Compressive strength of concrete in INDIAN STANDARDS is denoted by fck(characteristic compressive strength).The METHODS OF TESTS FOR STRENGTH OF CONCRETE is given in IS:516–1959.
The compressive strength of concrete is given in terms of the characteristic compressive strength of 150 mm size cubes tested at 28 days (fck). The characteristic strength is defined as the strength of the concrete below which not more than 5% of the test results are expected to fall.
Compressive strength of concrete =fck
When we take into account factors like shrinkage and creep into account,extensive research has found the extent of relaxation of compressive strength in steel to be 15%.
Compressive strength of concrete = 0.85fck(after shrinkage and creep)
Now,I want to quote the text from IS:516–1959 directly here. This excerpt is as follows,
5.6.1 A correction factor according to the height/diameter ratio of specimen after capping shall be obtained from the curve shown in Fig(not reproduced here owing to copyright). The product of this correction factor and the measured compressive strength shall be known as the corrected compressive strength, this being the equivalent strength of a cylinder having a height/diameter ratio of two. The equivalent cube strength of the concrete shall be determined by multiplying the corrected cylinder strength by 5/4. Also, the comparison between the compressive strength of cube and compressive strength of cylinder, a factor of 0.8 to the cube strength is often applied for normal strength concrete .
Compressive strength of concrete = 0.8*(0.85fck)=0.68fck=(fck/1.5)
Thus,this factor of 1.5 was arrived at after extensive amount of research, experimentation and applying proper reasoning..