Relative strength of square steel tubing in different orientations
Category: Science > Technology
Asked by: kaan-ga
List Price: $5.00
18 May 2005 20:09 PDT
Expires: 17 Jun 2005 20:09 PDT
Question ID: 523190
This should be a straightforward question for anyone who remembers their strength of materials class from engineering school. We have a boom made from square steel tubing 3" x 3" x 11 gage (about 1/8" wall)and 20 feet long. The boom is freely hinged at one end and supported by a diagonal chain attached 12 feet from the hinged end with the other end about 3 feet above the hinged end. The boom does not carry very much weight, but it is mounted on an agricultural tractor and drivers tend to whack it into obstructions such as fence posts. The question currently being debated is whether it is better to have the tube mounted "square" (flat faces horizontal and vertical) or rotated 45 degrees in a "diamond" orientation. Mandatory question: Which orientation of the tube is stronger and stiffer, and by approximately how much? Why? Optional question: Which orientation will tolerate fence post impacts better? Why?
Re: Relative strength of square steel tubing in different orientations
Answered By: redhoss-ga on 19 May 2005 06:43 PDT
Hello kann, you are correct in your thinking. The section modulus, which is used to calculate bending strength, does depend on orientation in the case of a square shape. Whether the section is a piece of square tubing or a solid square bar the same ratio holds true. In the first case where your boom is mounted "square", the technical term is "axis of moments through center". In the second "diamond" mounting, it would be said to have "axis of moments on diagonal". The formulas for the two cases are as follows: Axis of moments through center: Section modulus = d^3 / 6 = d^3 x 0.167 Axis of moments on diagonal: Section modulus = d^3 / (6 x sqrt 2) = d^3 x 0.118 In both formulas d is the length of a side or 3 inches in your case. You can see by this that the section modulus is larger when the boom is mounted "square" by the ratio of 0.167/0.118 or 1.42. This means that your boom is 1.42 times stronger when it is mounted as you have it now in the "square" orientation. However, this is only true if you are using the boom to pick up a load in a straight vertical pull. If you were to pull at 45 degrees, the "diamond" mounting would be stronger. Now to the problem of fence post impacts. If the boom impacts the post and the load applied is in a purely horizontal plane, then the boom is still stronger by exactly the same ratio. The only thing that would change this is if the post were to hit the boom at an odd angle. I think I have answered all the points of your question. However, if I have left something out or there is anything you don't understand, please ask for a clarification and I will do my best to answer. Hope this wins your bet, Redhoss
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A good clear answer. Thank you very much, Redhoss.
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