Shear Strength in the New Eurocode 2. a Step Forward

Shear strength in the new Eurocode 2. A step forward?A. Cladera and A. R. Marı

The shear strength of reinforced concrete beams with stirrups has been a highly controversial matter since Ritter

and Morsh proposed the first truss models. Since then, different analytical models have been discussed, such

as truss models with concrete contribution, shear/compression theories, truss models with variable angle of

inclination, and compression field theories. However, some of these models were too complex to be implemented

in a code of practice and they had to be simplified. As Regan has pointed out, for simpler models the problem is

mostly that of the need to neglect some factors, considered secondaries. However, what is secondary in one case

may be primary in another. With the release of the new Eurocode 2 (prEN 1992-1-1:2003) the controversy has been

raised again. The EC-2 proposes a very simple formulation based on a truss model. However, the authors think that

it is a gross oversimplification of a complex problem as it neglects important key variables. In this paper the new EC-

2 shear procedure predictions are compared to empirical tests and to other simplified formulations. It is concluded

that the EC-2 procedure is very easy to use by practising engineers but it presents a great scatter of results. On the

one hand, it may be too conservative for slightly shear-reinforced beams or for prestressed beams. On the other, it

may be slightly unconservative for heavily reinforced members.

[doi: 10.1680/stco.2007.8.2.57]

Antoni CladeraUniversity of BalearicIslands, Palma deMallorca, Spain

Antonio R. MarıTechnical Universityof Catalonia, Barcelona,Spain

Introduction

The new Eurocode 2 Design of Concrete Struc-

tures – Part 1-1: General Rules and Rules for

Buildings is going to be launched in some

months.! This new Eurocode1 is adapted to

the challenges that practising engineers must

confront in their everyday work, improving

the previous code in many respects.

The shear strength procedure has changed

considerably from the previous Eurocode. For

beams with web reinforcement, the shear

strength is based on a truss model, with a vari-

able angle of inclination of the struts and

without any concrete contribution. This leads

to a very simple procedure that allows practis-

ing engineers to calculate the shear strength,

for any case, very quickly. In fact, it is almost

as simple as the Ritter2 and Morsch3 models

formulated in the early 20th century.

However, it is the authors’ opinion that this

significant simplification may overlook some

important parameters affecting shear strength,

as Regan already sentenced for some simplified

models.4 The EC-2 shear procedure is based on

a truss model and it verifies the equilibrium con-

dition, therefore the EC-2 model satisfies the

lower bound theorem if the concrete and the

steel do not exceed the yield condition any-

where, and consequently the method is safe.

The latest models found in the technical litera-

ture, even the simplified models, try to satisfy

the equilibrium and the compatibility con-

ditions. In fact, complex models such as the

modified compression field theory (MCFT)5

may be explained as a truss model in which

the shear strength is the sum of the steel and

concrete contribution. The main difference

from a classic truss model with concrete contri-

bution (i.e. the procedure in the EC-2 of 19916)

is that the concrete contribution in the MCFT is

the vertical component of the shear stress trans-

ferred across the crack (Figure 1), yci, and not

the diagonal cracking strength.

Models based on compatibility and equili-

brium conditions predict that the angle of incli-

nation of the struts at failure depends, among

other factors, on the cross-sectional dimen-

sions, the amount of longitudinal and trans-

verse reinforcement and the bending moment

concomitant with the shear force acting at

the studied section. For this reason, these

models predict a non-linear response based

on the amount of web reinforcement. The

greater the number of stirrups the less effective

they are7 because the angle of inclination of

diagonal compressive stresses with respect to

the longitudinal axis of the member increases.

The truss model of the new Eurocode 2 pro-

poses a linear response (without concrete

contribution) until the failure is governed by

crushing of the compression struts. As it will

be discussed later, this leads to very conserva-

tive results when compared with experimental

tests on lightly shear-reinforced beams and

slightly unconservative results for highly

shear-reinforced members.

Shear strength procedure forbeams with web reinforcementin the new Eurocode 2

For reinforced concrete members with vertical

shear reinforcement, the shear resistance,

VRd,s, should be taken to be the lesser, either

VRd;s "Asw

szfywd cot u #1$

or

VRd;max " acbwznfcd=#cot u% tan u$ #2$

where VRd,s is the design value of the shear force

which can be sustained by the yielding shear

reinforcement; VRd,max is the design value of

!This paper was first submitted to StructuralConcrete in October 2004.

1464–4177 (Print) 1751–7648 (Online) # 2007 Thomas Telford and fib

the maximum shear force which can be

sustained by the member, limited by crushing

of the compression struts; Asw is the cross-

sectional area of the shear reinforcement; s is

the spacing of the stirrups; z is the lever arm,

that may be considered as z ¼ 0.9d; fywd is the

yield strength of the shear reinforcement; u is

the angle of the inclined struts; bw is the width

of the web; fcd is the design compressive cylin-

der strength of concrete at 28 days; and ac is

a coefficient that takes into account the effect

of normal stresses on the shear strength. The

recommended value of ac follows from the fol-

lowing expressions: 1 for non-prestressed struc-

tures; (1% scp/fcd) for 0 , scp & 0.25fcd; 1.25

for 0.25fcd , scp & 0.50fcd; and 2.5(12 scp/

fcd) for 0.50fcd , scp & 1.00fcd. scp is compres-

sive stress in concrete from axial load or

prestressing. n is a coefficient that takes into

account the increase of fragility and the

reduction of shear transfer by aggregate inter-

lock with the increase of the compressive con-

crete strength. It may be taken to be 0.6 for

fck & 60 MPa, and 0.92 fck/200 . 0.5 for

high-strength concrete beams.

The recommended limiting values for cot u

are given by

1 & cot u & 2:5 #3$

The new EC-2 proposes, as the minimum

amount of web reinforcement,

Aswfykbs

' 0:08!!!!!!fck

p#4$

where fck is the characteristic compressive

cylinder strength of concrete at 28 days; and

fyk is the characteristic yield strength of

stirrups. To carry out this study, the final draft

of the Eurocode 2 prEN 1992-1-1, dated

December 2003, has been used.1 No major

amendments are assumed to be carried out

to this draft.

