fiber reinforced concrete design - sharjah.ac.ae · • in design, the type, size, geometry, and...

Workshop on

FIBER REINFORCED CONCRETE (FRC): MATERIALS, APPLICATIONS AND DESIGN ASPECTS

UNIVERSITY OF SHARJAH, UNITED ARAB EMIRATES

22-23 APRIL 2018

ORGANIZED BY

Sustainable Construction Materials and Structural Systems Research Group,

Department of Civil & Environmental Engineering, University of Sharjah

JOINTLY WITH

Structural Design Research Group, University of Brescia (Italy)

SPONSORED BY

University of Brescia, Italy Sharjah Research Academy, UAE

KEY SPEAKERS

Prof. Giovanni Plizzari, University of Brescia, Italy

Prof. Salah Altoubat, University of Sharjah, UAE

Prof. Mohamed Maalej, University of Sharjah, UAE

Dr. Moussa Leblouba, University of Sharjah, UAE

Fiber Reinforced ConcreteDesign concepts

Prof. Salah Altoubat

Department of Civil & Environmental Engineering

SCMASS Research Group

College of Engineering

University of Sharjah

Workshop on

FIBER REINFORCED CONCRETE (FRC): MATERIALS, APPLICATIONS AND DESIGN ASPECTS

UNIVERSITY OF SHARJAH, UNITED ARAB EMIRATES

22-23 APRIL 2018

Outline

1. Introduction

2. Design concepts

3. Design for flexure

4. Design for flexure – hybrid reinforcement

5. Design Examples

6. Slab on Ground Design

7. Design Example

8. Design for shear

1. Introduction

• Fibers influence the mechanical properties of concrete in all failure modes (compression, tension,

shear,…);

• The most important variables governing the properties of FRC include: fiber bond efficiency (controlled

by pullout test) and dosage rate;

• When a concrete matrix is subjected to tension, stresses are transferred by interfacial shear. When the

matrix cracks, the stress gets transferred to the fibers, progressively;

• This process results in: increase in the load carrying capacity, the energy dissipation, and the ductility at

serviceability and at ultimate limit design states for FRC.

also affect the post-crack properties of FRC. High performance fiber-reinforced concrete 1

(HPFRC) incorporates higher dosage rates of fibers with a high performance / high strength 2

concrete mixture resulting in improved mechanical and durability related properties (Naaman 3

and Reinhardt 1996). 4

The stages involved in FRC failure is schematically shown in Figure 1 and are summarized here 5

as: 1) cracks form in cement matrix, 2) debonding and sliding between fiber and matrix, 3) 6

bonded fiber bridging the cracks, 4) frictional sliding, deformation of anchorage, and eventual 7

fiber pullout, and 5) potential fiber failure under tension. For specific types or geometries of 8

fibers, not all, or only some of the described stages may occur. The load level (or stress level) 9

carried by fibers in a cracked concrete section is referred to as residual load (or residual or post-10

cracking stress). The area under the load-deflection curves is the energy absorbed by the FRC 11

system and is referred to as toughness and which is used for design purposes. Figure 2 shows 12

different stages of crack control for an FRC beam under a flexural load test. There are, however, 13

certain types of fibers that do not pull out of the matrix, but elongate and provide the toughness. 14

15

Figure 1: Schematics of the mechanism in which fiber reinforcement works 16

22

What do structural fibers add to concrete

Toughness and ductility are key properties thatFibers impart to concrete structure

Material level

1) Toughness

2) Ductility

3) Residual strength

Structural level

1) Yield capacity, post-cracking capacity

2) Rotational capacity

3) Yield strength

• FRC: Substantially enhance the post-cracking response of the composite (toughness).

• Post-cracking response: is evaluated through toughness testing

• Toughness: area under the load deformation curve

Where does FRC as structural material stand ?

