foundation mat with a cracked section

huangyhg

foundation mat with a cracked section?
i鈥檓 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鈥檇 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鈥?br />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鈥?(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鈥檓 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鈥檛 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?
i appreciate your time and help...

well, your w isn't uniform anymore.  when you consider the effects of cracking and how it effects your i where it actually cracks (at midspan) more of the load moves toward the support (column) - hence the increased pressure.  that increased pressure near the support and decreased pressure at midspan will decrease your moments.
i think, you are getting different results when you are considering reduced "i" is due to the fact that you are introducing flexibility in the foundation. in other words, rather than a rigid foundation now you are designing a flexible foundation.
before you start reducing the moment of inertia you may need to figure out if your mat foundation is really flexible. if it is not, then you should use gross moment of inertia.
if it helps.
the differences are probably due to the relative stiffness of the concrete slab compared with the subgrade. if you had a mat bearing on an infinitely rigid subgrade, the displacments/moments would approach 0.  as the section properties and subgrade stiffness decrease and the difference between the slab/subgrade properties increase, it would be reasonable to expect the displacements/moments would increase.  the increase in [maximum] bearing pressure is probably due to a local load [e.g., a building column] being distributed through the slab to the subgrade.  the more flexible the slab is, the less it can distribute the pressure to the elastic soil. also, if this is a slab supporting perimeter walls, and the walls are modeled with fixed bottoms, the relative stiffness of the walls/slab could affecting the stiffness of the slab.
keep in mind that the cracked section isn鈥檛 over the entire mat slab, so in reality the slab has varying section properties.  depending on how 鈥減recise鈥?one wanted to be, different cracked section properties could be assigned to different elements to model the varying properties.  but this can be a tedious, iterative process. and in reality, the analysis isn鈥檛 that exact. the actual forces are probably somewhere in between the 鈥渃racked鈥?results and the 鈥渇ully cracked鈥?results.  i would consider sizing reinforcing based on the highest moment from each analysis.  from the values you have shown, there probably won鈥檛 be a difference in the sizes anyway.  but the maximum bearing pressure also needs to be acceptable, so the mat thickness may need to be adjusted for that.
interesting discussion--i always design mats as uncracked--never thought of using cracked section properties.
howver, adamu, you have it backwards--under service loads, the mat will probably remain uncracked, so the uncracked section properties should be used.  under ultimate loads, the section will crack and the loads will redistribute as discussed above (and as your model indicates).  use whichever design moments you are comfortable with, but i would not worry about that 7091 psf bearing pressure--i don't think it is realistic.
daveatkins
agree with jkw05 that the moments are a function of the relative stiffness between the strucural elements and the support springs, so shear and moment are not independent of the section properties.
article 10.11 is more applicable to frame analyses than mat foundations.  if you are just modelling the mat, i would use article 9.5.2.3 and 9.5.2.4 (i'm using 318-02, so the reference numbers may be different from 318-05).  i believe that the reduction in stiffness is not so great.  seventy five percent reduction may apply to elevated flat plates and flat slabs, but it doesn't feel right for a foundation mat.
for deflections and bearing pressure, i would use service loads, using service load moments to calculate effective moment of inertia.
for strength, i would use factored loads, using factored moments to calculate effective moment of inertia.
daveatkis, yes i did have it backwards. i did mean to say uncracked/service loads and cracked/strength design. thanks for pointing that out to me.
others, thank you all for very useful insights. eng-tips is truly one of the best engineering resources around...
i don't quite agree with daveatkins about using the uncracked section for service loads.  ieff is related to mcr and ma.  ma is the unfactored moment.  and i don't think it is appropriate to consider applying a service load to a different section than the ultimate loads. the ultimate load is just a "factored" load for strength design, not a real applied load. and once the section cracks, it stays cracked.
i do agree that if the mat is relatively thick, ma may not exceed mcr, then it doesn't matter anyway.
why not take the moments that you get out of analysis with uncracked section and actually see if it cracks under service loads before making the wrong assumptions?