Civil Engineering Materials

By Peter A. Claisse

Civil Engineering Materials explains why construction materials behave the way they do. It covers the construction materials content for undergraduate courses in civil engineering and related subjects and serves as a valuable reference for professionals working in the construction industry. The book concentrates on demonstrating methods to obtain, analyse and use information rather than focusing on presenting large amounts of data. Beginning with basic properties of materials, it moves on to more complex areas such as the theory of concrete durability and corrosion of steel.

• Discusses the broad scope of traditional, emerging, and non-structural materials
• Explains what material properties such as specific heat, thermal conductivity and electrical resistivity are and how they can be used to calculate the performance of construction materials.
• Contains numerous worked examples with detailed solutions that provide precise references to the relevant equations in the text.
• Includes a detailed section on how to write reports as well as a full section on how to use and interpret publications, giving students and early career professionals valuable practical guidance.

• Language: English
• Publisher: Elsevier Science
• Release date: Sep 3, 2015
• ISBN: 9780128027516

Peter A. Claisse

Peter A. Claisse is Professor Emeritus at Coventry University and the author of more than 100 publications on construction and materials, including the Woodhead title Transport Properties of Concrete: Measurements and Applications. He graduated with a degree in Physics from Oxford University and then spent the next 9 years working as a Civil Engineer on major UK construction sites including 4 years on the Torness nuclear power station.?After obtaining a PhD in Civil Engineering at Leeds University, studying Silica Fume in concrete, he then went to the AEA Technology Harwell laboratory for 3 years to work on Nuclear waste containment.?He was at Coventry University for 20 years, teaching Civil Engineering Materials and researching transport processes in concrete and the use of secondary materials in cement.