Material characterization Structural Performance

1) Test Standards

2) Specification

1) Demonstrated by experiment

2) Structural tests and models

ASTM C 1609JCI-SF 4ASTM 1399ASTM 1550EN 14651

Structural design

Well establishedRecognized at research level

Progressing

Progressing in North America

Recognizedin Europe

• When fibers are intended to contribute to the structural performance of an element or structure, the FRC needs to be designed accordingly and the fibers contribution to the load-bearing capacity needs to be properly assessed and justified.

Requirements

Fibers intersect cracks when

they initiate. This allows for a

uniform distribution of the

stresses that develop and slow

down crack propagation

ACI 544: Fiber Reinforced Concrete

ACI544-9R, and ACI 544.2R-17: Report on the Measurement of Fresh State Properties, Mechanical Properties, and Fiber Dispersion of Fiber-Reinforced Concrete

ACI 544.8R-16 Report on Indirect Method to Obtain Stress-Strain Response of Fiber-Reinforced Concrete

ACI544-4R: Design Guide for Fiber Reinforced Concrete

544.6R-15 Report on Design and Construction of Steel Fiber-Reinforced Concrete Elevated Slabs

544.7R-16 Report on Design and Construction of Fiber-Reinforced Precast Concrete Tunnel Segments

ACI 544.5R-10 and New Document on Testing, Creep, Shrinkage, Service life, Crack Width Prediction

1. Introduction

• Since the fibers are randomly distributed with small spacing (compared to typical steel bars), the tensile

stresses in FRC are borne by the fibers are early stages;

• In design, the type, size, geometry, and dosage rates for fibers is dependent on the application, loading

level, and exposure conditions;

• Fibers change the post-crack response of concrete from brittle to ductile under all types of loads.

The Concrete Conventionand Exposition

Strain softening and strain hardening

Fiber contribution to tensile/flexural performance, obtained from flexural test, showing softening and hardening behaviors.

2. Design concepts

• The material properties (such as the residual strength

determined by standard tests–ASTM C1609) are inserted

into equations to determine the performance of an FRC

element and its load-carrying capacity.

• Tensile strength of plain concrete is insignificant, hence,

not taken into account in the design of conventional RC

sections.

• Effective tensile strength of FRC sections is used in

the design process.

• Direct tensile test on FRC is difficult, instead, the

residual tensile strength is derived from the measured

flexural strength by means of conversion factors.

1

Figure 9: Schematics of a typical stress-strain diagram for FRC in uniaxial tension and 2

compression, according to RILEM TC 162-TDF [Vandewalle etl al. 2003]. 3

4

Correlation of Tensile and Flexural Response for FRC 5

Experimental studies have been performed on FRC specimens using both direct tension and 6

bending tests, showing the correlation between the tensile and flexural response in the post-crack 7

region of material behavior (Vandewalle et al. 2003). Analytical studies using various stress-8

block models have shown that in the post-crack state, the residual flexural strength of FRC is 9

typically between 2.5 and 3 times its residual tensile strength (Naaman 2007). This means that 10

the tensile resistance can be back-calculated from the flexural resistance using a factor between 11

0.4 and 0.33. The comparison of numerical studies with experiments confirms such results 12

(Mobasher et al. 2014). For design purposes, the tensile residual strength of FRC may be taken 13

as 0.37 times the flexural residual strength obtained from a standard beam test (Vandewalle et al. 14

2003 - RILEM TC 162-TDF). 15

Typically two levels of design can be considered: 1) design for serviceability limit state (SLS) at 16

small deflections, corresponding to smaller crack widths in the range of 0.4-1.0 mm and 2) 17

design for ultimate limit state (ULS) with larger deflections, related to larger crack widths in the 18

compression

tension

34

Typical stress-strain diagram of FRC

Stre

ssStrain

5.1,,37.0 eqctF

axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

3,,eqctF Equivalent strength at deflection of 3 mm (L/150)

Plain ConcreteFiber Reinforced Concrete

5.1,,eqctF Equivalent strength at deflection of 1.5mm (L/300)

Stre

ss

StrainaxctF ,

-2.5 -3.0

cF

KEY PROPERTY : Stress-strain

diagram

RILEM TC162

Post-cracking behavior• The cracked section of fiber-reinforced concrete (FRC) does carry

tensile load while plain concrete becomes ineffective after cracking as indicated in the stress-strain diagram

Z Z

Conventional RC FRC

Stre

ss

Strain5.1,,37.0 eqctF

axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctFNeed to be characterized

2. Design concepts

• In the post-crack state, the residual flexural strength of FRC is typically between 2.5 and 3 times its

residual tensile strength, hence, the tensile resistance is calculated from the flexural resistance

using a factor between 0.4 and 0.33.

