Circular Storage Tanks and Silos

455 Pages·2000·4.9 MB·English

by  Amin Ghali

Circular Storage Tanks and Silos
Second Edition
A.Ghali
Professor of Civil Engineering
The University of Calgary, Canada

London and New York

title: Circular Storage Tanks and Silos 2Nd Ed.
author: Ghali, A.
publisher: Taylor & Francis Routledge
isbn10 | asin: 0419235604
print isbn13: 9780419235606
ebook isbn13: 9780203301579
language: English
Storage tanks--Design and construction, Silos--Design and
subject
construction, Concrete tanks--Design and construction.
publication date: 2000
lcc: TA660.T34G47 2000eb
ddc: 690/.53
Storage tanks--Design and construction, Silos--Design and
subject:
construction, Concrete tanks--Design and construction.

i
First published 1979
Second edition 2000
by E & FN Spon
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by E & FN Spon
29 West 35th Street, New York, NY 10001
E & FN Spon is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2005.
To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks
please go to www.eBookstore.tandf.co.uk.
© 1979, 2000 A.Ghali
All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any
electronic, mechanical, or other means, now known or hereafter invented, including photocopying and
recording, or in any information storage or retrieval system, without permission in writing from the publishers.
The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that
may be made.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Ghali, A. (Amin)
Circular storage tanks and silos/A.Ghali.—2nd ed.
p. cm.
Includes bibliographical references.
ISBN 0-419-23560-4 (alk. paper)
1. Storage tanks-Design and construction. 2. Silos–Design and construction. 1. Title.
TA660.T34G47 2000
690′.53–dc21 99–43604
CIP
ISBN 0-203-30157-9 Master e-book ISBN
ISBN 0-203-35199-1 (OEB Format)
ISBN 0-419-23560-4 (Print Edition)
ii
Contents

Preface to second edition xi
Preface to first edition xiii
The SI system of units and British equivalents xv
Notation xvii

PART 1 Analysis 1

1 Introduction to the analysis of circular tanks 3
1.1 Scope 3
1.2 Basic assumptions 4
1.3 General methods of structural analysis 4
1.4 The displacement method 5
1.5 The force method 7
1.6 Flexibility and stiffness matrices 8
1.7 Moment distribution 9
1.7.1 Notation and sign convention 10
1.7.2 Steps of analysis 11
1.8 Adjusted stiffness and flexibility coefficients 11
1.9 General 13
2 Circular walls of constant thickness 15
2.1 Introduction 15
2.2 Beam-on-elastic-foundation analogy 15
2.3 General solution of the differential equation of the deflection of a wall of constant thickness 18
2.4 Characteristic parameters 20
2.5 Stiffness and flexibility matrices 21
2.6 End-rotational stiffness and carry-over factor 24
2.7 Fixed-end forces 25
2.7.1 Uniform or linearly varying load 25
2.7.2 Concentrated load 26
2.7.3 Couple 28
2.8 Semi-infinite beam on elastic foundation and simplified equations for long cylinders 29
2.9 Classification of beams on elastic foundation and circular walls as long or short 32
2.10 Examples 32
Example 2.1 Circular wall, hinged at the bottom 32
Example 2.2 Circular wall, on bearing pads 34
Example 2.3 Circular wall, with thickness change 35
2.11 General 39
3 Circular walls of varying thickness 40
3.1 Introduction 40
3.2 Finite-difference equations 41
3.3 Boundary conditions and reactions 45
3.4 Generation of simultaneous equations 47
3.5 Sudden change in thickness 47
iii
3.6 Examples 48
Example 3.1 Circular wall, on bearing pads, with linearly varying load 48
Example 3.2 Circular wall, with bottom edge encastré and top edge hinged 50
3.7 Flexibility and stiffness of circular walls of variable thickness 52
3.8 Effect of temperature 53
3.9 General 57
4 Design tables and examples of their use 58
4.1 Introduction 58
4.2 Description of design tables 58
4.3 Variables 61
4.4 Arbitrary edge conditions 61
4.5 Examples 62
Example 4.1 Circular wall of varying thickness, on bearing pads, with trapezoidal normal load 62
Example 4.2 Circular wall, with circumferential prestressing tendons 64
Example 4.3 Reinforced tank, on rigid foundation 67
Example 4.4 Circular wall, with variable thickness, subjected to temperature rise varying linearly 72

