Research ArticleStructural Model for Fibre-Reinforced Precast ConcreteSandwich Panels

Luis Segura-Castillo ,1 Nicolas Garcıa,1 Iliana Rodrıguez Viacava,2

and Gemma Rodrıguez de Sensale2

1Faculty of Engineering, Universidad de la Republica, UdelaR, Montevideo, Uruguay2Faculty of Architecture/Faculty of Engineering, Universidad de la Republica, UdelaR, Montevideo, Uruguay

Correspondence should be addressed to Luis Segura-Castillo; lsegura@fing.edu.uy

Received 30 April 2018; Revised 27 August 2018; Accepted 2 October 2018; Published 22 November 2018

Academic Editor: Hugo Rodrigues

Copyright © 2018 Luis Segura-Castillo et al. )is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Fibre-reinforced concrete (FRC) has been used in numerous types of precast elements around the world, as has been shown thatreductions in production costs and time can be obtained; however, there is little experience of this material in Uruguay. )erefore,our study analysed the feasibility of its utilisation in this country. )is paper reports on the development of a simple analysis modelthat is useful for the design of FRC precast elements. )e model efficiency was evaluated through its application to a practical casestudy—vertical precast concrete sandwich panel systems tested by bending. )ree different types of reinforcement were analysed:synthetic fibres, metal fibres, and steelmesh.With the developedmodel, the cost-efficiency of different panel geometries and amountsof reinforcement were evaluated.)emodel allowed consideration of the contribution of the fibres to withstand internal tensile forcesof the panels and therefore be able to substitute for the steel mesh in the panel wythes. It was found that it was possible to optimisepanel reinforcement and geometry, thereby reducing wythe thickness. Besides the reduction in production time, it was possible toachieve cost savings of up to 10% by replacing steel mesh with fibres and of more than 20% if the geometry was also modified.

1. Introduction

Fibres have been successfully used in precast elements sincethe early days of development of fibre-reinforced concrete(FRC) [1]. Numerous types of FRC precast elements can befound around the globe [2, 3], including roof elements [4],tunnel segmental linings [5], and pipes [6]. Besides thereduction in costs and production times associated with theuse of FRC, further advantages can be obtained if the use offibres is combined with a self-compacting concrete (SCC)matrix, obtaining self-compacting fibre-reinforced concrete(SCFRC), which allows the casting of structural elementswith complex geometry and/or composed of thin compo-nents [7].

Although there are several local applications that useFRC in Uruguay, mainly in industrial pavements and smallprecast elements, and the use of this technique is in-creasingly common, there are very few cases in which its

design and use are based on criteria endorsed by guidelinesor recommendations, with only two documented caseswhere a quality-control programwas followed [8, 9]. In mostcases, the design is based on recommendations from fibresuppliers, whilst different recommendations and criteria areavailable; in practice, quality control of such materials is notcarried out. )erefore, it is not possible to know whether thespecifications meet the requirements for the design.

)e vast majority of precast elements produced inUruguay are based on heavy prefabrication, largely usingconventional reinforced concrete (CRC), while SCC andFRC are rarely used. )erefore, there is potential to improvethe national precast industry with the use of these materials.Precast concrete sandwich panel (PCSP) systems can bementioned among the elements that could be improved.)ese panels are composed of two concrete wythes (orconcrete layers) separated by a layer of insulation [10].Different ways of connecting the concrete wythes through

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 3235012, 11 pageshttps://doi.org/10.1155/2018/3235012

the insulation layer include concrete webs, metal or plasticconnectors, or a combination of these.

Panel prototypes have been tested by Barros et al.[11–13] to assess benefits to the flexural and shear resistanceof thin structural systems when CRC wythes are replacedwith SCFRC. A smeared multifixed crack model, imple-mented into a finite-element method-based computerprogram, was used to simulate panel structural behaviour upto failure. Other research has assessed the use of fibre-reinforced polymer as concrete wythe connectors for thissolution [14, 15]. FRC panels have also been used as partialsupport in the study of a fibre-reinforced slab [16].