• For design purposes, the tensile residual strength of FRC may be taken as 0.37 times the flexural

strength obtained from a standard beam test.

• Two levels of design can be considered: design for serviceability limit state (SLS) at small

deflections (cracks in the range of 0.4-1.0 mm and design for ultimate limit state (ULS) with larger

deflections (larger crack widths: 2.0-3.0 mm).

2. Design concepts

When ASTM C1609/1609M-12 is used to characterize FRC, parameters such as 𝑓600𝐷 , 𝑓150

𝐷 , 𝑅𝐷,150𝑇 (or

𝑓𝑒,3) may be used for design.


Standard test methods for FRC

Schematics of a typical ASTM C1609/C1609M-12 test result (strain-softening FRC) and FRC beam under four-point flexural test.

150

,150 2

150 D

D

T

P

TR

f b h


Standard test methods for FRC

Schematics of a typical ASTM C1609/C1609M-12 test result (strain-softening FRC) and FRC beam under four-point flexural test.

150

,150 2

150 D

D

T

P

TR

f b h𝑓600𝐷

: Residual strength at a deflection of L/600 (psi or MPa)

𝑓150𝐷

: Residual strength at a deflection of L/150 (psi or MPa)

𝑇150𝐷

: Toughness or area under the curve up to a deflection of L/150

𝑅𝐷,150𝑇

: Equivalent flexural strength ratio at a deflection of L/150 (%)

𝑓𝑒,3 : Equivalent flexural strength at a deflection of L/150 (psi or MPa)

𝑓𝑒,3 = 𝑓𝑝 × 𝑅𝐷,150𝑇

𝑓𝑝 : Peak strength (psi or MPa)

ASTM C-1609

Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete

To determine the first-peak, peak and residual strengths the respective load value is substituted in the modulus of rupture formula:

𝑓 =𝑃𝐿

𝑏𝑑2

Where:f = the strength, MPa (psi),P = the load, N (lbf), L = the span length, mm (in.), b = the average width of the specimen, mm (in.), at the fracture, and d = the average depth of the specimen mm (in.), at the fracture.

This test method provides for the determination of first-peak and peak loads and the corresponding stresses calculated by inserting them in the formula for modulus of rupture. It also requires determination of residual loads at specified deflections, and the corresponding residual strengths calculated by inserting them in the formula for modulus of rupture. At the option of the specifier of tests, it provides for determination of specimen toughness based on the area under the load-deflection curve up to a prescribed deflection

Values of loads at specified deflection points are used for measuring residual strength of FRC

17

Equivalent Flexural Strength: Have the same

toughness, T150,3.0, obtained from experiment to a deflection of L/150 (same area under load-deflection curve)

ASTM C1609-06

JSCE, JCI-SF4

NBN B15-238

,3ef

Fle

xu

ral

Str

ess

Deflection (mm) 3, (L/150)

pf

Equivalent flexural strength, fe,3

For Span, L= 450 mm

2

150,3.0

2

150,3.0

e,3DW

T150

DW3

T450 = f

2

150,3.0

e,3

D(mm)W(mm)150

)(L

)(T)(L =(MPa) f

mm

Nmmmm

100f

f =(%) R

p

e,3

e,3

3. Design for flexure (Fiber Reinforced Section)

The same stress block concept can be applied to a fiber-reinforced concrete section. ASTM 1