through the thickness
4.6 Long cylinders 79
Example 4.5 Circular wall, fixed at the base and free at the top 81
4.7 Poisson’s ratio 82
4.8 Beams on elastic foundations 82
4.9 General 84
5 Finite-element analysis 85
5.1 Introduction 85
5.2 Nodal displacements and nodal forces 85
5.3 Transformation of stiffness matrix 89
5.4 Displacement interpolations 89
5.5 Stress resultants 90
5.6 Stiffness matrix of individual element 91
5.7 Analysis for effect of temperature 92
5.8 Assemblage of stiffness matrices and load vectors 93
5.9 Nodal forces 95
5.10 Examples 96
Example 5.1 Cylindrical wall, with uniform radial force on bottom edge 96
Example 5.2 Cylindrical wall, bottom edge encastré and top edge free, with temperature rise 98
Example 5.3 Circular plate, with outer edge encastré, subjected to uniform load 99
Example 5.4 Circular cylinder, monolithic with spherical dome 100
6 Time-dependent effects 102
6.1 Introduction 102
6.2 Creep and shrinkage of concrete 102
6.3 Relaxation of prestressed steel 106
6.4 Basic equations for stress and strain distributions in a homogeneous section 106
6.5 Time-dependent stress and strain in a section 109
6.5.1 Special case: section subjected to axial force only 112
iv
Example 6.1 Time-dependent stresses in a prestressed section: effect of presence of non-prestressed steel 114
6.6 Normal force N and bending moment M due to prestressing 115
6.6.1 Circumferential prestressing 116
6.6.2 Vertical prestressing of a circular-cylindrical wall 117
Example 6.2 Internal forces due to vertical prestressing of a circular wall 118
6.7 Time-dependent internal forces 119
Example 6.3 Time-dependent internal forces in a cylindrical wall on elastomeric pads 122
Example 6.4 Time-dependent internal forces in a cylindrical tank wall monolithic with base 126
7 Thermal stresses 131
7.1 Introduction 131
7.2 Effects of temperature variation in a cylindrical wall 133
7.3 Linear temperature variation through wall thickness 135
7.4 Thermal internal forces in deep tanks and silos 135
7.4.1 Bottom edge encastré and top edge free 136
7.4.2 Bottom edge hinged and top edge free 136
7.4.3 Bottom edge free to slide and rotate and top edge free 136
Example 7.1 Thermal stresses in a cylindrical concrete wall 137
7.5 Internal forces due to shrinkage of concrete 142
Example 7.2 Shrinkage stresses in a cylindrical concrete wall 142
7.6 Significance of linear analysis 145
8 Optimum design of prestressing 146
8.1 Introduction 146
8.2 Trapezoidal distribution of circumferential prestressing 146
Example 8.1 Trapezoidal distribution of circumferential prestressing; cylindrical wall encastré at the 148

bottom edge
8.3 Improved distribution of circumferential prestressing 149
Example 8.2 Improved distribution of circumferential prestressing 150
8.4 Design objectives 153
8.5 Design of circumferential prestress distribution 154
Example 8.3 Design for distribution of circumferential prestressing 156
9 Effects of cracking of concrete 161
9.1 Introduction 161
9.2 Stress and strain in a cracked section 161
9.3 Decompression forces 162
9.4 Equilibrium equations 163
9.5 Rectangular section analysis 165
9.6 Tension stiffening 166
9.7 Crack width 167
Example 9.1 Analysis of cracked prestressed section 169
9.8 Time-dependent strain and stress in cracked sections 173
9.9 Influence of cracking on internal forces 173
10 Control of cracking in concrete tanks and silos 176
10.1 Introduction 176
10.2 Causes of cracking 177
10.3 Tensile strength of concrete 177
10.4 Force-induced cracking 178
v
10.4.1 Effect of prestressing 181
Example 10.1 Hoop force versus elongation for a circular reinforced concrete ring 182
10.5 Displacement-induced cracking 184
10.6 Cracking by bending: force-induced and displacement-induced 186
10.7 Motives for crack control 187
10.8 Means of controlling cracking 188
10.9 Minimum reinforcement to avoid yielding of reinforcement 188
10.10 Amount of reinforcement to limit crack width: displacement-induced cracking 191
Example 10.2 Reinforcement required to limit the width of cracks caused by temperature variation 192
10.11 Change in steel stress at cracking 193

PART II Design tables 197

11 Tables for analysis of circular walls of thickness varying linearly from top to bottom 199
12Tables for analysis of circular walls of thickness constant in upper part and varying linearly in 260

lower three-tenths of height
Appendix : Stiffness and fixed-end forces for circular and annular plates 320
A.1 Governing differential equation 320
A.2 Stiffness and fixed-end moments of circular plates 321
A.3 Stiffness of annular plates 322
A.4 Fixed-end forces of annular plates 326
A.5 Approximate analysis for annular plates 327
Index 328
vi
Preface to second edition
The contents of this edition include six new chapters, added to the chapters of the first edition. There is a new
chapter on the finite-element method of analysis. A conical-shaped finite element, which is relatively simple but
gives accurate results, is selected. The wall of a tank or a silo, monolithic with the cover or the base, is idealized
as an assemblage of small axisymmetrical shell elements, each in the shape of a frustum of a cone.
Creep and shrinkage of concrete as well as relaxation of prestressed steel produce time-dependent variations in
stresses in sections and also in the internal forces. A chapter focuses on the analysis of these variations.
Another chapter is added to help in the design of circumferential prestressing of circular cylindrical tank walls,
which are monolithic with the base (as opposed to sliding on the base). The distribution of the prestressing is
designed to minimize the bending moments in the wall in the vertical direction.
Finally, there are three new chapters concerned with analysis and design for serviceability of concrete tanks and
silos. Analysis of the internal forces and stresses before and after cracking is discussed, including the effects of
temperature variations and shrinkage (or swelling) of concrete. Control of cracking is explored and equations
are given to calculate the minimum amount of reinforcement.
Like the first edition, the new one is intended to be suitable for use by practising engineers, students and
researchers in any country. No specific system of units is used in the major part of the solved examples.
However, there are a small number of example problems where it is advantageous to use actual dimensions of
the structure and specify the magnitude of forces. These problems are set in SI units and British units (still
common in the United States). The answers and the graphs related to these problems are presented in both SI
and British units. The methods of analysis and design procedures presented are independent of codes. However,
occasional reference is made to European and North American codes. The inevitable future revisions of the
codes should not influence the relevance of the material presented.
The new chapters have been reviewed by Dr G.S.Tadros, Consulting Engineer, Calgary, Canada. Mr
N.Ariyawardena, a PhD Candidate at the University of Calgary, checked solutions of some of the examples and
prepared the figures for the new chapters. Miss Tracey Robertson typed the manuscript. The author is grateful to
them as well as to the engineers whose views have helped in selecting the contents of the second edition.