Book preview

Civil Engineering Materials

Peter A. Claisse

Table of Contents

Cover

Title page

Copyright

Summary

Abbreviations

Introduction

Chapter 1: Units

Abstract

Notation

1.1. Introduction

1.2. Symbols

1.3. Scientific notation

1.4. Unit prefixes

1.5. Logs

1.6. Accuracy

1.7. Unit analysis

1.8. MKS SI units

1.9. US customary units

1.10. CGS units

1.11. Properties of water in different units

1.12. Summary

Chapter 2: Strength of materials

Abstract

Notation

2.1. Introduction

2.2. Mass and gravity

2.3. Stress and strength

2.4. Strain

2.5. Deformation and strength

2.6. Modulus of elasticity

2.7. Poisson’s ratio

2.8. Fatigue strength

2.9. Creep

2.10. Conclusions

Chapter 3: Failure of real construction materials

Abstract

Notation

3.1. Introduction

3.2. The steel sample

3.3. The concrete sample

3.4. The timber samples

3.5. Summary

Chapter 4: Thermal properties

Abstract

Notation

4.1. Introduction

4.2. Temperature

4.3. Energy

4.4. Specific heat

4.5. Thermal conductivity

4.6. Thermal capacity, thermal diffusivity, and thermal inertia

4.7. Coefficient of thermal expansion

4.8. Heat generation

4.9. Heat absorption, reflection, and radiation

4.10. Typical values

4.11. Summary

Chapter 5: Pressure

Abstract

Notation

5.1. Introduction

5.2. Pressure on a fluid

5.3. The effect of gravity on pressure

5.4. The effect of temperature on gas pressure

5.5. Propagation of waves

5.6. The bulk modulus

5.7. Attenuation of waves

5.8. Conclusions

Chapter 6: Electrical properties

Abstract

Notation

6.1. Introduction

6.2. Electric charge

6.3. Electric current

6.4. Voltage

6.5. Electric field

6.6. Resistance

6.7. Capacitance

6.8. Power

6.9. Electric current in concrete

6.10. Electrical test apparatus

6.11. Conclusions

Chapter 7: Chemistry of construction materials

Abstract

Notation

7.1. Introduction

7.2. The components of the atom

7.3. Chemical elements

7.4. Molecules

7.5. Chemical reactions

7.6. Acids and bases

7.7. Oxidizing agents and reducing agents

7.8. Chemicals dissolved in water

7.9. The lime cycle

7.10. The gypsum cycle

7.11. Summary

Chapter 8: Properties of fluids in solids

Abstract

Notation

8.1. Introduction

8.2. Viscosity

8.3. Water and water Vapour

8.4. Porosity

8.5. Condensation in pores

8.6. Water in pores

8.7. Drying of materials

8.8. Summary

Chapter 9: Transport of fluids in solids

Abstract

Notation

9.1. Introduction

9.2. Flow in a porous solid

9.3. Pressure driven flow

9.4. Thermal gradient

9.5. Capillary suction

9.6. Osmosis

9.7. Electro-osmosis

9.8. Summary

Chapter 10: Transport of ions in fluids

Abstract

Notation

10.1. Introduction

10.2. Ions in solution

10.3. Flow rates

10.4. Diffusion in a nonadsorbing system

10.5. Adsorption in a porous solid

10.6. Diffusion with adsorption

10.7. Electromigration

10.8. Conclusions

Chapter 11: Ionising radiation

Abstract

Notation

11.1. Introduction

11.2. Types of ionising radiation

11.3. Sources of radiation

11.4. Half-lives

11.5. The effect of radiation on materials

11.6. The effect of radiation on the body

11.7. Shielding

11.8. Conclusions

Chapter 12: Variability and statistics

Abstract

Notation

12.1. Introduction

12.2. Sampling

12.3. Distributions

12.4. Probability

12.5. Correlations

12.6. Conclusions

Chapter 13: Use of test results

Abstract

Notation

13.1. Introduction

13.2. Sources of variations in concrete strength test results

13.3. Making decisions about failing test results

13.4. Identifying the source of the problem

13.5. Multivariate analysis

13.6. Designing for durability

13.7. Conclusions

Chapter 14: Specifications and standards

Abstract

14.1. Introduction

14.2. Specifications

14.3. Standards

14.4. Building codes

14.5. Repeatability and reproducibility

14.6. Quality assurance

14.7. Conclusions

Chapter 15: Reporting results

Abstract

15.1. Introduction

15.2. Graphs

15.3. References

15.4. How to get good marks for your materials lab reports

15.5. How to publish a paper on materials

15.6. Verbal presentation

15.7. Conclusions

Chapter 16: Testing construction materials

Abstract

16.1. Introduction

16.2. How to find references

16.3. Types of references

16.4. Defining the objectives of a research programme

16.5. Carrying out a research programme

16.6. The statistical basis

16.7. The publication

16.8. Conclusions

Chapter 17: Introduction to cement and concrete

Abstract

17.1. Introduction

17.2. Cement and concrete

17.3. Uses of cement

17.4. Strength of concrete

17.5. Reinforced concrete

17.6. Prestressed concrete

17.7. Cement replacements

17.8. Admixtures

17.9. Environmental impact

17.10. Durability

17.11. Conclusions

Chapter 18: Cements and cement replacement materials

Abstract

18.1. Introduction

18.2. Cements

18.3. Cement replacement materials (also known as mineral admixtures)

18.4. Cement standards

18.5. Conclusions

Chapter 19: Aggregates for concrete and mortar

Abstract

19.1. Introduction

19.2. Environmental impact of aggregate extraction

19.3. Aggregate sizes

19.4. Mined aggregates

19.5. Artificial aggregates

19.6. Major hazards with aggregates

19.7. Properties of aggregates

19.8. Conclusions

Chapter 20: Hydration of cement

Abstract

Notation

20.1. Introduction

20.2. Heat of hydration

20.3. Types of porosity

20.4. Calculation of porosity

20.5. Influence of porosity

20.6. Curing

20.7. Conclusions

Chapter 21: Concrete mix design

Abstract

21.1. Introduction

21.2. UK mix design

21.3. US mix design

21.4. Mix design with cement replacements

21.5. Mix design for air-entrained concrete

21.6. Mix design for self-compacting concrete

21.7. Redesigning mixes using trial batch data

21.8. US units

21.9. Conclusions

Chapter 22: Testing wet and hardened concrete

Abstract

Notation

22.1. Introduction

22.2. Workability

22.3. Bleeding and segregation

22.4. Air content

22.5. Compressive strength testing

22.6. Tensile and bending strength testing

22.7. Measurement of modulus of elasticity

22.8. Durability tests

22.9. Conclusions

Chapter 23: Creep, shrinkage, and cracking of concrete

Abstract

23.1. Creep

23.2. Shrinkage

23.3. Cracking

23.4. Preventing problems caused by shrinkage and cracks

23.5. Conclusions

