Strength is probably the most important single property of concrete, since the first consideration in structural design is that the structural elements must be capable of carrying the imposed loads. The maximum value of stress in a loading test is usually taken as the strength, even though under compressive loading the test piece is still whole (but with substantial internal cracking) at this stress, and complete breakdown subsequently occurs at higher strains and lower stresses.
Strength is also important because it is related to several other important properties that are more difficult to measure directly, and a simple strength test can give an indication of these properties.
We are primarily concerned with compressive strength since the tensile strength is very low, and in concrete structural elements reinforcement is used to carry the tensile stresses.
However, in many structural situations concrete may be subject to one of a variety of types of loading, resulting in different stress conditions and different potential modes of failure, and so knowledge of the relevant strength is therefore important.
For example, in columns or reinforced concrete beams, compressive strength is required; for cracking of a concrete slab the tensile strength is important. Other situations may require torsional strength, fatigue or impact strength or strength under multiaxial loading.
As we shall see, most strength testing involves the use of a few, relatively simple tests, generally not related to a particular structural situation. Procedures enabling data from the tests described in this chapter to be used in design have been obtained from empirical test programmes at an engineering scale on large specimens. You should refer to texts on structural design for a description of these design procedures.
In this article we shall describe the most common test methods used to assess the strength of concrete and then discuss the factors influencing the results obtained from them. We follow this with a more detailed consideration of the cracking and fracture processes taking place within concrete. Finally, we shall briefly discuss strength under multiaxial loading conditions.
Strength Tests of Concrete
Compressive Strength Test of Concrete
The simplest compressive strength test uses a concrete cube, and this is the standard test in the UK and many other countries. The cube must be sufficiently large to ensure that an individual aggregate particle does not unduly influence the result; 100 mm is recommended for maximum aggregate sizes of 20 mm or less, 150 mm for maximum sizes up to 40 mm.
The cubes are usually cast in lubricated steel moulds, accurately machined to ensure that opposite faces are smooth and parallel. The concrete is fully compacted by external vibration or hand tamping, and the top surface trowelled smooth.
After demoulding when set, the cube is normally cured under water at constant temperature until testing. The cube-testing machine has two heavy platens through which the load is applied to the concrete. The bottom one is fixed and the upper one has a ball-seating that allows rotation to match the top face of the cube at the start of loading. This then locks in this position during the test.
The load is applied to a pair of faces that were cast against the mould, i.e. with the trowelled face to one side. This ensures that there are no local stress concentrations, which would result in a falsely low average failure stress.
A very fast rate of loading gives strengths that are too high, and a rate to reach ultimate in a few minutes is recommended. It is vital that the cube is properly made and stored; only then will the test give a true indication of the properties of the concrete, unaffected by such factors as poor compaction, drying shrinkage cracking, etc.
The cracking pattern within the cube (Fig. 1a) produces a double pyramid shape after failure. From this it is immediately apparent that the stress within the cube is far from uniaxial. The compressive load induces lateral tensile strains in both the steel platens and the concrete owing to the Poisson effect.
The mismatch between the elastic modulus of the steel and the concrete and the friction between the two results in lateral restraint forces in the concrete near the platen, partially restraining it against outward expansion. This concrete is therefore in a triaxial stress state, with consequent higher failure stress than the true, unrestrained strength. This is the major objection to the cube test.
The test is, however, relatively simple and capable of comparing different concretes. (We shall consider triaxial stress states in more detail later in the chapter.) An alternative test, which at least partly overcomes the restraint problem, uses cylinders; this is popular in North America, most of Europe and in many other parts of the world.
Cylinders with a height:diameter ratio of 2, most commonly 300 mm high and 150 mm in diameter, are tested vertically; the effects of end restraint are much reduced over the central section of the cylinder, which fails with near uniaxial cracking (Fig. 1b), indicating that the failure stress is much closer to the unconfined compressive strength.
As a rule of thumb, it is often assumed that the cylinder strength is about 20% lower than the cube strength, but the ratio has been found to depend on several factors, and in particular, increases with increasing strength. The relationship derived from values given in the Eurocode 2 (BS EN 1992) is:
fcyl = 0.85fcube – 1.6
where fcyl = characteristic cylinder strength, and fcube = characteristic cube strength (values in MPa).
Figure 2 shows how the ratio of the two strengths varies with strength. A general relationship between the height:diameter ratio (h/d) and the strength of cylinders for low- and medium-strength concrete is shown in Fig. 3.
This is useful in, for example, interpreting the results from testing cores cut from a structure, where h/d often cannot be controlled. It is preferable to avoid an h/d ratio of less than 1, where sharp increases in strength are obtained, while high values, although giving closer estimates of the uniaxial strength, result in excessively long specimens which can fail due to slenderness ratio effects.
