precast concrete structures second edition pdf

a Axis distance to bar; distance to point load; lever arm from topping to precast centroids; axial load factor in biaxial column design; distance to bracing ment from shear centre; lengt

Precast

Concrete Structures

Precast

Concrete Structures

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Library of Congress Cataloging‑in‑Publication Data

Names: Elliott, Kim S.

Title: Precast concrete structures / Kim S Elliott.

Description: Boca Raton : Taylor & Francis, CRC Press, 2017 | Includes

bibliographical references and index.

Identifiers: LCCN 2016010309 | ISBN 9781498723992

Subjects: LCSH: Precast concrete construction.

Classification: LCC TA683.7 E43 2017 | DDC 624.1/83414 dc23

LC record available at https://lccn.loc.gov/2016010309

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Contents

3A Appendix A: Summary of Eurocode EC2: Design of concrete structures

4.2.1 Definitions of precast floor units and slab fields 136

5.2.2 Calculating A s and A¢s from the design moment M Ed 225

5.3 Composite reinforced beams 239

6.1.2.1 Method A for first-order e fi /h ≤ 0.15 319

6.1.2.2 Method B for first-order e fi /h ≤ 0.25 319

7.4.1 Precast concrete infill walls 376

flexural strength and stiffness 508

10 Beam and column connections 513

11.5.5 Vertical ties 623

12 Design exercise for 10-s torey precast skeletal frame 629

12.3 Solution 637

12.6.2 Composite prestressed concrete beam

12.6.4 Composite prestressed concrete beam

12.7.3 Edge column at 9.0 m centres: fifth to

12.7.4 Edge column at 9.0 m centres: Foundation

to third floor and third to fifth floors 668

12.7.5 Design of double-sided steel billet at

12.7.6 Internal column between 9.0 and 8.0 m

centres: Fourth to sixth floors 671

12.7.7 Internal column between 9.0 and 8.0 m

12.7.8 Design of double-sided steel billet at

12.8 Stability ties 676

Preface to the First Edition

In 1990, the then chairman of the British Precast Concrete Federation (BPCF), Geoff Brigginshaw, asked me what level of teaching was carried out in British universities in pre-cast concrete construction for multistorey buildings The answer, of course, was very little, and it remains that way today in spite of considerable efforts by the BPCF and sections of the profession to broadcast the merits, and pitfalls, of precast concrete structures Having given lectures at about 25 UK universities in this subject, the author estimate that less than 5% of our civil/structural engineering graduates know about precast concrete and less than this have a decent grounding in the design of precast concrete structures Why is this so?The precast concrete industry commands about 25% of the multistorey commercial and

domestic building market if frames, floors and cladding (facades) are all included In higher

education (one step away from the market) precast education commands between zero and

(about) 5% of the structural engineering curriculum This in turn represents only about 1/8

of a civil engineering course The 5% figure claimed earlier could indeed be an overestimate.

The reasons are twofold:

1 British lecturers are holistic towards structural engineering

2 British lecturers have no information in this subject

This book aims to solve these suggestions simultaneously Suggestion no 2 is more readily solved This book is, unfortunately, one of the very few textbooks in this subject area aimed

at students at a level which they can assimilate in their overall structural engineering ing process It does this by considering design at both the macro and micro levels – global issues such as structural stability, building movement and robustness are dissected and ana-lysed down to the level of detailed joints, localised stress concentrations and sizes of bolts and welds

learn-Suggestion no 1 is more complex Having been acquainted with members of the FIB1

( formerly FIP2) Commission on Prefabrication, it has come to my notice the differing tudes towards the education of students in certain forms of building construction – precast concrete being one of them (and timber another) In continental Europe, leading precast industrialists and/or consultants hold academic posts dedicated to precast concrete con-struction Chairs are even sponsored in this subject In South America, lecturers, students and practitioners hold seminars where precast concrete is a major theme It is not uncommon

atti-1 FIP, Federation International de la Prefabrication; an international, but predominantly European, organisation for the welfare and distribution of information on prefabricated concrete.

2 FIB, Federation Internationale du Beton, born from a merger of FIP with CE; an international, but nantly European, organisation for the welfare and distribution of information on structural concrete.

predomi-for there are as many as 10 master’s students to study this subject in a civil engineering department In the United States, collaborative research between consultants, precast manu-

facturers and universities is common, as the number of papers published in the PCI Journal

testifies

The attitude in Britain is more holistic and less direct First, basic tuition is given in solid mechanics, structural analysis and material properties Students are required to be capa-ble of dealing with structural behaviour – independent of the material(s) involved Second, given the fundamental principles of design (and a reminder that code equations are often simulations and their data conservative), students can assimilate any design situation, with

appropriate guidance This may be true for structural steelwork and cast in situ concrete

structures where the designers may (if they wish) divorce themselves from the fabricator and contractor It is not true for precast concrete (and timber) structures where the fabricator and site erector form part of the ‘design team’

Precast concrete design is an iterative procedure, linking many aspects of architecture, design, detailing, manufacture and site erection together in a 5-point lattice

Many students will be familiar with these names, but a few will see or hear them in a single lecture Some of the links are quite strong Note the central role of ‘designing’ (this does not mean wL2/8, etc.) in establishing relationships with architectural requirements, detailing components and connections and manufacturing and erecting the said compo-nents at their connections Could similar diagrams be drawn for structural steelwork or cast

in situ concrete structures?

Further, there are a number of secondary issues involving precast concrete construction Prefabrication of integrated services, automation of information, temporary stability and safety during erection all result from the primary links

Some of these are remote from ‘designing’ The illustration reminds us of their presence

in the total structure The design procedure will eventually encompass all of these aspects.

