Size effect in punching of rc slabs

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 6, Issue 1, January (2015), pp. 147-160 © IAEME
147
SIZE EFFECT IN PUNCHING OF RC SLABS
Rizgar A. Agha
Faculty of Engineering-University of Sulaimani,
Kurdistan Region of Iarq
ABSTRACT
There appears to have been no review made of existing test data in which the size effect in
punching has been given any special consideration and the proposed paper seeks to fill this gap. Its
objectives are to set out the current state of knowledge on size effects and the parameters that
influence them by considering of experimental results of 87 reinforced concrete flat slabs without
shear reinforcement. These tests are carefully selected to form a large database, including specimens
with a significant variation of effective depth. These experimental results are compared with design
codes of EUROCODE 2, FIB Model 2010 and to the Critical Shear Crack Theory (CSCT) by
Muttoni et al. The comparison show that both EC2 and CSCT have good prediction to test results
while MC90 is rather underestimate the punching shear strength of thinner slab compared to EC2
particularly for reinforcement ratio less than 0.1% and this is due to ignoring the limit on the factor
of size effect beyond of 2.0.
Keywords: Slab; Size Effect; Punching Shear Strength; Flexural Reinforcement; Slab Rotation:
Compressive Strength
INTRODUCTION
Punching shear strength in reinforced concrete flat slabs is not entirely understood despite of
many theoretical methods that have been developed by researchers since last century. Theses
approaches are aiming in considering different parameters or in modifying of the existing parameters
from previous researchers. The parameters were considered are geometric dimensions, compressive
strength of concrete, flexural reinforcement, size effect, shear reinforcement, slab rotation and finally
aggregate type and diameter. However the current design of punching in flat slabs is according to the
recommendations by codes of practice and researchers are not purely theoretical but are semi-
empirical. So the main differences in the estimation of punching shear strength between codes and
other methods are due to different calculation approaches in considering these parameters. The
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 6, Issue 1, January (2015), pp. 147-160
© IAEME: www.iaeme.com/Ijciet.asp
Journal Impact Factor (2015): 9.1215 (Calculated by GISI)
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IJCIET
©IAEME

148
existence of size effects in the resistance of reinforced concrete has been recognised increasingly in
recent years. The effects are greatest in members without shear reinforcement and thus in slabs rather
than beams. Where slabs are supported by beams or walls the shear stresses are generally quite low,
so the main areas of concern are punching in flat slab floors and foundations and shear in slab
bridges.
Sherif and Dilger[ ]1 reviewed CSA A23.3-94 and compared its prediction with test results
from literature. They concluded that CSA is unsafe for slabs with low flexural reinforcement( )%1<ρ ,
they observed the decrease in shear capacity with increasing of slab thickness and a size effect factor
is necessary in the code only where mmd 300> . They proposed an equation which includes
reinforcement ratio and size effect but not the steel stress.






+
=
d
fv c
1000
1300
.1007.0 3 ρ ( )mmandN ........ (1)
Gardner and Shao [ ]2 reviewed the provisions of the ACI[ ]3 , BS8110[ ]4 and CEB-FIP 1990
Model Code[ ]5 and compared their predictions with tests results from literature. The both BS8110
and CEB-FIP Model Code include the size effect and flexural reinforcement parameters but ACI
does not. He found that they predict closer results due to the influence from these two parameters on
the shear strength capacity rather than ACI which does not include them. They observed that the
punching shear strength is approximately proportional to the cube root of the concrete strength,
reinforcement ratio and yield stress. But they cautioned that beneficial from high percentage of
reinforcement causes a more brittle behaviour. So, they added further factors into the expression for
evaluating the shear strength capacity which are size effect, reinforcement ratio and steel stress
( ) ( )ocmy
o
u
u bdffd
db
V
v /../200179.0 33 ρ+== ….. (2)( )mmandN
Where cmf is the mean concrete strength in MPa and ob is the perimeter of the loaded area.
Muttoni et al. [ ]6 described the relationship between the punching shear strength in slab and
its rotation at failure in a critical shear crack theory (CSCT). They assumed that the shear strength of
members without shear reinforcement is governed by the width and roughness of an inclined shear
crack develops through the inclined compression strut carrying shear.
Elstner and Hognestad [ ]7 observed that the situation in footings having a thicker slab than
roof slab are different in regards of span-to-depth ratio which is lower in the footings and the
moment to shear ratio is higher in the roof slabs. Other researchers believe that the soil structure
interaction in footing has its influence in estimating the shear strength. However, the codes of
practice do not distinguish between the punching shear strength in flat slab and footing in their
expressions for design engineers.
Collins and Kuchma [ ]8 studied the size effect factor in beams, slabs and footings and
concluded that the shear strength capacity decreases as the depth of the member increases and the
maximum size of the used aggregate decreases. Also, they observed that the members with higher
strength concrete showed a more significant size effect and believe that this factor should be
considered in shear strength capacity. They recommends for a special study about size effect in slabs
and footings as they are thick and lightly reinforced.
Mitchell, Cook and Dilger [ ]9 studied the size effect factor influence on punching shear
resistance according to the codes of the existing expressions in the codes of practice. They analysed

