DESIGN TABLES FOR WATER- RETAINING STRUCTURES

Copublished in the United States with John Wiley & Sons, Inc., 605 Third Avenue , Nell' York , NY 10158@ Longman Group UK Ltd 1991

Design tables for wateryretaining structures

Longman Scientific & Technical. Longman Group UK Limited. Longman House, Burnt Mill, Harlow. Essex CM20 2JE, England and Associated Companies throughout the world.

Copublished in the United States with John Wiley & Sons. Inc .. 605 Third Avenue. New York. NY 10158

Longman Group UK Ltd 1991All rights reserved: no part of this publication may be reproduced, stored in a retrieval system. or transmitted in any form or by any means. electronic. mechanical. photocopying. recording. or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London WIP 9HE.

First published 1991

Library of Congress Cataloging-in-Publication DataBatty, Ian. 1939The design of water-retaining structures / Ian Batty. Roger Westbrook. p. cm. ISBN 0-470-21846-0 I. Hydraulic structures--Design and construction I. Westbrook. Roger. II. Title. TC180.B36 1991 627 --dc20 91-43516 CIP Set in Compugraphic Times 10111 Printed and Bound in Great Britain at the Bath Press. Avon

Contents

Preface Acknowledgements List of design tables for water-retaining structures (Chapter 9) 1 Standards for the design of water-retaining structures 2 Design and constructional aspects 3 Design of cantilever walls to retain liquids 4 Design of rectangular tanks 5 Design of circular tanks 6 Design of prestressed concrete circular tanks 7 Design of a flat slab roof and columns for a reservoir 8 Design of conical tanks 9 Design tables for water-retaining structures Appendix I ,!he analysis of ground-supported open circular concrete tanks Appendix II Metric/Imperial conversion factors

iv ivv

10 29 54 78 lOS 119 134 152 188 202

Preface

This book provides a comprehensive understanding of the design and construction of waterretaining structures. allowing graduate civil and structural engineering students. as well as the practising engineer. to design with speed and economy. Assuming some familiarity with BS 8110 Structural Use of Concrete the book draws on examples. many of which are based on actual completed structures. and upon extensive tables. related to the analysis of rectangular. circular and conical structures, to develop good working practice. The tables and examples will enable the engineer to check, by hand, the often complex results of computer analysis and output. usually based on the finite element method. for most structures. This is particularly so in those cases where the forces within a structure are affected by the ground upon which they sit. Thus, methods of designing for the soil/structure interaction, which normally require the aid of complex computer programs. are included. The tables and examples will prove to be a good reference for carrying out new work to modern methods and regulations. and will give direction to the student engineer in the use of currrent British Standards for the design of many types of concrete structures. An essential part of the book are the listed computer programs and output which further assist the designer in obtaining a range of options from which the most effective and economical solution may be determined for a particular structure; whilst a useful appendix covers the analysis of ground-supported open circular concrete tanks.

AcknowledgementsThe authors wish to express their appreciation to the BSI and the HSE for permission to use extracts from their publications. In particular they wish to thank the Portland Cement Association of America for permission to use extracts from their tables which assist in the analysis of circular and rectangular tanks. They are also grateful to the editor of Construction Weekly for allowing them to include, as an appendix. the article prepared by Lightfoot and Michael on the design of circular tanks supported by ground having elastic or plastic properties. The permission by Yorkshire Water to use photographs of construction and the help and encouragement of colleagues in the Central Division of that Authority has been invaluable and is greatly appreciated. We are grateful to the following for permission to reproduce copyright material: British Standards Institute for extracts from BS 8007 and BS 8110, also for Fig. 2.2 from BS 8007. Fig. 7.1 from BS 8110, Tables 1.1. 1.2 from CP 2007, Tables 1.3, A.I from BS 8007, Tables 7.1. 7.2. 9.2 from BS 8110, Table 9.3 from BS 4466 (Extracts from British Standards are reproduced with the permission of BSl. Complete copies can be obtained by post from BSI, Linford Wood. Milton Keynes. MKI4 6LE.); the editor, Construction Weekly for Appendix 1 Lightfoot E, Michael D 1965 'The design of groundsupported open circular tanks'; Health & Safety Construction for Fig. 1.2; Portland Cement Association for adapted Tables 9.20,9.21.9.22.9.23.9.24,9.25.9.29,9.30,9.31.9.32. 9.33.9.34,9.35.9.36. Whilst every effort has been made to trace the owners of copyright material. in a few cases this may have proved impossible and we take this opportunity to offer our apologies to any copyright holders whose rights we have unwittingly infringed.