This book is aimed at providing sufficient information to enable graduates to carry out structural design operations, whilst recognising the role of the designer in precast concrete construction Its content is in many parts similar to but more fundamental than the author’s

book, Multistorey Precast Concrete Framed Structures (Blackwell Science 1996) The

Blackwell book assumed that the readers already have acquired a prior knowledge of the building industry and some experiences in designing concrete structures This book takes a backward step to many of the design situations and does not always uphold the hypotheses given Reference to the Blackwell book may therefore be necessary to support some of the design solutions

The design examples are carried out to BS8110, and not EC2, as might be expected from a textbook published today The reason for this is that the clauses relevant to precast concrete

in EC2 have yet to find a permanent location Originally Part 1.3 was dedicated to precast concrete, but this was withdrawn and its content merged into the general code Part 1.1 For this reason specific design data relevant to precast concrete are not available

The author is grateful to the contributions made by the following individuals and tions: the members of the FIB Commission on Prefabrication, in particular Arnold Van Acker (Addtek Ltd., Belgium), Andre Cholewicki (BRI Warsaw), Bruno Della Bella (Precompressi Centro Nord, Italy), Ruper Kromer (Betonwerk + Fertigteil-Technik (Germany), Gunner Rise (Stranbetong, Sweden), Nordy Robbens (Echo, Belgium) and Jan Vambersky (TU Delft

organisa-& Corsmit, Netherlands); to a few organisations, namely, Trent Concrete Ltd (United Kingdom), Bison Ltd (United Kingdom), SCC Ltd (United Kingdom), Tarmac Precast Ltd (United Kingdom), Tarmac Topfloor Ltd (formerly Richard Lees, United Kingdom), Techcrete Ltd (United Kingdom and Ireland), Composite Structures (United Kingdom), British Precast Concrete Federation, British Cement Association and Reinforced Concrete

Council (United Kingdom), Betoni (Finland), Bevlon (Netherlands), C&CA (Australia), Cement Manufacturers Association (southern Africa), CIDB (Singapore), Andrew Curd and Partners (United States), Echo Prestress (South Africa), IBRACON (Brazil), Grupo Castelo (Spain), National Precast Concrete Association (Australia), Nordimpianti Otm (Italy), Hume Industries (Malaysia), Prestressed Concrete Institute (United States), Spaencom

Major links Manufactur

Figure 1

Structural zones and facades

Sequence ofdeliverie s

stab ility

Figure 2

Betonfertigteile GmbH (Germany), VarioPlus (Germany), Spancrete (United Staes), AB Stranbetong (Sweden) and Tammer Elementti Oy (Finland); to his research assistants Wahid Omar, Ali Mahdi, Reza Adlparvar, Dennis Lam, Halil Gorgun, Kevin Paine, Aziz Arshad, Adnan Altamimi, Basem Marmash and Marcelo Ferreira; and to his secretarial assistant Caroline Dolby.

Preface to the Second Edition

For 14 years since the publication of the first edition of this book (April 2002), precast crete elements and structures have become

(i) Taller (36-storey skeletal frame, Belgium, Figure 3) and 54-storey wall frame (the Netherlands)

(ii) Longer (50 m long prestressed concrete beams, Figure 4)

(iii) Deeper (1000 mm deep prestressed hollow core floor units produced in Italy in 2014) (iv) Shallower (span/depth ratio approaching 40 for prestressed composite and continuous beams)

(v) Stronger (grade C90/105 used in columns in buildings such as in Figure 3)

Also, they have generally become more ambitious and creative in terms of integrating structural engineering and architecture, using semi-rigid connections to enhance frame stability in 10-storey sway frames, using high-strength hidden connections up to about

700 kN, applying automation and robotics in manufacturing, and using recycled concrete

as aggregates, PFA, GGBS, reclaimed mixing water from cement slurry and sustainable

materials At a recent seminar chaired by myself on behalf of the fibUK Group, David Scott,

FREng, of Laing O’Rourke, made his angle on prefabrication as ‘Concrete in the Age of Digital Enlightenment’

These advancements have been complimented by an increase in the available literature, not only from myself (Goodchild, Webster & Elliott 2009, Elliott & Jolly 2013) but also from other books from Germany, Brazil, United Kingdom, and several excellent bulletins

from fib Commission 6 on Prefabrication, together with 8 European product standards

covering a wide range precast concrete elements (hollow core floor slabs, walls, stairs, etc.) Structural design engineers have never had it so good, and yet the important knowledge and understanding concerning the behaviour of precast concrete structures continues to

remain the same, as the author mentioned in the preface of his book Multi-Storey Precast

Concrete Framed Structures (Elliott 1996), a ‘black box’ Even our critics now acknowledge

that the realm of precast concrete and off-site manufacture of building components and systems in steel, timber, plastics, etc., has taken major steps forwards in the past 15 years; but there is still work to do beyond the textbook Seminars on precast concrete are seldom organised, and teaching in universities or technical colleges is almost non-existent (apart from Belgium, the Netherlands, Scandinavia and odd pockets elsewhere) Whilst our sec-

ond edition of the book Multi-Storey Precast Concrete Framed Structures (Elliott & Jolly

2013) was aimed at the already accomplished structural concrete designer, this book is once again intended for undergraduate, postgraduate and young structural engineers Hopefully

this book will be used as an accompanying text (it will never form a core text in today’s UK

syllabus) to undergraduate courses in concrete structures With one or two exceptions, the

author does not find precast concrete being taught in the United Kingdom; it’s still perceived

as a specialist building system He is frustrated by this – he finds himself advising ate students to study in Delft or Eindhoven in the Netherlands or at the FEBE organised courses in Belgium (Hasselt, Ghent, ECAM Institut Supérieur Industriel Brussels), leading to

postgradu-an MSc in Precast Concrete, or even with Prof Marcelo Ferriera in Brazil in order to gain

a sound background in this subject My own half-day seminars to two-day workshops have

Figure 3 North Galaxy Buildings, Belgium (c Ergon, Belgium).

Figure 4 Prestressed concrete beams 55 m long by VBI, the Netherlands.

been organised worldwide (16 countries) from South Korea (Figure 5) to Malaysia, South Africa, Brazil and Europe, but now that those events have ceased there in an even bigger gap in the exposure to design and good practice, particularly for young/30-something structural engineers.

