# Flexural Strength and Stiffness of Donut-Type Voided Slab
## 1 Introduction  
### Research Scope and Objectives  
The increase of the length of span in buildings have brought about the increase in slab thickness in an attempt to mitigate slab deflection, noise and vibration. However, the application of thicker slabs weighing more causes the increase in the size of vertical members such as columns, walls, and bases, which results in the rise in the overall weight of a building and the amount of material. The increase in building weight and the amount of material is a negative factor in construction because it deteriorates the building's economic efficiency and increases seismic load. In the early 20 th century, voided slab systems were developed using a segmented void shaper such as spherical or oval plastic balls for two-way slab applications, and the segmented void shaper was expected to eliminate the slab's directivity and reduce its weight while maintaining its flexural capacity [1]. The main idea of the voided slab system is that lightweight void shapers are placed between the top and the bottom reinforcements before concrete casting to replace concrete in the middle of the slab, which exerts little influence upon the flexural capacity (refer to Figure 1). [PERSON] [2] argued that voided slabswith segmented void shaper can reduce the slab weight by as much as 35% compared to a RC solid slab with the same flexural strength and maintain the flexural strength equivalent to a RC solid slab with the same thickness, theoretically. As reported by [PERSON] et al. [3], a voided slab with spherical voids behaved like a conventional two-way solid slab, and the voided slab carried 89-100% of the ultimate load of a solid slab with the same thickness. For the advantages of voided slabs using segmented void shaper, the concept and practice of voided slabs have been used, and several types of voided slabs have been developed currently. Many tests have been conducted to evaluate the flexural capacities of voided slabs. According to the previous studies conducted by [PERSON] [1], [PERSON] et al. [4] and [PERSON] et al. [5], the flexural capacities of the voided slabs, such as flexural strength, stiffness and ductility, were lower than that of the solid slabs with the same condition, even if some of specimen failed with shear (refer to Table 1). The studies pointed out that the shape and size of voids influenced the flexural capacities of voided slabs. [PERSON] and [PERSON] [6] demonstrated that the void shape significantly influenced the flexural strength of voided slabs, and spherical voids gave better results than the cubical ones. [PERSON] [7] reported that the flexural strength of a voided slab with spherical voids is the same as that of a solid slab with equal depth if the compression zone used to apply the bending force to the slab sections does not enter the void zone, and the flexural stiffness of this voided slab is approximately 80-90% of that of the solid slab due to the cross-sectional loss caused by voids. [PERSON] [8] conducted finite element analysis of a voided slab with spherical voids and reported that the in-plane bending stiffness of the voided slab decreased by 20% compared to that of a solid slab with equal depth. [PERSON] et al. [9] reported that the flexural stiffness and ductility of voided slabs with plastic ball decrease as the ratio of ball diameter to slab depth increase and argued that the reduction in the flexural stiffness of voided slabs could be attributed the direct reduction in the moment of inertia, fast enlargement of cracks and the decrease in bond strength of rebar due to voids. According to the results of these previous studies, the void shape is an important factor affecting the flexural capacity. However, the effect of the void shape on the flexural capacity of voided slab has not been clearly verified yet, and especially, the hole in the void shaper, in which focused on this study, has not been addressed as a variable.