FLEXURAL BEHAVIOR OF CONCRETE BEAMS REINFORCED WITH HIGH STRENGTH STEEL REINFORCING BARS

13th ICSGE

27-29 Dec. 2009

Cairo - Egypt

Ain Shams University

Faculty of Engineering

Department of Structural Engineering

Thirteen International Conference on Structural and Geotechnical Engineering

FLEXURAL BEHAVIOR OF CONCRETE BEAMS REINFORCED

WITH HIGH STRENGTH STEEL REINFORCING BARS

R. G. ELTAHAWY

Department of Civil Engineering, Faculty of Engineering, Ain Shams University

E-mail: [email protected]

T. K. HASSAN & O. H. ABD EL-WAHED

Department of Civil Engineering, Faculty of Engineering, Ain Shams University

1 El-Sarayat street, Cairo, Egypt


S. H. RIZKALLA

Department of Civil and Environmental Engineering, NCSU, Raleigh, NC 27695, USA


Abstract

Corrosion of steel reinforcement in aging highway infrastructure is a major problem

currently facing the transportation engineering community worldwide. Use of Micro-

composite Multi-structural Formable Steel, commercially known as “MMFX”, as a

replacement for convention steel is gaining popularity in many concrete structures. The

high-corrosive resistance nature and high-strength characteristics of the MMFX rebars

provide additional service life to concrete structures in areas that are prone to severe

environmental conditions. This paper presents a multi-phase experimental program

designed to examine the mechanical characteristics of the MMFX steel, evaluate their

corrosion resistance, and assess their structural performance as main flexural

reinforcement using typical full-scale T-section concrete beams. All MMFX reinforced

concrete beams experienced higher ultimate strength and a comparable amount of

ductility in comparison to beams reinforced with conventional steel rebars. The failure

mode of most beams was classified as ductile flexural failure accompanied by yielding

of the tension reinforcement preceding the crushing of the concrete. Only two beams

failed prematurely due to rupture of the MMFX rebars. Design guidelines are proposed

based on the results of the experimental program.

KEYWORDS: beams, concrete, deflection, flexural, high strength.

1 INTRODUCTION

Corrosion of steel reinforcement in an aging highway infrastructure is a major problem

currently facing the transportation engineering community. The use of deicing salts has

resulted in steady deterioration of bridge decks due to corrosion. This problem has been

documented by several researchers and recognized by highway agencies as one of the

most serious problems facing the civil engineering infrastructure worldwide [1]. Similar

and even worse conditions have been documented in Egypt due to the salt

Mediterranean environment in cities like Alexandria. The condition is more severe since

it is combined by relatively low quality controlled and low strength concrete.

As such, there is a need to use reinforcement that is less susceptible to corrosion than

conventional steel. The microstructure of the steel used to produce MMFX is altered to

eliminate the internal mechanisms that cause corrosion in steel. Its microstructure

consists of alternating bands of austenite and martensite [2]. Consequently, MMFX is

practically carbide free (less than 1% carbon) and consequently, the micro galvanic cell

formation is minimized.

2 EXPERIMENTAL INVESTIGATION

2.1 Test Specimens

All specimens were designed to simulate typical field behavior of concrete beams. All

beams were T-section of 500 mm flange width by 80 mm thick. The web was 250 mm

wide by 400 mm deep. The nominal length of all beams was 4000 mm with clear span

of 3800 mm. The concrete dimensions of the test specimens are shown in Fig. 1. Overall

concrete dimensions were kept constant in all specimens. Details of the tested beams are

given in Table 1. All beams were designed to achieve a minimum strain in the steel of

0.4 %. The reinforcement ratios for all beams satisfied the minimum and maximum

values recommended by ECP [3] and ACI 318-05 [4]. Three concrete compressive

strengths were used in design. All specimens were loaded statically up to failure using a

four point bending scheme.

