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Braced Cantilever




Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 32
    © Machinery Dynamics Research, LLC, 2015

Braced Cantilever


    Anyone who has actually gotten into machine design is familiar with this difficulty. Consider the situation where a project is well advanced, many plans have been made, and it is all based on the assumption of the adequacy of one particular part. When you finally get to the detailed analysis of that part, the calculations show that it is not adequate. What can you do?
    To make the problem much more concrete, consider the cantilever beam shown in Figure 1. It supports a weight W at the free end, and when someone finally makes the calculation, the tip deflection, δ, is unacceptably large. The whole system design has been developed on the assumed adequacy of that cantilever, and there is no room to put in a beam with a larger section to give more stiffness. What can be done?

    Any of countless machine design texts, mechanics of materials texts, etc., give the formula for the end deflection,


    E= Young's modulus for the beam material
    I= area moment of inertia for the beam cross section
    L= length of the beam
    W= tip load value
    While we can argue that someone should have checked this earlier, finger-pointing does not fix the problem.




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I presume that your very brief comment is a suggestion to use a stiffer material. The calculations were made based on steel. It is very expensive to go to anything stiffer than that, so a material change is not usually a feasible solution.

In any event, the purpose for the note was to demonstrate a method, not to solve a specific problem.


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The only reference document I see is Dr.D's paper on braced cantilever. Since you have painted yourselves into a corner it would be helpful to those you are asking for help to provide a drawing of said corner. E=about 30,000,000 psi for all steels. Some a little lower some higher. As far deflection is concerned going to a different steel will not help unless you are just a small amount beyond the allowable deflection. Having a design that just gets past the min or max requirement is a risky approach. If the cantilever is an H or I section you can add material on the inside surface of the flanges. This is not an efficient use of material. If a tube go to thicker wall by selecting a smaller OD. Again, less efficient use of material.   

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I guess the way it came to me in the e-mail it looked like the someone had asked a question about what to do when your boxed into a corner. I read your original paper a week ago. If came up again when someone suggested a different material and I reread what you wrote but you header stayed above the top of my computer screen so I did not realize that was the into to the paper.

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