This book aims to fill many of these shortcomings It is based on the Eurocodes (EC0, EC1, EC2 and briefly EC3) and where relevant the EC Product Standards (e.g pulling in

of tendons and splitting stresses in hollow core slabs in EN 1168) Finding the relevant clauses in Eurocode EC2 can be a nightmare; for example, (a) the service loading and per-missible service stress in prestressed concrete in tension for exposure XC1 (so clearly given

in BS 8110) requires clauses 7.3.2.(4), 7.3.2(2) and Table 3.1; (b) iteration is necessary, for example, slenderness checks on columns require the area of steel, ω in clause 5.8.3.1, to be

known before the design can commence; and (c) it requires 26 clauses and/or equations in

Chapters 3, 5 and 10 and Appendix B to determine the total losses of prestress This book pieces everything together, both strategically throughout the chapters and logically in the text and via the design examples Although the chapters follow the same sequence as in the first edition, a new feature is introduced, that is, the complete design of a 10-storey precast concrete framed building (Chapter 12) This focuses on stability, sway due to imperfec-tions in the frame and floor diaphragm, load combinations and component design It might (if they wish) be worth to study this chapter first (without necessarily having background knowledge on the design techniques) to appreciate the procedures that make up the entity and to consequently work through the chapters in sequence

Worked examples to BS8110 are not present because (i) the first edition is still available and relevant (except γms = 1.15 and f yk = 500 [or 600] N/mm2) and (ii) parallel EC2 versus

BS8110 examples are given in the second edition of Multi-Storey Precast Concrete Framed

Structures Having said that, codes do not dominate precast concrete design and detailing

as much as in other building mediums – the focus is more on principles, understanding and construction methods – and with those attributes the rest is easy

Figure 5 The author’s precast concrete workshop in Seoul, South Korea, organised by Samsung Precast in 2013.

As before the author is grateful to the contributions and assistance made by the following individuals and organisations (in addition to those named in the first edition): to the members

of the fib Commission on Prefabrication, in particular Arnold Van Acker (Belgium), Andre

Cholewicki (Warsaw, Poland), Barry Crisp (Australia), Bruno Della Bella (Precompressi Centro Nord, Italy), Iria Donaik (Cassol Pre-Fabricados, Brazil), Bjorn Engström (Chalmers University, Sweden), Marcelo Ferreira (UFSCAR, University Sao Carlos, Brazil), George Jones (CDC Ltd., United Kingdom and Ireland), Holgar Karutz (Concrete Plant International, Germany), Stef Maas (FEBE, Belgium), Alessandra Ronchetti (Secretary, Italy) and Jan Vambersky, (Netherlands); to a few organisations, namely, Bison Manufacturing Ltd (United Kingdom), British Precast Concrete Federation (United Kingdom), Reinforced Concrete Council/Concrete Centre/MPA (United Kingdom) and Prestressed Concrete Institute (United States); to some helpful people specifically Stephen McAvoy (Acheson & Glover Ltd., Northern Ireland, United Kingdom), Simon Bullivant and Richard Morton (Bullivant Taranto Ltd., Northern Ireland, United Kingdom), Mark Magill, Simon Kelly and Seamus McKeague (Creagh Concrete Ltd., Northern Ireland, United Kingdom), Zuhairi Abd Hamid and Ahmad Hazim Abdul Rahim (CREAM, Malaysia), Jon Pendleton (Coltman Precast, United Kingdom), Kamel Bensalem (Charcon Construction Solutions), Tang Lai Peng (Eastern Pretech, Malaysia), Daniel Petrov (Echo Prestress, South Africa), Cliff Billington (Invisible Connections, United Kingdom), Charles Goodchild (MPA/Concrete Centre, United Kingdom), Khoo Tian (O-Stable Panel, Malaysia), George McAllister and Mark Maloney (Preconco, Barbados), Jureik Im and Yongnam Kim (Samsung C&T Corp., South Korea), Mounir El Debs (University of Sao Paulo, Brazil), Haraldo (T&A Pre-Fabricada, Brazil) and Colin Jolly (co-author, United Kingdom); to his colleagues in the Civil Engineering Department at the University of Nottingham’s campuses in Nottingham and Malaysia, in particular Gwynne Davies (retired) and John Owen and technicians Nigel Rook, Bal Loyla and Mike Langford; and to his research assistants Ali Mahdi (United Kingdom), Reza Adlparvar (Tehran, Iran), Sarakot Hasan (Iraq), Dennis Lam (University of Bradford, United Kingdom), Halil Gorgun (University of Dicle, Turkey), Kevin Paine (University of Bath, United Kingdom), Ho Lee (Sangju National University, South Korea), Jong-Young Song (Samsung C&T Corp., South Korea), Kamaluddin Rashid and Aziz Arshad (JKR, Malaysia), Farah Abdul Aziz (UPM, Malaysia) and Izni Ibrahim and Roslli Noor (UTM, Malaysia)

This book is dedicated to the late Dato Dr Wahid Omar, my first PhD student, the former Director General of JKR (Public Works Dept., Kuala Lumpur) and my friend in the United Kingdom and Malaysia for 28 years

Permission to reproduce extracts from British Standards is granted by BSI British Standards  can be obtained in PDF or hard copy formats from the BSI online shop: www.bsigroup.com/Shop or by contacting BSI Customer Services for hardcopies only: Tel: +44 (0)20 8996 9001, Email: cservices@bsigroup.com

About the Author

Dr Kim S Elliott is a consultant to the precast industry in the United Kingdom and Malaysia

He was senior lecturer in the School of Civil Engineering at Nottingham University, United Kingdom, from 1987 to 2010 and was formerly at Trent Concrete Structures Ltd., United

Kingdom He is a member of fib Commission 6 on Prefabrication where he has made tributions to six manuals and technical bulletins, and he is the author of the book Multi-

con-Storey Precast Concrete Framed Structures (1996, 2013) and co-authored the Concrete

Centre’s Economic Concrete Frame Manual (2009) He was chairman of the European research project COST C1 on Semi-Rigid Connection in Precast Structures (1992–1999)

