Buildings 12 02092

buildings
Article
Flat Slabs in Eccentric Punching Shear: Experimental Database
and Code Analysis
Daniel Vargas 1 , Eva O. L. Lantsoght 1,2, * and Aikaterini S. Genikomsou 3
1 Politécnico, Universidad San Francisco de Quito, Quito 170901, Ecuador

2 Concrete Structures, Department of Engineering Structures, Civil Engineering and Geosciences,
Delft University of Technology, 2628 CD Delft, The Netherlands
3 Faculty of Engineering and Applied Science—Civil Engineering, Queen’s University,
Kingston, ON K7L 3N6, Canada
* Correspondence: e.o.l.lantsoght@tudelft.nl
Abstract: Eccentric punching shear can occur in concrete slab–column connections when the connec-
tion is subjected to shear and unbalanced moments. Unbalanced moments occur in all floor slabs
at the edge and corner columns. As such, this problem is of practical relevance. However, most
punching experiments in the literature deal with concentric punching shear at internal columns.
This paper presents a developed database of 128 experiments of flat slabs under eccentric punching
shear, including a summary of the testing procedure of each reference and a description of the slab
specimens. Additionally, a linear finite element analysis of all the specimens is included to determine
the relevant sectional shear forces and moments. Finally, the ultimate shear stresses from the database
experiments are compared to the shear capacities determined with ACI 318-19, Eurocode 2 and
the Model Code 2010. The comparison shows that the Model Code 2010 is the most precise in the
predictions with an average tested to predicted ratio of 0.82 and a coefficient of variation of 29.63%.
It can be concluded that improvements to the current design methods for eccentric punching shear
Citation: Vargas, D.; Lantsoght, are necessary.
E.O.L.; Genikomsou, A.S. Flat Slabs
in Eccentric Punching Shear: Keywords: code provisions; database; eccentric punching shear; experiments; flat slab; linear finite
Experimental Database and Code
element models; punching; reinforced concrete; shear; unbalanced moments
Analysis. Buildings 2022, 12, 2092.
https://doi.org/10.3390/
buildings12122092
Academic Editors: Elena Ferretti and 1. Introduction

Andreas Lampropoulos
Reinforced concrete flat slab floor systems are an interesting solution for building
Received: 6 July 2022 design due to the simplicity of the construction process, story height reduction in com-
Accepted: 23 November 2022 parison to systems with beams and the associated economic advantages. Nevertheless, a
Published: 29 November 2022 difficulty lies in predicting the slab–column connection behavior and capacity when lateral
loads or unbalanced gravity loads cause the transfer of moments between the slab and the
Publisher’s Note: MDPI stays neutral
column [1], as occurs at the edge and corner columns. Unbalanced moments can also be
with regard to jurisdictional claims in
caused by asymmetrical spans, creep and differential shrinkage between two continuous
published maps and institutional affil-
slabs [2].
iations.
A few collapses caused by punching failure have been reported throughout the years,
which gained the attention of researchers and practitioners [3]. One example is the collapse
of the underground parking garage in Gretzenbach, Switzerland, in November 2005 [4].
Copyright: © 2022 by the authors. The collapsed structure had no shear reinforcement; only column capitals were provided
Licensee MDPI, Basel, Switzerland. for shear enhancement. This collapse caused the deaths of seven people.
This article is an open access article Typically, the most critical slab–column connections are located at the corners and
distributed under the terms and edges, as these connections are subjected to moment transfer and eccentric loading. How-
conditions of the Creative Commons ever, these cases are less studied experimentally in comparison with internal slab–column
Attribution (CC BY) license (https:// connections under concentric loads. The vast majority of experiments are carried out on
creativecommons.org/licenses/by/ slab–column connections with concentric loading.
4.0/).
Buildings 2022, 12, 2092. https://doi.org/10.3390/buildings12122092 https://www.mdpi.com/journal/buildings

Buildings 2022, 12, 2092 2 of 49
The first comprehensive studies on punching shear were performed in the 1960s by
Kinnunen and Nylander [5], but their mechanical models resulted in complicated expres-
sions, which code makers found impractical for use [6]. Instead, empirical expressions
based on the available test results were created for the development of the code provisions.
Given that there is a lack of experimental information on eccentric punching shear on large-
scale flat slabs, it became difficult to provide a satisfactory design expression [2]. To account
for the eccentric loading, ACI 318-19, Eurocode 2 EN 1992-1-1:2005 and the fib Model Code
2010 models considered the shear stress distribution on the critical perimeter [7–9], assum-
ing either a linear or plastic stress distribution. The punching perimeter is at a distance d/2
from the column in ACI 318-19, and it is at the same distance, but with rounded corners,
in the fib Model Code 2010. Eurocode 2 uses a perimeter at a distance 2d from the column,
and the perimeter has rounded corners as well.
Despite the efforts undertaken by investigators through the years, the current design
methods cannot accurately predict the punching shear strengths when unbalanced mo-
ments act on slabs. Nowadays, the advances in materials and new analysis methodologies,
such as nonlinear finite element analysis and better instrumentation techniques for ex-
perimental campaigns, have helped researchers start proposing a reshaping of the design
codes to best meet the real performance of the slab–column connections under eccentric
loading [10].
This work aims to present a wider view of the problem by compiling and analyzing
experiments on eccentric punching shear from the literature. The analysis of the compiled
experiments can be used to examine the performance of the currently available build-
ing codes and identify which types of experiments would be a valuable contribution to
the body of knowledge. Additional experiments could be used to refine and improve
the existing models. In addition, the developed database can serve those who are work-
ing on mechanical models of punching shear to check the performance for the case of
eccentric punching.
This article compiles 128 experiments on flat slabs in eccentric punching shear. Vertical,
horizontal and combined loading setups are reported in the literature. Both slabs with and
without shear reinforcement are included in the developed database. The internal forces
of the slabs for the maximum applied load, i.e., at the onset of punching shear failure, are
typically not available in the references. To complete the missing information, a linear finite
element model of each experiment is constructed. The experimental shear capacities from
the database are then compared to the strengths predicted by the design expressions found
in ACI 318-19 [7], Eurocode 2 NEN-EN 1992-1-1:2005 [8] and the fib Model Code 2010 [9].
2. Methods
2.1. Overview of Code Provisions
2.1.1. ACI-318-19
The punching shear provisions from ACI 318-19 are based on empirical equations
derived from test results by Moe [11] and analyses by the ACI-ASCE Committee 426 [12].
The ACI 318-19 method is based on the maximum shear stress vu on the critical perimeter
bo of the slab, which is located at 0.5 d from the face of the column, where d is the average
slab effective depth. The maximum shear stress vu should not exceed the nominal shear
strength of the slab vn . Figure 1 is a sketch of the shear stresses produced by axial load and
moment transfer on an internal slab–column connection [1].
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Figure 1. Shear stress produced by applied load and moment transfer, modified from Ref. [1]:
(a) transfer of unbalanced moments to column; (b) shear stress caused by direct shear; (c) shear stress
caused by unbalanced moments; (d) total shear stress: sum of (b,c).
MacGregor and Wight [1] define vu using the following equation:
Vu γv Mu c
vu = ± (1)
bo d Jc
where Vu is the factored shear being transferred from the slab to the column acting on the
centroid of the critical section; c is the distance from the centroid of the critical section to
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the point where the shear stress is calculated; Jc is the polar moment of inertia of the critical
section; and γv Mu is the fraction of moment transferred by the shear, with γv as follows:
γv = 1 − γ f (2)
where γf is the fraction of moment transmitted by flexure
1
γf = q b1 (3)
2
1+ 3 b2
where b1 is the total width of the critical section measured perpendicular to the axis around
which the moment acts, and b2 is the total width parallel to the axis [1]. Figure 2 shows a
sketch of the critical perimeter of an interior, edge and corner slab–column connection.
Figure 2. Critical perimeter of an interior, edge and corner slab–column connections, modified
from Ref. [1]: (a) interior slab–column connection; (b) edge slab–column connection; (c) corner
slab–column connection.
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The ultimate shear capacity vn is calculated as follows, with vu as determined by

Equation (1):
vn = vc + vs ≥ vu (4)
According to ACI 318-19 Section 22.6.5.2, in slabs without reinforcement, the shear
stress shall not exceed the least of the following three expressions, with f’c in [MPa] [7]:
p
vc = 0.33λs λ f c0 (5)

2 p
vc = 0.17 1 + λs λ f c0 (6)
β

αs d p
vc = 0.083 2 + λs λ f c0 (7)
bo
The value of αs is 40 for interior columns, 30 for edge columns and 20 for corner columns;
λs is the size effect modification factor; λ is the lightweight factor; and β is the ratio of long
to short column sizes [7].
The contribution of the shear reinforcement vs is determined as
Av f yt
vs = (8)
bo s
where Av is the sum of the area of all legs of reinforcement on the peripheral line, which
is geometrically like the perimeter of the column section; fyt is the yield strength of the
transverse reinforcement; and s is the spacing of transversal reinforcement [7].
Section 22.6.6.1 [7] indicates that the value of vc for shear-reinforced slabs shall not
exceed the following: p
vc = 0.17λs λ f c0 (9)
p
vc = 0.25λs λ f c0 (10)

0.33 p
vc = 0.17 + λs λ f c0 (11)
β

0.083αs d p
vc = 0.17 + λs λ f c0 (12)
bo
Equation (9) is used for stirrup reinforcement, and Equations (10)–(12) are used for
headed shear stud reinforcement, where the least of them shall be taken. When shear
reinforcement is used, the critical perimeter bo shall be taken outside the reinforced section,
as illustrated in Figure 3 [7].
2.1.2. NEN-EN 1992-1-1:2005

The punching shear provisions of NEN-EN 1992-1-1:2005 contain empirical equations
for concrete contribution to the two-way shear capacity, based on the elastic analysis
performed by Mast [13]. It is assumed that the concrete contribution to the shear capacity
in terms of shear stresses is equal for one-way shear (beam shear) and two-way shear
(punching shear), although for two-way shear, the reinforcement ratio is taken as the
geometric average of both reinforcement directions, whereas for one-way shear, only the
reinforcement ratio of longitudinal reinforcement is considered.
According to the provisions of NEN-EN 1992-1-1:2005, the punching shear is checked
at the face of the column and at the basic control perimeter U1 [8]. The basic control
perimeter U1 is located at 2d from the loaded area, with d as the average effective depth
of the slab. Figure 4 shows the basic control perimeter for an interior, edge and corner
slab–column connection [8]. Note that rounded corners are used for the perimeter.
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Figure 3. Critical perimeter for a shear-reinforced interior, edge and corner slab–column connection,
modified from Ref. [7]: (a) interior slab–column connection; (b) edge slab–column connection;
(c) corner slab–column connection.
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Figure 4. Basic control perimeter for an interior, edge and corner slab–column connection, modified
from Ref. [8]: (a) interior slab–column connection; (b) edge slab–column connection; (c) corner
Punching shear is evaluated based on the following stresses: vRd,c —the design value
of the punching shear resistance of a slab without punching shear reinforcement; vRd,s —the
value of the punching shear resistance of a slab with punching shear reinforcement; and
vEd —the maximum acting shear stress along the control section. If vEd ≤ vRd,c , then punch-
ing shear reinforcement is not necessary. If the support reaction is eccentric with respect to
the control perimeter, the maximum shear stress is
VEd
v Ed = β EC (13)
U1 d
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MEd U1
β EC = 1 + k c (14)
VEd W1
where W 1 represents the shear distribution on the control perimeter; VEd is the design value
of the sectional shear force; MEd is the design value of the sectional bending moment; and kc
is a coefficient on the ratio between the column dimensions given by Table 6.1 of NEN-EN
1992-1-1:2005 [8]. A few values of kc are 0.6 for a c1 /c2 ratio of 1.0 and 0.70 for a c1 /c2 ratio
of 2.0, where c1 and c2 are the dimensions of the column (see Figure 5). W 1 is calculated as
Z U
i
W1 = |e|dl (15)
0
where Ui is the length of the control perimeter under consideration; dl is a length increment
of the perimeter; and e is the distance of dl from the axis around which the moment MEd
acts [8]. Figure 5 shows shear distribution due to an unbalanced moment at a slab–column
connection, indicating that the Eurocode approach assumes a fully plastic distribution of
the shear stresses.
Figure 5. Shear distribution due to an unbalanced moment at a slab–column connection, modified

from Ref. [8].
For an internal rectangular column where the loading is eccentric to both orthogonal
axes, βEC shall be calculated as follows:
s 2 2
ey