Two φ 10 mm Grade (40/60) longitudinal bars were used as compression reinforcement

for all beams, except for beam XC1-4, where three φ 10 mm were used, to simplify

construction of steel cage. Steel mesh φ 8 mm Grade (24/35) was used as top flange

reinforcement. Typical detailing of reinforcement for the all eight specimens is shown

in Fig. 1. To prevent undesired shear failure in the beams, adequate shear reinforcement

was provided. A total of 40 closed stirrups of Grade (40/60) were positioned at 100 mm

spacing along the whole beam length to prevent shear failure.

2.2 Materials

High-strength steel: The high-strength and corrosive-resistant steel used in the current

study was provided by MMFX Technologies Corp., CA, USA. The mechanical

characteristics of the material compared to conventional steel bars are given in Table 2

based on test results conducted at Ain Shams University. The properties of MMFX

rebars are presented in terms of modulus of elasticity (Es), yield strain and strength (εy,

fy), ultimate strain and strength (εsu, fsu), and strain and strength at failure (εsf, fsf) [5].

Concrete: Three concrete mixes were used for all beams and were designed according to

ECP [3], using locally manufactured ordinary Portland cement, sand and fine gravel as

well as additives when needed. Six standard 150 x 300 mm cylinders were cast with

each beam, cured in the same manner and kept under the same environmental conditions

as the beams to obtain the average compressive strength. Three concrete cylinders were

tested at seven days and the other three were tested at the time of testing of each beam.

2.3 Corrosion Resistance

A set of φ 13 mm, φ 16 mm and φ 19 mm MMFX and Grade (40/60) steel bars were

tested in tension to evaluate the mechanical characteristics of the bars before and after

exposure to wet/dry cycles for one year. Each cycle consisted of dipping the bars in a

10% concentration NaCl solution for one week and leaving the bars to dry for another

week. The bars were 500 mm long and were placed inside a reservoir of 1500 mm long,

300 mm wide and 300 mm deep as shown in Fig. 2.The bars were tested in tension after

six and twelve months of exposure. All tests were conducted in accordance with ASTM

A370-024[6].

2.4 Instrumentation

To monitor the behavior of the tested beams under the applied loading, the

instrumentation included Linear Voltage Displacement Transducers (LVDTs) for

deflections and electrical resistance strain gauges for steel and concrete strains. Detailed

descriptions of the instrumentation are shown in Fig. 3.

2.5 Test Configuration

All beams were tested under four point bending. Each beam was tested up to failure

using a 400 kN capacity hydraulic jack. The specimens were positioned on top of a

strong structural concrete floor. A steel pin support was carefully set between the

specimen and the floor at a distance of 100 mm from the left end of the beam, while a

steel roller support was positioned at the same distance but at the right end of the beam

to allow for proper sectional rotation. The setup was carefully leveled and aligned to

prevent any source of errors due to the lateral eccentricity. The loading procedure

comprised one loading cycle, during which the load was incrementally increased by 5

kN up to the appearance of the first visible crack, then the load step was increased to 10

kN. At the end of each load step the load was held constant for 1.5-2 minutes during

which measurements and observations as well as marking the visible cracks were

carried out.

3 EXPERIMENTAL RESULTS

A summary of the test results is presented in Table 3 including failure loads, maximum

mid-span deflections, steel strain gauge readings and concrete strain gauge readings.

The failure mode of most beams was classified as ductile flexural failure accompanied

by yielding of the tension reinforcement preceding the crushing of the concrete. Only

two beams failed due to rupture of the MMFX rebars. One more beam exhibited shear

failure. No bond failure was observed during testing.

3.1 Corrosion Test Results

Typical tension tests results after six and twelve months of exposure are shown in Fig. 4

and Fig. 5 for MMFX and conventional steel bars, respectively. After corrosion, MMFX

bars attained the same behavior but with slightly lower yield and ultimate strength

values. The measured decrease in the yield strength using the 0.2% offset method was

less than 10% after twelve months of exposure. Conversely, a considerable reduction in

the yield strength was observed for conventional steel bars after twelve months of

exposure. The measured decrease in the yield strength was about 20%. It is also

remarked that the shape of the curve for conventional steel bars changed to some extent

especially after yielding of the bars.

