Concrete is a well-known, widely used building stuff in todays society. The components of concrete consist of cement and H2O, sums such as sand and crushed rock, and additives, as either minerals or chemicals. Concrete is readily used in edifices and constructions because of its strength and rigidness, and opposition to enduring. Concrete is long lasting, is easy to keep, maintaining costs down, and easy forms a assortment of utile forms, whilst besides being corrosion resistant. While concrete is really strong under compressive tonss, it is really weak in tenseness, making restrictions in its usage countries where important tensile emphasiss are developed, such as in beams, columns or slabs. However, carefully placed steel bars within the concrete allow it to transport tonss in tenseness. This is known as strengthened concrete ( Warner et al. 2007 ) .
As clip has gone by, the strength of concrete has increased, taking to the development of what is known as High Strength Concrete ( HSC ) . AS 3600-2009 defines High Strength Concrete as concrete that has a compressive strength greater than 50MPa. High Strength Concrete can be reinforced with High Strength Steel ( HSS ) , and has a broad assortment of utile applications.
Base and Red ( 1965 ) showed that by helically restricting HSC beams, the strength and ductileness of the beam could be increased. Hatanka and Tanigawa ( 1992 ) showed that a parturiency utilizing a round spiral was more effectual than the usage of ties in the signifier of rectangles or squares.
With clear advantages coming from the usage of coiling parturiency in the compaction zone of concrete beams, farther geographic expedition into heightening the confining consequence is desirable.
Finite component modeling is used in this thesis to analyze the ductile and strength behaviors of high strength concrete beams provided with coiling support in the compaction zone. FEM provides applied scientists within the industry with a non-linear analysis of the behavior of beam that reduces the demand of experimental proving if the consequences can be calibrated to its existent life opposite number.
Whitehead and Ibell ( 2005 ) analysed the shear behavior of Fibre-reinforced polymers in the compaction zone of concrete beams. Their analysis attempted to relieve the hapless design jobs that nullify the advantages of FRP ‘s. With FRP ‘s being progressively used as support and in constructions under fix, this thesis undertakes the modeling of High Strength Concrete beams reinforced helically with Fibre-reinforced polymers utilizing the Finite Element Modelling plan, Strand7.
1.2 Aim and Aims
The purpose of this probe is to develop a finite component theoretical account to analyze the strength and ductile behavior of high strength concrete beams helically reinforced in the compaction zone with Fibre-reinforced polymers. An analysis will be carried out to verify Cush ‘s ( 2009 ) experimental consequences where polymer reinforced spirals ( PRH ) were used with changing pitches and were compared with a steel spiral.
The aims of this thesis are ;
Review literature of HSC reinforced with HSS and assorted polymers utilizing coiling parturiency, and the usage of FEM package and its application to reenforce HSC beams.
Develop a finite component theoretical account utilizing Strand7 and graduate the theoretical account to verify the experimental consequences of Cush ( 2009 )
Analyse the strength and ductile behavior of HSC beams reinforced helically with FRP ‘s and do a comparing between the usage of FRP ‘s and HSS.
Conclude on the viability of the usage of FRP ‘s for coiling support in HSC beams.
Provide way for farther research at the University of Wollongong.
The project of this thesis effort to go on the analysis of the viability in utilizing FRP ‘s as an alternate support to HSS in HSC beams. The confirmation of the consequences of Cush ( 2009 ) and the farther modeling of the strength and ductile behavior of HSC beams reinforced helically with FRP ‘s will supply analysis on the public presentation of FRP ‘s and expose its reenforcing capablenesss in comparing to HSS.
1.4 Summary of Chapters
Chapter 2 reviews the literature in relation to HSC beams helically reinforced with HSS, and the effects of modifying assorted parametric quantities in the support agreement, including the pitch and diameter of the spiral, the figure of spirals used, the form of the spiral, the type of stuff supplying the parturiency, and the tensile support ratio.
Chapter 3 provides a brief debut to the usage of FEM and provides item on their analysis of the behavior of HSC beams reinforced with HSS, and the ability of FEM to retroflex experimental consequences.
HELICAL REINFORCEMENT IN HSC BEAMS
Promotions in the production of concrete has lead to the handiness of particular purpose concretes, with strengths in surplus of 100MPa. The combination of such high-strength concretes with reenforcing steel efforts to relieve the jobs with the tensile strength of concrete and take advantage of the high strengths of both stuffs.