Comparison of the EC-2predictions with test results

Shear database

In order to evaluate the EC-2 shear procedure for

reinforced concrete members with web

reinforcement, a database with 202 beams

was developed. It relied basically on the data-

bases developed by Bentz,8 Kuchma9 and

Zararis.10 Although all these 202 beams were

reported to have failed in shear, some may actu-

ally have failed in flexure. For this reason, and in

order to obtain a fair comparison of shear code

predictions and experimentally observed failure

loads, a filter to eliminate those beams failing

in flexure was applied to the database. All

beam specimens whose calculated flexural

strength was lower than the actual value

reached during the test (with a 5% security

margin) were removed from the database.

Finally, the database was composed of 122

beam specimens. All the beamswere simply sup-

ported and loaded with one or two point loads.

The longitudinal reinforcement was constant

along the beam. The shear span to depth ratio,

a/d, for all these beam specimens was greater

than 2.49. Figure 2 shows the shear span of a

typical reinforced concrete beam specimen

tested by the authors. Table 1 summarises

the ranges of the different variables in the

database.

It is important to highlight that the main

objective of this research was not to develop

the most accurate database to justify the use

of one or another model, but to qualitatively

compare some shear procedures with different

tested beams. Great efforts were made in

order to avoid inaccuracies in the database.

Nonetheless, if any errata existed in the final

database it would affect all the compared

procedures.

All the beams in the database contain at

least the minimum amount of shear reinforce-

ment proposed by the CSA-94 provision,11

shown by

Aswfybs

' 0 ( 06!!!!fc

p#5$

where fy is the yield strength of stirrups. The

previous expression was chosen because it is

the minor minimum amount of shear reinforce-

ment of the different studied codes. Yoon

et al.12 justified that it offers an adequate

reserve of strength after the web cracking.

Comparison with the test results

Comparisons between the experimental results

and those obtained by the code procedure are

given in Table 2 and in the Appendix. The value

of the ratio Vfail/Vpred (shear force causing

failure in the empirical test/predicted shear

resistance by different compared formulations)

has been calculated for each beam specimen. If

the shear strength calculated by the EC-2 pro-

cedure was higher than the concomitant shear

force at the flexural failure load, the latter has

been considered as the value of the EC-2

shear strength.

The average Vfail/Vpred ratio for the 122

beam specimens is 1.64 with a coefficient of

variation (CoV) of 32.24% for the new EC-2

formulation.

It can be seen in Table 2 that the average of

the Vfail/Vpred ratio for the EC-2 shear pro-

cedure varies significantly for different subsets

of beams. For heavily shear-reinforced concrete

beams (rwfy . 2 MPa where rw is the

reinforcement ratio for shear reinforcement)

the EC-2 is slightly unconservative with a

Avfy Avfy

f1

q

uci

q

4 Figure 1 Concrete contribution in the MCFT

Structural Concrete ( 2007 ( 8 ( No 2

58 Cladera and Marı

Vfail/Vpred ratio equal to 0.86. On the other

hand, for lightly reinforced concrete beams (rw-

fy & 1 MPa) the EC-2 is excessively conservative

with a Vfail/Vpred ratio equal to 1.80. In Figure 3

the relationship between the EC-2 shear

strength predictions and the amount of web

reinforcement is presented.

The conservative results for slightly

reinforced concrete beams are evident as the

concrete contribution is neglected, a very

important factor when the steel contribution

is low. The slightly unconservative results for

highly reinforced concrete beams are due to

the assumption of the EC-2 procedure

that the angle of the concrete struts can be as

low as cot u ¼ 2.5; meanwhile for highly

reinforced beams cot u may only reach values

around 1.10–1.30 according to models based

on equilibrium and compatibility.

Comparison of the test resultswith other formulations

The empirical shear strength of the 122 beam

specimens of the database has been compared

with four other formulations: the truss model

with concrete contribution of the old EC-26

(ENV 1992-1-1:1991), the equation 11-3 of

the ACI 318-02 Code,13 the draft for public

comment of the CSA14 (CSA Committee

A23.3, 2003), and a semi-analytical method

proposed by Cladera and Marı.7 All these

methods are summarised in Table 3.

The procedure proposed by Cladera and

Marı7 is based on a truss model with a variable

angle of inclination of the struts plus a concrete

contribution. The angle is obtained by compat-

ibility, based on the MCFT. To adjust the con-

crete contribution, an artificial neural network

was developed to predict the shear strength

of reinforced beams failing on diagonal

tension failure and, based on its results, a

parametric study was carried out. The concrete

contribution takes into account the main

observations of this parametric study.

To calculate the shear strength predicted by

the methods that consider the influence of the

bending moment on the shear strength (CSA

200314 and Cladera and Marı7) a critical

location must be selected. This has been

taken as a distance 0.9d from the edge of the

loading plate. As the dimensions of the

loading plate were not always known, it has

been considered a 150 mm wide ()6 inch)

loading plate.

The results shown in Table 2 indicate that

for reinforced concrete members with web

reinforcement the average of the Vfail/Vpred

ratio is equal to 1.19 for the old EC-2 shear

procedure, 1.38 for the ACI 318-02 shear

procedure, 1.13 for the CSA formulation and

1.06 for the proposed method by Cladera

and Marı. The coefficients of variance (CoVs)

are 17.95, 22.25, 17.27 and 15.44% respect-

ively. It can be seen that even the very simple

equation 11-3 of the ACI 318-02 correlates

better with the empirical tests than the new

EC-2 does. The old EC-2 formulation of 1991

also offers a better correlation with the test

results than the new EC-2 shear procedure.

