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Publication Number: FHWA-HRT-13-061
Date: June 2013

 

Lightweight Concrete: Mechanical Properties

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FHWA Publication No. of this TechBrief: FHWA-HRT-13-061
FHWA Contact: Ben Graybeal, HRDI-40, (202) 493-3122, benjamin.graybeal@dot.gov.

 

This document is a technical summary of the Federal Highway Administration report, Lightweight Concrete: Mechanical Properties (FHWA-HRT-13-062), available through the National Technical Information Service at www.ntis.gov.(1)

NTIS Accession No. of the report covered in this TechBrief: PB2013-107688

 

Objective

There is a limited amount of test data on the mechanical properties of high-strength lightweight concrete (LWC) with a concrete unit weight (wc) between that of traditional LWC and normal weight concrete (NWC). Concrete with a wc in this range is also not covered in the American Association of State Highway and Traffic Officials (AASHTO) Load-and-Resistance Factor Design (LRFD) Bridge Design Specifications. (2) This research program includes a significant number of mechanical property tests on this type of concrete. The results from this research project are included into a LWC database that covers a range of wc to determine trends for LWC as a function of wc. New design expressions for mechanical properties are proposed for LWC as a function of wc as opposed to the more common method of using concrete constituent materials. The design expressions represent potential revisions to the AASHTO LRFD Bridge Design Specifications relating to the mechanical properties of LWC. (2)

Introduction

Much of the fundamental basis for the current LWC provisions in the AASHTO LRFD Bridge Design Specifications is built on research of LWC from the 1960s. (See references 2–6.) The LWC that was part of this research used traditional mixes of coarse aggregate, fine aggregate, portland cement, and water. Broad-based advancement in concrete technology over the past 50 years has led to significant advancements in concrete mechanical and durability performance. Research during the past 30 years, including the recent National Cooperative Highway Research Program (NCHRP) studies on different aspects of high-strength concrete, has resulted in revisions to the AASHTO LRFD Bridge Design Specifications to capitalize on the benefits of high-strength NWC. However, as described by Russell, many of the design equations in the AASHTO LRFD Bridge Design Specifications are based on data that do not include tests of LWC specimens, particularly with regard to structural members with compressive strengths in excess of 6 ksi (41 MPa). (7)

The Federal Highway Administration's (FHWA) Turner-Fairbank Highway Research Center (TFHRC) has executed a research program investigating the performance of LWC with concrete compressive strengths in the range of 6 to 10 ksi (41 to 69 MPa) and equilibrium densities between 0.125 and 0.135 kcf (2,000 and 2,160 kg/m3). The research program used LWC with three different lightweight aggregates that were intended to be representative of those available in North America. The program included tests from 27 precast/prestressed LWC girders to investigate topics including transfer length and development length of prestressing strand, time-dependent prestress losses, and shear strength of LWC. The development and splice length of mild steel reinforcement used in girders and decks made with LWC was also investigated using 40 reinforced concrete (RC) beams. While much of the research program focused on structural behavior, it also included a material characterization component wherein the compressive strength, elastic modulus (Ec), and splitting tensile strength (fct) of the concrete mixes used in the structural testing program were assessed. One key outcome of the research program is to recommend changes to the AASHTO LRFD Bridge Design Specifications; relevant to LWC. (2)

This TechBrief summarizes the results of mechanical property testing that was conducted as part of the prestressed girder and RC beam testing. The mechanical properties of LWC tested in this study are included in a database of mechanical property tests on LWC that was collected from test results available in the literature. This TechBrief also summarizes the LWC database and the analysis of mechanical properties in the database. Design expressions in the current edition of the AASHTO LRFD Bridge Design Specifications are compared to the database. (2) Potential revisions to the AASHTO LRFD Bridge Design Specifications relating to LWC are also presented.

LWC Mix Designs

The Expanded Shale, Clay, and Slate Institute assisted FHWA in obtaining LWC mixes that had been used in production. One of the criteria for this research project was to use lightweight aggregate sources that were geographically distributed across the United States. Additional selection criteria included mixes using a large percentage of the coarse aggregate as lightweight coarse aggregate, mixes using natural sand as the fine aggregate, and mixes with a target equilibrium density between 0.125 and 0.135 kcf (2,000 and 2,160 kg/m3). The concrete density needed to be in the range of densities not currently covered by the AASHTO LRFD Bridge Design Specifications. (2)

Three mix designs were selected with a design compressive strength greater than or equal to 6.0 ksi (41.4 MPa) to represent concrete that could be used for bridge girders. Another mix design was selected that had a design compressive strength less than 6.0 ksi (41.4 MPa) to represent concrete that could be used for a bridge deck. The selected mix designs are shown in table 1. Each uses partial replacement of the coarse aggregate with lightweight aggregate to achieve their reduced wc. The lightweight aggregates in the mixes were Haydite (an expanded shale from Ohio), Stalite (an expanded slate from North Carolina), and Utelite (an expanded shale from Utah). The normal weight coarse aggregate was No. 67 Nova Scotia granite. Natural river sand was used as the fine aggregate. Type III portland cement was used to obtain the high early strengths typically required in high-strength precast girders. Admixtures included a water reducer, an air entrainer, and a high-range water reducer.