C1609/1609M-12 is performed to obtain the required design parameters. The nominal bending 2

moment for a fiber-reinforced concrete (FRC) section, Mn-FRC is calculated according to the 3

following equations from the force equilibrium in the cross section as shown in Figure 11. Here, 4

the compressive stresses are carried by concrete while the tensile stresses are carried by fiber-5

reinforced concrete. The tensile strength of fiber-reinforced concrete, ft-FRC, can be much higher 6

than that of plain concrete and is in fact taken into account in these calculations. For ULS design 7

the tensile strength of fiber-reinforced concrete, ft-FRC, is equal to 0.37 times the flexural residual 8

strength of fiber-reinforced concrete, fe3, measured from ASTM C1609/1609M-12 test. Eq. 5 9

shows the calculations for the moment capacity of a cracked FRC section, developed in 10

conjunction with the similar method of RILEM TC 162-TDF (Vanverwalle et al, 2003). 11

12

Figure 11: Schematics of stress block for FRC in a flexural member (ASTM C1609 parameters) 13

6

.)(

..166.0

).5.0).(9.0).(37.0(

).5.0).(9.0).((

2

3

2

3

3

hbfM

hbf

bhhf

bhhfM

eFRCn

e

e

tFRCn

≈≈

≈

≈

(Eq. 5) 14

≈

D

TPe

eFRCt

Rff

ffNote

150,3,

337.0: 15

37

FRC section

Schematics of stress block for a cracked RC and FRC flexural member

𝑀𝑛−𝐹𝑅𝐶 = 𝑓150𝐷 𝑏ℎ2

6

Stre

ss


axctF ,

1 %10 % -2.5 -3.5

cF

3,37.0 eF

3,37.0 eF

3. Design for flexure

range of 2.0-3.0 mm. Higher values of residual strength become necessary for SLS as the crack 1

widths must be maintained smaller. Hence, the specified residual strength for FRC is determined 2

based on the desired limit state. When ASTM C1609/1609M-12 is used to characterize FRC, 3

parameters such as Df600 , Df150

T

DR 150, (or 3,ef ) may be used for design and specification and in the 4

case of EN 14651, the design parameters are 1,Rf , 1,Rf , 1,Rf , and 1,Rf . The implementation of 5

these parameters in the design process is explained in the following sections. 6

7

Design of RC for Flexure (Stress Block) 8

The nominal bending moment for a conventional reinforced concrete (RC) section, Mn-RC is 9

calculated according to the following equations from the force equilibrium in the cross section as 10

shown in Figure 10. The compressive stresses are carried by concrete and the tensile stresses are 11

carried by steel only. The tensile capacity of plain concrete is negligible and is not taken into 12

account in these calculations. Eq. 4 shows the classical equation for the moment capacity of a 13

cracked RC section. 14

15

Figure 10: Schematics of stress block for RC in a flexural member 16

17

35












12


6

.)(

..166.0

).5.0).(9.0).(37.0(

).5.0).(9.0).((

2

3

2

3

3

hbfM

hbf

bhhf

bhhfM

eFRCn

e

e

tFRCn

≈≈

≈

≈

(Eq. 5) 14

≈

D

TPe

eFRCt

Rff

ffNote

150,3,

337.0: 15

37

RC section

FRC section

Schematics of stress block for a cracked RC and FRC flexural member

𝑀𝑛−𝑅𝐶 = 𝐴𝑠 𝑓𝑦 𝑑 −𝑎

2

𝑀𝑛−𝐹𝑅𝐶 = 𝑓150𝐷 𝑏ℎ2

6

4. Design for flexure – hybrid reinforcement

FRC section

with hybrid

reinforcement

Schematics of stress block for a cracked FRC (with and without hybrid reinforcement

𝑀𝑛−𝐹𝑅𝐶∗ = 𝑓𝑒,3𝑏ℎ2

6+ 𝐴𝑠 𝑓𝑦 (𝑑 − 0.03ℎ)












