In this article we will discuss about:- 1. Tensile Strength of Concrete 2. Flexure Strength 3. Impact Strength 4. Resistance to Abrasion of Concrete 5. Fatigue Strength.

#### Tensile Strength of Concrete:

The actual tensile strength of cement paste or similar brittle material as that of stone is very much lower than the theoreti­cal strength estimated on the basis of mole­cular cohesion of the atomic structure and calculated from the energy required to create the new surfaces by fracture of a perfectly homogeneous and flaw (fracture) less mate­rial. This theoretical strength has been found to be 1000 times higher than the actual mea­sured strength.

This difference between the theoretical and actual strength can be explained by the presence of cracks in the concrete as accep­ted as a fact (postulated) by “GRIFFITH”. These cracks lead to high stress concen­tration in the material under load so that a very high stress is reached in very small volumes of the specimen at the edges or tips of the crack as shown in Fig.13.1, resulting in localized microsco­pic fractures, while the average stress in the whole specimen is very low.

Actually the flaws or cracks vary in size and only the few large cracks cause failure. The concentration of stress at the top edge is in fact three dimensional, but the greatest weakness is when the orientation of the crack is at right angle (normal) to the applied load. Maximum stress is higher, for the longer and sharper the crack i.e., the greater the value of c and smaller the value of-

It has been observed that when two unequal principal stresses are compressive, the stress along the edge of an internal flaw is tensile at some points so that fracture can take place The fracture criteria is represented graphically in Fig. 13.2 for a combina­tion of two principal stresses P and Q, where K is the tensile strength in direct tension. Fracture occurs under a combination of P and Q such that the point representing the state of stress crosses the curve out wards on to the shaded side. From this Fig. 13.2 it can be seen that fracture may occur when uniaxial compression is applied. In fact this fact has been observed while testing concrete specimen in com­pression.

The nominal compressive strength is 8 K i.e., the eight times the tensile strength determined in a direct tension test. This figure is in good agreement with the observed values of the ratio of the compres­sive to tensile strengths of concrete.

Fracture Pattern of Concrete :

The fracture pattern of concrete under different states of stress is shown in Fig. 13.3. Under uniaxial tension, fracture occurs more or less in a plane normal to the direction of the load as shown in Fig. 13.3 (a).

Under uniaxial tension, fracture occurs more or less in a plane normal to the direction of the load. Under uniaxial compression the cracks are approximately parallel to the applied load, but some cracks are formed at an angle to the applied load. The parallel cracks are caused by a localized tensile stress in a direction normal to the compressive load.

The inclined cracks are formed due to the collapse caused by the develop­ment of shear planes. Thus it should be noted that the cracks are formed in two planes parallel to the load, resulting in the disintegra­tion of the specimen into column type fragments as shown in Fig.13.3 (b).

Under biaxial compression the failure takes place in one plane, parallel to the applied load, resulting in the formation of slab type fragments as shown in Fig. 13.3 (c). Here it shall be noted that the fracture pattern of Fig.13.3 are for direct stresses only. Thus there is no restraint from the platens of the testing machine, but in practice these platens introduce some lateral compression due to the friction between the specimen and steel platens. In case of ordinary testing machines, it is difficult to eliminate this friction. However this effect can be minimised by keeping length/width ratio of the specimen greater than 2.0. This ratio ensures the elimination of platen restraint from the central portion of the specimen.

#### Flexure Strength shown by Concrete:

When concrete subjected to bending, compressive as well tensile stresses are developed. In many cases direct shear stresses are also developed. The strength shown by the concrete against bending is known as flexure strength. The strength per unit area is known as flexure stress ‘S’ and is given by the relation-

S = M.y/I

where,

S = stress in the fibre farthest from the neutral axis

M = B.M. at the section

y = distance from neutral axis to farthest fibre

I = moment of inertia of the cross section

The value of modulus of rupture depends upon the dimensions of the beam and on the arrangements of loading.

Two systems of loading may be used as:

This loading system gives a triangular B.M. distribution, such that maxi­mum stress occurs at one section of the beam only.