He has lectured on precast concrete structures 45 times in 16 countries worldwide ing Malaysia, Singapore, South Korea, Brazil, South Africa, Barbados Austria, Poland, Portugal, Spain, Scandinavia and Australia) and at 30 UK universities

a Axis distance to bar; distance to point load; lever arm from topping to precast

centroids; axial load factor in biaxial column design; distance to bracing ment from shear centre; length of bearing ledge in corbels; vertical deflection due to elongation of catenary tie

ele-a ʹ Distance to point load in cantilever

a b Edge distance or half of centre-to-centre distance between bars

a c Distance to forces from centre line of column; distance to load from column

face in corbels

a CΔcrit Critical value of deflection in catenary action under accidental loading

a e Effective distance to load from main rebars in corbels and connections

a eff Required structural bearing length a in corbels

a sd a sd,m Side axis distance to bars or groups of bars

a v Distance to load from face of column in corbels

a 1 Net (structural) bearing length

a 2 a 3 Ineffective bearing lengths or permitted deviations at supports

αIαII Deformation parameters in serviceability design

b b 1 b 2 Breadth, in stage 1 and 2 loading

b c Total breadth of cores (in hollow core slab)

b e Breadth of precast floor unit

b eff Breadth of in situ topping

b f Breadth of flanges in beams or slabs

b i Interface contact length between beams and slabs or infill

b l Bearing length of localised support (e.g pad, plate)

b min Breadth of column and beam (in fire)

b p Breadth of bearing; breadth of localised support (e.g pad, plate); bearing

breadth of the infill at the top of column pockets

b t Mean width of section in the tension zone

b v b w Breath of upstand in beam

b w Breath of web(s)

b 1 Effective breadth of bearing

b 1 b 2 Depth of bays in horizontal floor diaphragm

c Cohesion factor in interface shear stress

c c ov Cover to bars

c d Edge distance to rebars or gap between rebars

c 1 c 2 Column depths

d Effective depth to tension bars from compression face; net depth of floor slab in

horizontal floor diaphragm; root depth of shear key; distance to holding down bolts in tension from compression face

d ʹ Effective depth to compression bars; depth to the centre of the bottom bars in

deep beam wall; distance to holding down bolts from compression edge of plate

d ʺ Effective depth to links (in beam boot or nibs)

d c Effective depth from top of composite section

d ct Net depth to dowel bar in shear

d eff Effective height of bottom flange of beam

d f Effective depth from column pocket to the edge of the foundation

d h Effective depth to tension bars in nibs

d n Depth to centroid of concrete in compression

d t Distance from the top of the insert to the uppermost link in connections

d T Effective depth to tendons in tension (ultimate limit state)

d 1 d 2 Effective depth in stage 1 and 2 loading

d 2 Axis distance to tension bars from tension face in columns; axis distance to

starter bars in base plates

d 2 d 3 Ineffective bearing lengths (e.g in nibs and corbels)

e Eccentricity to centre of pressure or load from shear centre; eccentricity due to

ultimate loads = M Ed/NEd

eʹ Net eccentricity of upper and floor loads of deep beam wall

e b e h Eccentricity of point loads acting over breadth and depth of section

e fi Eccentricity due to fire loads = M 0Ed,fi/N0Ed,fi

e i Eccentricity due to imperfection

e net Net eccentricity in column due to eccentric loads

e o Eccentricity due frame or floor effects; minimum eccentricity

e tot Total eccentricity e o + e i

e y e z Eccentricity of load due to moments about y- and z-axes in columns

e nib Eccentricity of load due to load acting on nib of deep beam wall

e up Eccentricity of load due to upper storey deep beam wall

for multiple columns

f Horizontal shear force per unit length

f b f m Strength of brick element and mortar

f b General term for final stress in bottom fibre of prestressed section

f b1 f t1 f b2 f t2 Bottom and top fibre stress due to stage 1 and 2 bending moments

f t2ʹ Top of topping stress due to stage 2 bending moment

f bed Design strength of bedding material

f c Mean cylinder strength of concrete required for lifting

f cd f cdi Design strength of concrete; in situ/mortar bedding

f ci Design stress in infill beneath base plate

f ck Characteristic cylinder strength of concrete

f cki f ck of in situ or infill concrete

f ck (t i ) f ck (t i ) Value of f ck at time t and at installation t i

f cm (t) Value of f cm after time t

f ctd f ctdi Design strength of concrete and in situ concrete in tension = f ctm/γm

f ctd (t) Value of f ctd at transfer or at time t

f ctm f ctmi Mean strength of concrete and in situ in tension

f Ed Ultimate design bearing stress (or σEd)

f Edw Ultimate design stress in welds

f k Characteristic strength of brickwork in compression

tendons

f LOP f pʹ Stress in tendons at εLOP; at intercept in σ-ε diagram

f pbt Bond stress at transfer

f pd Design strength of prestressing tendon = f pk/γm

f pk Characteristic strength of prestressing tendon

f Rd f Rdu Ultimate bearing stress; for partially loaded area

f s As-measured yield strength of rebar; service stress in rebars

f sc Design stress in column bars, yield or elastic

f u Ultimate tensile strength of hot rolled structural steel

f ub Ultimate strength of bolts

f vk Ultimate shear strength of brickwork

f y Yield strength of hot rolled structural steel

f yd Design strength of steel rebar = f yk/γm

f yk Characteristic yield strength of steel rebar

f ykh Value of f yk of tie bars welded to bearing plates

f yk,b Buckling strength of steel rebar

f ywk Value of f yk of stirrups

f u Ultimate tensile strength of steel sections

f ub f uw Ultimate tensile strength of bolts and dowels and welds

f y Yield strength of steel sections (see p yd for design values of sections, bolts, etc.)