Table 1. Selected concrete mix designs.

Cast Date

Haydite Girder (HG)

Stalite Girder (SG)

Utelite Girder (UG)

Stalite Deck (SD)

Design 28-day strength (ksi)

6.0

10.0

7.0

4.0

Design release strength (ksi)

3.5

7.5

4.2

Target wc (kcf)

0.130

0.126

0.126

0.125

Water/cementitious materials ratio

0.36

0.31

0.34

0.43

— Indicates release strength not necessary for nonprestressed elements.
1 ksi = 6.89 MPa
0.001 kcf = 16.01 kg/m3

Specimen Fabrication and Testing

The girders were fabricated at a concrete precasting plant in Mobile, AL. The fabricator was asked to prescriptively produce the concrete mixes without trying to adjust them for target strengths or wc. This was intended to remove batch-to-batch variations as a variable in the study. The lightweight aggregates were stored in three piles at the plant and watered continuously using a sprinkler on each pile as shown in figure 1.

Figure 1. Photo. Lightweight aggregate stockpiles with continuous sprinklers. This photo shows three separate piles of lightweight aggregate. A small garden sprinkler on top of each aggregate pile is spraying water into the air above each pile.
Figure 1. Photo. Lightweight aggregate stockpiles with continuous sprinklers.

Compression tests were performed on 4- by 8-inch (102- by 203-mm) and 6- by 12-inch (152- by 305-mm) cylinders to determine the compressive strength at release of prestressing, at 28 days, and at girder testing. Ec was determined using one of the 4- by 8-inch (102- by 203-mm) cylinders intended for compressive strength testing. The indirect tensile strength was measured on 4- by 8-inch (102- by 203-mm) cylinders using the fct test. Density measurements were made to determine the air-dry density of cylinders used for compression testing. They were also conducted on separate cylinders to determine the oven-dry density and equilibrium density. Average compressive strength, Ec, fct, and air-dry wc for each concrete mix are provided in table 2

Table 2. Mean concrete properties from tests on 4- by 8-inch (102- by 203-mm) cylinders.

Concrete Mix

Specimen Age

Compressive
Strength
(ksi)

Air-Dry Density

(kcf)

fct

(ksi)

Ec

(ksi)

HG

Release

7.07

0.133

0.607

3,840

28 days

9.50

0.132

0.714

4,470

Test day

10.45

0.130

0.771

4,320

SG

Release

7.32

0.125

0.604

3,770

28 days

9.66

0.125

0.680

4,140

Test day

10.56

0.123

0.717

4,360

UG

Release

6.04

0.131

0.569

3,500

28 days

8.68

0.130

0.685

4,110

Test day

10.10

0.127

0.757

4,150

SD*

28 days

5.67

0.138

Test day

7.59

0.137

*Release strength not necessary for nonprestressed elements.
— Indicates no value was recorded.
1 ksi = 6.89 MPa
 0.001 kcf = 16.01 kg/m3

Summary of Specimen Test results

The LWC test results were compared to design expressions for a lightweight modification factor and for Ec. Nearly all fct tests on all three girder mixes gave splitting ratios that were greater than the splitting ratio requiring modification of LWC for shear and development length of mild steel in tension in the AASHTO LRFD Bridge Design Specifications.(2) On average, Ec was overestimated by the AASHTO LRFD expression and underestimated by the NCHRP 12-64 expression and the ACI 363-10 expression.(2,8,9)

TFHRC LWC Database

A thorough literature review was performed to find published journal papers, conference papers, technical reports, and university dissertations that included tests, analyses, and discussions of LWC. Over 500 references were found that mentioned LWC. These documents were reviewed for LWC data consisting of a compressive strength value and data from at least one other mechanical test. The citations for the reviewed documents are provided in the full report.(1) The recorded mechanical tests included compressive strength, Ec, fct test, modulus of rupture (fr), and Poisson's ratio. The concrete density was also recorded. Unpublished test data, data in graphs, and NWC test data were not included in the database.

