Final Long Paper FIB2014

8/13/2019 Final Long Paper FIB2014

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SHEAR ANALYSIS AND EXPERIMENTAL RESEARCH

PROGRAM ON ANCHORAGE CRITERIA IN RC SLABS:

COMPARISONS BETWEEN FIBMC2010 AND NBR6118

Marquesi, M. L. G.Department of Civil Engineering, Federal University of So Carlos, So Carlos, BrazilEGT Engenharia, So Paulo, Brazil

Stucchi, F. R.Department of Structural and Geotechnical Engineering, University of So Paulo, So Paulo, BrazilEGT Engenharia, So Paulo, Brazil

Ungaretti, M. C., Fujii, G.

EGT Engenharia, So Paulo, Brazil

Abstract

This paper investigates the shear strength and anchorage of one-way RC slabs without stirrups.

Comparison between FIB Model Code 2010 Final Draft and Draft of Brazilian Standard NBR6118

2013 is presented. A total of 64 results of experiments in slab strips reinforced with steel bars or

steel mesh are analyzed. All specimens were designed with part of the beams at the ends of the slab

strips in order to provide support. A preliminary horizontal loading was applied to allow a

cracking, just beside the support beam, and to ensure that a strut and tie resisting behavior is

mobilized. 13 specimens failed by loss of anchorage, 13 failed by shear and 38 failed by flexure. Aqualified database of 81 slab strips was created and conclusions based on these tests are made

concerning the safety and accuracy of the shear provisions. Level of approximation 1 of new model

code predicted the strength with an average experimental-over-predicted shear strength ratio of

2.01 with a coefficient of variation (COV) of 14.6%, level 2, with an average of 1.29 with COV of

14.5% and NBR, with an average of 1.08 with COV of 14.3%.

Some comments are made in order to stand out an engineers point of view regarding economy,

safety, design and research models.

Keywords:Anchorage, Analytical models, Design models, Shear, Shear database

1 IntroductionDifferently from beams, that must have at least a minimum shear reinforcement according to

Brazilian and European standards, slabs are typically dimensioned so that no shear reinforcement is

needed, as placing stirrups in slabs is perceived to be difficult and costly. When designing

buildings, slabs are responsible for a significative concrete consumption. Therefore, an economic

design associated with an enough safety is required.

The design of slabs in flexure and shear consider a slab as a series of independent strips of

arbitrary width, usually per meter. In experiments that are carried out to evaluate the model

uncertainties in resistances, conventionally, the ratios of observed and predicted values, slab strips

are most common used. Establishing a relationship between what is done in lab and what

potentially happen in reality the volume of concrete involved in a slab as a whole is greater, i.e.strips would not collapse independently as in the usual experiments without redistribution of


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internal forces. In addition, most part of the practical cases consists of slabs subjected to uniform

loads where the maximum shear force does not coincide with the maximum moment, and the

reinforcement ratios are small enough to ensure failure by bending. Kani (1966) commented about

point load and uniform distributed load: A comparison of point loading tests shows, as could beexpected, that a uniformly distributed loading produces somewhat more favorable results. Thus, it

is slightly conservative if the design requirements for beams under point loadings are extended to

beams under uniform distributed loads. Thus, it is reasonable take that into account in the pursuit

of an optimal point between economy and safety.

This paper presents a comparison between FIB Model Code 2010 Final Draft [1] and the Draft

of Brazilian Standard NBR6118 2013 [3] regarding shear and anchorage failures. A total of 64

results of experiments in slab strips without transversal reinforcement are analyzed. 13 specimens

failed by loss of anchorage, 13 by shear and 38 by flexure, as described in [15]. As the universally

accepted theory for predicting flexural strength showed a very good result and the equivalence

between bars and steel mesh, only a few comments are made about flexure. Anchorage and shear

receive more attention and a special effort is made about shear since there is no generally accepted

physical or empirical model explaining the response of members without stirrups. A qualified sheartest results database was created. A sanctioned set of criteria was then developed for accepting a

test result into an evaluation-level database.

Some comments are also made in order to stand out an engineers point of view regarding

economy, safety, design and research models.

2 Economy, safety, design models and research modelsMore now than ever before the world demands sustainable engineering solutions. In structural

engineering field it means do what has to be done with economy and safety enough in order to

guarantee infrastructure and quality of life. For each situation an adequate construction system need

be chosen taking into account their advantages, local techniques and available materials. Besides,analytical models found in code provisions need agree with the sustainability concept. For that, an

optimal point between economy and safety must be sought considering practical experience and

representative experiments, not mixing apples with oranges.

