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## Revista IBRACON de Estruturas e Materiais

##
*versão On-line* ISSN 1983-4195

### Rev. IBRACON Estrut. Mater. vol.7 no.4 São Paulo ago. 2014

#### http://dx.doi.org/10.1590/S1983-41952014000400005

**Punching strengthening in flat plates of
reinforced concrete with carbon fiber reinforced polymer (CFRP)**

**G. S. Santos ^{I}; W. G. Nicácio^{I};**

**A. W. Lima**

^{I};**G. S. S. A. Melo**

^{I}^{I}Departamento de Engenharia Civil e
Ambiental, Universidade de Brasília, Brasília, DF, Brasil; galileueng@yahoo.com.br ; wanderley.nicacio@gmail.com ; wagnercivil@yahoo.com.br ; melog@unb.br

**ABSTRACT**

This research evaluates the behavior of slab-column connections in a reinforced concrete flat slab system and subjected to symmetrical loading, strengthened to the shear with carbon fiber reinforced polymer (CFRP). The strengthening method consists in applying CFRP sheets as shear resistant element, by bonding it through perpendicular holes to the plane of the slab. As the current standards do not deal with strengthening to shear with CFRP reinforcement, it was assessed the application of the code’s required from by ACI 318 (2011) [2], by Eurocode 2 (2004) [3] by ABNT NBR 6118 (2007) [4] and by Model Code (2010) [5], associated to the limitations of ACI 440.2R (2008) [6] which provides guidance for the selection, design, and installation of FRP systems for concrete structures. The results showed that the NBR 6118 (2007) [4] provided the lowest degree of dispersion, with some results against security. The ACI 318 (2011) [2] has a more conservative trend, and Eurocode 2 (2004) [3] and Model Code (2010) [5] have intermediate results.

**Keywords**: strengthening, punching, CFRP.

**1. INTRODUCTION**

Uncertainties regarding structural safety – like suspicions of project and execution error, doubts about the stability due to apparently pathological demonstrations and changes of service loads – are situations that justify an intervention with the strengthening of a structure. For the case of punching in a slab-column connection, some constructive systems which make possible this strengthening with improvement. However, these systems are invasive and, usually, imposes changes of the structure geometry.

The use of carbon fiber reinforced polymer sheets (CFRP) as an alternative for the increase of the load bearing capacity of flat slabs is a simple and fast intervention, which efficiency has been proved by experimental research in the last years. The main idea of strengthening method is to install CFRP as a member resistant to shearing. The application occurs by bonding the CFRP sheets through perpendicular holes to the plane of the slab. It is necessary to pay attention to the requirements of the sheet anchorage and for the later filling of the holes with resistance grout and elasticity modulus compatible with the ones from the substratum.

There are not regulations specifically dealing with the use of CFRP as slab punching reinforcement. Then, the objective of this research is to evaluate the safety, economy and the accuracy of the application of some of the main project regulations in the slab punching resistance in reinforced concrete strengthened to punching with CFRP.

Four regulations will be tested: ACI 318 [2], E urocode 2 [3], ABNT NBR 6118 [4] and CEB- FIP:2010 [5]. An adjustment suggested by Sissakis (2002) [1] will be adopted so that these regulations can be used in the case studied, with CFRP reinforcement, in which the deformation limits of ACI 440.2R is considered. This last code deals only with the strengthening of reinforced concrete structures using fiber-reinforced polymers. From the calculation results, will be evaluated the dispersion and the conservatism level of each case.

**1.1 Justification**

The study of strengthening to flat slab punching is justified by the progressive use of this structural system, combined with the dangerous awareness of a ruin by shear.

The common strengthening to punching techniques, basically, consist in the use of capitals (made of concrete or metal) in the strengthening of a flexure reinforcement or in the posterior introduction of a shear reinforcement composed by steel bolts.

The additional resistance provided by the posterior fastening of steel bolts in the critical shear area is an alternative that rules out the possibility of part geometry change. However, several studies indicate that the system anchorage has a great interference in the efficiency of the shear reinforcement element.

Thus, the use of CFRP arises as an appropriate alternative because it is both a simple, fast intervention, and has a guaranteed anchorage mechanism and high resistance with low weight.