ex
β EC = 1 + 1.8 + (16)
bx by
where ey and ex are the eccentricities MEd /VEd along the axes y and x, respectively, and bx
and by are the dimensions of the control perimeter. For edge slab–column connections,
where the eccentricity is perpendicular to the slab edge toward the interior, and there
is no eccentricity parallel to the edge, the control perimeter may be reduced to U1 *, as
illustrated in Figure 6a. For corner slab–column connections, where the eccentricity is
toward the interior of the slab, the control perimeter may be reduced to U1 *, as illustrated
in Figure 6b [8]. This approach was adopted for safety reasons, considering that when
there is a moment around an axis parallel to the slab edge or a moment at a corner column,
the experimental results showed that punching failure is typically preceded by torsional
cracking at the edge of the slab [14].
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Figure 6. Reduced basic control perimeter, modified from Ref. [8]: (a) edge slab–column connection;
(b) corner slab–column connection.
For edge slab–column connections, if there are eccentricities in both orthogonal direc-
tions, βEC shall be calculated as
U1 U
β EC = + k c 1 e par (17)
U1∗ W1
where epar is the eccentricity parallel to the slab edge. For edge and corner column connec-
tions, where the eccentricity is toward the interior of the slab, βEC shall be calculated as
U1
β EC = (18)
U1∗
If the eccentricity is toward the exterior, βEC shall be calculated using Equation (16).
The punching shear resistance of slabs without shear reinforcement vRd,c is calcu-
lated as 1
v Rd,c = CRd,c k (100ρl f ck ) 3 ≥ vmin (19)
with vRd,c taken as 0.18/γc , with γc the material factor for concrete (γc = 1.5) and k the size
effect factor, calculated with the following expression, with d in [mm]
r
200
k = 1+ ≤2 (20)
d
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The reinforcement ratio is the geometric average of the reinforcement ratio in the y (ρly )
and x (ρlx ) direction:
p
ρl = ρlx .ρly (21)
The lower bound of the shear capacity is a nationally determined parameter, with a
recommended expression for vmin as
1/2
vmin = 0.035k3/2 f ck (22)
The punching shear resistance of slabs with shear reinforcement is calculated as

d 1
v Rd,cs = 0.75v Rd,c + 1.5 Asw f ywd,e f sin α (23)
sr U1 d
where Asw is the area of one perimeter of shear reinforcement around the column; sr is the
radial spacing of perimeters of shear reinforcement; fywd,ef is the effective design strength of
the punching shear reinforcement; and α is the angle between shear reinforcement and the
horizontal plane of the slab.
2.1.3. Model Code 2010

The fib Model Code 2010 punching shear provisions are based on the critical shear
crack theory [15,16]. The design shear demand VEd acts on the basic control perimeter
b1,MC at 0.5dv from the supported area, where dv is the effective depth of the slab. Figure 7
illustrates the basic control perimeter for different supported areas.
Figure 7. Basic control perimeter, modified from Ref. [9]: (a) interior column; (b) edge slab–
column connection.
Then, for calculating the punching shear resistance of the slab, a control perimeter b0
is used. This perimeter accounts for the non-uniform distribution of shear forces along
b1,MC , which can be caused by concentrations of the shear forces due to moment transfer
between the slab and the supported area because of eccentricities in the load application [9].
Figure 8 illustrates the eccentricity of the resultants [9].
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Figure 8. Resultant of shear forces, modified from Ref. [9].
The control perimeter b0 is determined as
b0 = k e b1,MC (24)
The factor ke represents the coefficient of eccentricity:
1
ke = (25)
1 + beuu
where eu is the eccentricity of the resultant shear forces with respect to the centroid of b1,MC ,
and bu is the diameter of a circle with the same area as the region inside b1,MC .
The punching shear resistance VRd is calculated as
VRd = VRd,c + VRd,s ≥ VEd (26)
The design shear resistance attributed to the concrete is calculated using the following
expression, with the compressive strength of the concrete, fck , in [MPa]:
p
f ck
VRd,c = k ψ b0 dv (27)
γc
kψ is a parameter that depends on the rotations of the slab and shall be calculated as
1
kψ = ≤ 0.6 (28)
1.5 + 0.9k dg ψd
where d is the mean value of the effective depth of the slab for x and y directions, and kdg
shall be calculated as follows, with dg in [mm]:
32
k dg = ≥ 1.15 (29)
16 + d g
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where dg is the maximum aggregate size.

The design shear resistance attributed to the shear reinforcement is calculated as
VRd,s = ∑ Asw ke σswd sin α (30)
where ∑Asw is the sum of the area of all the shear reinforcement acting on the zone between
0.35dv and dv , which has a length of 0.65dv (see Figure 9) [9].
Figure 9. Shear reinforcement resisting shear crack, based on Ref. [9].
The stress σswd is calculated as
Es ψ
σswd = ≤ f ywd (31)
6
where fywd is the yield strength.
The load-rotation behavior of the slab is calculated as follows:
rs f yd msd 1.5

ψ = 1.5 (32)
d Es m Rd
where rs is the distance from the column axis to the line of contra-flexure of the radial
bending moments; fyd is the yield strength of the flexural reinforcement; Es is the modulus
of elasticity of the flexural steel; msd is the average moment per unit length for calculating
flexural reinforcement in the support strip; and mRd is the average flexural strength per
unit length in the support strip [9]. The values of the mechanical parameters in the formula
can be calculated with different levels of approximation (LoA), where increasing levels of
approximation indicate increasing precision but also increasing computational time and
effort [6].
LoA I assumes that msd = mRd , which implies that the strength of the slab will be
governed by its bending moment capacity. For regular slabs with a long-to-short span
length ratio 0.5 ≤ Lx /Ly ≤ 2.0, rs can be estimated as follows:
rsx = 0.22L x ; rsy = 0.22Ly (33)
Figure 10 illustrates Lx and Ly [9].

LoA II includes a simplified estimation of msd . LoA III replaces the coefficient 1.5 in
Equation (32) with 1.2 if rs and msd are calculated with a linear elastic model. LoA IV is
based on a nonlinear analysis of the structure, and it considers cracking, tension-stiffening
effects, yielding of the reinforcement and any other relevant nonlinear effects [9]. LoA III
was used for the present investigation.
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Figure 10. Slab dimensions and support strip dimensions, modified from Ref. [9].
2.2. Database of Eccentric Punching Shear Experiments

2.2.1. Development of the Database
The database developed for this study contains 128 experiments of eccentric punch-
ing shear on flat slabs with longitudinal reinforcement and with or without transverse
shear reinforcement reported in the literature. The references consulted are works by
Krüger [2], Moe [11], Albuquerque et al. [17], Hammill and Ghali [18], Narayani [19],
Zaghlool [20], Anis [21], Hanson and Hanson [22], Stamenkovic [23], Pina Ferreira [24],
Ritchie [25], Sudarsana [26], Zaghloul [27], Desayi [28], Walker [29] and Stamenkovic [30].
Tables A1–A7 present the database developed for this study, see Appendix A. The full
spreadsheet is available in the public domain in .xlsx format [31]. The notations used in
this database are given in the “List of notations”. Figure 11 illustrates the different slab
geometries and slab–column connections found in the literature [2,11,17–30].
Figure 11. Cont.

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Figure 11. Slab geometries and test slab–column connection: (a) square interior slab–column connec-
tion [19]; (b) rectangular edge slab–column connection [17]; (c) square corner slab–column connec-
tion [18].
For Refs. [2,17,18,22,24,25,28,29], the age of the specimens at the time of testing was not
provided, and thus, it is assumed to be 28 days. For Refs. [2,11,18,21–23,25–30], the tensile
strength of the concrete fct was not reported by the authors. To complete this information,
the expression developed by Sarveghadi [32] was used:
p
f ct = 0.76 f c (34)
with fc as the cylinder concrete compressive strength in [MPa].

For Refs. [18,19,23,25,28–30], the modulus of elasticity of the flexural reinforcement
was not provided; for Refs. [18,23,25,28–30], it was assumed as 200 GPa, and for Ref. [19], it
was estimated from the stress–strain graph reported by the author.
Refs. [2,17–19,24,27] present slabs with transverse shear reinforcement; stirrups, shear
hats (see Figure 12) and studs were the shear reinforcement types found in these works.
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Figure 12. Shear hat setup, as used in Ref. [19].
For internal slab–column connections, Refs. [2,11,19] presented the ultimate load ap-
plied to the slab–column connection and its eccentricity; on the other hand, Refs. [21–24]
reported the ultimate moment applied to the slab–column connection. For the edge
slab–column connections, Refs. [17,19,22] presented the ultimate load applied to the slab–
column connection and its eccentricity, and Refs. [20,23,25–27] reported the ultimate mo-
ment applied to the slab–column connection. Finally, for corner slab–column connections,
Refs. [18,20,26,30] reported the ultimate moment applied to the slab–column connection.
In all the works, the test setup caused this moment to act diagonally on the slab. Figure 11c
illustrates this type of loading. On the other hand, Refs. [28,29] reported the ultimate load
applied to the slab–column connection and its eccentricity. For the database, the diagonally
applied moment was divided into its components in the x and y directions. All values
in the database are presented in SI units. The information from Refs. [11,20–23,30] was
converted from US customary to SI units.
2.2.2. FEM Modeling Process

The FEM models were developed in Scia Engineer [33] as similar to the reported
experiments as possible, including the contribution of the self-weight when testing occurred
in the gravity direction (i.e., self-weight increases sectional shear).
To model the slab–column connections, rigid line links were placed through the center
of the column on the y and x axis. The result of a rigid link is that the deformation of
both nodes in the direction of the line connecting both nodes will be identical, and the
orientation of the line connecting both nodes after the calculation depends on the selected
type of rigid link [33]. The average size for two dimensional elements on the models was
0.01 m.
For test setups where the load was applied directly to the slab, free node point loads
were applied on the model. On the other hand, when loads were applied to the column
in the experiments, point loads were applied similarly in the FEM models; this applies to
vertical and horizontal loads. The results presented in Tables A8–A10 are the maximum
shear internal forces of the slab at failure, measured on the punching perimeter described
in the ACI 318-19 code [7] divided by the effective depth of the slab d. Figure 13 illustrates
the various steps in the process.
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Figure 13. Cont.

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Figure 13. Example of finite element analysis on an Albuquerque [17] specimen: (a) Applied loads
in the model and support conditions (side view); (b) Rigid line links on the column x and y axis,
punching perimeter defined by ACI 318-19 code [7] (plan view); (c) Mesh generation (diagonal view);
(d) Internal shear stress on the critical perimeter, calculated from the applied load and the self-weight
of the specimen.
The internal, edge and corner specimens followed the same modeling process. Figure 14
shows the typical shear stress distributions around the control perimeter considered; note
that the loads applied are displayed to show the loading eccentricity.
Figure 14. Cont.

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Figure 14. Example of typical shear stress distributions around the control perimeter defined by ACI
318-19 code [7]: (a) Internal slab–column connection; (b) Edge slab–column connection; (c) Corner
2.2.3. Parameter Ranges in the Database

In this section, an evaluation of the distribution of the values of the parameters in the
database is made. Table 1 gives the ranges of the most important parameters in the database.
The value of ρl is either taken directly from the referenced work, where available, or
calculated as the geometric average of the longitudinal and transverse reinforcement ratios.
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Table 1. Ranges of parameters in the database.
Parameter Min Max Mean Median STD

Lx (mm) 530 3000 1275 1075 631
Ly (mm) 530 3000 1383 1525 632
h (mm) 76 180 126 150 39
d (mm) 56 151 98 114 33
ρl (%) 0.53% 2.23% 1.3% 1.2% 0.3%
fc (MPa) 15.5 59.3 37.4 37.0 8.8
dg (mm) 9.5 38.1 13.2 10.0 7.8
a (mm) 419 2000 905 860 422
av (mm) 343 1850 788 749 405
Figure 15 shows the distribution of the most important parameters in the database.
Figure 15a shows that the majority of the slabs are made of normal strength concrete.
The developed database cannot be used to gain insight into the eccentric punching shear
capacity of high-strength concrete slab–column connections. Figure 15b shows that a tensile
reinforcement ratio in the range of 1.25–1.50% was commonly used in the tested slabs.
Typical slab designs use reinforcement ratios of 0.6–0.8%. None of the experiments in
the database used these practical values, with most slabs being over-reinforced in flexure
to achieve a punching shear failure. The distribution of the average effective depth of
the slabs is presented in Figure 15c. This plot shows that at least half of the specimens
had an effective depth d in the range 100 mm–125 mm, and another large portion of the
specimens had an effective depth close to 75 mm. The reported specimens are small-scale
specimens that do not give us insights regarding the size effect for eccentric punching shear.
Figure 15d shows the ratio between the shear span and the average effective depth a/d.
The range of a/d in the experiments covers only situations in which no direct load transfer
can occur; as such, for this database, there is a consistency in the range of a/d. Figure 15e
shows the maximum aggregate size values reported in the literature. The values reported
are consistent with the values shown in Figure 15c; relatively small maximum aggregate
sizes are used for the fabrication of specimens with small depths.
Figure 15. Cont.

