dbf

V oc

cn ⎥

⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

621

'

β

COMPARISON OF PUNCHING SHEAR CAPACITY OBTAINED FROM

ACI 318-02, MODEL CODE 90 AND EUROCODE 2

Wanchalearm Kornkasem

Department of Civil Engineering, Mahanakorn University of Technologywanchale@mut.ac.th.

Prakit Premthamakorn

Department of Civil Engineering, Mahanakorn University of Technologyprakit@mut.ac.th.

ABSTRACT: This paper examines methods for the design of reinforced concrete slab for punching shear capacity asrecommended by ACI 318-02, Eurocode EC-2 and CEB FIP Model Code 90 (MC-90). The paper describes ananalytical investigation of differences in the design, and examines the effects of parameters (the ratio of flexuralreinforcement, critical parameter, effective depth, concrete strength, etc.) on the punching shear capacity of the slab asreflected in the Codes. The results show that the punching shear capacity obtained from EC-2 is overall mostconservative as compared to MC-90 and ACI318-02 except when the ratio of flexural reinforcement (ρ) is less than0.004, and when the ratio of column length to breadth (βc) is greater than 2.2. In case the ratio ρ is less than 0.004, thedesign expression of MC-90, which does not consider the direct shear resistance of concrete, is highly conservative ascompared to those of EC-2 and ACI318-02. This conservatism raises some concerns and emphasizes the need to reviewthe design equation of MC-90.

KEYWORDS: CONCRETE SLAB, PUNCHING SHEAR CAPACITY, SLAB-COLUMN CONNECTION

1. INTRODUCTION

The three codes, ACI 318-02, Eurocode EC-2 and ModelCode 90 (MC-90), present rather different expressions indesigning the slabs in vicinity of columns or concentratedloads for punching shear. While there may be somesimilarly used parameters such as the ratio of flexuralreinforcement, prestressing forces and critical parameterthat is a function of an effective depth and opening, theway that each parameter is taken into consideration isdistinct. Moreover, some parameter that is relied upon incalculation of punching shear capacities of the slab byMC-90 and EC-2 is not at all considered in ACI 318-02.That is the ratio of flexural reinforcement, for example.ACI 318-02 does not consider the contribution of flexuralreinforcement to the punching shear resistance of theslab. In contrast, Model Code 90 considers that theresistance to punching shear is zero for unreinforcedconcrete. And, EC-2 considers both the contribution offlexural reinforcement and also the direct shear resistanceof concrete.

It is therefore worthwhile particularly for practicingengineers to understand in detail design proceduresrecommended by the three widely used Codes of practice,the difference among them, and the effects of suchdifference on the final design results so that betterunderstanding in applying the Codes with regard to the

conservatism of one Code as compared to the others canbe achieved.

This paper presents in detail methods for the design ofreinforced concrete slab for punching shearrecommended by the three codes. In addition, thecomparison study is conducted to examine the effects ofthe compressive strength of concrete, the ratio of flexuralreinforcement, effective depth, column dimensions on thepunching shear capacity of the slab as reflected in theCodes.

2. COMPARISON OF PUNCHING SHEARDESIGN OF THE THREE CODES

Following are methods of calculating punching shear capacity adopted by the three Codes.

Design Formula

ACI318-02 gives 3 equations for the design of nonprestressed slab and footing without shear reinforcement. The punching shear capacity shall be the smallest of the following three equations.

(1)

dbfV ocn ⎥⎦⎤

⎢⎣⎡= '

31

dbf

bd

V oc

o

sn ⎥

⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

122

'α

( ) dbkV oRdn 1402.1 ρτ +=

015.0. 111 ≤= yx ρρρ

( ) 2/yx ddd +=

( )[ ] dbfV ockn3

110012.0 ρξ=

( )d/2001+=ξ

yx ρρρ .=

(2)

(3)

where bo is perimeter of critical section, d is effective depth of the slab, fc’ is compressive cylinder strength of concrete at 28 days (MPa), βc is the ratio of long side to short side of the concentrated load, and αs is the constant; 40 for interior columns, 30 for edge columns and 20 for corner columns.