Another important aspect related to analytical models in codes is about their complexity. For an

engineer is very important to distinguish between design model and research model [12]. The

design models should be established in a simple way, neither simplistic nor sophisticated. The first

causes uneconomic solutions and the second distracts the mind potentiating the human error.

Schlaich (1991) stated The art of finding the right model and applying the right method of

analysis consists in defining and asking for just enough and not as much as possible. Any

redundant refinement is destructive as is any substantial omission. A design model tries to

parameterize the reality through the most important variables.

On the other hand, a research model tries to represent the reality. Many variables, manyequations, constitutive laws and nonlinear finite element analysis are used. Research models and

experiments must agree with high accuracy.

Some general theories, for instance, the Modified Compression Field, have been successfully

applied to members without shear reinforcement [14]. However, simplifications in these theories

were needed in order to introduce them in codes of practice [4] [5]. How better are these simplified

physical models in relation to the traditional empirical or semi-empirical ones?

3 Anchorage provisions3.1 Fib New Model Code 2010 [1]Reinforcement in tension may be anchored by bond or by a combination of bond along the straight

portion with a resistance provided by welded transverse bar, a head welded at the end of the bar, a


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hook or a bend. Providing some minimum detailing requirements (NMC 6.1.3.2), design bond

strength is given by:

2, 0.4.

(1)

where ptr is the mean compression stress perpendicular to the potential splitting failure surface at

the ultimate limit state, it is negative when transverse stress is compressive; and fbd,0 is the basic

bond strength given by:

, (2)

where:

1 is a coefficient taken as 1.75 for ribbed bars (including galvanised and stainless

reinforcement), 1.4 for fusion bonded epoxy coated ribbed bars and 0.90 for plain surfacebars.

2 represents the casting position of the bar during concreting:

2=1.0 when good bond conditions are obtained, as for:

all bars with an inclination of 45 - 90 to the horizontal during concreting and; all bars with an inclination less than 45 to the horizontal which are up to 250mm

from the bottom or at least 300mm from the top of the concrete layer during

concreting.

2= 0.7 for all other cases where ribbed bars are used, or

2= 0.5 where plain bars are used.

3represents the bar diameter:

3= 1.0 for 25mm;

3= (25/)0.3for > 25mm.4represents the characteristic strength of steel reinforcement being anchored or lapped:

4= 1.20 for fyk = 400MPa;

4= 1.00 for fyk = 500MPa;

4= 0.85 for fyk = 600MPa;

4= 0.75 for fyk = 700MPa;

4= 0.68 for fyk = 800MPa;

Intermediate values may be obtained by interpolation.

Thus, for cases of straight bars in tension the design anchorage length is:

,, ,,

(3)

, 0.3

,10,100mm (4)

3.2 Draft of NBR6118 2013 [3]The design value of the ultimate bond stress may be taken as:

(5)


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. (6)

0.3

/

50 (7)

2.12 10.11 50 (8)

where

1is a coefficient taken as 2.25 for ribbed bars, 1.4 for welded wire reinforcement and 1.0

for plain surface bars.

2 represents the casting position of the bar during concreting: 1.0 for good conditions and

0.7 for all others cases.

3represents the bar diameter:

3= 1.0 for 32mm;3= (132-)/100 for > 32mm.

The design anchorage length for cases of straight bars in tension is given by equations 3 and 4.

4 Shear provisions4.1 Fib New Model Code 2010 [1]The shear provisions of the NMC have been significantly changed from previous model codes.

NMC proposes equations stemmed from the work of Collins et al. The Modified Compression

Field Theory (MCFT) produces accurate estimates of shear strength but the requirement to solve 15

simultaneous nonlinear equations is not compatible to a design model. As such, some simplifying

assumptions were taken into account in order to make design practical. These assumptions reduce

the number of equations from 15 to two and they were used in the Canadian code for structural

concrete and in NMC [4] [13].

Another significantly change in shear provisions is the inclusion of a Level of Approximation

(LoA) concept. The first level is low time-consuming and in theory, is typically sufficient for

preliminary design or to check that a design provision is not governing. The highest level provides

the most accurate results, but at the cost of the most arithmetic.

Fig. 1 Level-of-Approximation approach [9].