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Figure 15. Distribution of the most important parameters in the database: (a) concrete compressive
strength fc ; (b) tensile reinforcement ratio ρl ; (c) effective depth d; (d) shear span to average effective
depth ratio a/d; (e) maximum aggregate size dg .
3. Results
3.1. Parameters Studied
The raw data from the database are used to analyze the effect of different experi-
mental parameters on the sectional shear stress at failure. The ACI 318-19 [7] expression
(Equation (1)) is used for determining the shear stress on the perimeter vu . Normalized
shear stresses are used to discard the influence of the concrete compressive strength fc .
An analysis of the shear stress normalized to the square root and to the cubic root of the
concrete compressive strength is carried out first. Figure 16a,b show the relation between
the normalized shear strength and fc , and, as can be seen, for the experimental results
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studied, normalizing the shear strength to the square root of the concrete compressive
strength is preferable. A similar observation was made for the shear capacity of steel fiber
reinforced concrete beams [34].
Figure 16. Shear stresses normalized to the concrete compressive strength: (a) normalized to the
square root; (b) normalized to the cubic root.
Thus, the influence of different important parameters is studied as a function of the

shear stress normalized to the square root of fc . Figure 17 shows the influence of the most
important parameters on the shear stress normalized to the square root of fc . Figure 17a
shows the influence of the effective depth d on the normalized shear stress. For the
specimens in the database compiled, the influence of the effective depth on the normalized
shear capacity is negligible. However, experiments on slabs with a larger effective depth
are not available; therefore, this database cannot give insights regarding the size effect
in eccentric punching shear. Figure 17b shows the influence of the reinforcement ratio
ρl . Larger reinforcement ratios result in larger shear capacities, as expected. As more
tension reinforcement is provided, the contribution of dowel action to the shear capacity
increases. Other factors that could explain the influence of the reinforcement ratio on the
shear capacity are improved aggregate interlock due to a reduction in crack width for
specimens with more flexural reinforcement, and a larger contribution of the uncracked
concrete zone due to an increase in the flexural compression block depth. However, the
overall scatter on the trendline is large. Figure 17c shows the influence of the shear span to
the effective depth a/d. For the experiments in the database compiled, this parameter had
negligible influence on the normalized shear stress.
Buildings 2022, 12, 2092 22 of 49
Figure 17. Parameter studies based on the normalized shear stress at failure of all entries in the
database: (a) effective depth d; (b) longitudinal reinforcement ratio ρl ; (c) shear span to depth
ratio a/d.
3.2. Comparison with Code Predictions

The measured shear capacities from the database are then compared with the shear
capacities predicted by three different codes: ACI 318-19 [7], NEN-EN 1992-1-1:2005 [8]
and the fib Model Code 2010 [9]. Figure 18 shows the comparison between the tested and
predicted results, with the statistical properties of the tested-to-predicted shear stresses
Buildings 2022, 12, 2092 23 of 49
in Tables 2–4. Figure 19 shows the comparison between the SCIA Engineer [33] FEM
results vFEM and the predicted shear capacities vpred for ACI 318-19 [7], with the statistical
properties of this comparison in Table 5. The FEM results of the shear stress were compared
only to ACI 318-19 [7], as NEN-EN 1992-1-1:2005 [8] and fib Model Code 2010 [9] assume a
plastic stress distribution on the punching perimeter. ACI 318-19 [7], on the other hand,
assumes a linear stress distribution. The results of the linear finite element analysis were
compared to check the alignment of the assumptions of linear behavior. The results for
all the entries of the database are presented in Tables A8–A10. Some experiments only
use the moment on the slab-column connection and do not use a load on the slab. For
these referenced works, the NEN-EN 1992-1-1:2005 [8] and fib Model Code 2010 [9] models
were not evaluated. Equation (14) from NEN-EN 1992-1-1:2005 [8] uses the value of shear
force applied to the slab–column connection for calculating the enhancement factor for
eccentric shear, βEC , so that the shear stress caused by unbalanced moment only cannot
be determined. The same problem arises when applying Equations (24) and (25) from the
fib Model Code 2010 [9]; the eccentricity eu is calculated from the resultant shear forces
applied to the slab–column connection.
Figure 18. Comparison between experimental vtest and predicted shear capacities vpred for three
design methods from existing codes.
The validation of the spreadsheet used for calculating the code predictions is available
in the public domain [35].
In Table 2, the statistical results are first presented in general and are then presented
separately by the type of slab–column connection being analyzed. The number of experi-
ments evaluated varies from code to code because specimens that were not tested under
direct shear could not be evaluated by NEN-EN 1992-1-1:2005 [8] and Model Code 2010 [9].
Buildings 2022, 12, 2092 24 of 49
Table 2. Statistical results from the comparison between the tested and predicted capacities, Part I.
The number of specimens used for the evaluation is shown within brackets. First, all results are shown
together. Then, the results are subdivided into interior slab–column connections with unbalanced
moment, edge slab–column connections and corner slab–column connections.
All Results
AVG STD COV (%)
ACI (128) 1.65 0.58 35.39
EC2 (122) 1.52 0.69 45.38
MC2010 (122) 0.82 0.24 29.63
Internal slab–column connections
AVG STD COV (%)
ACI (37) 1.41 0.31 22.27
EC2 (37) 1.15 0.22 19.00
MC2010 (37) 0.81 0.17 20.47
Edge slab–column connections
AVG STD COV (%)
ACI (55) 1.79 0.61 33.78
EC2 (51) 1.70 0.88 51.93
MC2010 (51) 0.79 0.21 26.20
Corner slab–column connections
AVG STD COV (%)
ACI (36) 1.67 0.69 41.18
EC2 (34) 1.66 0.54 32.75
MC2010 (34) 0.88 0.34 38.70
Table 3. Statistical results from the comparison between the tested and predicted capacities, Part
II. The number of specimens used for the evaluation is shown within brackets. First, all results
are shown together. Then, the results are subdivided into interior slab–column connections with
unbalanced moment, edge slab–column connections and corner slab–column connections.
Slabs without Shear Reinforcement

AVG STD COV (%)
ACI (110) 1.65 0.58 35.24
EC2 (104) 1.51 0.68 45.17
MC2010 (104) 0.80 0.25 30.70
AVG STD COV (%)
ACI (28) 1.45 0.28 19.43
EC2 (28) 1.15 0.23 19.71
MC2010 (28) 0.77 0.15 19.25
AVG STD COV (%)
ACI (48) 1.78 0.62 34.60
EC2 (44) 1.64 0.86 52.58
MC2010 (44) 0.79 0.22 27.57
AVG STD COV (%)
ACI (34) 1.63 0.67 41.16
EC2 (32) 1.66 0.56 33.56
MC2010 (32) 0.86 0.34 39.07
Buildings 2022, 12, 2092 25 of 49
Table 4. Statistical results from the comparison between the tested and predicted capacities, Part
III. The number of specimens used for the evaluation is shown within brackets. First, all results
are shown together. Then, the results are subdivided into interior slab–column connections with
unbalanced moment, edge slab–column connections and corner slab–column connections.
Shear-Reinforced Slabs
AVG STD COV (%)
ACI (18) 1.64 0.61 37.32
EC2 (18) 1.59 0.75 47.54
MC2010 (18) 0.93 0.20 21.35
AVG STD COV (%)
ACI (9) 1.30 0.40 30.64
EC2 (9) 1.18 0.21 17.65
MC2010 (9) 0.93 0.16 17.14
1.89 0.57 30.02
ACI (7) 2.10 0.99 46.99
EC2 (7) 0.83 0.14 17.27
MC2010 (7) 1.89 0.57 30.02
AVG STD COV (%)
ACI (2) 2.29 0.90 39.09
EC2 (2) 1.61 0.29 18.30
MC2010 (2) 1.25 0.26 20.88
Figure 19. Comparison between the SCIA Engineer [33] FEM results and the predicted shear capaci-
ties for ACI 318-19 [7].
Buildings 2022, 12, 2092 26 of 49
Table 5. Statistical results from the comparison between SCIA Engineer [33] FEM results for the
acting shear stress and the predicted shear capacities for ACI 318-19 [7].
AVG STD COV (%)

All specimens 1.81 0.85 46.94
Internal slab–column connections 1.70 0.85 50.02
Edge slab–column connections 1.57 0.66 42.15
Corner slab–column connections 2.30 0.93 40.18
As can be observed in Table 2, ACI 318-19 [7] and NEN-EN 1992-1-1:2005 [8] tend to
be on the conservative side in terms of the average tested to predicted shear stresses. The
Model Code 2010 [9] predicted shear capacities that are on average below the tested shear
stress at failure (average = 0.82). Considering the overall results, the Model Code 2010 [9]
also has the smallest coefficient of variation (COV = 29.63%) on the tested to predicted
shear stresses. These results could be considered generally unsatisfactory. Nevertheless,
all three codes performed better when evaluating only internal slab–column connections
without shear reinforcement, with COV values under 20% for all. The tested to predicted
values using NEN-EN 1992-1-1:2005 [8] show the lowest maximum value for one entry
(0.24); however, the tested to predicted value using the Model Code 2010 [9] for this entry is
small as well (0.58). The entry analyzed is named C/C/4, from Ref. [30], and it is a corner
slab–column connection, unreinforced in shear (see Table A8 in Appendix B).
All three models evaluated performed differently when predicting strengths on internal,
edge and corner slab–column connections. ACI 318-19 [7] and NEN-EN 1992-1-1:2005 [8]
tend to render more conservative results for edge and corner slab–column connections, as
shown in Tables 3 and 4. NEN-EN 1992-1-1:2005 [8] showed the largest scatter when evalu-
ating edge slab–column connections (COV = 51.93%), which is considered unacceptable.
As can be observed in Figure 19 and Table 5, the ACI 318-19 [7] assumption of a
linear elastic model distribution leads to an overestimation of the real performance of the
specimens. Replacing the shear stresses calculated assuming a linear stress distribution with
the results presented in Tables A8–A10, which are the maximum shear internal forces of the
slab at failure, measured on the punching perimeter described in the ACI 318-19 code [7]
divided by the effective depth of the slab d in the comparison to the shear capacity from ACI
318-19 (see Table 5), results in larger (i.e., more overly conservative) values for the tested
to predicted shear. At the same time, the COV on the tested to predicted values increases,
indicating that when using ACI 318-19, both the shear stress from the code provisions
and the shear capacity should be used together. Using the results from the FEM models,
increasing the level of precision of the assumption of a linear elastic model distribution,
which was demonstrated to lead to an overestimation of the shear capacity of the slab,
tends to enlarge this overestimation.
As can be observed in Figure 20 and Table 6, the ACI 318-19 [7] assumption of a
linear elastic model distribution does not hold up for finer calculations using the SCIA
Engineer [33] FEM results. Although the average value for the comparison between the
shear capacities for ACI 318-19 [7] and SCIA Engineer [33] FEM results for the acting shear
stress is relatively close to 1.0, the COV on these results is not acceptable (COV = 54.37) (see
Tables A11–A13).
Buildings 2022, 12, 2092 27 of 49
Figure 20. Comparison between the SCIA Engineer [33] FEM results and the shear stress for ACI
318-19 [7], calculated using Equation (1).
Table 6. Statistical results from the average value for the comparison between the acting shear stress
for ACI 318-19 [7] and SCIA Engineer [33] FEM results for the acting shear stress.
AVG STD COV (%)

All specimens 1.09 0.59 54.37
Internal slab–column connections 0.99 0.49 49.09
Edge slab–column connections 1.33 0.63 47.85
Corner slab–column connections 0.82 0.48 58.59
3.3. Influence of Parameters on Tested to Predicted Punching Capacities

Figure 21 shows the vtest /vpred values as a function of the different parameters, studied
in Section 3.1, for the various codes with the objective of obtaining an insight in which
codes over- or underestimate the various parameters.
Figure 21. Cont.

Buildings 2022, 12, 2092 28 of 49
Figure 21. Cont.

