Seismic Damage Assessment of Reinforced Concrete Slab-Column Connections—Review of Test Data, Code Provisions and Analytical Models

Abstract

Reinforced concrete slab-column connections are vulnerable to punching shear failure when subjected to combined gravity and lateral loadings during earthquakes. Over the years, many experimental campaigns have been conducted and assessed the seismic performance of flat slabs. The experimental findings were used to derive empirical equations for the design provisions. The paper aims to provide a detailed description of the code development for seismic punching shear. Two current code provisions (ACI 318-19, EC 2 & EC 8-2004) for seismic punching shear are presented and discussed. Relevant and updated experimental data of interior slab-column connections without and with shear reinforcement are selected and assessed against the current design provisions with a focus on key response parameters such as the drift ratio and the gravity shear ratio. The ACI 318-19 limit drift line is considered to assess the lateral deformation demand for the connections with respect to the updated database. The gravity shear ratio is shown to have a considerable impact on the limit drift ratio of slab-column connections without shear reinforcement. The majority of the test specimens with no shear reinforcement experienced punching shear failure, followed by the specimens which showed a combined flexure–punching failure. Punching shear failures occurred for a range of gravity shear ratios of 0.2 to 0.9, while all combined flexure–punching shear failures occurred for gravity shear ratio values below 0.5. The shear-reinforced concrete slab-column connections can achieve much higher drift ratios. Most of the slabs were reinforced with shear studs, particularly in the range of gravity shear ratios of 0.4 to 0.6. Most test specimens failed by flexure for gravity shear ratio values of 0.1 to 0.7, followed by the specimens which failed in combined flexure–punching for gravity shear ratio values that ranged from 0.3 to 0.9. Finally, the available numerical and analytical models for seismic punching shear are presented with the objective of observing their potential strengths and limitations.

1. Introduction

Reinforced concrete two-way slabs can be found in monolithic concrete construction. This type of structure started to be constructed in the early 20th century in North America and Europe. Slab-column connections provide many advantages over other construction systems, such as a reduction in floor height since no beams are present, ease of construction, simple formwork and a reduction in the construction cost, making them a popular floor system. In 1901, George M. Hill designed the first reinforced concrete two-way slabs; however, Turner (1869–1955) in the USA and Maillart (1872–1940) in Switzerland in Europe are mentioned as the most significant contributors to the construction of flat slabs [1]. The first reinforced concrete two-way slabs were supported on columns with large column capitals to avoid potential shear problems. Slabs without shear capitals on columns or drop panels, supported directly on columns, were constructed in the 1950s. The first flat slab building was constructed by Turner in Minneapolis in 1906 [1]. One of the disadvantages associated with the use of reinforced concrete slab-column connections in frames is the brittle punching shear failure that happens due to the development of high shear stresses in the connection area, developed from combined gravity loads and unbalanced moments during earthquakes. The three-dimensional state of stresses and strains results in principal tension stresses that are inclined with respect to the slab’s plane. Cracking develops inside the slab, in the proximity of the column, and propagates through the thickness of the slab. These inclined cracks occur around the column and lead to the separation of the slab. To make the connection more ductile and avoid a brittle shear failure, shear reinforcement, such as shear studs, is installed to the connection. Since reinforced concrete slabs are susceptible to punching shear failure, they can be found in areas of low-to-moderate seismic risk as lateral force-resisting systems and in areas of high seismic risk in gravity systems associated with moment frames or shear walls. However, past and recent earthquakes demonstrated the vulnerability of flat slabs. A few examples include the 1985 [2] and 2017 [3] Mexico City earthquakes, where more than half of the building collapses were due to punching shear failure. The 1994 Northridge earthquake showed punching shear failures, too, with the discontinuous flexural being the main reason for the observed punching shear failures [4].

In the last 60 years, many experimental campaigns have been conducted to assess the seismic performance of slab-column connections. This paper focuses on reviewing the available experimental data of interior reinforced concrete slab-column connections under combined gravity and lateral loadings. The available tests provide a relation between the gravity shear ratio and the drift, which can be used to evaluate the deformation compatibility. The drift ratio is the design story drift divided by the story height, and the gravity shear ratio is defined as the factored shear force divided by the punching shear capacity. The relation between lateral drift ratio and gravity shear ratio provided by ACI 318-19 is used to evaluate the design lateral deformation demand for slab-column connections. Shear reinforcement should be provided for slab-column connections when the design story drift exceeds the lateral drift ratio. Since the development of the seismic punching shear code provisions is based on empirical equations derived from experimental data, the paper discusses the current design provisions and their development over the years. Mechanical and analytical models for eccentric punching shear are also presented and discussed. These models can provide significant information and, together with the experimental data, can lead to the development of future design codes. Thus, the objective of this paper is to present an updated developed testing database of reinforced concrete slab-column connections with and without shear reinforcement tested under combined gravity and lateral loadings to assist the development of future seismic punching shear design provisions. The database developed and used in the work is focused only on monolithic reinforced concrete slab-column connections, and thus, the analysis of precast reinforced concrete slab-column connections is outside the scope of the present paper. Consistent criteria for selecting key response parameters (drift ratio and gravity shear ratio) are considered. The test results are critically assessed and discussed with a focus also on the developed failure mode, type of shear reinforcement, and type of loading.