The TFHRC LWC database consists of 3,835 data lines. These data were collected from 128 publications. Data lines were selected for evaluating material properties based on the presence of available data and on being within a range of material property values. A full list of references for the TFHRC LWC database and more information about the data selection criteria is included in the full report.(1)

Design Expressions For Ec

A total of 2,556 data lines are in the TFHRC subset database for Ec. To compare design expressions for Ec to both NWC and LWC data, the Ec database from NCHRP Project 12-64 was utilized.(8) The NWC and LWC data contain lines of compressive strength, Ec, and wc.(8) For this evaluation, test data from concrete with a wc greater than or equal to 0.135 kcf (2,160 kg/m3) (i.e., NWC data) from the NCHRP 12 64 database was combined with test data from concrete with a wc less than 0.135 kcf (2,160 kg/m3) (i.e., LWC data) from the TFHRC database.

The Ec data were compared to three designs expressions: (1) the expression in the AASHTO LRFD Bridge Design Specifications, (2) the expression in the NCHRP Project 12 64 final report, and (3) the expression in the ACI Committee 363 report on high-strength concrete. (2,8,9) The ratio of the tested Ec to the predicted Ec by the three design expressions is provided in table 3. A test-to-prediction ratio greater than unity indicates an underestimation of Ec, while a ratio less than unity indicates an overestimation of Ec. The mean test-to-prediction ratios in table 3 show that the AASHTO LRFD expression overestimates Ec of LWC, and the NCHRP 12-64 expression underestimates Ec of LWC. The ACI 363-10 expression closely predicts Ec of LWC but underestimates Ec of NWC. The test-to-prediction ratios using the AASHTO LRFD expression is compared to compressive strength in figure 2. This figure shows that the AASHTO LRFD expression tends to overestimate Ec at higher compressive strength levels for both NWC and LWC.

Table 3. Mean test-to-prediction ratio of Ec for LWC data from the TFHRC database and NWC data from the NCHRP 12-64 database.

Data Source

AASHTO
LRFD(2)

NCHRP
12-64(8)

ACI 363(9)

Proposed

TFHRC LWC and NCHRP NWC

0.957

1.087

1.056

1.000

TFHRC LWC

0.936

1.206

1.001

1.019

NCHRP NWC

0.972

1.007

1.094

0.987

 

Figure 2. Graph. Ec Test-to-prediction ratio compared to compressive strength for AASHTO LRFD equation. This scatter plot shows the test-to-predicted modulus of elasticity (E subscript c) plotted versus concrete compressive strength for the American Association of State Highway and Transportation Officials (AASHTO) Load-and-Resistance Factor Design (LRFD) equation. The y-axis shows test-to-predicted modulus of elasticity from 0.2 to 1.8, and the x-axis shows the compressive strength from 0 to 25 ksi (0 to 172.4 MPa). The plot includes 2,556 lightweight concrete (LWC) data points and 3,795 normal weight concrete (NWC) data points. The mean test-to-prediction ratio for the LWC data is 0.94, indicating a trend of overestimating the modulus of elasticity. The mean test-to-prediction ratio for the NWC data is 0.97, indicating a trend of slight overestimating the modulus of elasticity. Modulus of elasticity is overestimated for most of the NWC data, with a compressive strength greater than 15 ksi (103 MPa).
1 ksi = 6.89 MPa

Figure 2. Graph. Ec Test-to-prediction ratio compared to compressive strength for AASHTO LRFD equation.

Optimization of Ec Equation Variables

An analysis was performed to evaluate the effect of different exponents on the basic form of the expression for Ec. The analysis was performed on a database consisting of the TFHRC LWC subset database combined with the NCHRP 12-64 NWC database.(1,8) The analysis was divided into three parts. In the first part, the exponent applied to the wc term was varied and showed that an exponent of 1.5 or 2.0 applied to wc resulted in the lowest coefficient of variation (COV) and a test-to-prediction ratio near unity for the LWC data. In the second part, the exponent applied to the compressive strength term was varied and showed that the exponent applied to compressive strength should be 0.33 or 0.5 for a low COV without considerable overestimation of Ec for LWC data. The third part was to vary the exponents applied to both wc and compressive strength. A new proposed expression with an exponent of 2.0 for wc and 0.33 for compressive strength was evaluated and had the lowest COV of the four expressions evaluated in the third part of the analysis. The proposed expression slightly underestimated the prediction of Ec for LWC and gave a close prediction of Ec for NWC.

