ACI 232-3 Punching Shear

39

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.


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).


tests reported by Nylander and Sundquist (1972).


tests reported by Regan (1986) and Birkle (2004).


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).


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).


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.

Documents

ACI 232-3 Punching Shear