Foundation mat with a cracked section?
Foundation mat with a cracked section?
(OP)
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?
I appreciate your time and help...
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?
I appreciate your time and help...






RE: Foundation mat with a cracked section?
RE: Foundation mat with a cracked section?
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.
RE: Foundation mat with a cracked section?
Keep in mind that the cracked section isn’t over the entire mat slab, so in reality the slab has varying section properties. Depending on how “precise” 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’t that exact. The actual forces are probably somewhere in between the “cracked” results and the “fully cracked” results. I would consider sizing reinforcing based on the highest moment from each analysis. From the values you have shown, there probably won’t 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.
RE: Foundation mat with a cracked section?
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
RE: Foundation mat with a cracked section?
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.
RE: Foundation mat with a cracked section?
Others, thank you all for very useful insights. Eng-Tips is truly one of the best engineering resources around...
RE: Foundation mat with a cracked section?
I do agree that if the mat is relatively thick, Ma may not exceed Mcr, then it doesn't matter anyway.
RE: Foundation mat with a cracked section?