[PROBLEM] About empirical formulas

[magicstone1412]

I am studying about floating slab track and I need to find a relationship between 1 dependent variable and 3 or 4 independent variables. I read some documents of AASHTO and found that they construct many formula from empirical. Please let me know how to construct it.
Thank you.

[ynopum]

Usually your task is called "fitting", or "approximation". In general for a chosen function you must find such parameters (coefficients) that the sum of the squared errors between the data and the function is minimum. This is called "least squares method". It will be very useful if you know the physical relationship first, transfer it in mathematical equation with coefficients, and then "fit" the equation to your data by changing the coefficients.

[mdmh10]

Dear Magicstone,

As Ynopum mentioned typically you make a fit of the data using the "square root of the sum of the square method", a.k.a. SRSS, to obtain a coefficient. It is called an empirical formula because you obtain it from matching common parameters from several experimental runs.

The number obtained from the SRSS fit is not derived from mathematical logic, it is derived from changing one variable at a time through several experiments. From only changing a variable at a time a number will emerge using the SRSS method. This is the number you are looking for. It is more of an Statistical Approach, than a physics understanding approach. Hence the name empirical.

Hope this helps your investigation. Personally, I am not a big fan of AASHTO, I rather the simpler approach presented by ACI. Although AASHTO still rules most of Highway designs.

Kind regards,
MDMH