CIV415 CONCRETE TECHNOLOGY

Chapter VIII

Properties of Hardened Concrete

Assist.Prof.Dr. Mert Yücel YARDIMCI Spring, 2014/2015

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STRENGTH OF HARDENED CONCRETE

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STRENGTH OF HARDENED CONCRETE

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Strength is defined as the ability of a material to resist the stress generated by an external force without failure. For concrete, failure is frequently identified with the appearance of cracks. Since the development of a crack is closely related to the development of deformation, in fact, the real criteria of failure for concrete is the limiting strain rather than the limiting stress. The limiting strain for a concrete is different for different loading conditions and different strength levels.

Limiting strain for concrete

Uniaxial tension Uniaxial compression

100 × 10−6 – 200 × 10−6 4 × 10−3 (for 14 MPa concrete) 2 × 10−3 (for 70 MPa concrete)

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STRENGTH OF HARDENED CONCRETE

Compressive strength and corresponding tests - Failure mechanism -

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In compression, the failure mode is less brittle because considerably more energy is needed to form and to extend cracks in the matrix. It is generally agreed that in a uniaxial compression test on medium- or low-strength concrete, no cracks are initiated in the matrix below about 40–50% of the failure stress.

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Factors affecting the measured compressive strength

• Loading rate

• End condition

• Size effect

Test parameters

Loading rate

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In general, the lower the rate of the loading, the lower the measured compressive strength. This may be attributed to the fact that deformation generated by loading needs time to develop. The slow rates of loading may allow more subcritical crack growth to occur, thus leading to the formation of larger flaws and hence a smaller apparent load. On the other hand, it may be that slower loading rates allow more creep to occur, which will increase the amount of strain at a given load. When the limiting value of strain is reached, failure will occur. More likely, the observed rate of loading effect is due to a combination of these, and perhaps other factors as well.

Loading rate

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To make the compression results comparable, a standard load rate has to be followed. For a cylinder specimen, ASTM regulates 0.15–0.34 MPa/sec as the standard loading rate. For a cube specimen, BSI sets 0.2–0.4 MPa/sec as the standard loading rate. In the real situation, the loading rate can be transferred to N/sec by multiplying the area of the specimen under the loading.

End condition

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The compression test assumes a state of pure uniaxial compression. However, this is not really the case, because of friction between the ends of the specimens and the platens of testing machine that make a contact with them.

The frictional force arises due to the fact that, because of the differences in the moduli of elasticity and Poisson’s ratio for steel and concrete, the lateral strain in the platens is considerably less than the lateral expansion of the ends of the specimen if they were free to move.

End condition

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The friction between the platens and the cube specimen ends confines a much greater portion in the specimen than is the case with the cylindrical specimen, as shown in Figure 5-7. This leads to higher strength values when measured on cubes rather than cylinders. Usually, the ratio between cube strengths and cylinder strengths is commonly assumed to be 1.25 for normal-strength concrete. However, for higher-strength concretes, the ratio will be reduced.

Uniaxial tensile strength and corresponding tests - Failure mechanism -

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Uniaxial tension test is more difficult to conduct for three reasons. It is difficult to center the loading axis with the mechanical

centroid.

It is difficult to control the loading process due to the quasi-brittle nature of concrete under tension.

The tension process is more sensitive to a sudden change in cross-sectional area, and the specimen-holding devices introduce secondary stress that cannot be ignored.

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Uniaxial tensile strength and corresponding tests - Failure mechanism -

Why the tensile strength of concrete is much lower than its compressive strength?

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The tension strength of concrete is much lower than its compression strength, which can be attributed to the stress concentration generated by the defects in the materials.

The hole (2a x 2b) represents the defect!

Kt is the concentration factor. It can be seen that if a = b, Kt = 3. Kt depends not only on the geometry of the hole but also on the loading pattern. If the loading is pure shear, Kt can reach 4.