This loading system produces a constant B.M. between the load points. Nowadays this method is taken as the standard method and central point method has been disconti­nued in many countries such as U.K. and U.S.A. etc. The relati­onship between flexural strength with compressive and tensile strengths have been shown in Fig. 13.5 and 13.6 respectively.

#### Impact Strength of Concrete:

The impact force is the product of the mass of a body and its velocity. The necessity of the kno­wledge of impact force in practical life is felt in driving concrete piles and in the construction of foundations for machines which exert impulsive load and also in situations where accidental impact is possible as in the case of handling pre-cast concrete members.

There is no unique relation between the im­pact strength and the static compressive strength of concrete. Thus to assess the impact strength, the principal criteria was considered as the ability of concrete specimen to withstand the repeated blows and to absorb energy. Thus the number of blows which the concrete can withstand (bear) before reaching the no rebound condition indica­tes a definite state of damage.

Generally for a given type of aggregate, higher the compressive strength of the concrete, lower the energy absorbed per below before cracking, but greater the number of blows to reach no rebound con­dition. Thus the impact strength and the total energy absorbed by concrete increases with its static compressive strength and age. The relation between the strength of concrete and number of blows to no rebound condition is shown in Fig. 13.9.

Factors Affecting the Impact Strength:

It has been observed that the relation between the static compressive strength of concrete and its impact strength is affected by the following factors:

1. Type of Coarse Aggregate:

The impact strength of concrete made with crushed rock aggregate with rough and angular surface is greater for the same strength made with natural gravel. This feature indicates that the impact strength of concrete is more closely related to its flexural strength than to its compressive strength. Thus the concrete made with natural gravel has low impact strength due to the weaker bond between the mortar and coarse aggregate.

2. Storage Condition of Concrete:

The impact strength of moist or water stored concrete is lower than that of dry concrete, though water stored concrete can withstand more blows before cracking Thus the compressive strength without reference to storage conditions of concrete does not give an adequate indication of impact strength.

3. Size of Aggregate:

Concrete made with smaller maximum size aggregate gave significantly greater impact strength.

4. Modulus of Elasticity and Poisson’s Ratio of Aggregate:

The aggregate of low modulus of elasticity and low poisson’s ratio gives greater impact strength than high modulus of elasticity and poisson’s ratio aggregate.

5. Cement Content:

To get a concrete of satisfactory impact, strength, the cement content should be less than 400 kg/m3.

Impact load­ing can be considered as the application of a uniform stress extremely rapidly, in which case strength measured will be much higher. It has been observed that if the rate of application of stress exceeds 5 x 106 MPa/s, the static com­pressive strength obtained is more than double the static compressive strength at normal rate of loading (0.25 MPa/sec.) Fig.13.10.

#### Resistance to Abrasion of Concrete:

In practice concrete surfaces can be subjected to various types of abrasive wear. For example scraping or sliding can cause wearing rubbing friction. In case of hydraulic structures, the action of abrasive solids as sand and other debris carried by water generally cause erosion of concrete. For these reasons it is desirable to know the resistance of concrete to abrasion. However it is difficult to assess the resistance of concrete to abrasion as the damaging action varies depending on the cause of wear. Thus no one test procedure is satisfactory for the evaluation of the resistance of concrete to the various conditions of the wear.

In all the tests, the depth of wear of a specimen is used as a measure of abrasion. ASTMC 779-89 has prescribed three test procedures for laboratory or field use.

The tests are as follows:

1. The revolving disc test

2. Steel ball abrasion test

3. Dressing wheel test

1. The Revolving Disc Test:

The equipment consists of three flat surfaces which revolve along a circular path with a specified velocity of 0.2 Hertz (Hz), each plate also turn on its axis at 4.7 Hz. Silicon carbide is fed between the plates and the concrete as an abrasive material.

2. Steel Ball Abrasion Test:

In this method a load is applied to a rotating head. Steel balls are put in between the head and the concrete. During the test a circulating water jet is applied to remove the eroded material.

3. The Dressing Wheel Test:

In this method a modified drill press is used to apply the load to three sets of seven rotating wheels, which are in contact with concrete surface. The driving head is rotated for 30 minutes at a specified speed of 0.93 Hz. (One Hertz is equal to one cycle per second).