iv

Table 9.1 Details of (a) bar reinforcement, and (b) fabric reinforcement Table 9.2 Ultimate anchorage bond and lap lengths as multiples of bar size (BS 8110) Table 9.3 Reinforcement scheduling details for (a) preferred shapes, and (b) other shapes Table 9.4 'As' for design crack width 0.2 mm, bar diameter TIO Table 9.5 'As' for design crack width 0.2 mm, bar diameter TI2 Table 9.6 'As' for design crack width 0.2 mm, bar diameter TI6 Table 9,7 'As' for design crack width 0.2 mm, bar diameter T20 Table 9.8 'As' for design crack width 0.2 mm, bar diameter T25 Table 9.9 'As' for design crack width 0.2 mm, bar diameter T32 Table 9.10 'x' and 'z' factors for sections reinforced in tension only serviceability limit state Table 9.11 'zJd' lever arm factors for ultimate bending moment Table 9.12 Concrete grade C25: permitted values of shear stress 'vc' for a range of As x lOO/(bv x d) and effective depth, d (BS 8110, Table 3.9) Table 9.13 Concrete grade C30: permitted values of shear stress 'vc' for a range of As x lOO/(bv x d) and effective depth, d (BS 8110, Table 3.9) Table 9.14 Concrete grade C35: permitted values of shear stress 'vc' for a range of As x 100/(bv x d) and effective depth, d (BS 8110, Table 3.9) Table 9.15 Shear reinforcement spacing (mm) for beams, where 'v' is greater than (vc + 0.4) Table 9.16 Minimum percentage of reinforcement to resist early thermal cracking (BS 8007 Appendix A) Table 9.17 Deflection - modification factors for tension reinforcement for varying values of Mu/(bdd) and serviceability stresses Table 9.18 Deflection - modification factors for tapered cantilever walls subjected to different types of loads Table 9.19 Values of 'k' factor used for estimating deflections of cantilever walls under hydrostatic pressure Table 9.20 Moment and shear force coefficients for walls subjected to hydrostatic pressure in a three-dimensional rectangular tank, assuming a hinged base, free top and continuous sides Table 9.21 Moment and shear force coefficients for walls subjected to hydrostatic pressure in a three-dimensional rectangular tank, assuming a hinged base, hinged top and continuous sides Table 9.22 Moment and shear force coefficients for wall panels subjected to hydrostatic pressure, assuming hinged base, free top and continuous sides Table 9.23 Moment and shear force coefficients for wall panels subjected to hydrostatic pressure, assuming fixed base, free top and continuous sides Table 9.24 Moment and shear force coefficients for wall panels subjected to hydrostatic pressure, assuming pinned base, pinned top and continuous sides Table 9.25 Moment and shear force coefficients for wall panels subjected to hydrostatic pressure, assuming fixed base, pinned top and continuous sides Table 9.26 Deflection of two way spanning slabs with various edge conditions subjected to (a) triangular pressure, (b) rectangular pressure Table 9.27 Ground pressure created beneath a base slab carrying an edge force 'Q'

v

and an edge moment 'M' and supported upon ~ elasdc soil Table 9.28 Bending moments created within a base slab carrying an edge force 'Q' and an edge moment 'M' and supported upon an elastic soil Table 9.29 (a) tension, and (b) moment coefficients in cylindrical tanks supporting a triangular load, assuming a fixed base and a free top Table 9.30 (a) tension, and (b) moment coefficients in cylindrical tanks supporting a triangular load, assuming a pinned base and a free top Table 9.31 (a) tension, and (b) moment coefficients in cylindrical tanks subjected to a moment per m, 'M' applied at base Table 9.32 (a) tension, and (b) moment coefficients in cylindrical tanks subjected to a shear per m, 'V' applied at top Table 9.33 (a) tension, and (b) moment coefficients in cylindrical tanks supporting a rectangular load, assuming a fixed base and a free top Table 9.34 (a) tension, and (b) moment coefficients in cylindrical tanks supporting a rectangular load, assuming a pinned base and a free top Table 9.35 (a) shear at base of cylindrical tanks subjected to: triangular load, rectangular load, moment at edge; (b) stiffness coefficients for cylindrical walls; (c) sti ffness coefficients of circular plates with and without centre support Table 9.36 Supplementary coefficients for values of Lv 2/(2 x r x h) greater than 16 Table 9.37 (a,b) coefficients for calculating forces in a conical tank supported at base level, resulting from fixity at the base of the cone Table 9.38 (a,b) coefficients for calculating forces in a conical tank supported at base level, resulting from fixity at the apex of the cone

vi

The necessity to store and supply purified water, and to treat the residual effluents, has been a major source of civil engineering activity for many civilisations. There are many remnants of great structures used for this purpose which demonstrate the skills of those earlier engineers. These indicate that then, as now, if you wish to retain water and prevent it being polluted you had to build well. In more recent times an evolutionary system of Codes of Practice and British Standards were developed, based upon continuing experience and research, in order to help engineers design water-retaining structures more effectively. The earliest codes, CP 7 (1938) and CP 2007 (1960), considered that if the stresses in the steel and concrete were of a relatively low order then there should be few problems. To minimise cracking those areas of concrete in tension were designed to ensure that the tensile resistance of the concrete was greater than the actual tensile force. The permitted design service stresses given in Tables 1. I and 1.2 are extracts from CP 2007 (1960).

