Book contents
- Frontmatter
- Contents
- Preface
- 1 The theory of structures
- 2 Virtual work
- 3 Betti, Maxwell, Müller-Breslau, Melchers
- 4 Jettied construction
- 5 Clebsch, Macaulay, Wittrick, Lowe
- 6 The elastica
- 7 Mechanisms of collapse
- 8 The absolute minimum-weight design of frames
- 9 Inverse design of grillages
- 10 The relation between incremental and static plastic collapse
- 11 The bending of a beam of trapezoidal cross-section
- 12 The simple plastic bending of beams
- 13 Leaning walls; domes and fan vaults; the error function ∫e−t2dt
- Bibliography
- Name index
- Subject index
10 - The relation between incremental and static plastic collapse
Published online by Cambridge University Press: 18 December 2009
- Frontmatter
- Contents
- Preface
- 1 The theory of structures
- 2 Virtual work
- 3 Betti, Maxwell, Müller-Breslau, Melchers
- 4 Jettied construction
- 5 Clebsch, Macaulay, Wittrick, Lowe
- 6 The elastica
- 7 Mechanisms of collapse
- 8 The absolute minimum-weight design of frames
- 9 Inverse design of grillages
- 10 The relation between incremental and static plastic collapse
- 11 The bending of a beam of trapezoidal cross-section
- 12 The simple plastic bending of beams
- 13 Leaning walls; domes and fan vaults; the error function ∫e−t2dt
- Bibliography
- Name index
- Subject index
Summary
A structure will in practice be acted upon by a number of independent loads (superimposed floor loads, snow, wind, crane loads, and so on). Moreover, each load will vary between limits which will be specified – the wind may blow from east to west, or not at all, or from west to east. The engineer making an elastic check of a given design will arrange for calculations to be made separately for each load; for any particular cross-section, the value of each load is then chosen to give the greatest and least action at that section. The designer is then able to determine the range of stress at the cross-section due to all the loads, and to make an assessment, according to given elastic rules of design, of the safety of the structure.
By contrast, the engineer making an estimate of the static plastic carrying capacity of a framed structure must arrange all the loading in the way expected to be most critical before the single plastic-collapse calculation is made. In practice there is no great difficulty in arriving at the worst combination of loads (although even for the simple portal frame the most critical position of a crane crab is not immediately obvious).
However, if loads on a frame do act randomly and independently within specified limits, then there is the possibility of incremental collapse of the frame.
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- Chapter
- Information
- Elements of the Theory of Structures , pp. 94 - 102Publisher: Cambridge University PressPrint publication year: 1996