Chapter 24: Admixtures for concrete

Abstract

24.1. Introduction

24.2. Plasticisers and superplasticisers

24.3. Viscosity modifying admixtures

24.4. Air entrainers

24.5. Retarders

24.6. Accelerators

24.7. Other admixtures

24.8. Using admixtures on site

24.9. Conclusions

Chapter 25: Durability of concrete structures

Abstract

25.1. Introduction

25.2. Transport processes in concrete

25.3. Corrosion of reinforcement

25.4. Sulphate attack

25.5. Alkali–silica reaction

25.6. Frost attack

25.7. Salt crystallisation

25.8. Delayed ettringite formation

25.9. Durability modelling

25.10. Conclusions for corrosion and corrosion protection

Chapter 26: Production of durable concrete

Abstract

26.1. Introduction

26.2. Design for durability

26.3. Specification for durability

26.4. Placing durable concrete

26.5. Curing

26.6. Conclusions

Chapter 27: Assessment of concrete structures

Abstract

27.1. Introduction

27.2. Planning the test programme

27.3. Test methods for strength

27.4. Test methods for durability

27.5. Presenting the results

27.6. Conclusions

Chapter 28: Mortars and grouts

Abstract

28.1. Introduction

28.2. Masonry mortars

28.3. Rendering

28.4. Cementitious grouts

28.5. Cementitious repair mortars

28.6. Floor screeds

28.7. Conclusions

Chapter 29: Special concretes

Abstract

29.1. Introduction

29.2. Low cost concrete

29.3. Concrete with reduced environmental impact

29.4. Low density concrete

29.5. High-density concrete

29.6. Underwater concrete

29.7. Ultra-high strength concrete

29.8. Ultra-durable concrete

29.9. Concrete with good appearance (architectural concrete)

29.10. Fast setting concrete

29.11. Concrete without formwork

29.12. Self-compacting concrete

29.13. Roller-compacted concrete

29.14. Conclusions

Chapter 30: Steel

Abstract

30.1. Introduction

30.2. Iron–carbon compounds

30.3. Control of grain size

30.4. Manufacturing and forming processes

30.5. Steel grades

30.6. Mechanical properties

30.7. Steel for different applications

30.8. Joints in steel

30.9. Conclusions

Chapter 31: Corrosion

Abstract

Notation

31.1. Introduction

31.2. Electrolytic corrosion

31.3. The effect of pH and potential

31.4. Measuring corrosion rates with linear polarisation

31.5. Corrosion of steel in concrete

31.6. Corrosion prevention

31.7. Conclusions

Chapter 32: Alloys and nonferrous metals

Abstract

32.1. Introduction

32.2. Alloys

32.3. Comparison of nonferrous metals

32.4. Copper

32.5. Zinc

32.6. Aluminium

32.7. Lead

32.8. Plating

32.9. Conclusions

Chapter 33: Timber

Abstract

Notation

Notation subscripts

33.1. Introduction

33.2. The environmental impact of forestry

33.3. Production

33.4. Engineered wood products

33.5. Strength of timber

33.6. Jointing timber

33.7. Durability of timber

33.8. Preservation of timber

33.9. Bamboo

33.10. Conclusions – timber construction

Chapter 34: Masonry

Abstract

34.1. Introduction

34.2. Clay bricks

34.3. Calcium silicate bricks

34.4. Concrete bricks

34.5. Concrete blocks

34.6. Natural stones

34.7. Roofing tiles

34.8. Slates

34.9. Masonry construction detailing

34.10. Masonry construction supervision

34.11. Conclusions – masonry construction

Chapter 35: Plastics

Abstract

35.1. Introduction

35.2. Terminology

35.3. Mixing and placement

35.4. Properties of plastics

35.5. Modes of failure (durability)

35.6. Typical applications in construction

35.7. Conclusions

Chapter 36: Glass

Abstract

36.1. Introduction

36.2. Glass for glazing

36.3. Glass fibres

36.4. Glass wool

36.5. Conclusions

Chapter 37: Bituminous materials

Abstract

37.1. Introduction

37.2. Binder properties

37.3. Binder testing

37.4. Binder mixtures

37.5. Asphalt mixtures

37.6. Testing asphalt mixtures

37.7. Mix designs for asphalt mixtures

37.8. Use in road construction

37.9. Other applications of binders

37.10. Conclusions

Chapter 38: Composites

Abstract

38.1. Introduction

38.2. Reinforcing bars in concrete

38.3. Fibre reinforcement in concrete

38.4. Steel/concrete composite bridge decks

38.5. Fibre reinforced plastics

38.6. Structural insulated panels

38.7. Conclusions

Chapter 39: Adhesives and sealants

Abstract

39.1. Introduction

39.2. Adhesives

39.3. Sealants

39.4. Conclusions

Chapter 40: Comparison of different materials

Abstract

40.1. Introduction

40.2. Comparing the strength of materials

40.3. Comparing environmental impact

40.4. Health and safety

40.5. Conclusions

Chapter 41: New technologies

Abstract

41.1. Introduction

41.2. 3D printing

41.3. Photocatalytic admixtures

41.4. Self-healing concrete

41.5. Zero cement concrete

41.6. Durability modelling

41.7. Hemp lime

41.8. Wood–glass epoxy composites

41.9. Bamboo

41.10. Conclusions

Tutorial Questions

Subject Index

Copyright

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Notices

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Summary

This book covers the construction materials content for undergraduate courses in Civil Engineering and related subjects, and will also be a valuable reference for professionals working in the construction industry.

The topics are relevant to all the different stages of a course, starting with basic properties of materials and leading to more complex areas, such as the theory of concrete durability, and corrosion of steel.

The first 16 chapters cover the basic properties of materials, and how they are measured. These range from basic concepts of strength to more complex topics, such as diffusion and adsorption. The following 13 chapters cover cementitious materials. The production and use of reinforced concrete, as well as its durability, are considered in detail because this is the most ubiquitous material that is used in construction, and its premature failure is a massive problem worldwide. The subsequent chapters consider the other materials used in construction, including metals, timber, masonry, plastics, glass, and bitumens. The final chapters discuss examples of composites, and adhesives and sealants, and then cover a number of potentially important technologies that are currently being developed.

The book is intended for use both in the United Kingdom and the United States, as well as in other countries, so both metric and imperial units are discussed.