The relationship between the predictions by

different methods considered in this paper and

the amount of web reinforcement is presented

4 Figure 2 Cracking at shear failure for a typical reinforced concrete beam

Table 2 Verification of different shear procedures for reinforced concrete beams withstirrups

Beam specimens # Average Vfail/Vpred CoV Vfail/Vpred

EC-22003

EC-21991

ACI11-3

CSA2003

Cladera2004

EC-22003

EC-21991

ACI11-3

CSA2003

Cladera2004

All 122 1.64 1.19 1.38 1.13 1.06 32.24 17.95 22.25 17.27 15.44d ' 750 mm 9 1.20 1.04 0.97 0.93 1.07 10.04 17.41 18.83 14.15 12.08rwfy & 1 MPa 92 1.80 1.20 1.41 1.15 1.09 27.01 18.48 23.04 17.94 15.37rwfy . 1 MPa,rwfy & 2 MPa

22 1.23 1.18 1.34 1.12 1.02 17.79 14.32 15.78 11.55 10.82

rwfy . 2 MPa 8 0.86 1.06 1.13 0.95 0.88 12.54 18.92 17.28 13.41 13.11fc & 70 MPa 73 1.64 1.14 1.35 1.09 1.04 30.14 14.47 14.16 19.61 12.11fc . 70 MPa 49 1.63 1.26 1.42 1.18 1.09 35.47 20.31 25.26 19.93 18.93rl & 2 % 25 1.50 1.03 1.12 1.01 1.09 30.17 13.80 20.23 12.74 11.94

Table 1 Range of parameters in thedatabase

Parameter Minimum Maximum

d: mm 95 1200rl: % 0.76 5.80rwfy: MPa 0.31 3.28fc: MPa 21 125.2a/d 2.49 5.00Vfail: kN 15.6 1172.2


Shear strength in the new Eurocode 2 59

EC-2prEN 1992-1-1:2003

CSA 2003

0·00

0·50

1·00

1·50

2·00

2·50

3·00

3·50

4·00

0·00 1·00 2·00 3·00 4·00

rwfy: MPa

Vfa

il/V

pred

0·00

0·50

1·00

1·50

2·00

2·50

3·00

3·50

4·00

Vfa

il/V

pred

ACI 318-02 Eq.11-3

Cladera and Mari (2004)

0·00 1·00 2·00 3·00 4·00

rwfy: MPa

4 Figure 3 Correlation of the EC-2, ACI 318-02, CSA 2003 and Cladera and Marı procedures with empirical tests. Influence of the

amount of web reinforcement

Table 3 Summary of different shear design procedures

Formulation Comments

EC-2 final draft prEN 1992-1-1:2003 VRd,s " #Asw=s$zfywd cot u VRd,c " 0 1 & cot u & 2(5VRd,max " acbwznfcd#cot u=#1% cot2 u$$

EC-2 ENV 1992-1-1:1991 VRd,c " tRdk(1(2% 40rl)% 0(15scp

" #bwd fc , 50 MPa

VRd,s " #Asw=s$ zfywd rl & 2.0VRd,max " 1

2 nfcdbw0(9d tRd " 0(25fctk0(05k " 1(6* d ' 1 d(m)

Public review draft CSA Sept 2003 Vc " b!!!!fc

pbwz b and u are given in simple design equations

as function of the longitudinal strainat mid-depth. fc & 64 MPa

Vs " #Avfy=s$ z cot u Vmax = 0(25fcbwd

ACI 318-02 (11-3) Vc "!!!!fc

p=6

$ %bwd fc , 70 MPa

Vd/M & 1Vs " #Asw=s$ zfywd & 0(67!!!!fc

pbwd

There are other expressions for prestressed beams orfor beams with axial forces

Prop. Cladera and Marı (2004) Vc " 0(17j(100rl)1=2f0(2c t1=3 % 0(15scp

h ibwd u is expressed as a equation which depends

on the longitudinal strain in the web andthe non-dimensional shearVs " dv#Aw=s$fywd cot u

j: size effect factor; j ¼ 1%p(200/sx) & 2.75 (sx is the smallest of 0.9d or vertical distance between longitudinal distributed reinforcement, where

d is effective cross-section depth); t: t ¼ Vd/(bw 0.9d) & 3 MPa (Vd is designing (factored) shear strength)



in Figure 3. In the method proposed by Cladera

and Marı,7 the Vfail/Vpred ratio is reduced by

1.24 as the amount of stirrups increases

(Vfail/Vpred ¼ 1.09 for beams with rwfy & 1

MPa and Vfail/Vpred ¼ 0.88 for beams with

rwfy . 2 MPa). However, this ratio was

reduced by 2.09 times for the EC-2 procedure

(Vfail/Vpred ¼ 1.80 for beams with rwfy & 1

MPa and Vfail/Vpred ¼ 0.86 for beams with

rwfy . 2 MPa). The reduction for the CSA

procedure is equal to 1.21.

As other formulations could have been used

for this comparison, the authors encourage the

researchers and engineers to correlate the test

results with their national code procedure or

any other shear formulation. The basic infor-

mation of the beam specimens is presented

in the Appendix.

EC-2 predictions for prestressedconcrete beams compared withother formulations

To study how well the EC-2 predicts the shear

strength of prestress tested beams, 40 beam

specimens in the works reported by Bennett

and Balasooriya,15 Elzanaty et al.,16 Kaufman

and Ramırez,17 Lyngberg,18 Shahawy and

Batchelor19 and Rangan20 have been studied.

The photograph in Figure 4 illustrates a

typical test configuration on a prestressed

beam specimen. Table 4 compares the

correlations of the different shear formulations

with the empirical results.

If the results of all beams are studied

together, the new EC-2 shear procedure gives

a Vfail/Vpred ratio equal to 1.22with a coefficient

of variation of 34.26%. However, it is possible

to divide the beam specimens into two sets

(Table 4). The first set includes the beams that

collapsed because of concrete crushing (22

beam specimens). The second contains the

beams that failed after yielding of stirrups (18

beams). For the second set the new EC-2

shear procedure is more conservative.

The new EC-2 procedure does not consider

the influence of the prestressing force on the

shear strength (Table 3). For this reason, the

average of the Vfail/Vpred ratio increases from

1.11 to 1.96 as the concrete compressive

stress at the centroidal axis due to prestressing

increases from scp & 4.5 MPa to scp . 9 MPa.

