Maximum Deflection in Columns: Fixed & Free End

[Gurasees]

How can I find maximum deflection in a column with one end fixed and other free?

 

[russ_watters]

https://www.engineeringtoolbox.com/cantilever-beams-d_1848.html

 

[Gurasees]

https://www.engineeringtoolbox.com/cantilever-beams-d_1848.html

But the column is vertical and it has axial load on it.

 

[russ_watters]

But the column is vertical and it has axial load on it.

Isn't that the same thing, just rotated 90 degrees? Can you post a diagram?

 

[Gurasees]

Isn't that the same thing, just rotated 90 degrees? Can you post a diagram?

https://www.engineeringtoolbox.com/euler-column-formula-d_1813.html
need the deflection for 4th case (n=0.25)

 

[russ_watters]

https://www.engineeringtoolbox.com/euler-column-formula-d_1813.html
need the deflection for 4th case (n=0.25)

Oh, right - axial. I don't think there is a specific deflection, since the column is either stable - and returns to center - or unstable - and catastrophically fails

 

[256bits]

How can I find maximum deflection in a column with one end fixed and other free?

Keywords:
deflection,
column,
axial,
loaded

so I looked up "deflection axial loaded column"
and received a bunch of hits to look through.
Perhaps one discussion can be found that is acceptable, as the mathematics is most likely something you are not yet acquainted with. ( Maybe you are. )

Such as,
http://ocw.nthu.edu.tw/ocw/upload/8/258/Chapter_9-98.pdf --> for a cantilever beam
https://ocw.mit.edu/courses/aeronau...ng-2006/materials-structures/gm12_13notes.pdf
http://www.engr.mun.ca/~katna/5931/Buckling2.pdf --> discusses pin-support
( But also a discussion on EXTENSION OF EULER'S FORMULA TO COLUMNS WITH OTHER END CONDITIONS )

You will notice that the equation for bending

d²w/dx² = M / EI

applies to either transverse or axial loading. ( As far as I remember from beam loading )

Boundary conditions are what makes the difference.
the support and loading points can be either fixed or pinned or free, and that makes a difference on how much load the column can support safely.

 

[Dr.D]

Oh, right - axial. I don't think there is a specific deflection, since the column is either stable - and returns to center - or unstable - and catastrophically fails

Often this is correct, but not in all cases. With the necessary material properties, a column can buckle but remain elastic. This has been studied extensively in the classical literature under the title "theory of the elastica." In such cases, the mode of deformation shifts from axial compression to bending. It can remain stable in bending just as well.. Long ago, I built a spring using columns in the post-buckled state and it worked beautifully.