**2. STRENGTHNING OF FLAT PLATES AGAINST PUNCHING FAILURE**

**2.1 Punching**

In conventional structural systems, the slabs are supported on beams and these ones are supported on columns. In this system, the charges (accidental and permanent), which are directly applied on the slabs, are transferred to the beams, which transmit them to the columns and, lately, these ones discharge them on the foundations (Figure 1) (a).

In the flat slabs systems, the loading on the slabs is transferred directly to the columns. In this case, the slabs must rigidly connect to the columns, according to Figure 1 (b) to (e).

Nowadays, people have been more frequently using the flat slab system for presenting a series of advantages when compared to the conventional structural systems. Among these advantages, we can say a higher architectural freedom in the definition of internal environments or future layout changes; the reinforcement simplification and consequent labor and material cost reduction; ease of installation arrangement and the simplification of the forms and scaffolding.

The system also presents disadvantages in relation to the conventional ones, as higher levels of vertical structural dislocation; reduction of the global stability of the building by the action of the horizontal efforts and the possibility of rupture by punching.

Punching is a type of ruin that may occur in a brusque form by shear. This phenomenon is associated to the action of concentrated forces on the slabs, in reduced areas, which may cause its punching. In flat slabs, this situation is typical in the area of the slab-column connection. Figure 2 represents a shear surface with cracks coming from the outline of the loaded area and extend at an angle to the other slab side.

Usually this inclination varies between 26º and 45º in relation to the slab plan.

**2.2 Conventional
systems of strengthening of flat
plates against punching failure**

Figure 3 shows some typical solutions for shear strengthening of a slab-column connection, which address the broadening of the column section (with introduction of chapiters or with the column widening); addition of upper concrete layer; or with the post-installed shear reinforcement.

The introduction of a post-installed shear reinforcement in the critical area is an alternative that may rule out the possibility of the part geometry change. However, several studies indicate that the system anchorage substantially interferes in the efficiency of the element used as shear reinforcement.

Hassanzadeh and Sundqvist (1998) [7] experimentally analyzed the use of capitals (Figure 3 (a)). They noticed that if they double and triple the column diameter in the area of the slab connection, it could increase the capacity resistant to punching respectively about 60% to 100%, comparing to a control slab. The authors also tested a type of capital, like a collar made by steel plates. L ater, Widianto (2006) [8] adapted this device. Figure 4 shows the result.

Ghali *et al*. (1974) [9] experimentally
evaluated a strengthening system with prestressed shear bolts vertically
installed after the concrete treatment (Figure 5). Several researchers
posteriorly evaluated this system.

In Brazil, Carvalho (2001) [10] also verified the efficiency of post-installed shear reinforcement with steel plates as anchorage and of the resin to fill the holes, see Figure 6.

Fernández Ruiz, Muttoni and Kunz (2010) [11] presented a post-installed shear reinforcement mechanism for slabs (Figure 7) with the advantage that it is not necessary to access the other face, without the destruction of the superior floor and which can be applied in the footings.

By the systems presented, it is possible to impede or delay the formation of the rupture surface, which may take a considerable increment in the resistance to punching. It is also possible to see that the resistance increase is accompanied by a ductility increase of the slab-column connection.

Anyway, the efficiency of the shear reinforcement to combat punching depends on a correct dimensioning and positioning, and a good anchorage.

**2.3 Strengthening
system with CFRP**

When compared to metallic materials, usually used in the structures strengthening, CFRP may present superior performance, with the advantage of offering an elevated resistance with low weight; execution speed and practicality; corrosion resistance in aggressive environment and resistance to fatigue. CFRP malleability makes possible an easier application in limited spaces and its adaptation to the several structure geometries.

In
spite of the CFRP use has been showing practical and efficient, some
disadvantages can still be identified, as performance lost at high
temperatures; the vulnerability at impact loads or vandalism actions, and the
specialized labor demanded. In relation to the action of high temperatures, the
practice among designers is to completely not to consider CFRP strengthening in
a fire situation, taking into account the structure in a not reinforced condition.
For the system protection to impact loads or vandalism actions, the
manufacturers indicate several solutions, like, for instance, the use of gluing
grouts or resin produced for

this purpose.

