2008 SEISMIC ENGINEERING CONFERENCE COMMEMORATING THE

1908 MESSINA AND REGGIO CALABRIA EARTHQUAKE Reggio Calabria, Italy 8 – 11 July 2008 PART ONE

EDITORS

Adolfo Santini Nicola Moraci University of Reggio Calabria, Italy SPONSORING ORGANIZATIONS Municipality of Reggio Calabria Regional Council of Reggio Calabria Regional Province of Reggio Calabria Mediterranean University of Reggio Calabria Faculty of Engineering of Reggio Calabria Department of Mechanics and Materials (University of Reggio Calabria) Department of Computer Science, Mathematics. Electronics and Transportations (University of Reggio Calabria) University of Catania CARICAL Foundation Chamber of Commerce of Reggio Calabria Regional Province of Messina Association of Architects of Reggio Calabria Association of Architects of Messina

Melville, New York, 2008 AIP CONFERENCE PROCEEDINGS

VOLUME 1020

Downloaded 11 Oct 2013 to 192.167.111.193. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions

Experimental Tests and FEM Model for SFRC Beams under Flexural and Shear Loads Piero Colajannia, Lidia La Mendolab, Salvatore Priolob and Nino Spinellaa a

Dipartimento di Ingegneria Civile, Università di Messina, C.da di Dio 1 – 98166, Vill. S. Agata, Messina – Italy b Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Palermo, Viale delle Scienze – 90128, Palermo - Italy Abstract. The complete load-vs-displacement curves obtained by four-point-bending tests on Steel Fiber Reinforced Concrete (SFRC) beams are predicted by using a nonlinear finite element code based on the Modified Compression Field Theory (MCFT) and the Disturbed Stress Field Model (DSFM) suitably adapted for SFRC elements. The effect of fibers on the shear-flexure response is taken into account, mainly incorporating tensile stress-strain analytical relationship for SFRC. The numerical results show the effectiveness of the model for prediction of the behavior of the tested specimens reinforced with light amount of stirrups or with fibers only. Keywords: Experimental tests, fiber-reinforced concrete, shear and flexure, FEM analysis.

INTRODUCTION Many reports published during the last few decades have considered the possibility to add fibers in the concrete mixture to help the post-cracking constitutive behavior of the final composite. Fibers influence the mechanical properties of concrete in all failure modes, showing a consistent ductile branch of constitutive curves under uniaxial compression, direct shear and, especially, direct tension. In fiber reinforced concrete structures, fibers furnish a noticeable contribution to transfer stress between different parts of matrix, specially in presence of cracks. Stress is shared by the fiber and matrix in tension until the matrix cracks, and then the total stress is progressively transferred to the fibers [1]. A popular valuable and effective application of fibrous concrete is in shear reinforcement of members, allowing a total or partial substitution of transversal reinforcements. Fibers increase the first cracking load and improve the ability of concrete to sustain higher stress level corresponding to high strain values, especially in tension. First, this paper presents the results of experimental tests carried out on rectangular simply supported beams made of hooked steel reinforced high strength concrete with and without stirrups, subjected to two-point symmetrically placed loads. The tests show that the inclusion of fibers in adequate volume percentage can change the brittle mode of failure, typical of shear collapse, into a ductile flexural mechanism. Secondly, the behavior of the beams is analyzed herein using a nonlinear finite element code based on the modified compression field theory (MCFT) [2] and the

disturbed stress field model (DSFM) [3]. The analytical model is suitable adapted for steel fiber reinforced concrete (SFRC), introducing several modifications to take into account the different constitutive behavior of fibrous concrete and his complex interaction with concrete matrix.

EXPERIMENTAL PROGRAMME Specimen geometry Among the 18 couples of flexure and shear tests carried out at University of Palermo [4], the following discussion will focus on those experiments conducted to investigate the influence of only a limited amount of fibers (volume percentage Vf = 1%) and the interaction mechanism between fibers and stirrups, with spacing s = 200 mm, employed as shear reinforcement.

FIGURE 1. Geometry and reinforcement details: N1=2 Φ20 mm; N2=2 Φ10 mm; N3= Φ6 mm.

Figure 1 shows the details of the beams. All the beams had a rectangular nominally identical cross-section of dimensions b= 150 mm, h= 250 mm, effective depth d= 219 mm and length of the span L = 2300 mm. The flexural reinforcements (two longitudinal deformed bars with diameter 20 mm) were designed to obtain a shear failure for members without transversal reinforcement, and bars were hooked upwards beyond the supports to preclude the possibility of anchorage failure, which can be important in practice. Finally, when a lightly amount of stirrups were used, two longitudinal bars with diameter 10 mm were inserted in the top zone to ensure an adequate operation of stirrups. To evaluate the influence of shear span-effective depth ratio (a/d), beams have divided in two groups: A series with a/d = 2.8 and B series with a/d = 2.0. The former shear span-effective depth ratio was chosen to obtain a shear failure for diagonal tension, where the beam mechanism and the tensile strength of material govern the collapse mode. The latter was chosen to obtain a shear-compression failure, governed by arch mechanism and principally depending by compression strength of concrete.

