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 . Note: There is no axial stress generated in the cylinder wall in this application. 1. Elastic Stress Distributions in a Single Cylinder a) At an operating pressure of 200 MPa, calculate using Lame’s equations the radial and circumferential stresses at the cylinder bore and the outer surface. Graphically present (sketch) the general form of variation of each of these stresses across the cylinder wall, clearly indicating the calculated values at the cylinder bore and at the outer surface. b) For the same operating pressure, calculate the maximum shear stress values at the cylinder bore and the outer surface. Hint: For axisymmetric problems, there are no shear stresses generated on the faces of a radial element in the cylinder wall. Therefore, and are (also) the Principal stresses. (Please refer to Stress Transformation). Graphically present (sketch) the general form of the maximum shear stress variation across the cylinder wall clearly indicating the values at the cylinder bore and the outer surface.
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
.
Note: There is no axial stress generated in the cylinder wall in this application.
1. Elastic Stress Distributions in a Single Cylinder
a) At an operating pressure of 200 MPa, calculate using Lame’s equations the
radial and circumferential stresses at the cylinder bore and the outer
surface.
Graphically present (sketch) the general form of variation of each of these
stresses across the cylinder wall, clearly indicating the calculated values at
the cylinder bore and at the outer surface.
b) For the same operating pressure, calculate the maximum shear stress
values at the cylinder bore and the outer surface.
Hint: For axisymmetric problems, there are no shear stresses generated on
the faces of a radial element in the cylinder wall. Therefore, and are
(also) the Principal stresses. (Please refer to Stress Transformation).
Graphically present (sketch) the general form of the maximum shear
stress variation across the cylinder wall clearly indicating the values at the
cylinder bore and the outer surface.
C) Verify the values of the maximum shear stress calculated in 1(b) at the
cylinder bore and the outer surface by drawing to a suitable scale (using
computer-aided graphical construction) the Mohr's circle representations of
the stresses acting on a 2-D element at each of these two locations. (You
may take radial direction as the x direction)
Comment on the angle that the maximum shear stress makes with the radial
direction.
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