The strength can be defined as the ability to resist force. With-regard to concrete for structural pur­poses it can be defined as the unit force required to cause rupture. Strength is a good index of most of the other properties of practical importance. In general stronger concretes are stiffer, more water tight and more resistant to weathering etc.

#### Nature of Strength in Concrete:

Rupture of concrete may be caused by applied tensile stress, shearing stress or by compressive stress or a combination of two of the above stresses. Concrete being a brittle material is much weaker in tension and shear than compression and failures of concrete specimens under compressive load are essentially shear failures on oblique planes as shown in Fig.14.1 (a).

It is called as shear or cone failure. As the resistance to failure is due to both cohesion and internal friction, the angle of rupture is not 45° (plane of maximum shear stress), but is a function of the angle of internal friction. It can be shown mathematically that the angle ϕ which the plane of failure makes with the axis of loading is equal to (45° – ϕ/2) as shown in Fig. 14.2 (a).

The angle of internal friction ϕ of con­crete being of the order of 20°, the angle of inclination of the cone of failure in the con­ventional test specimen is approximately 35° as shown in Fig.14.1 (a). Further the angle of the rupture may deviate from theoretical value due to the complex stress condition induced in the end conditions of the compression specimens. This deviation results from restraint to lateral expansion under the load caused by friction of the bearing plates on the end surfaces.

When the strength of concrete is high and lateral expansion at the end bearing surfaces are relatively unrestrained, the specimen may separate into columnar fragments, known as a splitting or columnar fracture as shown in Fig.14.1 (c). Usually failure occurs through a combination of shear and splitting as shown in Fig.14.1 (b). Mostly concrete in structures is subjected to some combinations of compressive, tensile and shear stresses either directly or due to restraint of surrounding portions. The results of such combinations of stresses may be interpreted by mohar rupture diagrams as shown in Fig. 14.2 (b).

#### Kinds of Strength in Concrete:

Strength may be classified as follows:

1. Compressive strength

2. Tensile strength

3. Shear strength, and

4. Bond strength.

1. Compressive Strength:

For structural design the compressive strength is taken as the criterion of quality of concrete and the working stresses are prescribed as per codes in terms of percentages of the compressive strength as determined by standard tests.

Compressive Tests:

To determine the compressive strength of concrete following three types of specimens can be used:

i. Cubes

ii. Cylinders

i. Cube Tests:

Generally specimens are cast in steel or cast iron moulds of 150 mm dimensions, which should confirm to cubical shape. The dimensions and planeness should be within the limits of tolerance. The mould should have rigid connection with base. The rigid connection with base is essential when the compaction is effected by means of vibration. This reduces the leakage of mortar.

The cube is filled in three layers and compacted well either by vibration or standard tamping rod as per IS 516-1964. After compaction the top surface is made flush with edges of mould and the top surface finished by means of trowel. The finished surface is left undisturbed for 24 hours at a temperature of 66°F to 70°F and relative humidity not less than 90%. After 24 hours, the mould is stripped and the specimen is stored in water for further curing. As far as possible the curing temperature should be maintained at 66°F to 70°F, usually these specimens are cured upto 28 days. The test should be carried out as per IS 516-1964.

ii. Cylinder Test:

The standard cylinder is 15 cms in diameter and 30 cms height and is cast in a mould generally made of cast-iron or steel, preferably with a clamped base. Cylinder speci­mens are made as cubes specimens, but are com­pacted in three layers by a 16 mm diameter rod having one end of bullet shape. The top surface of cylinder finished with a float is not smooth enough for testing and requires further prepa­ration.

To overcome this difficulty capping of cylinders is done by cement paste or some other suitable material. Cylinders are used for the determination of compressive strength of con­crete in United States, France, Canada, Australia and New Zealand, while cubes are used in U.K. Germany, India and Europe etc.

The concrete strength is affected by the shape and size of the specimens, but high strength concretes is less affected than the low strength.  Concrete Fig.14.3 shows the influence of height/diameter ratio on the strength of cylinder for different strength of concrete as suggested by Murdok and Kesler.

Failure of Compression Specimens:

Compression test develops a more complex system of stresses. The compression load develops the lateral expansion in the test specimen (cube or cylinder) due to the Poisson’s ratio effect. The steel platens do not undergo the same lateral expansion as that concrete goes. Thus the steel restrains the expansion tendency of the concrete in the lateral direction. This restraint induces a tangential force between the end surfaces of the concrete specimen and the adjacent steel platens of the testing machine.