Six couples of beams with the same setup, three for each series, are herein analyzed. Each beam is marked with the letter that represents the shear span chosen (A or B); the numerical indexes that follow refer to the presence of fibers (0 in absence of fibers and 1 for Vf = 1%) and to the stirrups (0 in absence of stirrups and 1 for s = 200 mm, corresponding to a geometrical transverse reinforcement ratio ρw = A w /(bs) = 0.188%) respectively.

Material properties The concrete used to cast the beams is made by Portland cement type 42.5 (450 kg/m3), sand (850 kg/m3), aggregate with a maximum size of 10 mm (1050 kg/m3) and water (160 kg/m3). The hooked-end steel fibers have the following characteristics: length lf = 30 mm; diameter df = 0.55 mm (aspect ratio lf/df=54.5), and nominal tensile strength 1100 MPa. The yield stress (fy) of longitudinal and transverse reinforcement is 599 MPa and 473 MPa respectively. Vf (%) 0 1

TABLE 1. Properties of concrete mixtures. Ec (MPa) fc’(MPa) ε0 (mm/m) 75.53 2.55 43385 75.41 2.83 37343

fsp (MPa) 4.19 8.34

The measured values of compressive strength fc’, the corresponding strain value ε0 and the initial tangent modulus Ec for concrete with and without fibers are presented in Table 1. In particular they are obtained as the mean value of results of three compressive tests carried out for each type of concrete. As shown in Table 1, the addition of 1% of fibers didn’t change the compressive strength respect the value obtained for plain concrete, but it allows a more gradual micro-cracking process with a consequent increasing of the ε0 value and of the ductility in the post-peak phase. These constitutive characteristics of fibrous concrete play an important role in the global response of structural members under shear loading. In addition some splitting tension-tests were performed to determine increasing in the tensile strength due to the fibers. The mean values of maximum stress (fsp) obtained from the three tests are reported in Table 1 for plain and fibrous concrete showing the considerable increasing induced by fibers in the mixture.

Test results Two equal loads were applied to the specimen using a steel spreader beam and 100 mm-wide loading plates with spherical joints between them. Each test was controlled by gradually increasing the beam deflection. Total load P and the beam deflection at midspan (δ), were recorded continuously until failure. The experimental force-deflection curves are shown in Figure 2 for the six beams with a/d = 2.8 and a/d = 2.0 respectively. It can be observed that in all cases the presence of fibers allows to increase the load capacity and the ultimate deflection with respect to the values recorded for the plain concrete members. In particular the SFRC beams A10 and B10 reach ultimate loads higher than those of the corresponding beams A00 and B00 by 158% and 96% respectively.

However, as shown in Figure 3, the amount of fibers employed for the beams A10 and B10 was not able to change the collapse mechanism and failure was characterized by a diagonal crack extended from the load point to the support. 400

a) a/d = 2.8 (A series)

b) a/d = 2.0 (B series) B11 Vf = 1% ρw = 0.188%

P (kN)

300

200

A11 Vf = 1% ρw = 0.188%

A10 Vf = 1% ρw = 0

100

B10 Vf = 1% ρw = 0

A00 Vf = 0 ρw = 0

B00 Vf = 0 ρw = 0

0 0

10

20

30

δ (mm)

40

0

10

20

30

δ (mm)

40

50

FIGURE 2. Load-deflection curves for beams with a) a/d = 2.8 and b) a/d = 2.0.

a/d=2.8

a/d=2.0

P=87 kN δ=5.53 mm

P=139 kN δ=9.94 mm

P=227 kN δ=14.96 mm

P=284 kN δ=16.76 mm

P=257 kN δ=33.00 mm

P=357 kN δ=32.50 mm

FIGURE 3. Crack patterns at ultimate conditions.

Nevertheless, for beams A00 and A10 the beam effect is predominant in the rupture mechanism and failure was due to the overcoming of the tensile strength of the material, with a more spread cracking in the members with fibers; for the beams B00 and B10 the arc effect governs the failure and slippage along the predominant crack was observed. As shown in Figure 2, when beams are reinforced with both fibers and stirrups (beams A11 and B11), the ultimate deflection increases more than the shear resistance of specimens. For example, the addition of stirrups with geometrical ratio equal to 0.188% increased the load capacity of beam B11 by only 17%, but increased the ultimate deflection by 130%. Further, beams A11 and B11 were able to reach full flexural capacity and crack patterns were characterized by vertical cracks close to the midspan.

