A theory and design method for cylindrical shell roofs and an experimental determination of certain basic data

324 Pages·036.764 MB·English

by  Morice, P. B

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ProQuest Number: 10148129
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Thesis submitted for the degree of PhoD
in the Faculty of Engineering of the
University of London
A THEORY M D DESIGN METHOD FOR CYLINDRICAL
SHELL ROOFS AND AN EXPERIMENTAL DETERMINATION
OF CERTAIN BASIC DATA
PeBe Moriceg B«Scog
Battersea PolyteohniOj
London 8,W@llg
October. 1951o
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The author wishes to aoimowledge his indebtedriess to Mr V C Davies^
under #iosG supervision this work was carried out» He also wishes
to thank Professor A Gr Pugsley who first suggested the work^^
Mr E H Cooley who assisted in the dieoking of the mathematicsg
Mr H E Lewis who helped to take readings during experiments and
Messrs F L Wilson and A G Mossg who made most of the apparatus =
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LIST OF CONTENTS
PART I « INTRODUCTION AND THEORY Pag©
Chapter 1 Introduction 1 - - 8
2 A review of shell theory 9 «*> BS
3 Elasticity theory 24 37
4 General shell equations 38 58
5 The membrane condition of
cylindrical shells 59 68
6 The edge disturbance equation 69 85
7 Edge beams 86 98
8 The general solution 99 105
PART II ^ DESIGN
Chapter 1 Factors affecting design 1 - 4
2 Design methods 5 ^ 8
3 Design examples 9 « 56
PART III » EXPERIMENTAL STUDIES
Chapter 1 Concrete 1 12
2 Apparatus 13 23
5 Poisson*s ratio tests 24 »=■ 34
4 Edge beam torsion 35 48
LIST OF COHTMTS continued
PART IV - APPEND I0B8 . Page
Chapter 1 References pp 2
2 Notation pp 8
3 Bibliography pp 33
4 A note on the plotting ofp rojeotories
of principle stress pp 7
5 List of expressions required in
developing the edge disturbance
equation pp 3
6 Solution of the equation (x^ )^4* 4 “ 0 pp S
PART I
Introduction and Theory
CHAPTER 1
Introductd.on
The inherent strength of a curved structure when loaded
normally is evinced by the use of shells in nature as a protective
covering to certain eggs, nuts^ insects, etc. It is therefore
not surprising that structural shells should be used extensively
in civil engineering constructions It was not possible' to make
full use of shells until comparatively recently because early
building materials possessed little or no tensile strength, The
complications involved are well demonstrated by the use of flying
buttresses in G-othi.c cathedrals to provide an arch thrust to the
vaulted roof. The advent of wrought iron and later steel had
little influence since these materials when used in an economi­
cally thin membrane are well within the range of buckling for
normal roof sizes and loadingSo
It was not, therefore, until the advent of reinforced
concrete, a comparatively cheap bulk material capable of resist­
ing both tensile and compressive stress, that the full advantage
of shell structures could be used.
In its most generally used form, and that with which this
work is concerned, the shell consists of a thin membrane curved
in one direction only, forming a segment of a right cylinder
which is supported at its ends and not along its edges, (Figure 1),
m,.n)i##&ri###
Figure ^,
It is evident that in the direction of a generator the shell
is spanning as a beam and therefore the lower portions of the shell
will be in tension. In small spans the tensile stresses induced
are small, and sufficient steel can be introduced into the membrane
itself without much thickening. (Figure 2)«
DUCT
--‘No.3/24'0'‘BAYS
Figure 2.
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