In *stitch *technique, idealized by Sissakis (2002) [1], they produce CFRP stripes
which are inserted through holes perpendicular to the slab plan. The stripes
are passed in continuous laps between hole pairs, like sewing points, until it
is reached the desired strengthening amount.

Initially, they make carbon fiber sheets as wide as the holes diameter or less, holes previously made in the slab. Then, it is necessary to impregnate the internal wall of the hole in the slab with epoxy resin – stabilizing components of CFRP system. Immediately after the holes impregnation, the fiber carbon sheets must be applied. In the end, it is applied a new resin layer on the stripe to guarantee that it is completely soaked by resin.

In
this system, it is necessary to pay attention to the lapped joints indicated by
the manufacturer. Figure 8 represents *stitch *strengthening system.

**3. TREATMENT OF PUNCHING SHEAR IN CODES OF PRACTICE**

No available regulation in the literature specifically deals with CFRP use as shear reinforcement in slabs. For this reason, this study will evaluate only adaptations of the recommendations of the main codes, national and international, applicable to reinforced concrete slabs subjected to symmetric loading with and without the use of shear reinforcement. The codes evaluated are:

- ACI 318 - American Building Code for Reinforced Concrete, ACI 318 (2011);
- EUROCODE 2 - Design of Concrete Structures, E C2 (2004);
- NBR 6118 - Projeto de Estruturas de Concreto-Procedimento, NBR 6118 (2007);
- CE B-FIP MODE L CODE 2010 -
*fib*Model Code for Concrete Structures 2010, Model Code 2010.

For all the punching regulations above, the general expression for the capacity calculation of the flat slabs without shear reinforcement consists in the nominal shear tension product, control perimeter and useful height (E quation 3.1). E ach regulation, however, sets in a particular way the control perimeter and the nominal shear tension. The project loading capacity, , of flat slabs without any shear reinforcement is defined as follows:

Where v is the nominal shear tension, u_{in} is the control
perimeter set for slabs without shear reinforcement, and *d* is the slab useful height.

For strengthened slabs, the resistant capacity to punching inside the area with shear reinforcement is calculated as E quation 3.2:

Where V_{R,c} and V_{R,c} are the contributions of the concrete and the shear reinforcement in
the slab resistance and Øc and
Øs,
the factors that ponder these contributions. E ach regulation, however, considers
these factors in a particular way. When
the slabs have shear reinforcement, we must also verify the resistant capacity
in a rupture surface outside the area of the shear reinforcements (V_{R,out}). In this case, the resistant capacity is given by Equation 3.3 for
a control perimeter, u_{out}, placed out of the reinforced area.

No regulation, however, deals specifically with reinforcement to punching with Carbon Fiber

Reinforced Polymer – CFRP. For this case, as mentioned before, it is necessary an adaptation of the resistance to shear inside the reinforced area. Item 3.5 shows this application, according to the recommendations of the regulation ACI 440.2R [6], which deals with the project and reinforcement installation of FRP in reinforced concrete structures.

**3.1 ACI 318:2011**

ACI 318 [2] estimates the resistance to punching of a slab without shear reinforcements as the minimum from three expressions (Equation 3.4). These three equations take into account the column rectangularity effect, its location in the structure and the loading area in relation to the useful height.

where F_{c} is
the resistance to the concrete compression, B_{C} is the ratio between the
higher or lower

column
dimension, a_{s} is
a constant that assumes value equals 4 for the case of internal columns, d is the useful height of the slab and u1 is the length of a control
perimeter that must be located at d⁄2
from the column face, as shown in Figure 9.

For
reinforced slabs to shear with *studs *the distance between the
column and the first reinforcement layer must not exceed the value of d/2.
The space between the reinforcement layers must not exceed 0,75. d V/(u_{1.d})≤0,5. √fc and 0,5.d and 0,5.d for for V/(u1.d)>0,5. √fc.

The
loading capacity out of the reinforced area to shear V_{Rout} for the elements of flat slab with shear reinforcement must be
calculated by Equation 3.5, using the perimeter definition of control (u_{out}) shown in Figure 9.