Abbreviations

ac

Alternating current

ASR

Alkali silica reaction

ASTM

American Society for Testing and Materials

BS

British Standard

BTU

British thermal unit

CE

Conformité Européenne

cgs

Centimetre gram second

CSF

Condensed silica fume

CSH

Calcium-silicate hydrate

dc

Direct current

DEF

Delayed ettringite formation

DIN

Deutsches Institut für Normung (German standards)

dpc

Damp proof course

EN

EuroNorm

ENV

Draft EuroNorm

GGBS

Ground granulated blast furnace slag

GRP

Glass reinforced polyester

HAC

High-alumina cement

HC

Hydrated cement

HDPE

High density polyethylene

ISAT

Initial surface absorption test

ISO

International Standards Organization

kip

Thousands of pounds (lb)

ksi

Thousands of pounds per square inch

Ln or Loge

Natural logarithm

Log or Log10

Logarithm to base 10

LPRM

Linear polarization resistance measurement

MKS SI

Meter kilograms seconds, Systéme International

OPC

Ordinary Portland cement

PFA

Pulverised fuel ash

psf

Pounds per square foot

psi

Pounds per square inch

QA

Quality assurance

RH

Relative humidity

SCC

Self-compacting concrete

SIP

Structural insulated panel

VFA

Voids filled with binder (for bituminous mix)

VMA

Viscosity modifying admixture (for concrete)

VMA

Voids in the mineral aggregate (for bituminous mix)

VTM

Voids in the total mix (for bituminous mix)

w/c

Water to cement ratio

Introduction

This book covers the construction materials content for undergraduate courses in Civil Engineering, and related subjects. The aim of the method or presentation is to cover the basic science, before moving on to a detailed analysis of the materials. The chapters on the science include mechanical, thermal, electrical, and transport properties of materials, and discuss the basic theory, as well as the relevance to applications in construction. The book then moves on to consider in detail each of the key materials, such as concrete and steel, and to discuss their properties, with reference to the basic science from the initial chapters.

The book is written for the age of the Internet, in which facts are readily obtained from websites. It therefore concentrates on demonstrating methods to obtain, analyse, and use information from a wide variety of sources.

Improving materials offers great scope for energy saving and environmental gains. These gains should be considered at all stages of the design and specification process, so they are discussed throughout the book.

The subject of construction materials is an area where there have been some very expensive mistakes, such as the use of High-alumina cement and calcium chloride in concrete, at times when there was ample published research to show that they should not have been used. Therefore, in addition to Chapter 15 explaining how to write detailed reports on materials experiments, Chapter 16 includes details of methods of assessment of published literature.

With the wide availability of research reports on the properties of materials, clients are now asking for calculations for the design life of structures, particularly reinforced concrete, for which the durability generally depends on the transport properties. This book presents the basic theories, and equations necessary for these calculations, and gives numerical examples of how they may be applied.

Construction materials are continually being replaced with new products. This book is, therefore, intended to give guidance on the assessment of new materials, rather than simply concentrating on those that are currently available. This includes methods to assess and analyse data on physical properties such as strength, permeability, and thermal conductivity. Similarly, new standards are continually being produced, and are now immediately available for all engineers to download. This book seeks to show the principles of test methods, so new ones can be understood and applied.

Materials cause many problems on site, and are a major area for improvement. There are, however, few simple right answers. Students will find this different from, say, the study of structures, where calculations give just one correct value for the size of a structural member. When considering the correct solution for a problem with durability, there are many different possibilities that may be appropriate for different situations, and the aim of this book is to provide the basis for the choice.

It is no longer possible for engineers in Europe to treat US Customary (Imperial) units as things of the past that are only found in the United States. When looking for a material property on the Internet, the data that is found will frequently come from the United States, and will frequently be in pounds per square inch, or degrees Fahrenheit, or similar units. All engineers should be familiar with these units, so they can make use of all the mass of data that is available on the web. The different units and the methods needed to use them are discussed in Chapter 1.

Detailed suggestions for appropriate chapters to be included at each level of a course, together with solutions to tutorial questions, and suggested laboratory exercises, are included in an Instructor’s Manual that accompanies this book (available online to instructors who register at textbooks.elsevier.com/9780081002759).

Students with a particular interest in transport processes in concrete and durability modelling are referred to Transport Properties of Concrete by the same author, also published by Elsevier (Woodhead imprint).

Chapter 1

Units

Abstract

This is an introductory chapter, which introduces units and methods that will be used later in the book. The main part of the chapter is expressed in MKS SI Units, but separate sections give common US customary and CGS units and their conversion factors. Scientific notation is described, and common errors in its use are discussed. Unit prefixes for the MKS system are presented. Guidance is given on the use of logarithms, and the conventions used to show natural logs, and logs to base 10. Unit analysis is introduced with a simple example.

Keywords

scientific notation

unit prefixes

MKS SI units

US customary units

Chapter outline

1.1 Introduction 1

1.2 Symbols 2

1.3 Scientific Notation 3

1.4 Unit Prefixes 3

1.5 Logs 4

1.5.1 Logs to Base 10 4

1.5.2 Logs to Base e 4

1.6 Accuracy 4

1.7 Unit Analysis 5

1.8 MKS SI Units 5

1.9 US Customary Units 5

1.10 CGS Units 6

1.11 Properties of Water in Different Units 6

1.12 Summary 7

Notation

e

Mathematical constant = 2.718

L

Length (m)

m

Mass (kg)

ρ

Density (kg/m³)

1.1. Introduction

This chapter provides an overview of some mathematical notation and methods that are essential to engineering. All students should read through it, and many will be able to confirm that they have covered it all in previous studies. It is essential that any students who are not familiar with this material should study it further because, if it is not fully understood, many section of this book and many other aspects of a degree in engineering will be impossible to understand.