Buildings 2022, 12, 2092 29 of 49
Figure 21. Parameters studied based on the comparison between experimental vtest and predicted
shear capacities vpred for three design methods from existing codes: (a) concrete compressive strength
fc ; (b) effective depth d; (c) longitudinal reinforcement ratio ρl ; (d) shear span to depth ratio a/d;
(e) eccentricity.
As can be observed in Figure 21a, ACI 318-19 [7] tends to underestimate the influence
of the compressive strength of the concrete fc . On the other hand, the fib Model Code [9]
and NEN-EN 1992-1-1:2005 [8] correctly take the influence of the concrete compressive
strength into account.
When considering the influence of the effective depth d on the tested to predicted ratios
(Figure 21b), we can see that NEN-EN 1992-1-1:2005 [8] and the fib Model Code [9] take the
size effect correctly into account for the specimens tested. In contrast, for ACI 318-19 [7],
no influence of size is considered. Additionally, we observe an important increase in the
Buildings 2022, 12, 2092 30 of 49
conservativism of NEN-EN 1992-1-1:2005 [8] as the effective depth increases. For the tested
sizes, the value of d only influences the size and location of the punching perimeter. None
of the specimens were of a thickness at which the size effect factor from the code equations
starts to play a role.
As can be seen in Figure 21c, NEN-EN 1992-1-1:2005 [8] and the fib Model Code
2010 [9] consider that the influence of the longitudinal reinforcement is larger than that
observed in the experiments. The influence is taken into account more realistically in
ACI 318-19 [7]. As the specimens in the database contained large reinforcement ratios,
experiments on slabs with lower reinforcement ratios are necessary to further study the
effect of the reinforcement ratio on the tested to predicted ratios determined with the
studied codes.
Figure 21d shows that, for the Model Code 2010 [9] and NEN-EN 1992-1-1:2005 [8], as
the shear span to depth ratio a/d increases, the values of vtest /vpred tend to become more
conservative. On the other hand, for ACI 318-19 [7], the values of vtest /vpred tend to remain
relatively constant as the shear span to depth ratio increases. None of the studied specimens
are in the range of small a/d values for which direct transfer of the load to the support
plays a role.
Figure 21e shows that, for the Model Code 2010 [9] ACI 318-19 [7], the values of
vtest /vpred remain constant despite the increase in the absolute value of eccentricity. Nonethe-
less, for NEN-EN 1992-1-1:2005 [8], these values drastically decrease and become unsafe
when eccentricities exceed 1000 mm. This observation can be explained by Equation (18) for
most edge and corner slab–column connection entries due to the direction of the eccentricity.
This equation does not consider the magnitude of the eccentricity being evaluated, just its
direction; thus, for large eccentricities, this approach becomes unsafe.
4. Discussion
High-strength concrete slabs are not included in the study due to the lack of experi-
ments on high-strength concrete slab–column connections. Future studies may investigate
the behavior of this type of slabs in comparison with the ones considered in this study.
Ngo [36] presented a study on concentric experiments on high-strength concrete slabs
without shear reinforcement and concluded that the use of high-strength concrete improves
the punching shear resistance. However, as the aggregate interlock capacity decreases for
higher strength concrete, further research on this topic is warranted.
Real-scale slab–column experiments on punching shear are not commonly found in
the literature. None of the entries in this database is considered a realistic size slab, as none
of these has an effective depth over 200 mm. Since a size effect occurs in punching shear
for concentric slab–column connections [37], experimental research on larger slabs under
eccentric punching shear is necessary.
In most cases, the results found in the literature indicate that there is an important
reduction in the punching capacity when unbalanced moments occur in the slab–column
connection. Nevertheless, most experiments and research works focus on concentric
punching shear. The code provisions are based on empirical equations, which include the
effect of eccentricities by different methods, such as critical perimeter reduction or increase
in the applied shear stress, but a mechanics-based model that is practical enough to be
implemented in the building codes is lacking. Mechanics-based models, such as the critical
shear crack theory used in the Model Code 2010 [9], are developed for the case of concentric
punching shear and use simplified methods for the extension to eccentric punching shear.
For this database, the empirical methods showed large scatter in the results of the
tested to predicted capacities, represented by the high coefficients of variation. This
observation may be explained by the fact that all methods under consideration were
originally developed for concentric punching shear and validated with concentric punching
shear tests and were then extended to the use for eccentric punching shear. For the future
development of design codes, more attention should be paid to eccentric punching shear
and the mechanical basis of the problem. Lower bound plasticity-based models have been
Buildings 2022, 12, 2092 31 of 49
shown to lead to good results in an exploratory study [38] and are a promising path toward
better code models for all cases of punching shear.
5. Conclusions
The lack of understanding regarding eccentric punching shear presents a practical
problem because local forces typically control the slab’s design. The transfer of unbalanced
moments from the slab to the column causes an increase in the resulting shear stresses.
When this effect is not well understood, it may lead to a punching failure of the slab–column
connection and a possible collapse of the building. This study evaluates the available code
provisions against 128 experimental results reported in the literature.
Analyzing the available experimental results from the database resulted in the follow-
ing conclusions:
• There is a lack of experiments on eccentric punching shear.
• All experiments are carried out on slabs of under 200 mm in depth. As such, the
experiments cannot be used to evaluate the size effect in shear.
• Most specimens have large reinforcement ratios to avoid a flexural failure before
reaching the punching shear capacity of the slab and are not representative of typical
floor slabs.
• All specimens are cast using normal-strength concrete.
From the comparison between the experimental shear capacities and the capacities
predicted by the available codes, the following conclusions result:
• The presence of unbalanced moments has a large impact on the capacity of the codes
to accurately predict the performance of slab–column connections, especially for edge
and corner connections.
• The closest to 1.0 average value for tested to predicted shear capacity is obtained
with the Model Code 2010 [9] provisions, although the results are on the unsafe side
(average of tested/predicted = 0.82).
• Evaluating all experiments, the coefficient of variation of the tested to predicted shear
capacities is lower for the expressions of the Model Code 2010 [9], based on the critical
shear crack theory, than for the empirical expressions of NEN-EN 1992-1-1:2005 [8]
and ACI 318-19 [7].
• In general, the coefficient of variation of the tested to predicted shear capacities is
lower for the experiments without shear reinforcement than for the experiments
with shear reinforcement. This observation indicates that further studies should
address the distribution of shear stresses for shear-reinforced slab–column connections
with unbalanced moments, as well as the contribution of the various shear-carrying
mechanisms for the case with shear reinforcement.
• The NEN-EN 1992-1-1:2005 [8] results for tested to predicted shear capacity showed a
smaller scatter for internal and corner slab–column connections than the results of the
Model Code 2010 [9] and ACI 318-19 [7].
• The Model Code 2010 [9] has the lowest coefficient of variation for the tested to
predicted shear stress for edge slab–column connections, whereas NEN-EN 1992-1-
1:2005 [8] has the smallest COV for internal and corner slab–column connections.
• The fib Model Code generally results in the best performance in the parameter studies
of the tested to predicted ratios, indicating that this mechanics-based model has a
better representation of the parameters than the empirical models in NEN-EN 1992-1-
1:2005 [8] and ACI 318-19 [7].
• For eccentricities over 1000 mm, the use of NEN-EN 1992-1-1:2005 [8] becomes unsafe
for inward eccentricities at edge slab–column connections.
From the comparison between the SCIA Engineer [33] FEM results and the predicted
shear capacities for ACI 318-19 [7], the following conclusions result:
• Using a more refined calculation method to determine the acting shear stresses does
not improve the results in terms of tested to predicted shear stresses when using
Buildings 2022, 12, 2092 32 of 49
the ACI 318-19 [7] shear capacities. This observation indicates that the shear stress
distribution that follows from a linear finite element analysis does not correspond to
the slab at failure when cracking and redistribution of stresses occur.
• The ACI 318-19 [7] shear capacity should be combined with the method for determin-
ing the shear stress on the punching perimeter described in ACI 318-19 [7].
• Further research is necessary on the capacity methods that can be combined with a
linear finite element analysis.
A better understanding of eccentric punching shear and further experiments on
deeper slabs, slabs with high-strength concrete and carefully instrumented slabs with shear
reinforcement are necessary to obtain safe designs, optimize the design of building floors
and develop better tools for the assessment of existing building slabs.
Author Contributions: Conceptualization, E.O.L.L.; methodology, D.V. and E.O.L.L.; software, D.V.;
validation, A.S.G. and E.O.L.L.; formal analysis, D.V.; investigation, D.V. and E.O.L.L.; resources,
E.O.L.L.; data curation, D.V. and E.O.L.L.; writing—original draft preparation, D.V. and E.O.L.L.;
writing—review and editing, A.S.G.; visualization, D.V.; supervision, E.O.L.L.; project administration,
E.O.L.L.; funding acquisition, E.O.L.L. All authors have read and agreed to the published version of
the manuscript.
Funding: This research is part of the program of Collaboration Grants 2019 of Universidad San Fran-
cisco de Quito. The APC was funded by the open access initiative of Delft University of Technology.
Data Availability Statement: The data and calculations are available in the public domain through
https://doi.org/10.5281/zenodo.7317297 (accessed on 3 April 2022).
Acknowledgments: The authors would like to thank the program of Collaboration Grants 2019 of
Universidad San Francisco de Quito for the financial support.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
Asw area of the shear reinforcement for NEN-EN 1992-1-1:2005

Av area of the shear reinforcement for ACI 318-19
CRd, c constant used for determining the shear capacity
Es modulus of elasticity of the steel
Jc polar moment of inertia of the critical section
Lx dimension of the slab
Ly dimension of the slab
MEd design moment
Mmu model ultimate internal moment
Mu factored moment applied on the slab
U1 control perimeter for NEN-EN 1992-1-1:2005
U1 * reduced critical control perimeter for NEN-EN 1992-1-1:2005
VEd design shear strength
VRd punching resistance for Model Code 2010
VRd,c punching resistance provided by the concrete for Model Code 2010
VRd,s punching resistance provided by the steel for Model Code 2010
Vu factored shear applied on the slab
Vmu model ultimate internal shear
Wsup width of the support
W1 plastic modulus of control perimeter for NEN-EN 1992-1-1:2005
a shear span
av clear shear span
b0 control perimeter for Model Code 2010
b0,int critical perimeter inside the shear-reinforced zone for CSCT
b1 dimension of the critical perimeter for NEN-EN 1992-1-1:2005
Buildings 2022, 12, 2092 33 of 49
b1,MC basic control perimeter for Model Code 2010