LWC Modification Factor

The AASHTO LRFD Bridge Design Specifications account for the reduced tensile strength of LWC in a variety of ways.(2) Article 5.8.2.2 of the report gives a modification for LWC that is applicable to the articles of the specifications involving sectional analysis of nominal shear resistance.(2) In this article, a 0.75 factor is used for all-lightweight concrete, and a 0.85 factor is used for sand-lightweight concrete. The article allows interpolation between the two factors for partial sand replacement. Article 5.11.2.1.2 describing the development length of mild reinforcement in tension also includes modification factors all-lightweight concrete and sand-lightweight concrete and allows for interpolation to be used with partial sand replacement.(2) Unfortunately, the amount of sand replacement is rarely known during the design phase of a project. Also, a definition based on the proportions of constituent materials becomes more cumbersome if partial replacement of normal weight coarse aggregate with lightweight coarse aggregate is also considered. A lightweight modification factor based on a specified mix property, such as concrete density, may be preferable.

Prediction of the Splitting Ratio

The ratio of fct to the square root of the compressive strength is known as the splitting ratio, Fsp. Early references to Fsp was made by Hanson and ACI Committee 318.(4,10) The term "splitting ratio" is no longer used in the AASHTO LRFD Bridge Design Specifications, but the definition is still a part of the modification factor for LWC in Articles 5.8.2.2 and 5.11.2.1.2.(2) Concrete with a Fsp greater than 0.212 does not require modification of the expressions in Articles 5.8.2 and 5.8.3 for LWC. Fsp implied by the AASHTO LRFD Bridge Design Specifications for sand-lightweight concrete and all-lightweight concrete are based on the 0.85 and 0.75 modification factors described in Article 5.8.2.

The fct subset of the TFHRC LWC database was used to evaluate the expression for Fsp implied by the AASHTO LRFD Bridge Design Specifications.(2) The database includes 954 lines of sand-lightweight and 311 lines of all-lightweight concrete. The test-to-prediction ratios for the sand-lightweight and all-lightweight AASHTO LRFD expressions for Fsp are given in table 4. A test-to-prediction ratio greater than unity is an overestimation of the splitting ratio and indicates a conservative prediction of concrete tensile strength when used for calculating nominal shear resistance or development length of mild reinforcement. The AASHTO LRFD expression gave conservative predictions of concrete tensile strength for most of the data.

Table 4. Test-to-prediction ratios of Fsp using the AASHTO LRFD expression and proposed expression.

LWC

Fsp Expression

Total

wc
0.090 kcf

0.090
< wc ≤ 0.100 kcf

0.100
< wc ≤ 0.110 kcf

0.110
< wc ≤ 0.120 kcf

0.120
< wc ≤ 0.135 kcf

Sand-lightweight

AASHTO LRFD

1.222

1.011

0.920

0.992

1.181

1.279

Proposed

1.150

1.138

1.036

1.061

1.137

1.169

All-lightweight

AASHTO LRFD

1.129

0.991

1.143

1.094

1.190

1.188

Proposed

1.078

0.984

1.135

1.034

1.050

0.956

0.001 kcf = 16.01 kg/m3

Linear Expressions for Fsp Using wc

An expression for predicting Fsp as a function of wc was developed. This section describes this piecewise continuous function for predicting Fsp. Other types of expressions for Fsp are evaluated in the full report. (1) The expression consists of a constant predicted Fsp of 0.159 for wc = 0.100 kcf (1,600 kg/m3). The prediction then assumes a linearly increasing Fsp with wc to a limit on wc of 0.135 kcf (2,160 kg/mM3). For wc = 0.135 kcf (2,160 kg/m3), a constant predicted value of 0.212 for Fsp is used since this aligns with the existing provisions for NWC. A lower limit of 0.159 on Fsp is used because this value is specified in Article 5.8.2.2 as Fsp for all-lightweight concrete (0.75 x 0.212).(2) The test-to-prediction ratios for the proposed expression are shown in figure 3.

Figure 3. Graph. Test-to-prediction ratios of <em>F<sub>sp</sub></em> predicted by the proposed expression. This scatter plot shows the test-to-predicted splitting ratio (F subscript sp) versus unit weight. The y-axis shows the test-to-predicated splitting ratio from 0.20 to 1.80, and the x-axis shows the unit weight from 0.06 to 0.14 kcf (0.96 to 2.24 kg/m3 × 103). The plot includes 1,332 lightweight concrete data points that have an average test-to-prediction ratio of 1.15, indicating a slight underestimation of the splitting ratio.  A total of 76 percent of the data have a unit weight that is between 0.110 and 0.135 kcf (1,790 and 2,160 kg/m3).
0.001 kcf = 16.01 kg/m3

Figure 3. Graph. Test-to-prediction ratios of Fsp predicted by the proposed expression.

