Rotated stiffness values of a skewed pile bent 3

[AR_PE]

The stiffness of a non-integral 5 column pile bent can be idealized as [5 piles]*12EI/h^3 for the transverse direction (along the bent - assuming a fixed-fixed condition) and [5 piles]*3EI/h^3 for the longitudinal direction (perpendicular to the bent - assuming a fixed-pinned condition). My question is, for a skewed bent, how would you calculate the stiffness of the bent in the global axes direction of the bridge? - Put another way, I can calculate by hand the stiffness of the skewed bent along its local axes with 12EI/h^3 and 3EI/h^3. I am unsure of how to resolve these stiffnesses into the global axes direction of the bridge, which are rotated by the skew angle.

I know this is very simple to model, and I've already done so. I'm just wanting to prove to myself that the numbers provided by the model are valid.

 

[ProgrammingPE]

Here's the model for your system:

You have a diagonal load resisted by two springs with different stiffnesses. You can determine the diagonal stiffness by splitting up the applied load, P, into its X and Y components. Then determine the displacements in the X and Y directions. Then combine them to determine the total displacement. Diagonal stiffness is then P/Delta.

Structural Central

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[KootK]

I feel that programmingPE's solution needs a minor tweak as follows:

Diagonal stiffness is then P/Delta P/(component of Delta parallel to P).

That, because the combined [Delta] won't be parallel to [P].