b2 dimension of the critical perimeter for Model Code 2010
bo perimeter of the critical perimeter for ACI 318-19
bu diameter of the circle with the same area as the region inside b1, MC
by dimension of the critical perimeter U1
bz dimension of the critical perimeter U1
c distance to the centroid of the critical perimeter
c1 dimension of the column
c2 dimension of the column
d average effective depth of the slab
dg maximum aggregate size
dv average effective depth of the slab for Model Code 2010
e eccentricity M/V
epar eccentricity parallel to the edge of the slab
eu eccentricity of the resultant forces
ey eccentricity caused by a moment acting on the y-axis
ez eccentricity caused by a moment acting on the x-axis
fbd bond strength
fc compressive strength of the concrete for ACI 318-19
fck compressive strength of the concrete for Model Code 2010
fct tensile strength of the concrete
fyt yield strength of the reinforcement
fywd design yield strength of the shear reinforcement
fywd,ef effective design strength of shear reinforcement
h depth of the slab
k size effect factor
kc column size effect factor
kdg coefficient of aggregate size
ke coefficient of eccentricity
kψ coefficient of rotation
mrd average flexural strength per unit length in the support strip
msd average moment per unit length for calculation of flexural reinforcement in the support strip
rs distance from column axis to line of contra-flexure of the radial bending moments
mxD model design moment on the x-axis
myD model design moment on the y-axis
sr radial spacing of the reinforcement
vc punching resistance provided by the concrete for ACI 318-19
vEd design shear stress
vn nominal shear strength for ACI 318-19
vRd, c shear resistance provided by the concrete
vRd shear resistance for Model Code 2010
vRd,cs shear resistance for NEN-EN 1992-1-1:2005
vRd s shear resistance provided by the steel
vs punching resistance provided by the steel reinforcement for ACI 318-19
vu maximum shear stress for ACI 318-19
vpred shear capacity predicted for all the models
vFEM maximum shear stress resulting from the FEM model
γf fraction of the unbalanced moment transmitted by flexure
γv fraction of the unbalanced moment transmitted by shear
α angle between shear reinforcement and horizontal plane of the slab
αs constant used for determining shear capacity according to ACI 318-19
β column dimension factor according to ACI 318-19
βEC enhancement factor for eccentric shear for NEN-EN 1992-1-1:2005
ρl longitudinal steel reinforcement ratio
ρv shear steel reinforcement ratio
σswd shear reinforcement stress
φw shear reinforcement diameter
ψ rotation of the slab
Buildings 2022, 12, 2092 34 of 49
Appendix A
Table A1. Internal slab–column connections—Slab geometry.
Reference Name Lx (mm) Lx (mm) c1 (mm) c2 (mm) h (mm) d (mm) a (mm) av (mm)
L1 2280 2280 305 305 178 151 1026 874
L3 2280 2280 305 305 178 151 1026 874
L4 2280 2280 305 305 178 151 1026 874
Narayani [19]
L5 2280 2280 305 305 178 151 1026 874
L6 2280 2280 305 305 178 151 1026 874
L10 2280 2280 305 305 178 151 1026 874
P16A 3000 3000 300 300 150 121 1375 1225
Krüger [2] P30A 3000 3000 300 300 150 121 1375 1225
PP16B 3000 3000 300 300 150 121 1375 1225
M2A 1829 1829 305 305 152 114 787 635
M4A 1829 1829 305 305 152 114 787 635
M2 1829 1829 305 305 152 114 787 635
M3 1829 1829 305 305 152 114 787 635
Moe [11] M6 1829 1829 254 254 152 114 787 660
M7 1829 1829 254 254 152 114 787 660
M8 1829 1829 254 254 152 114 787 660
M9 1829 1829 254 254 152 114 787 660
M10 1829 1829 254 254 152 114 787 660
B.3 1524 1524 203 203 102 76 737 635
B.4 1524 1524 203 203 102 76 737 635
Anis [21]
B.5 1524 1524 203 203 102 76 737 635
B.6 1524 1524 203 203 102 76 737 635
C/I/1 914 914 127 127 76 56 419 355
C/I/2 914 914 127 127 76 56 419 355
C/I/3 914 914 127 127 76 56 419 355
C/I/4 914 914 127 127 76 56 419 355
Stamenkovic [23]
C/Ir/1 914 914 152 76 76 56 419 343
C/Ir/2 914 914 152 76 76 56 419 343
C/Ir/3 914 914 152 76 76 56 419 343
C/Ir/4 914 914 152 76 76 56 419 343
A12 2134 1219 152 152 76 62 1067 991
Hanson [22] B16 2134 1219 152 305 76 62 1067 991
C17 2134 1219 305 152 76 62 1067 914
S3 2500 2500 300 300 180 145 1250 1100
S4 2500 2500 300 300 180 143 1250 1100
Pina Ferreira [24]
S6 2500 2500 300 300 180 144 1250 1100
S8 2500 2500 300 300 180 144 1250 1100
Buildings 2022, 12, 2092 35 of 49
Table A2. Internal slab–column connections—Material properties.
Reference Name ρ (%) fy (MPa) Es (GPa) fc (MPa) Age (Days) fct (MPa) dg (mm)
L1 1.78% 398 188 32.80 28 2.70 19.00
L3 1.78% 398 188 33.10 28 2.66 19.00
L4 1.78% 398 188 45.80 28 3.45 19.00
Narayani [19]
L5 1.78% 398 188 35.00 28 2.98 19.00
L6 1.78% 398 188 42.10 28 3.07 19.00
L10 1.78% 398 188 41.80 28 2.47 19.00
P16A 1.30% 480 200 35.00 28 4.50 16.00
Krüger [2] P30A 1.30% 480 200 35.00 28 4.50 16.00
PP16B 1.30% 480 200 35.00 28 4.50 16.00
M2A 1.50% 481 196 15.51 25 2.99 38.10
M4A 1.50% 481 196 17.65 23 3.19 38.10
M2 1.50% 481 196 25.72 22 3.85 38.10
M3 1.50% 481 196 22.72 20 3.62 38.10
Moe [11] M6 1.34% 328 196 26.48 26 3.91 38.10
M7 1.34% 328 196 24.96 24 3.80 38.10
M8 1.34% 328 196 24.61 24 3.77 38.10
M9 1.34% 328 196 23.24 22 3.66 38.10
M10 1.34% 328 196 21.10 25 3.49 38.10
B.3 2.19% 331 205 38.06 28 4.69 9.53
B.4 2.19% 331 205 37.23 28 4.64 9.53
Anis [21]
B.5 2.19% 331 205 36.20 28 4.57 9.53
B.6 2.19% 331 205 39.16 28 4.76 9.53
C/I/1 1.17% 413 192 45.02 7 5.10 9.53
C/I/2 1.17% 413 192 37.09 7 4.63 9.53
C/I/3 1.17% 413 192 31.92 7 4.29 9.53
C/I/4 1.17% 413 192 31.37 7 4.26 9.53
Stamenkovic [23]
C/Ir/1 1.17% 413 192 28.27 7 4.04 9.53
C/Ir/2 1.17% 413 192 36.54 7 4.59 9.53
C/Ir/3 1.17% 413 192 35.71 7 4.54 9.53
C/Ir/4 1.17% 413 192 33.23 7 4.38 9.53
A12 1.36% 372 192 33.23 28 4.38 9.53
Hanson [22] B16 1.36% 341 192 30.41 28 4.19 9.53
C17 1.36% 341 192 35.99 28 4.56 9.53
S3 1.46% 540 213 50.30 28 4.30 9.50
S4 1.48% 540 213 49.20 28 4.40 9.50
Pina Ferreira [24]
S6 1.47% 540 213 50.10 28 4.90 9.50
S8 1.47% 540 213 48.40 28 4.00 9.50
Buildings 2022, 12, 2092 36 of 49
Table A3. Edge slab–column connections—Slab geometry.
L1 2350 1700 300 300 180 147 2000 1850
L2 2350 1700 300 300 180 146 2000 1850
L3 2350 1700 300 300 180 146 2000 1850
L4 2350 1700 300 300 180 146 2000 1850
L5 2350 1700 300 300 180 146 2000 1850
L6 2350 1700 300 300 180 146 2000 1850
Albuquerque [17] L7 2350 1700 300 300 180 146 2000 1850
L8 2350 1700 300 300 180 146 2000 1850
L9 2350 1700 300 300 180 146 2000 1850
L10 2350 1700 300 300 180 146 2000 1850
L11 2350 1700 300 300 180 146 2000 1850
L12 2350 1700 300 300 180 146 2000 1850
L13 2350 1700 300 300 180 146 2000 1850
ES1 1295 2280 305 305 178 151 1029 876
ES2 1295 2280 305 305 178 151 1029 876
ES3 1295 2280 305 305 178 151 1029 876
Narayani [19] ES4 1295 2280 305 305 178 151 1029 876
ES5 1295 2280 305 305 178 151 1029 876
ES6 1295 2280 305 305 178 151 1029 876
ES7 1295 2280 305 305 178 151 1029 876
Z—IV (1) 965 1829 178 178 152 121 870 781
Z—V (1) 965 1829 267 267 152 121 826 692
Z—V (2) 965 1829 267 267 152 121 826 692
Z—V (3) 965 1829 267 267 152 118 826 692
Zaghlool [20]
Z—V (4) 965 1829 267 267 152 121 826 692
Z—V (5) 965 1829 267 267 152 121 826 692
Z—V (6) 965 1829 267 267 152 121 826 692
Z—VI (1) 965 1829 356 356 152 121 781 603
M(T)/E/1 914 914 127 127 76 56 812 749
M(T)/E/2 914 914 127 127 76 56 812 749
C(T)/E/1 914 914 127 127 76 56 812 749
C(T)/E/2 914 914 127 127 76 56 812 749
C(T)/E/3 914 914 127 127 76 56 812 749
C(T)/E/4 914 914 127 127 76 56 812 749
Stamenkovic [23]
V/E/1 914 914 127 127 76 56 812 749
M(II)/E/1 914 914 127 127 76 56 812 749
C(II)/E/1 914 914 127 127 76 56 812 749
C(II)/E/2 914 914 127 127 76 56 812 749
C(II)/E/3 914 914 127 127 76 56 812 749
C(II)/E/4 914 914 127 127 76 56 812 749
Buildings 2022, 12, 2092 37 of 49
Table A3. Cont.
Hanson [22] D15 1143 1219 152 152 76 62 1067 991
Ritchie [25] 1 1350 1900 250 250 150 122 1175 1050
E1 711 1219 203 203 140 105 610 508
E2 711 1219 203 203 140 105 610 508
E4 711 1219 203 203 140 105 610 508
E1-1 1571 1719 203 203 140 105 1220 1118
E1-2 1571 1719 203 203 140 105 1220 1118
Sudarsana [26]
E1-3 1571 1719 203 203 140 105 1220 1118
E1-4 1571 1719 203 203 140 105 1220 1118
E2-1 961 2940 203 203 140 105 610 508
E2-2 961 2940 203 203 140 105 610 508
E2-3 961 2940 203 203 140 105 610 508
E2-4 961 2940 203 203 140 105 610 508
ZJESSS 1060 1770 250 250 150 119 850 725
Zaghloul [27]
ZJES 1060 1770 250 250 150 119 850 725
Table A4. Edge slab–column connections—Material properties.
L1 1.00% 558 192 46.80 28 3.40 9.50
L2 1.30% 558 192 44.70 28 3.00 9.50
L3 1.30% 558 192 45.10 28 3.10 9.50
L4 1.30% 558 192 46.00 28 3.30 9.50
L5 1.30% 558 192 51.40 28 4.10 9.50
L6 1.30% 558 192 52.10 28 4.30 9.50
Albuquerque [17] L7 1.50% 558 192 50.00 28 3.70 9.50
L8 1.40% 558 192 50.50 28 3.90 9.50
L9 1.50% 558 192 57.60 28 3.20 9.50
L10 1.50% 558 192 59.30 28 3.60 9.50
L11 1.50% 558 192 43.10 28 3.10 9.50
L12 1.50% 558 192 43.60 28 3.30 9.50
L13 1.50% 558 192 44.10 28 3.40 9.50
ES1 0.88% 398 188 33.80 28 2.70 19.00
ES2 0.88% 398 188 32.80 28 2.70 19.00
ES3 0.88% 398 188 51.30 28 3.10 19.00
Narayani [19] ES4 0.88% 398 188 50.00 28 3.31 19.00
ES5 0.88% 398 188 37.60 28 2.63 19.00
ES6 0.88% 398 188 40.40 28 2.23 19.00
ES7 0.88% 398 188 45.80 28 3.38 19.00
Buildings 2022, 12, 2092 38 of 49
Table A4. Cont.
Z—IV (1) 1.23% 476 207 27.34 28 2.99 19.05
Z—V (1) 1.23% 474 207 34.34 28 3.52 19.05
Z—V (2) 1.65% 474 207 40.47 28 3.61 19.05
Z—V (3) 2.23% 475 207 38.75 28 3.79 19.05
Zaghlool [20]
Z—V (4) 1.23% 475 207 35.03 28 4.10 19.05
Z—V (5) 1.23% 476 207 35.16 28 3.58 19.05
Z—V (6) 1.23% 476 207 31.30 28 3.63 19.05
Z—VI (1) 1.23% 476 207 25.99 28 2.83 19.05
M(T)/E/1 1.17% 413 192 30.34 7 4.19 9.53
M(T)/E/2 1.17% 413 192 33.09 7 4.37 9.53
C(T)/E/1 1.17% 413 192 38.47 7 4.71 9.53
C(T)/E/2 1.17% 413 192 32.41 7 4.33 9.53
C(T)/E/3 1.17% 413 192 33.99 7 4.43 9.53
C(T)/E/4 1.17% 413 192 34.34 7 4.45 9.53
Stamenkovic [23]
V/E/1 1.17% 413 192 35.85 7 4.55 9.53
M(II)/E/1 1.17% 413 192 36.20 7 4.57 9.53
C(II)/E/1 1.17% 413 192 34.82 7 4.48 9.53
C(II)/E/2 1.17% 413 192 35.51 7 4.53 9.53
C(II)/E/3 1.17% 413 192 34.89 7 4.49 9.53
C(II)/E/4 1.17% 413 192 36.54 7 4.59 9.53
Hanson [22] D15 1.15% 365 192 31.10 28 4.24 9.53
Ritchie [25] 1 1.12% 432 192 26.20 28 3.89 9.50
E1 0.90% 420 183 43.62 28 5.02 10.00
E2 0.90% 420 183 42.41 28 4.95 10.00
E4 0.90% 420 183 43.62 28 5.02 10.00
E1-1 1.60% 420 183 52.80 28 5.52 10.00
E1-2 1.60% 420 183 52.80 28 5.52 10.00
Sudarsana [26] E1-3 1.60% 420 183 55.00 28 5.64 10.00
E1-4 1.60% 420 183 52.80 28 5.52 10.00
E2-1 0.80% 420 183 52.80 28 5.52 10.00
E2-2 0.80% 420 183 52.80 28 5.52 10.00
E2-3 0.80% 420 183 55.00 28 5.64 10.00
E2-4 0.80% 420 183 55.00 28 5.64 10.00
ZJESSS 1.40% 400 192 42.00 28 4.93 10.00
Zaghloul [27]
ZJES 1.40% 400 192 42.00 28 4.93 10.00
Buildings 2022, 12, 2092 39 of 49
Table A5. Corner slab–column connections—Slab geometry.
Z—I (1) 1067 1067 178 178 152 121 965 1067
Z—II (1) 1067 1067 267 267 152 121 921 1067
Z—II (2) 1067 1067 267 267 152 121 921 1067
Zaghlool [20] Z—II (3) 1067 1067 267 267 152 118 921 1067
Z—II (4) 1067 1067 267 267 152 121 921 1067
Z—II (6) 1067 1067 267 267 152 121 921 1067
Z—III (1) 1067 1067 356 356 152 121 876 1067
C5 711 711 305 305 140 105 559 711
C6 711 711 305 305 140 105 559 711
Sudarsana [26]
C7 711 711 305 305 140 105 559 711
C8 711 711 305 305 140 105 559 711
S101 530 530 100 100 100 80 480 530
S201 530 530 100 100 100 80 480 530
S301 530 530 100 100 100 80 480 530
Desayi [28]
S102 530 530 100 100 100 80 480 530
S202 530 530 100 100 100 80 480 530
S302 530 530 100 100 100 80 480 530
SC1 1525 1525 300 300 125 100 1375 1525
SC2 1525 1525 300 300 125 100 1375 1525
SC3 1525 1525 300 300 125 100 1375 1525
SC4 1525 1525 220 220 125 100 1415 1525
SC5 1525 1525 220 220 125 100 1415 1525
Walker [29]
SC7 1525 1525 220 220 125 100 1415 1525
SC8 1000 1000 160 160 80 64 920 1000
SC9 1000 1000 160 160 80 64 920 1000
SC11 1000 700 160 160 80 60 920 1000
SC12 1000 700 300 300 80 60 850 1000
C/C/1 914 914 127 127 76 56 813 914
C/C/2 914 914 127 127 76 56 813 914
Stamenkovic [30]
C/C/3 914 914 127 127 76 56 813 914
C/C/4 914 914 127 127 76 56 813 914
NH1 1075 1075 250 250 150 114 910 1075
NH2 1075 1075 250 250 150 114 910 1075
Ghali [18] NH3 1075 1075 250 250 150 114 910 1075
NH4 1075 1075 250 250 150 114 910 1075
NH5 1075 1075 250 250 150 114 910 1075
Buildings 2022, 12, 2092 40 of 49
Table A6. Corner slab–column connections—Material description.
Z—I (1) 1.23% 379 207 32.68 28 4.34 19.05
Z—II (1) 1.23% 389 207 33.03 28 4.37 19.05
Z—II (2) 1.65% 405 207 33.44 28 4.39 19.05
Zaghlool [20] Z—II (3) 2.23% 451 207 27.72 28 4.00 19.05
Z—II (4) 1.23% 389 207 30.75 28 4.21 19.05
Z—II (6) 1.23% 381 207 33.58 28 4.40 19.05
Z—III (1) 1.23% 379 207 33.65 28 4.41 19.05
C5 1.11% 420 183 44.40 28 5.06 10.00
C6 1.11% 420 183 44.40 28 5.06 10.00
Sudarsana [26]
C7 1.11% 420 183 44.40 28 5.06 10.00
C8 1.11% 420 183 44.40 28 5.06 10.00
S101 0.53% 720 192 45.00 28 5.10 9.50
S201 0.80% 720 192 45.00 28 5.10 9.50
S301 1.07% 720 192 25.00 28 3.80 9.50
Desayi [28]
S102 0.53% 720 192 31.00 28 4.23 9.50
S202 0.80% 720 192 34.00 28 4.43 9.50
S302 1.07% 720 192 28.00 28 4.02 9.50
SC1 1.14% 595 192 43.30 28 5.00 20.00
SC2 1.11% 595 192 47.90 28 5.26 20.00
SC3 1.13% 595 192 37.40 28 4.65 20.00
SC4 1.14% 595 192 40.80 28 4.85 20.00
SC5 1.71% 595 192 46.50 28 5.18 20.00
Walker [29]
SC7 1.71% 595 192 43.80 28 5.03 20.00
SC8 1.37% 595 192 37.40 28 4.65 20.00
SC9 1.24% 595 192 34.30 28 4.45 20.00
SC11 1.27% 595 192 27.20 28 3.96 20.00
SC12 1.18% 595 192 40.70 28 4.85 20.00
C/C/1 1.17% 413 192 38.06 28 4.69 9.50
C/C/2 1.17% 413 192 35.37 28 4.52 9.50
Stamenkovic [30]
C/C/3 1.17% 413 192 32.27 28 4.32 9.50
C/C/4 1.17% 413 192 38.27 28 4.70 9.50
NH1 1.45% 440 200 41.50 28 4.90 9.50
NH2 1.45% 440 200 42.20 28 4.94 9.50
Ghali [18] NH3 1.45% 440 200 36.40 28 4.59 9.50
NH4 1.45% 440 200 36.90 28 4.62 9.50
NH5 1.45% 440 200 33.20 28 4.38 9.50
Buildings 2022, 12, 2092 41 of 49
Table A7. Database—Shear reinforcement.
Reference Name Type fy (MPa) Es (GPa) Φw (mm) s (mm)