The highest stress occurs at the edge of the ellipse and can be expressed as

Relationship between compressive strength and tensile strength

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It is known that other mechanical properties of a concrete can be related to its compressive strength. However, there is no direct proportionality between tensile and compressive strength. As the compressive strength of concrete increases, the tensile strength also increases but at a decreasing rate.

The tensile/compressive strength ratio depends on the general level of the compressive strength; the higher the compressive strength, the lower the ratio. The research work done by Price (1951) showed that the direct (uniaxial) tensile/compressive strength ratio is 10 to 11% for low-strength, 8 to 9% for medium-strength, and 5 to 7% for high-strength concrete.

The relationship between the compressive strength and the tensile/compressive strength ratio seems to be determined by the effect of various factors on the properties of both the matrix and the transition zone in concrete.

Indirect tension test (split-cylinder test or Brazilian test)

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The indirect tension test is also called the splitting test or Brazilian test. The standard specimen for the splitting test is a 150 × 300-mm cylinder (BS 1881: Part 117:1983, ASTM C496-71).

The loading rate is 0.02 to 0.04 MPa/sec according to BS, 0.011 to 0.023 MPa/sec according to ASTM C496-71.

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Indirect tension test (split-cylinder test or Brazilian test)

Flexural strength and corresponding tests

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Flexural strength is also called the modulus of rupture (MOR).

The specimen for a flexural strength test is a 150 × 150 × 500-mm beam according to ASTM C78 150 × 150 × 750-mm beam according to BS 1881: Part 118: 1983. A beam size of 100 × 100 × 500mm can be used when the maximum size of aggregate is less than 25 mm.

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Flexural strength and corresponding tests

?

Valid only the crack occurs in between loading points!

Modulus of elasticity

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The modulus of elasticity can be measured directly from the initial slope of a specially designed stress–strain curve.

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5MPa

0,4*fc

Load and unload cycles 3 times

Wait at the level of 5MPa Measure deformation (δb) Wait at the level of 0.4*fc stress

Measure deformation (δa).After Calculate (δa − δb), the result is denoted as δ4

Record deformation (δ5) Take off the gages if (δ5 − δ4)<0.003 mm.

Relationship between compressive strength and modulus of elasticity

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According to the British Standard for the structural use of concrete (BS 8110: part 2), modulus of elasticity concrete can be related to the cube compressive strength by the expression

when the density of concrete is 2320 kg/m3, i.e., for a typical normal-weight concrete.

If the density of concrete is between 1400 and 2320 kg/m3, the expression for Young’s modulus is

where ρ is the density of concrete in kg/m3.

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According to the ACI Building Code 318-83, the relationship between Young’s modulus and compressive strength for normal density concrete is

Relationship between compressive strength and modulus of elasticity

where fc is the cylinder compressive strength.

For concrete with density of 1500 to 2500 kg/m3, the relationship changes to

It should be noted that in all the above equations, MPa is used for strength and stress, and Gpa for Young’s modulus.

Constitutive equations

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A constitutive equation is a relation between two physical quantities that describes the response of a material or substance to external functions, such as load, temperature, water flow, or ionic transport.

In concrete structural analysis, the most popular constitutive equation is the stress–strain relationship that connects applied stress or forces to strain or deformation in concrete. The stress–strain relationship is also called Hooke’s law.

For concrete, the constitutive equations are mostly obtained by the curve fitting of experimentally obtained stress–strain (deformation) relationships.

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Constitutive equations

where σc is the compressive stress, σc,u the ultimate compressive stress, εc the compressive strain, εc,u the strain corresponding to σc,u.

General stress–strain equation for a prismatic concrete specimen, having an aspect ratio of 2.5, under uniaxial compression,

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Constitutive equations

where Ec,u is the modulus of elasticity.

the constitutive model presented above is only one typical example in this area.

What is the E modulus expression of Turkish Standards by means of the compressive strength of concrete?