A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm has been designed to withstand a maximum internal pressure of 200 MPa in service. During operation, the pressure within the cylinder is retained by a freely sliding piston. The steel used in the manufacture has Young’s modulus of 210 GNm-2. In an alternative design, the cylinder has been constructed as a compound cylinder (duplex cylinder) with the same bore and outer radii by shrink-fitting two tubes of the same steel. The nominal radius at the common interface is 150 mm and the radial interference (shrinkage allowance, δ) is 100 μm (micro-meters). a) Determine using Lame’s equations, the radial and circumferential stresses at the cylinder bore, common interface, and outer surface. b) Graphically present (sketch) the variation of each of these stresses across the cylinder wall, clearly indicating the values at the inner and outer surfaces of each cylinder. c) Draw the Mohr's circles representing the stresses acting on a 2-D element at the inner and outer surfaces of each cylinder. From the Mohr’s circles, determine the maximum shear stress values at each of these 4 locations.
A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm
has been designed to withstand a maximum internal pressure of 200 MPa in
service. During operation, the pressure within the cylinder is retained by a freely
sliding piston. The steel used in the manufacture has Young’s modulus of 210
GNm-2. In an alternative design, the cylinder has been constructed as a compound
cylinder (duplex cylinder) with the same bore and outer radii by shrink-fitting two
tubes of the same steel. The nominal radius at the common interface is 150 mm
and the radial interference (shrinkage allowance, δ) is 100 μm (micro-meters).
a) Determine using Lame’s equations, the radial and circumferential
stresses at the cylinder bore, common interface, and outer surface.
b) Graphically present (sketch) the variation of each of these stresses across
the cylinder wall, clearly indicating the values at the inner and outer surfaces
of each cylinder.
c) Draw the Mohr's circles representing the stresses acting on a 2-D element
at the inner and outer surfaces of each cylinder. From the Mohr’s circles,
determine the maximum shear stress values at each of these 4 locations.
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