Lecture-Introduction to EC2

1

Practical Design to Eurocode 2

Course Outline

24th SeptemberBasics

EC0, EC1, Materials, CoverJenny Burridge

1st OctoberBeams

Bending, Shear, DetailingCharles Goodchild

8th October

Columns

Axial load, Column

Moments, Buckling

Jenny Burridge

15th October

Slabs

Serviceability, Punching

Shear

Charles Goodchild

22th OctoberFoundations

Pads, Piles, Retaining WallsPaul Gregory

2

Basics

Lecture 1

24th September 2013

Summary: Lecture 1 Basics

• Background & Basics

• Eurocode 0 & load combinations

• Eurocode 1 loads/actions

• Eurocode 2

– Background

– Materials

– Cover

– Analysis

3

Background & Basics

6

Setting 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

4

• 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

Eurocode Hierarchy

8

+ PDs

+ NA + NA

+ NAs

+ NA

+ NAEN 1990

Basis 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

These

affect

concrete

design

5

Each Eurocode Contains:

• National front cover

Format of the Eurocodes



• National foreword


6




• CEN front cover





• CEN front cover

• Main text and annexes (which must

be as produced by CEN)


7




• CEN front cover

• Main text and annexes (which must

be as produced by CEN)

• Annexes - can by normative and/or

informative


National Annex (NA)


8

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 columns

φmin = 8 mm in text φmin = 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

9

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 and serviceability limit states.

Eurocode (EC0)

10

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,stb

Internal failure or excessive structural deformation (STR)

Ed ≤ Rd;

Failure or excessive deformation of ground (GEO)

Failure caused by time dependent effects e.g.fatigue (FAT)

Limit State Design

11

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 = γγγγf ⋅⋅⋅⋅ Frep

Where: Frep = representative value of action

= ψ ⋅ Fk

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

ψ converts the characteristic value ofaction to the representative value.

Compare to

Fd = γf ⋅ Fk BS8110

Design Value of Action

12

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 ψψψψfactors, which can take one of four values, namely, 1.00 or ψ0 or ψ1

or ψ2.

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

ψ0⋅Qk is the combination value of a variable action.

ψ1⋅Qk is the frequent value.

ψ2⋅Qk 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

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

ΣΣΣΣ γγγγG, j⋅⋅⋅⋅Gk,j + γγγγQ,1⋅⋅⋅⋅ Qk,1 + ΣγΣγΣγΣγQ,i⋅ψ⋅ψ⋅ψ⋅ψ0,i⋅⋅⋅⋅Qk,i Exp. (6.10)

Either

ΣγγγγG, j⋅⋅⋅⋅Gk,j + γγγγQ,1⋅⋅⋅⋅ ψψψψ0,1⋅⋅⋅⋅Qk,1 + ΣγΣγΣγΣγQ,i⋅ψ⋅ψ⋅ψ⋅ψ0,i⋅⋅⋅⋅Qk,i Exp. (6.10 a)

or

ΣΣΣΣ ξξξξ⋅⋅⋅⋅ γγγγG, j⋅⋅⋅⋅Gk,j + γγγγQ,1⋅⋅⋅⋅Qk,1 + ΣγΣγΣγΣγQ,i⋅ψ⋅ψ⋅ψ⋅ψ0,i⋅⋅⋅⋅Qk,i Exp. (6.10 b)

Or (for STR and GEO) the more adverse of

The value for ξξξξ 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)

Comb’tionexpression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) γG,j,sup Gk,j,sup γG,j,inf Gk,j,inf γQ,1 Qk,1 γQ,i Ψ0,i Qk,i

Eqn (6.10a) γG,j,sup Gk,j,sup γG,j,inf Gk,j,inf γQ,1Ψ0,1Qk,1 γQ,i Ψ0,i Qk,i

Eqn (6.10b) ξ γG,j,supGk,j,sup γG,j,inf Gk,j,inf γQ,1 Qk,1 γQ,i Ψ0,i Qk,i

Eqn (6.10) 1.35 Gk 1.0 Gk 1.5 Qk,1 1.5 Ψ0,i Qk,i

Eqn (6.10a) 1.35 Gk 1.0 Gk 1.5 Ψ0,1 Qk 1.5 Ψ0,iQk,i

Eqn (6.10b) 0.925x1.35Gk 1.0 Gk 1.5 Qk,1 1.5 Ψ0,i Qk,i

Eurocode – ULS (GEO/STR)

14

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

Action ψψψψ0 ψψψψ 1 ψψψψ2

Imposed 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 0

Wind loads on buildings 0.5 0.2 0

UK Values of ψψψψ Factor

Partial Factors for Actions (ULS)

