Punching Shear Capacity of RC Biaxial Voided Slab – Prediction by Critical Shear Crack Theory

In this study the applicability of critical shear crack theory (CSCT) to biaxial voided slab is investigated, which predicts the punching shear capacity of solid slab. Based on the experimental results of biaxial voided slab available in the literature (40 specimens) the research is carried out. The experimental results showed that the load-rotation behaviour of biaxial voided slab is remain same as that of solid slab except for specimens with void located within 0.5 d from face of the column. Further, the punching shear capacity of slab specimens with voids located beyond 2 d distance from column face is almost the same as that of the solid slab. Depends on the available load-rotation data modified CSCT was developed depends on the location of the void from face of the column. The predictions were observed to be very scattered with a mean and standard deviation of 0.752 and 0.412, respectively. This is reasonable as the modified CSCT estimates the capacity with respect to the location of voids and ignores the area of void at the section considered. The CSCT approach needs to be further modified by including location and area of void to predict the punching shear capacity of biaxial voided slab with reasonable accuracy.


Introduction
Biaxial voided reinforced concrete slab is being adopted as an alternative to conventional reinforced concrete (RC) flat slab.It is mainly because of its many advantages over conventional RC slabs, such as reduced self-weight (up to 50%), reduction in consumption of materials in other structural members (about 15%), green technology, reduces carbon emission, and reduction in overall cost [1].The flexural performance of the biaxial voided slab system is almost remain the same as that of RC solid slab.For example, the one-way ultimate flexural capacity of biaxial voided slab is 84-97% of the solid slab capacity whose dimension and properties are remain the same [2][3][4][5].Similarly, the two-way ultimate flexural capacity of biaxial voided slab is remain the same as that of solid slab.However, the presence of voids affect the initial stiffness marginally [6,7].As the presence of voids leads to reduction in the effective concrete area, the one-way shear capacity of biaxial voided slab reduces [8].Similarly, the two-way shear (punching shear) capacity is also significantly affected by the presence of voids [9].However the punching shear capacity of biaxial voided slab is affected by many parameters such as location of void from the face of column, size of void and void pattern.From the detailed research, it is found that the punching shear capacity of biaxial voided slab is remain the same as that of solid slab, if the void is located beyond 3d (d is effective depth of slab) distance from the face of column [10].The prediction of punching shear capacity becomes complicated as the presence of voids alters the critical section.Further, the conventional methodology available for solid slab in the building standards (ACI 318-14, EN 1992-1-1 2004 and IS 456 2000) does not applicale for the void slabs.Hence the Authors [10] introduced an alternate way to predict the punching shear capacity by incorporating suitable modification to the control perimeter and using effective concrete area in the existing equations of various building standards.As the equations available in the building standards and proposed by Authors are semi-empirical in nature, an effective way to predict the punching shear capacity needs to be established.

Critical Shear Crack Theory
"The punching shear strength decreases with increasing rotation of the slab (Figure 1), i.e., the shear strength is reduced by the presence of a critical shear crack that propagates through the slab into the inclined compression strut carrying the shear force to the column" [11].The typical correlation between opening of critical shear crack, thickness of slab, and rotation is shown in Figure 2. In continuation with that critical shear crack theory (CSCT) was adopted to develop a failure criterion for punching shear [12,13].This criterion describes the relationship between the punching shear strength of a solid slab and its rotation at failure (Eq.1).
where, V R is punching shear strength, f c ' is characteristic compressive cylinder strength of concrete, b 0 is perimeter of critical section (which is located at a distance of 0.5d from face of the column) for two-way shear in slabs, d is effective depth of slab, ψ is rotation, d g0 is reference aggregate size (= 16 mm), and d g is maximum aggregate size.The failure criterion (Eq. 1) was developed by Muttoni [13] based on the 99 experimental results as shown in Figure 3.For more details regarding the experiments that were considered for the same can be obtained in the article by Muttoni [13].

