Dear Javad,

In 2015, we published a paper entitled "Evaluation of the Splitting Tensile Strength in Plain and Steel Fiber-Reinforced Concrete Based on the Compressive Strength". In this paper, we used artificial intelligence -based models to develop models for the prediction of splitting tensile strength in both normal and fiber-reinforced concrete. Table 1 of this paper also provides a summary of previously suggested equations by other researchers.

You should be able to get access to the paper via the following link:

Article Evaluation of the Splitting Tensile Strength in Plain and St...

Regards,

Ali.

Dear Javad,

The Relationship between Compressive Strength – Split Tensile Strength is given by

ft= 0.043fck

1.064 with coefficient of variation R² = 0.990

The Relationship between Compressive Strength –Flexural Strength is given by

fcr=0.031fck1.125 with coefficient of variation R² = 0.989

There are some recommendations for this relationships. The are shown in Sergey Makarenko link. They are also in Eurocode 2 (EN 1992-1-1) and in Model Code 2010. Probably they are similar.

Nguyen Van Quang, you have to be careful because relationships f.ct - f.c and E.cm-f.c can be dependent on various things (some of them are not in codes) for example: quality of aggregate. In some countries some rocks are stronger than other rocks from the same type.

In the design of concrete structures, engineers have the flexibility to specify particular concrete type(s) aimed at meeting the specific performance requirements for their project. For instance, where calculated deflections exceed serviceability limits, the designer can achieve lower deflections by increasing the class of concrete and the associated modulus of elasticity, rather than by resizing members

Dear Javad,

I found one paper with good literature survey related to your question:

https://www.sciencedirect.com/science/article/pii/S1018363916300538#b0150

Best regards

Łukasz Sadowski

Dear Javad,

In 2015, we published a paper entitled "Evaluation of the Splitting Tensile Strength in Plain and Steel Fiber-Reinforced Concrete Based on the Compressive Strength". In this paper, we used artificial intelligence -based models to develop models for the prediction of splitting tensile strength in both normal and fiber-reinforced concrete. Table 1 of this paper also provides a summary of previously suggested equations by other researchers.

You should be able to get access to the paper via the following link:

Article Evaluation of the Splitting Tensile Strength in Plain and St...

Regards,

Ali.

I agree with Ali. This table will be very helpful for your purposes.

Best regards

Łukasz

dear Ali and dear Łukasz

Thank you so much for your comments

but there is just one problem....

This article is about splitting tensile strength and i think it is not useful for my present article, because it seems to me that the use of the splitting tensile strength relation type instead of the direct tensile strength relation type is unreasonable when my tension experiment is direct tension.

Please see the image added here.

The criteria of these three types of tension experiments is different and

the coefficient behind the second root of the compressive strength phrase is different too and for this reason, i cant use the splitting tensile strength relation when my tension experiment is direct tension.

I will sincerely use your feedback and thank you for helping me.

Javad,

I agree with you. These experiments are different and to be more precise you should use the relationship developed specifically for each of them.

Regards,

Ali.

Please have a look at enclosed paper:

Conference Paper RELATIONSHIP BETWEEN SPLITTING TENSILE STRENGTH AND COMPRESS...

go to the book : Properties of Concrete by AM Nevile:

compressive strength = K ( tensile strength )^n

certain tests yield n = 0.5 and average k= 8.3 other experiments indicate that n may vary between .5 and .75

and k may vary between 6.2 and 10.4 depends on type of aggregates

Thank you dear friends Ali, Boriana and Iqbal so much.

I am glad you've found the paper useful. Good luck with your research!

Numerical Relationship

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 trhat any incrase in compression strength, such as that achieved by lowering the water- cement ration, is accompanied by a much smaller percentage increase in tension strength.

Hello dear, now , i work to complete my research about mechanical properties of concrete , in brief , i found strong this relation between the compressive strength and split tensile strength.