Paper Flexural Design Using High-Strength Concrete …srizkal/TechPapers2006/CBC2006_flex_design_bridg… · FLEXURAL DESIGN USING HIGH-STRENGTH CONCRETE UP TO 20 KSI ... by bridges

Mertol, Rizkalla, Zia and Mirmiran 2006 CBC

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FLEXURAL DESIGN USING HIGH-STRENGTH CONCRETE UP TO 20 KSI

H. C. Mertol, North Carolina State University, Raleigh, NC

S. Rizkalla, PhD, PEng, North Carolina State University, Raleigh, NC

P. Zia, PhD, PE, North Carolina State University, Raleigh, NC

A. Mirmiran, PhD, PE, Florida International University, Miami, FL

ABSTRACT

This paper summarizes the research findings of the fundamental

characteristics of high-strength concrete for the flexural design of bridge

girders. The main objective of the research is to provide recommended

provisions to the AASHTO-LRFD Bridge Design Specifications to extend the

use of concrete strength up to 18 ksi. A total of 15 plain concrete specimens

were tested under eccentric compression to evaluate the stress-strain

distribution of high-strength concrete in the compression zone of flexural

members. The variables considered in this investigation are the strength of

concrete (11 ksi to 16 ksi) and the age of the concrete. Two independent loads,

concentric and eccentric, were applied with a specific rate to the specimen so

as to locate neutral-axis at one face of the specimen and the maximum strain

at the opposite face. The specimens were 9 by 9 inches cross-section and 40

inches long. Stress-strain curves and stress block parameters for high-

strength concrete were obtained, evaluated and compiled with the results

available in the literature. The current equation for α1 specified by AASHTO

LRFD Bridge Design Specifications needs to be modified to show a reduction

for high-strength concrete. The current equation for β1 and current value for

ultimate concrete strain specified by AASHTO LRFD Bridge Design

Specifications is appropriate for high-strength concrete.

Keywords: Combined Compression and Flexure; High-Strength Concrete; Stress Block

Parameters; Tests


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INTRODUCTION

The use of high-strength concrete (HSC) has become a common practice in recent years with

strengths ranging up to 20.0 ksi. With high-strength concrete longer distances can be spanned

by bridges with fewer beams which reduce the complexity of a project with reduced

construction time and cost. High strength concrete not only implies the increased strength but

also the increased durability which corresponds to a reduced maintenance of a bridge

structure with longer lifetime. The AASHTO LRFD Bridge Design Specifications1, first

published in 1994, limits its applicability to a maximum concrete strength of 10.0 ksi, unless

physical tests are made to establish the relationship between concrete strength and its other

properties. These limitations reflected the lack of research data at the time, rather than the

inability of the material to perform its intended function. Many design provisions stipulated

in the AASHTO LRFD Bridge Design Specifications1 are still based on test results obtained

from specimens with compressive strengths up to 6 ksi. The NCHRP has initiated separate

projects to expand the AASHTO LRFD Bridge Design Specifications1, allow broader use of

high-strength concrete, and meet the needs of the bridge design community. The objective of

this paper is to recommend revisions to the AASHTO LRFD Bridge Design Specifications1

to extend the applicability of its flexural and compression design provisions for reinforced

and prestressed concrete members to concrete strengths up to 18 ksi. The recommended

provisions are intended to be seamless and unified over the full range of concrete strengths.

When a simple reinforced concrete beam is loaded to failure, the critical section reaches its

ultimate capacity when the extreme compression fiber reaches the ultimate concrete strain.

The concrete in the compression zone has a stress distribution similar to its stress-strain

relationship which is referred to as the generalized (actual) stress block. As a part of this

research program, this paper focuses on the evaluation of the generalized stress block of

high-strength concrete ranging from 10.0 to 20.0 ksi in the compression zone of flexural

members.

Many researchers have investigated the stress-strain distribution of compression zone of

flexural concrete members. Hognestad et al.2, developed a test set-up to determine the stress-

strain distribution for concrete. Their specimens were mostly referred to as C-Shaped

Specimens or Eccentric Bracket Specimens. In their test set-up, they simulated the

compression zone of a flexural member on a rectangular cross-section by varying the axial

load and the moment on the section. In the research presented in this paper, the same method

was utilized to obtain the stress-strain distribution of high-strength concrete.

