the optimal void shape, because the self-weight reduction is the major reason for the use of voided slab system in buildings. The direct evaluation of the base shapes was not conducted for the determination of the optimal void shape in this study, because the proper self-weight reduction would be varied case by case. However, the effect of the base shapes on the flexural strength should be considered for the determination of the optimal void shape, because the base shape also influences the flexural strength. The voided slab can secure the same or more level of the flexural strength by proper application of the base shape and the curvature radius of edge compared to solid slab. In addition, the  
Figure 5: Load–deflection relationship of voided slab according to the parameters: (**a**) the base shape of void; (**b**) the radius curvature of edge; (**c**) the hole diameter. lack of flexural stiffness of voided slab due to the base shape and the curvature radius of edge can be complemented partly by the hole in void. Thus, when all these considerations take into account, it is expected that the optimal void shape has the base shape of cuboid, the curvature radius of edge by 70 mm and the hole in void shaper. To verify the hypothesis, the above void shapes were compared to each other again focused on the load-bearing capacity and the flexural stiffness. The residual load-bearing capacity was compared in terms of the load-bearing capacity of voided slab, and the deflection at 20.4 kN/m\({}^{2}\), which was the load corresponded to 0.6\(M_{y}\) was compared in terms of the flexural stiffness. The reasons of comparing these values are as follows. It is not reasonable to use the ultimate load for comparing the load-bearing capacity of voided slab because the self-weight of voided slabs was varied according to void shapes, and the self-weight influenced the ultimate load-bearing capacity. As the difference between the design load and the ultimate load means the rest of load-bearing capacity of slab after the design load, the residual load should be used to compare the load-bearing capacity instead of the ultimate load. Therefore, the residual load-bearing capacities were used as the criterion to determine the optimal void shape. In addition, voided slabs were vulnerable to flexural stiffness due to the loss of cross-section area, and the flexural stiffness could be evaluated by the deflection. For comparing the flexural stiffness by the deflection, the deflections at a certain load should be compared. The limit of deflection is usually evaluated at a service load, and the service load is generally assumed as 0.6\(M_{y}\). Therefore, the deflections at 20.4 kN/m\({}^{2}\) were also used as the criterion to decide the optimal void shape. The sequential elimination method was used to decide the optimal voids shape with these two criterions. The sequential elimination method is a one of reasonable method to select the one from among several. The concept of this method is the eliminating something sequentially according to a certain criterion. The eliminating procedure is performed repeatedly until only the one thing is left in the order of importance of the criterions. Thus, the order of importance of criterions should be defined. In this study, it was assumed that the load-bearing capacity of a voided slab was more important than the flexural stiffness, because the load-bearing capacity closely related with the safety of the voided slab system. Following these rules, the top three void shapes were selected among the above eight types of void shape, and the others were eliminated according to the residual load-bearing capacity in terms of the load-bearing capacity.