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SP-232—3
Effects of Size, Geometry andMaterial Properties on Punching
Shear Resistance
by D. Mitchell, W.D. Cook, and W. Dilger
Synopsis:Synopsis:Synopsis:Synopsis:Synopsis: This paper presents some code expressions for the punching shear strengthof slab-column connections. The influence of slab thickness (size effect), columnaspect ratio and concrete compressive strength are investigated by examiningexperimental results.
Keywords: column aspect ratio; concrete design codes; concretestrength; punching shear; size effects
40 Mitchell et al.Denis Mitchell, FACI, is a James McGill Professor and Chair of Civil Engineering at
McGill University. He is a member of ACI Committees 318-B, Structural Concrete
Building Code, Reinforcement and Development; 408, Bond and Development of
Reinforcement; and Joint ACI-ASCE Committee 445, Shear and Torsion. He is Chair of
ACI’s Fellows Nomination Committee. He also chairs the Canadian Standards
Association Committee A23.3, Design of Concrete Structures.
William D. Cook, MACI, is a research engineer in the Department of Civil Engineering
at McGill University. His interests include the non-linear analysis of reinforced concrete
structures, the influence of high-strength concrete and the use of new construction
materials.
Walter H. Dilger, FACI, FRSC, Professor Emeritus of Civil Engineering at the
University of Calgary, Canada, is a member of ACI/ASCE Committee 445 and has been
engaged in shear research since the 1960s. He is co-inventor of the shear stud
reinforcement for flat slabs. Other research interests include effects of creep, shrinkage
and temperature on structural concrete. He is also active in ACI Committee 209.
INTRODUCTION
This chapter provides a summary of the design expressions for punching shear strength in
a number of international codes and standards such as ACI 318 (ACI 2005), CSA A23.3
(CSA 2004), CEB-FIP (1990), Eurocode 2 (EC2 2003) and the BS 8110 (1997). In
particular, the influences of size effect, column aspect ratio and concrete strength are
discussed.
The fib report (fib 2001) on punching of structural concrete slabs provides a comparison
of codes and behavioral models as well as providing a data bank of test results on
punching shear failures.
DISCUSSION OF CODE PROVISIONS
This chapter discusses the punching shear resistance of slab-column connections without
shear reinforcement. A consistent set of symbols has been adopted for all of the code
expressions and the equations are given in SI units (MPa and mm units). It is noted that
the equations given below are for the nominal shear resistance (all capacity reduction
factors and material resistance factors are taken as 1.0). The code equations for the
nominal concrete shear capacity, Vc, are summarized below:
American Concrete Institute Code, ACI 318-05 (ACI 2005)
According to ACI 318-05 the nominal shear resistance, Vc, for normal density concrete is
taken as the smallest of:
Punching Shear in Reinforced Concrete Slabs 41
6
2
1
avoc
c
dbf
V
′
+=
β
(3-1)
12
2
avoc
o
avs
c
dbf
b
d
V
′
+=
α
(3-2)
avocc
dbfV ′=
3
1
(3-3)
where dav
is the average effective depth, bo is the perimeter of the critical section located
at a distance 0.5dav
from the face of the column, β is the ratio of the long side to short side
of the concentrated load or reaction area and αs is a factor accounting for the location of
the slab-column connection (40 for interior columns, 30 for edge columns and 20 for
corner columns). The ACI Code places an upper limit on c
f ′ of 8.33 MPa (100 psi).
The special features of the ACI code expressions for punching shear include a factor for
the rectangularity of the column, β, and a size effect when the critical shear periphery, bo ,
becomes large compared to the effective depth, dav
. The shear strength is a function of the
square root of the concrete compressive strength and is limited to a shear stress
corresponding to a concrete with a compressive strength of 69 MPa (10,000 psi).