The nominal punching shear stress of slabs subjected to bending in two directions in the vicinity of square columns is limited to '3/1 cf . However, for rectangular column or loaded area that has the ratio of length to breadth (βc) greater than 2.0, test results have indicated that the limit of '3/1 cf is unconservative. The results show that the actual shear stress on the critical section varies from a maximum of '3/1 cf around the corners to

'6/1 cf or less along the long sides of the column or loaded area. Therefore, the larger the value βc, the smaller the punching shear capacity as reflected in Equation (1).

The punching shear capacity also depends on the ratio of critical perimeter to slab depth (bo/d) and location of concentrated loads or columns. This effect is taken into consideration in Equation (2).

Eurocode (EC-2) gives the following expression for calculating the shear resistance of non-prestressed slabs:

(4)

where τRd = basic design strength of memberswithout shear reinforcement (Table 1)depending on the compressive cylinderstrength of concrete at 28 days (fck ),

k = 1.6 - d ≥ 1.0 (d in meter),

in which, ρ1x and ρ1y relate to the tension steel in x and y direction, and dx and dy are effective depths of the slab in x and y direction, respectively.

Table 1: Basic design strength of members without shear reinforcement τRd.

Fck(MPa) 12 16 20 25 30 35 40 45 50

τRd(MPa) 0.18 0.22 0.26 0.30 0.34 0.37 0.41 0.44 0.48

Figure 1. Basic design strength v.s. compressivecylinder strength of concrete

EC-2 has a limit on the contribution of flexural reinforcement. That is the maximum ratio of flexural reinforcement (ρ1) of 0.015 is to be considered in the design.

Modal Code 90 (MC-90) adopts the following equation for the shear resistance of a reinforced concrete slab on a control perimeter:

(5)

where (d in meter),

ρx and ρy are the ratios of flexural reinforcement in orthogonal directions, calculated for a width equal to the side dimension of the loaded area plus 3d to either side (or to the slab edge if closer). MC-90 does not seem to have a limit on the ratio of flexural reinforcement.

Critical Perimeter

In ACI318-02, the critical section is taken at a distance d/2 from the edges or corners of the loaded area or changes in slab thickness such as edge of capitals or drop panels. For interior rectangular columns, the critical section is defined by straight lines drawn parallel to and at a distance d/2 from the edge of the columns as shown in Figure 2. By taking a critical section at a distance d/2 from the periphery of the concentrated load, the shear strength is almost independent of the ratio of column size to slab depth.

Figure 2. Critical perimeters at interior columns(ACI318-02).

In EC-2, the critical perimeter for circular or rectangular loaded areas located away from unsupported edges is

d/2 d/2

d/2

0

0.1

0.2

0.3

0.4

0.5

0.6

10 15 20 25 30 35 40 45 50Cylinder strength of concrete (MPa)

Bas

ic d

esig

n sh

ear s

treng

th(M

Pa)

defined as a perimeter surrounding the loaded area and at a distance 1.5d as shown in Figure 3.

Figure 3. Critical perimeters at interior columns (EC-2).

The punching provision is applicable to

(a) circular shape having perimeter not exceeding 3.5d,(b) rectangular shape having perimeter not exceeding

11d and the ratio of length to breadth not exceeding2.

In case of elongated supports such as wall, the shear force is concentrated in the corners, the critical perimeters as shown in Figure 4 may be used in the absence of a more detailed analysis.

Figure 4. Critical perimeters for non-standard cases(EC-2).

MC-90 recommends that the control perimeter be taken at a distance 2.0d from the periphery of loaded area as shown in Figure 5.

Figure 5. Critical perimeters at interior columns(MC-90).

The expression given by MC-90 is applicable to the typical case as shown in Figure 5. For more complex cases such as wall-shaped support, MC-90 recommends that an appropriate structural analysis be performed.

Load Factors

ACI318-02 adopts load factors as recommended in ASCE-7 (1.2 for dead load and 1.6 for live load). EC-2 and MC-90 use similar load factors, which are 1.35 for permanent load and 1.50 for live load.