The proposed expression gave a larger predicted fct than the expression in the AASHTO LRFD Bridge Design Specifications for sand-lightweight concrete with a wc up to 0.110 kcf (1,760 kg/m3). (2) For larger unit weights, the AASHTO LRFD expression gave a very conservative prediction of fct.

The proposed expression for Fsp can be converted to LWC modification factor by dividing it by 0.212, the upper limit on Fsp. The term λ-factor is used to refer to a LWC modification factor.

Modulus of Rupture

The accuracy of the fr expression is important for the strength, serviceability, and ductility of structural concrete bridges. The AASHTO LRFD Bridge Design Specifications have different expressions for fr depending on the use of the calculation and the type of concrete. (2) For normal weight concrete, one expression for fr is used to calculate the nominal shear resistance provided by concrete when inclined cracking results from combined shear and moment (Vci) (Article 5.8.3.4.3), and another expression for fr is used for all other calculations such as effective moment of inertia, cracking control, and minimum flexural reinforcement.(2) For LWC, there are two different expressions for fr depending on the use of sand-lightweight concrete or all-lightweight concrete. Unlike NWC, the AASHTO LRFD Bridge Design Specifications do not give different expressions for fr of LWC depending on the use of the concrete.(2) This creates varying levels of conservatism in the calculations of cracking control, effective moment of inertia, and cracking moment for Vci when used for members made from LWC.

Comparison of fr to fct

In this section, fr is compared to the fct in order to justify defining the material property fr in terms of another material property fct (through the λ-factor).

For this comparison, a new subset database was created for concrete mixes with test results in both the fct subset database and a wet fr subset database. An alternate wet fr subset database was created to include only specimens that remained wet until tested due to the reduction in the tested fr of specimens allowed to dry. A comparison of fr and fct is shown in figure 4. The figure shows fr increasing proportional to fct, which supports the observations of previous research on a limited number of data points. (4)

Figure 4 scatter plot graph. This scatter plot shows the modulus of rupture (fr) versus splitting tensile strength (fct) for 134 lightweight concrete data points with American Association of State Highway and Transportation Officials (AASHTO) Load-and-Resistance Factor Design (LRFD) expression and linear regression. The data points are separated into five ranges by unit weight. Modulus of rupture is on the y-axis from 0 to 1.2 ksi (1 to 8.3 MPa), and splitting tensile strength is on the x-axis from 0 to 1.2 ksi (1 to 8.3 MPa). The ratio of modulus of rupture to splitting tensile strength implied by the AASHTO LRFD specifications is 1.13, and a line representing this relationship is shown. Nearly all of the lightweight data points are above this line. Another line, representing a linear regression of the data, is also shown. The linear regression has a ratio of modulus of rupture to splitting tensile strength of 1.34, which is 19 percent greater than the relationship implied by the AASHTO LRFD specifications.
1 ksi = 6.89 MPa
Figure 4. Graph. fr compared to fct with AASHTO LRFD expression and linear regression.

Proposed Design Expression for ƒr

A new expression for fr was proposed that includes the LWC modification factor (λ-factor). The proposed expression for fr is applicable to the calculation of the effective moment of inertia, cracking control requirements, and minimum area of flexural reinforcement.

The ratio of the tested fr from the wet fr subset database to the fr predicted by the AASHTO LRFD expressions and proposed expression is given in table 5. Both the proposed expression and the AASHTO LRFD expression gave predictions of fr that were larger than the tested values.

Table 5. Test-to-prediction ratios of fr using the AASHTO LRFD expression and proposed expression.

LWC

fr
Expression

Total

wc
0.090 kcf

0.090
< wc ≤ 0.100 kcf

0.100
< wc ≤ 0.110 kcf

0.110
< wc ≤ 0.120 kcf

0.120
< wc ≤ 0.135 kcf

Sand-lightweight

AASHTO LRFD

1.394

1.277

1.222

1.344

1.415

1.414

Proposed

1.299

1.419

1.357

1.412

1.351

1.227

All-lightweight

AASHTO LRFD

1.571

1.328

1.664

1.538

1.498

1.901

Proposed

1.409

1.254

1.571

1.387

1.253

1.428

0.001 kcf = 16.01 kg/m3

Preliminary Recommendations

A set of preliminary recommended changes to the AASHTO LRFD Bridge Design Specifications were developed in this research effort.(2) This TechBrief has only considered the analysis of tests on the mechanical properties of LWC. Additional analysis on the structural performance of LWC members is needed before final recommendations can be made. The areas needing additional analysis include the development of mild reinforcement in tension, the transfer and development length of prestressing strands, and the shear resistance of reinforced and prestressed members. The effects of the preliminary recommendations will be included in those further analyses.