Canadian Standard CSA A 23.3-04 (CSA 2004)
The punching shear equations in the 2004 Canadian Standard CSA A23.3 are based on
the same expressions as ACI for the nominal resistance. The shear stress coefficients in
the design expressions for the factored punching shear resistance have been increased by
14% from the nominal values given in Equations (3-1) to (3-3) (e.g., from 1/3 to 0.38 in
Equation (3-3)) due to the use of a relatively low material resistance factor for concrete
( 65.0=
c
φ ). The nominal resistance differs from ACI only in that it includes a size factor
for slabs having an effective depth greater than 300 mm (12 in.). For such cases the
punching shear strength is multiplied by a factor of:
av
d+1000
1300
(3-4)
where dav
is the average effective depth for the slab.
Eurocode 2 (EC2 2003) and CEB-FIP Model Code (CEB-FIP 1990)
The expression for the nominal punching strength is:
42 Mitchell et al.
( )avockav
av
cdbf
d
V3/1
100
200
118.0 ρ
+= (3-5)
where bo is the perimeter of the critical section located at a distance of 2d
av from the face
of the column and fck
is the characteristic strength used in European codes. In using
Equation (3-5) fck
cannot be taken greater than 50 MPa. The nominal punching shear
strength has been determined by multiplying the Eurocode 2 design expression
coefficient of 0.12 by the concrete partial safety factor, γc, of 1.5 to give the 0.18
coefficient in Equation (3-5). The average reinforcement ratio, ρav
, is limited to a
maximum of 0.02. The Eurocode 2 includes a size effect depending on the value of dav
.
The term within the square brackets in Equation (3-5) must be less than or equal to 2.0.
The shear strength is a function of the average flexural reinforcement ratio in the slab and
the shear strength varies as the cube root of the concrete compressive strength. The size
effect can be written as:
0.1
200
15.0 ≤
+
av
d
(3-6)
It is noted that the Eurocode 2 has the same general form as the German Code (DIN
1045-1).
British Code BS 8110 (BS 8110 1997)
The expression for the nominal punching strength is:
avo
c
av
av
c
db
f
d
V
3/1
4
25
100
400
79.0
′
= ρ (3-7)
where bo is the perimeter of the critical section located at a distance of 1.5d
av from the
face of the column and ρav
is limited to 0.03. In using Equation (3-7) the concrete
compressive strength cannot be taken greater than 40 MPa. The influence of size is
included in the term:
0.1
400
4 ≤
av
d
(3-8)
EXPERIMENTAL PROGRAMS ON SIZE EFFECT
It is difficult to gather experimental data solely on the size effect. Many of the
experimental programs reported in the literature have varied not just the thickness of the
slab, but other parameters such as concrete strength, the reinforcement ratio ρ and the
Punching Shear in Reinforced Concrete Slabs 43column size. For example, keeping the reinforcement ratio constant while increasing the
slab thickness leads to a decreasing ratio of the flexural capacity to shear capacity.
Having a smaller flexural capacity increases flexural cracking prior to failure and reduces
the punching shear capacity. The results of many of the testing programs are also affected
by other factors such as having extremely small specimens, having extensive yielding of
the flexural reinforcement prior to punching shear failure or experiencing bond failures of
the flexure reinforcement.
The test series on six reinforced concrete slabs tested by Li (2000) provide some useful
data on the size effect. The overall thickness, h, of the slabs varied from 135 mm to 550
mm. The slabs were tested upside down by loading the centrally located high-strength
concrete (80 MPa) square columns and reacting against neoprene pads on HSS sections
sitting on the strong floor. Figure 3-1 shows the testing of Specimen P500, with an
average effective depth of 500 mm. The flexural reinforcement and the overall dimension
of the test slabs varied as shown in Table 3-1. Adequate anchorage of the flexural
reinforcement was ensured by welding steel plates on the ends of the bars. All of the
slabs were cast from the same batch of ready-mix concrete and the average concrete
compressive strength of the slab concrete was 39.4 MPa.
Figure 3-2 shows the variation of the normalized shear stress versus the average effective
depth for this series. The normalized shear stress was determined from the shear stress
calculated based on the ACI Code critical shear periphery and dividing byc
f ′ . It is
noted that the flexural reinforcement ratio was constant at 0.76% for the three thickest
slabs, with ρ varying from 0.83% to 0.98% for the thinner slabs (see Table 3-1). It is clear
from Fig. 3-2 that there is a size effect for punching shear for slabs thicker than about 200
mm.
