Energy equation and change in potential energy of a column?

[saintgeorges]

I am looking for an expression for bending energy and for the change in potential energy coming from the selfweight of a vertical circular solid column, or maybe from vertical point load on top of it.
Any ideas where I could find these?

Thank you.

 

[BUGGAR]

Physics, Parts I and II by Halliday, J. Wiley.

 

[rb1957]

"bending energy" for "vertical column" axially loaded = none ?

Quando Omni Flunkus Moritati

 

[saintgeorges]

Thank you for the reply, both of you.

It should be "potential" energy, instead of "bending". Terribly sorry about that. So "an expression for potential energy and for the change in potential energy coming from the selfweight/or point load on top of the column" is the right sentence.

@Buggar. Thanks.
I found a preview of a book "Fundamentals of Physics Extended 9th edition" by authors Halliday, Resnik. Could that be it?
It has a chapter 8 "potential energy and conservation of energy" (in part I). This is a page 171 preview:



But this equation is a classical example of a block attached to a spring.
How could that be applied to a rod, column under compression?

 

[rb1957]

heard of L/EA ? (the stiffness of an axially loaded rod (or column)

Quando Omni Flunkus Moritati

 

[saintgeorges]

Thank you rb1957.
So I could use the general expression for elastic potential energy? :

U(x) = (1/2) * k * x^2
k = (A*E)/L
U(x) = (1/2) * ((A*E)/L) * x^2
?
So that's the expression for elastic potential energy of axially loaded column?


The change in potential energy would be the derivative of upper expression:

U'(x) = 2 * (1/2) * ((A*E)/L) * x
U'(x) = ((A*E)/L) * x
?