In working stress method IS 456 considers modular ratio m = 280/(3 σcbc). Is it correct?

The short-term modulus of concrete does not take into account the effects of creep, shrinkage, and other long-term effects. Accordingly, the modular ratio m is not computed as m = Es/Ec = 200000/[5000 /sq. root(Fck)].??The value of m, as given in sec. 13.34.6 d, i.e., 280/(3σcbc), as per the code takes into account long-term effects such as creep. As per pp. 137 0f SP 24-1983, this formulae seems to have been derived based on long-term experiments. This is also mentioned in the note of cl. B-1.3 of IS 456.

?The values of Es/Ec and 280/(3σcbc) are compared below:

Grade 280/(3σcbc) Es/Ec

15 18.66 10.33

20 13.33 8.94

25 10.98 8

30 9.33 7.3

Using the expressions given in ACI and EuroCode2 for long term and short term Ec, it may be found that Ecl/Ec of concrete is not very high after 28 days and is 1.2 to 1.4 only and is dependent on the type of cement used. Thus, the modular ratio suggested by IS 456 seems to be very high.