12


6

.)(

..166.0

).5.0).(9.0).(37.0(

).5.0).(9.0).((

2

3

2

3

3

hbfM

hbf

bhhf

bhhfM

eFRCn

e

e

tFRCn

≈≈

≈

≈

(Eq. 5) 14

≈

D

TPe

eFRCt

Rff

ffNote

150,3,

337.0: 15

37

FRC section

𝑀𝑛−𝐹𝑅𝐶 = 𝑓𝑒,3𝑏ℎ2

6

3: 3R

FRCtu

ffNote ≈ 1

≈ Ftu-FRC: FRC ultimate tensile strength (the same as ft-FRC) 2

≈ fR,3 : FRC flexural residual strength (similar to f3) 3

4

Design of FRC for Flexure - Hybrid Reinforcement 5

Hybrid reinforcement could be a viable option where either the fiber dosage rate or the 6

reinforcement ratio is too high and impractical. The nominal bending moment for a hybrid fiber-7

reinforced concrete (FRC*) section, Mn-FRC* is calculated according to the following equations 8

from the force equilibrium in the cross section shown in Figure 13. The calculation for the 9

moment capacity of a cracked FRC section is shown in Eq. 7 .The design of flexural members 10

with hybrid reinforcement is further discussed by Mobasher et al. (2015). 11

12

Figure 13: Schematics of stress block in a concrete beam with hybrid reinforcement 13

)03.0.(.6

.)(

2

3*hdfA

hbfM yseFRCn ≈+

≈ (Eq. 7) 14

15

16

b

h d

0.1h

0.9h

ft

f’c f’c

ft

T=As.fy T=As.fy

Normal Stresses/Forces(Actual)

Normal Stresses/Forces(Simplified)

39

Ultimate resistance

• Assumptions

• Plane section remains plane

• Stress in tension and compression are derived from stress-strain diagram

• For FRC with additional rebars, the strain in tension is limited to 10% at the level of rebars

• The maximum crack width is limited to 1.5 mm (RILEM TC162)

Post-cracking behavior

• The cracked section of fiber-reinforced concrete (FRC) does carry tensile load while plain concrete becomes ineffective after cracking as indicated in the stress-strain diagram

Z Z

Conventional RC FRC

Fiber Reinforced Concrete

Fiber Reinforced Concrete + bar reinforcement

-3.5-2.0010

(%)

Stresses in fiber reinforced concrete

at ultimate loading

RILEM TC162

8. Example

Assume an 8” (200 mm) precast panel reinforced with #4@16” placed in mid-section to provide post-

crack moment capacity. Find the value of 𝑓150𝐷 for FRC to provide the same level of post-crack flexural

strength as rebar. Assume 5,000 psi concrete and grade 60 steel and a moment capacity factor of 0.9 for

steel.


Solved Examples

Example: Assume an 8” (200 mm) precast panel reinforced with #4@16” placed in mid-section to provide post-crack moment capacity. Find the value of 𝑓150

𝐷 for FRC to provide the same level of post-crack flexural strength as rebar. Assume 5,000 psi concrete and grade 60 steel and a moment capacity factor of 0.9 for steel.

inlba

dFAM ysRCn 120,312

17.0

2

8000,60147.09.0)

2.(...

inbf

FAa

c

ys17.0

12000,585.0

000,60147.0

.'85.0

.

6

..120,31..

2

150

hbfinlbMM D

RCnFRCn

)86.1(2708129.0

120,316

..

622150 MPapsi

hb

Mf FRCnD

200

1000

Stre

ss


axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

Z

.57 h

.43 h

ctF

Specify Fiber Dosage Accordingly

Str

ess


axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

Example 2: Determine the moment capacity of the concrete slab that

is reinforced with fibers (0.5% of Fiber below)

