9.4 calculation of the section effective modular ratio

From Australian Codes,  modular ratio’s can be obtained appropriate to selected dead and live loading. The effective modular ratio however, is dependent on the proportion of loading due to dead and live loads, and the modular ratio applicable to each loading. Based on these modular ratio’s, the moment of inertia associated to each loading can be found from tables 3A -3I for o.75mm Svelte-floor and tables 4A - 4I for 0.95mm Svelte-floor. From these parameters a realistic effective moment of inertia can be calculated particular to that set of loadings as follows:

Ieff          =            _______Io________
                                 Fdl . Kdl  + Fll . Kll

Ieff         =            effective second moment of inertia
Io           =            average of Icr and Ig  for modular ratio of No
Fdl          =            wdl / wt
Fll           =            wll / Wt
Kdl          =            Io / Idl
Kll           =            Io / Ill
Idl           =            moment of inertia applicable for Dead Load
Ill            =            moment of inertia applicable for Live Load
wdl          =            dead load UDL
wll           =            live load UDL
wt           =            total UDL

In the calculation for serviceability, Neff the effective modular ratio need not be calculated as it serves no purpose, as Ieff is the important parameter. For the purposes of span tables this has been back figured to compare the value of Neff to that used previously.
However, Neff  becomes important in the calculation of shrinkage, as shrinkage forces are dependent on the effective area of the composite section. As shrinkage is modified by creep over time, it is important to use the effective area  rather than the base area, otherwise shrinkage effects will be overestimated. Neff  can be backfigured using the tables 3A - 3I, and 4A - 4I in reverse. Once Neff  is found then values of Aeff  and r can be found from tables 4J and 4K for use in shrinkage calculations.