In line with this, a research project was developed toanalyse the feasibility of the utilisation in Uruguay of FRCand SCFRC for precast elements, in particular, in a PCSPsystem, which was chosen as the case study. An experimentalstudy was first carried out at the material level [17], and thenprototypes where cast in order to analyse the feasibility oftheir production in the concrete plant and tested underbending to assess the main responses [18].

)e objective of this work was twofold: on one hand, todevelop a simple analysis model useful for the design ofPCSPs reinforced with FRC, and on the other hand, tooptimise the design and analyse the cost-efficiency of thesolution.

A theoretical model for evaluating the structural be-haviour (moment-curvature and load-displacement re-lationships) of PCSP elements reinforced with concrete withfibres is proposed. )e model follows the guidelinesestablished in the Structural Concrete Instructions of Spain(EHE-08, Annex 14) and is based on results obtained at thematerial level.

2. Case Study: Precast ConcreteSandwich Panels

)emodel efficiency was evaluated through its application ina practical case study: vertical PCSP tested by bending. )epanels had a prismatic shape with the dimensions (height ×

width × thickness) 2.4 × 1.2 × 0.2m, with a central insulationlayer made of expanded polystyrene (EPS) foam sheets (2.1 ×

0.9 × 0.1m), as shown in Figure 1. According to the definedgeometry, an external-edge stiffening beam, 0.15m wide,was formed at the panel perimeter.

)ese panels were reinforced with steel trusses formed bythree longitudinal bars of 8mm nominal diameter, two topand one bottom (according to the direction of testing),connected by diagonal bars with a diameter of 4.2mm(Figure 2). In the two external layers of concrete (concretewythes), 0.05m thick, the following reinforcement alter-natives were evaluated (Figure 2):

(i) P_Mesh: steel mesh with a diameter of 4.2mm andmesh width of 150mm (ϕ4.2mm/150mm), placedin the middle plane of each concrete layer

(ii) P_FRCM20: 20 kg/m3 steel fibres with hooks madeof low-carbon steel, 50mm long, 1mm in diameter,with a tensile strength superior to 1100MPa andspecific weight of 7.85 kg/m3 (Wirand FF1)

(iii) P_FRCS6: 6 kg/m3 synthetic fibres, polyolefinmacrofibres with corrugated surfaces, 48mm long,equivalent diameter of 1.37mm, with a tensilestrength superior to 550MPa and specific weight of0.92 kg/m3 (Fiber Force PP-48)

Figure 3 shows the panel construction process usingtraditional steel reinforcement bars. )e reinforcement as-sembly and placement stages were eliminated in the case ofthe panels with fibres.

Concrete with a nominal compressive strength of fck �

35MPa and steel with a characteristic strength of fyk �

500MPa were used. )e mechanical parameters of theconcrete used in the model were determined experimentallyfrom the specimens made during the concreting of thepanels, as described in the following section.

)e flexural strength test of the panels was carried out onthree specimens of each type of reinforcement, applying thestandard ASTM E72 (2015) [19]. )e panel was tested ina horizontal position and was simply supported by a spanbetween supports of 2.1m. Two-point loading of equalmagnitude was applied, each load at a distance of one-quarter of the span from the supports, as shown in Fig-ure 4. In this way, the central section was subjected to purebending moment.

3. Structural Analysis

3.1. Structural Behaviour Model. )e expected structuralbehaviour can be divided in three stages [20], which arerepresented in the load-displacement diagram shown inFigure 5. In the first stage (linear elastic), the concrete matrixis in an uncracked phase and, therefore, the element behavesin a linear elastic way. In the second stage (postcracking), thematrix starts cracking.)is is a transition stage during whichthe tensile stresses are transferred from the matrix to thereinforcement. In the third stage (yielding), yielding takesplace in at least one of the materials. As there was a lowamount of reinforcement used in this study, yielding tookplace in the reinforcement whilst the concrete was still in thelinear elastic stage. Depending on the type and amount ofreinforcement, two types of behaviour can take place in theyielding stage [21]: hardening, in which the ultimate strengthis greater than the cracking strength of the element, orsoftening, where the ultimate strength is below the crackingstrength, as shown in Figure 5.