For EC-2 and MC-90, the strength factors are considered as a reduction in material strength. For example, the basic design strength (τRd) from EC-2 is derived based on the strength factor γc of 1.5 (denominator). Similarly, the expression given in MC-90 already considers the material strength factor. ACI318-02 suggests the strength factor of 0.75 to be applied to the nominal shear strength of members.

One might argue that there is somewhat different degree of safety for the overall design by taking different load combinations and/or resistance factors, which by no means is correct. However, as intended, the load factors are to account for unavoidable inaccuracies and uncertainties in the determination of loads. These factors could be changed as appropriate for any specific region.

In this paper, the main interest is to investigate the provisions for predicting the punching shear capacity of non-prestressed slab. Therefore; the load factors are not considered. However, to compare the punching capacity predicted by ACI318-02 with those by EC-2 and MC-90 design expressions, in which the strength reduction factors are inherently considered, the nominal shear capacity computed from ACI318-02 is adjusted with the strength factor of 0.75.

3. COMPARISON OF RESULTS FROMPARAMETRIC STUDY

The parametric study is conducted to examine the effectsof compressive strength of concrete, the ratio of flexuralreinforcement, the effective depth and the columndimensions on the punching capacity of the interiorcolumns or concentrated loads.

Compressive strength of concrete

Figure 6(a) and 6(b) show variations of punching shearresistance (in form of stress and force, respectively) withrespect to varying compressive cylinder strength ofconcrete for arbitrarily chosen constant effective depth of200 mm, square column width of 400 mm and ratio offlexural reinforcement of 0.01. It is observed that thepunching shear strength increases less rapidly withincreasing concrete strength.

ACI318-02 gives higher punching shear stress (about100% and 65% more than that from MC-90 and EC-2,respectively, at fc’ = 50 MPa). However, because of thesmaller critical perimeter, the design punching loads aremore comparable with those from EC-2 and MC-90. Thepunching capacities from EC-2 and MC-90 areconverging as the concrete strength increases.

The ratio of flexural reinforcement

In Figures 7(a) and 7(b), the design punching shearcapacity is plotted with varying ratios of flexuralreinforcement and constant d = 200 mm, square columnwidth = 400 mm, and fc’ = 30 MPa.

The design punching loads predicted by ACI318-02 areindependent of the ratio of flexural reinforcement and

they are higher than those from the other two codes whenthe ratio ρ < 0.012. MC-90 does not consider thecontribution of direct shear strength of concrete;therefore, gives most conservative punching capacitywhen ρ < 0.004.

(a)

(b)

Figure 6. Effects of compressive strength of concrete.

(a)

(b)

Figure 7. Effects of the ratio of flexural reinforcement.

Effective depth

The effects of effective depth are investigated throughFigure 8 for constant ρ = 0.01, square column width =400 mm, and fc’ = 30 MPa. Figure 8(a) shows that thedesign shear stress from ACI318-02 is insensitive to theeffective depth while the design stress from EC-2 andMC-90 slightly decreases as the effective depth of theslab increases.

ACI318-02 predicts higher punching load capacity thanEC-2 (most conservative) for about 30% and 20% higherfor d = 100 mm and d = 300 mm, respectively.

(a)

(b)

Figure 8. Effects of effective depth.

Column dimensions

The variations of punching shear capacity with respect tothe ratio of column length to breadth (βc) and squarecolumn width for constant d = 200 mm, ρ = 0.01, and fc’= 30 MPa are plotted in Figures 9 and 10, respectively. Itshould be noted that, for the considered case study, thesimilar concept of reducing the critical perimeter to thatof EC-2 is applied for MC-90.

In contrast to those obtained from EC-2 and MC-90,which are independent of the ratio βc and square columnwidth (the ratio bo/d), the design shear stresses fromACI318-02 decrease when the ratio βc is greater than 2.0and when the square column width is greater than 800mm (the ratio bo/d is greater than 20). The designpunching loads from ACI318-02 are more conservativethan those from others when the ratio βc is greater than2.2.