The
capacity inside the reinforced area to the shear (V_{R,cs}) is
expressed by Equation 3.6 limited by Equation 3.7.

where A_{sw} is the steel area of a shear reinforcement, f_{ys,w} represents
the yielding strength of shear reinforcement, and sr is the distance between layers.

**3.2 EUROCODE 2:2004**

The resistance to punching in reinforced concrete flat slabs without shear reinforcement is made taking into account the effect of the reinforcement rate and the size effect, according to Equation 3.8.

where ξ is
the *size effect*, assumed as ξ = 1 + √200⁄d ≤ 2,0, p is the reinforcement rate,
limited in 2%, and u1 is the control perimeter length 2d far
from the column faces, as presented in Figure 10.

The resistance to shear inside the reinforced area is defined according to Equation 3.9. And the verification the compressed strut resistance next to the column outline can be obtained through Equation 3.10.

where ,

The break happening out of the shear reinforcement area can be verified with Equation 3.8 using

the
control perimeter (u_{out}), according to Figure 10, that presents some typical
details recommended to this regulation when using shear reinforcements.

In Figure 10, u_{out} represents the perimeter length far 1,5d from the most external layer of shear reinforcements, observing a 2d limit for the maximum distance between two *stud *concentric
lines.

In
case that the limit is not attended, it must adopt an effective external
control perimeter (u_{out,ef}). In addition, f_{yw,ef} is the effective strength of the shear reinforcement.

**3.3 ABNT NBR
6118:2007**

The analysis for verification of the resistance to shear adoptedby the Brazilian regulation is analogue to Eurocode. The model differs by the size effect, which is calculated by the expression ξ = 1 + √200⁄d) (d in mm) that, in this case, may assume values superior to 2,0 and by the flexure reinforcement rate that may also assume value superior to 2%.

Equation 3.11 sets the resistance to punching in reinforcement concrete flat slabs without shear reinforcement. The resistance to shear inside the strengthened area is obtained with Equation 3.12. In addition, the verification of the compressed resistance near the column ends can be obtained with Equation 3.13.

The
value u_{out} is the control perimeter length far 2d from
the most external shear reinforcements, observing a 2d limit for the maximum distance between two reinforcement element in
concentric lines. In the case of this limit not being attended, the effective
external perimeter control is used (u_{out,ef}). f_{yw,ef} is the effective strength of the shear reinforcements and with f_{ck} MPa.

**3.4 CEB-FIP MODEL
CODE 2010**

The calculation of the resistance to shear by Model Code 2010 [5] has as a basis The Critical Shear Crack Theory – CSCT (MUTTONI, 2008) [12]. The CSCT evaluates the shear strength from the assumption that the shear strength in members without transverse reinforcement is governed by the width and roughness of a shear crack that develops due to the inclined compression strut carrying shear. The model can be applied to slabs with or without shear reinforcement verifying the possibility of break inside the reinforced area, out of this area or the crush of the compressed strut.

The
shear strength, V_{Rd,c} , for a slab without shear reinforcement is stablished by Equation
3.14.

where *b*0 is the control perimeter (Figure 12) and y_{c} , the factor of the material resistance.

The 𝑘𝛹 parameter
is calculated by Equation 3.26 and depends on the slab rotation, *ψ*,
at the support area. (Figure 13).

where *d**g *is the maximum
size of aggregate (accounting for the roughness of the lips of the cracks).

For a slab with shear reinforcement, the
resistance to punching is given by the sum of the portions resisted by concrete, *V**Rd,c*, and for the shear reinforcements, *V**Rd,s*, as Equation 3.17 shows:

The
resistance provided by the shear
reinforcement, *V**Rd,s*, is expressed by Equation 3.18:

where ∑A_{sw} is the sum of the transversal section area of the whole shear
reinforcement, properly anchored that, in the model, is intercepted by the
rupture surface (conical surface with a 45º angle).

The
term o_{SW} represents the shear reinforcement mobilized stress, according to
Equation 3.19.

