UNIVERSITY of PLYMOUTH

 

MECH115: Engineering Science 1

 

Tutorial examples: - Cylinders & Spheres                           

 

 

 

1.      A cylindrical compressed air receiver is designed for a maximum pressure of 12 bar gauge. It's outside diameter is 250mm, and its wall thickness is 2.5mm. Find the circumferential and axial stress when subjected to its maximum pressure. [58.8 and 29.4 MN/m2 ]

 

 

  1. A spherical vessel is subject to an internal pressure of 100 bar gauge. Its internal diameter is required to be 300mm. The maximum allowable stress in the material is 75 MN/m2. Find the minimum required wall thickness. [ 10 mm]



  1. A solid steel shaft 27mm in diameter is subject to an axial tension of 300 kN. Find its axial strain and hence its diametral shrinkage given that Esteel = 200 GN/m2, and ν = 0.29.       [2.62x10-3, diametral shrinkage of 0.021 mm]

 

 

  1.  For the cylinder in Question 1, find the circumferential and axial surface strain, and hence find the increase in outside circumference of the pressure vessel when the pressure increases from zero to its maximum pressure. Assume the receiver is constructed from aluminium where E = 70 GN/m2, and ν = 0.33.   [701.4x10-6 and 142.8x10-6, circumference increases by 0.55 mm]



  1. Copper pipe used in plumbing is typically 22mm outside diameter with a wall thickness of 0.7 mm. If the yield stress for copper is 120 MN/m2, find the maximum pressure the copper can be subjected to if the maximum allowable stress in the copper is 40% of its yield stress. [3060 kPa or 30.6 bar ]

 

 

 

 

 

 

 

 

115tut_cylinders&spheres