It has been observed that lateral strain developed in the steel plates is only 0.4 times of the lateral strain developed in the concrete. Thus the platens restrain the lateral expansion of the concrete in the part of the specimen near its ends. The degree of restraint exercised depends upon the friction actually develo­ped. In case the friction is eliminated by the application of any suitable greasing material as grease, graphite, or paraffin wax to the bearing surfaces, the specimen shows a greater lateral expansion, and eventually gets split along its full length.

Under normal conditions of the test, the elements within the specimen are subjected to shearing stresses as compressive stresses. The magnitude of shear stress decreases and the lateral expansion increases with the distance from the platens. Thus due to this restraint a cone of height of √3/2 d remain relatively undamaged in the specimen tested, where d is the lateral dimension of the specimen.

However if the length of the specimen is longer than 1.7 d, a part of it will be free from the restraining effect of the platens. Thus the specimens with lengths less than 1.5 d show considerably higher strength than those with greater lengths as shown in Fig. 14.4.

Fig. 14.4 shows the general pattern of the influence of the height diameter ratio on the compressive strength of cylinder. For values of H/D ratio smaller than 1.5, the measured strength increases rapidly due to non-restraining effects of the platens of the testing machine. For H/D between 1.5 to 4.0 strength variation is very little, and for H/D between 1.5 and 2.5 the variation of strength is within 5% of H/D ratio 2.0. For H/D ratio above 5, strength falls rapidly. Hence the choice of H/D ratio of 2 is suitable.

Comparison of Cube and Cylinder Strengths:

Experimental results have shown that there is no simple relation between the cylinder and cube strength of the same concrete. The ratio of cylinder/cube strength depends on the level of strength of concrete and is higher for high strength concrete. However for simplicity IS 516-1964 has suggested this ratio as 0.80. Table 14.1 below shows that this ratio varies from 0.77 to 0.96 in an irregular manner. The results are based on Evan’s work. For 1000 kg/cm2 strength concrete this ratio becomes 1.0.

2. Tensile Strength:

Concrete being a brittle material is not expected to resist direct tensile forces. However tension is of importance with regard to cracking, which is a tensile failure. Most of the cracking is due to the restraint of contraction induced by drying shrinkage or lowering of temperature. The tensile strength of concrete varies from 7% to 11% of the compressive strength but on average it is taken as 10% of compressive strength. Further it has been observed that higher the compressive strength, lower the relative tensile strength.

The maximum tensile strength of concrete has been found of the order of 42.0 kg/cm2. Some researchers have observed that the type of coarse aggregate has a greater relative effect on tensile strength than on compressive strength. Generally for concrete quality control, tensile test is never made. However to have an idea of tensile strength an indirect method known as splitting test is applied.

3. Shear Strength:

Shear is the action of two equal and opposite parallel forces applied in planes a short distance apart. Shear stress cannot exist without accompanying tensile and compressive stresses. Pure shear can be applied only through torsion of a cylindrical specimen in which case the stresses are equal in primary shear. Secondary tension (maximum at 45° to shear) and secondary compression (maximum at 45° to shear, per­pendicular to tension). As the concrete is weaker in tension than in shear, failure in tension invariably occurs in diagonal tension. Direct determination of shear is very difficult. Hence researchers have assumed the shear strength of concrete about 12% of the compressive strength.

I.S. 456-1978 has suggested the values of shear as follows:

4. Bond Strength:

It can be defined as the resistance to slipping of the steel reinforcing bars which are embedded in concrete. This resistance is provided by the friction and adhesion between the concrete and steel friction between concrete and the lugs of deformed bars. It is also affected by the shrinkage of concrete relative to the steel. Bond involves not only the properties of concrete, but also mechanical properties of steel and its position in the concrete member. In general bond strength is approximately proportional to the compressive strength of concrete upto about 200 kg/cm2.

For higher strengths of concrete, the increase in bond strength becomes progressively smaller. In the initial stages of failure (slip) the bond strength depends on the magnitude and uniformity of lateral pressure that exists or may be developed between steel and surrounding concrete. Bond strength varies considerably with the type of cement, admixtures and water cement ratio i.e., on quality of paste. It is not affected by air entrainment.

Further it has been observed that bond strength increases with delayed vibration. It is higher for dry concrete than for wet concrete. Its value reduces at high temperatures. At 200°C to 300°C (400°F to 570°F) bond strength has been found 50% of the bond strength at room temperature. Bond strength is also reduced by alternations of wetting and drying, freezing and thawing etc. Its value usually is determined by pull out test. The bond strength for deformed bars may be taken 40% more than ordinary bars of the same diameter.