This behaviour is not observed so clearly for the

other shear procedures. The proposed method

for prestressed beams with web reinforcement

by Cladera and Marı is an extension of the

method for reinforced concrete beams and it

is presented elsewhere.21

Conclusions

The new Eurocode 2 shear procedure for

members with web reinforcement is, indeed,

a very simple method to calculate the shear

strength for practising engineers and it verifies

the lower bound theory of plasticity. However,

it neglects variables that may be primary

for some beams, and it offers a great

scatter of results when compared to

empirical tests. These results may be slightly

unconservative for highly shear-reinforced

members, and they are too conservative for

slightly reinforced beams, as no concrete con-

tribution is considered. Moreover, the benefit

of prestressing is not taken into account due

to the excessive simplicity of the model. Other

formulations studied in this paper offers much

better correlation to the empirical tests than

the new Eurocode 2, even the well known

ACI Code formulation or the shear procedure

of the old Eurocode of 1991. Definitely, it is

4 Figure 4 Typical test configuration for a prestressed beam specimen

Table 4 Verification of the EC-2 shear procedure and other formulations for prestressedbeams with stirrups

Beam specimens #beams

Average Vtest/Vpred CoV Vtest/Vpred

EC-22003

EC-21991

ACI11-3

CSA2003

Cladera2004

EC-22003

EC-21991

ACI11-3

CSA2003

Cladera2004

All 40 1.22 1.42 1.23 1.22 1.18 34.26 14.75 16.87 12.44 14.62Concrete crushing 22 0.98 1.37 1.34 1.20 1.18 12.87 14.21 14.17 11.84 17.15Stirrups yielding 18 1.52 1.49 1.10 1.24 1.18 30.16 14.47 12.32 13.11 11.29

scp & 4.5 MPa 4 1.11 1.39 0.94 1.04 1.15 10.22 9.77 9.75 15.90 22.37scp .4.5 MPa,scp & 9 MPa

8 1.41 1.45 1.12 1.26 1.18 17.75 17.61 12.37 9.01 9.12

scp . 9 MPa 6 1.96 1.60 1.16 1.36 1.20 24.80 10.94 6.26 5.74 4.65



Appendix

Author[Source]

Bea

m

nam

e

b:

mm

d:

mm

f c:

MPa

r l:

%

r v:

%

f y:

MPa

a/d

Vfail:

kN

VEC-2

2003

Vfail/

VEC2-03

VEC-2

1991

Vfail/

VEC2-91

VACI

11-3

Vfail/

VACI

VCSA

2003

Vfail/

VCSA

VClad

2004

Vfail/

VClad

Vf,max

Bresler

and

Scordelis10

A-1

307

466

24

1. 8

0. 1

330

3. 92

233

106

2. 20

179

1. 30

164

1. 42

192

1. 22

181

1. 29

256

CRA-1

305

460

25

1. 69

0. 1

350

3. 98

168

110

1. 52

179

0. 94

166

1. 01

188

0. 90

177

0. 95

239

CRB-1

229

457

24

2. 28

0. 15

340

4. 01

173

120

1. 44

151

1. 14

138

1. 25

167

1. 04

173

1. 00

201

1WCRA-1

305

457

26

1. 71

0. 1

350

4. 01

215

110

1. 96

183

1. 17

168

1. 28

189

1. 14

178

1. 21

240

1WCA-1

305

462

25

1. 76

0. 1

350

3. 95

220

111

1. 98

182

1. 21

167

1. 31

192

1. 15

181

1. 21

249

1WCB-1

231

460

27

2. 34

0. 15

340

3. 97

202

122

1. 66

162

1. 25

145

1. 39

175

1. 15

182

1. 11

228

3WCA-1

305

460

26

1. 77

0. 1

350

3. 97

208

110

1. 88

186

1. 12

169

1. 23

193

1. 08

182

1. 14

251

Bah

l10

B45

240

1200

25

1. 26

0. 15

440

3468

428

1. 09

394

1. 19

432

1. 08

461

1. 02

406

1. 15

517

Placas

and

Reg

an10

R12

152

272

34

4. 16

0. 21

276

3. 6

117

54

2. 17

82

1. 43

64

1. 83

90

1. 30

111

1. 05

129

R25

152

272

31

4. 16

0. 21

276

3. 6

112

54

2. 07

78

1. 43

62

1. 80

88

1. 27

109

1. 02

119

Swam

yan

d

Andriopoulos1

0

C3

76

95

29

1. 97

0. 16

275

316

72. 18

14

1. 14

10

1. 61

13

1. 21

16

0. 99

17

O3

76

132

28

3. 95

0. 12

258

325

73. 63

17

1. 48

12

2. 12

19

1. 34

26

0. 97

32

Z376

132

26

3. 95

0. 34

179

328

14

2. 02

19

1. 46

15

1. 90

22

1. 26

30

0. 94

30

O4

76

132

28

3. 95

0. 12

258

420

72. 86

17

1. 17

12

1. 67

18

1. 14

24

0. 83

24

Mphondean

d

Fran

tz10

B50-3-3

152

298

22

3. 36

0. 12

292

3. 6

76

36

2. 14

63

1. 21

51

1. 49

74

1. 04

85

0. 90

95

B100-3-3

152

298

28

3. 36

0. 26

269

3. 6

95

71

1. 34

85

1. 12

72

1. 33

95

1. 00

113

0. 84

116

B100-7-3

152

298

47

3. 36

0. 26

269

3. 6

121

71

1. 69

109

1. 10

84

1. 44

106

1. 14

124

0. 97

150

B100-11-3

152

298

69

3. 36

0. 26

269

3. 6

151

71

2. 12

113

1. 34

94

1. 60

114

1. 33

130

1. 16

161

B100-15-3

152

298

82

3. 36

0. 26

269

3. 6

116

71

1. 62

113

1. 03

95

1. 22

114

1. 02

133

0. 87

164

B150-7-3

152

298

47

3. 36

0. 38

271

3. 6

133

105

1. 27

122

1. 09

98

1. 36

121

1. 11

139

0. 96

150

B150-15-3

152

298

83

3. 36

0. 38

271

3. 6

150

105

1. 43

126

1. 19

110

1. 37

128

1. 17

150

1. 00

164

Johnsonan

d

Ram

irez

22

1305

539

36

2. 49

0. 14

525

3. 1

338

271

1. 25

310

1. 09

286

1. 18

353

0. 96

361

0. 94

546

2305

539

36

2. 49

0. 07

525

3. 1

222

136

1. 64

255

0. 87

225

0. 99

293

0. 76

274

0. 81

546

5305

539

56

2. 49

0. 14

525

3. 1

383

271

1. 41

357

1. 07

325

1. 18

385

0. 99

384

1. 00

597

Andersonet

al.10

W1

406

345

29

2. 31

0. 39

549

2. 65

460

494

0. 93

445

1. 03

426

1. 08

489

0. 94

489

0. 94

494

Rolleran

dRussell23

7457

871

72

1. 88

0. 16

445

3788

638

1. 24

809

0. 97

838

0. 94

880

0. 90

791

1. 00

1116

9457

762

125

2. 35

0. 16

483

3749

606

1. 24

739

1. 01

755

0. 99

845

0. 89

854

0. 88

1248

10

457

762

125

2. 89

0. 23

464

31172

837

1. 40

831

1. 41

858

1. 37

994

1. 18

1044

1. 12

1459

Sarsam

and

Al-Musawi10

AL2-N

180

233

40

2. 23

0. 09

844

4115

72

1. 60

100

1. 15

76

1. 50

85

1. 35

96

1. 19

137

AL2-H

180

233

75

2. 23

0. 09

844

4123

72

1. 71

110

1. 11

90

1. 36

93

1. 32

105

1. 17

168

BL2-H

180

233

76

2. 81

0. 09

844

4138

72

1. 93

110

1. 25

90

1. 53

99

1. 39

118

1. 17

203



CL2-H

180

233

70

3. 5

0. 09

844

4147

72

2. 05

110

1. 33

90

1. 63

106

1. 39

129

1. 14

233

BS4

-H180

233

80

2. 81

0. 18

543

2. 5

207

92

2. 24

119

1. 74

99

2. 08

