A beam is made from two cylinders, where the inner cylinder is steel and the outer cylinder is aluminum. Which cylinder will yield first if beam is a simply supported cantilever beam?

Situation: We have a beam made up from two cylinder. Inner cylinder is Steel and outer cylinder is Aluminum. This beam is fixed on a wall on one end, and point load at the other end.

How do we figure out which cylinder (inner or outer) will experience yield stress first? How do we go on figuring out force distribution?

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Key concepts of note:

  • There are two types of stress experienced in a beam under load - normal stress (due to bending moment), and shear stress (due to shear force). This is best represented by creating a shear force & bending moment diagram.
  • The inner vs outer cylinder is important because that will change your area moment of inertia. Use the AMOI formula for a cylinder for the inner one, and the formula for a hollow cylinder for the outer one.

Solution Steps:

  1. Find the max bending moment and max shear force in the beam due to the point load.
  2. Calculate your AMOI for both cylinders.
  3. Find the max normal stress and max shear stress. Compare to the tensile yield stress and the shear yield stress[1], which can be found in material reference tables.

[1] Actually Iā€™m not 100% sure about how metal beams fail when external shear load is applied.