Bond strength is also a function of specific surface of gel. Cement having higher percentage of C2S will give higher surface of gel, giving higher bond strength. On the other hand cement having higher per­centage of C3S or concrete cured at higher temperature gives smaller value of specific surface of gel, resul­ting in lower bond strength. It has been observed that concrete cured at high pressure steam produces gel of about 1/20th specific surface of the gel surface produced at normal curing temperature. Thus the bond strength of high pressure steam cured concrete is lower.

The values of bond strength are shown in Table 14.4. as suggested by IS 456-2000. All values are in N/mm2:

#### Factors Affecting the Strength of Concrete:

Generally following factors affect the strength of concrete.

Here these factors are discussed in brief:

1. Type of cement

2. Type of aggregate

3. Richness of the mix

4. Curing temperature

5. Age of concrete

6. Effect of compaction

7. Aggregate-Cement ratio

8. Temperature at the time of placing, and

1. Type of Cement:

Type of cement influences the strength deve­lopment in concrete to a great extent depending upon its chemical composition and fineness of grind­ing. The percentage of C3S in con­crete is responsible for the higher strength development upto 28 days, while C2S contributes to strength development after 28 days.

In a well burnt modern cement clinker the C3S content is about 45% and that of C2S as 25%. Their sum in most of the cements varies from 70 to 80%. Thus in general the early strength say upto 28 days of port-land cement will be higher with higher percentage of C3S and after that percentage of C2S will affect the strength development of concrete.

Further presence of alkalis in cement also affects concrete strength after 28 days to a great extent. The greater the amount of alkalis present, lower the gain in strength. Further the finer the cement, rapid and greater the strength development.

The effect of different type of cement and w/c ratio on compressive strength has been shown in Fig. 14.5.

2. Type of Aggregate:

Following characteristics of aggregate affect the strength of Concrete:

(a) Shape and Texture of Particles:

Crushed rock aggregate with rough surface and angular particles develop about 15% higher strength in comparison of natural smooth surfaced gravel perhaps due to better bond between the aggregate and cement paste, other conditions being same.

(b) Size of Aggregate:

It has been observed that for structural concrete, the maximum size of aggregate upto 38 mm has produced highest strength after which strength started declining. It may be due to the fact that larger the aggregate size, the smaller the surface area to be wetted per unit weight of aggregate. Above 38.0 or 40 mm size aggregate the gain of water/cement is off set by the effect of lower bond area between aggregate and cement paste.

A well graded aggregate will produce a denser concrete resulting in higher strength. The influence of type of aggregate on the strength varies in magnitude and depends upon the water/cement ratio of the mix. For water/cement 50r ratio less than 0.4 the use of crushed aggregate has been found to give higher strength more than 38% than with the use of natural gravel.

3. Richness of the Mix:

For a particular workability, higher the cement content, lesser the amount of water required, resulting in higher strength. The richness of mix is useful upto a certain water/ cement ratio, beyond which it will exhibit retrogression in strength of concrete. Fig.14.6.

4. Curing Temperature of 100 200 300 Concrete:

The strength develop­ment of concrete is a function of time and temperature. Thus the strength of concrete is the product of time and temperature.

... Concrete strength = ∑ (time interval x temperature)

Thus the rise in the temperature accelerates the chemical reaction of hydration and affects the early strength of concrete.

5. Age of Concrete:

The strength in concrete is developed due to the hydration of cement. As we know that different types of cement hydrate at different rate. Thus the strength development in concrete continues. It was assumed that after 28 days, the rate of hydration is very small, nearly negligible, but recent studies have shown that rate of hydration continues upto 1 year. Strength after 1 year has been found 24% higher than the strength of 1 month.

The age factor is shown in the following Table 14.5:

6. Effect of Compaction:

It has been observed that each 1% of deficiency in compaction, results 5% reduction in compressive stren­gth of concrete. The effect of com­paction of concrete on its com­pressive strength is shown in Fig. 14.7.

7. Aggregate-Cement Ratio:

The mix proportion has a marked influence on the compression stren­gth of concrete. The effect of aggre­gate cement ratio with different workability in terms of compacting factor on its compressive strength is shown in Fig. 14.8.

8. Temperature at the Time of Placing:

If the temperature is below Density ratio 20°C the rate of hydration of cement will be very low resulting slow development of strength. On the other hand higher temperature during placing and setting will accelerate the process of hydration, but the quality of the gel formed will be poor, resulting in low strength.