3.2 Flexural Behavior

The load-midspan deflection behavior of XC1-1, XC1-3, SC1-1 and SC1-3 is shown in

Fig. 6. Linear behavior was observed up to the initiation of the first crack at a load level

of 35 kN followed by a non-linear behavior with significant stiffness reduction up to

failure. Yielding of conventional steel rebars Grade (40/60) was observed for SC1-1 and

SC1-3 at loading levels of 65 and 160 kN, respectively. The corresponding mid-span

deflections were 14 and 22 mm. Beam XC1-1 continued to maintain its original

stiffness up to a load level of 130 kN beyond which the MMFX reinforcement reached

the yield strength and led to reduction in the flexural stiffness. Beam XC1-3 continued

to maintain its original stiffness up to a load level of 343 kN, where no stiffness

reduction was observed. The load-midspan deflection behavior for XC1-1, XC1-2,

XC1-3 and XC1-4 are given in Fig. 7. Linear behavior was observed, for all beams up

to the initiation of the first crack followed by a non-linear behavior with significant

stiffness reduction up to failure. Beams XC1-1 and XC1-2 exhibited higher stiffness

reduction, after cracking, due to yielding of MMFX rebars. The measured stiffness loss

after flexural cracking was 90, 60, 45 and 38 percent for beams XC1-1, XC1-2, XC1-3

and XC1-4, respectively. High reduction in the stiffness is primary influenced by the

low reinforcement ratio used in beams XC1-1 and XC1-2. The nonlinear behavior for

beams, from cracking up to failure, is inherited from the non-linearity of the stress-

strain relationship of the MMFX bars. Yielding of the bottom MMFX bars in beams

XC1-1 and XC1-2 was observed at load levels of 150 and 259 kN, respectively. Both

beams suffered additional stiffness reduction where the measured pre-cracking stiffness

dropped from 35.67 to 3.5kN/mm. This behavior was demonstrated by flattening of the

load-deflection curves at these load values.

The load-midspan deflection behavior for beams XC1-3, XC2-3 and XC3-3 are shown

in Fig. 8. Linear behavior was observed for all beams up to the initiation of the first

crack at a load level of approximately 50 kN followed by non-linear behavior with

significant stiffness reduction up to failure. Beams XC2-3 and XC3-3 exhibited higher

stiffness reduction, after cracking, due to yielding of MMFX rebars. The pre-cracking

stiffnesses for beams XC1-3, XC2-3 and XC3-3 were 45, 77 and 230 kN/mm

respectively. The measured stiffness loss after flexural cracking was 80, 90 and 96

percent for beams XC1-3, XC2-3 and XC3-3, respectively.

3.3 Crack pattern

In general, cracks at the constant moment region occurred at an earlier stage and

continued to propagate after yielding of the main steel reinforcement. As the applied

load increased, flexural cracks started to appear outside of the constant moment region.

At high load levels, flexural cracks located within the constant shear region deviated

diagonally and turned into the flexural shear cracks. At approximately 75 percent of the

ultimate loads of the MMFX-reinforced beams, shear cracks began to appear at 45-

degree angle. All shear cracks were located near the supports. For beams SC1-1 and

SC1-3, cracks were spaced out evenly and ranged from 100 to 150 mm throughout the

beam, which suggested that the position of the crack is influenced by the location of the

stirrups. The observed cracks in beams SC1-1 and SC1-3 at failure were almost 50

percent fewer than those observed for beams XC1-1 and XC1-3 reinforced with MMFX

bars. More cracks were observed for beams with lower concrete compressive strength.

Due to the mechanical characteristics of MMFX bars, as the applied load increases,

more cracks are formed rather than widening of the existing cracks. It should be noted

that more cracks were observed in MMFX-reinforced beams compared to

conventionally-reinforced beams with the same reinforcement ratio.

