nonlinear finite element analysis of steel fiber reinforced

7/24/2019 Nonlinear Finite Element Analysis of Steel Fiber Reinforced

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ISSN : 1819-2076

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REPUBLIC OF IR Q

MINISTRY OF HIGHER EDUC TION

ND SCIENTIFIC RESE RCH

UNIVERSITY OF B BYLON

Issn : 1819-2076

**************************************************************************************

The Iraqi Journal for Mechanical and Materials Engineering

Babylon Univ./ Babylon/ Iraq P.O.Box(4) Tel: ++ 964 30 245387.(1155).

Email: [email protected]


3/17

No.Title

Page

No.

1Effect of Plate Load Test Curve Shape On Modulus Of

Subgrade Reaction Of Compacted Subbase Soil1-12

2Nonlinear Three Dimensional Finite Element Analysis

Of Steel Fiber Reinforced Concrete Deep Beam13-25

3

26-41

4Nonlinear Finite Element Analysis Of Typical

Composite Beams42-51

5Development Of An Application Program For

Lengthwise Engineering Projects52-60

6

61-74

7

Experimental Study Of Punching Shear For Reinforced

Lightweight Concrete Slabs Made With Plastic Waste 75-96

8An Attempt To Relate Consolidation Properties Of

Baghdad Soil To Other Soil Properties97-106

LIST OF CONTENTS


4/17

9

The Effect Of Web Opening On Prestressed Concrete

Double Tee Beams Under Flexure107-123

10

124-133

11Effects Of Using Crumb Rubber In Hma Surface On

Skid Resistance Properties (Dry Method)134-143

12Study The Effect Of Kiln Dust Addition

On Clay Soils Properties144-156

13

157-171

14 A Suggested New Material Used For A-KProsthetic Socket Lamination172-187


5/17

The Iraqi Journal For Mechanical And Material Engineering, Special Issue (E)

13

NONLINEAR THREE DIMENSIONAL FINITE ELEMENT

ANALYSIS OF STEEL FIBER REINFORCED

CONCRETE DEEP BEAM

Prof. S. A. Al-Taan, A. A. Mohammed, M. A. Al-Jurmaa

ABSTRACT

This study reports the details of the finite element analysis of three steel fiber concrete deep

beams and steel fiber reinforced concrete deep beams having steel fibers over full depth. Reinforced

concrete deep beams having a shear span to depth ratio of 2.65 and 1.59 that failed in shear have

been analyzed using the ANSYS program. The ANSYS model accounts for the nonlinearity,

such as, post cracking tensile stiffness of the concrete, stress transfer across the cracked blocks ofthe concrete and load sustenance through the bridging action of steel fibers at crack interface. The

concrete is modeled using SOLID65- eight-node brick element, which is capable of simulating the

cracking and crushing behavior of brittle materials.

The reinforcement bars have been modeled discretely using LINK8 3D spar element.

The steel reinforcement for the finite element models is assumed to be an elastic-perfectly plastic

material and identical in tension and compression. The estimated deflection of beam at ultimate

load was much closed to the experimental data when the accuracy ratios of deflection were (95.7,

100, and 81.5%) for B1, B2, and B3, respectively. So that ANSYS model correctly predicted the

diagonal tension failure and shear compression failure of concrete. The capability of the model to

capture the critical crack regions, loads and deflections for various types of shear failures in

reinforced concrete deep beam has been illustrated.

KEY WORD: Finite element, deep beam, aspect ratio, steel fiber, shear failure, ANSYS.

..

.

-.

.

Ansys

Solid

65

.

Spar

Element link 8

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B3, B2, B1

.

Ansys

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Nonlinear Three Dimensional Finite Element Analysis Of

Steel Fiber Reinforced Concrete Deep Beam

Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

1. INTRODUCTION

A reinforced concrete beam with a span-depth ratio less than approximately 5 may be

classified as a deep beam. Structural deep beams have many useful applications, particularly at the

lower levels in tall buildings as transfer girders, foundation pile caps, and offshore gravity-type

structures [ACI-ASCE Committee 445-1998, Kong 1990]. Because of their proportions, the shear

capacity of deep beams is important in design, and their shear strength is likely to be significantly

greater than that predicted by the usual equations.