The main discussion uses metre–kilogramme–second (MKS) units; but the use of Imperial (US customary), and centimetre–gramme–second (CGS) units is also described. The purpose of this is not that students in Europe should read one section, and students in the United States should read the other. When searching for values for material properties on the Internet, they may be found in any units. All students should be fully familiar with all these types of units, and able to recognize them, and convert between them. Unit conversion macros are found easily online. The important concept is to recognize which system of units the data is in, and make sure that all data in an equation or calculation is in the same system.

1.2. Symbols

This book is about the properties of construction materials. Where possible, these properties are measured quantitatively; this means that values are assigned to them. For example, if a large block of concrete is considered which has one side 10-m long, this may be represented by equation (1.1):

(1.1)

where L is the variable we are using for the length of that side.

If the length of the block in other directions is considered and these are 8 and 12 m, this may be represented by equation (1.2):

(1.2)

To calculate the mass of the block, the density must be known. This could be given by the equation (1.3):

(1.3)

where ρ is the Greek letter rho that is often used as a variable for density. Greek letters are used because there are insufficient letters in the English alphabet (correctly called the Roman alphabet) for the different properties that are commonly measured.

The Greek letters that are commonly used are in Table 1.1.

Table 1.1

Greek Letters in Common Use in Engineering

1.3. Scientific notation

The mass of the block is given by equation (1.4):

(1.4)

The result has been given in kilogrammes. It may be seen that the number is large, and not easy to visualize or use. In order to make the number easier to use, it is expressed commonly in scientific notation as 2.304 × 10⁶ kg.

It is important to express numbers correctly in scientific notation. The 2.304 should normally be between 1 and 10. To express this number as 0.2304 × 10⁷ or 23.04 × 10⁵ is mathematically the same, but should not normally be used. The number raised to a power must be 10, for example, 8⁶ or 7⁶ should not appear in this notation. The power must be a positive or negative integer, for example, numbers such as 10⁴.⁵ or 10⁶.³ should not appear, but negative powers such as 10−4 may be used.

Because many computer printers could not at one time print superscripts, an alternative notation is often used: 2.304 × 10⁶ is written as 2.304E6. This notation may be found in books and papers, but it is not recommended for use in formal reports. It is, however, a convenient notation, and is used in spreadsheets. The E is represented by the EXP key on some calculators. Note that, for example, 10⁸ is entered into a calculator as 1 EXP 8 not 10 EXP 8. 10 EXP 8 is 10 × 10⁸, which is 10⁹.

1.4. Unit prefixes

The alternative way of making the number easier to use is to change the units. For all metric units, the prefixes in Table 1.2 are used.

Table 1.2

Metric Prefixes

Thus 2,304,000 kg = 2,304 Mg (Megagramme). It would be technically correct, but very unusual to express it as 2.304 Gg. One Mg is equal to a metric tonne, so the mass would commonly be expressed as 2304 tonnes.

1.5. Logs

Another method of expressing large numbers is the use of logarithms, called commonly logs. These are particularly useful on graphs because both small and large numbers can be represented on the same graph (see, e.g., Fig 15.1). The log function is available on many calculators, and in all spreadsheets.

Logs are always relative to a given base, and the log of a number x to a base a is written as loga(x), and is defined from equation (1.5):

(1.5)

Some useful relationships with logs are:

(1.6)

(1.7)

(1.8)

1.5.1. Logs to base 10

Logs to base are the logs that were used for calculations before calculators were invented. The procedure for multiplying two numbers together was to obtain the log of each, and then add these together (as in equation (1.6)), and obtain the inverse log (shown as 10x on calculators) of the result.

It may be seen that:

(1.9)

1.5.2. Logs to base e

e is a constant (= 2.718), and logs to base e are called natural logs. Loge(x) is written as ln(x) (while Log10(x) is written as log(x)) in spreadsheets, and most calculators. It may be seen that if:

(1.10)

then

(1.11)

The function ey is, therefore, the inverse function to the natural log, and can be used to obtain the original number from a natural log. It is often called the exponential function and written as EXP(y) in spreadsheets.

1.6. Accuracy

Depending on the accuracy known or required, the number 2.304 × 10⁶ might be expressed as: 2.3 × 10⁶ kg or even 2 × 10⁶ kg. This may be correct, but numbers should never be rounded in this way until the end of a calculation. If numbers are rounded, and then used for further calculations very large errors may be caused.

1.7. Unit analysis

This is a method that can be used to check equations by reducing the terms on each side to base units (it is also often used without units and called dimensional analysis, but they are used in the method presented here). Thus, for example, equation (1.4) has the base units:

(1.12)

that may be seen to be the same on each side.

All equations should check in this way. If the two sides of the equation are different, then it is incorrect.

1.8. MKS SI units

The calculation in equation (1.12) has been carried out in MKS SI (metre–kilogramme–second Systéme International) units in which masses are measured in kilogramme, and lengths in metre. The MKS SI system was developed specifically to be consistent, easy to use, and is the legally recognised system of units in Europe, and has no local variations.

A system of units consists of base units and derived units. The base units are fixed (e.g., the metre was defined as the length of a piece of steel that was kept in Paris) and the derived units are obtained from them. The main base units in the MKS system are given in Table 1.3.