Ø_{w} indicates
the shear reinforcement bar diameter and *fywd *its strength
of shear reinforcements. Adherence tension f_{bd} can be taken, simplified, for 3,0 MPa or for Equation 3.20:

where:

n1 is a coefficient taken as 1,75 for ribbed bars (including galvanized
and stainless reinforcement),

1,4
for fusion bonded epoxy coated ribbed bars and 0,90 for plain (unribbed)
surface bars;

n2 represents the casting position of
the bar during concreting:

n2 = 1,0 when good bond conditions are
obtained, as for:

- all bars with an inclination of 45º – 90º to the horizontal during concreting, and;
- all bars with an inclination less than 45º to the horizontal which are up to 250 mm from the bottom or at least 300 mm from the top of the concrete layer during concreting (but see also ‘special circumstances’ section later);

n2 = 0,7 for all other cases where
ribbed bars are used, or

n2 = 0,5 where plain (unribbed) bars
are used

n3 represents the bar diameter

n3 = 1,0 for Ø ≤ 25 mm;

n3 (25/Ø) 0,3 for Ø > 25 mm (Ø in mm);

n4 represents the characteristic
strength of steel reinforcement being anchored or lapped;

n4 = 1,2 for f_{yk} = 400MPa;

n4 = 1,0 for f_{yk} = 500MPa;

n4 = 0,85 for f_{yk} = 600MPa;

n4 = 0,75 for f_{yk} = 700MPa;

n4 = 0,68 for f_{yk} = 800MPa;

Lastly,
the rotation calculation (*ψ*) can be carried out in four
approximation levels. The approximations are used in the evaluation of the
resistance to punching and vary as the complexity level of the analysis and the
result accuracy degree.

The approximation level I refers to the slabs analyzed by elastic theories and that do not present substantial redistributions of internal forces. Equation 3.21 gives a secure estimation of the rotation in the ruin moment.

where *r**s *indicates the
position, in relation to the column axis, in which the radial bending moment

is zero. The value of *r**s *can
be considered equals to 0,22*∙L *(in the directions *x*, *L**x*,
and *y*, *L**y*) in slabs where the relations between the
spans, *L**x/Ly*, is limited in 0,5 and 2,0.

The approximation level II refers to the slab that present substantial redistribution of moment in the calculation of the flexure reinforcement. For these cases, Equation 3.22 gives the rotation calculation of the slab.

where *m**sd *represents the value of the project
requester medium bending moment and *m**Rd *the value of the project resistant
medium bending moment. Both are calculated for a length range

b_{s},
being b_{s} = 1.5 · (r_{s,x} · r_{s,y} )0.5 ≤ L_{min}

The
approximate value of *m**sd *depends on the location of the
column in the building. The referred

regulation
considers three possible locations for the columns: internal to the building, edge
or corner. In the case of an inside
column, *m**sd *is
calculated by Equation 3.23.

In the
approximation level III, the coefficient 1,5 of Equation 3.22 can be replaced
by 1,2 if the values of *r**s *and *m**sd *are extracted from a linear elastic model.
In the approximation level IV, the rotation calculation *ψ *must
be obtained in nonlinear analysis.

**3.5 ACI 440.2R:2008**

This document provides orientation for the selection, project and installation of the reinforcement systems with Fiber Reinforced Polymers (FRP) externally installed in concrete structures. It presents the information on the material properties, project, installation, quality control and FRP systems maintenance used as external reinforcement. This information can be used to select a FRP system to increase resistance and rigidity of concrete reinforced beams or the ductility of columns and other applications.

For verifying to the shear on the rupture surface cutting reinforcement shears with CFRP, in this study called VR,c PRFC, Equation 3.24 is used.

VR,C and VR,PRFC are respectively, the contributions of the concrete and the CFRP reinforcement for the resistance capacity to the punching shear.

The
contributions in the shear reinforcements area can be calculated with Equations
3.25, 3.26, 3.27 and 3.28 for ACI 318 [2], Eurocode 2 [3], ABNT NBR 6118 [4]
and Model Code 2010 [5]. The recommendations of ACI 440.2R [6] project and the
studies of PRIESTLEY *et al *(1996) [13], limit the deformation value of
the FRP deformation in 0,004 for materials used in the shear reinforcement, due
to keep the concrete integrity confined by it.

where APRFC is the sum of the shear
reinforcements type CFRP area, by layer; F_{PRFC} is
CFRP tension and o_{PRDC} is the tension resisted by CFRP, in function of the slab rotation, *ψ.*

Replacing the equations above in the punching reinforcement verifications, shown in the previous chapters, we obtain Equations 3.29, 3.30, 3.31 and 3.32, which will be used to verify the tension in the CFRP reinforcement. For the other considerations, the punching regulations were followed without changes.