A series of studies on deep beams have investigated the influence of effective span-depth

ratio and different web reinforcements on the behavior of high-strength concrete deep beams and

embedment length of main tension steel on the behavior of lightweight concrete deep beams.[ Tan

1995, -Tan 1997] Siao investigated the shear strengths of short reinforced concrete walls, corbel,

and deep beams.[ Siao 1994, Ritter1899] Most of these studies are based on the analysis of

experimental results in light of strut-and-tie models introduced by [Ritter1899], and [Morsch1909]

and developed by [Schlaich and et al. 1987 ], and [Marti 1985]. Arch action is a dominant force

flow for a shear resistance in deep beams loaded in a compression zone. Deep beams transfer

applied top loads to the supports through the compression struts connecting the loads and support

points. The possible failure mode may be web compression or shear tension failure.

In general, it is difficult to prevent concrete from cracking because it is a non ductile and

brittle material. The formation of cracks, even micro cracks, from loading and environmental

effects, has been shown to lead to deterioration and in some cases failure. Micro cracks usually

form at the interface of coarse aggregates due to thermal and moisture activity in the cement paste

even before loading occurs. Upon loading, these micro cracks propagate and group to form cracks.

Short fibers evenly dispersed throughout the concrete increase the durability of concrete by

preventing the micro cracks from widening and spreading into larger cracks.

For more than twenty years now, steel fiber reinforced concrete (SFRC) has been used inshotcrete, precast concrete, slabs, concrete floors, and concrete repairs. It has gained acceptance in

the construction industry by continually exhibiting increased dynamic force resistance and effective

crack reduction, [ASTM 1996, Beaudoin 1990, Breen 1994].

The presence of fiber has a direct effect on the mechanical properties of concrete including

compression, direct tension, shear, and flexural strength. The fiber shares induced stress with the

concrete until the concrete cracks. Then, eventually the fiber carries all of the stress. There are

many advantages that suggest the reduction or replacement of conventional reinforcing steel with

steel fibers, such as the following:

Enhanced flexural strength, shear strength, ductility and toughness.

Impact and fracture resistance. Internal stresses are more evenly distributed throughout the structure because multi-

directional reinforcement is provided.

Crack widths are minimal, if cracks are found at all, because fibers bridge the cracks.

Decreased chance of corrosion due to crack control and the fact that fibers do not

provide a continuous path for corrosive currents to flow through.

Savings in labor and time costs of a project because FRC placement is less demanding

than conventional rebar placement.

Hemmaty1998 used the ANSYS finite element program to study the modeling of the shear

force transferred between cracks in reinforced and fiber-reinforced concrete structures. [ Huyse et

al.1994], used the ANSYS program to study the finite element modeling of fiber-reinforcedconcrete beams. [Wolanski 2004] studied flexural failure of reinforced concrete and prestressed

concrete beams by using ANSYS. The objective of this paper is 3D finite element analysis on the


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Prof. S. A. Al-Taan et., al.,

SFRC (steel fibers reinforced concrete) deep beams ultimate behavior. For this purpose, SFRC

Deep beams without reinforced, and with reinforcement were analysis in finite element solutions

were obtained by using ANSYS. The experimental and finite element modeling results are

compared.

2. SPECIMENS DETAILS

Three Experimental steel fiber deep beams were analyzed in this study. The first beam was

containing steel fiber only, and the two beams letter were contain steel fiber with steel

reinforcement, as illustrated below:

2.1 Details of Steel Fiber Deep Beam (B1)

The first test deep beam had constant span and width of 600 mm and 75 mm, respectively.

