Embedded Post / Pole Depth for Lateral Load (IBC 1807.3)
How deep the post actually goes - the question every fence, sign, deck-rail, and flagpole install starts with, which post-hole-concrete (volume) and anchor-embedment (concrete bond) never answer. The IBC 1807.3 nonconstrained formula d = 0.5A(1 + sqrt(1 + 4.36h/A)) with the lateral bearing taken at one-third depth (implicit in d, solved iteratively), the constrained slab-at-grade closed form, and the 1806.3.4 isolated-pole 2x increase. A 6-ft fence post with 200 lb of wind at 4 ft sets 52 in deep; a slab at grade cuts it to 34 in. Enter the lateral bearing from your local code - no table shipped.
Formula and source
Nonconstrained (Eq. 18-1): d = 0.5 A (1 + sqrt(1 + 4.36 h/A)), A = 2.34 P/(S1 b), S1 at one-third the embedment (implicit in d, solved iteratively). Constrained (Eq. 18-2): d^2 = 4.25 P h/(S3 b), S3 at the full embedment. Isolated poles: 2x lateral bearing per 1806.3.4.
The IBC Section 1807.3 embedded posts and poles design equations and the 1806.3.4 isolated-pole increase, by name; the formula pair dates to the legacy UBC and is unchanged across the 2018-2024 IBC editions.
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