STRUX 150

1000

ASTM 1609 Results for the fibers

used is shown in the next slide

Str

ess


axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

Example: Determine the moment capacity

Fibers 150

1000

JmmNT D 9.4545900150

MPabd

Tf

D

e 04.2150

2150

3 MPabd

Tf

D

e 04.2150

2150

3

mkNbhfM en 62.7166.0 23

Str

ess


axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

Example: Determine the Tension capacity

Fibers 150

1000

JmmNT D 9.4545900150

MPabd

Tf

D

e 04.2150

2150

3 MPabd

Tf

D

e 04.2150

2150

3

kNbhfT en 2.11337.0 3

3

076.0

AdfZ

Zw

cs

Gergely-Lutz

ACI requires that the term Z does not exceed 175 for interior exposure and 145 for exterior exposure (based on 0.4 mm and 0.3 mm crack width)

sf Stress in the steel

s

cteqct

s

s

s

s

A

AF

jdA

Mf

jdA

Mf

3,,37.0

(For RC)

(For RCwith fibers)

Example: ACI 318 cracking control

Z Z

Conventional RC FRC

Wider cracks a way from rebarsSteel

fibers Uniform crack width

3

5 )101.1(

AdfZ

Zxw

cs

Gergely-Lutz (mm)

50 KN

350 mm300

4000 mm200

2760mmAsMPaF

c30

'

MPajdA

Mf

s

s244 (For RC)w = 3 mm .

with 3.5 kg of synthetic fibers

MPaA

AF

jdA

Mf

s

cteqct

s

s 204760

200*350*9.0*28.1*37.0244

37.0 3,,

mmw 2.0

Example: ACI 318 cracking control

bhA tempshs 0017.0,,

MPaFc 25'

MPaFy 400

The steel ratio is

Example: 6” Slabs with 4” x 4” - W4

150

1000

~ W4 @ 4x4

3 AdfZ cs

6.2/ 12 hh

mNZ /20000

mmdc 75

212000mm10

1000x120A

MPafs 207

Zxw )101.1( 5

Crack Width

mmw 57.0

hbFF eqctct 3,,3.0

Stre

ss


axctF ,

1 %10 % -2.5 -3.5

cF

3,,37.0 eqctF

Z

.57 h

.43 h

ctF

Required STRUX 90/40 to Obtain Same Z-Value

s

eqct

s

cteqs

A

hbF

A

Ff

3,,

,

3.0

MPaf eqs 207, MPaF eqct 16.13,,

Fibers 150

1000

Specify Dosage of fibers accordingly

Failure and moment capacity of SOG

FiberPlain Concrete

Horst Falkner, Braunschweig,1995

• Bending moment distribution after cracking is different

• Plain concrete exhibit a regular hinge

• Fiber concrete exhibit plastic hinge (yield capacity

• Final design of PC slab is governed by slab stiffness and interaction with sub-base

• Final design of FRC slab is governed by the interaction between positive and negative moment as a function of slab stiffness and sub-base

FRC versus PC slabs

• Collapse load of FRC slab is a function of the sum of the negative and positive moment

• Collapse load of PC slab is a function of the cracking moment

)( + + MMM ult

crackingult MMM

FRC versus PC slabs

Resisted Moment by fiber

Pu

(Plastic Hinge)

Flexural capacity

6

2bhFM

FF

ctult

ctd

Plain concrete

ct

e

eF

FR 3,

3, Ductility factor, toughness dependent

+

+

6*

1001

)100

1(*

23,

3,

bhFRM

RFF

cte

ult

e

ctd

Fiber reinforced concrete

For a/l 0.2: (where a is the equivalent radius of the load patch, and l is the relative stiffness),

the ultimate load carrying capacity of the slab will be obtained from the following equations:

For Center Load

For Edge Load

For Corner Load

L is the radius of relative stiffness

Collapse Load for Point Load on Slab on Grade Using Yield Line Theory

Pu

Given Parameters

Ground Supported SlabThickness of Slab = 125 mmConcrete class S40Elastic modulus of Concrete = 35000 MPaModulus of Subgrade Reaction 68 MPa/mJoint spacing variable (6 m)

Example: 125 mm Slab with Center Point

Load of 100 kN over 0.025 m2

P = 100 kNArea = 0.025 m2a = equivalent radius = 89.2 mmradius of relative stiffness = = 538 mm

For Center Load

For Edge Load

Residual moment by fibers

Cracking moment by plain concrete

Use Factored Load = Pu= 1.5*100 = 150 kN

5.16 MPa

For center point load Re,3 will be equal to 25.6 % Fe,3 = 0.256*5.16 = 1.32 MPa fiber content

7. Slabs on ground

• Slabs on ground are designed according to ACI 360R specifications.