The design shear resistance in NMC of a web or slab without shear reinforcement is given by:

,

(9)

where the value of fckshould not be taken greater than 64MPa. Two levels of approximation arepresent in this case. In level I is considered the assumption that the mid-depth strain at the control


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section is x= 0.00125, that corresponds to half the yield strain for a reinforcing bar with fyk= 500

MPa. This level can be used in members with no significant axial load, with fyk600MPa, fck70

MPa and with a maximum aggregate size of not less than 10mm. Thus:

. (10)

For Level II the state of strain need be calculated and the maximum size of aggregate introduced:

. .

(11)

(12)

(13)

where z and dgare in mm and the variable z can be calculated as 0.9d. For high-strength concrete

(fck> 70 MPa) or lightweight concrete, the cracks will tend to pass through the aggregate and thus

for such concretes, the value of dg should be taken as zero.

4.2 Draft of NBR6118 2013 [3]The shear provision for slabs without transversal reinforcement is based on previous version of

EC2 [16]. As time goes by, however, some small changes were adopted. Considering a reinforced

member, the shear resistance takes into account three main parameters: tensile strength, size effect

and the influence of longitudinal reinforcement ratio. These parameters were establishedempirically in the formula and because of that some limitations are needed.

0.251.61.240 where 0.02 (14)

The tensile strength is presented in equations 7 and 8. For slabs with height greater than 600 mm

this equation is not recommended, neither for fckgreater than 70MPa. However, the vast majority

of cases are covered.

5 Experimental programThe last version of the Brazilian Standard for Structural Concrete Design recommends to RC slabs

with steel meshes the utilization of a straight anchorage length at support of the maximum between

10 cm or 10 times the diameter of the bar, with at least one transversal welded bar. This provision

considered smooth bars. As the steel meshes are now made with improved bond, it was supposed

the standard need no more require the transversal welded bar and may allow smaller anchorage

lengths. Thus, it was proposed a program of tests on samples of concrete reinforced with welded

steel meshes to evaluate the behavior with this type of reinforcement in relation to its anchorage at

supports using different lengths of anchorage, but also to evaluate shear, flexure and their

interaction with anchorage. For comparison some samples were reinforced with steel bars.

Due to good anchorage, some failures were conditioned by shear and they were analyzed all

together with a qualified database of shear test results.


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5.1 Specimen design and experimental setupThe specimens were constructed to a nominal width of 34 cm, 150 cm of total clear span and varied

in thickness from 7 to 15 cm. Diameters of bars ranged from 4.2 mm to 12.5 mm, with anchorage

length of 5, 7 and 10 cm. Beams, with bbeamvarying from 12 to 15 and hbeamvarying from 32 to 40,

were designed at the ends of the slab strips in order to provide support and allow a cracking just

beside the support beam. It is shown below the design of generic specimen A10-0-xxx.

Fig. 2 Design of specimen A10-0-xxx.

All specimens were cast using concrete with specified 28-day strength of 30 MPa. At the time

of testing the strength was close to this value or even higher. The concrete was made using

aggregate with a maximum size of 19 mm. More information is present in Table 2 and 3.

The specimens were submitted preliminarily to a horizontal loading, as shown in Fig. 3, in orderto cause a pre-cracking just on the inner face of the support beams. Thus, the strut and tie resisting

behavior is mobilized and the anchorage capacity evaluated. The tests were performed always

symmetrically with two span loads, at the third span points or 2hslab from the supports. All tests

were carried out in an upside down position, Fig.4.

Loading case a

Loading case b

Fig. 3 Horizontal loading. Fig. 4 Testing loading.


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Table 1

Details and nomenclature of specimensReinforcement Anchorage length

evaluable

Distance of the1st

transversal bar to the

border of the beam

Testing loadings Specimens

A SteelWeldedMesh

10 cm 0 cm a Symmetric loadat 1/3 of the span

distance of the

support

A10-0-xxx-a or bA10-7.5-xxx-a or bA10-10-xxx-a or b

A10-15-xxx-a or bA7- 0-xxx- a or bA5- 0-xxx-a or b

7.5 cm

7 cm

10 cm b Symmetric loadat 2 hslabdistance

of the support5cm

15 cm

B ReinforcingBars

10 cm 0 cm a Symmetric loadat 1/3 of the span

distance of thesupport

B10-0- a or bB10-7.5- a or b

B10-15- a or b

7.5 cm

b Symmetric loadat 2 hslabdistance

of the support15 cm

xxx refers to mesh type

5.2 Experimental resultsA total of 64 results, where all experimental data were clearly defined, are analyzed. See [15]. 13

specimens failed by loss of anchorage, 13 by shear and 38 by flexure. In Fig. 5 are presented thefailure modes of the experimental program.