f ybk f yw Yield strength of bolts and dowels and welds

g Gap (between ends of elements)

g k Pressure of permanent (dead) load per unit area

h Storey height; height of deep beam wall; depth of section; depth of slab

h a Equivalent height of deep beam wall

h agg Maximum nominal size of coarse aggregate

h eff Member thickness or depth (in fire)

h ft h fb Depth of top and bottom flanges

h i Pressure due to imperfection force; effective height of unbraced column

h l Overall depth of lattices in half slab

h o Notional depth or thickness of element

h s Slab depth in shrinkage effects calculation; depth of upstand in beams

h y h c Depth of face and total depth of corbel

h ʹ Height of infill wall (l w in BS EN 1992-1)

h 1 Minimum length of shear key

h 1 h s Slab thickness in fire calculation

i Radius of gyration of section

k 1 k 2 Column end ‘flexibility’ factors (ratio of column/beam stiffness); factors in

moment redistribution ratio

k Depth factor for shear strength; moment distribution factor; strength factors in

brick infill wall design

kc k Factors for minimum area of reinforcement

k n Size coefficient for shrinkage

k p(θcr) Stress ratio in prestressing tendons in fire

k T Limit for prestress ratio after initial losses

l Façade length of building; span; effective span for l/d ratio; clear height of

verti-cal element, length of bracing element; depth of pocket in column foundation

l b Bearing length (parallel with the span of the element) (termed a in the code)

l bd l b , rqd Design anchorage (bond) length; structural anchorage length required

l e Characteristic length (of beam) of uniform stress

l eff Effective span

l n Clear distance between the faces of the supports; actual length of beam

l o Effective length of lattice bars in half slab; clear span of deep beam wall

l p Length of the overlap in lapped bars or hooked bars; length of beam of

con-stant curvature

l pt Transmission length; lap length for strand in accidental loading

l pt2 Design value of l pt at ultimate limit state

l r Distance between the column or wall ties

l s Elastic elongation length of tie bar; straight part of a bar in anchorage

l td Length of spot welded transverse bar

l w Shear span; bearing width (perpendicular with the span of the element) (called

b 1 in the code); length of weld (not leg length)

l x Distance to shear plane from end of prestressed element; floor to ceiling height

l ʹ Cantilever span

l 0 Effective length or height of vertical element

l 0,fi l 0 in fire situation

l 0t Distance l 0 between torsion restraints

m Bending moment; modular ratio (long term); number of the elements

contribut-ing to imperfections; distance from holdcontribut-ing down bolts to starter bars in base

plates

m h Horizontal bending moment in floor plate

m 1 m 2 Long-term modular ratio for beam and in situ infill in two-stage design

n Normalised column axial load factor; number of storeys above a loaded

ele-ment; number of bars in cantilever wall

n bal Balanced stress ratio in column design

n o Number of storeys including basements

n u Ultimate axial stress ratio in column design

p Line pressure in billet connections

p bq Shear strength of bolts and dowels

p d Accidental load per area or unit length

p ybd p ywd Design strengths of bolts and dowels and welds

p yk(20°C) Strength of prestressing tendons at ambient temperature

q Mean wind pressure; line load due to wind plus imperfection

q Ed Variable (live) load per unit length

q k Pressure of variable (live) load per unit area

q 1 q 3 Perimeter and internal floor tie forces

r r b Radius of curvature in second-order and deflection calculations

r i r o Internal and external (outside) bend radius of bars

r m Column end moment ratio = M 01 /M 02

r supγsup Partial safety factor for variations in prestressing

s Cement factor; distance between bars or links; distance of load F from the

nearest lateral support in hollow core slabs; spacing of floor ties

t Time; thickness; depth of topping; thickness of wall (h w in BS EN 1992-1-1);

total breadth of the in situ concrete side walls of column pockets

t e Equivalent depth or thickness in fire of hollow core slabs

t o Time when load is first applied

t s Time to removal from mould (or detensioning for prestress)

t w Throat thickness of weld

t 0T Equivalent age at transfer for creep

u Perimeter of element; edge distance to partial area or point load

v Shear force per unit length; shear deflections

v v 1 Strength reduction factor for concrete cracked in shear

vʹ Concrete strength reduction factor

v Ed v Ed1 Shear stress, due to stage 1 loads

v Edi Design interface shear stress in horizontal floor diaphragm

v hx Shear stress in joints in horizontal floor diaphragm

v min Minimum ultimate shear resistance

v Rdi Interface shear resistance in horizontal floor diaphragm

v Rv Interface shear resistance of a smooth surface

w Width of the compressive strut

w b w t w 1 Width of compressive struts in deep beam wall

w Ed Ultimate uniformly distributed load per unit length

w h w u Self-weight precast plank,  upper precast plank and topping, in half-slab

design per unit length

w k Pressure of wind load per unit area; crack width

w max Limiting crack width

w s w s1 w s2 Service loads, stage 1 and imposed stage 2

w 0 Self-weight of element per unit length

w ʹ Diagonal length of infill wall

x Distance between props; distance from face of column to centre of load

x u x c Depth to centroidal axis, flexurally uncracked and cracked sections

x Distance to the centroid of the areas

x ʹ yʹ Distances to the centroid of stiffness

y Distances between bracing elements parallel to loading

y b y t Distances to centroid of section from bottom to top

y b,c Distance to centroid of composite section from bottom

y b,co y t,co Compound values of y b y t

y s Height to centroid of all tendons

y T Height to centroid of tendons in tension zone

z z 1 z 2 Lever arm, in stage 1 and 2 loading

z cp Eccentricity of prestressing force

z h Lever arm between lattices in half slab

A c,co Compound value of A c

A cc Cross-sectional area of precast and in situ topping

A ci Cross-sectional area of in situ concrete

A c (y) Concrete section area above height y from bottom of section

A c1 A c0 Partially loaded resistance and loaded areas

A d Design value of accidental load; area of diagonal bars in half joints

A gt Percentage total elongation in rebars at maximum force

A j Area of interface joint

A p A p1 A p2 Area of prestressing tendons, in stage 1 and 2 loading

A pT Area of prestressing tendons in tension (ultimate limit state)

A s A s1 A s2 Area of rebars in tension, in stage 1 and 2 loading

A sʹ Area of rebars in compression

A sc Compressive strut reinforcement in deep corbels

A sd Area of dowels to resist horizontal force

A sh Area of rebars to resist horizontal force

moments and shear forces

A svh Additional area to A shd in horizontal floor diaphragm

A si Area of interface shear dowels, stirrups; area of row i bars

A sj Area of coupling bars in horizontal floor diaphragm

A s,l Area of lattice bars in half slab

A st Area of transverse bars (lacer bars)

A sv Area of vertical ties

A sw Area of shear stirrups

A v A l Area of reinforcing loops and lacer bars between infill wall and column

B Depth of slab in horizontal floor diaphragm

C Column curvature factor; compressive force

C min Minimum cover for durability

C nom Nominal cover for durability

C pt (y) Factor according to position of tendons (V Rd,c (y) calculation)

