Practical Design to Eurocode 2

Charles Goodchild

Principal Structural Engineer

Course Outline

17th April 2013Charles Goodchild

Basics

EC0, EC1, Materials, Cover

24th April 2013Jenny Burridge

Beams

Bending, Shear, Detailing

1st May 2013Charles Goodchild

Columns

Axial load, Column Moments, Buckling

8th May 2013Jenny Burridge

Slabs

Serviceability, Punching Shear

15th May 2013Jenny Burridge

Foundations

Pads, Piles, Retaining Walls

Basics

Lecture 1

17th April 2013

Summary: Lecture 1 Basics

Background & Basics Eurocode 0 & load combinations Eurocode 1 loads/actions Eurocode 2

Background Materials Cover Analysis

Background & Basics

6Setting the scene

Eurocodes are being/ will be used in:

EU countries

EFTA Countries

Malaysia

Singapore

Vietnam

Sri Lanka

Others?

CEN National Members Austria Belgium Cyprus Czech Republic Denmark Estonia Finland France Germany Greece Hungary Iceland Ireland Italy Latvia Lithuania Luxembourg Malta The Netherlands Norway Poland Portugal Romania Slovakia Slovenia Spain Sweden Switzerland United Kingdom

BS EN 1990 (EC0) : Basis of structural design BS EN 1991 (EC1) : Actions on Structures BS EN 1992 (EC2) : Design of concrete structures BS EN 1993 (EC3) : Design of steel structures BS EN 1994 (EC4) : Design of composite steel and concrete structures BS EN 1995 (EC5) : Design of timber structures BS EN 1996 (EC6) : Design of masonry structures BS EN 1997 (EC7) : Geotechnical design BS EN 1998 (EC8) : Design of structures for earthquake resistance BS EN 1999 (EC9) : Design of aluminium structures

The Eurocodes

8+ PDs

+ NA + NA

+ NAs

+ NA

+ NAEN 1990Basis of Design

EN 1991Actions on Structures

EN 1992 ConcreteEN 1993 SteelEN 1994 CompositeEN 1995 TimberEN 1996 MasonryEN 1999 Aluminium

EN 1997Geotechnical

Design

EN 1998Seismic Design

Structural safety, serviceability and durability

Design and detailing

Geotechnical & seismic design

Actions on structures

Eurocode Hierarchy

These

affect

concrete

design

9 58 Parts to Eurocodes plus National Annexes

Culture shock / steep learning curve

New symbols and terminology

Affects all materials

Confusion over timescales

Costs: Training

Resources

Challenges of the Eurocodes

Each Eurocode Contains:

National front cover

Format of the Eurocodes

Each Eurocode Contains:

National front cover National foreword

Format of the Eurocodes

Each Eurocode Contains:

National front cover National foreword CEN front cover

Format of the Eurocodes

Each Eurocode Contains:

National front cover National foreword CEN front cover Main text and annexes (which must

be as produced by CEN)

Format of the Eurocodes

Each Eurocode Contains:

National front cover National foreword CEN front cover Main text and annexes (which must

be as produced by CEN)

Annexes - can by normative and/or informative

Format of the Eurocodes

National Annex (NA)

Format of the Eurocodes

The National Annex provides:

Values of Nationally Determined Parameters (NDPs)(NDPs have been allowed for reasons of safety, economy and durability)

Example: Min diameter for longitudinal steel in columnsfmin = 8 mm in text fmin = 12 mm in N.A.

The decision where main text allows alternatives Example: Load arrangements in Cl. 5.1.3 (1) P

The choice to adopt informative annexes Example: Annexes E and J are not used in the UK

Non-contradictory complementary information (NCCI)

Example: PD 6687 Background paper to UK National Annexes

National Annex

In this presentation UK Nationally Determined Parameters (NDPs) are shown in blue!

The Eurocodes contain Principles (P) which comprise: General statements and definitions for which there is no

alternative, as well as:

Requirements and analytical models for which no alternative is permitted

They also contain Application Rules, which are generally rules which comply with the Principles

The Eurocodes also use a comma (,) as the decimal marker

Features of the Eurocodes

Eurocode 0

BS EN 1990:2002

Basis of structural design

EN 1990 provides comprehensive information and guidance for all the Eurocodes, on the principles and requirements for safety and serviceability.

It gives the safety factors for actions and combinations of action for the verification of both ultimate andserviceability limit states.

