Punching strength of conventional reinforced concrete flat slabs

ABSTRACT The paper presents comparison between the punching shear calculations from six different codes and two equations from the literature. It utilizes 257 punching tests data collected from the literature. The concrete strengths, f’c, range between 12.3 MPa and 68 MPa, the reinforcement ratios range between 0.2% and 5.01%, and the slab depths range between 80 mm and 500 mm. It is found that the smallest error is for CEB-FIP-90 and EC2-2004 while the largest error is for JSCE-2002 and ACI318-19. Also, modifications to one of the equations of the Egyptian reinforced concrete code and two of the equations of ACI318-19 code for calculating the punching strength of flat plates without shear reinforcements are presented. The modified Egyptian and ACI318-19 codes equations for punching strength are compared to the experimental data and good correlations are noticed. The obtained errors are lesser than those of the original codes equations and the average errors are on the conservative side.


Introduction
International reinforced concrete codes such as ACI318-19, JSCE-2002, ECP-203-2017, BS-8110-97, EC2-2004, and CEB-FIP-90 provide different equations for calculating the punching shear strength of two-way slabs without unbalanced moment and without shear reinforcement which are empirical and based on the available test data. Similar trend is noticed for some of the equations in the literature as those of Elshafey et al. [1].
Mari et al. [2], proposed a punching strength model which considers shear reinforcement. The equation is accurate and simple. It considers the stress of the punching shear reinforcement and the high role of concrete to the punching capacity. The model of Mari et al. [2] can be extended to FRP and steel fiber reinforced concrete and corner and border columns. Theodorakapoulos and Swamy [3], proposed a model for calculating the ultimate punching capacity. The model is for normal weight and lightweight concrete. This equation assumes that punching occurs under threedimensional stresses. Finally, failure occurs when the stress reaches the splitting strength. Their model shows good correlation to experimental tests. Alkroosh and Ammash [4] used gene programming to obtain the punching capacity of high strength and normal strength two-way slabs. Their equation was proposed based on 58 punching tests. The obtained function proved that gene programming gives good performance in terms of predicting the punching capacity. Kueres et al. [5], proposed a punching shear design method for column bases and flat plates based on large number of experimental data. Their method is a uniform design method which is applicable for the cases of with or without punching reinforcement. Hamada et al. [6] proposed a simple equation for calculating the punching strength of flat plates. Comparing the calculated punching strength using this equation to test data, a small average error is obtained. Trekin and Pekin [7] presented punching tests for two-way slabs. They also formulated a sequence for calculating the punching capacity which proved to be accurate. Guo and Cheng [8] showed a punching strength formula which considers the flexural reinforcement ratio. Their equation was reasonable when compared to experimental data. Muttoni [9] provided a mechanical explanation for the punching of two-way slabs based on shear crack. He suggested a failure model based on rotation of the slab which proved to be good when compared to experimental results. His equation accounts for the size effect. Muttoni et al. [10] discussed the similarities and differences between squat footings and slender slabs based on the critical shear crack theory. They pointed the shear and bending deformations and their effect on the shear crack. A formula for punching strength was developed. Elshafey et al. [1], evaluated the punching capacity of flat slabs using nueral networks and simple new equations. They used 244 test results for internal columns. The results obtained from neural networks are in good agreement with the test data. They used regression analysis and arrived to two new and simple equations which in turn showed very good correlation to test data. Rankin and Long [11] presented a method for evaluating the punching capacity of flat slabs. This method is valid for circular and square columns. Their method considers slab depth factors, concrete strength, reinforcement ratio, and yield strength of reinforcement. A total of 217 test results were used to verify the method and they found that it correlates well with them.
The purpose of this research is to use the available large number of test data to evaluate the punching equations from the international reinforced concrete codes and from the literature. Best fit of 257 punching test data, taken from Elshafey et al. [1], Rankin & Long [11], and Metwally et al. [12] is then used to modify the most common equation for punching shear of the ECP-203-2017 code and two equations of the ACI318-19 code.

Equations for punching shear
The shear stress is calculated by dividing the floor column load by the area of a critical vertical section. The critical section is taken at distance from the column sides differs from one code, or one equation, to another. This punching shear stress due to load has to be lesser than the design values given by the different equations. These design equations are generally function of the column and slab dimensions and concrete's compressive strength.

ACI318-19 code [13]
Simple equations are proposed in this code. The critical perimeter is at 0.5d from the column faces. According to ACI318-19, the flexural reinforcement ratio has no effect on the punching shear strength. The expressions for the ultimate punching strength given by this code are as follows:

CEB-FIP-90 code [15]
This code considers the influence of reinforcement ratio. It assumes that the punching strength is proportional to the cubic root of the characteristic compressive strength of concrete. Similar to the EC2-2004 code, the critical perimeter is at 2d from the column faces. The equation is similar to that of EC2-2004 and is given by: ρ ¼ the effective flexural reinforcement ratio at the critical section f ck = the characteristic cylinder compressive strength of concrete, MPa

BS8110-97 code [14]
The critical perimeter for this code is at 1.5d from the column faces. This code considers the effect of the flexural reinforcement ratio. The equations of BS8110-97 are as follows:

EC2-2004 code [17]
The Euro-code 2 calculates the punching strength at relatively large distance from the loaded area which is equal to 2d. This code gives the punching shear strength as proportional to the cubic root of the characteristic compressive strength of concrete. EC2-2004 considers the effect of flexural reinforcement ratio. The equation given by this code is:

ECP-203-2017 code [16]
The critical perimeter for this code is at 0.5d from the loaded area. It relates the punching shear strength to the square root of the concrete compressive strength as follows:

JSCE-2002 code
The JSCE-2002 code [6] assumes that the punching strength is proportional to the square root of the concrete compressive strength. It considers the effect of flexural reinforcement ratio and assumes that the critical perimeter is at 0.5d from the column faces.

Used experimental results
The test results reported by Elshafey et al. [1], Rankin and Long [11], and Metwally et al. [12] are used in this study. They consist of 257 specimens which cover a wide range of variables. The flexural reinforcement ratios range between 0.2% and 5.0%, the slab depths vary from 80 mm to 500 mm, and the concrete cylinder compressive strengths vary from 12.3 MPa to 68 MPa. These data are to be used to calibrate and modify the most common equations for the punching capacity of the ECP-203-2017 code and two equations of the ACI318-19 code.

Comparison between the eight equations for punching capacity
The average of the punching strengths from tests divided by the punching strengths from the eight formulae along with the standard deviation for the same are given in Table 1.

Proposed modification to the common ECP-203-2017 and ACI318-19 codes equations
The 257 test data collected from the literature are used in a regression analysis and the following modification is suggested for the common equation for punching capacity of the Egyptian reinforced concrete code:     The same procedure is followed to propose the following two modifications for the ACI318-19 punching strength equations.

Disclosure statement
No potential conflict of interest was reported by the authors.