124

1. 66

139

1. 49

230

CS3

-H180

233

74

3. 5

0. 13

543

2. 5

247

67

3. 71

108

2. 28

88

2. 81

119

2. 07

135

1. 83

274

CS4

-H180

233

76

3. 5

0. 18

543

2. 5

221

92

2. 39

119

1. 86

99

2. 22

131

1. 68

150

1. 47

275

Xie

etal.10

NNW-3

127

203

41

3. 2

0. 49

322

387

92

0. 95

81

1. 07

68

1. 28

85

1. 03

95

0. 91

95

NHW-3

127

198

98

4. 54

0. 51

324

3102

93

1. 10

88

1. 17

77

1. 34

98

1. 04

119

0. 86

146

NHW-3a

127

198

90

4. 54

0. 65

323

3108

119

0. 91

98

1. 11

88

1. 23

110

0. 99

129

0. 84

144

NHW-3b

127

198

103

4. 54

0. 78

324

3123

143

0. 86

107

1. 14

99

1. 24

121

1. 01

141

0. 87

147

McG

orm

ley

etal.10

BUIS-3

203

419

57

3. 03

0. 34

426

3. 27

267

277

0. 96

254

1. 05

230

1. 16

267

1. 00

286

0. 93

295

EUIS-3

203

419

56

3. 03

0. 34

426

3. 27

267

277

0. 96

254

1. 05

230

1. 16

267

1. 00

286

0. 93

295

Yoonet

al.12

N1-N

375

655

36

2. 8

0. 08

430

3. 28

457

190

2. 40

357

1. 28

330

1. 38

438

1. 04

409

1. 12

685

N2-S

375

655

36

2. 8

0. 08

430

3. 28

363

190

1. 91

357

1. 02

330

1. 10

438

0. 83

409

0. 89

685

N2-N

375

655

36

2. 8

0. 11

430

3. 28

483

261

1. 85

386

1. 25

362

1. 33

470

1. 03

460

1. 05

685

M2-S

375

655

67

2. 8

0. 11

430

3. 28

552

261

2. 11

455

1. 21

451

1. 22

542

1. 02

505

1. 09

756

M2-N

375

655

67

2. 8

0. 16

430

3. 28

689

380

1. 81

502

1. 37

504

1. 37

591

1. 17

585

1. 18

756

H2-S

375

655

87

2. 8

0. 14

430

3. 28

598

333

1. 80

483

1. 24

490

1. 22

571

1. 05

574

1. 04

775

H2-N

375

655

87

2. 8

0. 23

430

3. 28

721

547

1. 32

569

1. 27

585

1. 23

660

1. 09

695

1. 04

775

Kongan

d

Ran

gan

24

S1-1

250

292

64

2. 8

0. 157

569

2. 5

228

147

1. 56

195

1. 17

162

1. 41

208

1. 10

221

1. 03

326

S1-2

250

292

64

2. 8

0. 157

569

2. 5

208

147

1. 42

195

1. 07

162

1. 28

208

1. 00

221

0. 94

326

S1-3

250

292

64

2. 8

0. 157

569

2. 5

206

147

1. 40

195

1. 06

162

1. 27

208

0. 99

221

0. 93

326

S1-4

250

292

64

2. 8

0. 157

569

2. 5

278

147

1. 89

195

1. 43

162

1. 71

208

1. 33

221

1. 26

326

S1-5

250

292

64

2. 8

0. 157

569

2. 5

253

147

1. 73

195

1. 30

162

1. 56

208

1. 22

221

1. 15

326

S1-6

250

292

64

2. 8

0. 157

569

2. 5

224

147

1. 53

195

1. 15

162

1. 38

208

1. 08

221

1. 01

326

S2-1

250

292

73

2. 8

0. 105

569

2. 5

260

98

2. 65

175

1. 48

145

1. 79

187

1. 40

197

1. 32

332

S2-2

250

292

73

2. 8

0. 126

569

2. 5

233

118

1. 97

183

1. 27

154

1. 51

195

1. 19

208

1. 12

332

S2-3

250

292

73

2. 8

0. 157

569

2. 5

253

147

1. 73

195

1. 30

167

1. 52

208

1. 22

224

1. 13

332

S2-4

250

292

73

2. 8

0. 157

569

2. 5

219

147

1. 50

195

1. 13

167

1. 31

208

1. 05

224

0. 98

332

S2-5

250

292

73

2. 8

0. 209

569

2. 5

282

195

1. 44

214

1. 32

189

1. 50

230

1. 23

249

1. 13

332

S3-2

250

297

67

1. 65

0. 101

632

2. 49

178

107

1. 67

171

1. 04

149

1. 19

166

1. 07

156

1. 14

207

S3-3

250

293

67

2. 79

0. 101

632

2. 49

229

105

2. 17

179

1. 28

147

1. 56

190

1. 20

199

1. 15

330

S3-4

250

293

67

2. 79

0. 101

632

2. 49

175

105

1. 66

179

0. 98

147

1. 19

190

0. 92

199

0. 88

330

S4-4

250

292

87

2. 8

0. 157

569

2. 5

258

147

1. 76

195

1. 33

167

1. 55

208

1. 24

229

1. 13

338

S4-6

250

198

87

2. 78

0. 157

569

2. 53

203

99

2. 04

139

1. 46

113

1. 79

143

1. 42

163

1. 24

225

S5-1

250

292

89

2. 8

0. 157

569

3. 01

242

147

1. 65

195

1. 24

167

1. 45

197

1. 22

222

1. 09

281

S5-2

250

292

89

2. 8

0. 157

569

2. 74

260

147

1. 77

195

1. 33

167

1. 56

203

1. 28

226

1. 15

309

(Tab

lecontinued

)



Author[Source]

Bea

m

nam

e

b:

mm

d:

mm

f c:

MPa

r l:

%

r v:

%

f y:

MPa

a/d

Vfail:

kN

VEC-2

2003

Vfail/

VEC2-03

VEC-2

1991

Vfail/

VEC2-91

VACI

11-3

Vfail/

VACI

VCSA

2003

Vfail/

VCSA

VClad

2004

Vfail/

VClad

Vf,max

S5-3

250

292

89

2. 8

0. 157

569

2. 5

244

147

1. 66

195

1. 25

167

1. 46

208

1. 17

229

1. 06

339

S7-2

250

294

75

4. 46

0. 126

569

3. 3

205

119

1. 73

184

1. 11

155

1. 32

205

1. 00

237

0. 87

365

S7-3

250

294

75

4. 46

0. 157

569

3. 3

247

148

1. 67

196

1. 26

168

1. 47

219

1. 13

254

0. 97

365

S7-4

250

294

75

4. 46

0. 196

569

3. 3

274

184

1. 48

211

1. 30

184

1. 48

236

1. 16

273

1. 00

365

S7-5

250

294

75

4. 46

0. 224

569

3. 3

304

211

1. 44

221

1. 38

196

1. 55

248

1. 23

286

1. 06

365

S7-6

250

294

75

4. 46

0. 262

569

3. 3

311

247

1. 26

235

1. 32

212

1. 46

264

1. 18

303

1. 02

365

S8-1

250

292

75

2. 8

0. 105

569

2. 5

272

98

2. 77

175

1. 55

145

1. 87

187

1. 46

197

1. 38

320

S8-2

250

292

75

2. 8

0. 126

569

2. 5

251

118

2. 13

183

1. 37

154

1. 63

195

1. 28

209

1. 20

320

S8-4

250

292

75

2. 8

0. 157

569

2. 5

266

147

1. 81

195

1. 36

167

1. 59

208

1. 28

225

1. 18

320

S8-5

250

292

75

2. 8

0. 196

569

2. 5

289

183

1. 58

209

1. 38

183

1. 58

225

1. 29

244

1. 19

320

S8-6

250

292

75

2. 8

0. 224

569

2. 5

284

209

1. 36

220

1. 29

195

1. 46

236

1. 20

257

1. 11

320

Karayiannisan

d

Chalioris1

0

A36

200

260

26

1. 47

0. 12

267

2. 77

89

37

2. 38

72

1. 23

61

1. 46

75

1. 19

69

1. 29

102

A48

200

260

26

1. 47

0. 16

269

2. 77

89

50

1. 77

78

1. 15

67

1. 34

81

1. 11

77

1. 15

102

A72

200

260

26

1. 47

0. 25

256

2. 77

93

75

1. 24

87

1. 06

77

1. 20

91

1. 02

91

1. 02

102

B90

200

260

26

1. 96

0. 13

262

3. 46

85

40

2. 13

80

1. 07

62

1. 37

77

1. 10

79

1. 08

103

Collinsan

d

Kuchma2

5

SE100B-M

295

920

75

1. 36

0. 16

500

2. 5

583

489

1. 19

533

1. 09

596

0. 98

594

0. 98

510

1. 14

764

SE50A-M

169

459

74

1. 03

0. 13

500

2. 72

139

113

1. 23

147

0. 95

154

0. 90

143

0. 97

122

1. 14

154

SE50B-M

169

459

74

1. 16

0. 13

500

2. 72

152

113

1. 34

150

1. 01

159

0. 96

149

1. 02

129

1. 18

173

SE100A-M

-69

295

920

71

1. 03

0. 16

500

2. 5

516

489

1. 06

507

1. 02

586

0. 88

543

0. 95

447

1. 15

586

Angelak

oset

al.26

DB120M

300

925

21

1. 01

0. 791

508

2. 92

282

250

1. 13

278

1. 01

323

0. 87

345

0. 82

282

1. 00

446

DB140M

300

925

38

1. 01

0. 791

508

2. 92

277

250

1. 11

364

0. 76

396

0. 70

391

0. 71

299

0. 93

483

BM100

300

925

47

0. 76

0. 791

508

2. 92

342

250

1. 37

376

0. 91

376

0. 91

371

0. 92

267

1. 28

376

Adeb

aran

d

Collins2

7

ST4

290

278

49

1. 95

0. 11

430

2. 88

158

86

1. 84

183

0. 86

132

1. 19

159

1. 00

155

1. 02

256

ST5

290

278

49

1. 95

0. 18

536

2. 88

169

175

0. 97

219

0. 77

172

0. 98

195

0. 87

205

0. 82

256

ST6

290

278

49

1. 95

0. 28

430

2. 88

230

218

1. 05

236

0. 97

191

1. 20

213

1. 08

224

1. 02

256

ST19

290

278

51

1. 95

0. 214

430

2. 88

201

167

1. 21

217

0. 93

170

1. 19

193

1. 04

202

1. 00

257

Tanet

al.28

2-2.58/0.25

110

443

55

2. 58

0. 48

499

2. 82

155

223

0. 70

185

0. 84

177

0. 88

193

0. 80

193

0. 80

223

4-5.80/2.50

110

398

74

5. 8

0. 48

538

3. 14

265

254

1. 04

177

1. 50

174

1. 52

219

1. 21

234

1. 13

335

G-2.70-5.38

110

463

43

1. 23

0. 333

555

2. 7

105

125

0. 84

125

0. 84

125

0. 84

125

0. 84

125

0. 84

125

Ozceb

eet

al.29

TS36

150

310

75

2. 59

0. 23

255

3156

61

2. 54

110

1. 42

92

1. 69

109

1. 42

116

1. 35

164

TH39

150

310

73

3. 08

0. 2

255

3143

53

2. 68

107

1. 34

89

1. 61

111

1. 28

120

1. 19

181

ACI59

150

310

82

4. 43

0. 13

425

597

58

1. 67

109

0. 89

91

1. 07

108

0. 90

134

0. 72

151



TH59

150

310

75

4. 43

0. 18

425

5119

80

1. 49

117

1. 02

100

1. 19

117

1. 02

144

0. 83

149

TS59

150

310

82

4. 43

0. 27

425

5125

120

1. 04

134

0. 94

118

1. 06

134

0. 94

151

0. 83

151

Claderaan

d

Marı30

H50/2

200

353

50

2. 28

0. 109

530

3. 06

178

92

1. 94

162

1. 10

124

1. 43

149

1. 19

150

1. 18

228

H50/4

200

351

50

2. 99

0. 239

540

3. 08

246

204

1. 21

206

1. 19

173

1. 42

209

1. 18

228

1. 08

281

H60/2

200

353

61

2. 28

0. 141

530

3. 06

180

119

1. 51

173

1. 04

145

1. 24

167

1. 08

171

1. 05

234

H75/2

200

353

69

2. 28

0. 141

530

3. 06

204

119

1. 72

173

1. 18

150

1. 36

169

1. 21

174

1. 17

237

H75/4

200

351

69

2. 99

0. 239

530

3. 08

255

200

1. 28

205

1. 25

186

1. 37

216

1. 18

236

1. 08

297

H100/4

200

351

50

2. 99

0. 239

540

3. 08

267

204

1. 31

206

1. 29

173

1. 54

209

1. 27

228

1. 17

281

Ahmad

etal.31

LNW-3

127

216

45

2. 07

0. 378

421

363

72

0. 87

72

0. 87

72

0. 87

72

0. 87

72

0. 87

72

LHW-3a

127

198

88

4. 54

0. 65

421

3107

144

0. 75

112

0. 95

104

1. 03

126

0. 85

144

0. 75

144

LHW-3b

127

198

87

4. 54

0. 78

421

3121

143

0. 84

125

0. 97

118

1. 03

140

0. 86

143

0. 84

143

LHW-4

127

198

83

4. 54

0. 51

421

495

107

0. 89

99

0. 96

89

1. 06

103

0. 92

107

0. 89

107

Etxeberria3

2HN-V3

200

303

42

2. 99

0. 166

530

3. 3

177

120

1. 48

148

1. 20

119

1. 49

148

1. 19

169

1. 05

217

HN-V4

200

303

42

2. 99

0. 118

530

3. 3

188

85

2. 20

134

1. 40

103

1. 82

133

1. 41

149

1. 26

217

Gonzalez-

Fonteboa3

3

V13HC

199

307

38

2. 9

0. 21

500

3. 25

190

144

1. 32

151

1. 26

127

1. 50

156

1. 22

176

1. 08

211

V17HC

199

306

39

2. 92

0. 16

500

3. 27

151

110

1. 38

139

1. 08

112

1. 34

142

1. 06

161

0. 94

212

V24HC

195

306

39

2. 99

0. 12

500

3. 27

128

81

1. 59

126

1. 02

98

1. 30

128

1. 00

143

0. 89

212

V17HCS

200

312

45

2. 86

0. 16

500

3. 21

200

112

1. 78

152

1. 31

120

1. 67

149

1. 34

167

1. 19

226

V24HCS

200

302

44

2. 95

0. 12

500

3. 3

150

82

1. 84

135

1. 11

103

1. 46

132

1. 14

147

1. 02

216

V17HR

200

306

42

2. 91

0. 16

500

3. 27

177

110

1. 61

144

1. 23

115

1. 54

144

1. 23

163

1. 09

216

V24HR

201

306

39

2. 9

0. 12

500

3. 27

164

83

1. 98

130

1. 27

101

1. 63

131

1. 26

145

1. 13

213

V13HRS

199

305

41

2. 93

0. 21

500

3. 28

202

143

1. 41

156

1. 30

129

1. 57

158

1. 28

178

1. 14

215

V17HRS

199

305

45

2. 93

0. 16

500

3. 28

193

109

1. 77

147

1. 31

116

1. 66

145

1. 33

164

1. 18

219

V24HRS

199

307

43

2. 91

0. 12

500

3. 25

147

82

1. 79

135

1. 09

104

1. 42

133

1. 11

147

1. 00

219

Average

1. 64

1. 19

1. 38

1. 13

1. 06

Stan

darddeviation

0. 53

0. 21

0. 31

0. 19

0. 16

CoV:%

32. 24

17. 95

22. 25

17. 27

15. 44

Minim

um

0. 70

0. 76

0. 70

0. 71

0. 72

Maxim

um

3. 71

2. 28

2. 81

2. 07

1. 83

5th

percentile

of

data

0. 87

0. 87

0. 88

0. 84

0. 83

EC-2

2003

EC-2

1991

ACI

11-3

CSA

2003

Clad

2004



the authors’ opinion that shear strength in the

new Eurocode 2 is a step forward in terms of

simplicity but, as has been shown, for specific

cases other methods are more accurate.

Acknowledgements

The research described in this paper was

financed by the Spanish Ministry of Science

and Technology’s project MAT2002-00615.

The authors wish to express their gratitude

for this financial support.