**4. ANALYSIS OF THE CODE PROVISIONS**

Initially,
it will be presented a database, formed by the experimental results of 39 slabs
of research of strengthening to punching with CFRP sheets in *stitch *technique.
There are 28 slabs essayed by Sissakis (2002) [1] and 11, by Binici (2003)
[14]. In
relation to the test scheme, all the slabs subject to symmetric loading, which
simulates the situation of building internal columns, without the action of
flexural moments. For the database slabs,
the resistance to concrete compression (*f*c), varies between 26,6 and 42,6 MPa and the reinforcement
ratios (ρ) varies between 1,50 and 2,34. The relation between the space
between the stregthening layers and the slab effective depth (*s/d*) is
0,50 or 0,75. Table 1 and Figure 14 bring the general features of the slab
tests.

The
result analysis will be always carried out for the ratio between the ultimate
loads obtained in the tests and the
calculated resistant load, *V**exp*/*V**Norma*. The charge *V**exp *corresponds to the last punching load measured in
laboratory and the force *VNorma *is the resistance value, according to
the normative criteria in study.

In determining the rupture loads by the regulations, no coefficient of material resistance or increase of request was used. The formulas are presented in items 3.1, 3.2, 3.3 and 3.4 with the adaptations described in 3.5.

For
ACI 318 [2], we used the dimensioning recommendations o *studs *type shear
reinforcement, for it considers better anchorage conditions in relation to the
stirrup type reinforcement, also set by the regulation.

CEB-FIP Model Code 2010 [5] equations take into account the slab ruin criterion for characteristic value. So that the evaluation of this regulation can be equivalent to the considerations set for the others, Equations 3.15 and 3.16 will be replaced by Equations 4.1 and 4.2, which, according to Fernández Ruiz and Muttoni (2009) [15], take into account the characteristic value of the slab ruin criterion.

In the calculation by the regulations, the CFRP system properties (fiber/resin) used for each one of the authors are presented on Table 2.

The resistance parcel of the composite system, Equations 2.29, 2.30, 2.31 and 2.32 are presented on Chapter 2.6. For the other materials, the properties were taken by the medium experimental values.

Figure 15 and Table 3 represent the relation between the experimental loads and the set by the regulations.

It can be observed that ABNT NBR 6118 [4]
was the regulation which relation *V**exp*/*VNorma *is closest of the unit, besides presenting the lower Coefficient of Variation, which can be seen in the points
dispersion along the straight line of coefficient one (Figure 15 (c)).

Using
the ACI 318 estimations we obtain an average of the relation v_{exp}/v_{aci}equals to 2,05 and Coefficient of Variation – *CV *of 0,20.
Eurocode 2 [3] also had its appropriate results, with average relation
v_{u}/v_{ec2} of 1,51 and *CV, *0,16. Model Code results were slightly more
conservative than the ones from Eurocode 2 [3], with relation v_{u}/v_{ec2} equals to 1,65 and *CV*, 0,13*. *For the result dispersion analysis,
besides the average of the relations *Vexp*/*VNorma*, we used the median analysis, which
represents the measure of a central trend and has the advantage on the

average for being less susceptible at extreme values of the sample. Figure 16 shows Boxplots with two rectangles representing sample quartiles.

Quartiles are values in the scale that divide the set dat in four parts, all of them with the same number of observations.

The lightest rectangle of each sample in Figure 16 represents the space between the inferior and the middle quartile. The darkest rectangle represents the difference between the median and the superior quartile. These rectangles, together, represent the range of 50% of the most typical values of the distribution. The lines above and below the rectangles compose the other two quartiles.

For
this analysis it is more evident and stronger the correlation ABNT NBR 6118
[4], with lower dispersion of the data in relation to the median. ACI 318 [2],
besides being the regulation with the most conservative *V**exp*/*V**Norma *average, was the one that presented the higher data dispersion in relation
to the median.

