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Re: Lateraly loaded piers [2nd attempt]
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- Subject: Re: Lateraly loaded piers [2nd attempt]
- From: Charles Greenlaw <cgreenlaw(--nospam--at)speedlink.com>
- Date: Wed, 26 May 1999 15:43:17 -0700
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
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