3.4 Failure Modes

The failure mode of all beams except XC1-1, XC1-2 and XC1-4 was due to crushing of

the concrete at the constant moment zone after considerable deflection following

yielding of the tension reinforcement. Failure of beams XC1-1 and XC1-2 was due to

rupture of tensile reinforcement. Beam XC1-4 exhibited undesirable shear failure mode.

Different failure modes are illustrated in Fig. 9.

4 FLEXURAL ANALYSIS

In order to predict the behavior of the tested beams, an analytical model using iterative

procedures was adopted. Each beam was analyzed using strain compatibility approach

in order to satisfy the section equilibrium. The analytical model was based on the

currently available concrete theory, which utilizes the material characteristics of the

concrete and reinforcement, as described by Collins and Mitchell, 1997 [7, 8].

4.1 Analytical Model

All specimens were designed according to the ACI 318-05 [4]. The designed specimens

also complied with the ECP [3] where the c/d ratio was checked to not exceed cmax/d,

where c is the depth of the neutral axis and d is the overall depth of the section.

Modeling of each material was based on the experimental measurements from testing

and the analytical models documented in published literature [9, 10]. The midspan

deflection for each beam was determined by integrating the curvature along the beam.

The corresponding curvature at each loading increment was determined from moment-

curvature relationship. The deflection prediction was performed numerically from the

support to the mid-span section. The numerical integration was performed for 10

sections along half of the span. Tension stiffening of the concrete was not accounted for

in the analysis.

4.2 Verification of the Analytical Model

In order to verify the analytical model, the predicted midspan deflections were

compared with the measured values as shown in Fig. 10. The verification process was

performed for both conventionally- and MMFX-reinforced concrete beams. Table 4

presents a summary of analytical and experimental failure loads for all beams.

Throughout the analysis, the predicted and measured service load deflections showed

good agreement with less than 5% difference.

5 DESIGN GUIDELINES

5.1 Basis of Current Design Practice

Based on the current design practice, the design of a flexural member should take into

account the overall behavior of the member throughout the service range and up to the

nominl capacity of the member. Beginning with the 1963 ACI 318 code, flexural

members were required to have reinforcement ratios not greater than 75 percent of the

balanced reinforcement ratio ρb. By 1993, this criterion had been in use for 30 years,

and the behavior of flexural members was judged to be satisfactory. The current

criterion based on tensile strain in the reinforcement was selected to provide similar

behavior to that experienced under the 0.75 ρb criterion.. Flexural members designed in

accordance with ECP are required to comply with the limitation of the (cmax/d) which

corresponds to steel strain ranges from 0.003 to 0.0045 mm/mm.

5.2 Desirable Behavior for Flexural Members

In general, good behavior of a member is related to ductility. Using high-strength

materials as flexural reinforcement, the ductility ratio defined as the ratio of ultimate

curvature/deflection to the curvature/deflection at yielding of the main reinforcement is

not the only measure of desirable behavior. Instead, the ratio of nominal strength

behavior to service load behavior, referred to as the deformability ratio, may be a more

suitable indicator.

5.2 Nominal Strength Analysis

Fig. 10 presents the relationship between the nominal moment capacity of a singly

reinforced T-section and the reinforcement ratio using cracked section analysis. The

measured capacities of the MMFX-reinforced concrete beams are also shown for

comparison. The experimental results are in good agreement with the predicted values

for different beams. The predicted balanced reinforcement ratio, ρb, was 1.36 percent

for the sections considered. For a given reinforcement ratio less than 1.36 percent and

above 0.67 percent, tension-controlled failure occurred. The minimum reinforcement

ratio to be used with the MMFX is 0.67 percent to prevent rupture of the reinforcement.