The test series by Nylander and Sundquist (1972), on the other hand, shows decreasing
normalized stresses for slabs with an increase in effective depth from 95.5 mm to
201 mm. These results indicate that there is an influence of slab thickness on the shear
stress at failure, even for effective depths less than 200 mm. Figure 3-3 shows the
variation in the normalized shear stress (c
fv ′/ ), based on the ACI critical shear
periphery, as a function of the average effective depth for these tests, including one test
by Tolf (1988) with a thickness of 619 mm. The slabs were supported by circular
columns having diameters of 120, 240 and 800 mm. The concrete strengths varied from
23.2 to 30.6 MPa. The results shown in Fig. 3-3 have been separated into two groups; one
with an average reinforcement ratio of 0.76% and the other for an average reinforcement
ratio of 0.53%. The slabs containing the higher ρ values had slightly higher capacities
than the tests with lower values of ρ, as expected. The trend of the data clearly shows a
size effect with the normalized shear stress decreasing with increased values of dav
.
Similar results were observed by Birkle (2004) who tested slabs with thicknesses of 160,
230 and 300 mm, and Regan (1986) who varied the slab thickness from 80 to 250 mm.
The normalized shear stresses at failure for both these test series are presented in Fig. 3-4.
It is to be noted that out of Regan’s 23 tests only the tests of the Group II Series which
focussed on size and depth of the specimens are considered. Also, the tests with varying
maximum aggregate size are not included.
44 Mitchell et al.Figure 3-5 compares the shape of the different size effect expressions from three codes.
The size effect factors are given by Equations (3-4), (3-6) and (3-8). In order to compare
these different expressions, the size effect factor has been normalized to give a value of
1.0 when the average effective depth is 200 mm. The CSA A23.3-04 expression gives a
size effect factor only for cases of average effective depths greater than 300 mm. The BS
8110 Code has a size effect factor that does not decrease beyond an average effective
depth of 400 mm.
Figure 3-6 compares the code predictions with the test results reported by Li (2000). For
these predictions the full design expressions for the nominal resistances were used,
including the influence of ρ for the predictions and no distinction was made
betweenc
f ′ andckf . All of the code predictions are very good up to and including an
average effective depth of 300 mm. The ACI Code does not have a size effect factor and
hence overestimates the punching shear capacity for the thicker slabs. The predictions
using the CSA expressions give similar results to the predictions using the expression in
Eurocode 2, both of them overestimating the shear capacity of the thickest slab by about
20%. The expression from BS 8110 is more conservative than the other code expressions
and only slightly over-predicts the strength of the thickest slab tested. When the tests by
Regan (1986) and Birkle (2004) are compared to relevant provisions of CSA A23.3-04
(see Fig. 3-7), the need for a size factor is clearly shown. While the ratio of tested to
predicted failure load is conservative for the thinner slabs, this ratio is 0.9 for the slab
with a total thickness, h, of 300 mm. It is to be noted that for h ≤ 300 mm the ACI code is
equivalent to CSA A23.3-04.
The comparisons of the predictions with the measured strengths emphasize the need to
include size effects in determining the punching shear resistance of slabs.
EXPERIMENTAL PROGRAMS ON COLUMN RECTANGULARITY
The first test series in which the column rectangularity was investigated systematically
was performed by Hawkins et al. (1971). These tests provided the basis for the
introduction of this parameter to the ACI punching shear equation. The column
“rectangularity” or “aspect ratio” β is the ratio of the larger to the smaller column
dimension. The ACI Commentary (ACI 2005) states that for β values larger than 2.0, “the
actual shear stress on the critical section at punching shear failure varies from a
maximum of about c
f ′33.0 around the corners of the column or loaded area, down to
c
f ′166.0 or less along the long sides between the two end sections”.
