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Re: Pile Cap Design--Strut and Tie method

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I hope the following may be helpful to you.

I am a ssuming you have two pile cap condition.

Based on the strut- tie model,

Ns = F/2tan alpha 
Ns = force in steel; F = Column load; 
alpha = angle between compression strut and tensile steel 

As = Ns/ fy

As = Tensile steel area. ; Fy = Steel stress

Nc = F/ 2 sin alpha

Nc = force in comression strut,

gc  = Nc/Acp sin alpha

Acp = area  of  pile 

gc   =  stress in concrete.

The distribution of tensile steel can be taken within 0.25 Z

Z = effective depth of pile cap.

I don't know whether you have a bottom bars bent upward or not. i.e. 

              1                                                               1
              1                                                               1
              1                                                               1
              1                                                               1    

In above case you have another compressive strut  from pile to upward.

If you use the above concept, you will not violate the strut-tie methodology 

>>> mhemstad(--nospam--at) 09/19/05 4:51 PM >>>
I am attempting to design some large caps carrying loads from single concrete columns into pairs of drilled piers constructed with about 2 feet clear between them.  In one example, the column is 40 inches square and the caps are 84 inches wide and about 16 feet long.  I am caught between what seem to be conflicting Code clauses in ACI 318-02.
Our columns are designed with fc' = 12,000 psi concrete.  Where they land on the pile caps, we invoked ACI  10.17, which allows bearing stresses up to double the allowable of (phi x 0.85 fc') considering the confinement offered by a bearing area larger than the column area.  This, we thought, allowed us to specify pile caps with fc' = 6000 psi.  The column load Pu = 8620 kips, resulting in a bearing stress of 5390 psi.  The allowable factored stress as I calculate it is 2.0 x (phi = 0.65) x 0.85 x fc' = 6000), or 6630 psi.  So far, so good.
However, when designing the caps and their reinforcing using the Strut and Tie provisions of Appendix A, I can find nothing which would allow us to double the stress.  So, the allowable (factored) stress in my struts is only (phi x Beta-s x 0.85 fc').  It seems that I therefore can't carry the 12,000 psi column on a 6000 psi cap.
Does anyone know if the doubling provision of 10.17 can be applied to struts in the Strut and Tie model?  Section A.5.2 may allow some increase in stress for "confining reinforcing," but seems to exclude confining concrete. 
Another, perhaps related question, is when the "bottle-shaped" struts come into play.  When can the struts be considered prismatic, and when will they  swell out to the bottle shape? The Commentary to the definition says that "a bottle shaped strut is a strut located in a part of the member where the width of the compressed concrete at midlength of the strut can spread laterally."  When is this not true?  It seems that all struts will meet this definition in at least one dimension.   This is problematic because if the swelled shape is assumed then confining reinforcing is mandated by A.3.3 to get up to a Beta-s value of 0.75.  If instead a prismatic strut can be assumed (by some unstated justification) then Beta-s can be taken as 1.0.  Yet the allowable stress for the bottle shaped strut is still taken at the ends, before it has swelled.
If anyone can shed some light on these questions, I'd appreciate it.
Mike Hemstad, P.E.
Minneapolis, Minnesota

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