CIVL3160 course notes September 2011 PDF

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UNIVERSITY OF NEWCASTLE

REINFORCED AND PRESTRESSED CONCRETE DESIGN FOR CIVL 3160

by

Paul F Walsh July 2011 Edition Revised in 2001 to include 500 MPa Steel and AS 3600 (2001), then AS 1170 (2002) plus extensive reorganisation and redrafting in 2003 followed by significant changes to Section 7 in 2005. Major changes were needed for revisions in AS 3600 (2006) and correction made in Dec 06 and Jun 07. Further revisions were then made in 2011 to reflect changes introduced by the release of AS3600-2009

ii

Preface Purpose. These notes include a discussion of material properties, analysis of buildings and reinforced concrete design for beams, columns and slabs along with an introduction to the design of simple prestressed concrete beams and slabs and to retaining walls and footings as the prescribed notes for CIVL 3160 Reinforced Concrete Design. The author was a member of BD/2 and BD/49 responsible for the drafting of many of the code rules discussed in these notes and some discussion is given to the origin and nature of the rules as well as their use. It is not intended for actual design use: indeed emphasis has been placed on the need to learn from basic principles rather than office design procedures. Source. This text was partly written using material from “Use of Australian Standard for Concrete Structures” by Paul F Walsh which was published in 1988. The material has been significantly updated to take into account changes published in the 1994, 2001, and 2009 editions of AS 3600 as well as examples, revisions and additions to make the notes more relevant to the course. It is solely intended as the prescribed notes for the course CIVL 3160 Concrete Design. Virtually all the additional material is based on the author’s personal interpretation of AS 3600. Revisions. A first major revision took place in 2001. This was based on the change to 500 MPa steel and the amendments to AS 3600. Further corrections to that version have resulted from new load factors in AS 1170 in 2002. A further major revision occurred in 2006 which made many of the past solutions non-compliant and the notes simplified in content. All past notes are superseded. Units.  N and mm are used in this course for all dimensions and loads, as well as moments and stresses. They are selfconsistent and consistent with AS 3600. (Conveniently N/mm2 is the same as MPa.)  It is accepted that most designers use the inconsistent units of kN and m for loads and dimensions and kNm for moments, while mm’s are used for cross sections. Consequently correction factors of 1000 are often necessary, and although this causes few problems to experienced designers, it has been found to be a difficulty for novices.  Discrepancies between the system here and practice can be minimized by using Nmm  106 for moments (i.e. kNm) and N 103 for shears and loads. Use of charts. While it is appreciated that in practice charts and computer programs are commonly used for design, for educational reasons, they will not be used in this course or in the assignments (except for column charts). For logistic reasons, computer structural analysis will not be used although it is acknowledged it is essential in practical design. Accuracy. These notes have been prepared to cover a wide range of topics and examples. They have been extensively updated recently and all examples had to be recalculated, consequently the examples could include minor errors. It would assist, if errors were brought to the attention of the author. Acknowledgement. The notes include many corrections from Dr Mark Masia which are gratefully acknowledged.

Paul Walsh The University of Newcastle June 2007 Latest revision by Mark Masia The University of Newcastle July 2011

iii TABLE OF CONTENTS 1

BACKGROUND TO AS 3600 AND MATERIALS FOR DESIGNERS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

2

Standards and AS 3600 Concrete introduction Concrete strength Deformation of concrete Durability of concrete and reinforced concrete Basic properties of steel Fire design Impact of materials technology on design performance

ANALYSIS OF BUILDING STRUCTURES 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

1

11

Introduction to analysis Simplified coefficients Two way supported slabs Flat slabs - simplified Buildings by idealised frame Linear elastic analysis Other forms of analysis Effect of cantilevers

3

DESIGN OF REINFORCED BEAMS 3.1 Introduction to flexural strength of reinforced concrete 3.2 Shear strength 3.3 Torsion in beams 3.4 Deflection design 3.5 Cracking of beams 3.6 Miscellaneous bending clauses 3.7 Checking a beam (analysis) 3.8 Designing a beam

31

4

DESIGN OF SLABS

63

4.1 4.2 4.3 4.4 4.5 4.6

Basic slab behaviour Shear strength of slabs Serviceability of slabs Width for point and strip loads Slab design procedure Design of two way slabs

iv 5

DESIGN OF COLUMNS

5.1 5.2 5.3 5.4

6

7.