149
test results for slabs with thickness varied between 100 to 600 mm and concluded that the size effect
is significant where the punching shear stress decreases as the thickness of the slabs increases even
for the thickness less than 200mm.
Guandalini et al. [ ]10 conducted a series of tests to investigate the punching behaviour in
slabs with low reinforcement ratios and without transverse reinforcement. They also studied results
from literature to conclude that the punching shear strength decreases with increasing slab thickness.
They found that for thick slabs with low reinforcement ratios the prediction by EC2[ ]11 is more
closer to test results than those by ACI and they explained the ignoring of the role of reinforcement
ratio and size effect factor. They compare the strength and rotation capacity predictions by CSCT
and found a good agreement for both prediction and particularly for slab PG-3
(6000x6000x500mm, mmd 456= and %33.0=ρ ) but it is unsafe by EC2.
Sacramento et al. [ ]12 studied the parameters that influence the punching shear resistance in
flat slab without shear reinforcement. They considered 74 experimental results of flat slabs without
transverse reinforcement where a few of thick slabs of 275mm were included. Although, the study
does not concentrate on the influence of size effect, once there is not much experimental evidence in
this topic, but it includes a separate consideration of this factor through tests by Li[ ]13 and
Birkle[ ]14 only, they were used as a reference for the analyses regarding size effect. However, these
tests were taken out from the study and the reason might be these slabs are relatively small in plan, if
compared to their thickness and possibly influencing the failure surface and thus the failure load.
They concluded that the prediction by ACI although it is safe but underestimate the punching shear
resistance in flat slab by 37% and shows a high coefficient of variation if compared to EC2 and
CSCT. They explained the reason is not taking into account the influence of parameters such as the
flexural reinforcement and size effect and relied only on the compressive strength of concrete. They
plot a large numbers of tests from literature in a comparison of experimental results with those
obtained using recommendation of EC2 and CSCT. The comparisons show for both codes no results
are below the design strength but EC2 shows about 11% of unsafe results and for CSCT about 11%
of results are below the nominal strength as shown in figs below.
Urban et al. [ ]15 verified the EC2 treatment on the dependence of punching shear stress on
the slenderness of the slab. They carried out the comparison between the prediction from EC2 and
test results from their own research of 9 slabs with thickness varied between 150mm-350mm and
results from Hallgren et al. [ ]16 They concluded that the shear slenderness is important for the shear
capacity. However, the problems in having short span of tests could require some allowance for the
spacings of the reactions in most of the tests.
CODES OF PRACTICE AND CSCT BY MUTTONI [6]
The first code of practice to make any allowance for a size effect seems to have been the British
CP110 of 1972[ ]17 , in which the design shear stresses for slabs reduced by 17% in the range of
effective depths from 150 to 250 mm .
In Europe the 1978 CEB Model Code[ ]18 introduced a depth factor 0.16.1 ≥−= dk , where
d was the effective depth in m . In the 1990 model code (3)
it was replaced by dk /2001+= , with
d inmm , which is used in the Eurocode (4)
of 2004 with an upper limit 0.2≤k . In the United States
ACI 318-11[ ]3 still has no depth factor, although its commentary does note that "Further information
has indicated that shear strength decreases as the overall depth of the member increases".
According to EC2[ ]11 characteristic punching resistances are given by

150
duvduvV cRkcRkcRk 0max,1,, ≤= ……..………….. (4)
where ( ) 3/1
1, .10018.0 ckcRk fkv ρ= , 0.2/2001 ≤+= dk , ( ) ckckRk ffv 250/124.0max, −= , 1u is the
length of a perimeter constructed to obtain the minimum length without coming closer to a column
than 2d from it, ( ) dccu π42 211 ++= for rectangular columns with side lengths , 1c and 2c and
( )dcu 41 += π for a circular column of diameter c , 1ρ is the ratio of flexural tension reinforcement
determined as yx 11 ρρ calculated for the orthogonal directions of the reinforcement and for widths
equal to those of the column plus 3d to either side. 02.0≤ρ for calculation purposes, d is the mean
effective depth of the reinforcement ( ) 2/yx dd += , ckf is the characteristic cylinder compression
strength of the concrete ( )90MPafck ≤ and 0u is the length of the perimeter of the column. This
definition ignores a minimum value given for cRkv , , which is of no practical significance for normal
reinforced concrete slabs.
The depth factors cited above are applied to different basic expressions for concrete shear
resistance, but can be compared by applying them to a reference resistance for a particular effective
depth. Fig.1 shows the ratios of shear capacities for other effective depths to the capacity when d =
200 mm plotted against the effective depth. An obvious feature of the figure is the way in which the
maximum depths up to which size effects are considered has increased with time. Something else to
be noted is EC2's introduction of a lower limit (200 mm) on the effective depth at which the size
factor continues to increase. The reason for the lower limit, which is within the range of practical
construction and larger than the effective depths of numerous test slabs, is unclear. It could possibly
be a precautionary measure taking account of the greater relative variability of effective depths in
thinner slabs. If the unit strength does in fact continue to increase with decreasing effective depth,
below 200 mm, comparisons of results of tests on shallower slabs with EC2 and its limit are likely to
be misleading.
Fig. (1) Parametric shear strength predictions for different slab thickness by some codes of practice
The expressions by MC90 are the same as EC2 except there is no limit on dk /2001+= in
its prediction.
The approach to punching used in the new fib model code 2010[ ]19 is based on the Critical
Shear Crack Theory of Muttoni et al. and is considerably more complicated than the existing codes.
In this approach there is no explicit expression for shear resistance, which instead is obtained by the
simultaneous solution of equations relating the resistance to the rotation of the slab and the rotation