RESEARCH SIGNIFICANCE

This paper presents the research findings of 15 unreinforced high-strength concrete members

with concrete compressive strengths ranging from 11.0 to 16.0 ksi, tested under combined

axial and flexure to evaluate the stress-strain distribution of compression zone of flexural

concrete members. Stress-strain curves and stress block parameters for high strength concrete

were obtained, evaluated and compiled with the results available in the literature. The results


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will serve as the basis for proposed revisions for the AASHTO LRFD Bridge Design

Specifications1 to increase the limits of the compressive strength of concrete to 18 ksi.

EXPERIMENTAL PROGRAM

TEST SPECIMENS

This test series consisted of 15 square specimens with 9x9x40 in. dimensions. A general view

of the concrete specimen is presented in Figure 1. The end sections of the eccentric bracket

specimens were heavily reinforced, while the test region in the middle of the specimens was

plain concrete. The main parameter was the concrete strength. Three different high-strength

concrete mix designs were used to cast the specimens. The target concrete compressive

strengths of these mixes at 28 days were 10.0 ksi, 14.0 ksi and 18.0 ksi. Three specimens

were tested for the target concrete compressive strength of 10.0 ksi while six specimens were

tested for each of the target concrete compressive strength of 14.0 and 18.0 ksi.

The ends sections of the specimens were reinforced with three #4 U-shaped longitudinal and

three #3 transverse reinforcement. Steel reinforcement configuration of the specimens is

shown in Figure 2. Furthermore, the ends of the specimens were confined with ½ in. thick 10

in. high rectangular steel tubes with holes on two opposite faces. The combination of the

steel tubes and heavy reinforcement ensures proper transfer of the axial load and moment and

eliminates possible localized failures at the ends of the specimens. The plain concrete test

section in the middle of the specimens is 16 in. long.

Figure 1 – General View Figure 2 – Steel Reinforcement Configuration


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The reinforcement cages were assembled and placed into the top and the bottom rectangular

steel tubes. PVC pipes were placed into the holes on the steel tubes to have clearance for the

threaded rods which were used to connect the steel arms to the specimen. A picture of an

assembled steel tube is presented in Figure 3. The assembly of the formwork is presented in

Figure 4. The specimens were cast vertically. Three 4x8 in. cylinders were cast for each

specimen to be tested at the testing day.

Figure 3 – Assembled Steel Tube Figure 4 – Assembly of the Formwork

After casting the specimens the top concrete surfaces were covered with wet burlap and

plastic sheets. The cylinder molds were covered with companion lids. The specimens and the

cylinders were stripped 24 hours after casting and they were covered with wet burlap and

plastic sheets for a week. The specimens were then stored in the laboratory where the

temperature was maintained at approximately 72° F with 50 percent relative humidity until

the time of testing. The cylinders were prepared by grinding both end surfaces to remove

irregularities in the surfaces and to ensure that the ends were perpendicular to the sides of the

specimen.

MATERIAL PROPERTIES

Mix designs for three different concrete target strengths, 10.0, 14.0 and 18.0 ksi, were

developed after numerous laboratory and plant trial batches (Logan3). The mixture designs,

water to cementitious materials ratio and 28-day compressive strength of the concrete are

provided in Table 1.


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Table 1 – Three Mixture Designs for Target Concrete Strength 10.0, 14.0 and 18.0 ksi.