2. Design Provisions for Punching Shear

2.1. General

The first punching shear design provisions adopted an equation suggested by Talbot (1913) [5] to estimate the shear stresses considering the critical perimeter at a distance varied from d to d/2 from the column. It was noticed that the shear strength of the connection depends on the diagonal tension; nevertheless, it was in ACI 318-63 [6] when the punching shear strength was correlated to the square root of concrete’s compressive strength. In the United States of America, punching shear research was started in the 1950s by Richart (1948) [7], Elstner and Hognestad (1956) [8] and Whitney (1957) [9]. Later, Moe [10] in 1961 proposed the shear strength of concrete to be proportional to the square root of the compressive strength of concrete, indicating that the shear failures are affected by the tensile strength of concrete. Then, ACI/ASCE Committee 326 in 1962 [11] suggested the critical perimeter to be located at a distance d/2 from the column. The European research initiated by Kinnunnen and Nylander (1960) [12], Regan (1981) [13] and Regan and Braestrup (1985) [14] recommended empirical equations to be used as the basis of the European punching shear provisions. Regan [13] suggested that the punching shear strength was affected by the reinforcement ratio and a size effect factor. Currently, the punching shear design provisions are mainly based on research conducted in the 1970s and 1980s, influenced by Hawkins (1974) [15], Corley and Hawkins (1974) [16], Langhor et al. (1976) [17] and Dilger and Ghali (1981) [18] in the USA and by Regan (1981) [13] and Regan and Braestrup (1985) [14] in Europe.

Regarding the seismic punching shear aspect in the design equations, the working stress method was used in ACI 318-56 [19] and ACI 318-63 [6], while the effect of the unbalanced moments was neglected. The ACI 318-63 required the research of punching shear stress due to unbalanced moments, and the “eccentric shear stress model” was used based on the work by DiStasio and Van Buren (1960) [20] and ACI-ASCE Committee 326 [11]. Later, ACI 318-71 [21] introduced the ultimate strength design and the equivalent column method to calculate the unbalanced moments. Shear stress due to gravity loads and unbalanced moments was calculated using the eccentric shear stress model and limited to a maximum allowable value of 4$\sqrt{f_c^{\prime }\left(psi\right)}$ (0.33$\sqrt{f_c^{\prime }\left(MPa\right)}$) at a critical section located at a distance d/2 from the column. A requirement for continuous flexural bottom reinforcement to prevent progressive collapse was added in ACI 318-89 [22]. In ACI 318-05 [23], new requirements were included regarding the lateral load resistance of the connections located in seismic-prone areas. Connections of nonparticipating slab-column frames were required to be checked to avoid punching failures when subjected to the design drift, and shear reinforcement was required under conditions where punching failures were expected. Also, a new provision that limits the lateral interstory drift as a function of gravity load level was added.

In Europe, the experimental research on seismic punching shear started in the 1990s by Farhey et al. (1993) [24] and Farhey et al. (1995) [25], who examined slab-column connections tested under cyclic loading. Flat slabs with and without shear reinforcement were examined experimentally by Almeida et al. 2016 [26], 2020 [27,28], Isufi et al. 2019 [29] and Isufi et al. 2021 [30]. Drakatos et al. (2016) [31] tested interior slab-column connections under monotonic and cyclic imposed rotations, investigating the drift capacity for different types of loading, gravity shear ratios and reinforcement ratios. Benavent-Climent et al. 2008 [32] and 2009 [33] tested both interior and exterior slab-column connections under lateral loadings, and Benavent-Climent et al. 2016 [34] and Benavent-Climent et al. 2019 [35] conducted shake table tests of a half-scale, one-bay floor system. Further experimental research was conducted by Coronelli et al. (2020) [36], with the results of the ultimate drift ratios being between 3% and 6% for gravity shear ratios corresponding to real seismic design conditions. Coelho et al. (2004) [37] tested a full-scale, three-storey slab-column structure with one bay in each direction. Coronelli et al. 2021 [38] tested a multi-storey and multi-bay flat slab frame to explore the deformation capacity of the connections. The current Eurocode 8-2004 [39] does not include provisions for flat slabs; however, the latest draft of the second generation of EC8 (CEN/TC 250/SC 8 2020) considers provisions for reinforced concrete flat slabs.

2.2. Current Design Provisions

Over the years, various lessons have been learned from past earthquakes. They advanced the knowledge for punching shear and, consequently, led to new construction methods (e.g., continuous tensile reinforcement) and materials (e.g., higher strength concrete and steel). Also, new and more efficient testing methods were proposed and used due to the gained knowledge and advancements in technology. All these influenced the development of punching shear design provisions.

Herein, two current design provisions (ACI 318-19, EC2&EC8-2004) for punching shear are discussed. The main differences between the two design codes are (a) the critical section in EC2 is located at a distance of 2d from the column, while in ACI 318-19, it is at a distance of d/2, and (b) ACI 318-19 does not account for the flexural reinforcement ratio directly, while EC2 considers the effect of the flexural reinforcement ratio.

2.2.1. ACI 318-19

ACI 318-19 suggests that the nominal punching stress of concrete for slabs with noshear reinforcement is

$$v_c=min\left\{\begin{array}{c}0.33{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\\ 0.17{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\left(1+\frac{2}{{\beta }_c}\right)\\ 0.083{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\left(2+\frac{{\alpha }_{s}d}{b_o}\right)\end{array}\right.{f^{\prime }}_{c}inMPa$$

(1)

$\lambda$ is a factor that denotes the density of concrete, ${\lambda }_s$ is the size effect modification factor provided in Equation (2), ${f^{\prime }}_c$ is the concrete’s compressive strength, ${\beta }_c$ denotes the ratio of the sides of the column (long/short), $b_o$ is the critical shear perimeter and ${\alpha }_s$ is a value related to the type of connection (40 for interior, 30 for edge and 20 for corner).

$${\lambda }_s=\sqrt{\frac{2}{1+\frac{d \left(\mathrm{mm}\right)}{254}}}\le 1$$

(2)

A new provision in ACI 318-19 requires that a minimum amount of bonded flexural reinforcement $A_{s,min}$ shall be provided in a two-way slab-column connection. The value of $A_{s,min}$ is calculated as

$$A_{s,min}=\frac{5v_{uv}{b}_{slab}{b}_o}{\varphi {\alpha }_s{f}_y}$$

(3)

where $v_{uv}$ is the factored shear stress on the slab critical section from the controlling load combination, without moment transfer; $b_{slab}$ denotes the effective slab width calculated in accordance with Section 8.4.2.2.3; $b_o$ is the critical shear perimeter measured at a distance of d/2 from the face of the column and $f_y$ is the tensile strength of the reinforcement.

