In this article we will discuss about the tests performed to determine the tensile and flexural strength of concrete.
Tensile Strength of Concrete:
Splitting Tension Test:
The splitting tension test was developed in Brazil in 1943. Some times this test is also called as Brazilian test. However at about the same period this test was also developed in Japan independently.
Usually this test is carried out on cylindrical specimen by placing it horizontally between the platens or loading surfaces of the testing machine and the load is increased until failure of the specimen takes place by splitting in the plane containing the vertical diameter of the specimen.
When the load is applied along the generatrix, then an element on the vertical diameter of the cylinder is subjected to compressive stress, whose vertical and horizontal components are given as follows:
(a) Vertical Component of Compressive Stress:
(b) Horizontal Component of Compressive Stress:
P = compressive load applied to cylinder
L = Length of cylinder
r = Distance of the element centre from the top load
(D–r) = distance of the element centre from the bottom load
D = diameter of the cylinder.
Horizontal Tensile Stress Distribution:
The loading condition produces a high compressive stress immediately below the two generators to which the load is applied and a larger portion corresponding to depth is subjected to a uniform tensile stress acting horizontally as shown in Fig. 19.4. It has been estimated that the compressive stress acts for about 1/6th depth and the remaining 5/6th depth is subjected to tensile stress.
In practice to reduce the magnitude of the high compressive stresses near the points of application of the load, narrow packing of strips of suitable material such as plywood are placed between the surface of specimen and loading platens of the testing machine. The packing strips should be flexible enough to allow the load distribution over a reasonable area uniformly. To avoid large contact area the strip should be thin and narrow. Normally a plywood strip 3 mm thick, 25 mm wide and 300 mm long is sufficient. If this strip is not used, an 8% lower strength is recorded.
During the spitting test, the platens of the testing machine should not be allowed to rotate in a plane perpendicular to the axis of the cylinder however a slight movement in the vertical plane containing the axis may be permitted to accommodate a possible non parallelism of the generators of the cylinder. This can be achieved by interposing a roller between one platen and the cylinder.
The load is applied at a constant rate of increase in tensile stress of 0.02 to 0.04 MPa according to BS 1881-Part-117-1983. The splitting strength can be calculated by the equation fst = 2p/πLD as equation (ii) above.
Advantages of Splitting Test:
The advantages of this method are as follows:
1. The test is simple to perform and it gives more uniform results than other tension tests.
2. In this test same type of specimen and same testing machine can be used as for the compression test.
3. Strength determined by splitting test in believed to be closer to the true tensile strength of concrete, than the modulus of rupture.
4. Splitting strength is 5 to 12% higher than the direct tensile strength.
However in case of cement mortar and light weight aggregate concrete, splitting test gives very low results.
Flexural Strength of Concrete:
In the flexure test, the theoretical maximum tensile stress reached in the bottom fibre of a test beam is known as the modulus of rupture, which is relevant to the design of highways and airfield pavements.
When concrete is subjected to bending, compressive as well as tensile stresses are developed. Sometimes direct shear stresses are also developed. The strength shown by the concrete against bending is known as flexural strength. The strength per unit area is called flexural stress and usually denoted by ‘S’.
The value of flexural stress can be calculated by the following relation:
S = (M x Y)/I …(iii)
S = stress in the farthest fibre from the neutral axis of the beam
M = bending moment at the section
Y = distance between neutral axis and farthest fibre
I = Moment of inertia of the cross section
The value of modulus of rupture (extreme fibre stress in bending) depends upon the size of the specimen (beam) and the arrangement of loading on the beam.
Size of Specimen:
The standard size of specimen is 15 x 15 x 70cms. Alternatively if the largest nominal size of aggregate does not exceed 20 mm the dimensions of the specimen may be 10 x 10 x 50 cms. IS 516-1964 has prescribed the size of specimen as 10 x 10 x 50 cms with in a span of 40 cms.
System of Loading:
For determining the flexural strength or modulus of rupture following two systems of loading of the specimen may be adopted:
1. One Point or Central Point Loading:
In this system, the load is applied at the mid or central point of the test specimen, which gives a triangular B.M. distribution. The maximum fibre stress will be below the point of loading where the B.M. is maximum. Thus the maximum stress occurs at one section of the beam, not necessarily the weakest section of the beam.
2. Two Point Loading (At Third Point of Span):
This system of loading produces a constant bending moment between the load points, so that one third of the span is subjected to the maximum stress and thus in this region cracking is likely to take place. Nowadays this system of loading is taken as the standard method of loading. In U.K. and U.S.A. also only this method is used. The test can be performed as per IS 516-1964 on a beam specimen of 10 x 10 x 50 cm with a span of 40 cm. The value of modulus of rupture is given by the relation.
When the value of ‘a’ is less than 20 cm but greater than 17.0 cm for 15 x 15 x 70 cm specimen or less than 13.3 cms but greater than 11.0 cm for 10 x 10 x 50 cm specimen. In case ‘a’ is greater than 20 cm for 15 cm specimen or greater than 13.3 as for 10.0 cm specimen, then-
fb = modulus of rupture
p = load applied on specimen in kg
b = width of beam in cms
d = depth of beam at failure point in cm
a = distance between the crack and nearest support
I = length of span in cm on which the specimen is supported.
On the basis of experiments, it has been observed that the variability of the results in two point loading system is less. The results of the flexural strength tested by central point loading and two point loading with a constant ratio of span to depth as 4, were analyzed statistically at Central Road Research Laboratory (Delhi) and the following general relation was obtained-
X1 = X2 + 0.72 …(19.5)
X1 = flexural strength of concrete in MPa under central point loading
X2 = flexural strength of concrete in MPa under two point loading
It has been observed that test results under central point loading gave higher average values than the two points loading irrespective of the size of the specimen. The higher strengths obtained in central point loading may be due to the fact that the beam specimen is subjected to a maximum stress at predetermined section not necessarily the weakest.
In the standard methods for determining the flexural strength of concrete, the span to depth ratio of the specimen was kept constant at 4. On the variation of span to depth ratio, the flexural strength also was found varying. 1% change in the span to depth ratio induced 3% and 2.5 variation in the strength when tested under two points loading and under one point loading respectively. With the increase in span to depth ratio, the flexural strength decreases.