Cracked Section for Foundation Mats?

[LicensedToPEe]

I’m modeling a foundation mat using STAAD and I wanted to know how you model cracked section mats supported on soil springs only. For flat plate and slabs, ACI 318-05, Section 10.11.1 recommends using 0.25 I_gross, which I’d put into STAAD as 0.25*E_concrete (since deflection is normally calculated as a factor*E*I in the denominator). Here are the results, as an example:

Un-cracked section mat:

Base Pressure min/max = 741/4,328 psf
Deflection max = 0.200”
Mx min/max = -104/78 kip-ft/ft
Mz min/max = -61/84 kip-ft/ft


Cracked section mat:

Base Pressure min/max = 200/7,091 psf (64% increase!!!)
Deflection max = 0.328” (64% increase as well, since proportional)
Mx min/max = -95/77 kip-ft/ft (slight reduction in moments)
Mz min/max = -65/46 kip-ft/ft (83% reduction in mid-span moments!!!)

I guess I’m a little confused why is there a difference in the moments? Where do the section properties such as E or I come in play in M=wL^2/8 (as a very simple case)? Isn’t loading, shear and moment independent of the section properties?

Also, am I right to think that service loads deflection and soil pressure should be calculated using a cracked section and then the analysis should be re-run with an uncracked section to obtain ultimate strength factored moments and shears?

Thank you,

 

[rapt]

Seems logical. The stiffer the matt (less cracked) compared to the supporting material the more even the pressure distribution (infinitely stiff would give even pressure), the smaller the deflections and the bigger the moments.