The nominal punching shear strength in stress units for slabs with shear reinforcement (stirrups) is estimated based on Equation (4), and the punching shear strength of slabs having shear reinforcement (shear studs) is computed using Equation (5):

$$v_u=v_c+\frac{A_{vs}{f}_{yv}}{b_{o}s}=0.17{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}+\frac{A_{vs}{f}_{yv}}{b_{o}s}\le 0.5\sqrt{{f^{\prime }}_c}\left(MPa\right)$$

(4)

$$v_u=v_c+\frac{A_{vs}{f}_{yv}}{b_{o}s}=min\left\{\begin{array}{c}0.25{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\\ 0.17{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\left(1+\frac{2}{{\beta }_c}\right)\\ 0.083{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\left(2+\frac{{\alpha }_{s}d}{b_o}\right)\end{array}\right.+\frac{A_{vs}{f}_{yv}}{b_{o}s}\le 0.66\sqrt{{f^{\prime }}_c}\left(MPa\right)$$

(5)

where $A_{vs}$ denotes the cross-sectional area of the shear reinforcement of one peripheral line, $f_{yv}$ denotes the yield strength of the shear reinforcement and $s$ denotes the shear reinforcement spacing in each perimeter.

The estimated punching shear resistance of slabs with shear reinforcement should also be calculated outside the shear reinforced area at a distance of $d/2$ from the outermost line of the shear reinforcement according to Equation (6):

$$v_u=0.17{\lambda }_s\lambda \sqrt{{f^{\prime }}_c}\left(MPa\right)$$

(6)

For slabs under gravity load and an unbalanced moment, the maximum factored shear stress can be derived from the following equation:

$$v_u=\frac{V_u}{b_{o}d}\pm \frac{{\gamma }_v{M}_{u}c}{J}$$

(7)

where $v_u$ denotes the factored shear stress; $V_u$ indicates the factored shear force; $d$ denotes the slab’s effective depth; $b_o$ denotes the critical perimeter; $M_u$ is the factored unbalanced moment; $J$ denotes the polar moment of inertia of the critical section; ${\gamma }_{\nu }=1-\frac{1}{1+\frac{2}{3}\sqrt{\frac{b_1}{b_2}}}$ is the fraction of the unbalanced moment transferred by shear eccentricity, where $b_1$ denotes the length of the critical perimeter perpendicular to the moment vector, $b_2$ is the other side’s length and $c$ denotes the centroid of the shear perimeter.

Based on ACI 318-19, Section 18.14.5.1, the slab-column connection is assessed using a limit between the design storey drift ratio (DR) and the factored gravity shear ratio. The maximum drift ratio (%) that a slab-column connection without shear reinforcement can tolerate is calculated as

$$\mathrm{DR}=\left\{\begin{array}{ll}3.5-5 VR& (for VR<0.6)\\ 0.5& \left(for VR\ge 0.6\right)\end{array}\right.$$

(8)

where $VR=\frac{V_u}{\phi v_c{b}_o\mathrm{d}}$ is the gravity shear ratio, and $V_u$ is the factored shear force. Figure 1 illustrates the above relationship, where if the DR exceeds the limit, shear reinforcement is needed.

2.2.2. EC2-2004

According to the current EC2 (2004) [40], the slab-column connection’s punching shear resistance should be first evaluated at the location of the perimeter of the column, and at this location, the punching shear stress $\left(v_{Ed}\right)$ must be less than the maximum punching shear stress resistance $\left(v_{Rd,max}\right)$.

The punching shear stress obtains its maximum value at the control section and is estimated as

$$v_{Rd,max}=0.5v{f}_{cd}$$

(9)

with $v$ being a factor that accounts for the strength reduction for cracked concrete in shear (Equation (10)) and $f_{cd}$ denoting the compressive strength of concrete for design (Equation (11)).

$$v=0.6\left(1-\frac{f_{ck}}{250}\right)\left(MPa\right)$$

(10)

$$f_{cd}={\alpha }_{cc}\frac{f_{ck}}{{\gamma }_c}$$

(11)

where ${\alpha }_{cc}$ denotes a coefficient which takes into account the long-term effects (the suggested value for this coefficient is 1), and ${\gamma }_c$ is the concrete’s partial safety factor with a value of 1.5.

When eccentricity exists in the support reaction, the maximum shear stress is considered equal to

$$v_{Ed}=\beta \frac{V_{Ed}}{u_{i}d}$$

(12)

where $d$ denotes the slab’s effective depth, $u_i$ denotes the length of the critical perimeter and $\beta$ is calculated according to Equation (13):

$$\beta =1+k\frac{M_{Ed}}{V_{Ed}}\frac{u_1}{W_1}$$

(13)

where $u_1$ is the critical perimeter’s length, $k$ is a coefficient based on the ratio between the column’s dimensions ($k=0.6$ for a square column) and $W_1$ is consistent with the shear distribution and depends on the critical perimeter. For rectangular columns, $W_1$ is given as

$$W_1=\frac{c_1^2}{2}+c_1{c}_2+4c_{2}d+16d^2+2\pi d{c}_1$$

(14)

where $c_1$ is the column’s dimension, which is parallel to the load’s eccentricity, and $c_2$ is the column’s dimension that is perpendicular to the load’s eccentricity.

For an interior rectangular column with eccentric loading, $\beta$ is calculated according to Equation (15):

$$\beta =1+1.8\sqrt{{\left(\frac{e_y}{b_z}\right)}^2+{\left(\frac{e_z}{b_y}\right)}^2}$$

(15)

with $e_y$ and $e_z$ being the eccentricities $\frac{M_{Ed}}{V_{Ed}}$ along the $y$ and $z$ axes, and $b_y$ and $b_z$ being the lengths of the critical perimeter. The critical perimeter ($u_{1\ast }$) for edge slab-column connections can be calculated based on the recommendations shown in Figure 2.