(a)

the limit state method based upon the current level of research; (b) the alternative method which was similar to the previous code of practice CP 2007; (c) the limited stress method which incorporates both limit state and elastic theory.

Table 1.2 Permissible steel stresses in strength calculations (CP 2007, Table 4)Permissible tensile stress in steel (mild) (Nlmm2) Members in direct tension On liquid-retaining face Members in bending On face remote from liquid Members less than 225 thick Members 225 or more thick 82 82

82 125 82

Table 1.1 Permissible concrete stresses in calculations relating to the resistance to cracking (CP 2007, Table 2)Permissible concrete stresses Concrete mix Direct (Nlmm2) Nominal mixes 1 : 1.6: 3.2 Grade 26 1 : 2: 4 Grade 21 Tension Due to bending (Nlmm2) ShearQ

In shear reinforcement

bl a (Nlmm2)

1.2 1.3

1.85 1.68

1.92 1.71

With the advent of limit state design theory a radical change was introduced into BS 5337 (1976), the waterretaining structures code of practice. The code drafters took into account the experiences of many engineers and essentially permitted three different ways of design:

The effect of this standard was to help engineers consider more closely how concrete behaved and how to prevent cracking of the concrete during the construction and working life of the structure. A great deal of attention was focused upon positions an.d types of joints, methods of construction and areas of reinforcement required to prevent early thermal cracking. Durability of the concrete both in the short and long term was now of as equal importance as the design. The previous design codes tended to result in thick concrete sections with relatively large amounts of mild steel reinforcement. This, however, did not prevent cracking. The new standard, BS 5337, required engineers to become more involved in the construction process particularly with regard to joint positions and methods of construction. The

limit state design method did lead to thinner sections and deflection under load was more noticeable, particularly with respect to cantilever retaining walls. One other result was that high tensile steel virtually replaced mild steel as the main reinforcement used in construction.

as 8007 (1987) Design of concrete structures for retaining aqueous liquidsAs a result of II years of experience with BS 5337, the most recent standard, BS 8007, is now based mainly on the limit state approach to design. Structures are generally designed to restrict crack widths by suitable amounts of reinforcement and appropriate joint spacing. The alternative method given in BS 5337 was removed from the code; a few elements of the limited stress approach, however, did remain. For the first time in a BS design code the designer is required to consider operational safety. The basic elements of the BS 8007 are now summarised, changes and additions to the previous code are highlighted. Where applicable, extracts from the standard are included with kind permission of the BSI.

General: (Section 1 of BS 8007)Scope: This British Standard provides recommendations for

the design and construction of normal reinforced and prestressed concrete structures used for the containment or exclusion of aqueous liquids. The term 'liquid' in this code includes any contained or excluded aqueous liquids but excludes aggressive liquids. The code does not cover dams, pipes, pipelines, lined structures, or the damp-proofing of basements. The term 'structure' is used herein for the vessel that contains or ex.cludes the liquid, and includes tanks, reservoirs, and other vessels. NOTE I The design of structures of special form or in unusual circumstances is a matter for the judgement of the designer NOTE 2 The titles of the publications referred to in this standard are listed on the inside back cover A design temperature range of 0 C to 35C is now specified for containment under normal conditions. Recommendations are also included with regard to structures subject to adverse ground conditions.

(b) The partial safety factor for retained water shall be 1.4 for most situations for ultimate limit state (ULS) and 1.0 for serviceability limit state (SLS). (c) There shall be a factor of safety of at least 1. I against flotation. (d) The maximum crack widths shall be: (i) RC - all faces of liquid containing or excluding structures - 0.2 mm max. RC - where aesthetic appearance is critical - 0.1 mm max. (ii) PS - limited to requirements of BS 8110; however, refer to Section 4.3 of BS 8007 for particular rules for cylindrical tanks. (iii) PS - except for the special recommendations for the design of cylindrical prestressed structures (see Section 4.3 of BS 8(07), the tensile stress in the concrete should be limited for prestressed concrete structures in accordance with the recommendations of Section 2.2.3.4.2 of BS 8110 : Part 1 : 1985. (e) Deflection - Walls designed by limit state theory are thinner than those designed by elastic theory and the designer is cautioned to ensure that deflection, due to loading or rotation of the supporting earth, is not excessive. The method of backfilling should be clearly defined. (Where deflection is the significant factor in the design of a wall the authors of this book recommend that the thickness of the wall be increased rather than the area of steel be increased to satisfy the BS 8110 requirements.)

Loads:(a) All structures required to retain liquids should be designed for both the full and empty conditions, and the assumptions regarding the arrangement of loading should be such as to cause the most critical effects. Particular attention should be paid to possible sliding and overturning. ULS condition liquid levels should be taken to the top of the walls for design purposes assuming all outlets blocked. SLS condition liquid levels should be taken to the overflow, or working top level, for design purposes assuming all outlets open. No relief should be allowed for beneficial soil pressures in designing walls subjected to internal water loading. Thermal movement in roofs should be minimised by appropriate means. It is noted that where a roof is rigidly fixed to a wall, forces will be generated in the wall should the roof expand or contract. Earth covering roofs should be treated as a dead load, excessive construction loads should, however, be considered in the design.

