Punching strengthening in flat plates of reinforced concrete with carbon fiber reinforced polymer ( CFRP ) Sistema de reforço à punção de lajes lisas de concreto

© 2014 IBRACON 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.


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.

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.

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

Conventional systems of strengthening of flat plates against punching failure
Figure 3 shows some typical solutions for shear strengthening of a slabcolumn 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 postinstalled 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.

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.Punching strengthening in fl at plates of reinforced concrete with carbon fi ber reinforced polymer (CFRP)

Treatment of punching shear in codes of practice
No available regulation in the literature specifi cally 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: 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 reg-ulation, however, sets in a particular way the control perimeter and the nominal shear tension.The project loading capacity, and the nominal shear tension.The project loading capacity, , of flat slabs without any shear reinforcement is defined as follows: Where  is the nominal shear tension,   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  , and  , are the contributions of the concrete and the shear reinforcement in the slab resistance and   and   , 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 ( , ).In this case, the resistant capacity is given by Equation 3.3 for a control perimeter,   , 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.

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.
(3.4) where   is the resistance to the concrete compression,   is the ratio between the higher or lower column dimension,   is a constant that assumes value equals 4 for the case of internal columns,  is the useful height of the slab and  1 is the length of a control perimeter that must be located at  ⁄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. for V/(u 1 .d)≤0,5.f c and 0,5.d for V/(u 1 .d)>0,5.f c .The loading capacity out of the reinforced area to shear  , for the elements of flat slab with shear reinforcement must be calculated by Equation 3.5, using the perimeter definition of control (  ) shown in Figure 9.
The capacity inside the reinforced area to the shear ( ,  ) is expressed by Equation 3.6 limited by Equation 3.7.
where    is the steel area of a shear reinforcement,   , represents the yielding strength of shear reinforcement, and s r is the distance between layers.

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  = 1 + √200⁄ ≤ 2,0,  is the reinforcement rate, limited in 2%, and  1 is the control perimeter length 2d far from the column faces, as presented in Figure 10.
The break happening out of the shear reinforcement area can be verified with Equation 3.8 using the control perimeter (  ), according to Figure 10, that presents some typical details recommended to this regulation when using shear reinforcements.
In Figure 10,   represents the perimeter length far 1,5 from the most external layer of shear reinforcements, observing a 2 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 ( , ).In addition,   , is the effective strength of the shear reinforcement.

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⁄ ) ( 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. (3.11) V R,c =0,18.ξ.(100.ρ.f c ) (3.12) V R,cs = 0,75.V R,c + ( 1,5.d s r . A sw .fyw,ef ) The value   is the control perimeter length far 2 from the most external shear reinforcements, observing a 2 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 ( , ).  , is the effective strength of the shear reinforcements and α v = ( 1-f ck 250 ) with f ck in MPa.Punching strengthening in flat plates of reinforced concrete with carbon fiber reinforced polymer (CFRP)

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,   , , for a slab without shear reinforcement is stablished by Equation 3.14. (3.14) where b 0 is the control perimeter (Figure 12) and   , the factor of the material resistance.
The   parameter is calculated by Equation 3.26 and depends on the slab rotation, ψ, at the support area.(Figure 13). (3.15) ) 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: (3.17) The resistance provided by the shear reinforcement, V Rd,s , is expressed by Equation 3.18: (3.18) where ∑    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     represents the shear reinforcement mobilized stress, according to Equation 3.19. (3.19) indicates the shear reinforcement bar diameter and f ywd its strength of shear reinforcements.Adherence tension   can be taken, simplified, for 3,0 MPa or for Equation 3.20: (3.20)   2 = 1,0 when good bond conditions are obtained, as for: n all bars with an inclination of 45º -90º to the horizontal during concreting, and; n 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);  2 = 0,7 for all other cases where ribbed bars are used, or  2 = 0,5 where plain (unribbed) bars are used  3 represents the bar diameter  3 = 1,0 for Ø ≤ 25 mm;  3 (25/Ø) 0,3 for Ø > 25 mm (Ø in mm);  4 represents the characteristic strength of steel reinforcement being anchored or lapped;  4 = 1,2 for   = 400;  4 = 1,0 for   = 500;  4 = 0,85 for   = 600;  4 = 0,75 for   = 700;  4 = 0,68 for   = 800; 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. (3.21) 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 /L y , 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. (3.22) 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   , being   = 1.5 • (  , •   , ) 0.5 ≤   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. (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.

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 V R,c PRFC , Equation 3.24 is used. (3.24) V R,cPRFC =ɸ c .V R,c +ɸ s V R,PRFC V R,C and V R,PRFC are respectively, the contributions of the concrete and the CFRP reinforcement for the resistance capacity to the punching shear.[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. (3.25) Punching strengthening in flat plates of reinforced concrete with carbon fiber reinforced polymer (CFRP) (3.28) where A PRFC is the sum of the shear reinforcements type CFRP area, by layer;   is CFRP tension and   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 consider-ations, the punching regulations were followed without changes.

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 (4.1) In the calculation by the regulations, the CFRP system properties (fiber/resin) used for each one of the authors are presented on Punching strengthening in flat plates of reinforced concrete with carbon fiber reinforced polymer (CFRP)     For the result dispersion analysis, besides the average of the relations V exp /V Norma , we used the median analysis, which represents the measure of a central trend and has the advantage on the Punching strengthening in flat plates of reinforced concrete with carbon fiber reinforced polymer (CFRP) 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 data 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 /V Norma 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

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.

Figure
Figure 1 -Systems for reinforced concrete slabs 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.

Figure 14 -
Figure 14 -Dimension and details of reinforced specimens

Figure 15 -
Figure 15 -Comparison of code estimations and experimental results

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 /V Norma is closest of the unit, besides

Figure 16 -
Figure 16 -Boxplots of database results 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,

Figure 17 -
Figure 17 -Evaluation of the demerit scale Figure 18 -Estimation of failure modes 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 V exp /V Norma 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 V exp /V Norma 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,   , 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 (V R, 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 semiempiric 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.

Table 1 -
Experimental database

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.

Table 3 -
Calculated and experimental punching strength of test specimens the lower Coefficient of Variation, which can be seen in the points dispersion along the straight line of coefficient one (Figure15 (c)).Using the ACI 318 estimations we obtain an average of the relation    /   equals to 2,05 and Coefficient of Variation -CV of 0,20.Eurocode 2 [3] also had its appropriate results, with average relation   /  2 of 1,51 and CV, 0,16.Model Code results were slightly more conservative than the ones from Eurocode 2 [3], with relation   /  2 equals to 1,65 and CV, 0,13. presenting