L3 Shear hats 309.00 207.00 9.50 90.00
L4 Shear hats 238.00 207.00 6.50 90.00
Narayani [19] L5 Shear hats 355.00 207.00 13.00 90.00
L6 Shear hats 355.00 207.00 8.00 90.00
L10 Shear hats 355.00 207.00 8.00 90.00
Krüger [2] PP16B Stirrups 480.00 200.00 10.00 120.00
S3 Shear studs 535.00 211.00 10.00 100.00
Pina Ferreira [24] S4 Shear studs 535.00 211.00 10.00 100.00
S8 Shear studs 518.00 204.00 12.00 100.00
L9 Shear heads 587.00 188.00 8.00 100.00
L10 Shear heads 587.00 188.00 8.00 100.00
ES3 Stirrups 238.00 207.00 6.50 70.00
Albuquerque [17]
ES4 Stirrups 309.00 207.00 9.50 70.00
ES6 Stirrups 238.00 207.00 6.50 70.00
ES7 Stirrups 238.00 207.00 6.50 70.00
Zaghloul [27] ZJESSS Shear stud 345.00 192.00 12.70 90.00
NH3 Shear heads 440.00 200.00 6.00 57.00
Ghali [18]
NH5 Shear heads 440.00 200.00 6.00 85.00
Figure 12 illustrates the “Shear Hats” type of shear reinforcement.
Appendix B
Table A8. Internal slab–column connections—Tested to predicted shear capacity.
ACI [7] EC2 [8] MC 2010 [9]

Reference Name Test Pred Test Pred Test Pred
Test/Pred Test/Pred Test/Pred
(MPa) (MPa) (MPa) (MPa) (MPa) (MPa)
L1 2.58 1.89 1.37 1.34 1.40 0.96 2.49 3.44 0.73
L3 3.23 2.98 1.08 1.68 1.34 1.25 1.23 1.40 0.88
L4 3.67 2.25 1.63 1.91 1.50 1.28 1.40 1.62 0.87
Narayani [19]
L5 3.23 4.41 0.73 1.68 1.37 1.23 1.23 1.46 0.84
L6 3.02 2.88 1.05 1.64 1.45 1.13 1.48 1.92 0.77
L10 3.22 2.87 1.12 1.75 1.45 1.21 1.57 1.92 0.82
P16A 2.51 1.95 1.28 1.46 1.29 1.13 2.54 3.47 0.73
Krüger [2] P30A 2.67 1.95 1.37 1.49 1.29 1.16 2.65 3.49 0.76
PP16B 3.22 3.41 0.95 1.87 2.73 0.69 0.61 0.75 0.82
M2A 1.75 1.30 1.35 1.03 1.03 1.00 1.74 2.36 0.74
M4A 1.73 1.39 1.25 0.98 1.07 0.91 1.66 2.52 0.66
M2 2.43 1.67 1.45 1.43 1.22 1.17 2.39 3.04 0.79
M3 2.17 1.57 1.38 1.24 1.17 1.06 2.09 2.86 0.73
Moe [11] M6 2.25 1.70 1.33 1.25 1.18 1.05 2.25 3.09 0.73
M7 2.28 1.65 1.38 1.32 1.16 1.14 2.36 3.00 0.79
M8 2.19 1.64 1.34 1.14 1.15 0.99 2.12 2.98 0.71
M9 2.30 1.59 1.44 1.29 1.13 1.14 2.32 2.89 0.80
M10 2.16 1.52 1.43 1.15 1.10 1.05 2.11 2.76 0.77
Buildings 2022, 12, 2092 42 of 49
Table A8. Cont.
ACI [7] EC2 [8] MC 2010 [9]

B.3 3.20 2.04 1.57 1.91 1.53 1.25 3.17 3.70 0.86
B.4 3.01 2.01 1.49 1.74 1.51 1.15 2.86 3.66 0.78
Anis [21]
B.5 3.48 1.99 1.75 1.95 1.50 1.30 3.20 3.61 0.89
B.6 4.08 2.07 1.98 2.24 1.54 1.46 3.65 3.75 0.97
C/I/1 3.25 2.21 1.47 1.81 1.35 1.34 3.19 4.03 0.79
C/I/2 3.20 2.01 1.59 1.71 1.27 1.35 3.01 3.65 0.82
C/I/3 3.00 1.86 1.61 1.52 1.20 1.26 2.67 3.39 0.79
C/I/4 3.16 1.85 1.71 1.55 1.20 1.29 2.72 3.36 0.81
Stamenkovic [23]
C/Ir/1 3.68 1.75 2.10 1.98 1.16 1.72 3.58 3.09 1.16
C/Ir/2 3.87 1.99 1.94 2.01 1.26 1.60 3.61 3.63 0.99
C/Ir/3 1.92 1.97 0.98 1.02 1.25 0.82 1.85 3.59 0.51
C/Ir/4 1.65 1.90 0.87 0.84 1.22 0.69 1.50 3.46 0.43
A12 2.64 1.90 1.39 1.35 1.28 1.06 2.63 3.46 0.76
Hanson [22] B16 2.21 1.82 1.22 1.12 1.24 0.90 1.98 3.31 0.60
C17 1.94 1.98 0.98 1.21 1.32 0.92 1.81 3.60 0.50
S3 4.63 3.16 1.47 2.45 1.72 1.42 1.87 1.74 1.08
S4 4.83 2.70 1.79 2.57 2.34 1.10 1.33 1.18 1.13
Pina Ferreira [24]
S6 3.52 2.34 1.51 1.86 1.51 1.23 3.50 3.95 0.89
S8 5.62 3.05 1.84 3.03 2.32 1.31 1.71 1.42 1.21
Table A9. Edge slab–column connections—Tested to predicted shear capacity.
ACI [7] EC2 [8] MC 2010 [9]

L1 2.66 2.26 1.18 1.65 1.30 1.27 3.07 3.49 0.88
L2 2.94 2.21 1.33 2.52 1.39 1.81 1.91 3.80 0.50
L3 4.98 2.22 2.25 3.14 1.40 2.24 2.57 4.03 0.64
L4 4.80 2.24 2.14 2.87 1.41 2.04 2.39 4.07 0.59
L5 4.75 2.37 2.01 3.52 1.46 2.41 2.76 3.99 0.69
L6 5.31 2.38 2.23 3.58 1.47 2.44 2.88 4.19 0.69
Albuquerque [17] L7 6.58 2.33 2.82 3.94 1.52 2.60 3.28 4.24 0.77
L8 7.31 2.35 3.12 4.38 1.49 2.94 3.64 4.26 0.85
L9 4.57 2.72 1.68 3.91 2.59 1.51 1.34 1.93 0.69
L10 7.16 2.75 2.60 4.82 2.61 1.85 1.22 1.41 0.86
L11 6.62 2.17 3.06 4.06 1.44 2.81 3.35 3.94 0.85
L12 5.24 2.18 2.41 3.69 1.45 2.54 2.93 3.81 0.77
L13 7.55 2.19 3.45 4.63 1.46 3.18 3.82 3.95 0.97
ES1 2.83 1.92 1.48 2.95 1.12 2.64 2.36 3.42 0.69
ES2 2.02 1.89 1.07 1.74 1.11 1.57 2.29 3.27 0.70
ES3 2.61 1.61 1.62 1.88 1.14 1.65 1.80 2.43 0.74
Narayani [19] ES4 3.00 2.29 1.31 2.16 1.13 1.92 2.07 2.42 0.85
ES5 3.28 2.02 1.62 3.31 1.16 2.86 2.76 3.68 0.75
ES6 3.39 1.47 2.30 3.53 1.05 3.37 1.51 1.98 0.76
ES7 3.85 1.54 2.50 3.88 1.09 3.55 1.26 1.59 0.79
Buildings 2022, 12, 2092 43 of 49
Table A9. Cont.
ACI [7] EC2 [8] MC 2010 [9]