Figure 3-8 shows the variation in the normalized shear stress (c
fv ′/ ), based on the ACI
critical shear periphery, as a function of β for different test series. In the tests reported by
Hawkins et al. (1971), β was varied between 2.0 and 4.3. The tests reported by Oliveira
et al. (2004) had columns that were 120 mm wide and 120, 240, 360, 480 and 600 mm
long. The reinforcement ratio ρ was about 1.1% and the concrete strength varied from 54
to 63 MPa. The results of two test series reported by Leong and Teng (2000) for slabs
with values of ρ between 1.64% and 1.81% are also shown in the figure. The concrete
Punching Shear in Reinforced Concrete Slabs 45compressive strengths varied from 33 MPa to 40.2 MPa. One series had a minimum
column dimension of 200 mm, while the other series had a minimum column dimension
of 250 mm, with β values for both series ranging from 1 to 5. As expected the slab
specimens with the larger values of ρ had higher normalized shear stresses at failure. This
figure clearly shows that the normalized shear stress decreases as the columns
rectangularity increases. Also shown in Fig. 3-8 are the predictions using the ACI Code
(ACI 2005). The ACI expression that includes the effect of column rectangularity
(Equation 3-1)) provides a conservative prediction for these test results and predicts the
trend in the data well.
EXPERIMENTAL PROGRAMS ON THE EFFECT OF CONCRETE STRENGTH
Figure 3-9 compares the predictions using the ACI code (ACI 2005) expressions for
experimental programs investigating the influence of concrete compressive strength.
There is considerable scatter in the test results because of the many different parameters
in the experimental programs and some specimens experienced flexural yielding. For
example, the specimen with the low shear stress for a concrete compressive strength of
67 MPa, tested by Marzouk and Hussein (1991), has a low ρ and is reported by the
researchers to have failed in flexure, however the databank from the fib report (fib 2001)
reports that according to its criterion, this specimen failed in punching shear.
In their 1956 study, Elstner and Hognestad systematically varied the concrete strength'
c
f
and the reinforcement ratio ρ. The shear stresses at failure, v, based on the ACI critical
shear periphery, are plotted as a function of the concrete strength for the three different
values of ρ in Fig. 3-10. Also shown in Fig. 3-10 are the variations of v as a function
of ( )n
c
f'
, where n = 1/3, 1/2 and 2/3. For each reinforcement ratio a reference test has
been selected to calibrate the constant for the three different functions (Sherif and Dilger,
1996). These figures show that the overall trend is reasonably represented by n = 1/3 as
well as n = 1/2.
Figure 3-11 shows the variation of the shear capacity as a function of the concrete
compressive strength for test results reported by Ghannoum (1998) and McHarg et al.
(2000). The slab specimens were 150 mm thick, supported by 225 by 225 mm columns
and loaded with 8 equal point loads around the perimeter of the square slab. The test
specimens had two different values of ρ, 1.18% and 2.15%. Also shown in Fig. 3-11 are
the predictions made using the expressions for the nominal punching shear resistance
from the ACI Code (ACI 2005), the Eurocode 2 (2003) and the BS 8110 (1997). The ACI
predictions are generally conservative with some data points close to the predicted
capacities. The Eurocode 2 gives conservative predictions for this test series, while the
BS 8110 standard gives slightly unconservative predictions for the cases with concrete
compressive strengths less than 40 MPa.
Figure 3-12 compares the shapes of the concrete strength functions, one with c
f ′ and
the other with3
c
f ′ , with the test results reported by Ghannoum (1998) and McHarg et al.
46 Mitchell et al.(2000). These two functions were normalized to give a value of 1.0 at a concrete strength
of 30 MPa. For each of these test results, the normalized shear ratio is taken as the failure
load divided by the failure load for the case with a concrete compressive strength of 30
MPa. It is difficult to conclude that the shape of one function is better than the shape of
another function because the different codes have different coefficients in the design
expressions. Based on Fig. 3-12, it appears that the cube root function, for the normalized
strength plot chosen, fits the data in a more conservative manner.
Marzouk and Hussein (1991), Gardner (1995) and Sherif and Dilger (1996) proposed
using a punching shear equation that is proportional to 3
c
f ′ rather thanc
f ′ . The cube
root function gives more conservative results for high-strength concrete. It is noted that
the ACI Code places an upper limit on c
f ′ of 8.33 MPa (100 psi). The ACI
Commentary (2005) indicates that this is a prudent limit because “there are limited test
data on the two-way shear strength of high-strength concrete slabs”.
