(Solved): 3. A short, cylindrical aluminium tube, shown in Figure 3, is part of a suspension system. It can b ...

3. A short, cylindrical aluminium tube, shown in Figure 3, is part of a suspension system. It can be considered to have closed ends (i.e. it carries a longitudinal load due to the internal pressure) and has an external diameter of $500\mathrm{mm}$ and a wall thickness of $3\mathrm{mm}$. The aluminium has a yield strength of $250\mathrm{MPa}$. (a) The internal pressure is raised such that the internal pressure is $2\mathrm{MPa}$ higher than the external pressure. Calculate the hoop and longitudinal stresses due to this pressure differential. (b) In addition to the internal pressure, the tube carries an axial compressive load of $1000\mathrm{kN}$ and a torque of $100\mathrm{kNm}$. i) Calculate the membrane stresses in the cylinder wall due to this combination of loads. ii) Sketch the state of stress on a small element of the curved cylinder wall. iii) Draw Mohr's circle for stress for a point in the curved cylinder wall for this combination of loads. iv) Using the von Mises yield criterion, assess whether the material in the curved cylinder wall will yield under this load combination. What is the load factor on yield? Figure 3: Geometry of the short cylindrical aluminium tube.