151
to the applied load. The equations from which the code is derived by Muttoni in a form suitable for
the analysis of typical punching rests. The size effect on punching shear strength is considered and
expressed via ( )016/ dd + depends on ψ and the ratio of the maximum load to the slab's flexural
capacity. Muttoni states that the factor for the reduction of strength for size effect is not a function of
the slab thickness, but rather of span which is represented by radius of the isolated slab element. This
approach introduces new factors into the size effect - the size and type of the aggregate and the
strength of the concrete. In view of [ ]6 it might be better to consider aggregate types more widely, as
aggregates such as granite and gravel generally give shear resistances superior to those obtained with
for example limestone. The basic CSCT equations are given in as
g
c
dd
fdb
V
++
=
16/151
75.0 0
ψ
………………… (5)
flex
ys
R V
fr
Ed
V
3/2
5.1 







=
ψ
………………… (6)
where ( )cqsrflex rrrmV −= /2π and 





−=
c
y
yR
f
f
dfm
2
2 ρ
ρ in ( )mmandN and MPa units , 0b is the length
of a control perimeter d/2 from the column,ψ is the rotation of the slab outside the critical shear
crack(in radians), gd is the maximum size of the aggregate, taken as zero for both high strength and
lightweight aggregate concretes, sE is the modulus of elasticity of the reinforcement, here taken as
200 MPa , yf is the yield or 0.2% proof stress of reinforcement, flexV is the yield- line flexural
capacity of the slab as given by Eqn.(6), Rm is the plastic moment of resistance at a yield line (
averaged for the length of the line) and all the radii cr , qr and sr are shown in Fig.2 for a circular
slab on a circular column. For rectangular columns with 1c and dc 32 ≤ , cr is taken as
( ) π/21 ccrc += . If the length of a side of a rectangular column is greater than d3 , a value of d3 is
substituted for it in calculating 0b and presumably also flexV . The final influence of size, expressed
via ( )gdd +16/ depends on ψ and the ratio of the maximum load to the slab's flexural capacity.
This approach introduces new factors into the size effect - the size and type of the aggregate
and the strength of the concrete. In view of (8)
it might be better to consider aggregate types more
widely, as aggregates such as granite and gravel generally give shear resistances superior to those
obtained with for example limestone.
DATA COLLECTION
It is very difficult in finding slab tests designed for size effect, except few test by Li[13] ,
Birkle et al.[14] and Urban et al.[15]. However, any experimental programme do the size effect
consideration would faces problems when focuses on changing the thickness of the slab and keeping
the other parameters constant such as compressive strength and flexural reinforcement. The later one
should be satisfying the require reinforcement for the particular volume of the slab and this affect the
slenderness of the slab. To carry out a reliable investigation on the influence of size effect on the
punching shear strength, it is necessary to collect reasonable results from literature where the
conditions of the factors that influence the punching shear strength in flat slabs are met and failed in

152
punching shear. To avoid unnecessary complicating factors the tests which are included are restricted
to those made with concentric shear around square or circular internal loads or supports. They are not
including lightweight concrete slabs or slabs with shear reinforcement and the maximum size of used
aggregates are known. Eighty nine slabs are selected in this study where the depth are between 64-
619 mm which includes 24 slabs with d>200mm.
The selected tests are from Refs. [ ]3029,10,13,28,27,26,25,24,23,22,16,21,20 and respectively: Kinnunen
et al (3 tests), Tolf (8 tests),Hallgren(7 tests), Marzouk and Hussein(12 tests), Rizk and Marzouk(3
tests),Rizk et al (4 tests),Birkle(3 tests),Moe(8 tests),Regan (20 tests),Lips et al.(5 tests),Li (6 tests),
Guandalini et al.(6 tests), Heinzman( 1 test) and Tomaszewics et al (3 tests). Therefore, the
parameters as shown in table (1) are shape of slabs (circular and square), thickness of slabs (64-619
mm),concrete compressive strength (9.0 to 108.8 MPa) and steel yield strength (328 to 720 MPa),
aggregate size (5-38mm) and types of gravel, crushed quartzite sandstone, sandstone, granite,
reinforcement ratio percentage (0.33-2.37), in addition to column types (circular and square).
It would be useful to explain some aspects and reasons for some of omitted tests from the
same series of test programme by the authors above as followings:
-According to the paper by Marzouk and Hussien, there are some problems in reporting the data as
slabs NS2, HS5 and HS6 all had effective depths of 150mm, while their effective depths were 12.0,
95.0 and 12.0mm respectively. Slabs HS8, HS9 and HS10 are also described as having h=150mm
and d=12.0mm. Making the obvious assumption that d should be 120mm in place of 12mm, the
details of the second group all make reasonable sense, but for the first three they do not .Various
people have used the tests in comparisons with rather varied data as in table (1)
Table (1) Varied data of d and ρ %of slabs by Marzouk et al.
Slab
no.
Bulletin 12( )
Hallgren( ) Sacrament et
al.( ) Table above
Marzouk
et al( )
NS2 120 0.5 120 0.94 - - 120 ? 0.94
HS5 125 0.5 125 0.64 - - 120 ? 0.64
HS6 120 0.5 120 0.94 - - 120 ? 0.94
HS8 120 1.0 120 1.11 120 1.00 120 1.11 1.11
HS9 120 1.5 120 1.61 120 1.50 120 1.61 1.61
HS10 120 2.1 120 2.33 120 2.10 120 2.33 2.33
(a)- Bulletin 12 is fib Bulletin 12, Punching of concrete slabs. It seems to think (wrongly) that M10
means 10φ and M15 is 15φ . - "Hallgren's Thesis"
(b)-Hallgren was one of the authors of Bulletin 12, which may account for his d values.

