compression buckling loads for horizontal beams 3

[kern50440]

I am looking for methods to determine the compressional critical buckling load for a horizontal box beam, includingthe effect of gravity that causes the beam to deflect down under its own weight. Please advise if you know of such an analysis or can suggest how to proceed.

Thank you

 

[JStephen]

The normal approach to the design of the beam would be to treat it as a column with bending due to its own weight, and use the interaction formulas in AISC-ASD or LRFD for combined bending/axial. For example, in AISC ASD, you have one section that gives you allowable bending, one section that gives you allowable compression, and a separate chapter for combination of stresses.

 

[rb1957]

i don't know the building codes, but you could calculate an answer by calculating the deflection of the beam due to it's weight (as a distributed load), and then calculate the critical column buckling load (of an imperfect column).

alternatively, you can calc the beam as a beam-column (a conventional beam with transverse loads and axial compression).

 

[kern50440]

I have calculated the weight based deflection and then added the moment caused by this deflection with the critical compressive load and found that moment to be lower than the moment caused by the weight, by about a factor of three.

Thus I am concerned that the weakening effect may be significant but am not convinced that I have captured it correctly.

I may try to go after an energy based method, any suggestions on doing that??

Thanks to all readera and for comments.

 

[mrMikee]

The AISC combined stress formula takes into account secondary moments (or moment magnification) caused by lateral bending in addition to an axial load. Part of the formulas are the Cm amplification factors in Table C-H1.1 page 5-154 in the 9th edition. Your design could be the first case shown with Cm=1.

Regards,
-Mike

 

[JStephen]

It might help to indicate exactly what the circumstances are. My answer above is for a steel section under US type building codes. And in that case, you don't need to fully analyze the interaction of the bending and compression; you just work through the code formulas. This approach won't give you a critical buckling load, at least not directly. This is the "suggest how to proceed" part of your question.

You might also refer to Roark's Formulas for Stress and Strain for various column formulas. (The column formulas specific to a material or code may be out of date.) He discusses combined bending and buckling and then says "Because these and other uncertainties generally preclude a precise solution, it is common practice to rely upon some interaction formula, such as one of those given below."

 

[rb1957]

i agree with JStephen, but from what you've told us, it sounds to me like a simple beam column. From Bruhn (table A5.1) a beam (with pinned ends) with an axial compression load P, and a transverse distributed load w, has a maximum moment of wj^2*(1-sec(L/(2j))), j = sqrt(EI/P)