Eccentric load on column

[Engguy86]

Just a quick question about eccentric loading on a pinned-pinned column.

My understanding was that if you had a column with an eccentric load P. If you took a Free body diagram half way down the column this eccentric load was cause a moment (P x e).
e being the eccentricity. But would this not cause a the column to bend increasing e hence increasing the moment which again increases e and so on?

Should that mean that a column could not support any load at all!... Doesnt seem right

Cheers!

 

[IDS]

If the load is equal to or greater than the buckling load, then yes the column will buckle.

If the load is less than the buckling load then the additional moment caused by the deflection will be less than the reaction moment caused by the deflection, so the total deflection will be finite.

This is the basis of the theory of buckling.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rb1957]

how do you balance the offset moment with a pinned column ? unless the reaction is offset (same as the load) ?
or do you have a lateral couple (which'd make is a beam column) ?

also i think the FBD assumptions are wrong, 'cause you have not accounted for column bending. look up "secant equation for columns with offset loads".

Quando Omni Flunkus Moritati

 

[DaveAtkins]

If the eccentric load is at the top of the column, the moment will be P*e at the top of the column, decreasing to zero at the bottom of the column. So the moment at midheight of the column is P*e/2.

But I am not sure I am addressing your question.

DaveAtkins

 

[rb1957]

if the load is offset, but the reaction is axial, then there'll be a transverse couple (= Pe/L) to react the offset moment ... which accounts for 1/2 the moment at the mid-length. tranverse loading on a column = beam column.

Quando Omni Flunkus Moritati

 

[JAE]

rb1957,
Like your latin sub-signature. I love the RG show.

But did you ever see this?:

http://www.vocabulary-lesson-plans.com/latin-phrase-when-all-else-fails.html

Check out Eng-Tips Forum's Policies here:
faq731-376

 

[paddingtongreen]

At the point of application, there is a total moment of Pe, there are horizontal reactions Pe/H, if H is the height of the column.

Above and below the point of application, the moment at any point along the column is the horizontal reaction multiplied by the distance to the reaction.

If the point of application is not at the mid-height of the column, there will be a small horizontal deflection. If P is huge and e is small, the deflection could conceivably add a significant amount to e, but it is unlikely. The calculation is not difficult.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[IDS]

Surely the loading described in the OP is a standard buckling case, as shown below:

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[paddingtongreen]

OP says it is an eccentric load. I generalized it to be applied anywhere on the column, as with a bracket part way up the strut. I limited myself to the eccentric load because OP doesn't mention any other load.

Looking back, I see there is just as good a case for your interpretation and answer.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[structSU10]

I think the OP is really just getting at what a P-delta analysis takes into account - an applied moment to the column creates an additional eccentricity for the axial load, and you keep iterating until convergence. The idea is there is going to be some loading that will not converge for a given member, but in any reasonable case the P-delta effects are very small, and the solution will converge. There is a closed form solution to a column with an eccentric axial load (See Structural Stability Theory and Implementation by WF Chen & EM Lui) where an amplification factor can be determined as Af = sec(pi/2 * SQRT(P/Pe)) where Pe is the euler buckling capacity. From this the maximum midspan deflection is Af*e and max moment is Af*P*e.

 

[DaveAtkins]

This is what is known as "P-little delta," and AISC Appendix 8 can be used for analysis and design.

DaveAtkins