• Steel fibers are typically used at a dosage rate between 10 and 36 kg/m3 as the sole reinforcement.

• Synthetic fibers are used at a dosage rate between 1.8 and 4.5 kg/m3 as the sole reinforcement.

• The residual strength of FRC is used for design and specifying FRC slabs.

5. Design for shear

• As per ACI 318, if used in lieu of stirrups in flexural members, steel fibers must have an aspect ratio

between 50 and 100 and provide a minimum of 𝑅𝐷,150𝑇 of 75% when tested according to ASTM

C1609 (ACI 318 sec 5.6.6).

• Altoubat et al. (2015) have shown that synthetic macrofibers can also provide the required shear

resistance in flexural members when used at a proper dosage rate.

• For members with conventional longitudinal reinforcement but without shear reinforcement, the

shear capacity for FRC is given by (Model Code 2010 sec 7.7.3.2):

𝑉𝑅𝑑,𝐹 =0.18

𝛾𝑐𝑘 100 𝜌𝑙 1 + 7.5

𝑓𝐹𝑡𝑢𝑘𝑓𝑐𝑡𝑘

𝑓𝑐𝑘

13

+ 0.15𝜎𝑐𝑝 × 𝑏𝑤 𝑑

• For members with conventional longitudinal reinforcement and shear reinforcement, the

contribution of fibers can be added to the equation: 𝑉𝑅𝑑 = 𝑉𝑅𝑑,𝐹 + 𝑉𝑅𝑑,𝑠

Macro Synthetic Fiber Improve Shear Strength of RC Beams

Shear Behavior of Macro-Synthetic Fiber Reinforced Concrete Beams without Stirrups,”

ACI Materials Journal, Vol. 106, No. 4, July – August , 2009, pp. 381-389

Effect of Synthetic Macro-Fibers on Shear Behavior of Concrete Beams “, ACI- Special

Publications, SP248, “Deflection and Stiffness Issues in FRC and Thin Structural

Elements”, 2007, pp. 41-52

Shear Strength of Beams reinforced with synthetic macro fibers,” Eighth RILEM

Conference on fiber reinforced Concrete BEFIB2012, Portugal, 2012

fib-MC2010 Formulations

sRdFRdRd VVV ,, +

dbff

fkV wcpck

ctk

Ftukl

c

FRd

+

+

15.0.5.71.100..

18.0 31

,

0).2.0.5.0.(5.2

)( 13 + RRFtsu

FtsuFtu fffw

fwf

2,2

3

sp

j

jRbh

LFf

1,45.0 RFts ff

• Fibers contributions embedded in

concrete

• Fiber contribution depends on residual

tensile strength

• Formulas based on characteristic

properties

Based on linear post-cracking

behavior constitutive model

FtuFtuk ff 51.0

Residual Flexural Tensile Strength Parameters (EN 14651)

j 1 2 3 4

CMODj 0.5 1.5 2.5 3.5

FR,j (MPa) for Vf =0.5% 1.94 1.80 1.63 1.43

FR,j (MPa) for Vf =0.75% 2.36 2.28 2.06 1.80

FR,j (MPa) for Vf =1.0% 2.66 2.62 2.37 2.06

Analysis: Prediction versus Experimental

• fib-MC2010 and RILEM can be both safely used to predict shear strength of

SNFRC

• The fib-MC2010 predict shear strength of long beams with reasonable

accuracy but is more conservative for short beams

Prof. Salah AltoubatCoordinator

[email protected]

fiber reinforced concrete design - sharjah.ac.ae · • in design, the type, size, geometry, and...

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