Target Strengths Material

10.0 ksi 14.0 ksi 18.0 ksi

Cement (lbs/yd3) 703 703 935

Microsilica Fume (lbs/yd3) 75 75 75

Fly Ash (lbs/yd3) 192 192 50

Sand (lbs/yd3) 1055 1315 1240

Rock (lbs/yd3) 1830 1830 1830

Water (lbs/yd3) 292 250 267

High Range Water-Reducing Agent (oz./cwt) 17 24 36

Retarding Agent (oz./cwt)* 3 3 3

w/cm 0.30 0.26 0.25

28-Day Compressive Strength (ksi) 11.5 14.4 17.1

* Ounces per 100 pounds of cementitious materials

The coarse aggregate was obtained from Carolina Sunrock Corporation. The aggregate

selected was #78M crushed stone with a nominal maximum size of 3/8 in.. Two types of fine

aggregate were used depending on the target compressive strength. The first type of fine

aggregate was a natural sand used by the Ready-Mixed Concrete Company in all of their

concrete mixtures. The second type of fine aggregate used was a manufactured sand known

as 2MS Concrete Sand produced by Carolina Sunrock Corporation. The cement used was a

Type I/II cement produced by Roanoke Cement Company. The fly ash producer was Boral

Material Technologies and the silica fume producer was Elkem Materials, Inc. Both the high-

range water-reducing and the retarding admixtures were manufactured by Degussa

Admixtures, Inc. The high-range water-reducing admixture (HRWRA) used was Glenium®

3030. DELVO® Stabilizer was used as the retarding admixture.

TEST METHOD AND TEST SET-UP

A conceptual view of the test setup is shown in Figure 5. The two axial loads of P1 and P2 are

adjusted during the test to maintain the neutral axis, i.e., zero strain at the exterior edge of the

specimen. On the opposite side of the cross-section, the extreme fiber will be subjected to a

monotonically increasing compressive strain. In each step, the main axial load from the

machine, P1, was applied to a level that creates a constant axial strain in the section. The

secondary load applied by the jack, P2, was applied to maintain zero strain at one face, and

the maximum strain at the other.


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Figure 5 – Test Set-Up

The test set-up used in this research was different from the usual eccentric bracket tests. Two

steel moment arms were connected to a rectangular concrete specimen confined with

rectangular steel tubes at the ends. These steel tubes had holes which enabled the transfer of

forces from the arm to the concrete section by using threaded rods. Each steel arm consisted

of two 24 in. long C8x11.5 in. channel sections welded to two 9x1x24 in. steel plates at the

top and the bottom. ½ in. stiffeners were used along the section. Two roller connections were

constructed to eliminate the end restrictions due to the applied axial load from the machine.

Each roller connection consisted of six 1 in. diameter rollers and two curved plates, tapering

through inside and outside, respectively. The roller connection assembly was fixed to side

plates which were released at the time of testing. Both the steel arms and the roller

connections were designed to have a factor of safety at least 2.0 against yielding to ensure a

failure in the test region.

INSTRUMENTATION

The main axial load, P1, applied by the 2,000,000 lbs. Baldwin-Lima-Hamilton load

controlled hydraulic compression machine, was measured by an internal load cell which is

mounted in the machine. The secondary load, P2, was applied with a 120,000 lbs. Enerpac

manual-hydraulic jack and was measured by a 100,000 lbs. Strainsert Universal Flat Load

Cell.

Each specimen was instrumented with PL-60-3L concrete strain gages supplied by Texas

Measurements, Inc. The length of the strain gages were 2.4 in. A total of 9 strain gages were

located on each test specimen. Two of them were applied on the zero strain face. Four of

them were mounted on the two sides of the specimen. Three of them were located on the

compression side of the specimen, one of which was used to measure the transverse strain of

concrete. Three 1 in. linear variable displacement transducers (LVDT) were placed at the top,


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bottom and mid-section in order to obtain the deflected shape of the specimen and to

incorporate the secondary moment effects. The location of the instrumentation for test

specimens is illustrated in Figure 6.

Figure 6 – Location of the Strain Gages for Test Specimens

The main and the secondary loads P1, P2, stroke, 3 LVDT readings and 9 strain gages were

recorded during the tests by a data acquisition system.

TEST PROCEDURE

The roller connections were placed into machine supplying the main axial load. The

specimen is positioned, aligned and leveled on the roller connection. A timber frame was

assembled around the specimen to ensure the stability of the test set-up after failure of

concrete specimen. The bottom and top arms were placed and connected to the specimen by

using threaded rods. The load cell and the jack, supplying the secondary load, were placed on

the top arm. The bottom arm and the top arm assembly were connected to each other by

using 1 in. threaded rod. The top roller connection was positioned and leveled. A thin layer

of hydrostone (gypsum cement) was placed between the roller connections and the specimen

at the top and the bottom. The instrumentation was connected to the data acquisition system.

