Entire/Portion of critical section is beyond the footing 2

[samjr]

This is my first time post, I have simple question.

I have been asked to make thicker shallow footings for a gravel wash plant. The footings will have a larger mass to prevent wheel loaders from digging them out or pushing them.

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Here are my parameters:

12 in column
50k load
depth 12 in.
d 8 in.
soil pressure 3000 psf
f'c 3000 psi

My simple calculations give

A 4.5ft x 4.5ft x 12 in.
actual net soil pressure 2469 psf
beam shear 14in/27in 30psi/60psi ok
punch shear 20in/27in 67psi/109psi ok
flexure 21in/27in 17k-ft/43 k-ft ok

fs 16, R 0.152, j 0.87, Steel area 1.83 in2

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When I increase the footing depth to 36 in I get

36 in depth footing
d 32 in

A 4.5 x 4.5ft x 3ft
beam shear 38in/27in ?
punch shear 44in/27in ?
flexures 21in/27in 17k-ft/700k-ft
Steel area 0.46 in2

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I have scoured the net for the condition of "the entire critical section is beyond the footing" and I have found nothing. Schaum only mentions to reduce the perimeter when "a portion" of the critical section lies beyond the footing. Ambrose says nothing.

Please help. Does this mean no beam shear? Does this mean no punch shear? Is it ok to make footings deeper than minimum?

Thanks, preparing for a grilling....

Sam Ricci Jr in southern NJ

 

[SlideRuleEra]

The equations used for the calculations mathematically model the behavior of the concrete footing. With the 36 in thickness and your other parameters the equations appear to "break down" because of the large depth/width ratio.
This is not a bad thing - I interpret your calcs to mean that the footing will work very well at the stated conditions with no reinforcement all (plain concrete footing are common in some applications). Be sure to check loading for all conditions, such as wind, seismic, impact, etc. However for an industial settings, which yours seems to be, I would suggest that you include at least a minimal amount of reinforcement even if it is not indicated by calculations.

As an aside sounds like you are getting good general advice to increase the footing thickness (36 in does sound like a little more than I would have expected however). In many industrial applications it is wise make "things" substantially more robust than calculations indicate.

 

[lowlydirtguy]

What you have is a deep beam. See the deep beam provisions of ACI 318 chapter 11. Traditional shear and flexure analysis methods aren't really valid, but the footing still needs minimum reinforcing. Also, probably not necessary due to the small loads, but consider checking the solution with a strut and tie model. See ACI 318-02 and the last few issues of Concrete International for background on this design technique.

 

[ERV]

For an increase from 12" to 36", to get viable results from you software increase min. steel to 3.70 in2. Punching shear will increase 9 times, beam shear is 0, allowable beam shear is 161,213 lb, all else being the same.

Try a mat of #5 bars 4.25" o.c., 12 min.

Design should also be ok without reinforcement as SlideRuleEra pointed out.

 

[ERV]

I should also mention that with the increase in depth of the footing, you can use an allowable soil bearing pressure increase. In this case, the bearing area of the footing can be decreased from 20.25 ft2 (4.5 ft X 4.5 ft) to 14.00 ft2 (3.75 ft x 3.75 ft), effectively reducing the critical perimeter Bo=90.00 in from Bo=178 in (for 4.5 ft x 4.5 ft footing).

Good Luck, hope this helps.

 

[BigH]

Just a thought - don't you think the actual net soil pressure of 2469 psf is a little "too exact"??? 2500 psf would be more appropriate, I would put forth. My comments are solely for use practictioners to think how accurate we have become since we have these "new" computers and calculators over, say, SlideRuleEra's time.
I believe there is a provision in ACI318 on PCC - Portland Cement Concrete (unreinforced).

 

[samjr]

SlideRuleEra, lowlydirtguy, ERV, BigH:

Thank you for your excellent tips.

I confirmed the "no reinforcement" and "increase allowable soil pressure" threads. I still have to confirm the "increase minimum steel" and "ACI 318 Chapter 11" before I'm happy.

2469 is over exact, but I like to follow the logic before I wave the magic wand...

Thank you.

Sam