9.3 numerical basis of modular ratio for dead and live loading

The value of modular ratio is based on  Australian Standards AS 3600:2000 “Concrete Structures Code”, AS 1481:1978 “Prestressed Concrete Code” and equations proposed by ACI committee 209 (1971) through Meyers et al, for the calculation of long term modulus of elasticity. it is a simple process to re-arrange in terms of modular ratio as follows:
:
Ne          =           No . ( 1 + Cct )
Cct         =           Ct . Ca . ke
No          =           Base modular ratio of  8.94  which occurs for Es of 210x10^3
                           mPa and Ec  applicable for  a concrete strength of 25 mPa.
Ct           =           Duration of loading factor.
Ca          =           Factor depending on the age of concrete at first load.
ke           =           Factor depending on slab theoretical thickness.

ke is dependent on the theoretical thickness of the member being considered. For ease of calculation ke has been calculated for the slab depths considered and is incorporated within Table 1C.

By making assumptions in regard to the time at first loading and duration of loading, simple formula can be calculated. In this manner, specific assumptions have been made in section 9.5 for dead load, short term live load, medium term live load, and long term live load, enabling calculations of these particular modular ratio values to be carried out.  These modular ratios are:

NG         =            8.94 + 19.67 ke
NQS       =            8.94 + 5.43 ke
NQM      =             8.94 + 12.86 ke
NQL       =           8.94 + 16.15 keNG  = Modular ratio for dead load acting on slab only.
NQS          =          Modular ratio for short term live load acting on slab only.
NQM          =         Modular ratio for medium term live load acting on slab only.
NQL           =         Modular ratio for long term live load acting on slab only.