If eccentricities are present, $\beta$ can be calculated based on Equation (16):

$$\beta =\frac{u_1}{u_{1\ast }}+k\frac{u_1}{W_1}{e}_{par}$$

(16)

where $e_{par}$ denotes the eccentricity parallel to the slab’s edge due to the action of a moment about an axis perpendicular to the slab’s edge. When a rectangular column exists, $W_1$ can be estimated based on Equation (17):

$$W_1=\frac{c_2^2}{4}+c_1{c}_2+4c_{1}d+8d^2+\pi d{c}_2$$

(17)

The concrete punching shear stress resistance for slabs with no shear reinforcement is estimated according to Equation (18):

$$v_{Rd,c}=C_{Rd,c}k{\left(100{\rho }_l{f}_{ck}\right)}^{1/3}\ge v_{min}=0.035{\left(k\right)}^{3/2}{\left(f_{ck}\right)}^{1/2}$$

(18)

$C_{Rd,c}=0.18/{\gamma }_c$, ${\gamma }_c$ is concrete’s safety factor given as 1.5, ${\rho }_l$ denotes the flexural reinforcement ratio with a maximum value equal to 0.02, $f_{ck}$ is the characteristic compressive strength of concrete and $k$ denotes a factor that accounts for the size effects and is calculated according to Equation (19)

$$k=1+\sqrt{\frac{200}{d}}\le 2\left(dinmm\right)$$

(19)

The slab’s punching shear stress resistance when vertical shear reinforcement is placed is determined as

$$v_{Rd}=0.75v_{Rd,c}+1.5\left(d/s\right)A_{vs}{f}_{ywd,ef}$$

(20)

where $A_{vs}$ denotes the area of the shear reinforcement (for one row), $s$ denotes the spacing of the perimeters of the shear reinforcement, and $f_{ywd,ef}$ denotes the effective design strength of the shear reinforcement, which can be calculated based on Equation (21), where $f_{ywd}$ denotes shear reinforcement yield stress.

$$f_{ywd,ef}=\left(250+0.25d\right)\le f_{ywd}\left(MPa\right)$$

(21)

The punching shear resistance must be verified next to the column and limited to a maximum value according to Equation (22):

$$v_{Ed}=\frac{\beta V_{Ed}}{u_{o}d}\le v_{Rd,max}$$

(22)

with $u_o$ denoting the length of the perimeter of the interior column. For edge columns, the length is $u_o=c_2+3d\le c_2+2c_1$, and for corner columns, the length is $u_o=3d\le c_1+c_2$. The critical perimeter for slabs with no shear reinforcement, $u_{out}$, is estimated according to Equation (23). The outermost perimeter of shear reinforcement should be located at a distance not larger than $kd$ within the $u_{out,ef}$. The suggested value for $k$ is 1.5.

$$u_{out,ef}=\frac{\beta V_{Ed}}{v_{Rd,c}d}$$

(23)

The current EC8 (2004) [39] does not consider the flat slab frames to act in seismic resisting systems of Ductility Class (DC) M or H. Flat slab frames are considered secondary seismic elements. However, the draft version of the second generation of Eurocode 8 (CEN/TC250/SC8 2021) allows flat slab frames to be part of the seismic-action-resisting system of buildings.

3. Developed Experimental Database

In the last 60 years, various experiments have been conducted to examine the seismic performance of reinforced concrete slab-column connections.

Table 1. Experimental data of slab-column connections without shear reinforcement.

