148 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 compres- sive 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 prop- erties that are more difficult to measure directly, and a simple strength test can give an indication of these properties. For example, we have already seen the relation of strength to elastic modulus; we shall discuss durability in Chapter 24, but in many cases a low-permeability, low-porosity concrete is the most durable and, as discussed when we considered the strength of cement paste in Chapter 13, this also means that it has high strength. 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 struc- tural 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 en- abling 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 chapter we shall describe the most com- mon 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 multi- axial loading conditions. 21.1 Strength tests 21.1.1 COMPRESSIVE STRENGTH The simplest compressive strength test uses a con- crete cube, and this is the standard test in the UK and many other countries. The cube must be suffici- ently 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 Chapter 21 Strength and failure of concrete