コンクリート工学年次論文集，Vol.31，No.2，2009- Technical Paper -PUNCHING STRENGTH OF TWO-WAY SLABS STRENGTHENEDEXTERNALLY WITH CFRP SHEETS
Ahmed Sabry FARGHALY*1 , Tamon UEDA*2
ABSTRACTIn this paper, the strengthening of two-way slabs using CFRP is evaluated experimentally andanalytically. The reinforcement ratio equal to 1.4% was chosen to serve the purpose of demarcating thepunching shear failure mode. Results show that the punching capacity of two-way slabs can increase to
40% over that of the reference specimen. Moreover, a 3D FEM program named “3D CAMUI”, which
was developed at Hokkaido University, was used to simulate the experimented slabs. Very good
agreement is obtained in terms of load carrying capacity and modes of failure.
Keywords: concrete, continuous fibers, finite element method, interfacial shear, punching shear, slab.

1. INTRODUCTION
Extensive applications of the fiber-reinforced
polymer (FRP) materials as new construction materials
have been recently accomplished. FRP materials arelightweight, high strength, and no-corrosive materials.
By virtue of these advantages, there is a wide range ofrecent, current, and potential applications of thesematerials that covers both new and existing structures.
Among different types of FRP materials, a carbon fiberreinforced polymer (CFRP) is used extensively in the
structural engineering field.
CFRP materials have been used for strengthening
reinforced concrete beams, columns, and one-way
slabs. The flexural capacity of concrete beams can beincreased by bonding CFRP sheets, strips, or laminates
to the tension side [1, 2]. In addition, the shear strengthof concrete beams can be increased by gluing CFRP
laminates to the concrete web at locations of high shear
stresses [3, 4].
Some research works dealt with the strengthening of
one-way slabs using FRP materials in which slabs weretreated in a very similar way to beams [5, 6]. Steelplates have been used in two-way slab punching shear
strengthening [7, 8]. Some studies have been conductedon the use of FRP for the shear strengthening of
reinforced concrete two-way slabs. These include
investigations where the slabs were strengthened using
FRP laminates around a central stub column [9, 10] orbonded over the whole width of the slab [11].
The determination of the structural behavior of
CFRP strengthened concrete slabs requires extensive
experimental and/or advanced analytical methods. As
far as theoretical methods are concerned, Reitman andYankelevsky [12]; have developed a nonlinear finiteelement grid analysis based on yield-line theory. Seimet al. [13] have used a beam-analogy technique toobtain an approximate solution for the overall behaviorof one-way slabs. Other researchers have employedfinite-element packages to investigate the structural
behavior of both un-strengthened [14] as well as CFRPstrengthened slabs [15, 16].
In the analysis of FRP-strengthened concreteelements, two approaches have been proposed tosimulate debonding. One method, referred to as themeso-scale analysis, involves simulating the cracking
and failure of the concrete elements adjacent to theadhesive layer [17]. This requires a very fine finiteelement mesh, with element sizes being one ordersmaller than the thickness of the fracture layer of theconcrete [18]. The meso-scale approach, which is basedon the fixed angle crack model, has the capability to
trace the crack paths as the deformation progresses. In
the second approach, interface elements having apredefined bond-slip relationship are used to link the
FRP and the concrete elements [17]. The meso-scalemodel is difficult to be implemented in the case of thethree dimensional modeling of two-way slabs, andrequires extensive computational resources. Thus, inthis study we adopt the second approach and implement
special interface elements to represent the interfacial
behavior between the concrete and FRP. Results arepresented in terms of load-deflection relationships,
ultimate load capacities, failure modes, and interfacialslip and stress distributions. The numerical predictions
are compared with test data, and very good agreement
is obtained.
2. EXPERIMENTAL PROGRAM
2.1. Test Specimens and Materials
Three specimens consisting of a 1600 mm X 1600

*1 JSPS Post-Doctoral Fellow, Div. of Built Environment, Hokkaido University, Dr.E., JCI Member*2 Professor, Div. of Built Environment, Hokkaido University, Dr.E., JCI Member-493-