The overall depth was 150 mm, such that, span to depth ratio of these beams was 4.0. The fiber

reinforced concrete with 1.0% steel fiber by volume, aspect ratio 100 were without tension and web

reinforcement. The beam notation (FC4) denotes the beams having span to depth ratio of 4.0 (i.e.

depth 150mm), [Shah 2004].

2.2. Details of Steel Fiber Reinforced Concrete Deep Beam (B2)

The second test deep beam had constant span and width of 600 mm and 75 mm,

respectively. The overall depth was 150 mm, such that, span to depth ratio of these beams was 4.0.

As shown in Fig.(2). The fiber reinforced concrete with 1.0% steel fiber by volume, aspect ratio

100.the beam had a single 16 mm diameter mild steel bar as the main longitudinal reinforcement

and 6 mm diameter mild steel bars as horizontal web reinforcement, placed at 100 mm c/c. The

beam notation (FS4) denotes the steel reinforced beam having span to depth ratio of 4.0 (i.e. depth

150mm) , [Shah 2004].

Fig. (1) Dimensions of the SFC deep beam (B1)

150mm

600

Fig. (2) Reinforcement details of the SFRC deep beam (B2)

span to depth ratio=4

150m

600m

6mm @100c/c

Web16mm (longitudinal Reinforcement)


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Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

2.3. Details of Steel Fiber Reinforced Concrete Deep Beam (B3)

Fig.(3) shown the geometry, loading, and reinforcement for the beam was selected to

analyzed in the present study with steel fiber content equal (1.0%) and span to depth ratio equal to

(2.6). the beam were provided with 16mm diameter deformed bar (fy=440MPa) to serve as principal

tensile reinforcement. Web reinforcement comprised 5 mm diameter bars having average yield

strength of (375MPa). Steel fibers used were 30mm long and 0.5mm2in cross section area, [Mansur

1991].

3. FINITE ELEMENT ANALYSIS

Finite element failure analysis was performed by using the ANSYS program. ANSYS is

capable of handling dedicated numerical models for the nonlinear response of concrete under static

and dynamic loading. ANSYS was chosen because it provides a wide range of elements and

constitutive models for different materials including concrete.

3.1 Element Types

Concrete: Eight-node solid brick elements (Solid65) were used to model the concrete. Theseelements include a smeared crack analogy for cracking in tension zones and a plasticity algorithm to

account for the possibility of concrete crushing in compression regions. The solid element has eight

nodes with three degrees of freedom at each node: translations in the nodal x, y, and z directions.

Steel plate and steel support: An eight-node solid element, Solid45, was used for the steel plates at

the supports in the beam models. The element is defined with eight nodes having three degrees of

freedom at each node translations in the nodal x, y, and z directions. The element has plasticity,

creep, swelling, stress stiffening, large deflection, and large strain capabilities. A reduced

integration option with hourglass control is available.

Steel reinforcement: A 3D spar element (Link 8) was used to model the internal reinforcement this

element allows the elasticplastic response of the reinforcing bars. Two nodes are required for this

element. Each node has three degrees of freedom at each node: translations in the nodal x, y, and z

directions.

3.2. Material Properties

There are three material models in this study as motion below:

Concrete:Material Model Number 1 refers to the Solid65 element. The Solid65 element requireslinear isotropic and multilinear isotropic material properties to properly model concrete. Themultilinear isotropic material uses the von Mises failure criterion along with the Willam and

Warnke [23] model to define the failure of the concrete. EX is the modulus of elasticity of theconcrete (Ec), andPRXYis the Poissons ratio (). The modulus of elasticity was based on eq. (1)[ACI-ASCE Committee 445-1998].

500

1300

5mm @100c/c

Web Reinforcement

4#16mm (Longitudinal Reinforcement)

Fig. (3) Reinforcement details of the SFRC deep beam

(B3) span to depth ratio =2.6


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A nonlinear elasticity model was adopted for concrete. This nonlinear elasticity model is

based on the concept of variable module and matches well with several available test data. For our

concrete, the stressstrain relation was used for the material model in the finite element modeling.