Limit states are conditions beyond which some design criterion is violated.

Ultimate Limit State: Any condition that concerns the safety of people or structure

Generally the structure shall be verified at:

Serviceability Limit State:Corresponds to conditions in use of the structure. The limit state could be related to cracking, deformation or vibration.

Limit State Design

Ultimate Limit State:

Loss of equilibrium (EQU)

Ed,dst Ed,stbInternal failure or excessive structural deformation (STR)

Ed Rd;

Failure or excessive deformation of ground (GEO)

Failure caused by time dependent effects such as fatigue (FAT)

Limit State Design

Principle: In all relevant design situations no relevant limit state is exceeded when design values for actions and effects of actions are used in the design models

Verification by Partial Safety Factor Method

Fd = gf Frep

Where: Frep = representative value of action

= y Fk

And: gf = partial factor for actionsSee NA to BS EN 1990: Table NA.A1.2

y converts the characteristic value of action to the representative value.

Compare to

Fd = gf Fk BS8110

Design Value of Action

Each variable action may take one of four representative values, the main one being the characteristic value. Other representative values are obtained by the application of yfactors

can take one of four values, namely, 1.00 or y0 or y1 or y2.

y = 1.00 when only one variable action is present in a combination.

y0Qk is the combination value of a variable action.

y1Qk is the frequent value.

y2Qk is the quasi-permanent value.

Representative Values of Variable Actions

Representative Values of Variable Actions

Ref: Gulvanessian, H ICE Proceedings, Civil Engineering 144 November 2001 pp.8-13

For each critical load case design values of the effects of actions are determined by combining the effects of actions that are considered to act simultaneously

S gG, jGk,j + gQ,1 Qk,1 + SgQ,iy0,iQk,i Exp. (6.10)

Either

SgG, jGk,j + gQ,1 y0,1Qk,1 + SgQ,iy0,iQk,i Exp. (6.10 a)

or

S x gG, jGk,j + gQ,1Qk,1 + SgQ,iy0,iQk,i Exp. (6.10 b)

Or (for STR and GEO) the more adverse of

The value for x for the UK is 0.925

Combination of Actions

Design values of actions, ultimate limit state persistent and transient design situations (Table A1.2(B) Eurocode)

Combtionexpression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,iEqn (6.10a) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,10,1Qk,1 Q,i 0,i Qk,iEqn (6.10b) G,j,supGk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,i

Eqn (6.10) 1.35 Gk 1.0 Gk 1.5 Qk,1 1.5 0,i Qk,iEqn (6.10a) 1.35 Gk 1.0 Gk 1.5 0,1 Qk 1.5 0,i Qk,i

Eqn (6.10b) 0.925x1.35Gk 1.0 Gk 1.5 Qk,1 1.5 0,i Qk,i

Eurocode ULS (GEO/STR)

Table NA.A1.1 UK National Annex of BS EN 1990

Action y0 y 1 y2Imposed loads in buildings, Category A : domestic, residential Category B : office areasCategory C : congregation areasCategory D : shopping areasCategory E : storage areas

0.70.70.70.71.0

0.50.50.70.70.9

0.30.30.60.60.8

Category F : traffic area, < 30kNCategory G : traffic area, 30 160 kNCategory H : roofs

0.70.70.7

0.70.50

0.60.30

Snow load: H 1000 m a.s.l. 0.5 0.2 0Wind loads on buildings 0.5 0.2 0

UK Values of y Factor

Partial Factors for Actions (ULS)

gG = 1.35 (NA 2.2.3.3 and Table NA.A1.2)

gQ = 1.5 (NA 2.2.3.3 and Table NA.A1.2)

Relevant y factors

y0 office areas = 0.7 (Table NA.A.A1.1)

y0 wind = 0.5 (Table NA.A.A1.1)

Example: ULS Combination of Actions

1.35 Gk + 1.5 Qk,1 + 0.75Qk,w Exp. (6.10)

1.35Gk + 1.05 Qk,1 + 0.75Qk,w Exp. (6.10 a)

or

1.25Gk + 1.5 Qk,1 + 0.75Qk,w Exp. (6.10 b)

Or the more adverse of

Example: ULS Combination of Actions

1.0

1.5

2.0

2.5

3.0

1 2 3 4 5 6Gk/Qk

Eqn (6.10)Eqn (6.10a)Eqn (6.10b)

Ratio Gk/Qk

Fact

or, F

(Ult

imat

e lo

ad =

Fx

Gk)

4.5

Eqn (6.10), (6.10a) or (6.10b)?