For
the evaluation of the conservatism level, we used an adaptation from the
penalty criterion proposed by Collins (2001) [16], *Demerit Points
Classification *–*DPC*. This criterion considers the quotient between
the experimentally resistance to punching and the prevision to the project
codes (*Vexp*/*VNorma*). Collins (2001) [16] considers the safety,
accuracy and economic aspects and classifies the different dimensioning
procedures in terms of a demerit scale. A score is given to each range of the relation

*V**exp*/*V**Norma*. This score has as a basis the idea that
a relation *V**exp*/*V**Norma*< 0,5 is more damaging in safety terms
than the relation *V**exp*/*V**Norma*> 2,0. However, according to DPC, extremely conservative
values, for being uneconomic, must also receive penalization. Table 4 shows
penalty criteria:

Each model DPC is obtained by summing the
percentage results of the values *V**exp*/*VNorma *existing in each interval, by its
corresponding score. The higher the total sum value, the worse is the
regulation process. Table 5 and Figure 17 bring the evaluation of the demerit
scale for the evaluated regulations.

By the
demerit Criterion, the regulation that best adapted to the application
suggested in this research was ABNT NBR 6118 [4], which presented the lower
demerit value, 35, with prevalence of results in the ranges of *Appropriate
Safety *and *Conservative.*

Eurocode
2 [3], ACI 318 [2] and Model Code 2010 [5] also had results in favor of safety,
however, were penalized for having several values predominantly in *Conservative *and *Extremely Conservative *ranges. In this case, ACI 318 (2011) was
the most penalized among the rules and, consequently the one that obtained the
worst performance according to the criterion adopted.

All the regulations, however, presented problems in determining the rupture surface position. This fact is evident in Figure 18 graphic, by which the percentage of correctness vary between 45,45% (Model Code 2010 [5]) to 57,58% (NBR 6118) [4].

It occurs due to a strong trend of three, from the
four regulations, in estimating the slab rupture as out of the reinforced area
to the shear. The rules ACI 318 [2], Eurocode: 2002 and NBR 6118 [4] pointed,
predominantly rupture type *out*. On the opposite of the others, Model
Code 2010 [5] showed rupture in the reinforced area (in).

**5. CONCLUSION**

This study deals with a recent technique of flat slab strengthening against the punching phenomena, using CFRP sheets as shear resistant element. In the research, we compared the application of enshrined regulations in the technical environment with the experimental results of 39 slabs that simulate the area next to the internal columns of a building and without the action of flexural moments.

All the regulations evaluated in this study are applicable at the slab shear reinforcements calculation and are not specifically addressed to the type of strengthening informed.

In a
general way, the adoption of the maximum deformation limit for the shear
strengthening of 0,004 (ACI 440.2R [6]) show appropriate as complement of three
of four of the regulations evaluated – Eurocode 2 [3], ACI 318 [2] and Model
Code 2010 [5] – which presented appropriate safety, conservative trend and values of Vexp/VNorma relation very representative in areas *Conservative *and *Extremely Conservative*.

For
NBR 6119 [4], despite the lower value according to the demerit criterion
adopted and the result prevalence in the range *Appropriate Safety *and *Conservative*,
we verified that 12,8% of the relation values Vexp/VNorma
were under 1,0, which does not
enable the immediate application of this code.

The most conservative results and with higher dispersion were ACI 318 [2]. This fact is the consequence for the formulation of this regulation not taking into account important factors like the flexure reinforcement ratio (ρ) and the size effect parameter, which correlates the reduction of the resistant tension with the increase of the effective depth.

Eurocode 2 [3] and NBR 6118 [4] are regulations that, for being conceived from the same origin, tend to present similar results. However, for the evaluated slabs, NBR 6118 [4] presents results inferior to the one o Eurocode 2 [3], due to not considering Brazilian code of the limitations of the flexure reinforcement rate and the size effect. Moreover, Brazilian regulation considers a superior

distance
than the European reference of the rupture surface position, u_{out}, in relation to the last strengthening layer. The two
regulations, Eurocode 2 [3] and NBR 6118 [4], did not evaluate in a
satisfactory way the rupture surface either, fact due to a strong tendency of
both in estimating rupture as out of the shear strengthening area. For this
case, we suggest formulation changes, especially to reduce the strengthening element (VR, PRFC) in the verification of the punching in
the reinforced area, which the reduction of the deformation limit in the
strengthening may achieve, which, in this study, was considered 0,004 (ACI
440.2R [6]).