5.3 Design Resistance Factor Guidelines

ACI 318-02 has included provisions to allow design of flexural members exhibiting

both compression- and tension-controlled failures using conventional steel. Since

sections exhibiting a compression controlled failure exhibit lower ductility and provide

inadequate warning prior to failure, ACI 318-02 requires that designers use a resistance

factor, φ, of 0.65 for members with a failure strain in the reinforcement of less than

0.002. For tension-controlled sections in which the reinforcement exhibits substantial

plastic deformation prior to failure (strain in the reinforcement greater than 0.005), a

resistance factor, φ, of 0.9 is permitted. Between these limits, sections are considered to

be in the transition region and the resistance factor varies linearly, Since MMFX has a

yield strain of 0.006, these limits need to be re-evaluated to ensure that design of

MMFX-reinforced concrete members also exhibit adequate ductility [11].

For a general reinforced concrete section and a specified reinforcement ratio, the

moment-curvature relationship of the section can be established. From the moment

curvature relationship, the ductility, µ, of the section can be calculated as Φu/Φy where

Φu is the section curvature at ultimate and Φy is the section curvature at yield. This

procedure can be followed for a series of reinforcement ratios, for a given concrete

strength. Fig. 11 presents the relationship between reinforcement ratio and ductility for

sections reinforced with conventional and MMFX steel for a concrete cylindrical

compressive strength of 25 MPa. Various values of the concrete compressive strength

can be used in ductility calculations to highlight the effect of concrete grade on the

balanced, minimum and maximum reinforcement ratios. Fig. 12 presents the

relationship between reinforcement ratio and ductility for sections reinforced with

MMFX rebars for a concrete cylindrical compressive strength of approximately 25, 42

and 57 MPa, respectively. The balanced reinforcement ratio, ρb, was calculated as 1.36,

1.4 and 1.42 percent for the sections using compressive strength of 25, 42 and 57 MPa,

respectively. For a given reinforcement ratio less than 1.4 percent and above 0.75

percent tension-controlled failure occurred for concrete compressive strength of 42

MPa. Whereas it is observed that for reinforcement ratios between 1.42 and 0.81 percent

for concrete compressive strength of 57 MPa, tension failure takes place. The minimum

reinforcement ratio to be used with the MMFX is 0.67, 0.75 and 0.81 percent using

concrete compressive strength of 25, 42 and 57 MPa, respectively. For design of

flexural members reinforced with MMFX, the maximum ratio of reinforcement, ρ is

0.75 of the balanced ratios proposed above. To permit using a resistance factor of 0.9,

sections reinforced with MMFX should provide a ductility comparable to that of

sections reinforced with conventional steel when the strain in the steel reinforcement at

failure is equal to or higher than 0.005. As recognized from Fig. 11, this corresponds to

ductility, µ, of 2.24 and a failure strain in the MMFX reinforcement of 0.015 mm/mm.

To maintain consistency with ACI 318-02, it is reasonable to use a reduction factor, φ,

of 0.9 for sections reinforced with MMFX when the strain at failure in the section is 2.5

times the yield strain or 0.015 mm/mm. Therefore, for MMFX-reinforced sections,

compression-controlled failures occurs, when the strain in the MMFX reinforcement at

ultimate is less than 0.006. A resistance factor, φ, of 0.65 should be used for

compression-controlled failures. Tension-controlled failures occurs when the strain in

the MMFX reinforcement at ultimate is greater than 0.015. A resistance factor, φ, of 0.9

may be used. In the transition region between these two strain limits, φ should vary

linearly between 0.65 and 0.9. The proposed variation of the resistance factor φ is

graphically in Fig. 13. The proposed strain limits for use with concrete members

reinforced with MMFX are selected to ensure sufficient ductility and warning prior to

failure of the members. At a reinforcement strain of 0.002 mm/mm, both members

reinforced with conventional steel and those reinforced with MMFX may exhibit similar

crack patterns and deflections. Beyond this strain conventional steel exhibits a

pronounced yielding plateau and substantial increases in crack width and deflections.

MMFX, however, still maintains appreciable stiffness well beyond this strain limit.