Design values of actions, ultimate limit state persistent and transient design situations (Table A1.2(B) Eurocode)

Combtion expression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,1 Qk,1 Q,i 0,i Qk,i

Eqn (6.10) 1.10 Gk 0.9 Gk 1.5 Qk,1 1.5 0,i Qk,i

Eurocode ULS (EQU)

Combinations of Actions (SLS)

Characteristic combination Gk,j + Qk,1 + Sy0,IQk,I(typically irreversible limit states)

Frequent combination Gk,j + y1,1Qk,1 + S y2,IQk,I(typically reversible limit states)

Quasi permanent combination Gk,j + S y2,IQk,I(typically long term effects and appearance of the structure)

Partial Factors for Actions (SLS)

gG = 1.00

gQ = 1.00

y0 - combination valuey1- frequent value.

y2- quasi-permanent value.

Eurocode SLS

Load combinations are also dealt with elsewhere

EC2: Load cases & combinationsEC2: Cl 5.1.3 gives one option: Concise: 5.4.2

EC2 NA additional load cases

EC2 & UK NA Load Arrangements(BS EN 1992, Cl 5.1.3)

The UK National Annex allows the use of simplified arrangements similar to BS 8110.

NB: gGj.Gkj on all spans for STR/GEO (but not EQU)

Alternate spans loaded

Adjacent spans loaded

All spans loaded

Concise: 5.4.2

gQj.QkjgGj.Gkj

EC2 cl 5.1.3

UK NA: Arrangement of Actions

All spans loaded

Alternate spans loaded

1.35 Gk or 1.25 Gk

1.5 Qk

1.35 Gk or 1.25 Gk

1.5 Qk

1.35 Gk or 1.25 Gk

1.5 Qk

NA gives additional options: Concise: 5.4.2

The UK National Annex refers only to Design Approach 1. Two combinations of partial load and partial soil factors need consideration.

Partial load factor Partial material factor, gm

gGk gQk tan f c cuCombination 1 1.35 1.5 1.0 1.0 1.0

Combination 2 1.0 1.3 1.25 1.25 1.4

Note: where variable action is favourable gQ = 0

f angle of shearing resistance (in terms of effective stress)c cohesion intercept (in terms of effective stress)cu undrained shear strength

Normally Combination 2 will be critical for sizing the foundation The loads from Combination 1 should be used to design the concrete section

Geotechnical design EC7

Q2. Continuous single-way slab. Assuming permanent actions = 6 kN/m2 and variable actions = 4 kN/m2, calculate the value of ULS total loading (kN/m2) using Exps (6.10), (6.10a) and (6.10b) (see BS EN 1990 Table A1.2(B) & UK NA).

Q1.Overhanging cantilever beam. Determine the gF factors that should be applied to Gk and Qk:-a) for equilibrium (EQU) (BS EN 1990, Table A1.2(A) & UK NA)b) for structural strength (STR) (BS EN 1990, Exp (6.10) & UK NA)

l a

Load Arrangement Exercise

l a

Load Arrangement Exercise (pro forma)

Q2 gGGk gQQk n

(6.10)

(6.10a)

(6.10b)

Q1 Span gGGk + gQQk Cant gGGk + gQQk

EQU

STR

STR

l a

Load Arrangement Solution (1)

Q2 gGGk gQQk n

(6.10) 1.35 x 6 + 1.5 x 4 = 14.1 kN/m2

(6.10a) 1.35 x 6 + 1.5 x 0.7 x 4 = 12.3 kN/m2

(6.10b) 1.35 x 0.925 x 6 + 1.5 x 4 = 13.5 kN/m2

Q1 Span gGGk + gQQk Cant gGGk + gQQk

EQU 0.9 Gk 1.10 Gk + 1.5QkSTR 1.0 Gk 1.35Gk + 1.5QkSTR 1.35Gk + 1.5Qk 1.0 Gk

a) Combination for equilibrium (EQU)BS EN 1990 Table A.1.2 (A) & UK NA

0.9Gk1.1Gk

1.5Qk

b) Combination for structural strength (STR) BS EN 1990 Table A.1.2 (B) & UK NA and BS EN 1992-1-1, Cl 5.1.3 & UK NA

