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Re: Lateraly loaded piers [2nd attempt]

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Replying to Luke Gunnewegh,

It appears that you have modeled a vertical beam cantilevering up from
embedment in soil, and the applied lateral load resultant is at or above
effective grade. You are interested in the location and amount of maximum
moment.  Yes?

One answer is absolutely certain, from principles of mechanics:  Maximum
moment is located where the transverse shear is zero, and its value is the
sum of the several resultant horizontal forces times their moment arms about
this zero shear location.

The uncertain part is the distribution and magnitude of horizontal soil
pressure on the pile (or pole,or vertical beam) from grade down far enough
that the applied shear above grade is all taken out by soil reaction shear
below grade.

There is a conventional soil distribution pattern assumed in the embedded
pole embedment depth formula in UBC Chap 18 for unconstrained poles. The
source is studies done at Notre Dame Univ and Purdue in the 1940's for the
OAAA, the advertising billboard sign people. This distribution has the
resisting horizontal soil pressure in a parabolic curve, zero at the
effective surface and zero at 0.68 of total effective depth. Maximum
resistance is at 0.34 of effective depth, and the resultant of resistance in
this direction is also at 0.34 of effective depth. (below 0.68 d, the soil
pressure acts the other way in practically a straight line distribution; its
resultant is at 0.90d)

The caveat here is that the pole or pile is apparently assumed "rigid" in
flexure compared to the soil, and for its entire depth; further, the soil
properties are assumed rather uniform the full depth of embedment.

If all of the upper soil resistance couple happened as a concentrated
reaction at 0.35 d, then the moment would be P(h+ 0.35d) as another reply
suggested. But the soil resistance is distributed, and the effect of this is
that zero shear is higher up than at 0.34d, and max moment less than as
shown above. 

I worked out in 1992 [in opposition to a SEAONC Code Committee proposal that
would have mandated M = P(h+.34d) in all cases] a range of values for
varying heights of P, from at effective grade (h/d =zero), to h/d= 16 for a
very tall pole.

For P at grade, zero shear came out at 0.39 d, and moment there was P(h+.24d)

For h = 0.5d, zero shear came out at 0.29 d, and max M there was P(h+ .19d)

For h = 4.0d, zero shear was at 0.14 d, and max M there was P(h+ .09d)

Again, these results are for the modest depths as obtained where lateral
resistance, not vertical, controls the depth of embedment, and the
structural element is comparatively rigid, and soil reaction follows that
idealized curve.

Where relative rigidity of soil compared to pile is substantial, then
getting the soil reaction distribution is more interesting. But principles
of mechanics still hold.

Amer Society of Agricultural Engineers has a detailed paper, EP486, titled
Post and Pole Foundation Design, that covers both constrained and
unconstrained conditions. ASAE, 2950 Niles Road, St. Joseph MI 49085-9659
USA, 616-429-0300   Dr Neil Meador at U. of Missouri-Columbia, 314-882-6680,
is an Ag Engr expert on this subject.

If you have too much M in the unconstrained condition, you can reduce it
some if you build in a restraint slab or other provision at grade. I did
this recently as a cure for such a problem.

Charles O. Greenlaw SE   Sacramento CA