NUMERICAL ANALYSES This section is focused on numerical analyses carried out by a finite element model (FEM), namely VecTor, based on the MCFT and DSFM [5]. These represent two well known models for prediction of nonlinear behavior of reinforced plain concrete members, in particular subjected to shear and torsion loads. They are smeared, rotating crack models where the cracked concrete and the steel reinforcements are treated as an unique orthotropic material with stress-strain relationships that are dependent on the amount of reinforcements eventually placed. Several constitutive laws can be implemented in the FEM code, developed on the basis of results obtained by series of experimental tests on reinforced plain concrete panels subjected to different load conditions. To extend the above models at SFRC members is needed to update the constitutive relationships, aiming to better representing the real constitutive behavior of SFRC. 100

a) Vf = 0%

b) Vf = 1%

exp HSC

80

fc (MPa)

NDG99

60 40 20 0 0

4

8

εc (mm/m)

12

0

4

8

εc (mm/m)

12

16

FIGURE 4. Uniaxial compressive behavior for a) plain and b) fibrous high strength concrete.

In Figures 4a) and 4b) the entire curves obtained from the compression tests performed on the concrete employed for the beams described in the previous section are shown for plain and SFR concrete respectively. The fibrous concrete behavior in compression is similar to that of plain concrete until the peak stress value (fc’) is attained, and it can be easily modeled using the same constitutive laws available in literature [3] for plain concrete (Figure 4a). By contrast, the post-peak branch of the stress-strain curve in compression of SFRC (Figure 4b) is more ductile than plain concrete one. This branch of the fc-εc curve is modeled by using the following relationship proposed by Nataraja et al. [6] (NDG99) for fibrous concrete:

β (ε c ε 0 ) fc = ' fc β − 1 + (ε c ε 0 )β

(1)

where the parameter β = 0.5811+1.93RI -0.7406 is evaluated on the basis of the index by weight of hooked steel fibers RI = Wf lf/df, Wf being the weight of fiber for weight unit of the mixture.

Concrete stress-strain curve in direct tension is assumed to be linear up to the tensile strength. Unfortunately direct tension tests couldn’t be performed on the concrete. Therefore, an analytical formulation proposed by Bentz [7] for high strength plain concrete is used to link tensile strength to compressive strength: ft’ = 0.45fc’0.4 (in MPa), while for fibrous concrete the tensile strength is calculated by the simple mixture rule as proposed by Lim et al. [8]. The post-peak behavior is modeled by the Variable Engagement Model (VEM06) suggested by Foster et al. [9]. The constitutive tensile law, expressed in terms of tensile tension and crack opening displacements (w), is the simple summation of stress contributions by matrix and fibers: σcf(w)= σc(w)+σf(w). The VEM06 considers that slippage between the fibers and the concrete matrix occurs before the full bond stress is developed, and the fibers can be broken before being pulled out across a crack. According to VEM06 the fibers are mechanically anchored to the matrix and some slips, between fiber and matrix, must occur before the anchorage is engaged. The crack opening w for which the fiber becomes effectively engaged in the tension carrying mechanism is termed the engagement length we= α tanθ, where α= df/3.5 is a material parameter and θ is the fiber inclination angle, evaluated respect to the crack plane. The bridging tension stress across the crack provided by fibers is:

σ f ( w) = f t ' [ K f ( w) Fτ ]

(2)

where Fτ = βτ Vf (lf /df ) with βτ =τf /f’t, being τf the mean value of the bond fibermatrix interface strength. The function Kf(w) in Eq. (2) is the following global orientation factor which depends by w: tan −1 ( w α ) ⎛ 2 w ⎞ K f ( w) = ⎜⎜ 1 − ⎟ π l f ⎟⎠ ⎝

2

(3)

To predict the value of residual tensile strength of fibrous concrete at shear failure of the beam, the contribute given by the matrix, σc(w), is computed by a simple linear law [3]. Because the FEM used is a smeared cracking model, the stress constitutive law (VEM06) expressed in terms of crack opening w is reduced in terms of tensile strain εt by an appropriate characteristic length [10]: εt = w/Sθ, where Sθ is the average crack spacing that is function of the crack angle value at the generic load step and of the reinforcement pattern. When transverse reinforcement is not present, the average crack spacing becomes Sθ = Sxef/sinθ. Sxef for fibrous concrete is equal to [10]: ⎛ 35 ⎞ ⎛ 50 ⎞ S xef = 0.9d ⎜ ⎜ a + 16 ⎟⎟ ⎜⎜ l d ⎟⎟ f f ⎝ g ⎠ ⎝



(4)

≤1

with ag the maximum dimension of aggregate (that have to be assumed equal to zero for concrete with strength up to 70 MPa).