The analysis of the TFHRC LWC database using the subset database for Ec and the subset database for fct has resulted in several new expressions for Ec, an LWC modification factor (λ-factor), and fr. The new expressions are not based on the proportions of constituent materials and include tests from types of mix designs that are not explicitly permitted by the current edition of the AASHTO LRFD Bridge Design Specifications.(2) These mix types include specified density LWC (typically a blend of lightweight and normal weight coarse aggregate) and inverted mixes (normal weight coarse and lightweight fine aggregate). The new expressions are instead based on wc and as a result the definitions of sand-lightweight concrete and all-lightweight concrete would no longer be needed. This section proposes a revised definition of LWC that does not include the terms sand-lightweight concrete or all-lightweight concrete.

Proposed Definition for LWC

The definition for LWC in Article 5.2 of the AASHTO LRFD Bridge Design Specifications limits wc for LWC to 0.120 kcf (1,920 kg/m3) and includes definitions for sand-lightweight and all-lightweight concrete.(2) The proposed definition for LWC expands the range of wc and eliminates the definitions for terms relating to the constituent materials in LWC. The proposed definition for LWC is as follows: concrete containing lightweight aggregate and having an equilibrium density not exceeding 0.135 kcf (2,160 kg/m3), as determined by ASTM C567. (11)

The term "air-dry unit weight" is used in the current definitions; however, this term is not found in ASTM C567.(11) The AASHTO LRFD Bridge Design Specifications term "air-dry unit weight" is interpreted to be equivalent to the ASTM C567 term "equilibrium density." (2,11) A statement could be added to the commentary to clarify the term "air-dry unit weight" or the term "equilibrium density" could be used in the definition for LWC.

Proposed Expression for Ec

The proposed new expression for Ec would have the same limits on wc and specified compressive strength as the current expression in Article 5.4.2.4.(2) The only proposed change is the expression for Ec itself. The proposed expression for Ec is shown in figure 5.

According to the AASHTO LRFD Bridge Design Specifications, in the absence of measured data, Ec for concrete with unit weights between 0.090 and 0.155 kcf (1,440 and 2,480 kg/m3) and specified compressive strengths up to 15.0 ksi (103 MPa) may be taken as follows:(2)

Figure 5. Equation. Expression for Ec. E subscript c equals 120,000 times K subscript 1 times w subscript c raised to the power of 2.0 times f prime subscript c raised to the power of 0.33.
Figure 5. Equation. Expression for Ec

Where:

Ec = Modulus of elasticity in ksi.
K1 = Correction factor for source of aggregate.
wc = Concrete unit weight in kcf.
f 'c = Compressive strength in ksi.

Figure 6 shows the expression compared to the current AASHTO LRFD expression for an assumed wc of 0.110 kcf (1760 kg/m3) and K1 equal to unity.

Figure 6. Graph. Ec for proposed expression. This scatter plot shows the modulus of elasticity (E subscript c) versus concrete compressive strength for 2,556 lightweight concrete data points and 3,795 normal weight concrete data points. Modulus of elasticity is on the y-axis from 0 to 6 ksi × 103 (0 to 41.4 GPa), and compressive strength is on the x-axis from 0 to 16 ksi (1 to 110.3 MPa). The data points are separated into three ranges by unit weight. Curves representing the modulus of elasticity predicted by the American Association of State Highway and Transportation Officials Load-and-Resistance Factor Design expression and the proposed expression for an assumed concrete unit weight of 0.110 kcf (1,790 kg/m3) are shown.

1 ksi = 6.89 MPa

Figure 6. Graph. Ec for proposed expression.

Proposed Expression for LWC Modification Factor

The concept of including a modification factor for LWC in expressions for predicting nominal resistance is included in many articles of the AASHTO LRFD Bridge Design Specifications.(2) However, a single unified expression or LWC modification factor is not specified. This section proposes a term, the λ-factor, to quantify the modification in nominal resistance that could be included in any expression for nominal resistance. The λ-factor relates to the material properties of structural LWC so the new article for the definition for the λ-factor could be located in Article 5.4.2. (2)

Where lightweight aggregate concretes are used, the LWC modification factor, λ , shall be determined using the equation in figure 7 where fct is specified.

Figure 7 equation. 4.7 times f subscript ct divided by the square root of f prime subscript c is less than or equal to 1.0.
Figure 7. Equation. Expression for λ-factor with fct specified.

Where fct is not specified, λ shall be determined using the equation in figure 8.

Figure 8 equation. 0.75 is less than or equal to lambda equals 7.5 times w subscript c is less than or equal to 1.0.
Figure 8. Equation. Expression for λ-factor with fct not specified.