Table 1 Specimens and material properties
CFRP sheet
ffrp
width
Thick
Efrp
(MPa)
(GPa)
(mm)
(mm)
SC
44.7
356
5.0
None
None
None
None
SF5
33.5
356
5.4
50
0.167
230
3500
SF10
39.6
356
5.4
100
0.167
230
3500
f’c : concrete compressive strength (MPa), fy : steel yielding strength (MPa), a/d : shear span-depth retio, Efrp :Modulus of Elasticity of CFRP (GPa), ffrp : tensile strength of CFRP (MPa).
f’c
(MPa)

Slab

fy
(MPa)

a/d

120

mm X 120 mm square slab with 100 mm X 100 mm
central loading point. The slabs were simply supported
over the four edges, thus permitting the corner to lift
when load was applied. Typical dimensions andrelevant reinforcement details are shown in Fig. 1.
CFRP flexible sheets of two different widths were
externally bonded to the tension face of the slab in two
perpendicular directions, parallel to the internal tension
reinforcement. The sheets were applied in one layer andto avoid debonding failure of the CFRP sheets, thesheets were extended along the full dimension of theslab. Two slabs were strengthened with CFRP while theremaining one is kept as a control specimen. Test
parameters, and details of each specimen are provided
in Table 1. Reinforcements were placed along two
perpendicular directions with average effective depth tothe center of the two layers of 97 mm.

100

650

100

650

a – Concrete dimension

19

8Ø10/dir15Ø13/dirb – Reinforcement details
7 x 200100
SF10Upper rft.

1400
Lower rft.

SF5

2.2. Test Procedure and Measurements
The specimens were mounted on to four steel I
beams with 30 mm wide pedestals on the four sides andloaded centrally with a monotonically load increase
until failure. The measurements included the magnitudeof the applied load, deflection of the slab at center andedges, and strain in the reinforcing bars and CFRP
sheets. The strain in the CFRP sheets was measured bystrain gauges attached at mid-width of the sheets.
3. OUT LINE OF NUMERICAL SIMULATION

100

1600

100

Two-way slabs with low or medium reinforcement
ratios tend to fail in flexure rather than in punching
shear. For two-way slabs that have reinforcement ratiosof 1.0% and more, the mode of failure tends to be thepunching shear type of failure [19]. Based on thisobservation; specimens with reinforcement ratio of
1.4% are designed to experience the punching shear
failure mode.

c – Reinforcement and FRP configuration
Unit: mmFig. 1 Details of specimen.

3.1. Finite Element Program
In this study, analyses were carried out with a 3D
nonlinear FE program named “3D CAMUI”, which was
created by the Laboratory of Engineering for
Maintenance System of Hokkaido University. “3D
CAMUI” was revised by the authors to analyze thestrengthened members with CFRP. It is based on thefinite element method and reproduces the nonlinear
material behavior characterizing composite structuresby superimposing the elasto-plastic behavior of the steel
plate and the tensile cracking of the concrete. The
Newton-Raphson method was used for non-linear
solutions. For the constitutive law of concrete before
cracking, a three-dimensional elasto-plastic and fracture
model [20] that considers the effect of confinement,
deformability and bi-axial compression in the concrete
constitutive law was applied. A three-dimensional
failure criterion in tension-tension and tensioncompression was developed by modifying an existing
two-dimensional failure criterion [21]. A constitutive
model for concrete after cracking has also been applied[22]. When the first crack occurs, the strains in the
global coordinate system are transformed into the local
coordinate system. In the case of a second crack, one of
the two axes in the plane coincides with the direction of
the intersecting line between the first and second crack
plane. Two local systems share one of their axes andanother axis in the plane is in the direction where thecrack opens. After calculating stresses from the strains-494-

in the crack coordinate system using constitutive laws,
the stresses are retransformed into stresses in the global
coordinate system and superimposed. Shear stresstransferred along crack is calculated based on aconstitutive law proposed by Li et. al [23]. A linear
elastic orthotropic constitutive relation is adopted for
the CFRP sheets.
3.2. CFRP-Concrete Interfacial Model
The mechanical behavior of the CFRP-concreteinterface is modeled as a relationship between the local
shear stress, τ, and the slip, s, between the CFRP
laminate and the concrete. The area under the τ-s curve
represents the interfacial fracture energy, Gf, whichcorresponds to the energy per unit bond area requiredfor complete debonding. The bond-slip relationship is
employed in this study proposed by Dai et al, [24]. The
τ-s relationship is given in Eq. 1:

Bond Stress (MPa)τ = 2 . B . G f . (exp(− B . s ) − exp(− 2 B . s ))
8
7
6
5
4
3
2
1
0

integration points in the interface can be calculated
from the displacement at each node [25]. And 8 nodes
shell element is representing the CFRP sheet [26].
Because of symmetry, a quarter of each specimen was
analyzed. The various strengthening configurations
considered are shown in Fig. 4. Prescribed
displacements were applied at the loading point directly.
The material properties used for the analysis are shownin Table 1. The tensile strength and modulus ofelasticity of the concrete were calculated from thecompressive strength, while Poisson's ratio was set at
0.2 (Standard Specifications for Concrete StructuresStructural Performance Verification - JSCE, 2002) [27].
All other properties were measured throughexperiments.
η

8
4

16

(τmax , so)

125Completedebonding

13
9

3

14

11

(1)

Debonding initiation

7

15

6
2

ξ

10
Concrete
Element

Interfacial Bond
Element

CFRP Sheet

1

Fig. 3 16-node isoparametric joint element
Gf
Plane concrete
R.C. elem

0

0.1

0.2

0.3

0.4

0.5

0.6

CFRP

Slip (mm)Steel plate

Fig. 2 CFRP-concrete interfacial model

Restricted in Plane
due to symmetry

One advantage of the τ-s interfacial model is its
simplicity and rigorous analytical procedure. Anotheradvantage is that parameters like the maximum bondstress and the corresponding slip value (Fig. 2), which
are difficult to calibrate directly from pullout test
results, can be determined mathematically as follows in
Eq. 2:

τ max = 0.5 B. G f , S 0 = 0.693 / B

0.236

,

B = 10.4 mm -1

direction at node
Given displacement

Fig. 4 Illustration of finite element mesh
4. NUMERICAL RESULTS AND DISCUSSION(2)

For commonly used adhesive Dai et al hadsuggested the following values for computing thefracture energy, Gf, and regressing parameter, B [24] as
expressed in Eq. 3.

G f = 0.514 . f c'

Restricted in indicated(3)

3.3. Geometrical ModelingA 20-node solid element with 8 Gauss integration
points is used in this program representing concrete andreinforced concrete elements. A 16-node isoparametricjoint element with 4 Gauss integration points is applied
for the interfacial bond as shown in Fig. 3. This joint
element is a two-dimensional element with unit
thickness. Slip (δ, λ) and opening (ω) at gauss

4.1. Failure Mode
(1) Experimental results
The three specimens showed clear signs of two-way
shear failure. Shear failure was evident in the formationof inclined cracks that extended a distance away fromthe slab center at the tension side of the specimen to theloading plate tip at the compression side, followed bypunching of the loading area through the slab.

Fig. 5 Typical cracks pattern in cut section
In the two strengthened slabs, the CFRP sheets at
failure load detached transversally near the shear crack-495-

Un-crushed

Fig. 7 shows the stress distribution along x-direction
through the mid line of the analyzed slab at 90% of theultimate load.
300

Load (kN)

250
200
150
100

exp SC miss-placedana SC miss-placed50

ana SC as planned

0
0

5

10

15

Deflection (mm)20

Fig. 8 Load-deflection of slab SC
300
250

Load (kN)

as a result of discrete shear deformation on either sideof the crack when punching failure occurred. The CFRP
sheets have no resistance in the transverse (out-ofplane) direction. Cracks pattern is shown in Fig. 5
The average distance from the outer edge of thepunching shear cracks at the tension face of thespecimens to the face of the loading area was 3.33h for
specimen SC, 3.2h for specimen SF5, and 3.05h for
specimen SF10, where h is the thickness of the slab.
Apparently, the corresponding distance or the angle atwhich the shear cracks propagated away from theloading area was generally the same for the control andthe CFRP strengthened specimens and was not
influenced by the area of the CFRP sheets used.
All specimens failed in a brittle manner, which isthe characteristic of punching shear failure.
(2) Numerical simulation results
In order to determine the mode of failure, Gauss
points in concrete elements near the loading area were
investigated in different concrete layers so as tounderstand the failure behavior of each slab. When the
stress-strain relationship at any Gauss point indicates‘unloading’, the concrete is considered to be un-crushed.
When ‘softening’ behavior is recognized, the concrete
is considered as crushed, as shown in Fig. 6.