153
(c)- Sacrament et al ignored the data and results for NS2,HS5 and HS6 as in case of some
difference in d between HS and HS6 it would not be enough to make ρ first 0.64% and then 0.94%
for exactly the same reinforcement. On this base the Bulletin 12 version is not help in these tests. So
there are ignored in this study as well.
The details and calculation of reinforcements are shown in table (2).
Table (2) Summary of ρ % of slabs by Sacrament et al.
Slab no.
Reinforcement
both ways
ρ % Calculation of ρ
NS2 M10@125 0.944
mmdymmdxmmd 114,126,120 ===
%53.084.063.0 == xρ
HS5 M10@125 0.90 %53.084.063.0 == xρ
HS6 M10@125 0.944 %53.084.063.0 == xρ
HS8 M15@150 1.111
mmdymmdxmmd 112,128,120 ===
%11.109.104.1 == xρ
HS9 M15@100 1.611 %67.179.156.1 == xρ
HS10 M15@71.4 2.333 %34.2509.219.2 == xρ
The first three columns are direct from the paper. The fourth is a result of calculations from
the first three and the assumption that d =120mm.
Note that the Canadian bar sizes are M10 bars have and M15 bars have and there is no in-
between size.
There are some omitted tests in these selections for various reasons:
-Slabs by Moe (S2/60,S3/60,S4/60, S3/70,S4/70 and S4A/70) and Regan (I/1,I/3 and I/5) are omitted
as they are with banded reinforcement.
-Moe's slab R1 is omitted as it is the only one test having a rectangular column in the whole series.
-slabs by Li K.K.L which cover a good range of slab depths in spite of having a very short span
particularly for the thicker slabs. The reason is to account for such cases in pad foundation which
often are small in their dimensions compared to other flat span and mat foundations.
-one slab by Heinzman et al.
-Slabs by Guandalini et al, in which slabs in a very low ratios of flexural reinforcement of 0.33%.
-slabs by Tomaszewicz are more designed to investigate the influence of high strength concrete on
punching shear resistance, but extra information on size effects is rather limited. The programme
includes three different slab thicknesses; therefore one of each group thickness is selected.
The summary and details of the selected specimens are shown in Table (3)

154
Table(3) Summary of Slabs from literature
Author
No.
of
test
Effective
depth of
slab
( )mm
Gravel
size
( )mm
Slab size
and type
Col.size
and type
( )mm
ρ %
yf