An illustration of the proposed expression for the λ-factor is shown in figure 9, and the predicted splitting ratios (λ-factor x 0.212) are shown in figure 10. The λ-factors implied in AASHTO LRFD for sand-lightweight concrete and all-lightweight concrete are also shown. Figure 10 shows that a considerable amount of sand-lightweight concrete data are not defined in the current AASHTO LRFD Bridge Design Specifications.(2)

Figure 9 illustration. This illustration shows the model for the proposed lambda-factor versus unit weight. The model has a constant value of 0.75 for the lambda-factor for unit weights less than 0.100 kcf (1,600 kg/m3). From a unit weight of 0.100 kcf (1,600 kg/m3) the lambda-factor increases linearly to 0.135 kcf (2,160 kg/m3) and a value of 1.0. The lambda-factor has a constant value of 1.0 for unit weights larger than 0.135 kcf (2,160 kg/m3).

0.001 kcf=16.01 kg/m3

Figure 9. Illustration. Proposed expression for λ -factor.

Figure 10 scatter plot graph. This scatter plot shows the  splitting ratio (f subscript ct divided by the square root of f prime subscript c) versus unit weight for 1,332 lightweight concrete (LWC) data points. The data points are separated into groups of sand-lightweight, all-lightweight, and other LWC. The proposed expression for the splitting ratio multiplied by 0.212 to convert it to a splitting ratio is shown. Splitting ratio is on the y-axis from 0 to 4.0 ksi (1 to 1.05 MPa), and unit weight is on the x-axis from 0.06 to 0.14 kcf (0.96 to 2.24 kg/m3 ×10 superscript 3). Vertical lines at unit weights of 0.120 and 0.135 kcf (1,920 and 2,160 kg/m3) represent the upper and lower boundaries of the unit weight gap in the American Association of State Highway and Transportation Officials (AASHTO) Load-and-Resistance Factor Design (LRFD) specifications. A considerable amount of the sand-lightweight concrete data are in the gap of unit weights not defined in the current AASHTO LRFD specifications. The figure shows that 79 percent of the sand-lightweight data and 63 percent of the all-lightweight data are above the proposed expression for splitting ratio.

1ksi=6.89 MPa
0.001 kcf=16.01kg/m3

Figure 10. Graph. Splitting ratio (fct / √f'c ) for the proposed expression ( λ-factor x 0.212).

As stated previously, the effect of using the λ-factor in expressions for nominal resistance needs to be evaluated. The proposed λ-factor could then be included in the expression for nominal resistance in the AASHTO LRFD Bridge Design Specifications.(2) For example, the λ-factor could be added directly to design expressions for nominal shear resistance in Articles 5.8.2 and 5.8.3 and would replace the existing modification factor for LWC.(2)

Proposed Expression for fr

The expression for fr in the AASHTO LRFD Bridge Design Specifications is in Article 5.4.2.6. (2) The proposed expression for fr is as follows for NWC and LWC:

Figure 11 equation. 0.24 times lambda times the square root of f prime subscript c.
Figure 11. Equation. Expression for fr except when used in Article 5.8.3.4.3. (2)

The proposed expression is as follows when used to calculate the cracking moment of a member in Article 5.8.3.4.3: (2)

Figure 12 equation. 0.20 times lambda times the square root of f prime subscript c.
Figure 12. Equation. Expression for fr when used in Article 5.8.3.4.3. (2)

The proposed expressions for fr include the proposed λ-factor and would be applicable to both NWC and LWC. The expression for fr used to calculate the cracking moment of a member in Article 5.8.3.4.3 (Vci) includes the proposed λ-factor for consistency. The fr expression for use with Article 5.8.3.4.3 will need to be validated on shear test data from LWC members available in the literature before it is proposed for inclusion into the AASHTO LRFD Bridge Design Specifications. (2)

The ratio of the predicted fr (see figure 11) to √f 'c is shown in figure 13 with sand-lightweight and all-lightweight concrete data. Figure 13 shows that most of the test data are above the predicted fr (i.e., underestimated) and that a considerable amount of the sand-lightweight concrete data are in the gap of wc not defined in the current AASHTO LRFD Bridge Design Specifications. (2)

Figure 13 scatter plot graph. This scatter plot shows the ratio of the modulus of rupture (f subscript r) divided by the square root of the concrete compressive strength (f prime subscript c) versus unit weight for 221 sand-lightweight concrete data points and 277 all-lightweight concrete data points. The proposed expression for modulus of rupture is shown. The ratio of modulus of rupture divided by the square root of the concrete compressive strength is on the y-axis from 0 to 0.50 ksi (0 to 1.31 MPa), and unit weight is on the x-axis from 0.06 to 0.14 kcf (0.96 to 2.24 kg/m3 ×103). Horizontal lines represent the ratios in the American Association of State Highway and Transportation Officials (AASHTO) Load-and-Resistance Factor Design (LRFD) specifications of 0.24 for normal weight concrete, 0.20 for sand-lightweight concrete, and 0.17 for all-lightweight concrete. Vertical lines at unit weights of 0.120 and 0.135 kcf (1,920 and 2,160 kg/m3) represent the upper and lower boundaries of the unit weight gap in the AASHTO LRFD specifications. The figure shows that 95 percent of the sand-lightweight data and 98 percent of the all-lightweight data are above the proposed expression for modulus of rupture.