200
150
100
50

Crushedana SF10

exp SF10

ana SF5

exp SF5

ana SC as plannedStress00UnloadingSoftening

5

10

15

Deflection (mm)20

Fig. 9 Load-deflection of slabs SF5 and SF10

StrainFig.6 Illustration of stress-strain behavior
C .L.
Compression zonezx
Unit: MPa
Fig. 7 Stress distribution in x-direction
The application of an increasing load to a slab that ismonolithically connected to the loading plate leads to asequence of events similar to the following.
1. The formation of a roughly circular crack begins
around the loading area with subsequent propagation
almost up to the plane of the neutral axis of the slab.
2. In the meantime, the formation of new circular cracks
begins in the lower concrete layers, and propagating
toward neutral axis plane until they spread throughmost of the concrete elements near the bottom surface.
3. As the load increases, the circular crack incompression develops towards the compression zone.
Ultimately, however, propagation is halted near theloading plate because no cracks have occurred in theconcrete element under the loading plate.
4. Finally, punching shear failure occurs in thecompression zone due to splitting of the concrete near
the loading plate.

4.2. Load-Deflection Response and Ultimate
Strength Capacity
In order to compare the results of specimens withdifferent concrete compressive strengths, the measured
applied load was normalized to a concrete compressive
strength of 39.6 MPa.
At the testing time, the un-strengthened slab SC was
mistakenly miss-placed under the loading jack which
result that the load was not at the center of the slab.
This made the shear span depth ratio was smaller thanplanned. And for that, the punching strength was higher
than expected [28].
Therefore, the slab SC was analyzed two times; thefirst was with the testing boundary conditions (missplaced), and the second with the planned boundary
conditions as shown in Fig. 8.
Figs 8 and 9 show comparisons between
experimental and numerical results in terms of theload–deflection relationships which are important toevaluate the accuracy in predicting the overall behavior
and stiffness characteristics of the slabs.
The load-deflection response of the specimens
consisted of a stiff pre-cracking stage, followed by anearly linear elasto-plastic stage until punching shear
failure occurred in a sudden manner and led to a sharp
drop in load resistance. The initial stiffness of the loaddeflection
responsewassimilar,meanwhilestrengthened slabs showed a higher stiffness for theelasto-plastic stage (Figs. 8 and 9). Also, the maximum-496-

deflection value for the un-strengthened specimen SC
was about 30% higher than those of the strengthened
specimens SF5 and SF10. By using CFRP as astrengthening material, the overall behavior changes toa more brittle behavior.
The numerical simulation tool proved its ability to
predict the ultimate load carrying capacity of the CFRPstrengthened slabs with an accuracy of about 96%.
Table 2 shows the comparison between theexperimental and the analytical results for the simulated
slabs. For all the cases, punching shear failure was thecommon failure mode.
Table 2 Experimental and analytical results for theload and failure mode
Pu anaPu anaP exp
kN

P u anakN

Pu expPu anaSC(asplanned)

NA

179.5

NA

1.00

SF5

215.3

221.8

1.03

1.23

SF10

260.6

250.7

0.96

1.40

Slab

(control)4.3. Slip Profiles along CFRP-ConcreteInterfacial Model
Based on the good agreement between the
numerical and the experimental results using the
proposed model in terms of the load-carrying capacityand deformational characteristics, some other quantities
that are difficult to measure in the laboratory can bepredicted. These quantities include the slip distribution
along the CFRP-concrete interface that will help
understanding the interfacial behavior between the
CFRP composites and the concrete.
0.60

Zones of intersecting CFRP

Slip (mm)

0.50
0.40
0.30

profiles over the CFRP plate length of slabs SF5 andSF10 at the maximum load level. In regions where the
CFRP laminates overlap, reductions in the slips wereobserved. This suggests that transverse “anchorage”
laminates at the ends of the CFRP strips could be aneffective means to enhance bond behavior. The slip

profile shows that the slip values at the plate end weresignificantly higher than those at the centre of slab.
5. CONCLUSIONSIn this study, finite-element analyses have been carriedout to simulate the nonlinear load-deflection behavior andfailure mechanisms for reinforced concrete two-way slabs
strengthened with externally bonded CFRP. The CFRPconcrete interfaces were modeled using appropriateelements connecting the CFRP to the concrete. These
interface elements were characterized by specific bond-slip
relationships that account for possible debonding failures.
It has been shown that this type of representation of theinterface is essential to determine accurate predictions ofultimate capacities and failure modes.

