It is expected that these two types of strengths are closely related, but there is no direct proportionality. It is noticed that with the increment of compressive strength, the tensile strength is also increased but at a decreasing rate.
A better correlation is found between the various measures of tensile strength and the square root of the compressive strength. A number of empirical formulae connecting ft and fc´ have been suggested, many of them of the following type:
ft = k (fc)n
where k and n are co-efficients. Values of n between ½ and ¾ have been suggested. The former value is used by the American Concrete Institute, but Gardner and Poon found a value near the later, cylinders being used in both cases. Probably the best fit overall is given by the expression:
ft = 0.3 (fc)2/3
where, ft is the splitting strength, and fc´is the compressive strength of cylinders, both in megapascal. If the stress is expressed in pounds per square inch the co-efficient is replaced by 1.7. The above expression was suggested by Raphael. A modification of Oluokun is
ft = 0.2 (fc)0.7
where the strength are in megapascals; the co-efficient becomes 1.4 in psi.
an expression used in British Code of practice BS 8007:1987 is similar, namely
ft = 0.12 (fc)0.7
Bearing in mind that the compressive strength is determined on cubes(in megapascals); ft represents the direct tensile strength.
The difference between the various expressions are not large. What is important, however, is that the power exponent used in the ACI Building Code 318-89( revised 1992) is too low so that the splitting strength is overestimated at low compressive strengths and underestimated at high compressive strength.
These approximate expressions show that tension and compression strength are by no means proportional, and that any increase in compression strength, such as that achieved by lowering the water-cement ration, is accompanied by a much smaller percentage increase in tension strength.
The ACI Code contains the recommendation that the modulus of rupture fr be taken to 7.5 √ fc´for normal weight concrete, and that this value be multiplied by 0.85 for “ sand-lightweight” and .075 for “all-lightweight” concrete giving values of 6.4 √ fc´ and 5.6√ fc´ respectively for those materials. The former refers to light weight concrete containing natural sand for fine aggregate. Linear interpolation may be used for mixtures of natural sand and lightweight weight fine aggregate.