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.