Consequently, concrete sections reinforced with MMFX may exhibit larger crack

widths and higher deflections at service load levels than other members reinforced with

conventional steel.

6 CONCLUSIONS

Based on observed behavior, experimental results and theoretical prediction, the

following conclusions can be drawn:

1. The stress-strain relationship of corroded MMFX rebars attained almost the same

behavior after 12 months of severe exposure to wetting/drying cycles.

2. MMFX-reinforced concrete beams exhibited ductile flexural failure and provided

adequate warning through large deformations, and extensive cracking prior to

failure.

3. The use of MMFX provided better crack control after the yielding of reinforcement

in comparison to conventional steel.

4. Flexural behavior of MMFX-reinforced concrete beams can be modeled accurately

using cracked section analysis.

5. New minimum and maximum reinforcement ratios are introduced according to the

concrete compressive strength. These proposed reinforcement ratios should be taken

into consideration in design to ensure tension-controlled ductile flexural failure for

flexural members reinforced with MMFX rebars.

7 ACKNOWLEDGMENT

The authors would like to acknowledge MMFX Technologies Corporation, CA, USA

for the donation of the materials used in this study. The authors are grateful to NSF for

its financial support for this research project. Special thanks are extended to the

technicians at the Structural Laboratory at the Faculty of Engineering at Ain Shams

University.

8 REFERENCES

[1] Vijay, P.V., Gangarao, V.S. H, and Prachasaree, W. Bending Behavior of Concrete

Beams Reinforced with MMFX Steel Bars. MMFX Steel Corporation: Technical

Resources. July 2002.

[2] MMFX Steel Corporation of America. Retrieved April 17, 2004 from the MMFX Steel

Corporation of America Web site,

http://www.mmfxsteel.com/technical_resources/Default.asp.

[3] ECP Committee, Cairo, 203-2007. Egyptian Building Code Requirements for Structural

Concrete and Design Aids.

[4] ACI Code (318-02) and Commentary (318R-02), American Concrete Institute,

Farmington Hills, MI. Building Code requirements for structural Concrete.

[5] El-Hacha, R., and Rizkalla, S.H. Fundamental Material Properties of MMFX Steel

Rebars. North Carolina State University, NCSU-CFL Report No. 02-04. July 2002.

[6] ASTM A370-97-02: Standard Test Method and Definitions for Mechanical Testing of

Steel Products.

[7] Dawood M., Seliem H. and Rizkalla S. Evaluation of the Moment Capacity of Concrete

Beams Reinforced with MMFX Reinforcing Steel. 2006.

[8] Collins, P.M., and Michell D. Prestressed Concrete Basics. 1987.

[9] Park R., and Pauly T. by John Wiley and Sons. Reinforced Concrete Structures. 1975.

[10] MacGregor, James G. and Wight, James K. Reinforced Concrete Mechanics and

Design.

[11] Dawood M., Seliem H., Hassan T. and Rizkalla S. Design Guidelines for Concrete

Beams Reinforced with MMFX Microcomposite Reinforcing Bars. International

Conference on Future Vision and Challenges for Urban Development. Cairo,

December 2004.

Table 1: Test Matrix

Beam

Label Steel Type Reinforcement Reinforcement ratio %

fc'

MPa

XC1-1 MMFX 2 φ13 0.26 24.5

XC1-2 MMFX 2 φ 16 0.46 24.5

XC1-3 MMFX 2 φ 19 0.65 21.5

XC1-4 MMFX 4 φ 19 1.3 24

XC2-3 MMFX 2 φ 19 0.65 42

XC3-3 MMFX 2 φ 19 0.65 57

SC1-1 40/60 2 φ 13 0.26 26

SC1-3 40/60 2 φ 19 0.65 26

Table 2: Tensile Strength of the MMFX

Stresses are given in MPa and strain in mm/mm

Table 3: Experimental Results Summary

Specimen

Max Load

Carrying Capacity

(kN)

Average

Maximum Steel

Strain

(µε)

Average

Maximum

Concrete Strain

(µε)