Stage 1: Linear elastic. Transverse deformations of the panelin Stage 1 are shown schematically in Figure 6. )e fol-lowing basic hypothesis on the behaviour of the reinforcedconcrete was taken into account in the model. )e concretewas in the precracked stage; that is, the tensile strength ofconcrete had not been reached, and therefore, it coulddevelop both tensile and compressive stresses. Also, a linearelastic behaviour of the concrete could be assumed. Finally,the Navier–Bernoulli hypothesis was assumed, meaningthat the planar sections would remain planar and per-pendicular to the deformed axis. )is hypothesis is basedon the assumption that the width of the external frame was

2 Advances in Civil Engineering

greater enough to act as a concrete web, e�ciently trans-ferring the shear forces.

Under the mentioned hypothesis, a classic formulationof the mechanics of materials is valid. �e cracking moment(Mcr) was determined using Equation (1).�e reinforcementcontribution was neglected for the three types of re-inforcements, being negligible in comparison with the forcescreated by the concrete in tension:

Mcr �fct,m,flex . Ic

h/2, (1)

where fct,m,flex is the mean  exural tensile strength ofconcrete, Ic is the second moment of area (uncrackedconcrete section), and h is the cross-sectional depth.

Also, in Stage 1, the relationship between moment (M)and curvature (χ) is linear up to the cracking moment, whichis given by

χ �Mcr

Ec . Ic, (2)

where Ec is the reduced modulus of elasticity of concrete.Given the static con�guration of the test, the moment

value can be related to that of the applied load (F), according

200mm1200mm

2400

mm

150mm 900mm 150mm

200m

m

150m

m15

0mm

2100

mm

(EPS)

A A

BB

Section A-A

Sect

ion

B-B

Traditionalreinforcement

Fibrereinforcement

(EPS)(E

PS)

(EPS

)

(EPS)

Figure 1: Plan and cross section of the panel.

Advances in Civil Engineering 3

Electrowelded meshØ4.2mm/15cm

Ø8mm

Trusses Ø4.2mm50

100

50150 Ø8mm

Electrowelded meshØ4.2mm/15cm

9001200

150

200

(EPS)

(a)

Trusses Ø4.2mm

5010

050

150 Ø8mm 9001200

150

200(EPS)

Ø8mm Fibres

(b)

Figure 2: Details of di�erent types of reinforcement tested: (a) traditional reinforcement with steel bars and (b) synthetic or steel �brereinforcement.

(a) (b) (c) (d)

(e) (f ) (g) (h)

Figure 3: Construction of lightweight concrete panels.

4 Advances in Civil Engineering

to Equation (3), where L is the span between the supports.Since it is a statically determined setup, this relationship ismaintained in all stages of the test:

F �8 ·ML

. (3)

Finally, the displacements can also be obtained usingclassic equations. �e displacement of the midpoint (δ) isgiven by the following expression, with the meanings of thevariables indicated above:

δ �11 · F · L3

768 · Ec · Ic. (4)

Stage 2: Postcracking. �e postcracking stage is a transitoryphase between Stages 1 and 3, in which progressive crackingof the matrix takes place, transferring the tensile stressesfrom the concrete matrix to the reinforcement (bars or

�bres). As the behaviour in this stage reports great com-plexity and, in turn, does not contribute signi�cant in-formation to the design, this section was not preciselydetermined. In a practical way, the structural behaviour inthis stage was completed by a linear transition from the lastpoint determined in Stage 1 with the �rst point in Stage 3.

Stage 3: Yielding. �e moment-curvature curve was de-termined by discretising the curvature curve (χi) at severalpoints, at which the values of the corresponding moment(Mi) were determined. For each curvature value (χi) ana-lysed, and for a given position of the neutral line (xi inFigure 7), it was possible to calculate the deformations in theentire section through the Navier–Bernoulli hypothesis. Bymeans of the constitutive equation of each material, thetensions were obtained for every position within the section.A triangular stress distribution was considered for concreteunder compression, and a multilineal constitutive equation(described below) was used for the FRC in tension. �eseassumptions are represented in the diagrams shown inFigure 7. �e stresses provided by the EPS, as well as thetensile stresses of plain concrete, were considered to be null.Also, a punctual load (Fs) was applied where reinforcementbars were present.