Based on the experimental and analytical results, thefollowing remarks can be concluded:• The use of CFRP increased the stiffness andimproved the punching shear strength of the slabs.
• Depending on the amount of CFRP sheets used, theincrease in punching shear resistance varied from 20%
to 40% of load-carrying capacity of the control slab.
• The interface between concrete and CFRP wasmodeled with appropriate bond interfacial element that
accounts for possible debonding failures.
• It was able to predict the slip profiles along the
CFRP-concrete interface, which are useful for a better
understanding of the expected debonding behavior.
• By increasing the CFRP sheet width, more uniform
stresses are transferred between the CFRP and theconcrete substrate. This results in a lower slip values at
the CFRP-concrete interface.
• The numerical simulation tool could predict theultimate load and simulate the strengthened slabs withreasonable accuracy.
• In regions where the CFRP laminates overlap,
reductions in the slips were observed.

• Given the predictive capability of the numerical

0.20

analysis, this tool can be exploited further to glean
information on the role of other factors on the performanceof CFRP-strengthened concrete slabs and thus contributetowards the optimization of CFRP strengthening
configurations.

SF5

0.10

SF10

0.00
0

200
400
600
Distance from end (mm)800

Fig. 10 Slip profiles of slabs SF5 and SF10
The tested slabs experienced punching shear failure.
It was found that increasing the CFRP plate width
resulted in a reduction in the slip values. This is because
the wider the width of the CFRP plate is, the more
uniform is the transferred shear stresses between the
CFRP plate and the concrete substrate, which in turnleads to a less interfacial slip. Fig. 10 shows the slip

It should be mentioned that, since the specimens
were not pre-loaded or cracked before the application of
CFRP, the results of the current investigation are
applicable in practice to existing slabs that did notexperience extensive structural tensile cracking or
damage as a result of excessive gravity load. Also, since
the increase punching shear resistance is accompanied
by a reduction in the ductility of failure, care should be
exercised in strengthening slabs in areas of seismic
hazard where the ductile behavior is of primary
importance for the survival of concrete structures underearthquake load reversals.

-497-

ACKNOWLEDGEMENT
Japan Society for the Promotion of Science (JSPS)
provided financial support to this research.
REFERENCES[1] Chaallal, O., Nollet, M. and Perraton, D.,“Strengthening of Reinforced Concrete Beams with
Externally Bonded Reinforced Plastic Plates:
Design Guidelines for Shear and Flexure,”
Canadian Journal for Civil Engineering, Vol.25,
1998, pp. 692-704[2] GangaRao, H. V. S. and Vijay, P. V., “Bending
Behavior of Concrete Beams Wrapped with Carbon
Fabric,” Journal of Structural Engineering, Vol.124,
1998, pp. 3-10
[3] Triantafillou, T. C., “Shear Strengthening ofReinforced Concrete Beams Using Epoxy-Bonded
FRP Composites,” ACI Structural Journal, Vol.95,
1998, pp. 107-115[4] Norris, T. and Saadatmanesh, H., “Shear andFlexural Strengthening of R/C Beams with Carbon
Fiber Sheets,” Journal of Structural Engineering,
ASCE, Vol.123, 1997, pp. 903-911[5] Karbhari, V. M. et al., “Strengthening of Concrete
Slabs,” Infrastructure: A New Materials andMethods of Repair, Proceedings of the Third
Materials Engineering Conference, San Diego,
Calif., 1994, pp.1163-1172[6] Kikukawa, K. et al., “Flexural Reinforcement ofConcrete Floor Slabs by Carbon Fiber Textiles,”Composite Interfaces, Vol.5, 1998, pp. 469-478[7] Ebead, U. and Marzouk, H., “Strengthening of twoway slabs subjected to moment and cyclicloading,” Structural Journal, ACI, Vol.99, 2002,
pp.435-444[8] Ebead, U. and Marzouk, H., “Strengthening of twoway slabs using steel plates,” Structural Journal,
ACI, Vol.99, 2002, pp.23-30.
[9] Ebead, U. and Marzouk, H., “Fiber-reinforced
polymer strengthening of two-way slabs,”
Structural Journal, ACI, Vol.101, pp. 650-659[10] Harajli, M. H. and Soudki, K. A., “Shear
StrengtheningofInterior
Slab-Column
Connections using Carbon Fiber-Reinforced
Polymer Sheets,” Journal of Composites forConstruction, ASCE, Vol.7, 2003, pp.145-153[11] Rochdi, E. H. et al., “Strengthening of slab-column
connections with externally bonded CFRP strips,”
Advanced composite materials in bridges andstructures, ACMBS-III, M. El-Badry and L.
Dunasazegi, eds., Canadian Society for Civil
Engineering, Calgary, Canada, 2004, CD-ROM[12] Reitman, M. A. and Yankelevsky, D. Z., “A new
simplified method for nonlinear RC slabs
analysis,” Structural Journal, ACI, Vol.94, 1997,
pp.399-408[13] Seim, W. et al., “External FRP post-strengtheningof scaled concrete slabs,” Journal of Composite
Construction, ASCE, Vol.5, 2001, pp.67–75[14] Marzouk, H. and Chen, Z. W., “Nonlinear analysis
of normal and high-strength concrete slabs,”