Model Code 2010 [5] differs from the other regulations by the semi-empiric ruin criterion adopted. This method has shown good results in shear strengthening researches and, for the present research, also presented satisfactory safety result and dispersion level.

**6. ACKNOWLEDGEMENTS**

The authors thank CNPq and CAPES for the financial support in all phases of this research.

**7. REFERENCES**

[01] SISSAKIS. K.;Strengthening concrete slabs for punching shear with CFRP la*minates. *M. A. Sc. Thesis, University of Toronto, Toronto, Canadá, 2002, 226p. [ Links ]

[02] ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary, American Concrete Institute, Farmington Hills, Michigan, 2011. [ Links ]

[03] Eurocode 2, Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings, CEN, EN 1992-1-1, Brussels, Belgium, 2004, 225 pp. [ Links ]

[04] ASSOCIACAO BRASILEIRA DE NORMAS TECNICAS. NBR 6118 – Projeto de Estruturas de Concreto. Rio de Janeiro, 2007. [ Links ]

[05] CEB-FIP (2010). Model Code 2010: Final Draft. Model Code prepared by Special Activity Group 5, Lausanne, September 2011. (This final draft has not been published). [ Links ]

[06] ACI Committee 440.2R (2008). "*Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures*." American Concrete Institute, Farmington Hills, Michigan. [ Links ]

[07] Hassanzadeh, G. and Sundqvist, H. (1998). *Strengthening of Bridge Slabs on Columns*.*Nordic Concrete Research, The Nordic Concrete Federation*, Publicação nº 21, paper nº 2. [ Links ]

[08] WIDIANTO, M. S. E.*Rehabilitation of Reinforced Concrete Slab-column Connectionsfor Two-way Shear*, Tese de Doutorado, The University of Texas at Austin, 2006. [ Links ]

[09] GHALI, A., M.A. SARGIOUS, e A. HUIZER, *Vertical prestressing of flat plates around columns*, 1974. ACI Special Publication SP-42, *Shear in Reinforced Concrete*. p. 905-920 [ Links ]

[10] CARVALHO. J. S. de. Lajes Cogumelo de Concreto Armado Reforçadas ao Puncionamento com Parafusos de Alta Resistência. Dissertação de Mestrado. Publicação E. DM 002A/2001. Departamento de Engenharia Civil e Ambiental, Universidade de Brasília, DF, 168p. [ Links ]

[11] FERNÁNDEZ RUIZ, M.,MUTTONI, A. e KUNZ, J.*Strengthening of Flat Slabs Against Punching ShearUsing Post-Installed Shear Reinforcement*,ACI Structural Journal, V. 107, July-Aug. 2010,pp. 434-442. [ Links ]

[12] MUTTONI, A., *Punching shear strength of reinforced concrete slabs without transverse reinforcement*, ACI Structural Journal, vol. 105, No. 4, 2008, pp. 440–450. [ Links ]

[13] PRIESTLEY, M. J. N. SEIBLE, F. CALVI, M. *Seismic Design and Retrofit of Bridges,*John Wiley e Sons, USA, 1996, 705 p. [ Links ]

[14] BINICI, B., *Punching shear strengthening of reinforced concrete slabs using fiber reinforced polymers.*PhD thesis, University of Texas at Austin, USA, 2003, 284p. [ Links ]

[15] FERNÁNDEZ RUIZ, M.; MUTTONI, A., *Applications of Critical Shear Crack Theory to Punching of Reinforced Concrete Slabs with Transverse Reinforcement*, ACI Structural Journal, vol. 106, 2009, pp. 485-494. [ Links ]

[16] COLLINS, M.P. (2001). *Evaluation of shear design procedures for concrete structures. *A Report prepared for the CSA technical committee on reinforced concrete design. [ Links ]

Received:
3 Mar 2014

Accepted: 04 Jun 2014

Available Online: 05 Aug 2014