The elastic modulus of concrete was calculated asEc= 26615MPa by using the slope of the tangent

to the stressstrain curve through the zero stress and strain point. The Poisson ratio is taken as 0.2.The ultimate uni-axial compressive strength of concrete was taken from the mean value of cylinder

test results as

fc= 34.4 MPa. The tensile strength of concrete was assumed to be equal to the value given below

[ACI-ASCE Committee 445-1998].

The multilinear isotropic stressstrain implemented requires the first point of the curve to be

defined by the user. It must satisfy Hookes Law.

The compressive uni-axial stressstrain relationship for the concrete model was obtained

using the following equations to compute the multilinear isotropic stressstrain curve for the

concrete. MacGregor, (1992),

where is the stress at any strain , MPA, is the strain at stress , and 0is the strain at the

ultimate compressive strengthfc.

The shear transfer coefficient for open cracks, t, represents the conditions at the crack face.

The value of tranges from 0.0 to 1.0, with 0.0 representing a smooth crack (complete loss of shear

transfer) and 1.0 representing a rough crack (no loss of shear transfer). Shear transfer coefficient of

0.3 was used to derive the theoretical loaddisplacement relationship for comparison with

experimental results. In fiber reinforced concrete, the shear transfer at the cracks depends on the

matrix strength fiber interaction in the fiber pullout mechanism [Job 2006, Shah 1994, Burdet

1990].

Willam and Warnke developed a widely used model for the triaxial failure surface of

unconfined plain concrete. a constitutive model for the concrete suitable for FEA implementation

was formulated. This constitutive model for concrete based upon the Willam and Warnke model

assumes an appropriate description of the material failure. The yield condition can be approximated

by three or five parameter models distinguishing linear from nonlinear and elastic from inelastic

deformations using the failure envelope defined by a scalar function of stress f()= 0 through a

flow rule, while using incremental stressstrain relations.

During transition from elastic to plastic or elastic to brittle behavior, two numerical

strategies were recommended: proportional penetration, which subdivides proportional loading intoan elastic and inelastic portion which governs the failure surface using integration, and normal

penetration, which allows the elastic path to reach the yield surface at the intersection with the

cfEc = 4730(1)

(3)

=E

ct ff = 62.0(2)

(4)

2

0

0

)(1

2

+

=

=

c

c

c

E

E

f


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Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

normal therefore solving a linear system of equations. Both these methods are feasible and give

stress values that satisfy the constitutive constraint condition. From the standpoint of computer

application the normal penetration approach is more efficient than the proportional penetration

method, since integration is avoided.

Steel plate and support:For the finite element models each load is distributed over a small area as

for the experimental beams. A 50mm thick steel plate modeled using SOLID45 elements, is addedat the support location, and load applied position in order to avoid stress concentration problems.

This provides a more even stress distribution over the support area and position of load. An elastic

modulus equal to 200GPa and Poissons ratio equal to 0.3 are used to plate.

Steel reinforcement: Steel reinforcement in the experimental beam was constructed with typical

steel reinforcing bars (fy= 440 MPa). Elastic modulus and yield stress for the steel reinforcement

used in tests were considered in the finite element modeling of reinforcement. The steel for the

finite element models is assumed to be an Elasticperfectly plastic material and identical in tension

and compression. Poissons ratio of 0.3 is used for the steel reinforcement. Material properties for

the concrete and steel reinforcement are summarized in Table 1.

Table (1) Material properties of beam tested [21, 22]

Beam No. Ec

MPa

Vf

%

fc

MPa

ft

MPa

fy

MPa

Es

MPa

B1 23051 1 23.75 2.8 440 200,000

B2 23249 1 24.16 3.0 440 200,000

B3 26615 1 34.4 3.28 440 200,000

3.3. Geometry and Meshing

The dimension of the full-size SFRC deep beam (B3) is 90*500*1300 mm. The spanbetween the two supports was 1050 mm. As shown in Fig. (3), by taking the advantage of the

symmetry of the beam, a quarter of the full beam was used for finite element modeling. This

approach reduced computational time and computer disk space requirements significantly. The

quarter of the entire model is shown in Fig. 6. To obtain satisfactory results from the Solid65

element, a rectangular mesh is recommended. Therefore, the mesh was setup such that square or

rectangular elements were created as shown in Fig. 5. The necessary element divisions are noted.