1. Overhanging cantilever beam

1.35Gk1.35Gk

1.5Qk

1.35Gk 1.35Gk

1.5Qk

Load Arrangement Exercise Solution (2)

a) Value using Combination from BS EN 1990 Expression (6.10)gG Gk + gQ Qk 1.35 x 6 + 1.5 x 4 = 14.1 kN/m2

Continuous single-way slab (using BS EN 1990 and UK NA and BS 1992-1-2 Cl 5.1.3 & UK NA)

5m 5m 5m

b1) Value using Combination from BS EN 1990 Expression (6.10a)and UK National Annex

gG Gk + gQ y0Qk 1.35 x 6 + 1.5 x 0.7 x 4 = 12.3 kN/m2

b2) Value using Combination from BS EN 1990 Expression (6.10b)and UK National Annex

gG x Gk + gQ Qk 1.35 x 0.925 x 6 + 1.5 x 4 = 13.5 kN/m2

Expression (6.10b) gives the most economic design

Load Arrangement Solution (3)

EC1 Loads/ActionsBS EN 1991

Actions on Structures

Eurocode 1 has ten parts:

1991-1-1 Densities, self-weight and imposed loads 1991-1-2 Actions on structures exposed to fire 1991-1-3 Snow loads 1991-1-4 Wind actions 1991-1-5 Thermal actions 1991-1-6 Actions during execution 1991-1-7 Accidental actions due to impact and explosions 1991-2 Traffic loads on bridges 1991-3 Actions induced by cranes and machinery 1991-4 Actions in silos and tanks

Eurocode 1

Eurocode 1 Part 1-1: Densities, self-weight and imposed loads

Bulk density of mass concrete is 24 kN/m3

Bulk density of reinforced concrete is 25 kN/m3

This represents 1.84% reinforcement

Add 1 kN/m3 for wet concrete

The UK NA uses the same loads as BS 6399

Plant loading not given

Eurocode 1

Category Example Use qk (kN/m2)

Char. value of udl

Qk (kN)

Char. value of pt load

A1 All uses within self-contained dwelling units 1.5 2.0

A2 Bedrooms and dormitories 1.5 2.0

A3 Bedrooms in hotels and motels, hospital wards and toilets 2.0 2.0

A5 Balconies in single family dwelling units 2.5 2.0

A7 Balconies in hotels and motels 4.0 min 2.0

B1 Offices for general use 2.5 2.7

C5 Assembly area without fixed seating, concert halls, bars, places of worship

5.0 3.6

D1/2 Shopping areas 4.0 3.6

E12 General storage 2.4 per m ht 7.0

E17 Dense mobile stacking in warehouses 4.8 per m ht (min 15.0)

7.0

F Gross vehicle weight 30 kN 2.5 10.0

Eurocode 1 UK NA - Extracts

Imposed load reductions

EC1 allows the imposed load for large floor areas and several storeys to be reduced by applying the factors aA and/or an.

The NA modifies the equation in EC1.

aA = 1.0 A/1000 0.75where A is the area (m2) supported

an = 1.1 n/10 1 n 5an = 0.6 6 n 10an = 0.5 n > 10

where n is the number of storeys supported

BS EN 1991 1-3 (NA)

Snow loads

BS EN 1991 1-4 (NA)

Wind speeds

vb,map

Eurocode 2

BS EN 1992

Design of concrete structures

Materials

54

Date UK CEB/fib Eurocode 21968 CP114 (CP110 draft) Blue Book (Limit state design)1972 CP110 (Limit state design) Red Book1975 Treaty of Rome1978 Model code1985 BS8110 Eurocode 2 (EC)1990 Model Code1993 EC2: Part 1-1(ENV) (CEN)2004 EC2: Part 1-1 (EN)2005 UK Nat. Annex.2006 BS110/EC2 PD 66872010 EC2 Model Code 2010

Eurocode 2 is more extensive than old codesEurocode 2 is less restrictive than old codesEurocode 2 can give more economic structures [?]

Eurocode 2: Context

BS EN 1992-1-1: General Rules and Rules For Buildings

BS EN 1992-1-2: Fire Resistance of Concrete Structures

BS EN 1992-2: Reinforced and Prestressed ConcreteBridges

BS EN 1992-3: Liquid Retaining Structures

Eurocode 2: Design of Concrete Structures

56

BS EN 1990 BASIS OF STRUCTURAL

DESIGN

BS EN 1991 ACTIONS ON STRUCTURES

BS EN 1992DESIGN OF CONCRETE

STRUCTURESPart 1-1: General Rules for

StructuresPart 1-2: Structural Fire Design

BS EN 1992Part 2:

Bridges

BS EN 1992Part 3: Liquid

Ret. Structures

BS EN 1994Design of

Comp. Struct.