A crane cable was attached to the top arm before releasing the roller connections. The

specimen was leveled by using the crane and the readings from the instrumentation were

balanced to zero. A very small axial load was applied on the specimen before the crane cable

was released. As the main axial load started to increase incrementally, the secondary load

was applied by a hydraulic jack and a hand-pump to maintain neutral axis on one face. The

loading rate was 2 microstrains per second on the compression face of the specimen. The

duration of each test was around 25 minutes. The tests were stopped when the concrete failed

in an explosive manner. Three cylinders were tested with each specimen in accordance with

ASTM C 39 on the same day.


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TEST RESULTS AND DISCUSSIONS

A total of 15 specimens were tested with cylinder concrete strengths ranged from 10.0 to

16.0 ksi. The cylinder strength, age at testing, the loading rate and the ultimate compressive

strain achieved by the specimens are summarized in Table 2. All the specimens had similar

explosive failure mode. No cracks were observed until failure. Typical failure mode for the

eccentric brackets is shown in Figure 7.

Table 2 – Tabulated Test Results

Specimen 'cf at Testing

(ksi)

Age at Testing

(days)

Loading Rate

( / secµε )

Ultimate Strain

( µε )

10EB#1 11.0 63 12.2 3738

10EB#2 11.4 109 2.0 3138

10EB#3 11.7 111 2.4 3407

14EB#1 14.6 49 2.3 3316

14EB#2 14.3 51 1.8 3162

14EB#3 14.7 52 2.2 3177

14EB#4 15.0 57 2.3 3032

14EB#5 15.4 100 5.3 2868

14EB#6 15.2 101 4.1 2954

18EB#1 15.8 76 2.2 3684

18EB#2 16.0 77 2.3 3364

18EB#3 15.6 81 2.4 2914

18EB#4 15.8 82 2.6 3306

18EB#5 16.0 83 2.1 3144

18EB#6 15.5 84 2.1 3404

Figure 7 – Typical Failure Mode for Eccentric Bracket Specimens (10EB#3)


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CONCRETE STRAIN MEASUREMENTS

The ultimate concrete compressive strain measured at failure on the compression face of

concrete are presented in Table 2. The values obtained in this research and available in the

literature indicate that the ultimate concrete compressive strain value of AASHTO LRFD

Bridge Design Specification1 for normal-strength concrete which is 0.003 is acceptable for

high-strength concrete up to 20.0 ksi concrete cylinder strength.

The surface strain measurements for different loading stages of Specimen 18EB#2 are shown

in Figure 8. The graph proves the assumption that plane sections remain plane after

deformation is valid for high-strength concrete.

Figure 8 – Strain Distribution on Side Face of Specimen 18EB#2

The measurements of horizontal strain gage on the compression face were used to obtain the

Poisson’s Ratio for high strength concrete. The calculated values of Poisson’s Ratio for all

target concrete strength specimens are illustrated in Figure 9. The graph is extended for

concrete compressive strains up to 1400 µε after which, the effect of micro-cracks in the

concrete matrix leads to higher Poisson’s Ratio’s than the actual. The figure indicates that the

Poisson’s Ratio is between 0.20 and 0.26 for high-strength concrete. There is no apparent

trend for Poisson’s Ratio as concrete strength increases.

0

1000

2000

3000

Concrete

Strain

(µε)

Strain Gages Compression

Face

Neutral

Face Center line

of the test

region

3 in. 3 in. 3 in.


10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 200 400 600 800 1000 1200 1400

Average Compressive Face Strain (µεµεµεµε)

Po

iss

on

's R

ati

o

10EB#310EB#414EB#114EB#214EB#314EB#414EB#514EB#618EB#118EB#218EB#318EB#418EB#518EB#6

Figure 9 – Poisson’s Ratio for Test Specimens

STRESS BLOCK PARAMETERS

The approach presented by Hognestad et al.2 was used to determine the stress-strain

relationship for each specimen. This approach can be used to calculate the concrete stress cf

as a function of measured strain at the most compressed fiber cε and the applied stresses of

and om . The following equations were obtained from equilibrium of external and internal

loads and moments. Note that, the eccentricities due to deflection of the member were also

considered in the calculation of applied moment, M .