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

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

Relevant ψ ψ ψ ψ factors

ψ0 – office areas = 0.7 (Table NA.A.A1.1)

ψ0 – wind = 0.5 (Table NA.A.A1.1)

Example: ULS Combination of Actions

15

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 6

Gk/Qk

Eqn (6.10)

Eqn (6.10a)

Eqn (6.10b)

Ratio Gk/Qk

Factor, F

(Ultimate load = F

x G

k)

4.5

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

16

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

Comb’tion expression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main(if any) Others

Eqn (6.10) γG,j,sup Gk,j,sup γG,j,inf Gk,j,inf γQ,1 Qk,1 γQ,i Ψ0,i Qk,i

Eqn (6.10) 1.10 Gk 0.9 Gk 1.5 Qk,1 1.5 Ψ0,i Qk,i

Eurocode – ULS (EQU)

Combinations of Actions (SLS)

Characteristic combination Gk,j + Qk,1 + Σψ0,I⋅Qk,I

(typically irreversible limit states)

Frequent combination Gk,j + ψ1,1⋅Qk,1 + Σ ψ2,I⋅Qk,I

(typically reversible limit states)

Quasi permanent combination Gk,j + Σ ψ2,I⋅Qk,I

(typically long term effects and appearance of the structure)

Partial Factors for Actions (SLS)

γG = 1.00

γQ = 1.00

ψ0⋅ - combination valueψ1⋅- frequent value.

ψ2⋅- quasi-permanent value.

Eurocode – SLS

17

EC2: Load cases & combinations

EC2: Cl 5.1.3 gives one option: Concise: 5.4.2

EC2 NA – additional load cases

18

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

Alternate spans

loaded

Adjacent spans

loaded

All spans loaded

Concise: 5.4.2

γQj.QkjγGj.Gkj

UK NA: Arrangement of Actions

All spans loaded

Alternate spans loaded

1.35Gk or 1.25 Gk

1.5Qk

1.35 Gk or 1.25 Gk

1.5Qk

1.35 Gk or 1.25 Gk

1.5Qk

NA gives additional options:Concise: 5.4.2

19

From EN1990:

Table A1.2(B) - Design values of actions (STR/GEO) (Set B)

NOTE 3 The characteristic values of all permanent actions from one

source are multiplied by γG,sup if the total resulting action effect is unfavourable and γG,inf if the total resulting action effect is favourable. For example, all actions originating from the self weight

of the structure may be considered as coming from one source; this

also applies if different materials are involved.

There is no such note for Table A1.2(A) - Design values of actions (EQU) (Set A)

Therefore there should be no pattern loading on permanent actions for STR and GEO verifications but there should be pattern loading on permanent actions for EQU.

Eurocode (EC0)

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 γF 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

5m 5m 5m

20

l a

Load Arrangement Exercise (pro forma)

Q2 γγγγGGk γγγγQQk n

(6.10)

(6.10a)

(6.10b)

Q1 Span γGGk + γQQk Cant γGGk + γQQk

a) EQU

b1) STR

b2) STR

5m 5m 5m

EC1 – Loads/Actions

BS EN 1991

Actions on Structures

21

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

22

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

αA and/or αn.

The NA modifies the equation in EC1.

αA = 1.0 – A/1000 ≥ 0.75

where A is the area (m2) supported

αn = 1.1 – n/10 1 ≤ n ≤ 5

αn = 0.6 6 ≤ n ≤ 10

αn = 0.5 n > 10

where n is the number of storeys supported

23

BS EN 1991 1-3 (NA)

Snow loads

BS EN 1991 1-4 (NA)

Wind speeds

vb,map

24

Eurocode 2

BS EN 1992

Design of concrete structures

Materials

51

Date UK CEB/fib Eurocode 2

1968 CP114 (CP110 draft) Blue Book (Limit state design)

1972 CP110 (Limit state design) Red Book

1975 Treaty of Rome

1978 Model code

1985 BS8110 Eurocode 2 (EC)

1990 Model Code

1993 EC2: Part 1-1(ENV) (CEN)

2004 EC2: Part 1-1 (EN)

2005 UK Nat. Annex.

2006 BS110/EC2 PD 6687

2010 EC2 Model Code 2010

Eurocode 2 is more extensive than old codes

Eurocode 2 is less restrictive than old codes

Eurocode 2 can give more economic structures [?]