C Rd Compressive strut resistance

C Rd,c Shear stress constant

D Depth of precast slabs in horizontal floor diaphragm

E cm Concrete Young’s modulus (secant value)

E cm(t) E cm at time t

E cmi E cm of in situ or infill concrete

E i Young’s modulus of infill wall

E p Young’s modulus for prestressing strand or wire

E pʹ Young’s modulus after εLOP

E s Young’s modulus for steel or rebars

F Force; horizontal shear force in columns

F bst Ultimate bursting force (EC2 uses T)

F bt Ultimate force in single bar at bends

F btd End bearing capacity of a spot welded transverse bar of length l td

F Ed Ultimate end reaction; ultimate forces above and below inserts; ultimate

horizontal force in column pockets

F Edh Ultimate horizontal force in bottom reinforcement of connections

F Linear load in hollow core floor slab distribution; force in holding down bolts

F c Ultimate force in concrete in compression

F cR Ultimate compressive capacity of strut in corbels

F c,t Horizontal interface shear force due to stage 2 loads

F d Ultimate force in diagonal bars in half joints

F q Ultimate shear resistance of dowels or bars

F R Three-line edge support for hollow core floor slab load F

F Rd,t Ultimate tensile capacity of top bars in corbels

F s Ultimate force in bars or tendons; tension force in column bars

F sc Ultimate compressive force in column bars

F s,db Ultimate force due to A s,db in deep beam wall

F shʹ Restoring force due to restraint of free shrinkage

F t F tʹ Basic and modified stability (catenary) tie force

beams

F wd Ultimate tensile capacity of the spot weld; tie force in corbels

F y Ultimate yield force in column bars

F 1 F 2 F 3 Ultimate reactions in column pockets

G′ Effective shear modulus of horizontal floor diaphragm

G k Characteristic permanent (dead) load

H Accidental load; horizontal tie force; total height of building; height of

col-umn; reaction forces in bracing elements

H crit Critical height for unbraced skeletal frames

H i Horizontal force due to imperfection; sum of horizontal loads due to wind

and imperfection

H Rd Horizontal tie steel capacity

H Rv Horizontal resistance of infill wall

I I c I x-x Second moment of area of section, concrete and about axis x–x

I c,co Compound values of I c

I u I cr I ef Uncracked, cracked and effective values of I

K Bending moment factor M Ed /f ck bd2

K 1 K 1w Value of K for stage 1 and for breadth of webs in stage 1

K ʹ Limiting value of K

K Curvature factor; span/depth factor

K r Kφ Column curvature factors for axial load and creep

K 1 K 2 K ef Uncracked, cracked and effective flexural rigidity

K s Shear stiffness of longitudinal joint in horizontal floor diaphragm;

nor-malised stiffness of connection to pin-ended beam

L Effective span (for deflection calculations); overall length of element;

over-hang of base plate from edge of column

L b Depth of bearing plate (deep beam wall); bearing length

L e Effective diagonal length of infill wall

L s Characteristic length of the tie bar in horizontal floor diaphragm

L sb Nodal distance from beam end connections

L t Width of bearing plate (deep beam wall)

Lʹ Length of infill wall (b in BS EN 1992-1)

L 2 L 3 L 4 Length of pressure zones in insert/billet connections

M col Net ultimate moment at column node due to patch loading

M cr M cr,c Cracking moment of resistance; for composite section

M E Design bending moment in semi-rigid connection

M ER Required moment capacity in semi-rigid connection

M Ed Ultimate design moment

M Ed1 M Ed2 Value of M Ed for stage 1 and 2 loading (composite design)

M Ed,h Value of M Ed due to self-weight of precast plank

M wEd Value of M Ed due to wind loading

M Ed,h M Ed in horizontal floor diaphragm

M h Bending moment in horizontal floor diaphragm

M i Overturning ultimate moment due to imperfections

M k Applied bending moment at serviceability

M max  M min Maximum and minimum column moments at a node

M net Net column moment M max  - M min

M prop Service moment at position of props

M RC Moment of resistance in semi-rigid connection

M Rd Ultimate moment of resistance

M Rd,c M Rd for composite section

M Rd2 M Rd3 M Rd for stages 2 and 3

M Rdy M Rdz Values of M Rd in y and z planes in biaxial column design

M Rd,r Increased value of M Rd with additional bars in connections

M s1 M s2 M s3 Value of M s for stages 1, 2 and 3 loading (composite design)

M sw M self Service moment due to self-weight

M sʹ M s due to frequent load combination

M sR M sR2 Serviceability moment of resistance, in stage 2

M s,QP Service moment due to quasi-permanent combination of loads

M u Ultimate failure bending moment in experimental test

M wk Overturning moment due to wind load

M zz Maximum ultimate moment in insert connector design

M 0Ed First-order value of M Ed due to frame action

M 01 M 02 First-order column end moments due to frame action

M 2 Second-order bending moment

N Compressive force; number of tendons; number of props

N b N a Ultimate design axial force below and above a certain floor level

N Ed Ultimate design compressive or axial force

N Rd Ultimate compressive or axial resistance

N T Number of tendons in tension (ultimate limit state)

P Prestressing forces; characteristic point load in accidental loading

P Ed Single ultimate point load in deep beam wall; precompression from external

sources

P pi Initial prestressing force

P r Prestressing force at release

P pm0 Prestressing force after initial loses

P pmi Prestressing force at installation

P po Final prestressing force after all loses (at transfer)

P t (l x ) Prestressing force at distance l x from end of element

Q k Characteristic variable (live) load

R Reaction (force); diagonal force in bracing elements; prop reaction

R Ed R 1 Support reaction at columns in deep beam wall

R Ed Ultimate diagonal force in infill wall

R e Yield strength of reinforcing bars

R m Tensile strength of reinforcing bars

R tr Ratio of prestressing force after initial losses (at transfer)

R wk Ratio of prestressing force after final losses (in service)