( )∫==+=c

xx

c

o dbc

bcfPPC

ε

εεσε

0

21 Equation 1

( )2

2

1 1 2 2 2

0

c

o x x x

c

bcM Pa P a m bc d

ε

σ ε ε εε

= + = = ∫ Equation 2

where, C is the total applied load, M is the total applied moment, 1P is the main axial load,

2P is the secondary load, 1a and 2a are the eccentricities with respect to the neutral surface,

b is the width of the section, c is the depth of neutral axis,

bc

PPfo

21 += Equation 3


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and

2

2211

bc

aPaPmo

+= Equation 4

are the applied stresses. Some of these definitions are illustrated in Figure 10.

Figure 10 – Eccentric Bracket Specimen

Differentiating the last terms of the equations for C and M with respect to c

ε would yield

the following equations.

o

c

o

cc fd

df+=

εεσ Equation 5

o

c

o

cc md

dm2+=

εεσ Equation 6

Using these equations, two similar stress-strain relationships were obtained for each eccentric

bracket specimen and the average of these two was used as the stress-strain relationship of

the specimen. These stress-strain relationships were used to calculate the stress block

parameters for high-strength concrete.

A generalized (actual) stress block is defined by three parameters, 1k , 2k and 3k . The

parameter 1k is defined as the ratio of the average compressive stress to the maximum

compressive stress. The parameter 2k is the ratio of the depth of the resultant compressive

force to the depth of neutral axis. The parameter 3k is the ratio of the maximum compressive


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stress ( maxσ ) to the compressive strength of concrete cylinder ( cf ' ). The design values of the

stress block parameters are determined at the ultimate strain ( cuε ), which corresponds to the

maximum moment of the section. These parameters are shown in Figure 11.

Figure 11 – Stress Block Parameters for Rectangular Sections

The 3k , 31kk , and 2k value can be obtained from the equilibrium of the external and internal

forces, as follows:

cfk

'

max3

σ= Equation 7

bcfkkC c'31= → bcf

Ckk

c'31 = Equation 8

( )ckdbcfkkM c 231 ' −= → ( )cC

Mk −= 12 Equation 9

The three-parameter generalized stress block can be reduced to a two-parameter equivalent

rectangular stress block, by keeping the resultant of the compression force at the mid-depth

of the assumed rectangular stress block. The two parameters of 1α and 1β are presented in

Figure 11 and can be defined as:

bcfC c'11βα= Equation 10

−=

2' 1

11

cdbcfM c

ββα Equation 11

where

2

31

12k

kk=α Equation 12

21 2k=β Equation 13

c

b εcu k3f’c

k2c

C = k1k3f’cbc

d

As

Section

Strain

Distribution

Generalized

Stress Block

Parameters

α1f’c

β1c

β1c/2

C = α1β1f’cbc

Rectangular

Stress Block

Parameters


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These stress block parameters were calculated for each specimen by using the above

equations. The results are presented in Table 3.

Table 3 – Generalized and Rectangular Stress Block Parameters for Test Specimens

Specimen 'c

f (ksi) 1k 2k 3k 1α 1β

10EB#1 11.0 0.65 0.38 1.03 0.90 0.75

10EB#2 11.4 0.62 0.36 1.12 0.95 0.72

10EB#3 11.7 0.65 0.36 1.14 1.02 0.73

14EB#1 14.6 0.63 0.37 1.00 0.85 0.74

14EB#2 14.3 0.60 0.36 1.08 0.85 0.72

14EB#3 14.7 0.61 0.36 1.09 0.93 0.71

14EB#4 15.0 0.58 0.35 1.10 0.92 0.70

14EB#5 15.4 0.57 0.34 1.10 0.92 0.68

14EB#6 15.2 0.60 0.35 1.06 0.91 0.69

18EB#1 15.8 0.69 0.38 0.82 0.74 0.77

18EB#2 16.0 0.67 0.37 0.85 0.77 0.74

18EB#3 15.6 0.63 0.37 0.81 0.69 0.73

18EB#4 15.8 0.65 0.36 0.88 0.78 0.73

18EB#5 16.0 0.65 0.36 0.85 0.76 0.72

18EB#6 15.5 0.66 0.37 0.88 0.78 0.74

The calculated values for 1 3k k and 2k is compared with available data in the literature in