General introduction Basic braced column theory AS3600 clauses Column design procedure

RETAINING WALLS AND FOOTINGS 6.1 6.2 6.3 6.4 6.5

96

Types of retaining walls Design methods Design principles for various wall types Design principles – footings Design method for concentric footings

INTRODUCTION TO SIMPLE PRESTRESSED BEAMS AND SLABS 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

86

106

Introduction to prestressing Stress limit states Bending limit state design Design simplifications Serviceability design Shear and torsion Design steps and example Special cases

Appendix A Questions and solution to examinations of prestressed concrete at the University of Newcastle129

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CHAPTER ONE

BACKGROUND TO AS 3600 AND MATERIALS FOR DESIGNERS

This chapter gives an introduction to AS 3600 and to the materials sections with particular emphasis on information needed by reinforced and prestressed concrete designers. Contents include: standards and AS 3600; concrete and steel technology; concrete design properties; durability design; steel properties; prestressing steel, fire provisions; and concluding comments. Basic material properties are in Section 3 of AS 3600

1.1

STANDARDS and AS 3600

1.1.3

1.1.1

Organisation and AS 3600

Composition. The committee is voluntary (unpaid), mainly from Sydney and consists of:  Material suppliers.  Government departments  Universities.  Professional organizations (ASCE & Inst Eng) .

Standards Australia.  SA is an independent organisation financed mainly by sales, quality programs and subsidies.  Recognised by the government as the body responsible for standards. Scope of AS 3600.  Includes material properties and principles,  Limited design formula but no design aids such as charts. Design aids consistent with AS 3600.  Formulae can be found in these notes  Charts are in HB 71 (SA in cooperation with C&CA.)  Various other texts are available Legal status. Standards become legally enforceable by being called up by building regulations. However, they may also be used as evidence of what a ‘reasonable engineer’ would do. Acceptable design methods.  The concrete, steel and similar codes contain design methods regarded as acceptable by the design profession.  This simplifies the design and approval while protecting the public.

1.1.2

Why Australian Codes

Advantages. The advantages of Australian structural design codes include:  Many building practices and conditions are unique to Australia, e.g. warm coastal not freeze thaw.  Encourage local research and development.  Provide for local materials Disadvantages. The disadvantages are:  Lack of expertise in some areas.  Overseas computer software is not then relevant.

Committee BD-002

Power. Most influence in the past has been:  Material suppliers, such as Cement and Concrete Assoc, Steel Reinforcement Industry Association and National Ready Mix Association.  Keen individuals such as myself (a member of various committees and subcommittees for some twenty five years)  University representatives particular in their personal research areas Editions.  Started in 1979, as a combination of the separate reinforced and prestressed concrete standards.  1988 edition was revised in 1994 with only corrections and minor revisions.  Major revisions occurred in 2001 to deal with 500MPa steel and ductility problems, then more patches  Significant changes to deal with higher strength concrete and a major reorganisation occurred in 2009.

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1.2

CONCRETE INTRODUCTION

1.2.5

1.2.1

Portland Cement (OPC or GP)

Workability. The ability to be placed and finished is termed workability and depends on:  Grading of aggregate  Amount of water and cement  Admixtures

Manufacture. Made from limestone (or chalk, marl or shells) and clayey materials that are dried, ground and blended; then fired in a kiln at 1400 to 1500ºC to produce a fused clinker. This is then finely ground and some gypsum (CaSO4.2H2O) added to control set.

1.2.2

Blended Cements (GB)

Fly ash and slag. Fly ash (PFA), ground granulated blast furnace slag (GGBF) and silica fume (SF) are all processed ‘waste’ products containing siliceous material, which react with free lime from hydration of cement to produce cementitious products. But;  Setting time of slag and fly ash blends is longer.  Reaction is slow, hence less heat production, but usually for specified 28-day strength the 7-day strength is lower, affecting stripping times and early cracking (particularly PFA).  With good curing blended cements are usually good for durability, particularly water retaining structures (PFA) and marine exposure (GGBF).  With poor curing, such as building facades made from blended cements could have low surface durability and poor carbonation resistance (PFA).  High strength concrete normally involves blends.  Environmentally advantageous to use blends.