�e xi value that solves the problem was determined byequilibrium equations. As the beam was under purebending, the axial force was equated to zero (N � 0) bymeans of an iterative procedure. Finally, for the value ofcurvature (χi) and xi found, the corresponding moment wascalculated. �e moment-curvature curve was obtained byjoining all pairs of values (Mi, χi) obtained from thisanalysis. It is important to take into account that it is notpossible to adopt curvatures that involve a deformation ofthe steel in tension greater than 10‰ or of the FRC intension greater than 20‰, as these values correspond to theultimate state limits [22]. As indicated above, the re-lationship between applied load and moment in the centralsection was determined by Equation (3).

A single crack was observed in the �bre-reinforcedpanels, where the deformation was concentrated. �ere-fore, to determine the displacements in the panels in theyielding stage, it was considered that each panel behaved astwo rigid bodies that rotated on a hinge where the crack wasformed, as illustrated in Figure 8. To simplify the analysis, itwas assumed that the crack opening (ω) was located in thecentral section of the panel.

Considering this scheme, it is possible to correlate thevalue of the de ection at the midpoint (δ) with the crackopening through trigonometric relationships (δ � L · ω/4 · h).In turn, the crack opening is related to the strain at any pointby the structural characteristic length, lcs, which, in this case,can be assumed to be equal to h [22]. �erefore, for thebottom �bre: ω � ε · lcs � ε · h. Finally, the strain in thebottom �bre of the cross section can be approximately cal-culated with the curvature (εinf � χ · h). Combining theprevious expression, the following equation can be obtained:

δ �L · ω4 · h

�L · εinf · h

4 · h�L · χ · h · h

4 · h⇒ δ �

L · h · χ4

. (5)

F/2 F/2

L/4 = 525mm L/4 = 525mmL = 2100mmL/2 = 1050mm

2400mm

Figure 4: Two-point load test setup.

2

F

Fu

Ffis

δfis δuδ

3

1

Figure 5: Load-displacement curves for panels subjected toa bending test.

F/2 F/2

δ

Figure 6: Deformation diagram on the linear elastic section.

Advances in Civil Engineering 5

To estimate the displacement in the mesh-reinforcedpanels, two strategies were used, depending on whether theyield moment (My) of the central section was exceeded. Ifthe maximum moment was belowMy, Branson’s empiricalformula [23] was used to calculate the equivalent moment ofinertia (Ie) of the element:

Ie �Mcr

Ma( )

3

· Ib + 1−Mcr

Ma( )

3 · If ≯ Ib, (6)

whereMcr is the cracking moment,Ma is the acting bendingmoment, Ib is the second moment of area (uncrackedconcrete section), and If is the moment of inertia of thecracked section.

If the maximummoment exceeds the yield moment, it isunderstood that large deformations take place in the centralsection. For this reason, the displacement of the central pointwas calculated by integrating the curvature of the sectionbetween loads (χmax, which was assumed to be constant inthis section) and neglecting the rest of the deformations.�evariation of the angle of rotation from the central section tothe point of application of the loads can be computed as

θmax � ∫L/4

0χmaxdx �

L

4· χmax. (7)

And, hence, the displacement of the central point:

υmax � ∫L/2

0θ(x)dx � ∫

L/4

0

x

L/4θmaxdx

+ ∫L/2

L/4θmaxdx �

L

4·3L8· χmax.

(8)

3.2. Ultimate Moment Approximation. Besides the pre-viously described procedure, it is possible to establishapproximated formulas that allow the calculation, byhand, of the ultimate moment and ultimate curvature ofthe element. For calculation of the simpli�ed ultimate

moment, it is assumed that the whole compressive force isconcentrated in the top �bre of the section.

In the case of �bre-reinforced panels, concrete tensilestresses are assumed to have a uniform value (fctR,d �0.33fR,3,d [22], see section 3.3) and are applied only to thelower layer of the sandwich. �erefore, tensile stresses inthe upper layer, and in the lateral beams, are neglected.Strain and stress diagrams representing the assumptionsare shown in Figure 9.