CONCLUSIONS
The following conclusions arise from comparison of code expressions with test results:
1. As the effective depth increases the shear stress at punching failure decreases.
This size effect is significant and is an important feature to include in code
design expressions.
2. As the rectangularity of a column increases the shear stress at punching failure
decreases. This geometric feature, expressed as the aspect ratio of the long side
to the short side of a column, is an important feature to include in code design
expressions.
3. It is well known that the shear stress at punching shear failure increases with
increasing compressive strength of the concrete. More experimental research is
needed, particularly on high-strength concrete slab-column connections, to
enable the development of design expressions for punching shear that are
applicable to a wide range of concrete strengths.
REFERENCES
ACI 318R-05, 2005, “Building Code Requirements for Structural Concrete and
Commentary,” American Concrete Institute, Farmington Hills, MI.
Base, G.D., 1968, “Dalles-Structures Planes, Thème-Poinçonnement”, Bulletin Nr. 57,
CEB, Lausanne, pp. 68-82.
Birkle, G., 2004, “Punching of Flat Slabs: Influence of Slab Thickness and Stud Layout”
PhD thesis, University of Calgary, Calgary, Alberta, 152 pp.
BS 8110-97, 1997, “Structural Use of Concrete, Part 1: Code of Practice for Design and
Construction”, British Standard Institute, London.
Punching Shear in Reinforced Concrete Slabs 47Criswell, M.E., 1970, “Strength and Behavior of Reinforced Concrete Slab-Column
Connections Subjected to Static and Dynamic Loadings”, Technical Report M-70-1,
United States Army Engineer Waterways Experimental Station, Vicksburg, Mississippi,
December.
CSA Standard A23.3-04, 2004, “Design of Concrete Structures,” Canadian Standards
Association, Mississauga, Ontario.
DIN 1045-1, 2001, “Tragwerke aus Beton, Stahlbeton und Spannbeton; Teil 1:
Bemessung und Konstruktion,” DIN - Deutsches Institut für Normung, Berlin.
Elstner, R.C. and Hognestad, E., 1956, “Shearing Strength of Reinforced Concrete
Slabs”, Journal of the American Concrete Institute, Vol. 53, No.1, July, pp. 29-58.
European Standard, 2003, “Eurocode 2: Design of Concrete Structures – Part 1-1:
General rules and rules for buildings,” European Committee for Standardization,
Brussels.
fib, 2001, “Punching of Structural Concrete Slabs”, Bulletin 12, Fédération
Internationale du Béton, Lausanne, 307 pp.
Gardner, N.J., 1995, “Discussion on Punching Shear Provisions for Reinforced and
Prestressed Concrete Flat Slabs”, Proceedings of the Canadian Society for Civil
Engineering Annual Conference, Ottawa, Ont., June, pp. 247-256
Ghannoum, C. M., 1998, Effect of High-Strength Concrete on the Performance of Slab-
Column Specimens, M. Eng. Thesis, Department of Civil Engineering and Applied
Mechanics, McGill University, Montreal, Québec, 91 p.
Graf, O., 1938, “Strength Tests of Thick Reinforced Concrete Slabs Supported on All
Sides Under Concentrated loads”, Deutscher Ausschuss für Eisenbeton, No. 88, Berlin.
Hawkins, N.M., Fallsen, G.B. and Hinojosa, R.C., 1971, “Influence of Column
Rectangularity on the Behavior of Flat Plate Structures”, SP-30, American Concrete
Institute, Farmington Hills, Mich., pp.127-146.
Leong, K.K. and Teng, S., 2000, “Punching Shear Strength of Slabs with Openings and
Supported on Rectangular Columns”, Nanyang Technological University, Singapore,
August.
Li, K.K.L., 2000, Influence of Size on Punching Shear Strength of Concrete Slabs, M.
Eng. Thesis, Department of Civil Engineering and Applied Mechanics, McGill
University, Montreal, Québec, 78 pp.