HSC beams with HSS support agreements have many benefits to the technology industry such as cut downing the size of columns in tall metropolis edifices, cut downing slab thicknesses, and therefore cut downing the weight and salvaging money in building.
While High Strength Concrete reinforced with High Strength Steel has big compressive strength, it has really low ductileness. The low ductileness of both stuffs leads to sudden failure without warning. This is known as brickle failure. Nawy ( 2001 ) identifies an addition in the crispness of concrete as its strength additions. Brittle failure is insecure and unwanted, hence restricting the usage of HSC reinforced with HSS in the industry despite is advantageous strength belongingss ( Warner et al. 2007 ) .
The coiling parturiency of concrete has been shown to increase the strength and ductileness features of HSC beams reinforced with either HSS or FRP ‘s. Despite the brickle nature of FRP ‘s, they still have a positive consequence on the ductileness features of HSC beams. They besides provide many advantages when being considered over the usage of HSS. FRP ‘s are highly light, strong, are non-magnetic, and are no susceptible to corrosion.
Further research into the viability of FRP ‘s as an alternate support to HSS could take advantage of their increased strength and elation features so that they can be to the full utilised in the technology industry.
2.2 Effect of Helical Reinforcement in Concrete Beams
Typically, coiling support in concrete beams uses a high strength steel in the form of a spiral. This is placed in the compaction part of concrete beams, and is considered to increase the strength and ductileness of High Strength Concrete Beams.
Hadi and Schmidt ( 2003 and 2005 ) confined high strength concrete beams in the compaction zone through the usage of one or two spirals. It was predicted that there would be an betterment in the strength, and therefore, burden transporting capacity of the concrete. This was supplemented by the anticipation that there would be an addition in the ductileness of the high strength concrete beams as the usage of high strength stuffs is usually to the hurt of a beams ductileness features.
Hadi and Schmidt ( 2003 ) found that usage of the coiling support in the compaction zone had the consequence of dramatically increasing the ductileness of the HSC beam. Poisson ‘s consequence is defined as the ratio between the alteration in length of an object due to either its elongation or compaction in the cross way, against the length alteration in the axial way. The parturiency of the concrete in the compressive part utilizing coiling support provides a sidelong compressive force on the confined concrete nucleus, which prevents the concrete from spread outing in the axial way. This allows the multi-axial compaction of the concrete nucleus ( Hadi and Schmidt, 2005 ) . Figure 1 ( Hadi and Schmidt, 2003 ) below shows the consequence of coiling support on ductileness, by doing a direct comparing between the mention beam UR-PL and the helically strengthened beam OR-SH-P1.
Figure 2.1: Load-central warp curves ( Hadi and Schmidt, 2003 )
Hadi and Schmidt ( 2005 ) found that usage of the coiling support in the compaction zone had the consequence of besides perceptibly increasing the strength and burden transporting capacity of the HSC beam. Beam 1 was the mention beam incorporating no coiling support whilst beam 2 contained an N12 spiral of pitch 50mm.
Figure 2.2: Cross-sections of Beam 1 and Beam 2 ( Hadi and Schmidt, 2005 )
Comparing the beams 1 and 2, the mention and helically confined beams severally, it was seen that there was a 24 % addition in the burden transporting capacity from beam 1 to beam 2, with beam 2 transporting a entire burden of 245.91KN compared to 198.5KN for beam 1.
Further surveies into the coiling parturiency of HSC beams in the compaction zone has found that effectivity of the coiling parturiency is influenced by a figure of factors including the pitch and diameter of the spiral, the figure of spirals used, the form of the spiral, the type of stuff supplying the parturiency, and the tensile support ratio.
2.2.1 Effect of Helical Pitch
The pitch of a spiral is defined as the distance in which one full bend of the spiral is achieved. The coiling pitch of support in compaction part of HSC beams has a critical impact on the strength and ductileness belongingss of the beam.
Hadi and Elbasha ( 2007 ) tested 5 beams confined helically with changing pitches. The beams had a transverse subdivision of 200mm ten 300mm and were a length of 4m. The diameter of the spiral was kept at a changeless 160mm while the pitches varied from 24, 50, 75, 100 and 160mm. A figure of decisions were drawn from the probe in respects to the consequence of coiling pitch on the public presentation of HSC beams.