With the assumed simpli�cations, the curvature can bedetermined as

χ �εsh− c

, (9)

where εs is the deformation of the reinforcement bar (which,in the ultimate state, is taken to be 10‰), h is the paneldepth, and c is the reinforcement mechanical cover.

On contrary, the resultant tensile force (T) is

T � fctR,d · b · h w + fyd · As (10)

where fctR,d is the residual resistance of the �bres, b is thepanel width, h_w is the thickness of the concrete wythes, fydis the design yield strength of the reinforcement steel, andAsis the cross-sectional area of the reinforcement steel.

�e approximate ultimate moment of the cross section ofthe element can then be determined by multiplying the leverarm of the internal forces (z � h− c) by the resultant tensileforce (T):

MU � T.z � fctR,d · b · h w + fyd · As( ).(h− c). (11)

3.3. Determination of Stress-Strain (σ − ε) Law for FRC bymeans of the Beam Test. Load-displacement curves for theFRC were experimentally obtained by a four-point bendingtest, according to UNE 83510 [24], carried out over threesamples cast during the production of each of the panel types[17].

From the average of these values, and applying the four-stage criteria indicated below, the multilinear stress-strainconstitutive equation (Figure 10), as indicated by EHE-08,was obtained. �e average values of these parameters aredetailed in Table 1 for the synthetic (P_FRCS6) and steel(P_FRCM20) �bres used in the panels.

Stage 1. ASTM C1609 [25] and UNE 83510 [24] standards,both strongly based on the Japanese standard JSCE-SF4 [26],

σc

(σ)σb

εc

(ε)

x

Fs

σa

εs

(EPS)

Figure 7: Diagrams representing strain (ε) and stress (σ).

αα

α

ω

δ

Figure 8: Displacement in the panel according to the rigid bodymodel.

6 Advances in Civil Engineering

are considered to be equivalent. �erefore, from the load-displacement curve of the material obtained from the test,the following values, considered by the ASTM standard,were obtained:

(a) First-peak load (F1) and �rst-peak de ection(b) Residual load (F0.75) corresponding to a net de-

 ection of L/600, equivalent to 0.75mm(c) Residual load (F3.00) corresponding to a net de-

 ection of L/150, equivalent to 3.00mm

Stage 2. �e �rst-peak strength (f1) and the residual strengthcorresponding to the de ections of 0.75mm (f600) and 3mm(f150) were calculated according to ASTM C1609, based onthe following equation:

f �F · Lb · h2

, (12)

where f is the strength in N/mm2, F is the load in N, L is thedistance between supports in mm, b is the average width ofthe specimen in mm, and h the average edge of the specimenin mm.

Stage 3. Values of fR,1 and fR,3, according to the three-pointbending test EN 14651 [27], can be calculated from theASTM C1609 [25] four-point bending test results, using thecorrelations indicated by Conforti et al. [28] Equation (13):

f600[MPa] � 1.17 · fR,1[MPa] R2 � 0.94( ),

f150[MPa] � 0.80 · fR,3[MPa] R2 � 0.90( ).(13)

Stage 4. Tensile strength (fct) and its corresponding de- ection (ε0), the tensile residual strengths (fct,R1 and fct,R3)associated with de ections ε1 and ε2, respectively, in thepost-peak regime, and the value of εlim were determined byapplying the equations indicated in point 39.5 of Annex 14of the Spanish Instructions for Structural Concrete EHE-08[22], which is based on EN 14651 test results.

3.4. Elastic Modulus. Table 2 shows the values of the elasticmodulus used, which were established as a function of thecompressive strength, determined by the standard testUNIT-NM 101 [29], from the following formula indicated inthe �b Model Code (2010) [21]:

Ect � Ec0 · αE ·fcm

10( )

1/3

. (14)

It should be noted that, taking into account Tables 5.1–6of the Model Code, for aggregates of quartzite origin, it isconsidered that Ec0 · αE � 21500 MPa.