A.Ghali
Calgary, Alberta, Canada
July 1999
vii
Preface to first edition
This book is concerned with the analysis of circular-cylindrical walls of constant or variable thickness subjected
to axisymmetrical loading. The main application of this analysis in practice is in the design of walls of concrete
circular storage tanks and silos.
Because of symmetry, it is sufficient to consider for the analysis under discussion the forces and deformations
of a typical elemental strip parallel to the cylinder axis. The radial deflection of the strip must be accompanied
by hoop forces, which make the strip behave as a beam on elastic foundation, receiving at every point transverse
reaction forces proportional to the deflection. The analysis of such a beam, or of a cylindrical wall, constitutes
solution of one governing differential equation which relates the deflection to the applied load.
Walls of circular storage tanks are often connected to other elements such as the base and the cover in the form
of circular, annular plates or other shells of revolution. When subjected to axisymmetrical loading, these
structures can be analysed as an assemblage of elements by the general force or displacement methods in the
same way as for plane frames. The flexibility or the stiffness coefficients needed for the analysis by these
methods are derived in this book for circular-cylindrical walls as well as for circular and annular plates, while
the coefficients for domes, cones or other forms of shells of revolution are beyond the scope of this work.
The objective of the book is to provide the designers of tanks and other circular-cylindrical axisymmetrical
shells with methods of analysis no more complicated than the plane-frame analysis commonly covered in the
undergraduate curricula of engineering schools. For the sake of simplicity in practical application, a set of
design tables is provided and their use illustrated by examples. The tables, which are intended mainly for use in
design of circular concrete tanks of constant or variable wall thickness, can also be employed in the analyses of
silos, pipes or any circular-cylindrical shell subjected to arbitrary axisymmetrical loading and support
conditions, and also in the analysis of the more general problem of a beam on elastic foundation. All tabulated
values are dimensionless, thus usable with any system of units.
The book fulfils a great need which is often expressed by designers of concrete storage tanks. This fact became
obvious to the author during his work as member of a technical committee of the American Concrete Institute
on Circular Prestressed Structures. The involvement with this committee helped to identify some of the practical
problems for which this study presents solutions.
The work of Dr G.S.Tadros, Structural Engineering Department Manager, Stanley SLN Consulting, Calgary, in
preparation of the computer programs used to generate the tables of the book is gratefully acknowledged. The
text and the numerical examples were conscientiously checked by Dr G.A.M.Ghoneim, post-doctoral fellow,
the University of Calgary. The typing of the manuscript was carefully done by Miss Sheila M.Diewold.
A.Ghali
Calgary, Alberta, Canada
January 1979
viii
The SI system of units and British equivalents
Length
metre (m) 1m=39.37inch
1m=3.281ft
Area
square metre (m2) 1m2=1550inch2
1m2=10.76ft2
Volume
cubic metre (m3) 1m3=35.32ft3
Moment of inertia
metre to the power four (m4) 1m4=2403×103 inch4
Force
newton (N) 1N=0.2248lb
Load intensity
newton per metre (N/m) 1N/m=0.06852lb/ft
newton per square metre (N/m2) 1N/m2=20.88×10−3lb/ft2
Moment
newton metre (Nm) 1Nm=8.851lb inch
1Nm=0.7376×10−3kip ft
1kNm=8.851kip inch
Stress
newton per square metre (pascal) 1Pa=145.0×10−6lb/inch2
1MPa=0.1450ksi
Curvature
(metre)−1 1m−1=0.0254inch−1

Temperature change
Celsius degree (°C) 1°C=(5/9)°F (Fahrenheit degree)
Energy and power
joule (J)=1N m 1J=0.7376lb ft
watt (W)=1J/s 1W=0.7376lb ft/s
1W=3.416Btu/h
Nomenclature for decimal multiples in the SI system
109giga (G) 106mega (M) 103kilo (k) 10–3milli (m)

ix