The meshing of the reinforcement is a special case compared to the volumes to satisfactory the full

bond between concrete and reinforcement. Each concrete mesh element is a prism with 25 * 25 * 25

mm.

Fig.(5) Finite element mesh of the

quarter SFRC deep beam

45mm

655mm

Fig. (4) The quarter of beam

model


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3.4. Nonlinear Solution

In nonlinear analysis, the total load applied to a finite element model is divided into a series

of load increments called load steps. At the completion of each incremental solution, the stiffness

matrix of the model is adjusted to reflect nonlinear changes in structural stiffness before proceeding

to the next load increment. The NewtonRaphson equilibrium iterations for updating the model

stiffness were used in the nonlinear solutions. Prior to each solution, the NewtonRaphsonapproach assesses the out-of-balance load vector, which is the difference between there storing

forces (the loads corresponding to the element stresses) and the applied loads. Subsequently, the

program carries out a linear solution using the out-of-balance loads and checks for convergence. If

convergence criteria are not satisfied, the out-of-balance load vector is re-evaluated, the stiffness

matrix is updated, and a new solution is carried out. This iterative procedure continues until the

results converge.

In this study, convergence criteria for the reinforced concrete solid elements were based on

force and displacement, and the convergence tolerance limits were initially selected by analysis

program. It was found that the convergence of solutions for the models was difficult to achieve due

to the nonlinear behavior of reinforced concrete. Therefore, the convergence tolerance limits wereincreased to a maximum of five times the default tolerance limits (0.5% for force checking and 5%

for displacement checking) in order to obtain the convergence of the solutions.

4. COMPARISON OF EXPERIMENTAL AND FINITE ELEMENT RESULTS

The loaddeflection responses for the beam from the test are plotted with the finite element

results in Fig. 6. The ultimate loads from the finite element and experimental models are calculated

as 465 kN and 546 kN, respectively. as illustrated in Table (2). The midspan deflection at the

ultimate load of the SFRC beam recorded in the tests, and finite element solutions are close to each

other as shown in Fig. 6. In general, the loaddeflection plots for the beam from the finite element

analyses agree quite well with the experimental data. The finite element loaddeflection curve is

slightly different from the experimental curve. There are several effects that may cause this

situation. First of all, microcracks are present in the concrete for the tested beam and could be

produced by drying shrinkage in the concrete and/or handling of the beam. On the other hand, the

finite element models do not include the microcracks.

B1 B2

Fig. (6) Experimental and FEM load-deflection responses


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Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

Table (2) Comparison of test results

Beam Notation Experimental

Load (kN)

Theoretical

Load (kN)

Experimental

Ultimate

Deflection

(mm)

Theoretical

Ultimate

Deflection

(mm)B1 65 65 1.4 1.34

B2 80 80 1.3 1.3

B3 570 465 4 3.25

The other is that perfect bond between the concrete and steel reinforcing is assumed in the

finite element analysis, but the assumption would not be true for the tested beam. In ANSYS,

stresses and strains are calculated at the integration points of the concrete solid elements.

Crack patterns obtained from the finite element analysis at the last converged load steps as

shown in Figs. (7a-d), which shows that numerous cracks occur at midspan of the finite element

model of four load levels, the cracks begin at the region of maximum bending moment at load 84kN, then the cracks have spreader toward the support and upward and the remained crack zone

looks likes an arch. This is in agreement with the simulation of deep beam with a strut (concrete)

and tie (the tension steel with almost constant stress). Fig. 8 shows cracking signs in the finite

element model. A side face of the quarter beam model is used to demonstrate cracking sign. As

shown in Fig. 10a, at the bottom of the beam at midspan, principal tensile stresses occur mostly in