Z—IV (1) 2.91 1.73 1.69 1.06 1.16 0.91 3.24 3.14 1.03
Z—V (1) 2.93 1.93 1.51 0.98 1.25 0.78 2.83 3.52 0.81
Z—V (2) 3.72 2.10 1.77 1.91 1.46 1.31 4.03 3.82 1.06
Z—V (3) 4.24 2.05 2.07 2.17 1.53 1.41 4.57 3.73 1.22
Zaghlool [20] Z—V (4) 4.38 1.95 2.24 - - - - - -
Z—V (5) 3.59 1.96 1.84 3.13 1.26 2.48 2.34 3.56 0.66
Z—V (6) 3.24 1.85 1.75 0.91 1.22 0.75 2.83 3.36 0.84
Z—VI (1) 2.95 1.68 1.75 1.86 1.14 1.63 3.16 3.06 1.03
M(T)/E/1 4.43 1.82 2.44 - - - - - -
M(T)/E/2 4.35 1.90 2.29 - - - - - -
C(T)/E/1 3.25 2.05 1.59 2.62 1.28 2.04 3.92 3.39 1.16
C(T)/E/2 3.62 1.88 1.93 1.96 1.21 1.62 3.94 3.30 1.20
C(T)/E/3 3.77 1.92 1.96 0.89 1.23 0.73 2.98 3.50 0.85
C(T)/E/4 3.95 1.93 2.05 0.39 1.23 0.32 2.21 3.52 0.63
Stamenkovic [23]
V/E/1 4.37 1.98 2.21 3.84 1.25 3.07 2.85 3.33 0.86
M(II)/E/1 2.64 1.99 1.33 - - - - - -
C(II)/E/1 3.74 1.95 1.92 1.64 1.24 1.32 2.73 3.53 0.77
C(II)/E/2 3.28 1.97 1.67 1.25 1.25 1.00 2.48 3.58 0.69
C(II)/E/3 3.42 1.95 1.76 0.84 1.24 0.68 2.79 3.54 0.79
C(II)/E/4 2.96 1.99 1.48 0.46 1.26 0.37 2.54 3.63 0.70
Hanson [22] D15 3.89 1.84 2.11 0.34 1.19 0.29 1.80 3.35 0.54
Ritchie [25] 1 1.61 1.69 0.95 1.10 1.11 0.99 1.35 3.07 0.44
E1 2.60 2.18 1.19 1.36 1.22 1.11 2.92 3.96 0.74
E2 4.18 2.15 1.94 3.53 1.21 2.91 2.71 3.73 0.73
E4 1.61 2.18 0.74 1.24 1.22 1.01 1.99 3.96 0.50
E1-1 1.13 2.40 0.47 0.85 1.58 0.54 1.13 4.36 0.26
E1-2 3.26 2.40 1.36 0.94 1.58 0.59 3.04 4.36 0.70
Sudarsana [26] E1-3 3.99 2.45 1.63 3.27 1.60 2.04 5.04 3.73 1.35
E1-4 2.79 2.40 1.16 1.21 1.58 0.77 3.02 4.36 0.69
E2-1 2.64 2.40 1.10 1.39 1.25 1.11 2.97 4.36 0.68
E2-2 2.62 2.40 1.09 1.90 1.25 1.52 3.19 4.31 0.74
E2-3 5.28 2.45 2.16 3.49 1.27 2.75 4.41 3.86 1.14
E2-4 2.39 2.45 0.98 2.12 1.27 1.67 3.10 4.35 0.71
ZJESSS 4.93 4.02 1.23 1.76 2.02 0.87 1.21 1.07 1.13
Zaghloul [27]
ZJES 2.52 2.14 1.18 1.52 1.40 1.09 2.87 3.89 0.74
Buildings 2022, 12, 2092 44 of 49
Table A10. Corner slab–column connections—Tested to predicted shear capacity.
ACI [7] EC2 [8] MC 2010 [9]

Z—I (1) 2.89 1.89 1.53 1.46 1.23 1.18 2.69 3.43 0.78
Z—II (1) 3.38 1.90 1.78 2.50 1.24 2.02 3.20 3.45 0.93
Z—II (2) 4.62 1.91 2.42 3.21 1.37 2.34 4.26 3.47 1.23
Zaghlool [20] Z—II (3) 5.13 1.74 2.95 3.38 1.37 2.46 4.57 3.16 1.45
Z—II (4) 2.00 1.83 1.09 - - - - - -
Z—II (6) 3.14 1.91 1.64 1.49 1.24 1.20 2.48 3.48 0.71
Z—III (1) 3.06 1.91 1.60 3.01 1.25 2.42 3.01 3.48 0.86
C5 1.69 2.20 0.77 1.38 1.32 1.04 1.52 4.00 0.38
C6 2.99 2.20 1.36 2.41 1.32 1.83 2.68 4.00 0.67
Sudarsana [26]
C7 2.78 2.20 1.26 2.08 1.32 1.58 2.41 4.00 0.60
C8 2.42 2.20 1.10 2.18 1.32 1.65 2.29 4.00 0.57
S101 3.86 2.21 1.74 1.49 1.04 1.44 3.44 4.02 0.86
S201 5.56 2.21 2.51 2.15 1.19 1.81 4.96 4.02 1.23
S301 6.52 1.65 3.95 2.52 1.08 2.34 5.82 3.00 1.94
Desayi [28]
S102 4.87 1.84 2.65 2.39 0.92 2.61 4.78 3.34 1.43
S202 3.80 1.92 1.98 1.86 1.08 1.72 3.73 3.50 1.07
S302 3.99 1.75 2.29 1.95 1.12 1.75 3.92 3.17 1.23
SC1 2.38 2.17 1.10 1.98 1.32 1.49 2.14 3.95 0.54
SC2 2.25 2.28 0.99 1.81 1.35 1.34 2.00 4.15 0.48
SC3 2.82 2.02 1.40 1.80 1.25 1.44 2.28 3.67 0.62
SC4 2.53 2.11 1.20 1.69 1.30 1.30 2.29 3.83 0.60
SC5 2.92 2.25 1.30 2.17 1.55 1.40 2.78 4.09 0.68
Walker [29]
SC7 4.02 2.18 1.84 2.17 1.52 1.43 3.34 3.97 0.84
SC8 2.35 2.02 1.16 2.06 1.34 1.54 2.31 3.67 0.63
SC9 2.82 1.93 1.46 2.06 1.26 1.64 2.55 3.51 0.72
SC11 2.02 1.72 1.17 2.30 1.17 1.96 2.47 3.13 0.79
SC12 1.97 2.02 0.98 3.56 1.31 2.72 1.83 3.83 0.48
C/C/1 2.67 2.04 1.31 2.09 1.28 1.64 3.65 3.70 0.99
C/C/2 2.52 1.96 1.28 1.34 1.25 1.07 3.16 3.57 0.88
Stamenkovic [30]
C/C/3 2.27 1.87 1.21 0.67 1.21 0.55 2.61 3.41 0.77
C/C/4 1.99 2.04 0.98 0.30 1.28 0.24 2.16 3.71 0.58
NH1 4.43 2.13 2.08 2.99 1.41 2.12 4.04 3.87 1.05
NH2 4.15 2.14 1.94 2.83 1.42 2.00 3.80 3.90 0.98
Ghali [18] NH3 4.28 2.58 1.66 2.98 2.13 1.40 1.58 1.48 1.07
NH4 2.79 2.00 1.39 - - - - - -
NH5 5.69 1.95 2.93 3.64 2.01 1.82 1.35 0.94 1.44
Buildings 2022, 12, 2092 45 of 49
Table A11. Internal slab–column connections—SCIA (FEM) [33] results compared with shear stress
according to ACI 318-19, Equation (1), and capacity results for ACI 319-19 [7].
ACI [7] SCIA (FEM) [33]

Reference Name
Pred (MPa) Tested (MPa) Result (MPa) FEM Result/Pred Tested/FEM Result
L1 1.89 2.58 4.24 2.24 0.61
L3 2.98 3.23 2.48 0.83 1.30
L4 2.25 3.67 2.83 1.26 1.30
Narayani [19]
L5 4.41 3.23 2.48 0.56 1.30
L6 2.88 3.02 2.33 0.81 1.30
L10 2.87 3.22 2.48 0.86 1.30
P16A 1.95 2.51 2.90 1.49 0.86
Krüger [2] P30A 1.95 2.67 2.96 1.51 0.90
PP16B 3.41 3.22 3.77 1.11 0.85
M2A 1.30 1.75 2.54 1.95 0.69
M4A 1.39 1.73 2.89 2.09 0.60
M2 1.67 2.43 3.58 2.14 0.68
M3 1.57 2.17 3.51 2.23 0.62
Moe [11] M6 1.70 2.25 3.23 1.90 0.70
M7 1.65 2.28 2.84 1.72 0.80
M8 1.64 2.19 3.66 2.24 0.60
M9 1.59 2.30 3.15 1.98 0.73
M10 1.52 2.16 3.42 2.26 0.63
B.3 2.04 3.20 3.80 1.87 0.84
B.4 2.01 3.01 3.28 1.63 0.92
Anis [21]
B.5 1.99 3.48 3.77 1.90 0.92
B.6 2.07 4.08 4.47 2.17 0.91
C/I/1 2.21 3.25 3.92 1.77 0.83
C/I/2 2.01 3.20 3.91 1.95 0.82
C/I/3 1.86 3.00 3.72 2.00 0.81
C/I/4 1.85 3.16 3.96 2.14 0.80
Stamenkovic [23]
C/Ir/1 1.75 3.68 3.20 1.83 1.15
C/Ir/2 1.99 3.87 3.31 1.66 1.17
C/Ir/3 1.97 1.92 1.64 0.83 1.17
C/Ir/4 1.90 1.65 1.37 0.72 1.20
Buildings 2022, 12, 2092 46 of 49
Table A12. Edge slab–column connections—SCIA (FEM) [33] results compared with shear stress

Reference Name
A12 1.90 2.64 3.40 1.79 0.78
Hanson [22] B16 1.82 2.21 4.53 2.49 0.49
C17 1.98 1.94 2.70 1.37 0.72
S3 3.16 4.63 2.13 0.67 2.17
S4 2.70 4.83 1.88 0.70 2.57
Pina Ferreira [24]
S6 2.34 3.52 12.76 5.46 0.28
S8 3.05 5.62 2.41 0.79 2.33
L1 2.26 2.66 2.59 1.15 1.03
L2 2.21 2.94 2.50 1.13 1.18
L3 2.22 4.98 2.92 1.32 1.71
L4 2.24 4.80 2.70 1.21 1.78
L5 2.37 4.75 3.33 1.41 1.43
L6 2.38 5.31 3.33 1.40 1.60
Albuquerque [17] L7 2.33 6.58 3.67 1.57 1.79
L8 2.35 7.31 4.07 1.74 1.80
L9 2.72 4.57 2.59 0.95 1.76
L10 2.75 7.16 2.77 1.01 2.58
L11 2.17 6.62 3.77 1.74 1.76
L12 2.18 5.24 3.46 1.59 1.51
L13 2.19 7.55 4.28 1.95 1.76
ES1 1.92 2.83 2.68 1.40 1.06
ES2 1.89 2.02 2.23 1.18 0.91
ES3 1.61 2.61 1.37 0.85 1.91
Narayani [19] ES4 2.29 3.00 1.56 0.68 1.92
ES5 2.02 3.28 3.01 1.49 1.09
ES6 1.47 3.39 1.61 1.09 2.11
ES7 1.54 3.85 2.02 1.31 1.91
Z—IV (1) 1.73 2.91 1.71 0.99 1.70
Z—V (1) 1.93 2.93 1.85 0.96 1.58
Z—V (2) 2.10 3.72 2.13 1.02 1.74
Z—V (3) 2.05 4.24 3.67 1.79 1.16
Zaghlool [20]
Z—V (4) 1.95 4.38 1.20 0.61 3.66
Z—V (5) 1.96 3.59 2.99 1.53 1.20
Z—V (6) 1.85 3.24 1.56 0.85 2.07
Z—VI (1) 1.68 2.95 4.30 2.56 0.69
M(T)/E/1 1.82 4.43 3.41 1.87 1.30
M(T)/E/2 1.90 4.35 3.34 1.76 1.30
C(T)/E/1 2.05 3.25 2.92 1.43 1.11
C(T)/E/2 1.88 3.62 3.87 2.06 0.93
C(T)/E/3 1.92 3.77 4.11 2.14 0.92
C(T)/E/4 1.93 3.95 3.57 1.85 1.11
Stamenkovic [23]
V/E/1 1.98 4.37 4.22 2.13 1.04
M(II)/E/1 1.99 2.64 3.20 1.61 0.82
C(II)/E/1 1.95 3.74 6.91 3.55 0.54
C(II)/E/2 1.97 3.28 5.63 2.86 0.58
C(II)/E/3 1.95 3.42 5.78 2.97 0.59
C(II)/E/4 1.99 2.96 4.26 2.14 0.70
Buildings 2022, 12, 2092 47 of 49
Table A12. Cont.

Reference Name
Hanson [22] D15 1.84 3.89 1.67 0.91 2.32
Ritchie [25] 1 1.69 1.61 1.35 0.80 1.19
E1 2.18 2.60 5.02 2.30 0.52
E2 2.15 4.18 2.53 1.18 1.65
E4 2.18 1.61 2.37 1.09 0.68
E1-1 2.40 1.13 0.83 0.35 1.36
E1-2 2.40 3.26 6.63 2.76 0.49
Sudarsana [26] E1-3 2.45 3.99 5.29 2.16 0.75
E1-4 2.40 2.79 5.64 2.35 0.50
E2-1 2.40 2.64 5.19 2.16 0.51
E2-2 2.40 2.62 4.37 1.82 0.60
E2-3 2.45 5.28 3.57 1.46 1.48
E2-4 2.45 2.39 3.18 1.30 0.75
ZJESSS 4.02 4.93 2.20 0.55 2.24
Zaghloul [27]
ZJES 2.14 2.52 4.80 2.24 0.52
Table A13. Corner slab–column connections—SCIA (FEM) [33] results compared with shear stress

Reference Name
Z—I (1) 1.89 2.89 1.83 0.97 1.58
Z—II (1) 1.90 3.38 3.77 1.99 0.90
Z—II (2) 1.91 4.62 4.28 2.24 1.08
Zaghlool [20] Z—II (3) 1.74 5.13 4.13 2.38 1.24
Z—II (4) 1.83 2.00 4.03 2.20 0.49
Z—II (6) 1.91 3.14 2.16 1.13 1.45
Z—III (1) 1.91 3.06 5.08 2.65 0.60
C5 2.20 1.69 2.44 1.11 0.69
C6 2.20 2.99 4.32 1.96 0.69
Sudarsana [26]
C7 2.20 2.78 4.21 1.91 0.66
C8 2.20 2.42 3.59 1.63 0.68
S101 2.21 3.86 3.72 1.68 1.04
S201 2.21 5.56 5.36 2.42 1.04
S301 1.65 6.52 6.29 3.81 1.04
Desayi [28]
S102 1.84 4.87 7.89 4.29 0.62
S202 1.92 3.80 6.16 3.20 0.62
S302 1.75 3.99 6.46 3.70 0.62
Buildings 2022, 12, 2092 48 of 49
Table A13. Cont.

