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I want to determine how much force in Newtons will be need to bend a solid cylinder of magnesium. The cylinder is (x) cm in diameter, and it is (l) cm long. The density of normal magnesium alloy is 1.8 grams per cubic cm. The yield strength is 130 MPa, the tensile strength is 220 MPa, the Young's modulus is 45 GPa, and the melting temperature is around 615 degrees Celsius. All the information about magnesium alloy can be found here.

How can I calculate the amount of force needed to bend a magnesium cylinder with variable diameter and length, or the minimum force needed to break the magnesium cylinder by bending? If I had a general formula, I could then use Newton's law to find how much mass can be put on the cylinder in order to bend it or break it by bending, based on the gravity of the planet Earth.

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  • $\begingroup$ @ViktorRaspberry - Bending under a uniform load, applied moment, or point force? Point force at the end, middle, or some other arbitrary location? When you say "bend", I'm assuming you're asking for the force required to permanently deform the metal. Is this correct? When you say break, how many forcing cycles are you interested in before breakage? How is the fixed (unforced) end of the cylinder retained? Is it welded, bolted, clamped, etc.? What are the specs of the fixing connection (weld shape, thread size, etc.)? $\endgroup$
    – Chuck
    Commented Jan 3, 2016 at 18:23
  • $\begingroup$ @Chuck The cylinder is held at the two ends so it won't rotate or move around, and the force is applied in the middle of the cylinder, and it bends by uniform load. Yes the force required to permanently deform the cylinder. By break, I mean the minimum amount of force needed to separate the cylinder in two pieces, by bending. The cylinder is strongly welded at the two ends. $\endgroup$
    – Viktor Raspberry
    Commented Jan 3, 2016 at 18:44
  • $\begingroup$ If it's welded at both ends and subjected to a uniform load then I think it will shear before it breaks by bending, unless you plan on cycling the load on it, but even then it still might not matter. $\endgroup$
    – Chuck
    Commented Jan 3, 2016 at 21:38

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The simple answer: Use classical beam theory to calculate the load distribution of your cylinder with your loads applied. Then compare against the strength of your material.

The more complex answer: Strength of materials is quite a large subject on its own, and providing a satisfactory answer to your question requires significant more information on your application. Why do you want to predict the behavior? Is it just for the sake of prediction? Do you want to prevent the cylinder from permanent deformation or breaking? Or do you want to deliberately deform and break the cylinder? Do you need to consider safety factors? How exactly is the normal force applied? How exactly is the cylinder mounted? How well do you know your material properties?

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