Canadian Journal of Civil Eng., Vol.20, 1993,
pp.696-707[15] Ebead, U. and Marzouk, H., “Fiber-reinforced
polymer strengthening of two-way slabs,”
Structural Journal, ACI, Vol.101, 2004, pp.650-659[16] Mosallam, A. S. and Mosalam, K. M.,“Strengthening of two-way concrete slabs with
FRP composite laminates,” Journal of Construction
Building Materials, Vol.17, 2003, pp.43-54[17] Wu, Z. S. and Yin, J., “Fracturing behaviour of
FRP-strengthened concrete structures,” Eng.
Fracture Mechanics, Vol.70, 2003, pp.1339-1355[18] Lu, X. Z. et al., “Meso-scale finite element model
for FRP sheets/plates bonded to concrete,” Journalof Eng. Structures, Vol.27, 2005, pp.564-575[19] Marzouk, H. and Hussein, A, “Experimental
Investigation on the Behavior of High-Strength
Concrete Slabs,” Structural Journal, ACI, Vol.88,
1991, pp.701-713[20] Maekawa, K. and Okamura, H., “Triaxial ElastoPlastic and Fracture Model for Concrete,”
Proceeding of JSCE, Vol.18(460), 1993, pp.131138[21] Farghaly, A., Ueda, T. and Sato, Y., “A Proposal of
Failure Criteria for 3D Concrete Structures,”
Proceeding of Hokkaido Chapter of the JSCE,
Vol.56(A), 2000, pp.528-531[22] Takahashi, R., Ueda, T. and Sato, Y., “Study on
Punching Shear Failure of Steel-Concrete
Sandwich Slab,” Proceeding of the ICCMC/IBST
2001, International Conference on Advanced
Technologies in Design, Construction and
Maintenance of Concrete Structures, Hanoi,
Vietnam, 2001, pp.182-187[23] Li, B., Maekawa, K. and Okamura, H., “ Contact
Density Model for Stress Transfer across Cracks in
Concrete,” Journal of the Faculty of Engineering,
University of Tokyo (B), Vol.40, 1989, pp.9-52[24] Dai, J., Ueda, T. and Sato, Y., “Unified Analytical
Approaches for Determining Shear Bond
Characteristics of FRP-Concrete Interfaces throughPullout Tests,” Journal of Advanced Concrete
Technology, ACT, Vol.4, 2006, pp.133-145[25] Farghaly, A., Furuuchi, H. and Ueda, T.,“Punching Shear Failure Mechanism of Open
Sandwich Slab and its Parameters’ Effects,”
Journal of Advanced Concrete Technology, ACT,
Vol.3, 2005, pp.283-296[26] Farghaly, A. and Ueda, T., “Numerical Analysis of
Punching Failure Mechanism and Debonding ofSlabs Strengthened With Externally Bonded FRP,”
Advanced composite materials in bridges andstructures, ACMBS-V, Pierre Labossière andKenneth W. Neale eds., Canadian Society for Civil
Engineering, Winnipeg, Canada, 2008, CD-ROM[27] Standard Specifications for Concrete StructuresStructural Performance Verification, JSCE, 2002[28] Lovrovich, J. S. and McLean D. I., “Punching
Shear Behavior of Slabs with Varying Span-Depth
Ratios,” Structural Journal, ACI, Vol.87, 1990,
pp.507-511-498-