The flexural theory predicts the strength of the 38 specimens with an average experimental-

over-predicted flexural strength ratio of 1.01 with a coefficient of variation of 5.2%.

Flexural failure Anchorage failure

Shear failure: flexure-shear Shear failure: diagonal tension

Fig. 5 Failure modes.


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Table 2

Characteristics and results of specimen that failed by anchorage

Specimen fc fy long lbevaluable fbNBR fbNMC Pexp. Pexp/PNBR Pexp/PNMC

A5-0-138-a 27.5 698 0.42 5.00 3.827 2.760 9.29 1.84 2.55A5-0-246-a 24.6 747 0.56 5.00 3.553 2.490 14.86 2.38 3.39

A5-0-503-a-1 21.7 674 0.80 5.00 3.268 2.530 12.34 1.50 1.94

A5-0-503-a-2 21.7 674 0.80 5.00 3.268 2.530 13.50 1.64 2.12

A5-0-503-b 21.7 674 0.80 5.00 3.268 2.530 17.25 2.10 2.71

A5-0-785-a-1 23.4 688 1.00 5.00 3.436 2.580 22.20 2.06 2.74

A5-0-785-a-2 23.4 688 1.00 5.00 3.436 2.580 32.60 3.02 4.02

A5-0-1131-a-1 26.8 632 1.20 5.00 6.045 2.964 47.57 2.09 4.26

A5-0-1131-a-2 26.8 632 1.20 5.00 6.045 2.964 54.75 2.40 4.90

A7-0-246-a 16.3 747 0.56 7.00 2.700 2.027 12.79 1.92 2.56

A7-0-503-a 20.4 674 0.80 7.00 3.136 2.453 26.48 2.40 3.07

A7-0-785-a 23 688 1.00 7.00 3.397 2.558 45.56 3.05 4.05

A7-0-1131-a 29.3 632 1.20 7.00 6.415 3.099 55.10 1.63 3.37

Note: fc indicates cylinder strength on day of test [MPa]; fy represents the yield stress

[MPa]; fb, the bond strength [MPa]; lb, the anchorage length [cm]; [cm]; Pexp. , the shear

force correspondent to anchorage failure [kN].

2.16 3.21

COV 22.6% 27.8%

Regarding anchorage failure, PNBR andPNMC represent the predicted vertical force, or reaction, at

inner face of support beam. These forces are correlated to horizontal tensile force in bars dividing

by cot corresponding to equals to 33.69, as NBR6118 prescribes. For analyzed cases, a

desirable safety is found. The average experimental-over-predicted bond strength ratio is 2.16 for

NBR and 3.21 for FIBMC2010 with coefficient of variation of 22.6% and 27.8%, respectively.

These values of the COV are not completely reliable due to the size of the sample (13 elements).

FIBMC2010 is more conservative and prescriptive than NBR.

All analyzed shear results has anchorage length of 10 cm. That implied, independent of bar

diameters, in a good anchorage and then shear failure was determinant. Two types of shear failure

were observed: 1. flexure-shear that is assumed to take place in regions where flexure cracks have

appeared and, 2. diagonal tension that is supposed to take place within regions of the structural

span not affected by flexural cracks.

In RC members, diagonal tension may be regarded as an upper limit. It may be predicted

conservatively with the same model that predicts flexure-shear. When both cases are analyzed all

together, as in this case it conducts to a large coefficient of variation. See Table 3, which indicates,

for each test, the failure observed. These values of the COV are not completely reliable due to the

size of the sample (13 elements).