References

1. European Committee for Standardization. prEN

1992-1-1:2003. Eurocode 2, Design of Concrete

Structures, Part 1: General Rules and Rules for

Buildings. Revised final draft, Brussels, Belgium,

December 2003.

2. Ritter, W. Die bauweise hennebique. Shweizer-

ische Bauzeitung, 1899, 33, No. 7, 59–61.

3. Morsch, E.Concrete-Steel Construction. McGraw-

Hill, New York, 1909 (English translation by

E. P. Goodrich).

4. Regan, P. Research on shear: A benefit to human-

ity or a waste of time? The Structural Engineer,

1993, 71, No. 19, 337–347.

5. Vecchio, F. J. and Collins, M. P. The modified

compression field theory for reinforced concrete

elements subjected to shear. ACI Structural

Journal, 1986, 86, No. 2, 219–231.

6. European Committee for Standardization.

ENV 1992-1-1. Eurocode 2, Design of Concrete

Structures, Part 1-1: General Rules and Rules

for Buildings. Spanish Edition, Brussels,

Belgium, 1991.

7. Cladera, A. and Marı, A. R. Shear design

procedure for reinforced normal and high-

strength concrete beams using artificial

neural networks. Part II: Beams with stirrups.

Engineering Structures, 2004, 26, No. 7,

927–936.

8. Bentz, E. C. Sectional analysis of reinforced

concrete members. PhD thesis, Department of

Civil Engineering, University of Toronto, 2000.

9. Kuchma, D. Shear Data Bank. University of

Illinois, Urbana-Champaign, www.cee.cd.uiuc.

edu/Kuchma, 2000.

10. Zararis, P. D. Shear strength and minimum shear

reinforcement of reinforced concrete slender

beams. ACI Structural Journal, 2003, 100,

No. 2, 203–214.

11. Canadian Standards Association. Design of

Concrete Structures CSA A23.3-94. Canadian

Standards Association, Rexdale, ON, 1994.

12. Yoon, Y. S., Cook, W. D. and Mitchell, D.

Minimum shear reinforcement in normal,

medium and high-strength concrete beams. ACI

Structural Journal, 1996, 93, No. 5, 576–584.

13. American Concrete Institute. ACI Building Code

Requirements for Reinforced Concrete. ACI,

Farmington Hills, ACI 318-02, 2002.

14. CSA Committee A23.3. Design of Concrete

Structures. Public review draft, Canadian

Standards Association, Rexdale, ON, September

2003, p. 233.

15. Bennet, E. W. and Balasooriya, B. M. A. Shear

strength of prestressed beams with thin webs

failing in inclined compression. ACI Journal,

1971, 68, No. 3, 204–212.

16. Elzanaty, A. H., Nilson, A. H. and Slate, F. O.

Shear capacity of prestressed concrete beams

using high-strength concrete. ACI Structural

Journal,1986, 83, No. 3, 359–368.

17. Kaufman, M. K. and Ramirez, J. A. Re-evaluation

of the ultimate shear behavior of high-strength

concrete prestressed I-beams. ACI Structural

Journal, 1988, 85, No. 3, 295–303.

18. Lyngberg, B. S. Ultimate shear resistance of

partially prestressed reinforced concrete I-beams.

ACI Journal, 1976, 73, No. 4, 214–583.

19. Shahawy, M. A. and Batchelor, B. D. V. Shear

behavior of full-scale prestressed concrete

girders: comparison between AASHTO specifica-

tions and LRFD code. PCI Journal, 1996, 41,

No. 3, 48–62.

20. Rangan, B. V. Web crushing strength of

reinforced and prestressed concrete beams. ACI


21. Cladera, A. and Marı, A. R. Shear design pro-

cedure for reinforced and prestressed high and

normal-strength concrete beams. Seventh

International Symposium on Utilization of

High-Strength/High-Performance Concrete, 1,

Washington, 2005, 654–668.

22. Johnson, M. K., and Ramirez, J. A. Minimum

shear reinforcement in beams with higher

strength concrete. ACI Structural Journal, 1998,

86, No. 4, 376–382.

23. Roller, J. J. and Russell, H. G. Shear strength of

high-strength concrete beams with web

reinforcement. ACI Structural Journal, 1990,

87, No. 2, 191–198.

24. Kong, P. Y. L. and Rangan, B. V. Shear strength

of high-performance concrete beams.

ACI Structural Journal, 1998, 95, No. 6,

677–688.

25. Collins, M. P. and Kuchma, D. How safe are our

large, lightly reinforced concrete beams, slabs

and footings? ACI Structural Journal, 1999, 96,

No. 4, 482–490.

26. Angelakos, D., Bentz, E. C. and Collins, M. P.

Effect of concrete strength and minimum stirrups

on shear strength of large members. ACI


27. Adebar, P. and Collins, M. P. Shear strength of

members without transverse reinforcement.

Canadian Journal of Civil Engineering, 1996,

23, No. 1, 30–41.

28. Tan, K., Kong, F., Teng, S. and Weng, L. Effect of

web reinforcement on high-strength concrete

deep beams. ACI Journal, 1997, 94, No. 5,

572–582.

29. Ozcebe, G., Ersoy, U. and Tankut, T. Evaluation of

minimum shear reinforcement requirements for

higher strength concrete. ACI Journal, 1999,

96, No. 3, 361–368.

30. Cladera, A. and Marı, A. R. Experimental study

on high-strength concrete beams failing in

shear. Engineering Structures, 2005, 27, No. 10,

1519–1527.

31. Ahmad, S. H., Khaloo, A. R. and Poveda, A.

Shear capacity of reinforced high-strength

concrete beams. ACI Journal, 1986, 83, No. 2,

297–305.

32. Etxeberria, M. Estudio experimental de la resis-

tencia a cortante en vigas de hormigon de

aridos reciclados. PhD thesis, Universidad Politec-

nica de Cataluna, 2003.

33. Gonzalez-Fonteboa, B. Hormigones con aridos

reciclados procedentes de demoliciones:

dosificaciones, propiedades mecanicas y

comportamiento estructural a cortante.

PhD thesis, Universidad de la Coruna,

2002.



Documents

Shear Strength in the New Eurocode 2. a Step Forward