4. Result Analysis

4.1. Qualitative Behaviour. �e numerical results for thethree analysed panels are shown in Figure 11, including themoment-curvature (Figure 11(a)) and load-displacement(Figure 11(b)) curves. In both �gures, the solid pointsrepresent the complete model, and open points are thesimpli�ed model. It can be seen that, in the complete model,the three stages expected (linear elastic, postcracking, andyielding) are represented. Also, due to the statically de-terminate setup, the structural behaviour re ects the sec-tional behaviour to a large extent.

�e simpli�ed calculation of the ultimate momentmatches, with great accuracy, the complete analysis for thebar-reinforced panels. For the FRC panels, a conservativevalue was obtained (around 17% smaller), due to the sim-pli�cations described above.

A usually accepted design criterion requires, to avoidbrittle failure under bending, that the ultimate bendingcapacity (MU) be larger than the  exural cracking moment(Mcr) [30, 31]. It can be seen that this criterion is approx-imately met for the three types of reinforcement, with a smalldrop for large curvatures in the case of steel �bres.

4.2. In�uence of the Amount of Reinforcement and Fibres.For the three types of reinforcement analysed, the in uenceof the amount of reinforcement in the structural responsewas analysed. �e load-displacement curves are shownin Figure 12 for the three types and di�erent amountsof reinforcement (20, 40, and 60 kg/m3 for steel �bres(Figure 12(a)); 4, 6, and 8 kg/m3 for synthetic �bres(Figure 12(b)); and ϕ4.2/15, ϕ6/15, and ϕ8/15 for meshreinforcement (Figure 12(c))).

It can be seen that the initial linear stage is the same in allcases because it is mainly controlled by the concrete matrix.On the contrary, a clear di�erence in behaviour can be seenamong the di�erent types of reinforcement after crackingtakes place, and the tensile loads are transferred to the re-inforcement. Also, for each type, the ultimate moment ishigher when the amount of reinforcement increases.

Finally, it can be seen that, for the amounts of re-inforcement analysed, which are in the usual ranges forconventional FRC, the ultimate loads obtained are in a rangeof between 80 and 180 kN. A similar range was observed forthe rebar-reinforced panels; however, for this type of re-inforcement, the amount of reinforcement could be con-sidered to be in the low range, regarding the bendingmoments. It can be said that, regarding the  exural re-sistance, �bres are capable of substituting for rebar re-inforcement at low to medium structural capacity.

(σ)fctR,d

εc

(ε)

(EPS)

Fsεs

Fc

Figure 9: Strain (ε) and stress (σ) diagrams for the approximationof the ultimate moment.

Advances in Civil Engineering 7

4.3. In�uence of Wythe �ickness. As there was no rebarreinforcement in the concrete wythes of the �bre-reinforcedpanels, a minimum reinforcement cover was not needed,and therefore, it was possible to reduce the wythe thicknessto optimise the panel geometry. Total cross-sectionalthickness, which usually meets insulation requirementsand architectural aspects, was kept constant (h � 200mm)for the analysis. Wythe thickness (h_w) was chosen as thestudy variable. �ree thicknesses (h_w � 50, 40, and 30mm)were analysed, which corresponded to EPS layer thicknessesof 100, 120, and 140mm, respectively.

�e load-displacement results for the wythe thicknessanalysis are shown in Figure 13. As expected, for both typesof �bre, the bending moments in the postcracking stageincreased with wythe thickness; however, the variation wassmaller than that observed for the di�erent amounts ofreinforcement studied. �erefore, it seems plausible thatthe resistance drop produced by a wythe thickness re-duction could be restored by an increase in the amount of�bres. �is would allow a reduction in the use of concrete,

whilst obtaining lighter panels with the same structuralcapacity.

4.4. Panel Optimisation. Based on the model developed,which takes into account the structural collaboration of the�bres, a parametric study was carried out in order to op-timise the geometry and reinforcement of the panels ata sectional level. �e aim of the analysis was to obtain themost economic combination of geometry and reinforcementfor six di�erent objective design moments (5, 10, 15, 20, 30,and 50 kNm). For the calculation of each panel cost, theunitary costs shown in Table 3, in US dollars (USD), wereconsidered.

