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When analyzing a pile or drilled shaft as a beam-column, how do you determine the unbraced length of the portion that is in the ground? Typically, the braced points on a beam or column are well defined, e.g. there are connections at discrete locations.

A pile in the ground will have some resistance to movement because of the soil. Is this resistance enough to consider the pile to be continuously braced (Lb = 0)?

Another way of considering the situation might be to look at the deflection diagram. Should the braced length be based off the first or second point where the deflection crosses zero? Or similarly where the moment diagram crosses zero?

706Astor
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hazzey
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1 Answers1

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$\require{cancel}$ A common method was devised by Davisson and Robinson (1965). By this method, what you need to determine is the "length of fixity", which is given by

$$L_f = 1.8\left(\dfrac{EI}{n_h}\right)^{0.20}$$

Where $EI$ is the pile's stiffness and $n_h$ is the soil's coefficient of horizontal subgrade modulus. This is the relevant length for a buckling analysis, even if your pile is longer than $L_f$. Obviously, if your pile has an uncovered length ($L_u$) , that needs to be added to $L_f$, in which case your buckling length is $L_f + L_u$.

It is worth noting that this equation is not set to a specific set of units, as can be seen by dimensional analysis:

$$L_f = [L] = 1.8\left(\dfrac{EI}{n_h}\right)^{0.20} = \left(\dfrac{\left[\dfrac{\cancel F}{\cancel{L^2}}\right][L^{\cancel{4}2}]}{\left[\dfrac{\cancel F}{L^3}\right]}\right)^{\frac{1}{5}} = [L]$$

This article explains it in greater detail.

Wasabi
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