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DMT69
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I would like to calculate the maximum stress in a hollow beam being bent laterally. There has been some discussion in my office about the correct way to view the system in question, and so would like some other opinions on the matter.
I will include pictures below. In simplified terms, the system can be though of as a pipe with small hollow beams welded across the pipe. The system then rests on another solid beam, so that the two hollow beams act as axial stops to prevent axial movement of the pipe.
The problem is that the pipe has a bending moment, which will be transferred in some manner to the axial stop hollow beams. There is concern that they will not be able to handle with load.
Some of the questions that have come up:
1) which moment of inertia to use: should the system be two parallel cantilever beams, add there thickness and then have a longer distance from the center for stress? Or is there some sort of twisting moment of inertia to use instead?
2) how is the pipe's bending moment transferred to the support beams? Does it induce the same moment in the beams? Is it transformed into a point/distributed load on the beams?
3) are both hollow beams affected, or only the one taking the downward load? Does the one on the other side help resist the load at all?
I haven't put in any numbers, since I want formulas. Assume hollow beams have a thickness of t, a square cross section with side length x, and length L. Bending moment from the pipe is M.
Here is the hollow beam and cross section:
https://drive.google.com/file/d/0B7abncbCKejtSmtHVUJoOGE1V1U/view?usp=sharing
Here is a side view. The purple pipe is welded to the blue hollow beams. This also shows how the bending moment is acting:
https://drive.google.com/file/d/0B7abncbCKejtV3ZNSVJybmNGa1E/view?usp=sharing
And here is a top view of the system:
https://drive.google.com/file/d/0B7abncbCKejtV2ItaXpiWDFESDA/view?usp=sharing
I will include pictures below. In simplified terms, the system can be though of as a pipe with small hollow beams welded across the pipe. The system then rests on another solid beam, so that the two hollow beams act as axial stops to prevent axial movement of the pipe.
The problem is that the pipe has a bending moment, which will be transferred in some manner to the axial stop hollow beams. There is concern that they will not be able to handle with load.
Some of the questions that have come up:
1) which moment of inertia to use: should the system be two parallel cantilever beams, add there thickness and then have a longer distance from the center for stress? Or is there some sort of twisting moment of inertia to use instead?
2) how is the pipe's bending moment transferred to the support beams? Does it induce the same moment in the beams? Is it transformed into a point/distributed load on the beams?
3) are both hollow beams affected, or only the one taking the downward load? Does the one on the other side help resist the load at all?
I haven't put in any numbers, since I want formulas. Assume hollow beams have a thickness of t, a square cross section with side length x, and length L. Bending moment from the pipe is M.
Here is the hollow beam and cross section:
https://drive.google.com/file/d/0B7abncbCKejtSmtHVUJoOGE1V1U/view?usp=sharing
Here is a side view. The purple pipe is welded to the blue hollow beams. This also shows how the bending moment is acting:
https://drive.google.com/file/d/0B7abncbCKejtV3ZNSVJybmNGa1E/view?usp=sharing
And here is a top view of the system:
https://drive.google.com/file/d/0B7abncbCKejtV2ItaXpiWDFESDA/view?usp=sharing