2
mm
N
cf






2
mm
N
Kinnunen 3 101-619 16-38 700-5820S 120-800C 0.51-0.55 622-720 23.7-30.6
Tolf 8 98-200 16-32 1270-2540C 125-250C 0.34-0.81 657-720 22.9-28.6
Hallgren 7 194-202 20 2540C 250C 0.33-1.19 596-634 84.1-108.8
Marzouk 12 70-120 20 1700C 150-300S 0.84-2.37 490 42-80
RIZK 3 205-255 20 1900-2650S 250-400S 0.52-0.66 400 40-76
RIZK &Huss 4 262.5-312.5 20 2650S 400S 0.50-1.58 460 40-76
Birkle 3 124-260 14-20 1000-1900S 250-350S 1.10-1.54 488-531 30.5-35.1
Moe 6 114 9.5-38 1830S 152-305S 1.06-1.52 328-482 20.8-26.6
Regan 20 64-200 5-20 1500-2745S 54-2745S 0.75-1.52 464-628 9.0-42.8
Lips 5 193-353 16 3000S 130-520S 1.5-1.63 583-709 31.9-36.5
Li 6 100-500 20 925-1975 200-300S 0.76-0.98 433-488 39.4
Guandalini 6 96-456 16 1500-6000s 130-520 0.33-1.5 520-577 27.6-34.7
Heinzman 1 350 32 4100S 294C 1.20 575 35.5
Tomaszewics 3 88-275 16 1500-3000S 100-200s 1.49-1.84 500 `64.3-85.1
The calculation of the predictions by EC2,MC90 and CSCT are shown in Table(5) and the
comparisons of test results with the predictions by them are plotted for three cases of d where all
tests together and for mmd 200≤ and mmd 200> . The plotting are formed in respect of the
normalized ratio of tests shear stress and ( ) 3/1
100 ckfk ρ against depth of slabs and shown in Fig.
(5a-c and 6a-f) for EC2 and MC90, while regarding to CSCT the ratio of the applied load to
punching shear strength on the order axis and the depth in a function of rotation capacity and
corrected to aggregate size on the abscissa are considered. The prediction by EC2 showed better than
MC90 for slabs with d<200mm and for all slabs with a mean of 1.15 and 1.02 respectively above the
test results and coefficient of variation of 0.15 and 0.10 respectively but they are 0.13 and 0.12for
slabs with d>200mm. For all tests, the prediction by CSCT obtains the mean value and c.o.v. of
1.09and 0.12 respectively which are better than those by EC2 and MC90 as shown in Table (6). The
case of all slabs in Fig.5 (a-c) shows that for EC2, MC90 prediction, there are 21% and 19% of
results are below the nominal strength and no results below the design strength. But for results
obtained according to CSCT there is no result below nominal strength. Fig(5.a) shows that slabs of
HSC9(Hallgren), 10( Birkle) V1 and (Regan) are very close to the nominal strength. Hallgren
reported that all slabs are failed by punching but note that the ultimate rotation of HSC9 was 0.035
radians, i.e. more than that of any of the other bars and this is shown on Fig.(5.c) where the abscissa
is 0.158 and enough above the normal strength. Fig. (5d-f) shows the comparison between the
predictions by EC2, MC90 and CSCT with respect to the flexural reinforcement ratio. It is noted that
most of the punching failure occurred in those slab having high reinforcement ratio ( )5.0>ρ and
thinner slab with mmd 200≤ . Regarding of thinner slab mmd 200< with ( )5.0>ρ the predictions
by EC2 are safer than MC90, the later is obviously safe for those with( )0.1>ρ . The influence of
reduction factor in EC2 to be 0.2≤ for mmd 200≤ is clear in achieving a conservative prediction
while ignoring an upper limit by MC90 causes in overestimating some slabs. The prediction by
CSCT shows a very good agreement with the experimental loads even for slabs with low
reinforcement ratio.

155
Table (4) Comparison of test results to predictions by CSCT, EC2 and MC90
Author Test 





d
rs
TestV CSCTV cRkV ,
EC2
cRkV ,
MC90 CSCT
Test
V
V
2EC
Test
V
V
90MC
Test
V
V
Kinnunen B2 5.94 185 192 141 169 0.96 1.32 1.09
C2 4.98 573 635 547 547 0.90 1.05 1.05
S1 4.70 5378 5470 4607 4602 0.98 1.17 1.17
Tolf S1.1 6.30 216 195 168 203 1.11 1.28 1.06
S1.2 6.36 194 175 154 187 1.11 1.26 1.04
S2.1 6.35 603 677 637 637 0.89 0.95 0.95
S2.2 6.38 600 658 620 620 0.91 0.97 0.97
S1.3 6.43 145 133 120 146 1.09 1.20 0.99
S1.4 6.36 148 131 119 144 1.13 1.24 1.03
S2.3 6.35 489 487 487 487 1.00 1.00 1.00
S2.4 6.45 444 477 471 473 0.93 0.94 0.94
Hallgren HSC 0 6.35 965 920 987 987 1.05 0.98 0.98
HSC 1 6.35 1021 921 991 991 1.11 0.97 1.03
HSC 2 6.55 889 867 927 934 1.03 0.96 0.95
HSC 4 6.35 1041 1080 1132 1132 0.96 0.92 0.92
HSC 6 6.32 960 852 963 962 1.13 1.00 1.00
N/HSC
8
6.41 944 915 986 989 1.03 0.96 0.95
HSC 9 6.29 565 601 731 729 0.94 0.77 0.78
Marzouk NS 1 8.95 320 268 243 297 1.19 1.32 1.08
HS 2 8.95 249 254 238 292 0.98 1.05 0.85
HS 7 8.95 356 298 272 334 1.19 1.31 1.07
HS 3 8.95 356 317 286 350 1.12 1.25 1.02
HS 4 9.44 418 333 285 355 1.26 1.47 1.18
HS 8 7.08 436 420 386 442 1.04 1.13 0.99
HS 9 7.08 543 490 447 512 1.11 1.21 1.06
HS 10 7.08 645 567 493 565 1.14 1.31 1.14
HS 12 12.14 258 200 180 243 1.29 1.43 1.06
HS 13 12.14 267 213 191 257 1.25 1.40 1.04
HS 14 8.95 498 380 335 410 1.31 1.49 1.21
HS 15 8.95 560 445 385 472 1.26 1.46 1.19
RIZK NS 4 4.63 882 777 780 780 1.14 1.13 1.13
HS 4 4.63 1023 888 915 915 1.15 1.12 1.12
HS6 5.20 1722 1240 1414 1414 1.39 1.22 1.22
RIZK &Huss HSS 1 4.95 1722 1392 1492 1495 1.24 1.15 1.15
HSS 3 5.05 2090 2080 2004 1955 1.00 1.04 1.07
NSS 1 4.24 2234 2250 2299 2225 0.99 0.97 1.00
HSS 4 4.24 2513 2756 2632 2547 0.91 0.95 0.99
Birkle 1 9.68 483 423 423 480 1.14 1.14 1.01
Birkle 7 8.95 825 774 843 854 1.07 0.98 0.97
10 8.08 1046 1190 1318 1316 0.88 0.79 0.79
Moe H 1 8.03 371 368 312 362 1.01 1.19 1.02
S1/60 8.03 389 351 292 340 1.11 1.33 1.15
S1/70 8.03 392 362 297 345 1.08 1.32 1.13
S5/60 8.03 378 319 267 310 1.18 1.42 1.22
R2 8.03 311 248 261 303 1.26 1.19 1.03
M1A 8.03 433 417 344 400 1.04 1.26 1.08
Regan I/2 12.99 176 156 146 191 1.13 1.20 0.92
I/4 12.99 194 155 149 195 1.25 1.30 1.00
I/6 12.66 165 132 127 165 1.25 1.30 1.00
I/7 12.66 186 149 145 188 1.25 1.28 0.99