Table 2.1: Summary of beam consequences ( Hadi and Elbasha, 2007 )
The spalling off burden refers to the burden that causes the concrete screen to divide from the nucleus of the concrete that is confined by the coiling support. As the pitch of the spiral increased, it was found that the spalling of burden increased proportionately. However, the failure burden of the beams decreased as the pitch of the spiral increased.
The ductileness of the beams was found to besides diminish as the pitch of the spiral increased. In this instance, the output warp and ultimate warp converged to a point where at a coiling pitch of 160mm they were equal. The staying beams experience ductile failure where by the supplanting ductileness index aE†aˆ u/aE†aˆ Y was greater than one. It was besides concluded that when the pitch of the spiral was equal to its diameter, the consequence of the coiling parturiency was considered minor.
2.2.2 Effect of rectangular and round spirals
The form of the confinement part in the compaction zone of HSC beams has an of import consequence on the strength and ductileness features of the beam. The compaction zone of the beam can be confined utilizing coiling support or through the us of rectangular or square ties.
As described earlier, the chief advantage of coiling support is that it provides a sidelong compressive force on the confined concrete nucleus, which prevents the concrete from spread outing in the axial way. This allows the multi-axial compaction of the concrete nucleus ( Hadi and Schmidt 2005 ) . A rectangular or square tie applies merely about 30-50 % of the sidelong force of a round spiral ( Hatanaka and Tanigawa, 1992 ) . The ensuing decrease in the compressive force means that the multi axial compaction of the nucleus is restricted to the country best confined by the rectangular or square tie, which occurs in the corners of the tie.
Figure 2.3: Confinement Areas of Helix and tie support ( Hadi and Schmidt, 2007 )
2.2.3 Consequence of the figure of spirals
The confining of HSC in the compaction part can be achieved through the usage individual or double spirals. Double spirals are placed straight following to one another in the compaction zone of HSC beams.
Hadi and Schmidt ( 2003 ) conducted research into the usage of a individual spiral in comparing to that of a double spiral agreement. A beam incorporating a individual spiral had a diameter of 50mm, while the agreement incorporating two spirals had diameters of 25mm each. Therefore the entire country confined in both beams was the same. The pitch of all spirals was kept changeless.
Comparisons between individual and double spirals found small difference in the ductileness and strength features of each beam, as the experiments for both beam produced really similar consequences. Hadi and Schmidt, nevertheless, did do the point that less steel was used in the support agreement utilizing a individual spiral, and that hence, in industry the more economical solution would be to utilize a individual spiral over double spirals.
2.2.4 Fibre-Reinforced polymers used for Helical Confinement in the compaction zone of HSC beams
The usage of fibre-reinforced polymers as opposed to the usage of high strength steel has been considered for helically reenforcing HSC beams in the compaction zone. However, there are some drawbacks to the usage of FRP ‘s including cost, and brickle failure mechanism of the stuff ( Whitehead and Ibell, 2005 )
Whitehead and Ibell ( 2005 ) analysed the shear behavior of FRP ‘s in concrete beams in an effort to relieve the hapless design jobs that nullify the advantages of FRP ‘s. The assorted agreements looked to better the support agreements of FRP ‘s as Ibell and Burgoyne ( 1999 ) found that bonding and geometry of the FRP was a big contributory factor in the influence of FPR ‘s used for shear support.
The agreements of the FRP support considered bonded and unbonded spirals, every bit good as spirals that were wholly in the compaction zone of the beam or draped into shear zones following the line of chief compaction.
Figure 2.4: Coiling Reinforcement forms ( Whitehead and Ibell, 2005 )
Whitehead and Ibell found that when comparing unbonded spirals to those who were intermittently or to the full bonded, the pitch of the spiral was required to be closer to accomplish similar additions in failure capacity. Unbonded spirals were 50 % less effectual than to the full or intermittently bonded spirals when it came to shear opposition. They besides found that prestressing within the FRP had a much greater consequence on the shear capacity, particularly when in comparing the HSS reinforced parturiency. The most effectual agreement determined was found the incorporated a to the full bonded handbill or rectangular spiral topographic point in the changeless minute country. This was combined with an intermittently bonded rectangular spiral placed within shear zones.