Table 1.3

Base Units in the MKS System

Derived units are obtained from the equations that define them, for example:

Within the MKS SI system, the only units that are used are based on the metric prefixes in Table 1.2 that increase or decrease by factors of 1000. Thus the metre, the kilometre, and the millimetre are used, but the centimetre is not.

1.9. US customary units

US customary units are also known as a type of British Imperial units. In the US customary system, force is measured generally in the same units as mass (pounds).

Some of the US customary units (such as the gallon, pint and ton) are not the same as the Imperial units still used informally in the United Kingdom. 1 US liquid pint = 473 mL but 1 UK pint = 568 mL. Similarly 1 US short ton = 0.907 metric tonnes but 1 UK ton = 1.016 tonnes. For this reason these imperial units are not used in this book.

Table 1.4 shows the commonly used US customary units. Definitions of these properties such as thermal conductivity are given in subsequent chapters of this book.

Table 1.4

Some US Customary Units

Conversions to US customary units are given in appropriate chapters of this book.

1.10. CGS units

CGS (centimetre–gramme–second) units were used in parts of Europe before the MKS SI system was adopted. As with the Imperial system, there are local variations within it. In addition to the metric prefixes listed in Table 1.2 the centi prefix (10−2) is commonly used. Some CGS units that may be encountered are given in Table 1.5.

Table 1.5

Some CGS Units

The kilocalorie may be also referred to as a Calorie (with an uppercase C) causing some confusion.

1.11. Properties of water in different units

Some properties of water in different units are given in Table 1.6.

Table 1.6

Properties of Water

1.12. Summary

• Scientific notation and unit prefixes should be used for clarity with large or small numbers.

• 10⁸ is entered into a calculator as 1 EXP 8 not 10 EXP 8. 10 EXP 8 is 10 × 10⁸, which is 10⁹.

• To maintain accuracy, numbers should never be rounded until the end of a calculation.

• Unit analysis should be used to check equations.

• MKS, CGS, and US customary are three different systems of units, and should never be mixed together in the same equation.

• Some US customary units differ from Imperial units previously used in the United Kingdom.

Chapter 2

Strength of materials

Abstract

In this chapter, the basic concepts of force, stress, strength, strain, and elastic modulus are introduced. Compressive, tensile, and shear strengths are defined depending on the type of loading. Strain is defined, and, from it, the elastic modulus. Stress–strain relationships are discussed, and the yield and failure of materials. The Poisson’s ratio is defined. Fatigue strength and creep are also discussed.

Keywords

stress

strain

Young’s modulus

elasticity

Poisson’s ratio

fatigue

creep

Chapter outline

2.1 Introduction 9

2.2 Mass and Gravity 9

2.3 Stress and Strength 10

2.3.1 Types of Loading 10

2.3.2 Tensile and Compressive Stress 11

2.3.3 Shear Stress 11

2.3.4 Strength 11

2.4 Strain 12

2.5 Deformation and Strength 13

2.6 Modulus of Elasticity 14

2.7 Poisson’s Ratio 14

2.8 Fatigue Strength 15

2.9 Creep 16

2.10 Conclusions 16

Notation

a

Acceleration (m/s²)

A

Area (m²)

B

Width (m)

E

Young’s modulus (Pa)

f

Force (N)

g

Gravitational constant (=9.81 m/s²)

L

Length (m)

m

Mass (kg)

W

Load (N)

x

Displacement (m)

γ

Shear angle (radians) or shear strain

σ

Stress (Pa)

τ

Shear stress (Pa)

2.1. Introduction

The strength of a material is almost always the first property that the engineer needs to know about. If the strength is not adequate, then the material cannot be used and other properties are not even considered. The next property to be considered is often the stiffness, or elastic modulus because this determines how far a structure will deflect under load. In this chapter, the basic concepts of force, stress, strength, strain, and elastic modulus are introduced.

2.2. Mass and gravity

In the MKS SI system, the mass of an object is defined from its acceleration when a force is applied, for example, from equation (2.1)

(2.1)

where f is the force in Newton, m is the mass in kg, a is the acceleration in m/s².

Gravity is normally the largest force acting on a structure. On the earth’s surface, the gravitational force on a mass m is given by equation (2.2)

(2.2)

where g is the gravitational constant = 9.81 m/s² (32.2 ft./s²).

The gravitational force on an object is called its weight. Thus, an object will have a weight of 9.81 N/kg of mass. An approximate value of 10 is often used for g to give the commonly used value of 10 kN weight for a mass of 1 tonne (=1000 kg). In the US customary system of units, force is generally measured as a weight in pounds and, if this is done, a constant term for g = 32.2 ft./s² must be included in equation (2.1).

2.3. Stress and strength

2.3.1. Types of loading

In engineering, the term strength is always defined by type, and is probably one of the following (see Fig. 2.1), depending on the method of loading.

• Compressive strength

• Tensile strength

• Flexural strength

• Shear strength

Figure 2.1   Compression, Tension, Flexure and Shear

A force acting on an object becomes a load on the object, so force and load have the same units.

In some structures, the compressive and tensile forces are not immediately apparent (Fig. 2.2).