BS EN 13369Pre-cast Concrete

BS EN 1997GEOTECHNICAL

DESIGN

BS EN 1998SEISMIC DESIGN

BS EN 13670Execution of Structures

BS 8500Specifying Concrete

BS 4449Reinforcing

Steels

BS EN 10080Reinforcing

Steels

Eurocode 2: relationships

BS EN 206Concrete

NSCS

DMRB?

NBS?

Rail?

CESWI?

BS EN 10138Prestressing

Steels

57

1. Code deals with phenomenon, rather than element types so Bending, Shear, Torsion, Punching, Crack control, Deflection control (not beams, slabs, columns)

2. Design is based on characteristic cylinder strength

3. No derived formulae (e.g. only the details of the stress block is given, not the flexural design formulae)

4. No tips (e.g. concentrated loads, column loads, )

5. Unit of stress in MPa

6. Applicable for ribbed reinforcement fy 400MPa 600MPa (Plain or mild steel not covered but info on plain and mild steel given in PD 6687)

7. Notional horizontal loads considered in addition to lateral loads

8. High strength, up to C90/105 covered

9. No materials or workmanship

Eurocode 2 & BS 8110 Compared

Differences -2

EC2:

10)Cover related to requirements for durability, fire and bond also subject to allowance for deviations due to variations in execution

11)Variable strut inclination method for shear

12)Punching shear checks at 2d from support

13)Rules for determining anchorage and lap lengths.

14)Serviceability checks

15)Decimal point replaced by comma

16)Units of stress MPa

17)1/1000 expressed as 18) Axes changed from x, y to y, z

19) Part of the Eurocode system

Eurocode 2 & BS 8110 Compared

59

Concrete properties (Table 3.1)

BS 8500 includes C28/35 & C32/40

For shear design, max shear strength as for C50/60

Strength classes for concrete

fck (MPa) 12 16 20 25 30 35 40 45 50 55 60 70 80 90

fck,cube (MPa) 15 20 25 30 37 45 50 55 60 67 75 85 95 105

fcm (MPa) 20 24 28 33 38 43 48 53 58 63 68 78 88 98

fctm (MPa) 1.6 1.9 2.2 2.6 2.9 3.2 3.5 3.8 4.1 4.2 4.4 4.6 4.8 5.0

Ecm (GPa) 27 29 30 31 33 34 35 36 37 38 39 41 42 44

fck = Concrete cylinder strength fck,cube = Concrete cube strength fcm = Mean concrete strength fctm = Mean concrete tensile strength Ecm = Mean value of elastic modulus

Eurocode 2

Design Strength Values (3.1.6)

Design compressive strength, fcdfcd = acc fck /gc

Design tensile strength, fctdfctd = act fctk,0.05 /gc

acc (= 0.85 (flexure) and 1,0 (shear)) and act (= 1,0) are coefficients to take account of long term effects on the compressive and tensile strengths and of unfavourable effects resulting from the way the load is applied

Concrete strength at time t (3.1.2)

Expressions are given for the specification of concrete at a time other than 28 days

To specify concrete strength at an age t

fck(t) = fcm(t) - 8 (MPa) for 3 < t < 28 days

= fck for t 28 days

fcm(t) = bcc(t) fcm

bcc(t) = exp {s [1- (28/t)1/2]}

Where fcm(t) is the mean concrete compressivestrength at an age of t days

Expressions are given for the estimation of strengths at times other than 28 days for various types of cement. Types of cement are defined in EN 197-1

(Class N is normally used in the UK)

s is a coefficient depending on type of cement= 0,20 for Class R (rapid hardening)= 0,25 for Class N (normal hardening)= 0,38 for Class S (slow hardening)

Concrete Strength at Time t (3.1.2)

Tensile Strength/Splitting Strength (3.1.2) An approximate relationship between the axial tensile strength and

splitting strength is:fct = 0,9fct,sp

An approximate expression is given for the estimation of tensile strength with time, fctm(t).Where this information is important for design, tests should be carried out.

fctm(t) = (bcc(t))a fctmWhere a = 1 for t < 28 days

= 2/3 for t 28 days

Elastic Deformation (3.1.3)

Values given in EC2 are indicative and vary according to type of aggregate.