(b)

Design objectives and general recommendations: (Section 2 of BS 8007)Design objectives: The purpose of design is the achievement of acceptable probabilities that the structure being designed will not become unfit in any way for the use for which it is intended. This code provides for a method of design based on limit state philosophy that is generally in accordance with the methods employed in BS 8110. Structural elements that are not part of the liquid-retaining structure should be designed in accordance with BS 8110.

(c)

(d)

(e)

Structural design:(a)

It is recommended that the design of sections be based upon crack width limitations initially and then other serviceability and ultimate limit states be checked.

Analysis of wall and junctions: The code states that bending and direct tension should be taken into account in the design process (refer to examples in Chapters 3 and 4). It is worth noting that significant horizontal bending moments occur at corners of rectangular containers particularly where the walls have a length/height ratio in excess of 2.

2

SUe condiJiOM:(a) Ground movements - for subsidence effects. guidance is given on methods to limit the damage that may result (see Chapter 2). (b) Reference is made to the recommendations of BS 8110 regarding the effect of aggressive soils upon concrete. Causes and control of cracking: Cracking in walls occurs as a result of external loading and changes in temperature during the working life of the structure; (b) chemical and physical changes generated particularly by changes in temperature and moisture content as the concrete matures and strengthens; (c) restraints to movement by adjoining stronger concrete sections; (d) inadequate detailing of reinforcement and of associated poor construction techniques. Concrete is particularly weak for the first few days following its construction. Careful thought and supervision prior to casting, and immediately afterwards, will assist in ensuring a sound structure. The code recommends that the prudent use of reinforcement, movement joints and construction techniques will heip in keeping crack widths within acceptable limits. The extract below from clause 2.6.2.2 of BS 8007 gives useful advice on particular methods of minimising and controlling cracking resulting from moisture and temperature changes within the structure:In order to minimise and control cracking thaI may result from temperature and moisture changes in the structure it is desirable to limit the following factors:

(a)

(a)

(b) (c)

(d) (el(I)

the maximum temperature and moisture changes liwing construction by: (I) using aggregates having low or medium coefficients of thermal expansion and avoiding the use of shrinkable aggregates, (2) using the minimum cement content consistent with the fe1:juirements for durability and, when necessary. for sulphate resistance, (3) using cements with lower rates of heat evolution, (4) keeping concrete from drying out until the structure is filled or enclosed, (5) avoiding thermal shock or over-rapid cooling of a cone rete surface; restraints to expansion and construction by the provision of movement joints (see Section 5.3 of BS 8007); restraints from adjacent sections of the work by using a planned sequence of construction or temporary open sections (see Section 5.5 of BS 8007); localised cracking within a particular member between movement joints by using reinforcement or prestress; rate of first filling with liquid (see Section 9.2 of BS 8007); thermal shock caused by filling a cold structure with a warm liquid or vice versa.

Design and detailing recommendations are also given at the end of Section 2.6 of BS 8007 and it is noted that: (a) where reinforcement is required to control placed as and thermal cracking, it should concrete surface as the cover requirements allow; (b) unless joints are placed at close centres (see clause 5.3.3 of BS 8007) the amount of reinforcement in each surface zone in both directions shall not be less than the amount shown in Fig. 1.1.

h---jr-O--;;/?'I'('--:;/?"'I--:":-.-~ '"'..0." . ... 0

"00.

I I1

b~,?

I'

1'':(;

~,,(J.tJ"

.R""

P

h 4500mm

(ilm1 Walls)

II1

h

> 500mm

For minimum areas of reinforcement see page 4

Figure 1.1

3

The reinforcement should be calculated in accordance with Section 5.3.3 and Appendix A of BS 8007. Except as provided for in option 3 in Table 5.1 and Section 5.3.3, the amount of reinforcement in each of two directions at right angles within each surface zone should be not less than 0.35 % of the surface zone cross section. as defined in Figures A.I and A.2 for deformed grade 460 requirement and not less than 0.64 % for plain grade 250 reinforcement. In wall slabs less than 200 mm in thickness the calculated amount of reinforcement may all be placed in one face. For ground slabs less than 300 mm thick (see A.2 of BS 8007). the calculated reinforcement should be placed as near to the upper surface as possible consistent with the nominal cover.

as is reasonably practicable the assumptions made at the design stage occur on site and that the quality of both materials and workmanship are satisfactory,

Operational safety considerations: The designer should take into account the requirements given in those sections of the Health and Safety at Works Act (1974). One of the most common 'dangerous occurrences' statistic which happens in the water industry is death or injury resulting from people entering unventilated enclosed structures without first checking that the atmosphere is satisfactory. The code takes this into account by stressing that:(i)

