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The main strength and deformational properties of concrete are discussed below.

2.3.1 Stress−Strain Relationship in Compression

Fig. 2.1 shows the stress−strain relationship for concrete in compression. The characteristic compressive strength of cylinder fck is defined as the strength below which not more than 5% of the results fall. The mean compressive strength fcm is related to fck as fcm = fck + 8 MPa.

For the design of cross sections, two simplified stress−strain relationships are proposed in Eurocode 2. The stress−strain relationship shown in Fig. 2.2 is a combination of a parabola and a straight line. The second simplified representation shown in Fig. 2.3 is bilinear.

The mathematical equation for the parabola−rectangle is given by

2 shows relationship between characteristic cylinder strength fck and cube strength fcu. An approximate relationship between cylinder strength fck and cube strength fck, cube is

fck ≈ 0.8 fck, cube

Fig. 2.1 Stress−strain curve for concrete in compression.

Fig. 2.2 Parabola−rectangle stress−strain relationship for concrete in compression.

2.3.2 Compressive Strength

The compressive strength is the most important property of concrete. The characteristic strength that is the concrete grade is measured by the 28-day cylinder/cube strength. Standard cylinders 150 mm diameter and 300 mm high or cubes of 150 or 100 mm for aggregate not exceeding 25 mm in size are crushed to determine the strength. The test procedure is given in BS EN 12390:2: 2009:

Testing Hardened Concrete: Making and curing specimens for strength tests and BS EN 12390:3: 2009: Testing Hardened Concrete: Compressive strength of test specimen.

fck

εc2 εcu2

εc

σc

fcm

0.4 fcm

Secant modulus Ecm

εc1 εcu1

εc

Fig. 2.3 Bilinear stress−strain relationship for concrete in compression.

Fig. 2.4 Split cylinder test.

2.3.3 Tensile Strength

The tensile strength of concrete is about a tenth of the compressive strength. It is determined by loading a concrete cylinder across a diameter as shown in Fig. 2.4.

The test procedure is given in BS EN 12390:6: 2009: Testing Hardened Concrete:

Tensile splitting strength of test specimens.

The mean characteristic tensile strength fctm is related to mean cylinder compressive strength fcm as follows.

fcm

εc3 εcu3

εc

MPa

2.3.4 Modulus of Elasticity

The short-term stress−strain curve for concrete in compression is shown in Fig.

2.1. The slope of the initial straight portion is the initial tangent modulus. At any point, the slope of the line joining the point to the origin is the secant modulus.

The value of the secant modulus depends on the stress and rate of application of the load. The code giving details of the method of determining the elastic modulus is BS 1881–121:1983 Testing concrete. Methods for determination of Static modulus of elasticity in compression. Note: A new Eurocode version is in preparation.

The dynamic modulus is determined by subjecting a beam specimen to longitudinal vibration. The value obtained is unaffected by creep and is approximately equal to the initial tangent modulus. The code BS 1881–209:1990 Testing concrete. Recommendations for the measurement of dynamic modulus of elasticity gives the details.

BS EN 1002-1-1:2004 Eurocode 2 Design of concrete structures gives the following expression for the short term secant modulus of elasticity (see Fig. 2.1) between zero stress and 0.4 fcm for concretes made with quartzite aggregates as

3

Because of the fact that the elastic modulus is greatly dependent on the stiffness of the aggregates, for limestone and sandstone aggregates the value from the equation should be reduced by 10% and 30% respectively. For basalt aggregates the value should be increased by 20%.

The tangent modulus Ec = 1.05 Ecm

2.3.5 Creep

Creep in concrete is the gradual increase in strain with time in a member subjected to prolonged stress. The creep strain is much larger than the elastic strain on loading. If the specimen is unloaded there is an immediate elastic recovery and a slower recovery in the strain due to creep. Both amounts of recovery are much less than the original strains under load.

The main factors affecting creep strain are the concrete mix and strength, the type of aggregate, curing, ambient relative humidity, the magnitude and duration of

sustained loading and the age of concrete at which load is first applied. In clause 3.1.4(2), Eurocode 2 specifies that provided the concrete is not subjected to a stress greater than 45% of the compressive strength at the time of loading, long term creep strain _cc(,t₀)is calculated from the creep coefficient (,t₀)_{by the} equation

) t , E ( stress )

t ,

( ₀

0 c

cc    



where Ec is the tangent modulus of elasticity of the concrete at the age of loading, t0. The creep coefficient (,t₀) depends on the effective section thickness, the age of loading and the relative ambient humidity. The creep coefficient is used in deflection calculations. Clause 3.1.4 and Annex B of Eurocode 2 give the equations for determining the creep coefficient. More details and examples are given in section 19.1.17, Chapter 19.

2.3.6 Shrinkage

The total shrinkage strain is composed of two parts, the drying shrinkage strain and the autogenous shrinkage strain. Drying shrinkage strain is the contraction that occurs in concrete when it dries and hardens. Drying shrinkage develops slowly due to migration of water and is irreversible but alternate wetting and drying causes expansion and contraction of concrete. The autogenous shrinkage strain develops during the hardening of concrete and develops quite fast during the early days after casting of concrete.

The aggregate type and content are the most important factors influencing shrinkage. The larger the size of the aggregate is, the lower is the shrinkage and the higher is the aggregate content; the lower the workability and water-to-cement ratio are, the lower is the shrinkage. Aggregates that change volume on wetting and drying, such as sandstone or basalt, produce concrete which experiences a large shrinkage strain, while concrete made with non-shrinking aggregates such as granite or gravel experience lower shrinkage strain. A decrease in the ambient relative humidity also increases shrinkage.

Eurocode 2 gives necessary data for calculating the drying shrinkage in equations (3.9)−(3.10) and in equations (3.11)−(3.13). Values of shrinkage strain are used in deflection calculations. More details and an example are given in section 19.1.18, Chapter 19.

2.4 TESTS ON WET CONCRETE