R v Compressive diagonal resistance of infill wall

R vc R vs Compressive diagonal and shear resistance of brick infill wall

S Shape factor for bearing pads

S E Rotational stiffness in semi-rigid connections

S q Confined stress enhancement factor

S Sx-x First moment of area of section, about centroidal axis

S y First moment of area above y from bottom of section

T Mean curing temperature; vertical tie force; bursting force

T Ed Axial tensile force in steel plate; tension capacity of steel column shoe;

cat-enary force under accidental loading

T i T p Internal and perimeter tie forces

T h T b T q Total chord tie force, due to bending moments and shear force in horizontal

floor diaphragm

T Rd Vertical tie steel capacity; catenary tie capacity

V beam Ultimate shear capacity of beam connector in infill wall design

V dt Value of V Rd,d without partial safety factors (from tests)

V Ed Ultimate design shear force

V Ed,d V Ed in dowel bar

V Ed,t V Ed,b Ultimate top and bottom loaded shear forces in deep beam wall

V h V hx V hy Horizontal shear force in floor diaphragm, in the direction perpendicular and

parallel to horizontal load

V Rd Ultimate shear resistance

V Rd,c V Rd due to flexurally uncracked concrete section

V Rd,c (y) V Rd,c at distance l x from the end of the unit and at height y

V Rd,d V Rd of dowel bar

V Rd,r Increased value of V Rd with additional bars in connections

V Rd,s V Rd due to steel stirrups

V Rds,b V Rd due to bottom steel stirrups in deep beam wall

W Elastic section modulus at tension face at serviceability; width of the hollow

core unit in horizontal floor diaphragm

W Ed Ultimate load from floor loads acting on deep beam wall

W ext W int External work and internal deformation energy in catenary tie

W k Characteristic wind load

W pl Plastic modulus for steel sections

X Depth to neutral axis; depth of stress block ratio in base plate design

X Distance to shear centre of bracing system

Y c Height from bottom to position to calculate V Rd,c (y)

Z b Z t Section modulus at bottom and top fibre

Z b2 Z b3 Section modulus at bottom fibre for composite stages 2 and 3 (ditto Z t)

Z z Section modulus at centroid of tendons

Z b,co Z t,co Compound values of Z b Z t

Z tc, co¢ Compound values of Z t at top of the topping

α Modular ratio (short term) E s/Ecm , E cmi /E cm; rebar buckling parameter; angle of

compressive strut; contact length between the wall and the column

α k Lateral load distribution factors in hollow core slabs

α β Inclination of diagonals in lattices along and perpendicular to span

αA Floor area imposed live load reduction factor

αcc Concrete strength factor

αcw Axial stress parameter for shear stress

αds1αds2 Coefficients of cement for shrinkage strains

αhαm Factors for column height and number m contributing to imperfection

αe Modular ratio (long term) E s /E c,ef

αl Ratio l x /l pt2

αn Imposed live load reduction factor

α2 Transmission length factor for tendons; modular ratio (long term) in stage 2

design

α1 α2 Anchorage length parameters

α1 α2 α3 Coefficients of concrete for creep

β Column or wall effective length or height factor; factor for short- or long-term

loading

β θ Inclination of compressive strut and soffit angle in corbels

β γ Inclinations of the holding bars to anchor plates

β(fcm) Strength factor for creep

βas Coefficient for autogenous shrinkage strain

βds (t,t s ) Age factor for shrinkage

βRH Relative humidity factor for shrinkage

β(ti) Age at installation loading factor for creep

β (t0) Age at release loading factor for creep

χ Stress reduction factor

δ Deflections

δs Longitudinal slip between two adjacent units in horizontal floor diaphragm

δt δt,max Transverse crack width in horizontal floor diaphragm, maximum value

δti Initial crack width between floor units in horizontal floor diaphragm

δu δy Deformation, deflection at ultimate and yielding

ε Strain

εcuεcu3 Ultimate crushing strain in concrete

εca Autogenous shrinkage strain

εcd Drying shrinkage strain

εcd,o Basic drying shrinkage strain

εcs Shrinkage strain

εLOP Strain in tendons at limit of proportionality (elastic limit)

εp Final strain in tendons

εpo Prestrain in tendons after losses

e¢sh Relative shrinkage between precast and in situ concretes

εsmεcm Concrete strains in crack width calculation

εud Limiting strain for rebars

εuk Elongation of rebars at the breaking load

εsεs1 εs2 Elastic strains in reinforcing bars; in layers 1 and 2

ϕ Tendon diameter (strand, wire); mean tendon diameter; rotations between

ele-ments in connections, inclination of surface in sawtooth model for shearϕs,l Lattice bar diameter in half slab

γ Fixity factor in semi-rigid connections; partial safety factor (general)

γG Partial safety factors for dead load

γG,supγG, inf Superior and inferior values of γG

γQ Partial safety factors for live load

γm Material partial safety factor (general)

γc Material partial safety factor for concrete

γmb γmv Partial safety factor for brickwork in compression and shear

γM Partial safety factor for steel sections

γMo Partial safety factor for lattice bars in compression

γM2 Partial safety factor for welds

γP Partial safety factor for prestressing action

γp,fav Favourable value of γP for effect of prestressing

γs Material partial safety factor for steel bars

γSH Partial safety factor for concrete shrinkage

γW Partial safety factors for wind load

η Factor (for stress block); initial factor for prestressing

n fi Axial load ratio if fire design

η1η2 Casting condition and bar diameter parameters for bond

φ Tendon diameter (wire, strand); creep coefficient (general)

φef Effective creep factor (column design)