Regarding the panel geometry, the wythe thickness waschosen as the study variable, with the three options describedin the previous section (h_w � 50, 40, and 30mm), main-taining constant total thickness (0.2m), as well as the panelexterior width (1.2m), the EPS width (0.9m), and the ex-ternal concrete web width (0.15m).

�e reinforcement design strategy consisted of, �rst ofall, setting the minimum reinforcement to be placed in thewythes to control shrinkage and thermal e�ects. �en, theconcrete web reinforcement was determined to cover, to-gether with the wythes, the objective ultimate bendingmoment. Reinforcing steel bars, with the diameters of 8, 10,12, 16, and 20mm, were considered.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5

σ t (M

Pa)

ε (%)

P_FRCS6P_FRCM20

(a)

P_FRCS6P_FRCM20

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10 12 14 16 18 20 22

σ t (M

Pa)

ε (%)

(b)

Figure 10: Multilineal σ − ε law obtained experimentally.

Table 1: Parameters for FRC constitutive equation in tension.

Stage 1: Loads(kN), ASTM

C1609

Stage 2:Strengths

(MPa), ASTMC1609

Stage 3:Residualstrengths(MPa),

EN 14651

Stage 4: Constitutive equation FRC

P_FRCS6

F1 31,65 f1 4,22 fct,m 2,53MPa ε0 0,075‰F0.75 18,18 f600 2,42 fR,1 2,07 fct,R1,m 0,93MPa ε1 0,175‰F3.00 21,07 f150 2,81 fR,3 3,51 fct,R3,m 1,34MPa ε2 12,50‰

fct,lim 1,59MPa εlim 20,00‰

P_FRCM20

F1 33,12 f1 4,42 fct,m 2,65MPa ε0 0,077‰F0.75 19,94 f600 2,66 fR,1 2,27 fct,R1,m 1,02MPa ε1 0,177‰F3.00 13,23 f150 1,76 fR,3 2,21 fct,R3,m 0,65MPa ε2 12,50‰

fct,lim 0,42MPa εlim 20,00‰

Table 2: Elastic modulus values used.

P_FRCS6 P_FRCM20fcm (MPa) 38,13 40,52Ecm (GPa) 33,59 34,28

8 Advances in Civil Engineering

A comparative analysis of the optimisation results isshown in Figure 14. �e mesh-reinforced panel for the15 kNm objective moment was chosen as the referencepanel. �e �gure shows the total cost of the optimised panelin relation to the reference panel for each objective moment,each wythe thickness and type of reinforcement. �e lowerobjective moments (5, 10, and 15 kNm) fell below the

 exural cracking moment (Mcr), and therefore, the brittlefailure criterion (MU ≥ Mcr) controls the design.

It can be seen that, for each type of reinforcement,the larger the objective moment, the greater the cost. �isincrease is mainly due to the amount of reinforcementneeded to withstand the acting moment. For a speci�c valueof objective moment and wythe thickness, there is a small

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Mom

ent (

kNm

)

Curvature (1/m)

P_FRCM20P_FRCS6P_Mesh

Simp_P_FRCM20Simp_P_FRCS6Simp_P_Mesh

(a)

P_FRCM20P_FRCS6P_Mesh

Simp_P_FRCM20Simp_P_FRCS6Simp_P_Mesh

0

20

40

60

80

100

120

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Load

(kN

)

Displacement (mm)

(b)

Figure 11: Structural results for the three types of reinforcement analysed: (a) moment-curvature and (b) load-displacement curves.

0

40

80

120

160

200

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Load

(kN

)

Displacement (mm)

P_FRCM60P_FRCM40P_FRCM20

Simp_P_FRCM60Simp_P_FRCM40Simp_P_FRCM20

(a)

020406080

100120140

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Load

(kN

)

Displacement (mm)

P_FRCS8P_FRCS6P_FRCS4

Simp_P_FRCS8Simp_P_FRCS6Simp_P_FRCS4

(b)

0

30

60

90

120

150

180

210

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Load

(kN

)

Displacement (mm)

P_Mesh ϕ8 Simp_P_Mesh ϕ8

P_Mesh ϕ4.2 Simp_P_Mesh ϕ4.2 P_Mesh ϕ6 Simp_P_Mesh ϕ6

(c)

Figure 12: In uence of the amount of reinforcement in (a) steel �bres, (b) synthetic �bres, and (c) steel mesh.