Reference	Label	Loading	GSR	Drift Ratio, %	Failure Mode
Hanson and Hanson [41]	B7	M	0.04	3.80	F-P
	C8	M	0.05	5.80	F
Hawkins et al. [42]	S1	UC	0.33	3.75	P
	S2	UC	0.45	2.00	P
	S3	UC	0.45	2.00	P
	S4	UC	0.40	2.60	P
Ghali et al. [43]	SM 0.5	M	0.31	6.00	F
	SM 1.0	M	0.33	2.70	F-P
	SM 1.5	M	0.30	2.70	F-P
Islam and Park [44]	1	M	0.25	3.67	P
	2	M	0.23	3.33	P
	3C	UC	0.23	4.00	F-P
Symonds et al. [45]	S-6	UC	0.86	1.10	P
	S-7	UC	0.81	1.00	P
	S-8	UC	0.62	0.64	P
Morrison and Sozen [46]	S1	UC	0.03	4.70	F
	S2	UC	0.03	2.80	F
	S3	UC	0.03	4.20	F
	S4	UC	0.07	4.50	F
	S5	UC	0.15	4.80	F
Zee and Moehle [47]	INTERIOR	UC	0.21	3.30	F-P
Pan and Moehle [48]	AP 1	UC	0.37	1.60	F-P
	AP 2	BC	0.36	1.50	F-P
	AP 3	UC	0.18	3.70	F-P
	AP 4	BC	0.19	3.50	F-P
Hwang [49]	b2	BC	0.24	4.47	P
	c2	BC	0.26	4.85	P
	b3	BC	0.25	5	P
	c3	BC	0.26	5.32	P
Robertson [50]	1	UC	0.21	2.75	F
	2C	UC	0.22	3.50	F-P
	3SE	UC	0.19	3.50	F
	5SO	UC	0.21	3.50	F
	6LL	UC	0.54	0.85	P
	7L	UC	0.40	1.45	P
	8I	UC	0.18	3.50	F-P
Wey and Durrani [51]	SC 0	UC	0.25	3.50	P
	SC 2	UC	0.18	6.00	F
	SC 4	UC	0.15	6.00	F
	SC 6	UC	0.15	5.00	P
Cao [52]	CD1	UC	0.85	1.04	P
	CD5	UC	0.64	1.26	P
	CD8	UC	0.51	1.48	P
Du [53]	DNY_1	UC	0.20	4.50	F
	DNY_2	UC	0.30	2.00	P
	DNY_3	UC	0.24	4.50	F
	DNY_4	UC	0.28	4.70	F-P
Farley et al. [24]	1	UC	0.00	5.60	F-P
	2	UC	0.00	5.10	F-P
	3	UC	0.26	3.80	F-P
	4	UC	0.30	2.50	F-P
Luo et al. [54]	II	UC	0.08	5.00	F
Eman et al. [55]	HHHC0.5	UC	0.26	5.20	F
	HHHC1.0	UC	0.26	5.20	F-P
	NHHC0.5	UC	0.35	3.80	F-P
	NHHC1.0	UC	0.36	3.80	P
Ali and Alexander [56]	SP-A	UC	0.31	4.50	F-P
	SP-B	UC	0.31	3.50	P
Robertson et al. [57]	1C	UC	0.15	3.25	P
Brown [58]	SJB-6	M	0.45	2.30	P
	SJB-7	UC	0.51	1.70	P
Tan and Teng [59]	YL-L1	UC	0.17	4.77	F
	YL-H2	BC	0.28	1.92	P
	YL-L2	BC	0.17	1.99	P
Robertson and Johnson [60]	ND1C	UC	0.23	3.00	F-P
	ND4LL	UC	0.28	3.00	F-P
	ND5XL	UC	0.47	1.50	P
	ND6HR	UC	0.29	3.00	P
	ND7LR	UC	0.26	3.00	F-P
	ND8BU	UC	0.26	3.00	F-P
Choi et al. [61]	S1	UC	0.30	3.00	P
	S2	UC	0.50	3.00	P
	S3	UC	0.30	3.00	P
Park et al. [62]	RI-50	UC	0.37	3.70	P
Kang and Wallace [63]	C0	UC	0.30	1.85	P
Tian et al. [64]	L0.5	UC	0.23	1.50	P
	LG0.5	UC	0.23	1.25	NF
	LG1.0	UC	0.23	1.25	NF
Bu and Polak [65]	SW1	UC	0.54	2.70	P
	SW5	UC	0.68	2.60	P
Park et al. [66]	RC-A	UC	0.45	1.40	F-P
	RC-B	UC	0.41	1.60	F-P
Song et al. [67]	RC1	UC	0.43	1.80	P
Kang et al. [68]	RC	UC	0.40	2.60	F-P
Fick et al. [69]	Floor 1	UC	0.21	2.39	NF
	Floor 2	UC	0.21	3.31	P
	Floor 3	UC	0.21	3.08	NF
Rha et al. [70]	LM-S2-C5	M	0.40	5.38	F-P
	LM-S3-C5	M	0.40	0.74	F-P
	LC-S2-C5	UC	0.40	1.50	P
Almeida et al. [26]	E-50	M	0.50	1.80	P
	C-50	UC	0.50	1.10	P
	C-40	UC	0.40	1.50	P
	C-30	UC	0.30	2.00	P
Drakatos et al. [31]	PD1	M	0.27	1.60	P
	PD4	M	0.42	2.01	P
	PD5	M	0.6	2.19	P
	PD3	M	0.87	0.45	P
	PD12	M	0.63	1.21	P
	PD10	M	0.9	0.49	P
	PD8	UC	0.45	1.30	P
	PD6	UC	0.57	0.86	P
	PD2	UC	0.87	0.36	P
	PD13	UC	0.6	0.86	P
	PD11	UC	0.9	0.43	P
Topuzi et al. [71]	SD01	UC	0.45	2.00	P

Note: F = flexural failure, P = punching shear failure, F-P = flexural and punching shear failure, NF = no failure.

and

Table 2. Experimental data of slab-column connections with shear reinforcement.