Figure 12 and Figure 13. These graphs also include the derived 1 3k k and 2k values from the

equations in the codes. Note that the upper bound for 2k is 0.5 , when the stress-strain

relationship of the concrete is rectangular and the lower bound for 2k is 0.33 , when the

stress-strain relationship of the concrete is triangular. The data in the literature consisted of

the tests performed by Hognestad et al.2, Nedderman

4, Kaar et al.

5, Swartz et al.

6, Schade

7,

Ibrahim and MacGregor8 and Tan and Nguyen

9. The equations in the codes used in the

comparison of the test data consisted of AASHTO LRFD Bridge Design Specification1, ACI

318-0510

, ACI 44111

, NZS 310112

, CSA A23.313

, CEB-FIB14

. The calculated values for 1α

and 1β are compared with both available data in the literature and the equations in the codes

in Figure 14 and Figure 15.


14

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Concrete Strength (ksi)

k1k

3

10EB#210EB#310EB#414EB#114EB#214EB#314EB#414EB#514EB#618EB#118EB#218EB#318EB#418EB#518EB#6Other Tests

CEB-FIB

NZS

LRFD - ACI

CSA

ACI 441

Figure 12 – 1 3k k vs. '

cf for Eccentric Bracket Specimens

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16 18 20


k2

10EB#210EB#310EB#414EB#114EB#214EB#314EB#414EB#514EB#618EB#118EB#218EB#318EB#418EB#518EB#6Other Tests

CEB-FIB

NZS

LRFD - ACI 318

CSA

ACI 441

Figure 13 – 2k vs. '

cf for Eccentric Bracket Specimens


15

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0


αα αα1

CEB-FIB

NZS

LRFD - ACI 318

CSA

ACI 441

x Other Tests

♦ NCHRP 12-64 (2005)

Figure 14 – 1α Relationship for Design Codes

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0


ββ ββ1

CEB-FIB

NZS

LRFD - ACI 318

CSA

ACI 441

x Other Tests

♦ NCHRP 12-64 (2005)

Figure 15 – 1β Relationship for Design Codes


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The graph for 1α indicates that as concrete strength exceeds 10.0 ksi, 1α tends to decrease

slightly. The current equation for 1α ( 1 0.85α = for all concrete strengths) specified by

AASHTO LRFD Bridge Design Specifications1

appears to overestimate the value of 1α for

high-strength concrete. An equation that represents the lower bound of the experimental data

such as that of CSA A23.313

would seem more appropriate for high-strength concrete up to

20.0 ksi.

The data for 1β obtained in this research are consistent with the data reported in the

literature. The current equation for 1β ( 1 0.65β = for ' 8c

f ksi> ) specified by AASHTO

LRFD Bridge Design Specifications1 represents well the lower bound value and should be

applicable for high-strength concrete up to 20.0 ksi.

SUMMARY AND CONCLUSION

A total of 15 unreinforced high-strength concrete columns were tested under eccentric

compression to simulate the compression zone of a flexural member by varying the axial load

and the moment at the section. The dimensions of the specimens were 9x9x40 in. and the

cylinder strength of concrete ranged from 10.0 to 16.0 ksi. The concept developed by

Hognestad et al. was adopted to accommodate largest possible specimen size. The

deflections, the strain on concrete surface, axial load and moment were monitored. Stress-

strain curves, ultimate concrete compressive strain and Poisson’s Ratio were obtained for

high strength concrete. Based on the test results and the data reported in the literature up to

20.0 ksi:

1. The ultimate concrete compressive strain value of 0.003 specified by AASHTO LRFD

Bridge Design Specifications1 is acceptable for high-strength concrete up to 20.0 ksi

cylinder concrete strength.

2. The assumption of plane sections remain plane after deformation is valid for high

strength concrete.