1 ksi=6.89 MPa
0.001 kcf=16.01 kg/m3

Figure 13. Graph fr / √f 'c for the proposed expression (0.24 λ √f 'c ) .

CONCLUSION

This TechBrief describes mechanical property tests on LWC, provides information about a LWC mechanical property database, and presents potential revisions to the AASHTO LRFD Bridge Design Specifications relating to the definition and mechanical properties of LWC.(2)  The proposed design expressions for Ec, LWC modification factor, and fr were compared to tested values in a LWC database collected as part of this research effort. A full description of the database and the development and evaluation of prediction expressions are included in the full report. (1) Future phases of this research compilation and analysis effort will include synthesis of past work on structural performance of LWC. The test results will be compared to the prediction expressions for nominal resistance in the AASHTO LRFD Bridge Design Specifications incorporating appropriate proposed revisions for LWC mechanical properties as presented in this TechBrief.

REFERENCES

  1. Greene, G. and Graybeal, B. (2013). Lightweight Concrete: Mechanical Properties, Report No. FHWA-HRT-13-062, Federal Highway Administration, Washington, DC.

  2. AASHTO. (2012). AASHTO LRFD Bridge Design Specifications, Sixth Ed., American Association of State Highway and Transportation Officials, Washington, DC.

  3. ACI Committee 213. (1967). "Guide for Structural Lightweight Aggregate Concrete," ACI Journal, 64(8), 433–469, American Concrete Institute, Farmington Hills, MI.

  4. Hanson, J.A. (1961). "Tensile Strength and Diagonal Tension Resistance of Structural Lightweight Concrete," ACI Journal, 58(1), 1–40, American Concrete Institute, Farmington Hills, MI.

  5. Ivey, D.L. and Buth, E. (1966). "Splitting Tension Test of Structural Lightweight Concrete," ASTM Journal of Materials, 1(4), 859–871.

  6. Pauw, A. (1960). "Static Modulus of Elasticity of Concrete as Affected by Density," ACI Journal, 57(6), 679–687, American Concrete Institute, Farmington Hills, MI.

  7. Russell, H. (2007). Synthesis of Research and Provisions Regarding the Use of Lightweight Concrete in Highway Bridges, Report No. FHWA-HRT-07-053, Federal Highway Administration, Washington, DC.

  8. Rizkalla, S., Mirmiran, A., Zia, P., Russell, H., and Mast, R. (2007). Application of the LRFD Bridge Design Specifications to High-Strength Structural Concrete: Flexure and Compression Provisions, NCHRP Report 595, NCHRP Project 12-64, National Cooperative Highway Research Program, Washington, DC.

  9. ACI Committee 363. (2010). Report on High-Strength Concrete, ACI 363R-10, American Concrete Institute Committee 363, Farmington Hills, MI.

  10. ACI Committee 318. (1962). "Building Code Requirements for Reinforced Concrete (ACI 318-56)," ACI Journal, 59(12), 1821–1848, American Concrete Institute, Farmington Hills, MI.

  11. ASTM C567. (2005). "Standard Test Method for Determining Density of Structural Lightweight Concrete," Book of Standards Volume 04.02, ASTM International, Conshohocken, PA

Researchers —This study was led by Ben Graybeal at FHWA's Turner-Fairbank Highway Research Center. It was conducted by Gary Greene of PSI, Inc. through laboratory support contract DTFH61 10 D 00017. For additional information, contact Ben at (202) 493-3122 or in the FHWA Office of Infrastructure Research and Development located at 6300 Georgetown Pike, McLean, VA, 22101-2296.

Distribution —The report (PB2013-107688) covered in this TechBrief is being distributed through the National Technical Information Service at www.ntis.gov.

Availability —This TechBrief may be obtained from the FHWA Product Distribution Center by email to report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at http://www.fhwa.dot.gov/research.

Key Words —LWC, lightweight concrete, bridge design, LRFD design specifications.

Notice —This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this TechBrief only because they are considered essential to the objective of the document.

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