Reference Name
SC1 2.17 2.38 3.88 1.79 0.61
SC2 2.28 2.25 3.56 1.56 0.63
SC3 2.02 2.82 3.53 1.75 0.80
SC4 2.11 2.53 2.70 1.28 0.94
SC5 2.25 2.92 3.49 1.55 0.84
Walker [29] SC7 2.18 4.02 3.49 1.60 1.15
SC8 2.02 2.35 5.06 2.50 0.47
SC9 1.93 2.82 5.06 2.62 0.56
SC11 1.72 2.02 5.23 3.04 0.39
SC12 2.02 1.97 3.61 1.79 0.55
C/C/1 2.04 2.67 6.69 3.29 0.40
C/C/2 1.96 2.52 6.13 3.12 0.41
Stamenkovic [30]
C/C/3 1.87 2.27 5.37 2.87 0.42
C/C/4 2.04 1.99 4.66 2.28 0.43
NH1 2.13 4.43 3.59 1.69 1.24
NH2 2.14 4.15 1.39 0.65 2.99
Ghali [18] NH3 2.58 4.28 7.72 2.99 0.55
NH4 2.00 2.79 5.36 2.67 0.52
NH5 1.95 5.69 8.91 4.58 0.64
References
1. Wight, J.; MacGregor, J. Analysis, and Design. In Reinforced Concrete Mechanics & Design, 6th ed.; Pearson: London, UK, 2010;
Volume 1.
2. Krüger, G. Résistance au Poinçonnement Excentré des Planchers-Dalles; EPFL: Écublens, Switzerland, 1999.
3. Muttoni, A.; Ruiz, M.F.; Simões, J.T. The theoretical principles of the critical shear crack theory for punching shear failures and
derivation of consistent closed-form design expressions. Struct. Concr. 2018, 19, 174–190. [CrossRef]
4. Mirzaei, Y. Post punching behaviour of reinforced concrete slab-column connections. In Proceedings of the 7th International FIB
PhD Symposium, Stuttgart, Germany, 11–13 September 2008.
5. Kinnunen, S.; Nylander, H. Punching of concrete slabs without shear reinforcement. Elander 1960, 158, 112.
6. Muttoni, A.; Ruiz, M.F. The levels-of-approximation approach in MC 2010: Application to punching shear provisions. Struct.
Concr. 2012, 13, 32–41. [CrossRef]
7. ACI Committee 318. ACI CODE-318-19: Building Code Requirements for Structural Concrete and Commentary; American Concrete
Institute: Farmington Hills, MI, USA, 2019.
8. European Committee for Standardization and British Standards Institution. Eurocode 2: Design of Concrete Structures; British
Standards Institution: London, UK, 2005.
9. The International Federation for Structural Concrete. fib Bulletin 55. Model Code 2010 First Complete Draft; fib: Lausanne,
Switzerland, 2010; Volume 1. [CrossRef]
10. Park, H.; Choi, K. Improved Strength Model for Interior Flat Plate-Column Connections Subject to Unbalanced Moment. ASCE J.
Struct. Eng. 2006, 694, 694–704. [CrossRef]
11. Moe, J. Shearing Strength of Reinforced Concrete Slabs and Footings under Concentrated Loads; Development Department Bulletin No.
D47; Portland Cement Association: Skokie, IL, USA, 1961.
12. ACI-ASCE Committee 426. The Shear Strength of Reinforced Concrete Members. Chapter 5, Shear Strength of Slabs. Proc. ASCE
J. Struct. Div. 1974, 100, 1543–1591. [CrossRef]
13. Mast, P.E. Stresses in Flat Plates Near Columns. J. Proc. 1970, 67, 761–768.
14. The International Federation for Structural Concrete. fib Bulleting 2. Textbook on Behavior, Design and Performance Updated Knowledge
of the CEB/FIP Model Code 1990; fib: Lausanne, Switzerland, 1999; Volume 2. [CrossRef]
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15. Muttoni, A. Punching Shear Strength of Reinforced Concrete Slabs without Transverse Reinforcement. ACI Struct. J. 2008,
105, 440–450.
16. Fernández Ruiz, M.; Muttoni, A. Application of Critical Shear Crack Theory to Punching of Reinforced Concrete Slabs with
Transverse Reinforcement. ACI Struct. J. 2009, 106, 485–494.
17. Albuquerque, N.G.B.; Melo, G.S.; Vollum, R.L. Punching Shear Strength of Flat Slab-Edge Column Connections with Outward
Eccentricity of Loading. ACI Struct. J. 2016, 113, 1117–1129. [CrossRef]
18. Hammil, N.; Ghali, A. Punching Shear Resistance of Corner Slab-Column Connections. ACI Struct. J. 1994, 91, 697–707. [CrossRef]
19. Narayani, N. Shear Reinforcement in Reinforced Concrete Column Heads. Ph.D. Thesis, Faculty of Engineering, Imperial College
of Science and Technology, London, UK, 1971.
20. Zaghlool, E.E.-D.R.F. Strength and Behaviour of Corner and Edge Column-Slab Connections in Reinforced Concrete Flat Plates.
Ph.D. Thesis, University of Calgary, Calgary, AB, Canada, 1971.
21. Anis, N.N. Shear Strength of Reinforced Concrete Flat Slabs without Shear Reinforcement. Ph.D. Thesis, Imperial College London,
London, UK, 1970.
22. Hanson, N.W.; Hanson, J.M. Shear and Moment Transfer between Concrete Slabs and Columns. J. PCA Res. Dev. Lab. 1968,
11, 2–16. Available online: https://www.concrete.org/publications/internationalconcreteabstractsportal/m/details/id/19463
(accessed on 3 April 2022).
23. Stamenkovic, A. Local Strength of Flat Slabs At Column Heads. Ph.D. Thesis, Imperial College London, London, UK, 1970.
24. De Pina Ferreira, M.; Oliveira, M.H.; Melo, G.S.S.A. Tests on the punching resistance of flat slabs with unbalanced moments. Eng.
Struct. 2019, 196, 109311. [CrossRef]
25. Ritchie, M.; Ghali, A.; Dilger, W.; Gayed, R.B. Unbalanced Moment Resistance by shear in Slab-Column Connections: Experimental
Assessment. ACI Struct. J. 2006, 103, 74–82.
26. Sudarsana, I.K. Punching Shear in Edge and Corner Column Slab Connections of Flat Plate Structures. Ph.D. Thesis, Department
of Civil Engineering, University of Ottawa, Ottawa, ON, Cananda, December 2001.
27. Zaghloul, A. Punching Shear Strength of Interior and Edge Column-Slab Connections in CFRP Reinforced Flat Plate Structures
Transferring Shear and Moment. Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Ottawa,
Ottawa, ON, Canada, February 2007.
28. Desayi, P.; Seshadri, H.K. Punching shear strength of flat slab corner column connections. In Part 1. Reinforced Concrete Connections;
Department of Civil Engineering, Indian Institute of Science: Bangalore, India, 1997.
29. Walker, P.R.; Regan, P.E. Corner column-slab connections in concrete flat plates. ASCE J. Struct. Eng. 1987, 113, 704–720. [CrossRef]
30. Stamenkovic, A.; Chapman, J.C. Local strength at column heads in flat slabs subjected to a combines vertical and horizontal
loading. Proc. ICE 1974, 57, 205–232.
31. Vargas, D.; Lantsoght, E.; Genikomsou, K. Spreadsheet for Flat Slabs in Eccentric Punching Shear: Experimental Database and Analysis;
Zenodo: Quito, Ecuador, 2022. [CrossRef]
32. Sarveghadi, M.; Gandomi, A.H.; Bolandi, H.; Alavi, A.H. Development of prediction models for shear strength of SFRCB using a
machine learning approach. Neural Comput. Appl. 2019, 31, 2085–2094. [CrossRef]
33. Nemetschek Group. SCIA Downloads. 17 May 2022. Available online: https://www.scia.net/en/scia-engineer/downloads
(accessed on 3 April 2022).
34. Lantsoght, E. Database of Shear Experiments on Steel Fiber Reinforced Concrete Beams without Stirrups. Materials 2019, 12, 917.
[CrossRef] [PubMed]
35. Vargas, D.; Lantsoght, E.; Genikomsou, K. Spreadsheet Validation for Flat slabs in Eccentric Punching Shear Experimental Database and
Analysis; Zenodo: Quito, Ecuador, 2022. [CrossRef]
36. Ngo, T. Punching shear resistance of high-strength concrete slabs. Electron. J. Struct. Eng. 2001, 1, 52–59. Available online:
https://ejsei.com/EJSE/article/view/14 (accessed on 3 April 2022). [CrossRef]
37. Guandallini, S.; Burdet, O.L.; Muttoni, A. Punching Tests of Slabs with Low Reinforcement Ratios. ACI Struct. J. 2009, 106, 87–95.
38. Carrera, B.; Lantsoght, E.O.L.; Alexander, S.D.B. Application of Strip Model to Edge Column-Lab Connections Loaded with Outward
Eccentricity; ACI: Farmington Hills, MI, USA, 2022; Volume 353, pp. 124–141. Available online: https://www.concrete.org/
publications/internationalconcreteabstractsportal.aspx?m=details&id=51737115 (accessed on 3 April 2022).

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1 Politécnico, Universidad San Francisco de Quito, Quito 170901, Ecuador

Academic Editors: Elena Ferretti and 1. Introduction

Buildings 2022, 12, 2092. https://doi.org/10.3390/buildings12122092 https://www.mdpi.com/journal/buildings

MacGregor and Wight [1] define vu using the following equation:

where γf is the fraction of moment transmitted by flexure

The ultimate shear capacity vn is calculated as follows, with vu as determined by

2.1.2. NEN-EN 1992-1-1:2005

Figure 5. Shear distribution due to an unbalanced moment at a slab–column connection, modified

The punching shear resistance of slabs with shear reinforcement is calculated as

2.1.3. Model Code 2010

Figure 8. Resultant of shear forces, modified from Ref. [9].

The control perimeter b0 is determined as

The factor ke represents the coefficient of eccentricity:

VRd = VRd,c + VRd,s ≥ VEd (26)

where dg is the maximum aggregate size.

VRd,s = ∑ Asw ke σswd sin α (30)

Figure 9. Shear reinforcement resisting shear crack, based on Ref. [9].

The stress σswd is calculated as

rsx = 0.22L x ; rsy = 0.22Ly (33)

Figure 10 illustrates Lx and Ly [9].

2.2. Database of Eccentric Punching Shear Experiments

Figure 11. Cont.

with fc as the cylinder concrete compressive strength in [MPa].

Figure 12. Shear hat setup, as used in Ref. [19].

2.2.2. FEM Modeling Process

Figure 13. Cont.

Figure 14. Cont.

2.2.3. Parameter Ranges in the Database

Table 1. Ranges of parameters in the database.

Parameter Min Max Mean Median STD

Figure 15. Cont.

Thus, the influence of different important parameters is studied as a function of the

3.2. Comparison with Code Predictions

Slabs without Shear Reinforcement

AVG STD COV (%)

AVG STD COV (%)

3.3. Influence of Parameters on Tested to Predicted Punching Capacities

Figure 21. Cont.

Figure 21. Cont.

Asw area of the shear reinforcement for NEN-EN 1992-1-1:2005

b1,MC basic control perimeter for Model Code 2010

Table A1. Internal slab–column connections—Slab geometry.

Table A2. Internal slab–column connections—Material properties.

Table A3. Edge slab–column connections—Slab geometry.

Table A3. Cont.

Table A4. Edge slab–column connections—Material properties.

Table A4. Cont.

Table A5. Corner slab–column connections—Slab geometry.

Table A6. Corner slab–column connections—Material description.

Table A7. Database—Shear reinforcement.

Reference Name Type fy (MPa) Es (GPa) Φw (mm) s (mm)

Table A8. Internal slab–column connections—Tested to predicted shear capacity.

ACI [7] EC2 [8] MC 2010 [9]

Table A8. Cont.

ACI [7] EC2 [8] MC 2010 [9]

Table A9. Edge slab–column connections—Tested to predicted shear capacity.

ACI [7] EC2 [8] MC 2010 [9]

Table A9. Cont.