Advances in Civil Engineering 9

reduction in the panel cost when �bres are used as re-inforcement (up to 10%, in the case of synthetic �bres).

On the contrary, it can be seen that, for a speci�c ob-jective moment, costs are smaller in the panels with reducedwythe thickness, with reductions greater than 20% for bothsynthetic and steel �bres. �is solution is viable only in the�bre-reinforced panels, where a minimum steel bar cover isnot needed. Wythe thickness then becomes conditionalmainly upon the concrete execution capacity, which shouldremain within the speci�ed tolerance range and with ac-ceptable surface �nishing.

5. Conclusions

A theoretical model, mainly based on the Spanish ConcreteInstruction Guidelines (EHE-08, Annex 14) and capable ofevaluating the structural behaviour of FRC panels, was in-tegrated. �e results showed the expected behaviour of thepanels under study. �e model allows consideration of the

contribution of �bres to withstand internal tensile forces ofthe panels and, therefore, be substituted for the steel mesh inthe panel wythes. Likewise, as the FRC tensile mechanicalproperties were de�ned based on normalised tests, it waspossible to establish a quality-control program to evaluatepanel production.

Finally, it was possible to optimise panel geometry andreinforcement, reducing wythe thickness and adjusting thedi�erent types of reinforcement to comply with the designconditions. It was found that it was possible to achieve a costreduction of up to 10% if the reinforcement was modi�edand of more than 20% when the geometry was also modi�ed.�is constitutes a signi�cant saving that is worthy of furtherexploration. In addition, besides the economic advantage,a reduction in production time was also achieved when FRCwas used.

Data Availability

No data are available for this manuscript.

Conflicts of Interest

�e authors declare that they have no con icts of interest.

Acknowledgments

�e authors would like to thank the National Agency forResearch and Innovation (ANII) for the economic supportreceived through Research Project (FMV_1_2014_1_104566“Application of new concretes for precasting”).

References

[1] R. F. Zollo, “Fiber-reinforced concrete: an overview after 30years of development,” Cement and Concrete Composites,vol. 19, no. 2, pp. 107–122, 1997.

0102030405060708090

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Load

(kN

)

Displacement (mm)

P_FRCM20_w = 30mmP_FRCM20_w = 40mmP_FRCM20_w = 50mm

Simp_P_FRCM20_w = 30mmSimp_P_FRCM20_w = 40mmSimp_P_FRCM20_w = 50mm

(a)

0

20

40

60

80

100

120

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Load

(kN

)

Displacement (mm)

P_FRCS6_w = 30mmP_FRCS6_w = 40mmP_FRCS6_w = 50mm

Simp_P_FRCS6_w = 30mmSimp_P_FRCS6_w = 40mmSimp_P_FRCS6_w = 50mm

(b)

Figure 13: In uence of concrete layer thickness on (a) steel �bres and (b) synthetic �bres.

Table 3: Unitary costs of materials and labour.

Steel �bres Synthetic �bres Steel mesh Steel bars Poured concrete Foreman Worker(USD/kg) (USD/kg) (USD/m2) (USD/kg) (USD/m3) (USD/hour) (USD/hour)3.3 11.2 5.7 1.2 210.5 10.5 6.0

–30

–20

–10

0

10

20

30

40

50

P_Mesh P_FRCM P_FRCS P_FRCM P_FRCS P_FRCM P_FRCSh_w = 50mm h_w = 40mm h_w = 30mm

Perc

enta

ge co

st va

riatio

n co

mpa

red

with

refe

renc

e pan

el (%

)

5 kNm10 kNm15 kNm

20 kNm30 kNm50 kNm

Figure 14: Variation in costs of the optimised panels.

10 Advances in Civil Engineering

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