Ecm(t) = (fcm(t)/fcm)0,3Ecm Tangent modulus, Ec , may be taken as 1,05 Ecm Poissons ratio

for uncracked concrete = 0,2 for cracked concrete = 0

Linear coeff. of thermal expansion = 10 x 10-6 K-1

Creep (3.1.4)

01,02,03,04,05,06,07,0100

50

30

1

2

3

5

10

20

t 0

j (, t 0)

SN R

100 300 500 700 900 1100 1300 1500

C20/25C25/30C30/37C35/45C40/50C45/55C50/60 C55/67C60/75 C70/85

C90/105C80/95

h 0 (mm)

Inside conditions RH = 50%Example: 300 thick slab, loading at 30 days, C30/37 - j = 1,8

h0 = 2Ac/u where Ac is the cross-section area and u is perimeter of the member in contact with the atmosphere

Shrinkage (3.1.4)

Shrinkage Strain, ecs, is composed of two components:

Drying Shrinkage Strain, ecd, develops slowly Autogenous Shrinkage Strain, eca, develops during the hardening of the

concrete.

Drying shrinkage, ecdecd(t) = bds(t,ts)kh ecd,0 (EC2, Exp (3.9)

Autogenous shrinkage, ecaeca(t) = bas(t)eca() (EC2, Exp (3.11)

Creep and Shrinkage Annex B

Creep j0 is the notional creep coefficient (in Figure 3.1 the notation

used is j(,t0))

j(t,t0) is the creep at any time, t after time of loading, t0

Shrinkage ecd,0 is the basic drying shrinkage strain ecd,(t) = bds(t,ts)kh ecd,0 (Section 3)

fcd

ec2

sc

e cu2 ec0

fck

For section analysis

Parabola-rectangle

c3 ecu30

fcd

e

sc

e c

fck

Bi-linearfcm

0,4 fcm

e c1

sc

e cu1 ec

tan a = Ecm

a

For structural analysis

Schematic

ec1 (0/00) = 0,7 fcm0,31ecu1 (0/00) =

2,8 + 27[(98-fcm)/100]4 fcm)/100]4

for fck 50 MPa otherwise 3.5ec2 (0/00) = 2,0 + 0,085(fck-50)0,53

for fck 50 MPa otherwise 2,0

ecu2 (0/00) = 2,6 + 35 [(90-fck)/100]4for fck 50 MPa otherwise 3,5

n = 1,4 + 23,4 [(90- fck)/100]4for fck 50 MPa otherwise 2,0

fn

cc cd c c2

c2

1 1 for 0e e ee

= - -

As

d

h fcd

Fs

lx

es

x

ecu3

Fc Ac

h = 1,0 for fck 50 MPa= 1,0 (fck 50)/200 for 50 < fck 90 MPa

400)50

8,0 ck-

-=(f

for 50 < fck 90 MPa

l = 0,8 for fck 50 MPa

Rectangular Concrete Stress Block (3.1.7, Figure 3.5)

up to C50/60

Stress

Strain

Ultimate strainreduces

Strain at maximumstress increases

C90/105

Change in Shape of Concrete Stress Block for high strength concretes

Flexural Tensile Strength (3.1.8)

The mean tensile strength, fctm,fl, depends on the mean axial strength and the depth of the cross section

fctm,fl = max{(1,6 h/1000)fctm; fctm}

This relationship also applies to the characteristic tensile values

For Serviceability calculations care should be taken in using fctm,fl(See Section 7)

Confined Concrete (3.1.9)

ec2,c ecu2,c

sc

ec

fck,c

fcd,c

0

A s2 s3 ( = s2)

s1 = fck,c

fck

ecu

fck,c = fck (1.000 + 5.0 s2/fck) for s2 0.05fck

= fck (1.125 + 2.50 s2/fck) for s2 > 0.05fckec2,c = ec2 (fck,c/fck)2

ecu2,c = ecu2 + 0,2 s2/fck

Reinforcement (1) (3.2.1 and 3.2.2)

EC2 does not cover the use of plain or mild steel reinforcement

Principles and Rules are given for deformed bars, decoiled rods, welded fabric and lattice girders.