156
II/1 7.49 825 715 770 770 1.15 1.07 1.07
II/2 7.66 390 316 310 349 1.23 1.26 1.12
II/3 7.66 365 295 313 353 1.24 1.16 1.04
II/4 7.66 117 92 78 107 1.27 1.51 1.09
II/5 7.66 105 87 78 108 1.21 1.34 0.97
II/6 7.66 105 84 80 110 1.25 1.32 0.95
III/1 7.89 197 186 150 183 1.06 1.32 1.07
III/2 7.89 123 134 93 136 0.92 1.32 0.90
III/3 7.89 214 220 176 216 0.97 1.21 0.99
III/4 8.06 154 150 113 142 1.03 1.36 1.08
III/5 8.06 214 220 185 229 0.97 1.15 0.94
III/6 8.06 248 270 220 272 0.92 1.13 0.91
V/1 6.78 170 198 142 178 0.86 1.20 0.96
V/2 6.78 280 282 253 291 0.99 1.11 0.96
V/3 6.78 265 238 229 264 1.11 1.15 1.00
V/4 6.78 285 237 246 283 1.20 1.16 1.01
Lips PL1 7.77 682 683 746 802 1.00 0.91 0.85
PL2 7.14 974 941 1019 1017 1.04 0.96 0.96
PL3 7.61 1324 1184 1249 1254 1.12 1.06 1.06
PL4 5.62 1625 1500 1569 1569 1.08 1.04 1.04
PL5 4.25 2491 2286 2501 2501 1.09 1.00 1.00
Heinzman S1 6.00 1710 2045 2053 2053 0.84 0.83 0.83
Guandalini PG1 7.14 1023 830 949 949 1.23 1.08 1.08
PG3 6.58 2153 1720 2345 2345 1.25 0.92 0.92
PG6 7.83 238 227 222 272 1.05 1.07 0.88
PG7 7.52 241 193 189 228 1.25 1.27 1.05
PG10 7.14 540 452 550 579 1.19 0.98 0.93
PG11 7.14 763 673 746 786 1.13 1.02 0.97
Li P100 4.63 330 358 250 302 0.92 1.32 1.09
P150 3.97 583 624 476 512 0.93 1.23 1.14
P200 3.63 904 872 762 762 1.04 1.19 1.19
P300 3.29 1381 1532 1390 1390 0.90 0.99 0.99
P400 2.47 2224 2610 2373 2373 0.85 0.94 0.94
P500 1.98 2681 3392 3409 3409 0.79 0.79 0.79
Tomaszewicz ND65-
1-1
5.45 2050 1740 1783 1783 1.18 1.15 1.15
ND65-
2-1
6.50 1200 1035 1112 1112 1.16 1.08 1.08
ND95-
3-1
8.52 330 291 257 322 1.13 1.29 1.03
Table (5) Summary of Comparison of test results to predictions by CSCT, EC2 and MC90
Test parameters
Statistical
values CSCT
Test
V
V
2EC
Test
V
V
90MC
Test
V
V
Tests with d<200mm
Mean 1.10 1.19 1.03
STD 0.12 0.16 0.08
C.O.V 0.11 0.14 0.08
Tests with d>200mm
Mean 1.05 1.00 1.00
STD 0.16 0.13 0.12
C.O.V 0.15 0.13 0.12
All tests
Mean 1.09 1.15 1.02
STD 0.13 0.17 0.10
C.O.V 0.12 0.15 0.10
Tests with d>200mm without tests by Li
Mean 1.08 1.01 1.02
STD 0.14 0.12 0.12
C.O.V 0.13 0.12 0.12