1.2.3

Concrete Aggregates

Purpose. Aggregates (gravel and sand) reduce cost and moderate shrinkage and creep. Creep and shrinkage. The amount of movement can be affected by aggregate selection (hard and impermeable best).

Workability of Fresh Concrete

Consistency. Slump of a cone of fresh concrete measures consistency and is a common but indirect measure of workability. It is also important that the fresh concrete is cohesive and not subject to segregation or bleeding. Water for slump. In batching concrete, allowance is made for some water to be added at the delivery point to bring the slump up to that specified. Extra water above this amount will reduce strength and increase creep and shrinkage properties.

1.2.6

Hydration

Hydration. Cements react with water to form complex gels. For highest strength and durability the voids should be minimised by using low water cement ratios (but cement is expensive) and good curing. Curing is particularly important for durability of the cover concrete.

1.2.7

Maturity

 Concrete gets stronger with time if water is available.  Rate depends upon temperature and cement composition.  Strength gain occurs in bulk of concrete without curing  Surface skin very sensitive to curing

Requirements. Aggregates should be clean, rounded or cuboid, smooth but not glassy surface, inert, not permeable and properly graded to give economical, workable concrete. Local sources. Transport costs usually dictate that local sources of aggregates be used and some can be less than ideal.

1.2.4

Admixtures

Important and common components of modern concrete including:  Water reducing  Air entrainment  Set control  Accelerators  Super plasticisers CaCl2 for set control and acceleration was a disaster and is now virtually banned.

Figure 1.1 Strength development with time for various cement types.

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1.3

CONCRETE STRENGTH

1.3.3

1.3.1

Design Compressive Strength

Production control.  Rules are based on modern principle that it is important to ensure that the manufacture of the concrete is subject to proper control from the start, rather than rely on project testing afterwards.  Statistically reliable estimates of grade are only possible with large numbers of tests at plant.

Technical definition. The most important property is the characteristic compressive strength, f’c, which is defined as the strength exceeded by 95% of compressive cylinder tests. The possibility of low strengths is allowed for in factors of safety.

Quality Control

Project control.  Project testing rules are statistically weak and are best avoided on most jobs.  Benefit of large doubt is given to manufacturer depending on control level.  Buy from a reliable manufacturer with good plant control, records and recent results.

1.3.4

Effect of Sample Size

Figure 1.2 Strength distribution Measurement. The 95% test strength is estimated from the mean (fmean) and the standard deviation (s) assuming the normal distribution. Thus; f’c

=

fmean

-

1.65 s

Design definition. For designers, f’c is:  Grade strength specified provided tests are OK and concrete is cured  Statistically determined from tests. Average strength. In some cases the mean in situ strength of concrete, fcm, is needed and values are tabulated for each grade.

1.3.2

Standard Grades

Grade numbers. The standard grades are 20, 25, 32, 40, 50, 65, 80 and 100MPa and were selected using internationally accepted numbers at 25% steps. The advantage of this group is that it reduces the number of grades needed to cover the range. Selection. The selection of the grade of concrete to be used in the design will depend upon:  Durability grade requirements.  Local availability (in some areas, higher grades are a problem due to weak local aggregates)  Economy (higher grades reduce column sections, but have little effect on beam or slab sizes for strength.)  Deflections (higher grades are stiffer and have less creep.)  Secondary effects (higher grades could have more problems with heat of hydration and AAR)

Target. Because of the definition of 95% strength the target strength for the mean of any group of tests should be f’c + 1.65 s. Production control level. For production control the rejection level is set at f’c + kc s. where kc is as low as 1.25. This low level is accepted because of the effect of sample size with some of the benefit of the doubt being given to the manufacturer. Nonetheless concrete with 30% defectives has a 98% chance of being rejected (this gives rise to large values of kc for small sample sizes). Project control level.  Project control can only be used to reject concrete.  Concrete is rejected, or is non-compliant, if the mean of three successive results is less than f’c.  Project control gives a low risk to manufacturer (1 in 450 chance of just satisfactory concrete being rejected).  Project control, on its own, would lead to a high consumers’ risk (i.e. substandard concrete passing). But production control is compulsory. Rejection vs compliance. Note that compliance with the project rules does not mean that the concrete is up to grade, however failure means all concrete represented by the three samples is below grade.

