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Photo: Rizkalla et al.(1)
Testing and Predicting the Modulus of Elasticity of Concrete
Henry G. Russell, Henry G. Russell, Inc.
The accuracy of predicting camber and prestress losses in long-span bridges can be improved when measured values of concrete material properties are used. This article describes the ASTM test for modulus of elasticity and compares measured values with the design equation predictions.
The procedure for measuring the static modulus of elasticity in compression is described in ASTM C469.(2) In this procedure, molded concrete cylinders or diamond-drilled concrete cores are subjected to a slowly increasing longitudinal compressive stress. Longitudinal strains are determined using either a bonded or unbonded sensing device that measures the average deformation of two diametrically opposite locations to the nearest 5 millionths of strain. ASTM C469 does not specify the diameter of the test specimens. However, molded concrete cylinders are usually the same size as those used for compressive strength measurements i.e. 6x12-in. or 4x8-in. (152x312-mm or 102x203-mm) cylinders. Concrete cores must have a length-to-diameter ratio greater than 1.50.
The applied load and longitudinal strain are recorded when the longitudinal strain is 50 millionths and when the applied load is equal to 40% of the cylinder compressive strength. Note that it is necessary to determine the compressive strength on companion specimens prior to testing for modulus of elasticity. The modulus of elasticity is calculated as the slope of the straight line between the 40% compressive stress point and the 50 millionths strain point. The same procedure may be used to obtain a stress-strain curve by taking more frequent readings either manually or automatically. ASTM C469 cautions that the modulus of elasticity values will usually be less than the modulus derived under rapid load application and usually greater than values obtained under slow load application, when all other test conditions remain the same.
When specifying tests in accordance with ASTM C469, it is important to define the specimen size, test ages, and curing conditions prior to testing. It should also be stated whether a stress-strain curve is needed or only the chord modulus. The specifier should also check that local testing laboratories have the equipment available to perform the test on the specified cylinder size. Otherwise, it may be necessary to ship the cylinders to a specialized testing laboratory.
The test procedure does not prohibit the use of the same cylinders for modulus of elasticity and concrete compressive strength provided the loading can be applied continuously. This means that the measuring device must be expendable or adequately protected. For high strength concrete cylinders, which fail in an explosive manner, it is highly desirable to use separate cylinders. Because ASTM C469 is a test procedure, it may be used for normal strength concrete, high strength concrete, lightweight concrete, self-consolidating concrete, and ultra-high performance concrete.
Predicting the Modulus of Elasticity
Article 126.96.36.199 of the AASHTO LRFD Bridge Design Specifications contains the following equation for predicting the modulus of elasticity, Ec:
Ec = 33,000K1wc1.5 (ksi units)
K1 = correction factor for source of aggregate to be taken as 1.0 unless determined by physical test
wc = unit weight of concrete, kcf
fc' = specified compressive strength of concrete, ksi
This equation represents average values and the actual modulus of elasticity can vary by ±25% as shown in the graph at the beginning of this article.(1) Many variables affect the modulus of elasticity in addition to those included in the equation. Consequently, when the modulus of elasticity is an important factor in design, more precise values can be obtained by testing with local materials than can be obtained from the equation.
1. Rizkalla, S., Mirmiran, A., Zia, P., Russell, H., and Mast, R., "Application of the LRFD Bridge Design Specifications to High-Strength Structural Concrete: Flexure and Compression Provisions," Transportation Research Board, NCHRP Report 595, Washington, DC, 2007, 28 pp.
2. Standard Test Method for Static Modulus of Elasticity and Poisson's Ratio of Concrete in Compression, ASTM C469, ASTM International, Volume 04.02, West Conshohocken, PA, 2002.
HPC Bridge Views, Issue 64, Nov/Dec 2010