A two dimensional plane stress model is developed for all specimens (Fig. 5). The numerical analyses are performed with a displacement controlled procedure, by imposing an increasing displacement in the node located at the middle of the load transfer steel plate. Figure 6 shows the comparison between numerical and experimental loaddisplacement curves for all the beams considered. The slope of numerical curves obtained for plain concrete beams (A00 and B00) is lightly greater than the experimental one, probably due to the effect of tension stiffening, which plays an important role at the onset of cracking.

FIGURE 5. FE mesh adopted for all specimens. 300

a)

c)

b)

P (kN)

200

100

A00

A10

A11

Vf = 0 ρw = 0

Vf = 1% ρw = 0

Vf = 1% ρw = 0.188%

0 e)

d)

P (kN)

300

200

f)

B00

B10

Vf = 0 ρw = 0

Vf = 1% ρw = 0

B11 Vf = 1% ρw = 0.188%

100

0 0

2

4

6

δ (mm)

8

10

0

4

8

12

δ (mm)

16

0

10

20

30

δ (mm)

40

50

FIGURE 6. Numerical and experimental load-deflection curves for: a) A00; b) A10; c) A11; d) B00; e) B10; and f) B11 beams.

For fibrous concrete beams (A10 and B10) the DSFM is able to capture the stiffness of the specimens and to estimate load capacity and ultimate deflection. The tension softening law, used with the adequate characteristic length, is appropriate to reproduce the mechanical role played by fibers in the shear capacity of the SFRC beams. The numerical model is very effective in representing the behavior of beams with stirrups, as shown in Figures 6c) and 6f). A11 and B11 beams showed a flexural failure, with a considerable post-peak branch that is captured with great accuracy by the analytical model. In this case the main role is played by the compression constitutive law adopted. During the ductile phase of the beam response, characterized by high level of compressive strains, fibers help the concrete to sustain considerable levels of compressive stresses.

In Figure 7 the numerical crack patterns for fibrous beams are depicted. An appreciable agreement between them and the experimental ones (Fig. 3) is found. A10 and B10 specimens exhibited a shear failure with a predominant crack and some secondary cracks that are well reproduced by the analytical model. Further, the FEM is capable to reproduce the flexural failure mode of fibrous beams with stirrups (A11 and B11), characterized by the vertical cracks at the midspan.

FIGURE 7. Numerical crack pattern for fibrous beams (half length of the beam).

CONCLUSIONS The complete load-vs-displacement curves obtained by four-point-bending tests on Steel Fiber Reinforced Concrete (SFRC) beams has been predicted by using a nonlinear finite element code based on the Modified Compression Field Theory (MCFT) and the Disturbed Stress Field Model (DSFM) suitably adapted for SFRC elements. The adopted constitutive relationships and the modifications introduced in the analytical model allow an accurate prediction of the beam responses in terms of strength, stiffness, crack patterns and failure modes.

REFERENCES 1.

ACI 544, Technical Committee, “Design Consideration for Steel Fiber Reinforced Concrete” (ACI544-88). Technical report, American Concrete Institute - Detroit - Michigan (USA) 1988. 2. F. J. Vecchio and M. P.Collins, “The modified compression field theory for reinforced concrete elements subjected to shear” . ACI Struct. J. 83 (2), 219– 231 (1986). 3. F. J. Vecchio, “Disturbed stress field model for reinforced concrete: Formulation” . ASCE J. of Struct. Eng. 9, 1070– 1077 (2000). 4. S.Priolo, “Influenza delle fibre di rinforzo sul comportamento di travi in c. a. sottoposte a taglio e flessione”(in Italian). Ph. D. Thesis, University of Palermo - Italy (2007). 5. P. S. Wong and F. J. Vecchio, “VecTor2 and Form Works Users Manual” . Technical report. Department of Civil Engineering, University of Toronto – Canada (2002). 6. M. C. Nataraja, N. Dhang and A. P. Gupta, “Stress-strain curve for steel-fiber reinforced concrete under compression” . Cement and Concrete Composites 21, 383-390 (1999). 7. E. C. Bentz, “Sectional Analysis of Reinforced Concrete Membrane” . Ph. D. Thesis, University of Toronto - Canada (2000). 8. T. Y. Lim, P. Paramasivam and S. L. Lee, “Analytical Model for Tensile Behaviour of Steel-FiberConcrete” . ACI Mat. J. 84 (4), 286-298 (1987). 9. S. J. Foster, Y. L. Voo, and K. T. Chong, “FE analysis of steel fiber reinforced concrete beams failing in shear: Variable Engagement Model” , ACI SP-237, 55– 70 (2006). 10. N. Spinella, “Modelli per la risposta a taglio e flessione di travi in calcestruzzo rinforzato con fibre d’acciaio”(in Italian). Ph. D. Thesis, University of Messina - Italy (2008).