Load -Rotation Relationship of Biaxial Voided Slab
The punching shear strength of solid slab is depends on its rotation, i.e., the strength decreases with increasing rotation.Hence, it is very important to understand the variation in the load-rotation relationship of biaxial voided slab in comparison with that of solid slab.The rotation is directly depends on the deflection of the slab.So the load-rotation relationship remains the same as that of load-deflection of the slab.In order to verify the load-deflection relation of solid and biaxial voided slabs, the experimental results available in literature [10,14] are considered.For more details regarding the experiments that were considered for the same can be obtained in the relevant articles.From the experimental results (Figure 4), it is observed that the load-deflection behaviour of biaxial voided slab remains the same as that of solid slab irrespective of the void shape.However, if the location of the void from face of the column lies within 0.5d, then the load-deflection behaviour gets affected marginally (specimen V2 in Figure 4b).As a summary, the relationship between the punching shear strength of a solid slab and its rotation at failure (Eq. 1) remains applicable for biaxial voided slab with necessary modification to account for reduction in punching shear strength depends on the location of void from the face of column.

Prediction of Punching Shear Capacity
The applicability of the CSCT (Eq. 1) for the biaxial voided slab is verified in this section.In this study, the experimental results available in the literature (40 specimens) were compared with the estimations.The details and experimental results of voided slab specimens are summarised in Table 1.The CSCT approach requires the ultimate load (punching shear) and corresponding deflection.Hence, the specimens (29 specimens) with both punching shear load and corresponding deflection are considered for initial observations.Figure 5 shows the data points of the normalised load and rotation of 29 test specimens.The punching shear capacity of slab specimens with voids located beyond 2d distance from column face is almost the same as that of the solid slab (Figure 5).However, if the void is located beyond d (and within 2d) distance from the column face, then the punching shear capacity is reduced about 30%.Similarly, for slab specimens with voids located close to column face (<d), the punching shear capacity is reduced about 60%.Hence capacity reduction factor (α) is introduced in the Eq. 1 as given in Eq. 2 depends on the location of void from the face of the column.
Based on this understanding, the modified CSCT (Eq.2) is applied to all 40 test specimens and found that the predictions were observed to be very scattered with a mean and standard deviation of 0.752 and 0.412, respectively (Figure 6).In particular the calculated capacity for the specimens with void located very close to column face (<0.5d) is observed to be  Note: # Concrete cylinder strength is taken as 80 % of cube strength and vice versa, if required lesser than that of experimental results.This is reasonable as the modified CSCT estimates the capacity with respect to the location of voids and ignores the area of void at the section considered.

Summary and Conclusions
The applicability of critical shear crack theory which predicts the punching shear capacity of solid slab to biaxial voided slab is investigated in this study.For the purpose of the same, the experimental results available in the literature (40 specimens) were collected.Based on the available load-rotation data modified CSCT was developed depends on the location of the void from face of the column.The experimental results showed the behaviour of biaxial voided slab is remain same as that of solid slab except for specimens with void located within 0.5d from face of the column.Further, the punching shear capacity of slab specimens with voids located beyond 2d distance from column face is almost the same as that of the solid slab.The predictions by modified CSCT were observed to be very scattered with a mean and standard deviation of 0.752 and 0.412, respectively.This is reasonable as the modified CSCT estimates the capacity with respect to the location of voids and ignores the area of void at the section considered.The CSCT approach needs to be modified by including location and area of void, which needs more experimental results.Further, the study needs to be extended to investigate the crack propagation through the voids, as the presence of voids affects the critical section of punching shear.

Disclosures
Free Access to this article is sponsored by SARL ALPHA CRISTO INDUSTRIAL.

Table 1 -
Details and Experimental Results of Voided Slab Specimens of Various Researchers (N/mm 2 ) 1/2 ψd/(d g0 +d g ) Fig. 5 -Failure Criterion: Punching Shear Strength as Function of Width of Critical Shear Crack Fig. 6 -Comparison of punching shear capacity of voided slab specimens (Table1) and CSCT