157
0.00
0.06
0.12
0.18
0.24
0.30
0.36
0 100 200 300 400 500 600 700
()3/1
100ckfk
v
ρ
( )mmd
(a) EC2
0.00
0.06
0.12
0.18
0.24
0.30
0.36
0 100 200 300 400 500 600 700
()3/1
100ckfk
v
ρ
( )mmd
(b) MC90
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
0.000 0.050 0.100 0.150 0.200 0.250
ggo dd
d
+
.ψ
CSCTtestVV/
(c) CSCT
0.00
0.10
0.20
0.30
0.40
0 100 200 300 400 500 600 700
-
-
-
( )mmd
ckofdb
V
0.1
0.15.0
5.0
>
≤<
≤
ρ
ρ
ρ
cko
EC
fdb
V 2
(d) EC2
0.00
0.10
0.20
0.30
0.40
0 100 200 300 400 500 600 700
-
-
-
( )mmd
ckofdb
V
0.1
0.15.0
5.0
>
≤<
≤
ρ
ρ
ρ
cko
MC
fdb
V 90
(e) MC90
0.00
0.10
0.20
0.30
0.40
0.00 0.05 0.10 0.15 0.20 0.25 0.30
-
-
-
ckofdb
V
0.1
0.15.0
5.0
>
≤<
≤
ρ
ρ
ρ
cko
CSCT
fdb
V
ggo dd
d
+
.ψ
(f) CSCT
Fig (2) Comparisons between the test results from literature and predictions by EC2, MC90 and
CSCT for all size and (d), (e) and (f) with respect of flexural reinforcement ratio
0.00
0.06
0.12
0.18
0.24
0.30
0.36
0 50 100 150 200 250
()3/1
100ckfk
v
ρ
( )mmd
(a) EC2
0.00
0.06
0.12
0.18
0.24
0.30
0.36
0 50 100 150 200 250
()3/1
100ckfk
v
ρ
( )mmd
(b) MC90

158
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
0.000 0.020 0.040 0.060 0.080 0.100
ggo dd
d
+
.ψ
CSCTtestVV/
(c) CSCT
0.00
0.06
0.12
0.18
0.24
0.30
0 100 200 300 400 500 600 700
()3/1
100ckfk
v
ρ
( )mmd
(d) EC2
0.00
0.06
0.12
0.18
0.24
0.30
0 100 200 300 400 500 600 700
()3/1
100ckfk
v
ρ
( )mmd
(e) MC90
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
0.000 0.050 0.100 0.150 0.200 0.250
ggo dd
d
+
.ψ
CSCTtestVV/
(f) CSCT
Fig(3) Comparisons between the test results from literature and predictions by EC2, MC90 and
CSCT (a),(b) and (c) for mmd 200≤ and (d) , (e) and (f) for d > mm200
CONCLUSION
Analysis on the influence of size effect on punching shear slab strength has been carried out.
The available test results from literature are useful to consider most of the other parameters affecting
the shear strength. The predictions by EC2, MC90 and CSCT are evaluated on the base of test results
and the following conclusions are obtained:
1-The available tests showed the differences between the approaches by codes of practice of EC2
and MC90 and the critical shear crack theory by Muttoni. In respect to the influence of size effect
and their upper limits for depth below 200mm. The predictions by EC2 and CSCT showed the better
correlation than MC90 although CSCT showed better.
2-CSCT showed a good prediction for slabs with lower reinforcement ratio for thin and thick slabs,
while EC2 and MC90 predict overestimated shear strengths for thick slab except one case with
d=267.5mm.
3-Predictions by CSCT are all above the nominal shear strength, while for EC2 and MC90 there are
about21% and 19% respectively of results can not achieve the nominal shear strength. This
recommends for lowering the factor of 0.18 for 0.15 or 0.16.
4-The upper limit of size effect factor to be 0.2≤ in EC2 gives the code a better evaluation than
ignoring it by MC90 which overestimate the thinner slabs clearly.
5-It is understood that the main reason of the size effect on the shear capacity is increasing of the
width of the diagonal cracks as the aggregate interlock damaged. Further investigation is required to
show the influence from the aggregate size in enhancing the aggregate interlock.

