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
10 - Cylindrical shell roofs
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
Reinforced concrete shells have been used in the construction of roofs for many large buildings such as airport terminals, exhibition halls and factories. From a structural point of view a shell is attractive for this purpose, since the continuity of surface which is required to keep out the weather is provided by the structural member itself. From an economic point of view, however, reinforced-concrete shell roofs cast in situ are less attractive, largely on account of the labour-intensive effort which is needed in the construction of the formwork.
According to chapter 5, it is easy to construct a surface having zero Gaussian curvature from rectangular plywood sheets, whereas the construction of other kinds of surface makes it necessary to cut the sheets individually into non-rectangular shapes. It is not surprising therefore that cylindrical shells have been popular for the roofing of relatively simple rectangular buildings according to the scheme shown in fig. 10.1 and extensions of it. Shells of this kind, simply supported at their ends, form the subject of the present chapter.
Several authors have written on the structural analysis of cylindrical shell roofs of this sort, and at least one conference has been devoted to this subject: see Timoshenko & Woinowsky-Krieger (1959, § 126), Flügge (1973, §5.4.4.2), Gibson & Cooper (1954) and Witt (1954).
Almost all of the work which has been reported, however, is devoted to the analysis of particular examples having specific dimensions, and it cannot be said that any clear design principles have yet emerged from these studies.
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- Information
- Theory of Shell Structures , pp. 318 - 360Publisher: Cambridge University PressPrint publication year: 1983