the x direction (longitudinally). When the principal stresses exceed the ultimate tensile strength of

the concrete, circles as cracking signs appear perpendicular to the principal stresses in the x

direction. Therefore, the cracking signs shown in Fig. 8a appear as vertical straight lines occurring

at the integration points of the concrete solid elements. Hereafter, these are referred as flexural

cracks. For a concrete structure subjected to uni-axial compression, cracks propagate primarily

parallel to the direction of the applied compressive load since the cracks result from the tensile

strains developed due to Poissons effect [23, 24]. Similar behavior is seen Fig. 8b in the finite

element analysis. Loads in the z direction result in tensile strains in the y direction by Poissons

effect. Thus, circles appear perpendicular to the principal tensile strains in the y direction at the

integration points in the concrete elements near the loading location. These are referred as

compressive cracks.

Fig. 8c shows cracking signs where both normal and shear stresses act on concrete elements.

At the location shown in Fig. 10c, normal tensile stresses generally develop in the x direction and

shear stresses occur in the xz plane. Consequently, the direction of tensile principal stresses

becomes inclined from the horizontal. Once the principal tensile stresses exceed the ultimate tensilestrength of the concrete, inclined circles appearing as straight lines perpendicular to the directions

of the principal stresses appear at integration points of the concrete elements. Hereafter, these are

referred as diagonal tensile cracks.

In our SFRC deep beam at a sufficiently high load, the concrete fails to resist tensile stresses

only where the cracks are located. Between the cracks, the concrete resists moderate amounts of

tension introduced by bond stresses acting along the interface in the direction. This reduces the

tensile force in the steel. There was no evidence that the reinforcing steel failed before overall

failure of the beam tests. This is confirmed by the finite element stress analyses. Maximum stresses

for the last converged load step are shown for the beam. Figs. 9 and 10 show the maximum stress

locations in the SFRC beam by element solution and by nodal solution, respectively.


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Fig. (7) FEM cracks at different loads values. [B3]

Fig. (8) Cracking signs in FEM: (a) flexural cracks; (b) compressive cracks;

and (c) diagonal tensile cracks.


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Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

B1B2

B3

Fig. (9) Maximum compressive and tensile stress (MPa)

for nodal solution

Fig. (10) Maximum compressive and tensile stresses (MPa)

for element solution

B1B2

B3


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5. CONCLUSION

Based on the comparison of the SF and SFRC deep beams with the corresponding

experimental data, Finite element failure analysis was performed by using the ANSYS program.

Eight-node solid brick elements (Solid65) were used to model the concrete. Internal reinforcement

was modeled by using 3D spar elements (Link 8). Following conclusions were drawn.

The predicted load in deep beams at various stages was found to be in good agreement with the

test data. Where the estimated deflection of beam at ultimate load was much closed to the

experimental data when the accuracy ratios of deflection were (95.7, 100, and 81.5%) for B1, B2,

and B3, respectively.

The failure mechanism of a SF and SFRC deep beam is modeled quite well using FEA, and the

failure load predicted is very close to the failure load measured during experimental testing.

Deflections and stresses at the centerline along with initial and progressive cracking of the finite

element model compare well to experimental data obtained from a reinforced concrete beam.

The effective coefficient on behavior of deep beam is the ratio of length span to beam depth ( l/d)

where increase of (l/d) decreased the ultimate load failure, and the shape of failure closed to flexural

failure. The beams failure began on all deep beams as flexural failure and transformed gradually to shear

failure when the load further increased.

REFERENCES

ACI-ASCE Committee 445, (1998), Recent Approaches to Shear Design of Structural Concrete, Journal

of Structural Engineering, ASCE, V. 124, No. 12, Dec. 1998, pp. 1375-1417.

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Prof. S. A. Al-Taan

A. A. Mohammed

M. A. Al-Jurmaa

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analysis. Master thesis, Marquette University, Milwaukee, Wisconsin, 2004.

nonlinear finite element analysis of steel fiber reinforced

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