Load bearing capacity of a tall column

[Barnsaver]

Could someone please tell me the load bearing capacity of an 8" x 8" x 10 foot tall white oak column. The oak is fully cured and would be placed on an appropriately sized concrete footing. It would be mechanically fastened to a beam that it would be supporting.
Any assistance or explanation with the calculation would be sincerely appreciated. Thank you.

 

[erobz]

If we consider the base as "fixed", and the opposite end as "free" end condition. Then the critical load from Euler's Formula:

$$ P_{cr} = \frac{ \pi^2 E I}{L_e^2} $$

Where

$P_{cr}$ is the critical load for the onset of buckling
$E$ is the Modulus of Elasticity for your material ( oak - white oak - if you can find it )
$I$ is the moment of inertial about the centroid of your 8 in square column $= \frac{1}{12} b^4$
$L_e$ is the effective length of the column for the given end condition $= 2 L$
$L$ is the height of the column

Make sure you convert all your units so they are consistent.

This model assumes the load is not eccentric ( i.e it can be effectively applied at the centroid of the column cross section )

Also, in practice there is most likely a Design Factor of Safety applied (depending on the application and material type)

You're probably ok if the actual load is less than half of the critical load, but I wouldn't say for sure.

You should consult a Structural Engineer for more accurate information on column design and applicable code, or if this thing collapses (because the actual loading situation was not accounted for) people could be seriously injured.

 

[jrmichler]

Before using the Euler formula, it is necessary to calculate the slenderness ratio to find if the Euler column buckling formula is applicable. The end support conditions are critical - uneven support can cause big problems.

If the Euler formula does not apply, it is a simple compressive stress problem. But even a simple compressive stress problem is critically dependent on a correct value for allowable stress. Allowable stress for wood varies widely depending on grain direction, defects, knots, moisture content, and other variables.

A complete and correct answer would require more information and a deeper engineering analysis, and is beyond what PF does. Therefore, and for liability reasons, this thread is closed.