Reference	Label	Loading	Shear Reinforcement	GSR	Drift Ratio, %	Failure Mode
Hawkins et al. [72]	SS1	UC	Stirrups	0.40	3.89	F
	SS2	UC	Stirrups	0.38	4.44	P
	SS3	UC	Stirrups	0.39	5.76	F
	SS4	UC	Stirrups	0.38	5.63	F
	SS5	UC	Stirrups	0.34	5.00	F-P
Islam and Park [44]	4S	M	Bent up bars	0.23	5.37	P
	5S	M	Shear head	0.23	4.63	F
	6CS	UC	Stirrups	0.24	4.44	F
	7CS	UC	Stirrups	0.24	4.07	F
	8CS	UC	Stirrups	0.27	5.56	F
Symonds et al. [45]	SS-6	UC	Stirrups	0.82	1.59	F-P
	SS-7	UC	Stirrups	0.81	2.25	F-P
Robertson [50]	4S	UC	Stirrups	0.16	7.00	F
Cao [52]	CD3	UC	Shear studs	0.90	3.41	F-P
	CD4	UC	Shear studs	0.61	4.81	F
	CD6	UC	Shear studs	0.68	4.89	F
	CD7	UC	Shear studs	0.50	5.19	F
Megally and Ghali [73]	MG-10	UC	Shear studs	0.60	5.20	NA
	MG-3	UC	Shear studs	0.56	5.40	NA
	MG-4	UC	Shear studs	0.86	4.60	F-P
	MG-5	UC	Shear studs	0.31	6.50	F-P
	MG-6	UC	Shear studs	0.59	6.00	F-P
Dechka [74]	S1	UC	Shear studs	0.46	4.40	P
	S2	UC	Stirrups	0.47	6.40	F-P
Robertson et al. [57]	2CS	UC	Stirrups	0.14	8.00	F
	3SL	UC	Single stirrups	0.09	8.00	F
	4HS	UC	Shear studs	0.13	8.00	F
Brown [58]	SJB-1	UC	Shear studs	0.48	4.50	F-P
	SJB-2	UC	Shear studs	0.46	4.90	F-P
	SHB-3	UC	Shear studs	0.48	4.90	F-P
	SJB-4	UC	Shear studs	0.43	6.40	F-P
	SJB-5	UC	Shear studs	0.47	7.60	F-P
	SJB-8	UC	Shear studs	0.46	5.70	F-P
	SJB-9	UC	Shear studs	0.49	7.10	F-P
Tan and Teng [59]	YL-H2V	BC	Shear studs	0.28	5.60	F-P
	YL-H1V	UC	Shear studs	0.28	8.14	F
Gayed and Ghali [75]	ISP-0	UC	Shear studs	0.84	3.76	F-P
Broms [76]	17c	UC	Ductile Rein	0.65	3.00	F-P
	17d	UC	Ductile Rein	0.65	3.00	F-P
	18c	UC	Shear studs	0.67	3.00	F-P
	18d	UC	Shear studs	0.67	3.00	F-P
Kang and Wallace [63]	PS2.5	UC	Shearbands	0.32	4.85	F
	PS3.5	UC	Shearbands	0.34	3.45	F-P
	HS2.5	UC	Shear studs	0.31	5.20	P
Cheng [77]	SU1	UC	Steel Fiber	0.42	5.00	F
	SU2	UC	Steel Fiber	0.33	5.00	F
	SB1	BC	Steel Fiber	0.40	3.25	P
	SB2	BC	Steel Fiber	0.41	2.95	P
	SB3	BC	Shear studs	0.43	1.46	P
Bu and Polak [65]	SW2	UC	Shear bolts	0.54	5.80	F
	SW3	UC	Shear bolts	0.54	4.50	F
	SW4	UC	Shear bolts	0.68	5.20	F
Park et al. [66]	LR-A1	UC	Lattice Rein.	0.44	7.00	F
	LR-A2	UC	Lattice Rein.	0.44	4.90	F
	SR-A	UC	Shear studs	0.45	4.00	F
	SB-A	UC	Shear bands	0.45	5.10	F
	ST-A	UC	Stirrups	0.45	3.00	F
	LR-B1	UC	Lattice Rein	0.41	4.70	F
	LR-B2	UC	Lattice Rein	0.41	3.60	F
	SR-B	UC	Shear studs	0.41	5.10	F
	SB-B	UC	Shear bands	0.41	6.50	F
	ST-B	UC	Stirrups	0.41	3.20	F
Song et al. [67]	SR1	UC	Stirrups	0.43	3.90	F
	SR2	UC	Shear studs	0.43	5.40	F
	SR3	UC	Shearbands	0.43	6.00	F
Kang et al. [68]	LR-A	UC	Lattice Rein	0.40	5.10	F
	LR-B	UC	Lattice Rein	0.40	3.20	F
	LR-C	UC	Lattice Rein	0.40	4.80	F-P
	LR-D	UC	Lattice Rein	0.40	5.10	F
	LR-E	UC	Lattice Rein	0.40	3.60	F
Matzke et al. [78]	B1	BC	Shear studs	0.45	2.62	F-P
	B2	BC	Shear studs	0.45	2.62	F-P
	B3	BC	Shear studs	0.47	2.95	F-P
	B4	BC	Shear studs	0.41	3.25	F-P
Topuzi et al. [71]	SD02	UC	Shear bolts	0.45	6.00	F-P
	SD03	UC	Shear bolts	0.50	5.70	F-P
	SD04	UC	Shear bolts	0.50	5.00	F-P
	SD05	UC	Shear bolts	0.45	5.20	F-P
	SD06	UC	Shear bolts	0.50	5.30	F-P

Note: F = flexural failure, P = punching shear failure, F-P = flexural and punching shear failure, and NA = not available.

summarize the needed information for the slab-column connections without and with shear reinforcement, respectively. The criteria set to select the experimental data include the type of connection (interior) and the type of loading (combined gravity and lateral). Experimental data of prestressed reinforced concrete slabs subjected to combined gravity and lateral loadings exist; however, the current study is limited only to conventional reinforced concrete slab-column connections. The provided information for each specimen includes (a) the failure mode, where punching shear failure is denoted with P, flexural failure is denoted with F and punching shear failure at a higher drift followed by flexural failure is denoted with F-P; (b) the gravity shear ratio and (c) the lateral drift ratio. The type of loading is noted in the developed database, where the connections that were tested under monotonic lateral loading are denoted by (M), the connections that were tested under unidirectional cyclic lateral loading are denoted by (UC), and the connections that were tested under bidirectional cyclic lateral loading are denoted by (BC). For the slab column connections with shear reinforcement (Table 2), the type of shear reinforcement is mentioned. The drift ratio (DR) mentioned in Table 1 and Table 2 was considered at failure and was taken according to the experimental data. When DR was not reported in the tests, it was calculated according to Equation (24) as the ratio of column lateral displacement (Δ) to the column height (h/2) or the ratio of slab displacement (Δ) to slab length (l). When unbalanced moments were applied, the slab deflections of the column’s sides were not equal, and therefore, DR was determined using Equation (25).

$$\mathrm{DR}=\frac{\mathsf{\Delta }}{h/2}$$

(24)

$$\mathrm{DR}=\left[\frac{\mathsf{\Delta }}{l/2}+\frac{\mathsf{\Delta }\prime }{l/2}\right]/2$$

(25)

Thus, the reported drift ratio (DR) in Table 1 and Table 2 is indicated as “DR limit”, which falls in with the lateral drift ratio when failure happens (P, FP or F). When flexure failure (F) or no failure (NF) is reported, the DR limit is taken as the drift at 80% of the peak lateral load. The gravity shear ratio (GSR) is the unfactored gravity shear $V_g$ divided by the theoretical punching shear strength without moment transfer $V_o=v_c{b}_{o}d$, where $v_c$ is calculated according to Equation (1) for slabs with no shear reinforcement and Equation (4) or (5) for slabs with shear reinforcement. EC2 is not considered since there is no relationship for the DR.