Design life and serviceability: The design life of the structure should be in the range of 40 to 60 years. It isnoted that elements of the structure may have a shorter working life than the main structure Uoints. sealants etc}. It is obviously prudent to ensure that replaceable items are accessible without major destruction of other elements. The designer should explain how often the structure is to be inspected and maintained. In particular the structure should be examined regularly for cracks. rust stains and other signs of deterioration. A schedule of precautions necessary to prevent potential damage to the structure should be written into the commissioning document. For example. if the media in a sunken filter bed is used to prevent flotation then it must not be replaced without first lowering the external water table! Pressure relief valves must be checked before any work is carried out which depends upon their effective operation. Both faces of a liquid containing or excluding structure. together with internal supports of a containment structure. shall be considered to have a minimum surface exposure rating of 'severe' as defined in clause 3.3.4 of BS 8110. Where exposed concrete is subjected to severe freezing conditions whilst wet. then a 'very severe' rating is to be used. The concrete design and specification in the code is considered adequate for a structure exposed to 'severe' conditions as defined in BS 8110. However the designer's attention is drawn to the possibility of biological decay resulting from adverse materials contained within the stored liquid or present in the external ground water. Where such conditions arise or where an 'extended design life' for the structure is required then additional cement content. cover or special reinforcement may be necessary.

(ii)

At least two access hatches should be provided at opposite ends of a structure and at least one in each compartment. The hatches should be large enough to enable personnel wearing breathing apparatus to enter. Provision should be made to ensure that there is adequate ventilation to limit dangerous accumulations of gas or toxic atmospheres to acceptable levels.

Increasing concern over accidents within the construction industry. often resulting from lack of training, has led to the inclusion of the following generalised statement in the contract documents: 'Personnel will only be allowed on site if they have evidence to prove that they have had recent training in the safety requirements necessary for this contract or that they are escorted during their visit by suitably qualified and approved staff. . The proposed draft HSC Construction Management Regulations includes the following definition of duties for designers under Regulation 7, in Fig. 1.2.

Constnu:tion management Proposals for Regulations and an Approved Code of PracticeFigure 1.2Any person who designs a structure shall ensure as far as is reasonably practicable that the structure is so designed that it can be built, maintained (including re-pointed, re-decorated and cleaned), repaired and demolished safely and without risk to health. Any person who designs a structure shall ensure, so far as is reasonably practicable, that his design shall include adequate information about any aspect of the design or materials which might affect the health and safety of any contractor or any other person at work on that structure. ( I ) Designers should consider whether there are any special factors which would affect the health and safety of those doing the work and. if so, should inform prospective contractors in terms at the tender stage and in more detail when specifying design details, construction methods or materials.

Note: All examples in the chapters that follow are designedwith 45 mm minimum cover since it is the authors' experience that clients generally expect their structures to have a design life well in excess of 40 to 60 years! The code stresses the requirement that the concrete should have a low permeability. This is one of the most significant factors in reducing the incidence of chemical attack, erosion, abrasion, frost damage and corrosion of reinforcement. The nominal cover for reinforcement is given as 40 mm minimum. However, if the cover is increased then surface crack widths resulting from bending and direct tension will also increase (see Appendix B and the design examples in the chapters that follow).

Specification: The designer is asked to ensure that as far

4

(d) hinged; (e) sliding; (0 construction. canaccount of the user's them in the course of the life eventual need to demolish them.(3)

which subsequent work on appropriate information by the designer for future reference.

reinforced concrete:Design: The basis of design should comply with the requirements of BS 8110, however, those areas of BS 8007 which are not in accordance with BS 8110 are stated. Methods of limiting crack widths taking into account constructional and design requirements in the immature and mature concrete are listed.

Descriptions and details and method construction. has to the position and type of joint cOl18id!en~ best for a particular situation. The spacing of joints is left to Some favour close joints whereas at all and use higher quantities of steel to control cracking. Table 1.3. extracted from the code, indicates that both systems are acceptable. Section 5.4 of the code specifies in some detail how a construction joint may be formed to continuity of strength and resistance to the need of a water bar. Where it is necessary no movement joints to exist such as in tanks where direct tension occurs Section 5.5 of the code refers to the possibility of temporary open sections being left between panels as shown in Fig. 1.3.

Design and detailing of prestressed concrete: (Section 4 of BS 80(7)The basis of design is stated. in the same manner as for reinforced concrete above. However, particular rules for cylindrical prestressed concrete structures are included (see Chapter 6). The nominal cover should be such as to satisfy the 'very severe' exposure condition ofBS 8110.

Figure 1.3

Design, detailing and workmanship of joints: (Section 5 of BS 8007)General:Joints in liquid-retaining structures are temporary or permanent discontinuities at sections. and may be formed or induced. This section describes the types of joint that may be required and gives recommendations for their design and construction. The types of joint are illustrated in Figure 5. I (BS 8007) and are intended to be diagrammatic. Jointing materials are considered in Appendix C of BS 8007. Joints may be used, in conjunction with a corresponding proportion of reinforcement. to control the concrete crack widths arising from shrinkage and thermal changes to within acceptable limits.

