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RE: Pole Embedment Formula

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At 03:38 PM 9/24/99 -0700, Mark Swingle, SE, wrote:
>Charles, can you elaborate on your [9/16/99] reply?
>
>1.  If the pole formlae don't apply in rock, then how would one 
>    determine the depth of embedment required to resist the 
>    lateral force P?

Answer:   Darned if I know. I would have to figure some way other than those
two formulas. I could ask this list, but that sorta already happened, to no
avail. Whoops, Joseph Grill's reply just came in with a method.

>2.  Then, how would one determine the point of fixity in rock?  
>    How did you come up with fixity at d/6 below the surface?
>    I was "taught" by several engineers that fixity is at d/3,
>    although no justification was given.  Sometimes soils 
>    engineers would allow fixity at 2' below the top of rock,
>    but not all are willing to give an answer.

Answer: I never said where the point of fixity is. I don't even know what
"point of fixity" means in these usages. That's why I suggested going back
to the soil engr for an explanation. That's who used the term.

Any engineer who can't or won't explain what they are recommending is an
engineer who worries me. This even includes soil engineers. I still believe
in "well-established principles of mechanics" that designs are supposed to
admit of a rational analysis in accordance with.

Suppose you had a "pole" to be of reinforced concrete cast in place, and
instead of it being cast in earth, or in rock, you cast it into a great mass
of monolithic poured concrete, that would have a cylindrical hole formed for
the purpose. (Or maybe you cast the surrounding concrete around a precast
pole.) The questions still are: How deep should the embedment be? How far
down is the point of fixity, whatever that is?  Fancy asking a soil engineer
the question now. The only difference is the "bedrock" now is man-made to a
specification, instead of the specification being discovered later by
testing old rock that's been found there.

In the max moment quantity and depth determinations I have made, I merely
used the shape of soil reaction against the pole that the original
researchers published for the unconstrained condition. I was taught this by
Walt Buehler, and later came across the research. They agreed. 

        In this shape the upper horizontal soil reaction curve, opposing the
applied load P, is parabolic with no load at both ground surface and at 0.68
d; max pressure in that stretch (and its centroid) is at 0.34d. At 0.68 d,
the pole is rotated but not displaced laterally, hence no reaction pressure
there. Below 0.68 d, soil reaction on the pole acts in the other direction;
max value of it is at the bottom and the centroid is at 0.90d. In the
published model, these proportions are constant. They evidently presume the
pole is stiff enough that it is rigid compared to the soil. (I am aware that
the subject of total rigidity is touchy right now --sorry.) At no location
is the pole unrotated, and at no point between ends is the pole moment
zero.(ie, no point of contraflexure.) How a so-called "point of fixity"
relates to this has me stumped.

        Knowing P, h, d, and the centroid locations for the resisting pair
of soil reactions, statics gives you the magnitude of the two horizontal
soil resultants. From the upper one the plf soil load distribution may be
figured from the ordinates of a parabola. At the depth below effective grade
where opposing soil reaction totals up to the magnitude of P, pole shear is
zero and that's where max moment occurs. Find moment it by statics. All done.

        In spite of the original research's reported findings, I'm not
satisfied that the height of soil reactions in terms of d are actually quite
so unvarying, for all ratios of h to d, but forseeable variations would not
change the outcome much compared to the effect of all the usual
uncertainties of load and material properties.           

Hope that's responsive, 

Charles O. Greenlaw  SE   Sacramento CA