Book contents
- Frontmatter
- Contents
- Preface
- List of symbols
- 1 Introduction
- 2 Generalised Hooke's law for an element of a shell
- 3 Cylindrical shells under symmetric loading
- 4 Purely ‘equilibrium’ solutions for shells: the membrane hypothesis
- 5 The geometry of curved surfaces
- 6 Geometry of distortion of curved surfaces
- 7 Displacements of elastic shells stressed according to the membrane hypothesis
- 8 Stretching and bending in cylindrical and nearly-cylindrical shells
- 9 Problems in the behaviour of cylindrical and nearly-cylindrical shells subjected to non-symmetric loading
- 10 Cylindrical shell roofs
- 11 Bending stresses in symmetrically-loaded shells of revolution
- 12 Flexibility of axisymmetric bellows under axial loading
- 13 Curved tubes and pipe-bends
- 14 Buckling of shells: classical analysis
- 15 Buckling of shells: non-classical analysis
- 16 The Brazier effect in the buckling of bent tubes
- 17 Vibration of cylindrical shells
- 18 Shell structures and the theory of plasticity
- Appendices
- Answers to selected problems
- References
- Index
13 - Curved tubes and pipe-bends
Published online by Cambridge University Press: 02 February 2010
- Frontmatter
- Contents
- Preface
- List of symbols
- 1 Introduction
- 2 Generalised Hooke's law for an element of a shell
- 3 Cylindrical shells under symmetric loading
- 4 Purely ‘equilibrium’ solutions for shells: the membrane hypothesis
- 5 The geometry of curved surfaces
- 6 Geometry of distortion of curved surfaces
- 7 Displacements of elastic shells stressed according to the membrane hypothesis
- 8 Stretching and bending in cylindrical and nearly-cylindrical shells
- 9 Problems in the behaviour of cylindrical and nearly-cylindrical shells subjected to non-symmetric loading
- 10 Cylindrical shell roofs
- 11 Bending stresses in symmetrically-loaded shells of revolution
- 12 Flexibility of axisymmetric bellows under axial loading
- 13 Curved tubes and pipe-bends
- 14 Buckling of shells: classical analysis
- 15 Buckling of shells: non-classical analysis
- 16 The Brazier effect in the buckling of bent tubes
- 17 Vibration of cylindrical shells
- 18 Shell structures and the theory of plasticity
- Appendices
- Answers to selected problems
- References
- Index
Summary
Introduction
Piping systems are an indispensable feature of many industrial installations. In such systems straight tubes predominate; but problems of plant layout, etc., obviously make it necessary for pipes to turn corners. There are, broadly, four ways of getting the line of a pipe to turn a corner. First, fig. 13.1a shows a so-called long-radius bend in which the radius b of the centre-line of the curved portion is much larger than the radius a of the tube itself. A rightangle bend is illustrated, but it is obvious that the angle through which the line of the pipe turns is arbitrary, in general. On the domestic scale, bends of this sort may be made, ad hoc, in ductile metal pipes by the use of a pipe-bending machine; but the resulting cross-section of the curved portion is usually not circular: see later. Second, fig. 13.1b shows a so-called shortradius bend, in which the ratio b/a has a value of less than 4, say. The curved section is specially fabricated by casting, or welding together suitably curved panels; and the curved unit is connected to the straight pieces by bolted or welded joints. The types shown in fig. 13.1a and b are known as smooth bends. Third, fig. 13.1c shows a single-mitre bend, which is made by joining a pipe which has been ‘mitred’ by a plane oblique cut. A mitre joint may either be unreinforced (as shown) or reinforced by an elliptical ring or flange.
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- Information
- Theory of Shell Structures , pp. 429 - 472Publisher: Cambridge University PressPrint publication year: 1983