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Table 3

Characteristics and results of specimen that failed by shear

Specimen d b/d a/d l fy fc Failure Vexp. Vexp./VNBR Vexp./VNMC.IIA100503b 81 4.20 2.47 0.548 674 25.2 FS 33.01 1.23 1.08

A1010503b 81 4.20 2.47 0.548 674 29.5 FS 34.36 1.15 1.07

A100785b 80 4.25 2.50 0.868 688 19.2 FS 34.62 1.44 1.10

A1010785b 80 4.25 2.50 0.868 688 26.4 FS 36.05 1.21 1.02

A10101131b 119 2.86 1.68 0.839 632 36.6 FS 62.51 1.18 1.06

A1001227a 129 2.64 2.33 0.700 632 23.0 DT 69.63 1.72 1.70

A107.51227a 129 2.64 2.33 0.700 632 23.0 DT 69.35 1.71 1.70

A10151227a 129 2.64 2.33 0.700 632 23.0 DT 68.67 1.69 1.68

A100785b 80 4.25 2.50 0.868 688 23.3 DT 42.09 1.54 1.54

A1001227b 119 2.86 2.53 0.839 632 22.8 DT 72.88 1.88 1.87

B1001227a 129 2.64 2.33 0.700 632 29.5 DT 79.98 1.67 1.81

B107.51227a 129 2.64 2.33 0.700 632 29.5 DT 76.52 1.60 1.73B10151227a 129 2.64 2.33 0.700 632 29.5 DT 86.15 1.80 1.94

Note: fc indicates cylinder strength on day of test [MPa]; fyrepresents the yield stress

[MPa]; d [mm]; l , reinforcement ratio [%]; Vexp. represents applied shear force

considering specimen selfweight in the upside down position [kN]. FS refers to flexure

shear and DT to diagonal tension;

1.52 1.48

COV 16.7% 24.1%

6 Shear database of RC slab stripsBecause of a small number of tests, a qualified database of shear test results was created. All slab

strips in this database do not contain shear reinforcement and the majority was subjected to point

loads, only four uniformly loaded tests. Besides the experimental program presented in this work,

two databases were used as source: Collins (2008) and Reineck (2010). As first criterion, 105 testswhose width-depth ratio (b/d) is greater than 2 were gathered.

A sanctioned set of criteria was then developed for accepting a test result from 105 into an

evaluation-level database. 81 tests were selected.

Fig. 6 Components of database.

These sanctioned set of criteria include: compressive strength from 18 to 59 MPa, a width-depth

ratio from 2.3 to 12.1, a longitudinal reinforcement ratio from 0.6 to 2.9% and minimum and

maximum shear span-to-depth ratio (a/d) based on Kanis strength envelope [7], of 2 and 6,

respectively. The shear presenting failure by diagonal tension were not included in the evaluation-

level database.In Fig. 7 the results are plotted in terms of shear stress for each of the codes for both collected

data (105 in left) and selected data (81 in right). The FIBMC results are presented in two levels of

13 2 4 4 7 4 9 41 4 17105tests

5 2 4 4 7 2 4 33 4 1681 tests

Stucchi2010 Marti1977 Kani1967 Ghannoum1998

Bentz2004 Aster1974 Richart1948 Leonhardt1962

Heger1982 Regan1988


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approximation. For the first level (FIBMC2010 - LoA I) a smaller amount of tests is shown (49

results) since there are some limitations, namely the yield stress must be less than 600 MPa and the

maximum diameter of the aggregate should be greater than 10 mm. Besides these limitations,

simplifications proposed for this level of approximation became it too conservative, even for whatwas proposed. The average for the 49 data is 2.01 with a coefficient of variation of 14.6%. For the

81 selected data the FIBMC2010 - LoA II has an average of 1.29 and COV of 14.5% and the

Brazilian standard (NBR) has an average of 1.08 and COV of 14.3%.

Analyzing the FIBMC LoA II and NBR for the 105 data the first has an average of 1.33 with a

COV of 16.6%, and the second, 1.18 and 23.1%, respectively.

Regarding some limitations for application of the NBR design model, namely height not greater

than 600 mm and fcknot greater than 70MPa, and what was commented about how slabs work in

reality, safety and economy, the NBR design model may be considered satisfactory despite an

average of 1.08. This mean value, that could be 1.0 for flexure for example, should be greater than

1.0 for shear due to the expected brittle failure and 8% could be considered enough.

The FIBMC LoA I need be improved in order to represent what it is proposed within a model

code. FIBMC LoA II, as expected, is better in accuracy in relation to LoA I but at the cost of themost arithmetic. Its coefficient of variation, as not expected, was almost the same than NBR one

for 81 selected data.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)NBR

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)NBR

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)FIBMC2010LoAI

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)FIBMC2010LoAI


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Fig. 7 Experimental versus predicted shear stresses: left - 105 tests, right - 81 tests.