The benefits are that the amount of reinforcement necessary to control early thermal cracking is minimised. The only thermal effects to be considered are those resulting from seasonal variations (T2 - see Appendix AA3. BS 8007). The section closes with advice on joints in ground slabs, roofs and walls; however, it is noted that for all vertical joints in the walls of circular tanks, including construction joints, it is necessary to provide water bars to prevent leakage.

Concrete: specification and materials: (Section 6 of BS 80(7)It is recommended that when blended cements are used the maximum proportion of ggbfs should not exceed 50 %. where pfa is used the maximum proportion should not exceed 35 %. The code specifies a particular concrete mix for general use with water-retaining structures classed as grade C35A with a minimum cement content of 325 kg/m3. Further comments are made regarding workability. blinding layers and pneumatically applied mortar. It is recommended that since cracking in concrete cannot be

Since the main source of leakage in water-retaining structures occurs at joint positions. considerable attention is given to this subject. The code lists six types of joint: (a) expansion; (b) complete contraction; (c) partial contraction;

5

Table 1.3 Design options for control of thermal contraction and restrained shrinkage (BS 8007, Table 5.1)Option Type of construction and method of controlContinuous: for full restraint

Movement joint spacing

5/eel ratio (see 00/92)Minimum ofPeril

Comments

No joints, but expansion jOints at wide spacings may be desirable in walls and roofs that are not protected from solar heat gain or where the contained liquid is subjected to a substantial temperature range (a) Complete joints, ~ 15 m (b) Alternate partial and complete joints (by interpolation), ~ 11.25 m (c) Partial joints, ~ 7.5 m (a) Complete joints, in metres~

Use small size bars at close spacing to avoid high steel ratios wen in excess of Peril

Semicontinuous: for partial restraint

Minimum ofPeril

Use small size bars but less steel than in option 1

3

Close movement joint spacing: for freedom of movement

213 Penl

4.8 + -

w

Restrict the joint spaCing for options 3(b) and 3(c)

,

(b) Alternate partial and complete jOints, in metres~

O.5s max + 2.4f

w

(c) Partial joints

Note 1 References should be made to Appendix A, BS 8110, for the description of the symbols used in this table and for calculating Peril' smax and, Note 2 In options 1 and 2 the steel ratio will generally exceed Peril to restrict the crack widths to acceptable values. In option 3 the steel ratio of 213 Penl will be adequate

totally avoided, any member that is permanently exposed to view is provided with a profile or type of finish which will minimise the effects of surface marking. The remaining sections of the code relate to the specifi-

cation of reinforcement, prestressing tendons and inspection and testing of the structure for water tightness and liquid retention.

6

minimumand crack ten'1pe!rat iure andThis section provides more information than the previous code on the concrete is affected by temperature and moisture. research work has been carried out by such organisations as CIRlA, BCA and many universities, which helps engineers to understand how durable concrete may be produced. Typical values of the fall in temperature between the hydration peak and the ambient, referred to as T 1 in the code, are given in Table A.I, which is an extract from BS 8007.

Further topics in Appendix A give guidance and ~ on: (i) minimum reinforcement; (ii) the spacing of cracks; (iii) crack control in thick sections; and (iv) external restraint factors. Table 9.16 at the rear of this book gives the percentage of steel necessary to comply with Appendix A for varying values ofT! & 1'2, steel diameters and crack widths. For example, for a temperature fall of 40 C, 16 mm diameter type 2 bar and a crack width of 0.2 mm, 0.64 % steel is required within the zone thickness.

Table 14..1 Typical values of T1 for ope concretes, where more particular information is not available (BS 8007, Table A,2)

Appendix B Calculations of crack widths In mature concreteOne of the features of BS 5337, the previous 'waterretaining structures' code, was that the cracks resulting from bending stresses should be calculated. Revised equations are given in BS 8007 to comply with BS 8110 requirements. In addition, equations to estimate the crack widths due to direct tension are now included. Clause 2.2.1 of BS 8007 suggests that the design process commences with the calculation of crack widths based on the Appendix B equations and recommendations. Tables 9.4 to 9.9 inclusive, are prepared to help the designer to obtain very quickly a range of concrete sections using differing thicknesses, cover and diameters of steel. These will, for a particular service bending moment. generate a crack width equal to or slightly less than 0.2 mm. In addition Program I.P, given on page 8 allows the designer to input the bending moment, thickness of slab and cover. The output gives a range of diameters of bars, spacing and resulting crack widths. Example: (Using Tables 9.5 to 9.7, and also using Program I.P,)

Section thickness (mm)

Walls 18mm Steel form work: OPC plywood form work: content, OPC content, (kglm 3)

Ground slabs: OPC content, (kglm 3)

325

350

400

325

350

400

325

350

400

300 500 700 1000

11 20 28 38

13 22 32 42

15 27 39 49

23 32 38 42

25 35 42 47

31 43 49 56

15 25

17 28

21 34

Note 1 For suspended slabs cast on flat steel formwork, use the data in column 2 Note 2 For suspended slabs cast on plywood formwork, use the data in column 4. The table assumes the following: (a) that the formwork is left in position until the peak temperature has passed; (b) that the concrete placing temperature is 20C; (c) that the mean daily temperature is 15C; (d) that an allowance has not been made for solar heat gain in slabs.