Testing cylinders have one major disadvantage; the top surface is finished by a trowel and is not plane and smooth enough for testing, and it therefore requires further preparation.
It can be ground, but this is very time consuming, and the normal procedure is to cap it with a thin (2 – 3 mm) layer of high-strength gypsum plaster, molten sulphur or high-early-strength cement paste, applied a day or two in advance of the test.
Alternatively, the end of the cylinder can be set in a steel cap with a bearing pad of an elastomeric material or fine dry sand between the cap and the concrete surface. Apart from the inconvenience of having to carry this out, the failure load is sensitive to the capping method, particularly in high-strength concrete.
Tensile Strength Test of Concrete
Direct testing of concrete in uniaxial tension, as shown in Fig. 4a, is more difficult than for, say, steel or timber. Relatively large cross-sections are required to be representative of the concrete and, because concrete is brittle, it is difficult to grip and align. Eccentric loading and failure at or in the grips are then difficult to avoid.
A number of gripping systems have been developed, but these are somewhat complex, and their use is confined to research laboratories. For more routine purposes, one of the following two indirect tests is preferred.
Splitting test A concrete cylinder, of the type used for compression testing, is placed on its side in a compressiontesting machine and loaded across its vertical diameter (Fig. 4b). The size of cylinder used is normally either 300 or 200 mm long (l) by 150 or 100 mm diameter (d).
The theoretical distribution of horizontal stress on the plane of the vertical diameter, also shown in Fig. 4b, is a near uniform tension (fs), with local high compression stresses at the extremities.
Hardboard or plywood strips are inserted between the cylinder and both top and bottom platens to reduce the effect of these and ensure even loading over the full length.
Failure occurs by a split or crack along the vertical plane, the specimen falling into two neat halves. The cylinder splitting strength is defined as the magnitude of the near-uniform tensile stress on this plane, which is given by:
fs = 2P/pld
where P is the failure load.
The state of stress in the cylinder is biaxial rather than uniaxial (on the failure plane the vertical compressive stress is about three times higher than the horizontal tensile stress) and this, together with the local zones of compressive stress at the extremes, results in the value of fs being higher than the uniaxial tensile strength.
However, the test is very easy to perform with standard equipment used for compressive strength testing, and gives consistent results; it is therefore very useful.
A rectangular prism, of cross-section b × d (usually 100 or 150 mm square) is simply supported over a span L (usually 400 or 600 mm). The load is applied at the third points (Fig. 4c), and since the tensile strength of concrete is much less than the compressive strength, failure occurs when a flexural tensile crack at the bottom of the beam, normally within the constant bending moment zone between the loading points, propagates upwards through the beam.
If the total load at failure is P, then analysis based on simple beam-bending theory and linear elastic stress–strain behaviour up to failure gives the stress distribution shown in Fig. 4c, with a maximum tensile stress in the concrete, fb, as:
fb = PL/bd2
fb is known (somewhat confusingly) as the modulus of rupture.
However, as we have seen in the preceding chapter, concrete is a non-linear material and the assumption of linear stress distribution is not valid. The stress calculated from the above equation is therefore higher than that actually developed in the concrete. The strain gradient in the specimen may also inhibit crack growth. For both these reasons the modulus of rupture is also greater than the direct tensile strength.
Relationship Between Strength and Measurements
The tensile strength, is measured roughly one order of magnitude lower that the compressive strength. The relationship between the two is non-linear, with a good fit being an expression of the form:
ft = a(fc)b
where ft = tensile strength, fc = compressive strength, and a and b are constants.
Eurocode 2 (BS EN 1992) gives a = 0.30 and b = 0.67 when fc is the characteristic cylinder strength and ft is the mean tensile strength. This relationship, converted to cube compressive and tensile strengths, is plotted in Fig. 5 together with equivalent data from cylinder splitting and modulus of rupture tests obtained over a number of years by UCL undergraduate students.
It is clear from this figure that, as we have already said, both the modulus of rupture and the cylinder splitting tests give higher values than the direct tensile test. The modulus of rupture is the higher value, varying between about 8 and 17% of the cube strength (the higher value applies to lower strengths).
The cylinder splitting strength is between about 7 and 11% of the cube strength, and the direct tensile strength between about 5 and 8% of the cube strength.
Figure 5 also shows that, as with all such relationships, there is a considerable scatter of individual data points about the best-fit line (although in this case some of this may be due to the inexperience of the testers).
Thanks for reading about “strength tests of concrete”.