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
4 - Purely ‘equilibrium’ solutions for shells: the membrane hypothesis
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
Triangulated structural trusses of the kind used for bridges, electric power transmission towers, etc. carry the loads applied to them mainly by tensile and compressive stresses acting along the prismatic members. But the applied loads are also carried to a minor extent by transverse shear forces in the members, which are related to bending moments transmitted between members at joints of the frame. It is usual to begin the analysis of structures of this type by imagining that the joints are all made with frictionless pins, and also that the loads are applied only at these joints. In direct consequence of this idealisation there are no bending moments and transverse shear forces, and the analysis is much simpler than it would be otherwise (e.g. Parkes, 1974).
The displacements of the simplified structure are relatively easy to compute. But they involve, in particular, relative rotations of the members at the joints; and thus it is possible to use these computed rotations in order to assess the order of magnitude of the bending moments which were dispensed with at the outset. If these turn out to be substantial, the initial hypothesis that bending moments are negligible is clearly not justified, and the whole calculation must be abandoned in favour of one which pays proper respect to the bending effects.
There is a closely analogous state of affairs in the action and analysis of thin-shell structures.
- Type
- Chapter
- Information
- Theory of Shell Structures , pp. 80 - 123Publisher: Cambridge University PressPrint publication year: 1983