Marzouk, H., and Hussein, A., 1991, “Experimental Investigation on the Behavior of
High-Strength Concrete Slabs,” ACI Structural Journal, V. 88, No. 6, pp. 701-713.
McHarg, P.J., Cook, W.D., Mitchell, D., and Yoon, Y.-S., 2000, “Benefits of
Concentrated Slab Reinforcement and Steel Fibers on Performance of Slab-Column
Connections,” ACI Structural Journal, V. 97, No. 2, pp. 225-234.
48 Mitchell et al.Moe, J., 1961, “Shearing Strength of Reinforced Concrete Slabs and Footings Under
Concentrated Loads”, Development Department Bulletin D47, Portland Cement
Association, Skokie, IL., April, 130 pp.
Narasimhan, N., 1971, Shear Reinforcement in Reinforced Concrete Column Heads, PhD
thesis, Imperial College, London.
Nylander, H. and Sundquist, H., 1972, “Genomstansning av Pelarunderstödd Plattbro av
betong med Ospänd Armering”, Meddelande Nr. 104, Institutionen för Byggnadsstatik,
KTH, Stockholm.
Oliveira, D.R.C., Regan, P.E. and Melo, G.S.S, 2004, “Punching Resistance of RC Slabs
with Rectangular Columns”, Magazine of Concrete Research, Vol. 56, No. 3, London,
pp. 123-138.
Petcu, V., Stanculescu, G., Pancaldi, U. and Ionescu, P., 1973, “Studiu de Sinteza Privind
Comportarea la Stapungere a placilor armate de dona durectii (Synthesis Study
Concerning the Punching Behavior of Two-Way Reinforced Concrete Slabs), St. Cerc.
Incerc., H. 3.
Regan, P.E., 1986, “Symmetric Punching of reinforced Concrete Slabs,” Magazine of
Concrete Research, V. 38, No. 136, Sept., London, pp. 115-128.
Sherif, G. and Dilger, W.H., 1996, “Critical review of the CSA A23.3-94 punching shear
strength provisions for interior columns,” Canadian Journal of Civil Engineering, Vol.
23, No. 5, October, pp. 998-1011.
Tolf, P., 1988, “Effect of Slab Thickness on Punching Shear Strength of Concrete Slabs –
Tests on Circular Slabs”, Bulletin 146, Division of Building Statics and Structural
Engineering, KTH, Stockholm.
Punching Shear in Reinforced Concrete Slabs 49
Figure 3-1: Two-way slab test for case with dav
of 500 mm (Li 2000).
50 Mitchell et al.
Figure 3-2: Normalized punching shear stress (cfv ′/ ) vs. average effective depth for
tests reported by Li ( 2000).
Figure 3-3: Normalized punching shear stress (cfv ′/ ) vs. average effective depth for
tests reported by Nylander and Sundquist (1972).
Figure 3-4: Normalized punching shear stress (cfv ′/ ) vs. average effective depth for
tests reported by Regan (1986) and Birkle (2004).
Punching Shear in Reinforced Concrete Slabs 51
Figure 3-5: Size effect factors normalized to an average effective depth of 200 mm.
Figure 3-6: Comparison of code expressions with results reported by Li (2000).
52 Mitchell et al.
Figure 3-7: Ratio of tested to predicted failure loads for tests by Regan (1986) andBirkle (2004).
Figure 3-8: Influence of rectangularity of column on shear strength from tests byHawkins et al. (1971), Leong and Teng (2000), and Oliveira et al. (2004).
Punching Shear in Reinforced Concrete Slabs 53
Figure 3-9: Influence of concrete strength on shear strength and comparison withACI Code (2005) expression.
54 Mitchell et al.
Figure 3-10: Effect of concrete strength on shear strength(tests by Elstner and Hognestad, 1956).
Punching Shear in Reinforced Concrete Slabs 55
Figure 3-11: Comparison of code expressions with test results reported byGhannoum (1998) and McHarg et al. (2000).
Figure 3-12: Comparison of square root and cube root functions with test resultsreported by Ghannoum (1998) and McHarg et al.(2000).
56 Mitchell et al.