Figure 2.2   A Complex Bridge on the Singapore River

2.3.2. Tensile and compressive stress

In order to define strength, it is necessary to define stress. This is a measure of the internal resistance in a material to an externally applied load. For direct compressive or tensile loading, the stress is designated σ, and is defined in equation (2.3), and measured in Newtons per square metre (Pascals) or pounds per square inch.

(2.3)

See Fig. 2.3.

Figure 2.3   Load and Stress

2.3.3. Shear stress

Similarly, in shear the shear stress τ is a measure of the internal resistance of a material to an externally applied shear load. The shear stress is defined in equation (2.4) (see Fig. 2.4):

(2.4)

Figure 2.4   Shear Stress and Strain

2.3.4. Strength

The strength of a material is a measure of the stress that it can take when in use. The ultimate strength is the measured stress at failure, but this is not normally used for design because safety factors are required.

2.4. Strain

In engineering, strain is not a measure of force, but is a measure of the deformation produced by the influence of stress. For tensile and compressive loads:

(2.5)

Strain is dimensionless, so it is not measured in metres, kilogrammes, etc. The commonly used unit is microstrain (μstrain), which is a strain of one part per million.

For shear loads, the strain is defined as the angle γ (see Fig. 2.4). This is measured in radians, and thus for small strains:

(2.6)

2.5. Deformation and strength

Strain may be elastic or plastic. Figure 2.5 shows the stress on an object, and the resulting strain as it is loaded and then unloaded. If the strain is elastic, the sample returns exactly to its initial shape when unloaded. If plastic strain occurs, there is permanent deformation.

Figure 2.5   Elastic and Plastic Deformation

The arrows show the sequence of loading and unloading during a test.

If the material exhibits plastic deformation (yields), and does not return to its original shape when unloaded, this is clearly unacceptable for most construction applications. Figure 2.6 shows a stress–strain curve for a typical metal. As the load is applied, the graph is initially linear (the stress is proportional to the strain), until it reaches a yield point. If the load is removed after yield, the sample will not return to its original shape, and is left with final residual strain.

Figure 2.6   Elastic and Plastic Strain

For a brittle material (such as concrete), strength is defined from the stress at fracture, but for a ductile material (e.g., some steels) that yields a long way before failure, strength is often defined from limits to the residual strain, after loading and unloading. This concept of proof stress is discussed in Chapter 30.

2.6. Modulus of elasticity

If the strain is elastic, that is, on the linear part of a graph of stress versus strain, Hooke’s law may be used to define Young’s modulus as the gradient:

(2.7)

Thus, from equations (2.4), (2.5) and (2.7)

(2.8)

where W/x may be the gradient of a graph of load versus displacement obtained from an experiment.

The Young’s modulus is also called the modulus of elasticity or stiffness, and is a measure of how much strain occurs due to a given stress. Because strain is dimensionless, Young’s modulus has the units of stress or pressure.

Some typical values are given in Table 2.1.

Table 2.1

Typical Values of Strength, Failure Strain and Modulus

Notes: 1 MPa = 1 N/mm²; 1 GPa = 1 kN/mm²

In reality, no part of a stress–strain curve obtained from an experiment is ever perfectly linear. Thus the modulus must be obtained from a tangent or a secant. The difference between an initial tangent and secant modulus is shown in Fig. 2.7.

Figure 2.7   Tangent and Secant Modulus

2.7. Poisson’s ratio

This is a measure of the amount by which a solid spreads out sideways under the action of a load from above. It is defined from equation (2.9). A material like timber which has a grain direction will have a number of different Poisson’s ratios corresponding to loading, and deformation in different directions.

(2.9)

2.8. Fatigue strength

If a material is continually loaded and unloaded (e.g., the springs in a car), the permanent strain from each cycle slowly decreases. This may be seen from Fig. 2.8. Eventually, the sample will fail, and the number of cycles it takes to fail will depend on the maximum stress that is being applied. The fatigue of steel is discussed in Section 30.6.4.

Figure 2.8   Fatigue Cycles to Failure

2.9. Creep

Creep is the slow irreversible deformation of materials under load. It is surprisingly large for concrete, and tall buildings get measurably shorter during use (the guide rails on the lifts sometimes buckle).

2.10. Conclusions

• In the MKS system, force is defined from mass and acceleration, and is measured in Newtons.

• Stresses may be compressive, tensile, flexural, or shear.

• The strength of a material is the stress at failure.

• Strain is a measure of the deformation produced by a stress.

• The elastic modulus is the ratio of stress/strain.

• The Poisson’s ratio is a measure of strain perpendicular to the load.

• Creep is a measure of long-term deformation under load.

Tutorial questions

Assume g = 10 m/s² for all questions

1.

a. A round steel bar with an initial diameter of 20 mm and length of 2 m is placed in tension, supporting a load of 2000 kg. If the Young’s modulus of the bar is 200 GPa what is the length of the bar when supporting the load (assuming it does not yield)?

b. If the Poisson’s ratio of the steel is 0.4, what will the diameter of the bar be when supporting the load?