EN 10080 [!] provides the performance characteristics and testing methods but does not specify the material properties. These are given in Annex C of EC2

Product form Bars and de-coiled rods Wire Fabrics Class

A

B

C

A

B

C

Characteristic yield strength fyk or f0,2k (MPa)

400 to 600

k = (ft/fy)k

1,05

1,08

1,15

0.2%euk

f0.2kft = kf0.2k

e

sft = kfykt

euke

s

fyk

Hot rolled steel Cold worked steel

The design value for Es may be assumed to be 200 GPa

Reinforcement (3)(3.2.4, figure 3.7)

76

Extract from BS 8666

Reinforcement (4)Different Types of Steel

Bendability: Bendability shall be verified by the bend and rebend tests in accordance with prEN 10080 and EN ISO 15630-1. In situations where verification is carried out just using a rebend test the mandrel size shall be no greater than the minimum specified in Table 8.1 of EC2. In order to ensure bendability no cracking shall be visible after the first bend.

Bond: Where it can be shown that sufficient bond strength is achievable with fR (projected rib factor, a measure of the rib size) values less than specified, the values may be relaxed. In order to ensure that sufficient bond strength is achieved, the bond stresses shall satisfy Expressions (C.2) and (C.3) when tested using the CEB/RILEM beam test:tm 0.098 (80 1.2f) (C.2)

tr 0.098 (130 1.9f) (C.3)where: f nominal bar size (mm)

tm mean value of bond stress (MPa ) at 0.01, 0.1 and 1 mm sliptr the bond stress at failure by slipping

Reinforcement (4) Annex C (Normative)

eud

e

s

fyd/ Es

fyk

kfyk

fyd = fyk/gs

kfyk/gs

Idealised

Design

euk

eud= 0.9 euk

k = (ft/fy)k

Alternative design stress/strain relationships are permitted:- inclined top branch with a limit to the ultimate strain horizontal - horizontal top branch with no strain limit

Reinforcement (5) Design Stress/Strain Curve (3.2.7, Figure 3.8)

UK uses horizontal top branch

Prestressing Steel (1)(3.3.1 and 3.3.2)

Unlike prEN 10080 the harmonised standard for prestressing steel, prEN10138, provides all the mechanical properties. The reason given is that there are only a few types of prestressing steel and they can all be included within the Standard. But there is still neither EN! In the meantime BS have published BS 5896:2012 High tensile steel wire and strand for the prestressing of concrete.

Prestressing steel losses are defined for: Class 1: wire or strand ordinary relaxation Class 2: wire or strand low relaxation Class 3: hot rolled and processed bars

Use BS5896!

Adequate ductility is assumed if fpk/fp0,1k 1.1 the mean density of prestressing tendons may be taken as 7850

kg/m3

Strand type

Steel Number

Nominal tensile

strength (MPa)

Nominal diameter (mm)

Cross-sectiona

l area (mm2)

Nominal mass

(kg/m)

Charact-eristic

value of maximum force (kN)

Maximum value of

maximum force(kN)

Charact-eristic

value of 0.1% proof

force (kN)

12.9 Super

1.1373 1860 12.9 100 0,781 186 213 160

12.7 Super

1.1372 1860 12.7 112 0.875 209 238 180

15.7 Super

1.1375 1770 15.7 150 1.17 265 302 228

15.7 Euro

1.1373 1860 15.7 150 1.17 279 319 240

15.2 Drawn

1.1371 1820 15.2 165 1.290 300 342 258

Pre-stressing Strands Commonly Used in the UK

fpd = fp0,1k/gs

eude

s

f /gpk s

fpk

fp0,1k

Design

f /E p

Idealised

pd

eud= 0.9 eukIf more accurate information is not known :eud = 0,02 andfp0,1k/fpk = 0,9

The properties of prestressing steel are given in EN10138

The design value for Ep for strand may be taken as 195 GPafor wires and bars may be taken as 205 GPa

Prestressing Steel (2) Design Stress/Strain Curve (3.3.6, Figure 3.10)

Prestressing Devices (3.4)

Anchorages and Couplers should be in accordance with the relevant European Technical Approval.

External non-bonded tendons situated outside the original section and connected to the structure by anchorages and deviators only, should be in accordance with the relevant European Technical Approval.

Eurocode 2

Durability and Cover

85

Nominal cover, cnom

Minimum cover, cmin cmin = max {cmin,dur; cmin,b ; 10 mm}

Axis distance, aFire protection

Allowance for deviation, cdevbond fdurability as per BS 8500

10 mm

Tables in Section 5 of part 1-2

Eurocode 2 - Cover