Maximum Mid-Span

Deflection (mm)

SC1-1 100 6000 3300 59

SC1-3 190 17000 3800 48

XC1-1 206 18000 2400 80

XC1-2 302 16000 3600 82

XC1-3 343 7000 3900 35

XC2-3 447 13000 3900 47

XC3-3 480 14500 3900 48

XC1-4 660 6950 4000 41

Table 4: Experimental and analytical Loads at failure

Specimen Max Load Carrying Capacity (kN)

Proportional

Limit

Strength

Yield

Strength

at 0.2%

offset

Young’s

Modulus

of

Elasticity

Ultimate

Strength

Strain

at 0.2%

offset

yield

Strength

Strain

at

Ultimate

stress

Strain

at

failure

φφφφ 13 mm 1244.7 1221.3 245000 1367.4 0.00325 0.00684 0.00715

φφφφ 16 mm 938.17 1104.9 163200 1126.4 0.00451 0.00901 0.00946

φφφφ 19 mm 1033.9 985 239800 1208 0.00414 0.00829 0.00863

Experimental Analytical Diff%

SC1-1 100 102 2.0

SC1-3 190 195 2.6

XC1-1 206 210 1.9

XC1-2 302 310 2.6

XC1-3 343 349 1.7

XC2-3 447 450 0.8

XC3-3 480 485 1.0

XC1-4 660 661 0.2

4000

Stirrups

Sec. (1-1)

Main Steel

1600 mm

P/2 Main tensile reinforcementP/2

3800

500

400

80

250

11

Hangers

Elevation Side view

Fig. 1: Test specimen

Fig. 2: Corrosion Test Reservoir

L3L4 L2 L1,4

4000

L1 L2,3

11

1200

400

16001200

250

Sec. (1-1)

500

400

80

Fig. 3: Locations of LVDTs on beams

Fig. 4: Measured stress-strain behavior for

Corroded MMFX rebars Fig. 5: Measured stress-strain behavior for

Corroded Grade (40/60) steel

Fig. 6: Load-midspan deflection behavior for

beams XC1-1, XC1-3, SC1-1& SC1-3

Fig. 7: Load-midspan deflection relationship for

beams XC1-1, XC1-2, XC1-3 & XC1-4

Fig. 8: Load-midspan deflection relationship for

beams XC1-3, XC2-3 & XC3-3

Fig. 9: Failure mode for different specimens

SC1-1 SC1-3

XC1-1 XC1-2

XC1-3 XC2-3

XC3-3 XC1-4

0

5000

10000

15000

20000

25000

30000

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Reinforcement Ratio, ρρρρ %

M/b

d2

Analytical Calculations

Experimental Results

Fig. 10: Moment capacity as a function of reinforcing ratios

0

1

2

3

4

5

6

7

8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5


Du

cti

lity

, µµ µµ

Compression Failure

µ = 2.24 ε40/60u = 0.005

ε40/60y = 0.002

εMMFXu = 0.015

εMMFXy = 0.006

MMFX Grade(40/60)

fc' = 24.5 MPa


Fig. 11: Effect of reinforcement ratios on ductility

0

1

2

3

4

5

6

7

8

9

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6


Du

cti

lity

, µµ µµ

fc = 24.5 MPa

fc = 42 MPa

fc = 57 MPa


Compression Failure

µ = 2.24 εMMFXu = 0.015

εMMFXu = 0.006

Fig. 12: Effect of reinforcement ratios with various concrete strength on ductility

0.40

0.0

Res

ista

nce

Facto

r, φφ φφ

Transition

εMMFXu = 0.015εMMFXu = 0.006

0.65

0.90

Compression Tension

Controlled Controlled

φ = 0.48 + 28ε

Fig. 13: Resistance factor for MMFX reinforced concrete flexural members

FLEXURAL BEHAVIOR OF CONCRETE BEAMS REINFORCED WITH HIGH STRENGTH STEEL REINFORCING BARS

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