It is noted that the mean daily temperature used in the preparation of this table is 15C. Once again close cooperation between designer and contractor is necessary to ensure that the estimated TI figure, assumed at the design stage, is valid at the construction stage. The long term seasonal temperature falls are denoted in Appendix A3 (BS 8(07) by the figure T2. This effect occurs in the mature concrete and is catered for by:

Table B.1 Bending moment to main steel - 45 mmTable

100 kNM; cover

Thickness Spacing of Crack width 'Type 2' bars (mm) from bar diameter (mm) (mm) Program IP 1 (mm) T12 T12 T16 T16 T20 T20 500 400 500 400 500 400 175 100 225 150300 200

9-05 9-05 9-06 9-06 9-07 9-07

0.20 0.19 0.18 0.20 0.18 0.20

0) where continuous construction is used T2 is added(ii) to T I and a greater area of reinforcement is required; the use of movement joints to absorb these variations in length.

7

Program 1P1 Design of a concrete slab to ensure that the crack width generated does not exc8ed 0.2 mm for a particular bending moment, depth of slab and any cover to steel

4 REM CALCULArES CRACK WIDrHS FOR RC SLABS - BOOKI IS rHE REFERENCE 5 LPRINl''':::::::::::::::::::::::::::::::::::::::::::::::::::::: f : II 6 LPRINr" fHE DESIGN OF R.C.SLABS FOR A CRACK WIDTH OF 0.2mm" 7 LPRINT"::::::::::::::::::::::::::::::::::::::::::::::::::::::::" 9 LPRINl'" " 10 DIM r(12,28) ,S!?(12,28) ,0(12,28) ,M(12,28) ,11.5(12,28) ,HQR(12,28) ,CW(12,28) ,N(12 28) ,OIA(12,2i} 11 LPRINr 12 INPur "1'HE BEN'OINJ MOMENr IS" iB"l 13 INPUT "THE 'rHICKNESS OF THE SIAB IS "iHI 14 INPur "rHE COVER ro THE MAIN REINFORCEMENr I3"iCOV 15 LPRINr II THE DESIGN SERVICE BENDING MOM'll' IS "i 8Mi" kNm" 16 LPRINr" " rHE rHICKNESS OF i'RE 3L~a IS ";Ml;" mm" 11 LPRINr " 18 LPRI~Ii''' " rHE COVER ro rHE D~SIGN sreEL IS "SCOVi" mm" 19 LPRHlr " 20 LPRINl''' " DI~ ARE~ STEEL 21 LPRIiH " sq.mm mm mm 22 LPtUtH " 23 LPRIlH" .. 30 FOR 3=4 TO 12 STEP 1 40 FOR H=12 "1'') 28 Si'EP .t 42 ~Il\(5,H)=H 45' IF OIA(S,H) = 24 rHE'J !JIA,(S,H) .. 25 46 IF DIA(S,H)= 28 i'HBN OIA(3,H)=32 50 SP(3,H)~ 3*25 60 'r ( s , H) = H 1 70 D(5,H)= HI-COV~DIA(S.H)/2 75 AS(S,H)=!.142* OIA(3,H)-2*.25*lOOO/SP(S,H) 76 HOR(S,H)~M(3,H)*1000/)(S,H)-2 Il'\pu~ : 80 GOSua 510110 NEXT H

BtYld",,'3 ~tKeH t

120 152 153 156 180 510 520 530 510 550 560 570 5 !3 0 590 600 510 620 G50 665 668 670 674 690

NE){r S Tk,ekH~$~ of s\ab LPRINi'" " C.vty to \MaiM stte.\ LPiUNr" " LPRINr"::::::::::::::::::::::::::::::::::::::::::::::::::::::::"END~1(S,H)=9~I*lOOOOJO!

~

AE '" 15 ~. ~ D'"" I?=AS(S,H)/(lJOO*')(S,H) CO,,&~):;q 0,,0 .;9 .",-t X=SOR(AE*P* (AE*P+2 -AE*P . ~:;;~ o~~: Z=1-X!3 ~~--------------------~ FS=:'I(S,H)/(A:3(3,H)*Z*0(S,H) Figure 81 55=F5/(200*1000) S E =5 5 * (r ( 3 , H) - 0 ( '3 , H) * X) I ( D ( :3 , Ii) - 0 ( S , J.j) * x ) SI=1000*(r(S,H)-D(S,H)*X)-1!(600*1000*AS(S,H)*D(S,H)*(I-X Si1=SE-Sl~CR=3QR{(.S*3P(S,H-2+(COVtOIA(S,H)/2)-2)-DIA(S,q)/2 CW(S,H).3*ACR*3~/(1+(2*(ACR-COV)/(r(S,H)-D(5,H)*X)

.,.:0

.A.J

IF 2i'l(S,H) IF CW(S,H)

SELF WEIGtiT WALL ONLt

rHg

,orAL v'E~TICAL WEIGH'f IS

46.80001

kN

fHE ';:CCENfRICI'U OF {'HE LOAD A80U'1' rHE CENrRE IS

.3816922 ID

... ".......... ".rtiE3~;l.ESS

'rliE HORI ZONTAL FORCE IS

0

kN

1'.1' FRQNf IS 3.193345 kN/3l.'1I

fHE S'fRESS 1'.'1' RElI.R

[S 29.08252 kN/sq.m

JL

IIl kit". If " "" "

".11'.