Solution:

a. Cross-sectional area = 3.14 × 10−4 m²

Load = 2000 kg × g = 2 × 10⁴ N    (2.2)

Stress = 2 × 10⁴/3.14 × 10−4 = 6.4 × 10⁷ Pa    (2.3)

Strain = 6.4 × 10⁷/200× 10⁹ = 3.2 × 10−4    (2.7)

New length = (3.2 × 10−4 × 2) + 2 = 2.00064 m    (2.5)

b. Lateral strain = 3.2 × 10−4 × 0.4 = 1.28 × 10−4    (2.9)

Change in diameter = 1.28 × 10−4 × 0.02 = 2.56 × 10−6 m    (2.5)

New diameter = 0.02 − 2.56 × 10−6 = 1.999744 × 10−2 m = 19.99744 mm

2. A 2 m long tie in a steel frame is made of circular hollow section steel with an outer diameter of 100 mm and a wall thickness of 5 mm. The properties of the steel are as follows:

Young’s modulus:    200 GPa

Yield stress:    300 MPa

Poisson’s ratio:    0.15

a. What is the extension of the tie when the tensile load in it is 200 kN?

b. What is the reduction in wall thickness when this load of 200 kN is applied?

Solution:

a. Area = π(0.05² − 0.045²) = 1.491 × 10−3 m²

Stress = 200 × 10³/1.491 × 10−3 = 1.34 × 10⁸ Pa    (2.3)

This stress is 134 MPa, which is well below the yield stress.

Strain = 1.34 × 10⁸/2 × 10¹¹ = 6.7 × 10−4    (2.7)

Extension = 2 × 6.7 × 10−4 = 0.00134 m = 1.34 mm    (2.5)

b. Strain = 6.7 × 10−4 × 0.15 = 1.005 × 10−4    (2.9)

Reduction = 1.005 × 10−4 × 0.005 = 5.025 × 10−7 m = 0.5 μm    (2.5)

3. A water tank is supported by four identical timber posts that all carry an equal load. Each post measures 50 mm by 75 mm in cross-section, and is 1.0 m long. When 0.8 m³ of water is pumped into the tank, the posts get 0.07 mm shorter.

a. What is the Young’s modulus of the timber in the direction of loading?

b. If the cross-sections measure 75.002 mm by 50.00015 mm, after loading, what are the relevant Poisson’s ratios?

c. If 300 L of water are now pumped out of the tank, what are the new dimensions of the post?

(Assume that the strain remains elastic.)

Solution:

Normally, all calculations should be carried out in base units, but these calculations of strain are an example of where it is clearly easier to work in mm.

a. 0.8 m³ of water has a mass of 800 kg and thus a weight of 800 × g = 8000 N

Stress = 8000/(4 × 0.075 × 0.05) = 5.33 × 10⁵ Pa    (2.3)

Strain = 0.07/1000 = 7 × 10−5    (2.5)

Modulus = 5.33 × 10⁵/7 × 10−5 = 7.6 × 10⁹ Pa    (2.7)

b. Change in width on long side = 75.002 − 75 = 0.002 mm

Strain on long side = 0.002/75 = 2.66 × 10−5    (2.5)

Thus, Poisson ratio = 2.66 × 10−5/7 × 10−5 = 0.38    (2.9)

Strain on short side = 0.00015/50 = 3 × 10−6    (2.5)

Thus, Poisson ratio = 3 × 10−6/7 × 10−5 = 0.043    (2.9)

c. 300 L of water has a mass of 300 kg.

Thus, the mass of water now in the tank is 800 − 300 = 500 kg

The changes in dimensions are proportional to the load, and thus they are 500/800 = 0.625 of those in part (b).

0.07 × 0.625 = 0.044, thus length = 1000 − 0.044 = 999.956 mm

0.002 × 0.625 = 0.00125, thus long side = 75.00125 mm

0.00015 × 0.625 = 0.000094, thus short side = 50.000094 mm

4. The below figure shows observations that were made when a 100 mm length of 10 mm diameter steel bar was loaded in tension. The equation given is for a trendline that has been fitted to the straight portion of the graph. Calculate the following:

a. the Young’s modulus,

b. the estimated yield stress,

c. the ultimate stress.

Solution:

Cross-section area = π × 0.01²/4 = 7.85 × 10−5 m²

a. The equation given on the graph has been generated by the Excel compute package, and is a best fit to the linear part of the data (this is real experimental data). This technique is discussed in Chapter 15.

The gradient taken from the equation is 157.76 kN/mm = 1.5776 × 10⁸ N/mE = 1.5776 × 10⁸ × 0.1/7.85 × 10−5 = 2.01 × 10¹¹ Pa = 201 GPa    (2.8)

b. Load = 33 kN (estimated from the end of the linear section on the graph)

Thus, stress = 420 MPa(2.3)

c. Load = 42 kN at failure (the highest point on the graph)

Thus, stress = 535 MPa(2.3)

5.

a. A 100 mm diameter concrete cylinder 200 mm long is loaded on the end with 6 tonnes. What is the stress in it?

b. The Young’s modulus of the cylinder is 25 GPa. What is its height after loading?

c. The Poisson’s ratio of the cylinder is 0.17. What is its diameter after loading?

d. A column 2 m high, measuring 300 mm by 500 mm on plan, is made with the same concrete as in the cylinder and supports a bridge. In order to prevent