3. Poisson’s Ratio is between 0.20 and 0.26 for high-strength concrete. There is no apparent

trend for Poisson’s Ratio as concrete strength increases.

4. As concrete strength increases, 1α decreases. The current equation for 1α ( 1 0.85α = for

all concrete strengths) specified by AASHTO LRFD Bridge Design Specifications1 needs

to be modified to show a reduction of 1α for high-strength concrete up to 20.0 ksi


5. The current equation for 1β ( 1 0.65β = for ' 8c

f ksi> ) specified by AASHTO LRFD

Bridge Design Specifications1 is appropriate for high-strength concrete up to 20.0 ksi



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ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of the NCHRP through the project 12-64

and the Senior Program Officer, David Beal. The authors also thank the contributions of

Henry Russell of Henry Russell, Inc. and Robert Mast of Berger/ABAM Engineers, Inc. who

serve as consultants on the project. The findings and the conclusion reported here are of a

preliminary nature and are those of the authors alone, and not of the supporting agency. This

project would not be possible without the contribution of Ready Mixed Concrete Company

and the personnel of the Constructed Facilities Laboratory. The efforts by the graduate

assistants, Andrew Logan, SungJoong Kim, Zhenhua Wu and WonChang Choi are also

greatly appreciated.

REFERENCES

1. AASHTO LRFD Bridge Design Specifications, Third Edition, American Association of

State Highway and Transportation Officials, Washington DC, 2004.

2. Hognestad, E., Hanson, N. W. and McHenry, D., “Concrete Stress Distribution in

Ultimate Strength Design”, ACI Journal, Vol. 52, No. 4, Dec. 1955, pp. 455-479.

3. Logan, A. T., “Short-Term Material Properties of High-Strength Concrete”, M.S. Thesis,

Department of Civil, Construction and Environmental Engineering, North Carolina State

University, Raleigh, NC, Jun. 2005, 116 p.

4. Nedderman, H., "Flexural Stress Distribution in Very-High Strength concrete”, M.S.

Thesis, Civil Engineering Department, University of Texas at Arlington, Dec. 1973, 182

p.

5. Kaar, P. H., Hanson, N. W. and Capell, H. T., “Stress-Strain Characteristics of High

Strength Concrete”, ACI Special Publication-55, Douglas McHenry International

Symposium on Concrete and Concrete Structures, Michigan, Aug. 1978, pp. 161-185.

6. Swartz, S. E., Nikaeen, A., Narayan Babu, H. D., Periyakaruppan, N. and Refai, T. M. E.,

“Structural Bending Properties of Higher Strength Concrete”, ACI Special Publication-

87, High-Strength Concrete, Sept. 1985, pp. 145-178.

7. Schade, J. E., “Flexural Concrete Stress in High Strength Concrete Columns”, M. S.

Thesis, Civil Engineering Department, the University of Calgary, Calgary, Alberta,

Canada, Sept. 1992, 156 p.

8. Ibrahim, H. H. H. and MacGregor, G., “Modification of the ACI Rectangular Stress

Block for High-Strength Concrete”, ACI Structural Journal, Vol. 94, No. 1, Jan.-Feb.

1997, pp. 40-48.

9. Tan, T.H., Nguyen, N. B., “Flexural Behavior of Confined High Strength Concrete

Columns”, ACI Structural Journal, Vol. 102, No. 2, Mar.-Apr. 2005, pp. 198-205.

10. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05)

and Commentary (318R-05)”, American Concrete Institute, Farmington Hills, MI, 2005,

430 p.

11. ACI Committee 441, “High Strength Concrete Columns: State of the Art (ACI 441R-

96)”, American Concrete Institute, Detroit, 1996, 13 p.

12. New Zealand Concrete Structures Standards (NZS 3101), New Zealand Standards, 1995.


18

13. Canadian Standards Association, “Design of Concrete Structures, CSA A23.3 1994”,

Rexdale, Ontario, 1994, pp.199.

14. CEB-FIB Model Code 1990, Thomas Telford Services Ltd., London, for Comité Euro-

International du Béton, Laussane, 1993, 437 p.

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