formula to calculate critical load of a free ends slender

[limct]

Can any one tell what's the formula to find the critical load like for a slender which has both it's ends free and subject to axial compression.

Many thanks.

Best regards,
ct

 

[rb1957]

does "free" mean pinned ? (no moment reaction)
slender means high (L/rho)
perfectly straight means euler equation (pi^2*E*I)/(L^2)

 

[Allen]

free cases:

1. rotation free (but guided) & translation fixed
2. rotation fixed & translation free (but guided)
3. rotation free & translation free (but guided)

Which one?

 

[limct]

OK, to be exact, it's case #3, meaning rotation free and translation free.

Best regards,
ct

 

[rb1957]

? i must be missing something ... both ends are free to rotate and translate, yet they still react endload ??

maybe your slender rod is supported on axial springs (or something like), 'cause there has to be some connection to ground, no?

 

[limct]

Let's put it this way, a rod that's simply compressed axially while both of it's ends are not locked nor screwed nor pinned to nothing.

Best regards,
ct

 

[Allen]

If like this:
F---> ------------- <---F

Then the rod won't behave statically, I mean it will JUMP,and after that no applied forces!

so this is not a buckling problem ( and can not be #3), because as soon as it starts to buckle it will jump out.

May I ask where is the application for this?

 

[rb1957]

I think you are describing something like a toothpick in the jaws of a bench vice ... the slender rod is not physically connected to the load but the ends are constrained. this is effectively a pinned connection. the rod should be able to resist compression loads up to the euler load, see earlier post, then as allen4 notes the buckled shape will induce side loads which the restaint cannot react so the rod fails.