φRH Creep coefficient for relative humidity

φ(t,ti) Creep coefficient

λ Slenderness ratio; relative stiffness ratio between infill wall and frame

λcrit Critical slenderness limit in bars in compression

λlim Limiting value of λ

λfi Slenderness in fire situation = l 0,fi /i

λyλz Value of λ in y and z planes in biaxial column design

λʹ Non-dimensional slenderness = λ/λcrit

μ Coefficient of friction; ratio of initial prestress

μfi Axial load ratio in fire situation = N Ed,fi /N Rd

μʹ Effective coefficient of shear friction and wedging combined

ν Poisson’s ratio

θ Temperature; angle of rotation; beam end rotation; inclination of strut in shear

design; angle of slope of infill wall; angle of taper in column pocket

θcr Critical temperature for rebars and prestressing tendons

θi Inclination of vertical element or frame due to imperfection

ρ Reinforcement ratio A s /A c

ρp,eff Value of ρ in crack width calculation = Ap /A c,eff

ρ1 Reinforcement ratio for bars extending beyond shear plane

ρo Concrete strength factor

ρ1000 Tendon relation loss at 1000 hours

σ Stress; prestress

σbσt Final prestress in concrete at bottom and top fibres

σb(t) σt(t) Prestress in concrete at transfer at bottom and top fibres

σc Concrete stress at centre of tendons after relaxation loss

σcm Ultimate bearing stress of concrete at anchorage points

σcp Prestress at centroidal axis after all losses (include γp,fav)

σcp(y) Value of σcp at height y from bottom of section

σc,p Limiting compressive stress in prestressed concrete

σct,p Limiting tensile stress in prestressed concrete for XC1 exposure = f ctm

σc0 Limiting unconfined compressive stress in concrete

σEd Ultimate bearing stress

σpi Initial prestress in tendons

σpd Ultimate stress in tendons (used in bond design)

σpm0 Prestress in tendons after initial losses (at transfer)

σpo Final prestress in tendons after all losses (in service) (Note EC2 uses σp∞)

σr Prestress at release

σRd,max Limiting compressive strength or strut strength of concrete

σs Stress in rebars; stress variation in tendons after decompression in crack width

calculations

s¢sh Free shrinkage stress due to e¢sh

σtd Concrete bearing stress at spot welded transverse bar

τ Shear stress; elastic shear stress distribution (shape) function

τcp(y) Concrete shear stress at height y from bottom of section

ω Reinforcement ratio

ξ Loss ratio after initial losses

ψiψ28 Creep coefficient for deflections at t or 28 days

ψ0 Characteristic combination load factor

ψ1 Frequent combination load factor

ψ2 Quasi-permanent combination load factor

ψ∞ Long-term creep coefficient

ζ Characteristic combination dead load factor; bursting force coefficient; ratio of

solid material to the whole of voided sections; tensioning stiffening distribution coefficient

X Concrete ageing coefficient

Δ Total tolerances to allow for manufacturing and erection errors

Δa Reduced additional axis distance to tendons in fire

Δcrit a C Critical value of deflection in catenary action under accidental loading

Δσpr Prestress loss due to initial relaxation of tendons

Δσel Prestress loss due to elastic shortening

Δσp,c Initial prestress losses Δσpr + Δσel

Δσpci Prestress loss due to creep before installation

Δσpc Prestress loss due to creep after installation

Δσp,s Prestress loss due to shrinkage

Δσpr Stress due to final relaxation of tendons (note same notation as for initial relax

loss)

Δσp,r Prestress loss due to final relaxation of tendons

Δt Deformation of bearing pad

ΔCdev Dimensional deviation for cover to bars

Δa2 Δa3 Ineffective bearing lengths or permitted deviations at supports

Φ Reinforcing bar diameter; rebar buckling parameter; slenderness load

reduc-tion factor

Ψ Exponential creep growth factor

Abbreviations and Other Nomenclature

Exp Expression or equation from code of practice

Eq Equation in this book

CEM Types of cements

DBW Deep beam wall

fi Fire situation (subscript)

hcu Hollow core unit

M-θ Moment versus beam end rotation

MRC Moment resisting connection

PSF Partial safety factor

RH s Relative humidity (%)

What is precast concrete

1.1 WHY IS PRECAST DIFFERENT?

What makes precast concrete different from other forms of concrete construction? Whether concrete is precast, that is statically reinforced or pretensioned (prestressed), is not always apparent It is only when we consider the role concrete will play in developing structural characteristics that its precast nature becomes significant The most obvious definition for precast concrete is that it is concrete which has been prepared for casting, cast and cured in

a location which is not its final destination The distance travelled from the casting site may only be a few metres, where on-site precasting methods are used to avoid expensive haulage (or VAT in some countries), or may be thousands of kilometres, in the case of high-value-added products where manufacturing and haulage costs are low The grit basted architec-tural precast concrete in Figure 1.1 was manufactured 600 km from the site, whereas the precast concrete columns, beams and walls shown in Figure 1.2a and b travelled less than

60 m; wall panels have been stack-cast in layers between sheets of polythene adjacent to the final building

What really distinguishes precast concrete from cast in  situ is its stress and strain

response to external (load-induced) and internal (autogenous volumetric changes) effects These are collectively known as ‘actions’ in the Eurocodes, and those mainly applicable

to precast concrete structures are the ‘keynote’ code EC0 (BS EN 1990 2002), the loading

or ‘actions’ code EC1 (BS EN 1991-1-1 2002) and the ‘concrete design’ code EC2 (BS EN 1992-1-1 2004)

A precast concrete element is, by definition, of a finite size and must therefore be joined

to other elements to form a complete structure A simple bearing ledge or corbel will suffice,

as shown in Figure 1.3 But when thermal shrinkage or load-induced strains cause metric changes (and shortening or lengthening), the two precast elements try to move apart (Figure 1.4a) Interface friction at the mating surface prevents movement, but in doing so

creates a force F = μR which is capable of splitting both elements unless the section was

suitably reinforced (Figure 1.4b) Figure 1.5a shows an example of where frictional forces due to relative, unreinforced movement between precast slabs and beams caused spalling in the beam In other cases, spurious positive bending moments due to the restraint of relative movement or end rotation have caused cracking in the soffit of slabs, or at a beam-to-column corbel connection, as shown in Figure 1.5b

Flexural rotations of the suspended element (the beam) reduce the mating length l b (bearing length), creating a stress concentration until local crushing at the top of the pillar (the column) occurs, unless a bearing pad is used to prevent stress concentration (Figure 1.4c) If the bear-ing is narrow, dispersal of stress from the interior to the exterior of the pillar causes lateral tensile strain, leading to bursting of the concrete at some distance below the bearing unless the section is suitably reinforced (Figure 1.4d)