Another survey was conducted by Leung and Burgoyne ( 2001 ) , who analysed the consequence of overlapping spirals of Aramid in the compaction part of HSC beams. The overlapping parts of the concrete within the compaction zone created parts of double strengthened concrete. Results found that both the burden transporting capacity and ductileness increased as a consequence of the dual parturiency. The failure of the beams in the experiment was due to the gradual suppression of the rim of the T-beam, as opposed to the sudden failure caused when there were no spirals contained in the compaction part ( Burgoyne and Guimararaes, 1992 ) .
2.2.5 Effect of Tensile Reinforcement Ratio
The ratio of tensile support to the effectual cross subdivision of the beam is known as the tensile support ratio. The maximal allowable tensile support ratio is defined in AS3600 by the undermentioned expression:
E? = ratio under design bending or combined bending and compaction of the deepness of false rectangular compressive emphasis block to kud ;
f’c = characteristic concrete compressive strength at 28 yearss, MPa ;
fsy = yield strength of reenforcing steel, MPa ;
ku = ratio of deepness to impersonal axis to the effectual deepness
vitamin D = effectual deepness
Hadi and Schmidt ( 2002 ) analysed the consequence of increasing the tensile support ratio by making 7 beams, including one mention beam, with the staying six beams proving spirals in the compaction part with design reinforcement ratios of pmax, 1.5pmax, and 2pmax. This was achieved through increasing the figure and size of the support bars in the tensile part, every bit good as diminishing the effectual deepness of the beams.
Table 2.2: Radio beam features ( Hadi and Schmidt, 2002 )
Hadi and Schmidt concluded that the pmax set of beams had the greatest ductileness, followed by 1.5pmax and eventually 2pmax. The burden transporting capacity besides increased as the tensile support ratio increased, peculiarly in beams 6 and 7 where the spirals benefited form the increased stableness given by the support provided.
2.3 Review of past thesis at the University of Wollongong
2.3.1 Review of Cush ( 2009 )
Cush conducted an experiment into the usage of Polymer rope spirals ( PRH ) , alternatively of the high strength steel typically used for coiling support. Constructing beams of 1200mm ten 150mm ten 100mm, Cush used a assortment of reinforcement agreements. The reinforcement agreements provided a comparing between the usage of a HSS spiral and a PRH. He besides verified the work of old surveies by looking at the consequence of changing the pitch and diameter of the spiral in PRH.
Table 2.3: Beam Reinforcement agreements ( Cush, 2009 )
( L x D x B, millimeter )
( millimeter )
( millimeter )
1200 x 150 x 100
1200 x 150 x 100
1200 x 150 x 100
1200 x 150 x 100
1200 x 150 x 100
Figure 2.5: Radio beam Cross-sections ( Cush, 2009 )
The four point burden trial was used to set about testing, nevertheless the trial was compromised due to the fact that the beams were non able to be loaded until failure, and hence consequences for the maximal mid-span warp were taken at the maximal burden produced by the setup. This was due to the fact that the setup was non designed for the testing of HSC beams.
The decreased beam sizes compared to old old ages lead to similar values for the output and ultimate tonss for each beam. This meant that there was small solid grounds in the consequences from which decisions could be drawn, peculiarly as there were no values available for burdens after the beams had failed.
For the PRH, the ultimate mid-span warp decreased as the pitch increased, nevertheless the ultimate burden increased. The debut of a larger diameter to the PRH and therefore an increased country of confined concrete caused a greater ultimate mid-span warp. Given that steel rope spiral was non of the same diameter as the polymer rope spiral, it is hard to pull direct comparings between steel spirals and PRH.
However, Cush was satisfied that the PRH were effectual in retroflexing the advantages of spirals in the compaction zone of HSC beams as both the strength and ductileness of the beams increased. The lightweight nature of the PRH and the cost of the polymer used provides an interesting way for farther research as happening the optimal agreement for such a stuff would harvest both cost and weight benefits to the industry.
The parturiency of the concrete in the compressive part utilizing coiling support provides a sidelong compressive force on the confined concrete nucleus, which prevents the concrete from spread outing in the axial way. This allows the multi-axial compaction of the concrete nucleus ( Hadi and Schmidt, 2005 ) .
Independently, the effectivity of the coiling parturiency is by the pitch and diameter of the spiral, the figure of spirals used, the form of the spiral, the type of stuff supplying the parturiency, and the tensile support ratio.