7 ConclusionsAs a result of this research, it was possible to conclude that:

1) When used as slab reinforcement, bars and welded meshes have equivalent behavior in serviceand at ultimate limit state.

2) The reliability of flexural results was really good. Theatrical results were 1% lower than

experimental, with a COV of 5% for both NBR and NMC.3) As it would be desirable, the theory for shear collapse without stirrups, flexure-shear, has highersafety margin than the flexure theory. The NBR margin of 8% seems to be enough, if we consider

that we tested only strips, not real slabs and under concentrated not distributed loads, to avoid

brittle failure. The Brazilian criteria for shear are equivalent to EC2 1992 version, not the last

version. The margin of the NMC LoA II of 23% is probably more than enough. The COV of both

is approximately 14.4%. The margin of LoA I is more than 100%, really too much.

4) If we consider in the database for shear failure, not only flexure-shear, but also diagonal tension,mean value and COV increase. It would be always better to study each type of failure, let say,

Ultimate Limit State, separately.

5) As it would be desirable, the theory for loss of anchorage is still safer. The margin of the NBRcriteria is a little higher than 50% and of NMC approximately 70%. The COV were 23 and 28%

respectively. This higher safety margin is really desirable to avoid the separation between steel and

concrete before a failure of reinforced concrete.

6) The minimum anchorage at the support (maximum between 10 and 10 cm) for steel meshmade of enhanced bond bars avoids the slip of reinforcement with that enlarged safe margin.

References

[1] Final Draft of fib Model Code 2010. Fdration international de bton (fib). Lausanne.

[2] NBR6118: 2004, Structural Concrete Design Brazilian Standard (available in English).

[3] Draft of NBR6118: 2013, Structural Concrete Design, Brazilian Standard.

[4] Bentz, E. C., and Collins, M. P. (2006), Development of the 2004 CSA A23.3 shearprovisions for reinforced concrete. Can. J. Civ. Eng., 335, 521534.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)FIBMC2010LoAII

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.

0

0.

5

1.

0

1.

5

2.

0

2.

5

3.

0

exp.

(MPa)

pred. (MPa)FIBMC2010LoAII


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[5] Bentz, E. C., Vecchio, F. J., and Collins, M. P. (2006), The simplified MCFT for calculating

the shear strength of reinforced concrete elements. ACI Journal, 1034, 614624.

[6] Collins et al. (2008), Where is Shear Reinforcement Required? Review of Research Results

and Design Procedures, ACI Struct. J., Vol. 105, No 5.[7] Kani, G. N. J. (1964), The Riddle of Shear Failure and Its Solution, ACI Journal,

Proceedings V. 61, No. 3, pp. 441-467.

[8] Kani, G. N. J. (1966), Basic Facts Concerning Shear Failure ACI Journal, Proceedings V. 63,

No. 6, pp. 675-692.

[9] Muttoni, A., Ruiz, M. F. (2012), Level-of-Approximation Approach in Codes of Practice.

Structural Engineering International, V. 2, pp 190-194.

[10] Muttoni, A., Ruiz, M. F. (2008), Shear Strength of Members without Transverse

Reinforcement as Function of Critical Shear Crack Width, ACI Journal, Vol. 105, No 2.

[11] Reineck, K. H., Kuchma, D. A. (2010), Extended databases with shear tests on structural

concrete beams without and with stirrups for the assessment of shear design procedures,

Research Report.

[12] Schlaich, J. (1991), The need for consistent and translucent Models, IABSE ColloquiumStructural Concrete, Proceedings V. 62, Stuttgart, p. 169-184.

[13] Sherwood, E. G. (2008), One-Way Shear Behaviour of Large, Lightly-Reinforced Concrete

Beams and Slabs, PhD dissertation, University of Toronto, Toronto, Ontario Canada, 546 pp.

[14] Vecchio, F. J., and Collins, M. P. (1986), The modified compression field theory for

reinforced concrete elements subjected to shear. J. Am. Concr. Inst., 832, 219231.

[15] IBTS Instituto Brasileiro de Tela Soldada Estudo do comportamento de Estruturas de

Concreto armadas com Tela Soldada Ensaios de Ancoragem (2010) Pesquisa EGT

(Stucchi, F.; Fugii, G.) e EEUSP-S. Carlos (Hanai, J.; Takeya, T.) www.ibts.org.br

[16] EUROCODE 2 Design of Concrete Structures Part 1.1 General Rules and Rules for

Buildings 1992 version.

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