TAILIEUCHUNG - Ebook Advanced mechanics of materials (6th edition): Part 2
(BQ) Part 2 book "Advanced mechanics of materials" has contents: The thick wall cylinder, elastic and inelastic stability of columns, flat plates, stress concentrations, fracture mechanics, progressive fracture, contact stresses, time dependent deformation. | CHAPTER I1 THE THICK-W M L CYLINDER BASIC RELATIONS In this section, we derive basic relations for the axisymmetric deformation of a thick-wall cylinder. Thick-wall cylinders are used widely in industry as pressure vessels, pipes, gun tubes, etc. In many applications the cylinder wall thickness is constant and the cylinder is subjected to a uniform internal pressure pl, a uniform external pressurep2, an axial load P, and a temperature change AT (measured from an initial uniform reference temperature; see Section ) (Figure ).Often the temperature change AT is a function of the radial coordinate r only. Under such conditions, the deformations of the cylinder are symmetrical with respect to the axis of the cylinder (axisymmetric). Furthermore, the deformations at a cross section sufficiently far removed from the junction of the cylinder and its end caps (Figure 1 ) are practically independent of the axial coordinate z. In particular, if the cylinder is open (no end caps) and unconstrained, it undergoes axisymmetric deformations owing to pressures p1 and p 2 and temperature change AT = AT(r), which are independent of z. If the cylinder’s deformation is constrained by supports or end caps, then in the vicinity of the supports or junction between the cylinder and end caps, the deformation and stresses will depend on the axial coordinate z. For example, consider a pressure tank formed by welding together hemispherical caps and a cylinder (Figure ). Under the action of an internal pressure pl, the tank deforms as indicated by the dotted inside boundary and the long dashed outside boundary (the deformations are exaggerated in Figure ). If the cylinder were not constrained by the end caps, it would be able to undergo a larger radial displacement. However, at the junctions between the hemispherical caps and cylinder, the cylinder displacement is constrained by the stiff hemispherical caps. Consequently, the radial displacement (and hence the strains .
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