beam deflection for axial load

[torqomatic]

Hi everyone, I am working on a compressive machining fixture that will support a copper rod with a through hole along the center. The boundary conditions I am assuming are fixed-fixed since the fixture will constrain either end of the rod preventing it from experiencing any rotation or pivoting. The issue I am having is that I want to calculate the vertical deflection of the rod as a function of distance from either end, assuming an axial compressive load, but I cannot seem to find any kind of handbook solution. Would I have to solve the diff equation for the elastic curve in order to get the maximum vertical deflection along the rod? This seems textbook for shear loads or transverse loads, but for axial loads I cannot seem to find the maximum vertical deflection. Thanks!

 

[Ppokooj]

Hi, I hope this is what you are looking for? Fl/EA

Regards

 

[rb1957]

research "beam columns" ... beams with transverse loads and axial compression.

an ideal (euler) column doesn't deflect out of straight untill it spontaneously buckles.

a non-ideal column (with eccentric load, end moments, non-straight, etc) will have a bending moment due to the imperfections which'll allow you to calculate deflections (double integration)

Quando Omni Flunkus Moritati

 

[LittleInch]

That was my concern, that in axial load a perfectly straight pipe (that's what I would call a rod with a hole thrugh the middle?) won't delfect until it buckles. The other problem I have is that unless your axial load is distance limited or reduces as it moves axially, then as soon as you get a deflection in your rod / pipe then with a constant axial force the rod/pipe will simply continue to deflect until it breaks unless the axial force is prevented from travelling beyond a certain distance or reduces once the pipe starts to deflect.

Can you advise on this or provide a sketch for people to understand your problem.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[rb1957]

to that tag line i'd add "never overlook the possibility that everyone could be wrong"

Quando Omni Flunkus Moritati

 

[LittleInch]

I do say "usually"...., but I'll consider adding that. Am I wrong?

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[torqomatic]

Hi again, I attached a photo to more clearly illustrate the problem. The locating pins fix the rod to the lathe chuck and prevent rotation or movement (tries to be a fixed support as much as possible). I am after the delta X between the centerline of the deformed rod and the non-deformed rod in the bottom sketch, which I would like to plot versus force. I was not aware that the beam experiences 0 deflection until it buckles as LittleInch stated.

 

[rb1957]

the out-of-striaght deflection depends on the imperfections assumed. as a perfect colum, it'll compress (slightly) untill it reaches it's buckling load and then (instantly) go unstable.

you're clamping end-to-end ... so parallelism of the ends (and real world lack thereof) would affect your column.

Quando Omni Flunkus Moritati

 

[Tmoose]

Like Ppokooj said, I'd think of it like this, but in reverse.

http://lh3.ggpht.com/_wp3no4qMw7Q/T...hrb34/bungeejump (11)_thumb[1].jpg?imgmax=800

http://altitude-blog.com/wp-content/uploads/2010/07/Bungee-Jump-Jean-Yves-Pikulik-13.jpg