.. "........................" .............. .THe H~tiONfAL FORCE IS

PRESSURES DUE 1'0 SELF >'IEIGHT WALL AND ElI.RTH

l' HE '1'0'1'1'.1.. Vt:RTICAL WEIGH'C IS

84.36

kN

'1'HE ECCENTRICI'r1lroF rHE LOAD 1I.8::>Uf THE CEN'1'RE IS

.2169322 m

29.49277

kN

riiE SfRESS 1'.1' FR;),n IS 16.03349 kN/3'~.'n IS 42.14582 kN/sq.m

'1' HE SfRess 1'.'1' REAR

PRESSURES DUE '1'0 SELF >'IEIGHT WALL AND .HIL'ER

l' HE '1'01'1'.1.. v'ER'fICAL WEIGH'r IS

LOS. 56

k;~

THE eCCENrRICI'f'i OF1'HE rHE HORI ZONTAL FORCt: IS " t

r~:)AO

0,80U'f1'HE Ce:WfRE IS ktl

.464 L822 m

44.145

raE SfRESS 1'.'1' FROtH IS 1.443551 kN/s1.,n

l' He: S'fRES5 1'.1' RElI.R

IS 71.425H kN/sq.m

JtJt

PRESSURES DUe: TO WALL FULL'i

r~;)ADEO

1'.'1' FRONf AND REAR

fH!:: TOTAL v'E:RTICAL .. I::;.l'l' IS

143.22

k,'/.3435407 m

l' HE "CCE:NfRICI'f'l ::>F rHE LJlI.O A6::>UT l' HE CEN'rRE IS

..................

1'HE: HJRIZO"l1'AL FORCE: IS

14.65223

kN

fHE SCRESS 1'.1' FRJtH IS 14. 28319 kN/s'~.n

ftiE SfRESS Af RF.: .. R

IS 84.48862 k;v .f~e. e

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j'12>.'-f ,,/"c:::a=0 THEN PF=P2 ELSE PF=Pl IF E < 0 tHEN PR=P2 ELSE PR=Pl LPRINf" rHE rOTAL ~ERrICAL WEIGHT IS ",w," kN" LPRINr" " X=X+l LPRINr" rHE ECCENtRICITY OF THE LO~~ ABOUT rHE CENTRE IS "IE/"m" LPRINr" " LPRIN'T" rHE HORIZONTAL FORCE IS "/p /" kN" LPRINT"****************" LPRIN'T LPRINT "rHE SrRgSS A'1' FRONr IS",PF;"kN/s::}.n" LPRINr LPRINT LPRIN'1' "1'HE s'rRESS 1\'1' REAR IS" ;PR;"kN/sq.rn" LPRINl' LPRIN1'''****************'' RETURN

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51

Program 3P 2

Calculation of the curvature of rc cantilever walls to assist in estimation of deflection

10 INPur "BREADTH 9 =";B 20 INPUT "THICKNESS H =";H 30 INPUT "EFFECTIVE DEPrH =";0 40 INPUT "AREA OF srEEL =";AS 50 EC=26666 b",c,Q,"k tluekM..,., 60 ES=200000! 70 1'=1 ..".d&~h 80 FP=1 90 INPur "BENDING MOMENT = remember *1 000 OOO";M I'IOMolC.1\ t ti M" 100 INPUT"INITIAL X VALUE =";X1 C\t. x AlII4 110 INPur "FINAL X VALUE =";X2 tlot. ~\tAQ\ ". " '... 120 IF T>l rHEN EC=EC/2 ..te.p vClI", bc.hvu.. 130 INPur "SrEP X =";5 lIHh,,1 L h",,,1 X C.~hll\ I) 140 FOR X = Xl ro X2 STEP S 150 IF 1'>1 THE~ FP=.55 160 IF r>2 THEN 500 170 FC=FP*(H-X)/(D-X) 180 FS=(M-B*H*FC*(H-X)/3)/(AS*(D-X/3)) 190 F1=X/(O-X)*(EC*FS/E5) 200 F2=(FS*AS+3*(H-X)*FC/2)/(B*X/2) 210 R=F1/F2 220 IF R>1 THEN 30SUB 580 240 PRINr "X=";X," Fe1/FC2=";R 491 IF R>l rHEN X = X2 492 NEX"r X 493 'r=T+l 495 LPRINr" " 497 LPRINr" " 498 IF T +o.3,.~,.

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