Table 1 includes 106 interior slab-column connection test data without shear reinforcement. The relationship between the DR limit and the GSR is shown in Figure 3. The graph includes the drift limit relation given in ACI 318-19 (Equation (8)). The test data show that GSR has a significant impact on the DR limit for reinforced concrete slab-column connections with no shear reinforcement. The majority of the examined specimens failed in punching (57 specimens), followed by the specimens which failed in combined flexure–punching (28 specimens) and the specimens which failed in flexure (17 specimens). Four specimens did not fail during the tests. Punching shear failure (P) occurs for a range of GSR (0.2 to 0.9), while flexural failures (F) and no failures (NF) occur for GSR values of 0.3 or less. Also, it is observed that all combined flexure–punching shear failures (FP) occur for GSR values below 0.5. A linear regression analysis using data with GSR less than 0.6 was conducted, and the line defined had a slope equal to −6.44 and a zero intercept of 5. This limit line can potentially be recommended for collapse prevention if a performance level should be indicated.

Table 2 includes the test data of 79 slab-column connections with shear reinforcement. Different types of shear reinforcement include shear stud reinforcement, stirrups, bent-up bars and shearheads. Lately, new types of shear reinforcement have been examined, such as shear bolts, “ductility reinforcement”, shearbands, steel fiber reinforcement and lattice reinforcement. The relationship between the DR limit and the GSR is shown in Figure 4 and Figure 5. The graphs show the drift limit relation given in ACI 318-19 (Equation (8)). The test data show that reinforced concrete slab-column connections with shear reinforcement can achieve much higher drift ratios. Figure 6 presents the DR limit versus the GSR for different types of shear reinforcement. Even if the vertical legs of stirrups together with the shear studs are the most common types of shear reinforcement in slabs, stirrups may not be as effective as shear studs in thin slabs because of their inadequate anchorage of the stirrups’ vertical legs. On the other hand, the anchorage with the shear studs is provided mechanically, mostly by forged heads. Shear stud reinforcement is also common in two-way floor slabs due to their ease of placement during construction. Thus, the largest number of tests were conducted with shear studs (31 specimens), particularly in the range of GSR = 0.4–0.6. There are many tests with steel stirrups (17 specimens), a more difficult placement method. The test data with the stirrups were conducted in the range of GSR = 0.2–0.4. The shear reinforcement increases the limiting lateral drift for interior reinforced concrete slab-column connections subject to varying levels of gravity shear. Yet, it should be noted that the detailing of the shear reinforcement is significant (extended length, spacing and layout). Most test specimens, as shown in Figure 5, failed by flexure (38 specimens), followed by the specimens which failed in combined flexure–punching (32 specimens) and the specimens which failed in punching (7 specimens). Two specimens did not fail. Punching shear failure (P) occurs for a range of GSR (0.2 to 0.4), while flexural failures (F) occur for GSR values of 0.1 to 0.7. Also, it is observed that all combined flexure–punching shear failures (FP) occur for GSR values that range from 0.3 to 0.9. In general, the observed variability in the limiting lateral drift for the slab-column connections with shear reinforcement can be attributed to discrepancies in the specimens, type and amount of shear reinforcement and type of lateral loading.

Figure 6 compares the test data of the slab-column connections without shear reinforcement with the test data of the slab-column connections with shear reinforcement. None of the specimens are below the ACI 318-19 drift limit line, while fourteen specimens without shear reinforcement are under the drift limit line. These fourteen slab-column specimens below the ACI 318-19 limit were examined to examine the reasons for these lower drift values. Figure 7 presents these data points below the ACI 318-14 limit based on the corresponding research study. The 14 test data (out of the total 106) below the drift limit correspond to 13%. This number could have been lower if the design considered a factor φ = 0.75 for the GSR. However, among the fourteen specimens, the specimens tested by Tian et al. [64] and Rha et al. [70] are far below the drift limit. Τian et al. [64] experimentally examined six specimens with no continuous bottom flexural reinforcement under combined vertical and lateral loads. Two of the specimens were subjected only to vertical loading after the drift ratio attained 1.25%. The slab tested by Rha et al. [70] (LM-S3-C5) had a high concentration of bottom integrity bars and a higher bottom reinforcement ratio compared to the other specimens tested during the same campaign, making this connection stiffer and less ductile. Thus, for both test campaigns, the lower drift ratios were identified due to the different designs of the specimens and the different loading protocols. The variability in the results for all slab-column connections (without and with shear reinforcement) can be attributed to many different aspects, such as the different dimensions of the specimens, the different loading protocols (monotonic versus cyclic) and the different experimental setups.

4. Mechanical and Analytical Models and Performance-Based Design Criteria

In seismic punching shear, various theoretical, analytical and numerical models have been developed that can definitely enhance the experimental findings and offer recommendations for future design code provisions. Ramos et al. [79] proposed an empirical expression to estimate the ultimate rotation of the slab as a function of the gravity shear ratio. Other models proposed by Drakatos et al. [80], Setiawan et al. [81] and Broms [82] estimate the rotation capacity of interior slab-column connections. The model proposed by Drakatos et al. [80] is an extension of the Critical Shear Crack Theory (CSCT) [83] for lateral seismic loading conditions. This mechanical model computes slab-column connections with no shear reinforcement subjected to monotonically and cyclically increased drifts in the moment–rotation relationship. It also considers the contribution of different mechanisms, flexure, eccentric shear and torsion. Nevertheless, the model does not consider the effect of the loading history. This limitation was addressed by introducing two failure criteria to differentiate the loading (monotonic versus cyclic). The other two models mentioned above [81,82] suggest simpler alternatives to the CSCT using a reduced control perimeter and a strut-and-tie model, respectively. These models indicate the need to examine experimental specimens with realistic dimensions and suggest further research in seismic punching shear.