0.0

0.4

0.8

1.2

1.6

2.0

10 15 20 25 30 35 40 45 50Compressive strength of concrete (MPa)

Punc

hing

shea

r stre

ss (M

Pa)

ACI-318-02 EC-2 MC-90

0

200

400

600

800

1000

10 15 20 25 30 35 40 45 50Compressive strength of concrete (MPa)

Punc

hing

shea

r for

ce (k

N)

ACI-318-02 EC-2 MC-90

0.00.20.40.60.81.01.21.41.6

0.000 0.005 0.010 0.015 0.020Ratio of flexural reinforcement

Punc

hing

shea

r stre

ss (M

Pa)

ACI 318-02 EC-2 MC-90

0

200

400

600

800

1000

0.000 0.005 0.010 0.015 0.020Ratio of flexural reinforcement

Punc

hing

shea

r for

ce (k

N)

ACI 318-02 EC-2 MC-90

0.00.20.40.60.81.01.21.41.6

100 140 180 220 260 300Effective depth (mm)

Punc

hing

shea

r stre

ss (M

Pa)

ACI 318-02 EC-2 MC-90

0

200

400

600

800

1000

1200

100 140 180 220 260 300Effective depth (mm)

Punc

hing

shea

r for

ce (k

N)

ACI 318-02 EC-2 MC-90

(a)

(b)

Figure 9. Effects of the ratio of column length tobreadth (βc).

(a)

(b)

Figure 10. Effects of square column width.

4. CONCLUSIONS

(1) The punching shear capacity obtained from EC-2 isoverall most conservative as compared to MC-90 andACI318-02 except when the ratio of flexuralreinforcement (ρ) is less than 0.004, for which MC-90 gives most conservative values, and when theratio of column length to breadth (βc) is greater than2.2, for which ACI318-02 gives most conservativeresults.

(2) The punching shear capacity from ACI318-02 isindependent of the ratio ρ and effective depth, whichis contrast to the provisions given by EC-2 and MC-90.

(3) In case the ratio ρ is less than 0.004, the designexpression of MC-90, which does not consider thedirect shear resistance of concrete, is highlyconservative as compared to those of EC-2 andACI318-02. This conservatism raises some concernsespecially for reinforced concrete members with lowflexural reinforcement such as spread footings, andemphasizes the need to review the design equation ofMC-90 [4].

(4) The punching shear stress from EC-2 and MC-90does not depend on the ratio βc, and square columnwidth (the ratio bo/d), while that from ACI318-02does. For rectangular columns or wall-shapedsupports, EC-2 considers reduced critical perimeter,posting a limit on the punching load capacity;however, the punching capacity predicted fromACI318-02 is still most conservative as the ratio ofcolumn length to breadth is greater than 2.2.

5. REFERENCES

[1] ACI 318-02. Building Code Requirements forReinforced Concrete. American Concrete Institute,2002.

[2] Eurocode 2. Design of Concrete Structures – Part 1:General Rules and Rules for Buildings, 1998.

[3] Model Code CEB-FIP 1990 for structural concrete.1999.

[4] Calavera, J., “Comparison of Eurocode 2, Model Code 90 and ACI 318-99 with regard to shear and punching provisions for footings,” Journal of the fib: Structural Concrete, Vol. 2, No. 4, 2001.

0.00.20.40.60.81.01.21.41.6

0 500 1000 1500 2000 2500Square column width (mm)

Punc

hing

shea

r stre

ss (M

Pa)

ACI 318-02 EC-2 MC-90

0.00.20.40.60.81.01.21.41.6

1.0 1.5 2.0 2.5 3.0 3.5 4.0Ratio of column length to breadth

Punc

hing

shea

r stre

ss (M

Pa)

ACI 318-02 EC-2 MC-90

Eq. (3) Eq. (2)

Eq. (3) Eq. (1)

0

200

400

600

800

1000

1.0 1.5 2.0 2.5 3.0 3.5 4.0Ratio of column length to breadth

Punc

hing

shea

r for

ce (k

N)

ACI 318-02 EC-2 MC-90

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500Square column width (mm)

Punc

hing

shea

r for

ce (k

N)

ACI 318-02 EC-2 MC-90