159
6-It would be a good idea to include something about size effects on the shear resistance of one-way
spanning slabs and beams without shear reinforcement as there have been far more test series in this
area with much greater ranges of depths.
REFERENCES
1. Sherif A.G. and Dilger W.H.(1989), Critical Review of the CSA A23.3-94 Punching shear
strength Provisions for inter Columns. Canadian Journal of Civil Engineering.V.23, No.5,
pp.998- 1101.
2. Gardner N.J. and Shao X. (1996), Punching shear of continuous flat reinforced concrete
slabs. ACI Journal .V.93.No.2, March-April, pp 218-288.
3. ACI 318-11, Building code requirements for structural concrete, American Concrete Institute,
Farmington Hills, MI, USA, 2011
4. BS 8110 (Part 1:1997), Codes of Practice for Design and Construction. British Standard
Institution, London, 1997.
5. CEB-FIP Model code for concrete structures 1990, Thomas Telford, London, 1993.
6. Muttoni A., Punching shear strength of reinforced concrete slabs without transverse
reinforcement, ACI Structural Journal, V105 No 4, July-August 2008, pp 440-450
7. Elstner R. and Hognestad E. (1956), Shearing strength of reinforced concrete slabs. ACI
Journal.V.28, No.1, pp.29-58.
8. Collins M.P and Kuchma D.,How Safe Our Large, Lightly Reinforced Concrete Beams,
Slabs and
Footings?,ACI Structural Journal, V.96, No.4,July- Aug.1999, pp.482-490.
9. Mitchell D., Cook W.D., and Dilger W., Effects of size, geometry and material properties on
punching shear resistance.SP-232,Ed.Polak,M.A.,ACI, Farmington Hill,MI,pp.39-56
10. Guandalini S.,Burdet O.L. and Muttoni A.(2009), Punching tests of slabs with low
reinforcement ratios.ACI Structural Journal, pp.87-95.
11. Eurocode 2, Design of concrete structures, Part 1-1, General rules and rules for buildings, EN
1992-1- 1, CEN, Brussels, Dec 2004
12. Sacramento P.V.P., Ferreira M.P., Oliveira D.R.C.and Melo G.S.S.A, Punching strength of
reinforced concrete flat slabs without shear reinforcement, Revista Ibracon De Estruturas E
Materials, Vol.5, No.5, Oct.2012.
13. Li K.K.L, Influence of size on punching shear strength of concrete slabs, MEng. Thesis, Dept
of Civil Engineering and applied Mechanics .Mc Gill University, Montreal, 2000,p78
14. Birkle G., Punching of flat slabs, The influence of slab thickness and stud layout, PhD
thesis, Dept. Of Civil Eng, University of Calgory, Mar 2004.
15. Urban T., Goldyn M., Krakowski J. and Krawczyk L.Experimental investigation on punching
shear behaviour of thick reinforced concrete slabs, Archives of Civil Engineering, Lodz
University of Technology, LIX, 2, 2013
16. Hallgren M., Punching shear capacity of reinforced high strength concrete slabs, TRITA-
BKN Bulletin 23, Dept. Of Structural Engineering, KTH Stockholm,1996.
17. CP110: Part 1, The structural use of concrete, Part 1, Design, materials and workmanship.
British Standards Institution, London, 1972.
18. CEB-FIP Model code for concrete structures, 1978.
19. Fib Model code 2010, First complete draft, Vol. 2, Bulletin 56, fib, Lausanne
20. Kinnunen S.,Nylander H. and Tolf P. Plattjocklekens inverkan pa betongplattors hallfasthet
vid genomstansning. Forsok med rektangulara, (Influence of slab thickness on the punching

160
strength of rectangular slabs), Meddlande nr 137, Institutionen for Byggnadsstatik,KTH
Stockholm, 1990.
21. Tolf P., Plattjocklekens inverkan pa betongplattors hallfasthet vid genomstansning-Forsok
med cirkulara plattor,(Influence of slab thiskness on the punching strength of concrete slabs-
Tests of circular slabs) Meddelande nr. 146, Institutionen for Byggnadsstatik, KTH
Stockholm, 1988.
22. Marzouk H. And Hussein A., Experimental investigation on the behavior of high-strength
concrete slabs, ACI Structural Journal, V88, No.6,Nov-Dec 1991,pp 701-713.
23. Rizk E. And Marzuk H., Experimental validation of minimum flexural reinforcement for
thick high- strength concrete plates, ACI Structural Journal, Vol.108 No 3, May-June 2011,
pp 332-340.
24. Rizk E., Marzuk H. and Hussein A., Punching shear of thick flat plates with and without
shear reinforcement, ACI Structural Journal, Vol. 108, No. 5, Sept-Oct 2011, pp 581-591.
25. Birkle G., Influence of slab thickness on punching shear strength, ACI Journal, Mar.-Apr.
2008, pp180-188.
26. Moe J., Shearing strength of reinforced concrete slabs and footings under concentrated loads,
Development Dept. Bulletin D47. Portland Cement Association, Skokie, Illinois, 1961.
27. Regan P.E., Symmetric punching of reinforced concrete slabs, Magazine of Concrete
Research, Vol. 38, No 136, Sept 1986, pp 115-128.
28. Lips S., Fernandez Ruiz M., and Muttoni A., Experimental investigation on punching
strength and deformation capacity of shear reinforced slabs, ACI Structural Journal, V109,
No 6, Nov-Dec 2012, pp889-900.
29. Heinzman D.,Etter S., Villiger S., and Jaeger T., Punching Tests on Reinforced Concrete
Slabs with and without Shear Reinforcement, ACI Structural Journal, Vol.109 No 6, Nov-
Dec 2012, pp787-794
30. Tomaszewicz,A.,High-Strength Concrete,SP2-Plates and Shells. Report 2.3 Punching Shear
Capacity of Reinforced Concrete Slabs. Report No.STF70 A93082,SINTEF Structure and
Concrete, Trondheim,36pp.

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