The debut of Helical support improves the strength and ductileness features of HSC ( Hadi and Schmidt, 2003 and 2005 ) beams and supports the viability of the usage of HSC beams reinforced with either HSS or FRP ‘s ( Whitehead and Ibell, 2005 ) .
FINITE ELEMENT MODELLING IN REIFORCED CONCRETE
Finite Element Analysis is a technique affecting the usage of a mathematical theoretical account that is used to supply solutions to technology jobs. The usage of Finite Element Analysis ( FEA ) package predicts the behavior of concrete constructions leting the experimentation and confirmation of assorted designs and reenforcing agreement within the construction.
Cook ( 1995 ) alludes to the division of elements into several smaller elements that are linked through nodes within the plan. The combination of nodes and elements forms the creative activity of what is known as a mesh. The mesh is calibrated through the input of assorted stuff and structural belongingss, and theoretical accounts the influence of these belongingss on the behavior of the mesh under the burden provided.
Reinforcing steel can be accurately represented utilizing three different theoretical accounts ; smeared, embedded, or discrete.
The smeared theoretical account is applied for theoretical accounts that are larger and hence the consequence of the support is less than it would otherwise be in a smaller construction ( Srinivasan and Sathiya, 2010 ) . Reinforcement is assumed to be changeless through concrete component subdivisions within a mesh, as shown below.
Figure 3.1: Smeared Model ( Wolanski, 2004 )
the distinct theoretical account portions nodes between support and concrete elements. This provides the disadvantage of non being able to separate the support volume from the concrete volume, every bit good as the limitation of the concrete mesh place due to the support ( Taravez, 2001 )
Figure 3.2: Discrete theoretical account ( Wolanski, 2004 )
the embedded theoretical account evaluates the stiffness of the reinforcing bars individually from the concrete mesh by supplying compatible supplantings between the concrete and support nodes severally. This nevertheless, does increase the complexness of the theoretical account.
Figure 3.3: Embedded Model ( Wolanski, 2004 )
3.2 Review of Past FEM of strengthened concrete
3.2.1 Fanning ( 2001 )
Faning ( 2001 ) modelled a merely strengthened concrete beam, of dimensions 3000mm x 240 mm x 155mm. The reinforcement consisting of two bars in the compaction zone and three bars in tenseness zone, is detail below.
Figure 3.4: Cross subdivision inside informations for beam ( Fanning, 2001 )
The bonding between the support and the concrete was assumed to be perfect in the FEM and that the support and the concrete displace uniformly together.
The FEM calculated the ultimate burden of the beam to be 66.1KN whilst adequately defying non-linear warp up until failure. This compared favorably with the experimental value of 66.18KN, supplying really good coaction between the FEM and the experimental information. The first cleft occurred in the FEM at a burden of 17KN, which coincided with the first cleft happening in the experimental theoretical account excessively. The FEM nevertheless, differed from the experimental values when comparing the ultimate warp, with the FEM theoretical account hurting a warp of 27mm during its analysis while the experimental theoretical account showed a warp of 45mm.
The smeared cleft theoretical account used in the survey for the snap of the concrete, while a distinct theoretical account was used to analyze the support. Fanning ( 2001 ) concluded that the usage of these theoretical accounts for their several analysis was justified as the accurate consequences showed the rightness of each theoretical account.
3.2.2 Wolanski ( 2004 )
Wolanski ‘s analysis utilizing a FEM consisted of verifying the consequences of the Buckhouse ( 1997 ) , who constructed beams that were 4725mm ten 254mm ten 457mm. Wolanski ( 2001 ) wanted to develop an accurate FEM inputting all component and stuff belongingss so to guarantee that the information from the FEM correlated every bit closely as possible with the experimental consequences of Buckhouse ( 1997 ) .
One one-fourth of the beam was modelled due to the symmetrical nature of Buckhouse ‘s beam. The theoretical account is shown in the figure below.
Figure 3.5: Concrete, steel home base and support component ( Wolanski, 2004 )
The mesh for the support was created through the usage of nodes already within the concrete volume mesh. Wolanski ( 2004 ) merged the points in ANSYS that had a common node to obtain an accurate theoretical account. The boundary conditions provided in the experiment by Buckhouse ( 1997 ) were recreated through delegating UX = UZ = 0 and with the support restraint conditions being UY = UZ = 0 to stand for the presence of a roller.