Except for the mechanical models, at the beginning of the 2000s, FEMA [84] established a non-linear static procedure that was further updated and then published in ASCE/SEI-41 (2017) [85]. This non-linear static procedure was used to assess the seismic performance of slab-column structures. The backbone curve was computed based on performance-based design criteria and analytical procedures. Recommended limits for deformation capacity based on the gravity shear ratio, together with a framework for performance levels and objectives, are included. These performance levels show the limitations on the maximum damage during a ground motion, while the objectives determine the target performance level for a specific intensity of ground motion. ASCE/SEI 41-17 [85] also suggests two approaches for analyzing slab-column connections: (a) the effective beam width model and (b) the equivalent frame model. The effective beam width method separately models the column’s behaviour, the moment at the slab-column connection and the shear transfer. The slab is modeled using a flexural slab-beam element, and the columns are simulated considering their actual properties. The equivalent beam used to model the slab is the same thickness as the slab and has an effective width that is analogous to the distance from midspan to midspan in the transverse direction, $l_2$ ($b_{eff}=\alpha \beta l_2$). $\alpha$ is the width reduction coefficient that affects the analytical moment and deflection capacities, with the latter to be determined as the slab-equivalent beam’s rotational stiffness, and $\beta$ is a factor that accounts for stiffness reduction due to cracking $\left(\beta =\frac{4c}{l}>\frac{1}{3}\right)$, where $c$ and $l$ are the column dimension and slab span parallel to the direction of the load, respectively. The effective width can be determined from Hwang and Moehle (2000) [86]. The equivalent frame method represents the three-dimensional slab-column system as a combination of two-dimensional frames, which consist of a slab, column and transverse torsional members. The stiffness of these transverse torsional members is calculated based on the equation suggested by ASCE/SEI 41-17 and calibrated using experimental results. However, this model does not show high accuracy in predicting the behaviour of slab-column connections subjected to unbalanced moments since it was impossible to obtain the interstorey drift at each floor level to determine the onset of the punching failure. This restriction was solved by Kang et al. (2009) [87] with the proposed limit-state method for slab-column connections. They improved the previous models and proposed an approach for the non-linear modeling of slab-column connections to assess the non-linear behaviour due to the yielding of slab’s reinforcement within the column’s strip equal to $\alpha \beta l_2$ or within the slab’s transfer width equal to $c_2+3h$. An adaption of a zero-length rigid-plastic torsional spring was considered in conjunction with the “Limit-State model” proposed by Elwood and Moehle (2003) [88] for shear failures in columns to determine the non-linear punching shear failure and to observe the transfer of the moment at the connection area. Also, two rotational springs with zero length were considered to observe the slab’s moments in both directions of the column strip. Based on this model, the degradation of strength happens when the determined limit state is gained. The limit-state model considers degradation once the torsional and flexural connections show punching failure and (c) punching failure after flexural yielding within the column strip. A different approach was suggested by Hueste and Wight (1999) [89], where both the capacity of the connection element and a limit story drift ratio for a given gravity shear ratio were considered in a non-linear analysis program. Recently, Zhou and Hueste [90] proposed a bilinear equation based on the gravity shear ratio and continuity of flexural reinforcement for the estimation of drift values. Muttoni et al. [91] developed a relationship for drift limits of interior slab-column connections with regard to gravity shear ratio, control perimeter, flexural reinforcement ratio and maximum aggregate size. Finally, Panahi and Genikomsou [92] proposed equations considering a non-linear regression model to calculate the unbalanced moment and the lateral drift of slab-column connections when punching shear failure happens under the action of lateral loadings.

5. Discussion and Conclusions

The paper presented the behaviour and development of the design provisions of reinforced concrete slab-column connections under combined gravity and lateral loadings. Several modifications were made to the current design provisions over the years based on failure observations after earthquakes and during the experiments. Experimental data of interior slab-column connections without and with shear reinforcement were collected, presented and assessed versus the ACI 318-19 design code. Two parameters were used to assess the connections’ seismic performance: (a) the gravity shear ratio and (b) the maximum storey drift ratio. The current version of the Eurocode 8-2004 does not provide any recommendations for seismic punching shear, and thus, only the ACI 318-19 design code was considered.

The updated test data set of interior reinforced concrete slab-column connections with no shear reinforcement (106 specimens) confirms that the limit drift ratio decreases when the gravity shear ratio increases. A linear regression analysis for the slabs without shear reinforcement was conducted, and a new limit line was recommended for collapse prevention if one uses the test data to indicate a performance level, while the limit that ACI 318-19 suggests is the lower bound life safety performance level. However, since some data were found below the limit line, a slightly lower limit can be provided as a conservative suggestion for design. The 14 test data (out of the total 106) below the drift limit corresponds to 13%. This number can be lower if the design considers a factor φ = 0.75 for the GSR. Most test specimens failed by punching (57 specimens), followed by the specimens which failed in a combined flexure–punching mode (28 specimens). Punching shear failure (P) occurred for a range of GSR (0.2 to 0.9), while combined flexure–punching shear failures (FP) occurred for GSR values below 0.5.

The updated test data set of interior reinforced concrete slab-column connections with shear reinforcement (79 specimens) confirms that these connections can achieve much higher drift ratios. The observed variability in the test data can be due to the different types of shear reinforcement. Most test specimens were reinforced with shear studs (31 specimens) in the range of GSR = 0.4–0.6. Test specimens reinforced with steel stirrups (17 specimens) were conducted in the range of GSR = 0.2–0.4. Most test specimens failed, as expected, in flexure (38 specimens), followed by the specimens which failed in a combined flexure–punching mode (32 specimens). Flexural failures (F) occurred for GSR values of 0.1 to 0.7, while the combined flexure–punching shear failures (FP) occurred for GSR values that ranged from 0.3 to 0.9.

The variability in the results for all slab-column connections (without and with shear reinforcement) can be attributed to many different aspects, such as the different dimensions of the specimens, the different loading protocols (monotonic versus cyclic) and the different experimental setups. Additional testing considering more realistic dimensions and shear reinforcements and including corner and edge connections are needed. The developed databases can be further examined to provide potential recommendations for future seismic punching shear design provisions through the development of new mechanical models.