The above tests are useful for determining the resistance of concrete to heavy foot traffic, wheeled traffic and to the tyre chain and track vehicles. Generally speaking, the heavier the abrasion, the more useful the test in the order, revolving disc, dressing wheel and steel ball.

In case of flowing water, the erosion by the solids in water is measured by the method known as shot blast method. In this case 2000 pieces of steel shots of size of 850 micron are ejected or fired under an air pressure of 0.62 MPa from a 6.3 mm nozzle against a concrete specimen located at a distance of 102 mm.

The relation between the abrasion resistance and compressive strength obtained by the three methods prescribed by ASTM C-779-89 has been shown in Fig.13.11. The results of all the three methods are quite different due to the arbitrary conditions of test. Though the values obtained by different methods are not comparable quantitatively, but the resistance to abrasion in all cases is found proportional to the water/cement ratio and thus related to the compres­sive strength.

Thus it can be concluded that the primary basis for the selection of abrasion resistant concrete is its compressive strength. The resistance to abrasion increases by the use of fairly lean mixes and crushed rock aggregate. Concrete which either does not bleed or bleeds only very little has been found to have stronger surface layer and thus is more resistant to abrasion. A delay in finishing the surface is found advantageous. Also for high abrasion resistance, adequate and prolonged moist curing is essential. In situations where surface wear is important the use of light weight concrete is not suitable.

#### Fatigue Strength of Concrete:

The application of repeated load on a material develops fatigue in it. In practice many structures are repeatedly loaded. When a material fails under a number of repeated loads, each load being smaller than the static compressive strength of concrete, then the failure taken place is called fatigue failure. Concrete and steel both have a characteristic fatigue failure.

Type of Fatigue Failures:

Generally there are two types of fatigue failure in concrete:

1. Simple fatigue failure

2. Static fatigue or creep ruptures failure

1. Simple Fatigue Failure:

In this type of failure the failure occurs under cyclic or repeated loading and is known simply as fatigue failure.

2. Static Failure:

In this case failure occurs under a sustained or slowly increasing load near or blows the strength under an increasing load, as in a standard test. This failure is known as static fatigue or creep rupture failure.

In both the cases a time dependent failure takes place only at stresses which are greater than a certain limiting value, but smaller than the short term static strength.

At this stage it will be appropriate to state that in the standard method of determining the compressive strength, the test is carried out in a short duration i.e., between 2 to 4 minutes. The duration of the test is important as the strength of concrete is dependent on the rate of loading.

That is why the standard rate of loading has been prescribed by all standards. IS 516-1959 has prescribed the rate of loading on 150 mm cubes as 0.2 MPa/Second (140 kg/cm2 per minute) and BS-1881 Part-116-1983 has prescribed this rate as 0.2 MPa to 0.4 MPa per second whereas ASTM C 39-86 has prescribed the rate of loading as 0.15 to 0.34 MPa/sec for 150 x 300 mm cylinders.

The rate of loading decreases, the observed strength also is recorded lower than obtained in the standard test. On the other hand if the rate of loading is inc­reased i.e., the load is applied extremely rapid (instantaneously), a higher stren­gth than at the standard test is obtained, but the strain at failure is recorded smaller. Thus it follows that at rapid rates of loading concrete appears more brittle in nature than under lower rates of loading when creep and micro crack­ing increase the strain capacity.

Under low rates of loading, (more duration of loading) static fatigue occ­urs when the stress exceeds about 70 to 80% of the short duration or standard test strength. This limiting (threshold) value represents the start of rapid development of micro cracks, which eventually link and cause failure. Thus when the stress exceeds the 70 to 80% of standard test strength called limiting value, concrete will fail after a certain period which is indi­cated by the failure envelop shown in Fig.13.12.

Under the sustained load also, a similar Phenomenon takes place as shown in Fig.13.13. In this case a certain load is applied fairly quickly and then kept constant. Above the same limiting value of 70 to 80% of the stan­dard test (short term test) strength, the sustained load ultimately will result in failure. At the stresses below this limit, failure will not occur and the concrete will continue to creep.

Static fatigue also occurs in tension at stresses greater than 70 to 80% of the short term strength. However the tensile strain capacity is much lower than com­pression strain capacity.