The non-linear Newton-Raphson method was used in the FEM to bring forth informations on the snap of the beam, steel support and its giving up, and the strength bound province of the constructed beam. The experimental consequence of a warp of 92.7mm was compared to the ANSYS computation of 91.14mm, meaning the truth of the theoretical account produced by Wolanski ( 2004 ) when comparing the FEM analysis and the experimental analysis.
The FEM efficaciously displayed the steel support giving at a force of 59606 N, and the subsequent warp addition and formation of flexural and diagonal tenseness clefts. The beam was found to hold failed at a burden of 59526 N.
3.3 Review of past FEM thesis at the University of Wollongong
3.3.1 Review of Brahim ( 2006 )
Brahim ( 2006 ) sought to further look into the application of coiling support in high strength concrete through the usage of finite component plans. Brahim used to Finite component package plans, ANSYS and Strand7.
Brahim modelled the HSC beams that were constructed by Elbasha and Hadi ( 2005 ) . Elbasha and Hadi ( 2005 ) were analyzing the effects of changing the size of the pitch of the coiling support on the features of strength and ductileness in HSC beams. Constructing beams of 4000mm ten 300mm ten 200mm, Elbasha and Hadi varied the pitches of the spirals from 25, 50, 75, 100 and 150mm. Brahim ( 2006 ) made a direct comparing between the consequences produced by finite component package and the experimental consequences found by Elbasha and Hadi ( 2005 ) .
In Brahim ‘s Strand7 theoretical account, reinforcement elements were modelled as trusses, while the concrete beam and steel home base were modelled as a brick elements. Brahim created an initial theoretical account in the 2D plane utilizing changeless strain trigon elements ( TRI3 ) elements and additive four-sided elements ( QUAD4 elements ) . Extruding the 2D plane theoretical account, the 3D concrete block was formed, with support being modelled by linking each node within the concrete block. The concrete block and support portion nodes as shown in figure 7 below.
Figure 3.6: Node sharing in Strand7 theoretical account ( Brahim, 2006 )
Brahim assumed that the bonding between the concrete and the support was seamless. The steel home base elements were modelled utilizing 8-node brick elements, while the burden applied to the steel home base was done so through the centre line of the steel home base formed by the brick elements. This replicated the locations of the burdens in the experiment conducted by Elbasha and Hadi ( 2005 ) .
Figure 3.7: Steel home base lading along centreline ( Brahim, 2006 )
The support supplying the boundary conditions was modelled as steel and given dimensions 100mm x 80mm ten 30mm, and provided restraint in the omega and ten way, ( UX = UZ = 0 ) .
Strand7 differed from ANSYS in convention used in the input of compressive and tensile strength values whereby compaction values were negative while tensile values were positive. All other informations input for Strand & A ; including stuff belongingss, was similar to ANSYS.
Strand7 used the Newton-Raphson method for work outing the non-linear jobs in Finite Element Models. In this non-linear analysis, stress-strain relationships are input into the system along with the application of incremental tonss, to more accurately pattern the behavior of the concrete beam. However, this increases the simulation tally clip.
In his sum-up of consequences, Brahim ( 2006 ) states that there were obvious differences in the burden versus warp curves produced by Strand7 and ANSYS in comparing to the experimental informations obtained by Elbasha and Hadi ( 2005 ) . The major differences in the curves is seeable after the spalling off of the concrete screen. An account may be given by the via medias made in the modeling of the spiral in both Strand7 and ANSYS. Brahim was forced to simplify the coiling theoretical account, replacing in a round support theoretical account. The premise was made that the public presentation of the round support theoretical account was the same as the coiling support theoretical account and that the compressive effects that create multi-axial compaction would be the same in both methods of support.
FEA package provides a feasible option to experimental proving that can salvage both clip and money for applied scientists if the FEM is calibrated right.
Faning ‘s ( 2001 ) theoretical account provided to within 2 % the information achieved during the experiment undertaken by Buckhouse ( 1997 ) demoing the viability of FEA.
Both Strand7 and ANSYS provide applied scientists with utile tools to measure the behavior of HSC beams helically reinforced with HSS. To accurately pattern this though, the via medias made by Brahim ( 2006 ) demand to be eliminated to suitably analyze the consequences of Cush ( 2009 )