1.3.5

Tensile Strength

Type of stress pattern. The tensile strength of concrete in flexure has been found to be higher than in biaxial tension and compression, thus strength is:  0.6 f’c for flexure or by flexural tests  0.36 f’c for uniaxial tension (or tension from shear) or from tests reduced by a factor.

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1.4

DEFORMATION OF CONCRETE

1.4.1

Stiffness

Modulus of Elasticity. Empirical formulae give the modulus in terms of the in-situ average concrete strength (fcmi) and ρ is density. It could be used for later ages if strength is known. Ecj = ρ1.5 (0.043√fcmi) = ρ1.5 (0.024√fcmi + 0.12)

fcmi ≤ 40MPa fcmi > 40MPa

Ec for standard grades may be taken as: Grade 20 25 32 40 50 65 80 100

1.4.2

Estimated fcmi 22.5 28 35.5 43.5 53.5 68.0 82.0 99.0

Ec (MPa) 24,000 26,700 30,100 32,800 34,800 37,400 39,600 42,200

Stress strain curves

Structural use. Stress strain curves can be of any accepted form, but AS 3600 provides a reminder that the shape should be reduced to give a maximum in situ value of 0.9f’c when such curves are used in the calculation of column or beam strengths.

1.4.3

Shrinkage Properties

Concrete shrinkage.  Concrete undergoes chemical shrinkage as it sets and hardens; this is termed autogenous shrinkage and is designated as εcse  Concrete shrinks as it dries over months or years; and this is designated εcsd Structural effects of shrinkage.  Unfortunately because of the faster drying at edges and the restraint by reinforcement or other structures, shrinkage is not even and gives rise to stresses and distortions.  For prestressed concrete it is necessary to estimate shrinkage distortions from shrinkage strain, although simpler alternatives are available for reinforced concrete.  Shrinkage stresses resulting in cracking is a common structural complaint and often avoidance is difficult. Concretes with low basic shrinkage reduce problems. Factors affecting shrinkage. Shrinkage is influenced by: stiffness, permeability, cleanliness, quality of the aggregate, and the proportion of aggregate in the concrete.

Timing. The timing and nature of shrinkage can be changed by the curing and subsequent drying conditions. Shrinkage cracking usually occurs months after casting. (Earlier cracking is often due to early age temperature changes, or drying before the concrete has hardened i.e. plastic shrinkage) Basic shrinkage value. The standard now - AS 3600 (2009) gives shrinkage in two components: Autogenous εcse =

(0.06f’c-1.0) 50 10-6(1.0-e-0.1t)

Drying εcsd =

k1k4(1.0 – 0.008f’c) ε*csd.b

Where t is time in days and in terms of th the hypothetical thickness; ε*csd.b may be taken as: 800 10-6 Sydney and Brisbane 900 10-6 Melbourne -6 Elsewhere 1000 10 k4 is given by 0.7 Arid environment, 0.65 Interior environment, 0.6 Temperate inland environment and 0.5 Tropical or near coastal environment k1 is given in a figure or may be found as: k1 = α1t0.8/(t0.8 + 0.15th) α1 = 0.8 + 1.2 e-0.005th Tests on the concrete or local values can also be used. Part Table 3.1.7.2 of AS 3600 gives design shrinkage values ( 10-6) (Normal class concrete) Exposure th=100mm 200 400 Interior 40MPa 740 `610 480 Near coast 40MPa 590 490 390 Interior 50MPa 690 580 460 Near coast 50MPa 550 470 380

1.4.4

Creep of Concrete

Design Use. AS 3600 permits the use of creep multipliers to estimate deflections of structures and this can improve accuracy and reliability when deflections are critical. Such techniques are essential for prestressed concrete. Factors affecting creep. Generally creep depends upon:  Type and amount of aggregate,  Paste quality and hence grade However many minor items can influence creep, such as sulphate content of cement or curing temperature.

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Figure 1.3 Creep strain vs time and aggregate. Basic creep factor. Basic creep factor is the ratio of ultimate creep strain to elastic strain for a 150mm cylinder loaded at 28 days in a laboratory. Code basic creep factor. AS3600 gives v...