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CHAPTER 3
ADVANCED LOADINGS
3.1 INTRODUCTION
In this chapter three advanced topics are presented: pressure loading, contact loading, and
rotational loading. All three are very important to the machine designer.
Pressure Loading. Pressure loading occurs when a pressure above atmospheric which
is typically internal, acts on a machine element such as a thin-walled sphere or cylinder,
a thick-walled cylinder, or the pressure caused by press or shrink fits. External pressure
on thin-walled vessels causes buckling, a very advanced topic requiring application of the
theory of elasticity. Therefore, buckling of thin shells is not included here.
Contact Loading. Contact loading occurs when two machine elements are in contact
owing to a compressive loading, particularly over a very small contact area. The stresses over
the contact area between two spheres, as well as between two cylinders, will be presented.
Contact stresses between either a sphere or cylinder rolling on a flat surface will also be
presented.
Rotational Loading. Rotational loading occurs when a machine element, such as a grind-
ing wheel or compressor blade, is rotating at a relatively high speed. The tangential and
radial stresses produced are similar to those found for thick-walled cylinders; however, the
source of the loading is caused by inertial forces that can be related to the rotational speed,
material density, and Poisson’s ratio of the machine element.
3.2 PRESSURE LOADINGS
In the case of a pressure loading on a thin-walled vessel, either spherical or cylindrical,
the circumferential stresses produced do not vary radially over the thin cross section of
the vessel. However, for thick-walled cylinders, not only does the circumferential stress
vary in the radial direction, there is an additional stress in the radial direction that is not
constant over the cross section. The equations for thick-walled cylinders will be applied to
the problem of press or shrink fits, where the interface between the two machine elements
is of primary interest and the deformation of the two elements will be presented. As it turns
out, only normal stresses are produced by pressure loadings, meaning there are no shear
stresses developed.
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