Eurocode 2: Context

25

• 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 Concrete

Bridges

• BS EN 1992-3: Liquid Retaining Structures

Eurocode 2: Design of Concrete Structures

Eurocode 2: relationships

53

BS EN 1990

BASIS OF STRUCTURAL

DESIGN

BS EN 1991

ACTIONS ON STRUCTURES

BS EN 1992DESIGN OF CONCRETE

STRUCTURES

Part 1-1: General Rules for

Structures

Part 1-2: Structural Fire Design

BS EN 1992

Part 2:

Bridges

BS EN 1992

Part 3: Liquid

Ret.

Structures

BS EN 1994

Design of

Comp.

Struct.

BS EN 13369

Pre-cast

Concrete

BS EN 1997

GEOTECHNICAL

DESIGN

BS EN 1998

SEISMIC DESIGN

BS EN 13670

Execution of

Structures

BS 8500

Specifying

Concrete

BS 4449

Reinforcing

Steels

BS EN 10080

Reinforcing

Steels

BS EN 206

Concrete

NSCS

DMRB?

NBS?

Rail?

CESWI?

BS EN 10138

Prestressing

Steels

26

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

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

27

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 = αcc fck /γc

• Design tensile strength, fctdfctd = αct fctk,0.05 /γc

αcc (= 0.85 (flexure) and 1,0 (shear)) and αct (= 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

28

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

• Poisson’s 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)

01,02,03,04,05,06,07,0

100

50

30

1

2

3

5

10

20

t 0

ϕ (∞, t 0)

S

N R

100 300 500 700 900 1100 1300 1500

C20/25

C25/30

C30/37C35/45C40/50C45/55C50/60

C55/67C60/75

C70/85C90/105

C80/95

h 0 (mm)

Inside conditions – RH = 50%

Example: 300 thick slab, loading at 30 days, C30/37 - ϕ = 1,8

h0 = 2Ac/u where Ac is the cross-section area and

u is perimeter of the member in contact with

the atmosphere

29

Shrinkage (3.1.4)

Shrinkage Strain, εcs, is composed of two components:

• Drying Shrinkage Strain, εcd, develops slowly

• Autogenous Shrinkage Strain, εca, develops during the hardening of the concrete.

Drying shrinkage, εcd

εcd(t) = βds(t,ts)·kh · εcd,0 (EC2, Exp (3.9)

Autogenous shrinkage, εca

εca(t) = βas(t)·εca(∞) (EC2, Exp (3.11)

Creep and Shrinkage Annex B

• Creep

– ϕ0 is the notional creep coefficient (in Figure 3.1 the notation used is ϕ(∞,t0))

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

• Shrinkage

– εcd,0 is the basic drying shrinkage strain

– εcd,(t) = βds(t,ts)kh εcd,0 (Section 3)

30

fcd

εc2

σc

ε cu2 ε c0

fck

For section analysis

“Parabola-rectangle”

c3ε

cu30

fcd

ε

σc

εc

fck

“Bi-linear”

fcm

0,4 fcm

ε c1

σc

ε cu1εc

tan α = Ecm

α

For structural analysis

“Schematic”

εc1 (0/00) = 0,7 fcm0,31

εcu1 (0/00) =

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

for fck ≥ 50 MPa otherwise 3.5

εc2 (0/00) = 2,0 + 0,085(fck-50)0,53

for fck ≥ 50 MPa otherwise 2,0

εcu2 (0/00) = 2,6 + 35 [(90-fck)/100]4

for fck ≥ 50 MPa otherwise 3,5

n = 1,4 + 23,4 [(90- fck)/100]4

for fck≥ 50 MPa otherwise 2,0

σ f

n

cc cd c c2

c2

1 1 for 0ε

ε εε

= − − ≤ <

σ f forc cd c2 c cu2ε ε ε= ≤ ≤

εc3 (0/00) = 1,75 + 0,55 [(fck-50)/40]


εcu3 (0/00) =2,6+35[(90-fck)/100]4


Concrete Stress Blocks (3.1.5 and 3.1.7)

As

d

η fcd

Fs

λx

εs

x

εcu3

Fc Ac

η = 1,0 for fck ≤ 50 MPa= 1,0 – (fck – 50)/200 for 50 < fck ≤ 90 MPa

400

)508,0 ck −

−=(f

for 50 < fck ≤ 90 MPa

λ = 0,8 for fck ≤ 50 MPa

Rectangular Concrete Stress Block (3.1.7, Figure 3.5)

31

up to C50/60

Stress

Strain

Ultimate strain

reduces

Strain at maximum

stress increases

C90/105

Change in Shape of Concrete Stress Block for high strength concretes

Confined Concrete (3.1.9)

εc2,c εcu2,c

σc

εc

fck,c

fcd,c

0

A

σ2 σ3 ( = σ2)

σ1 = fck,c

fck

εcu

fck,c = fck (1.000 + 5.0 σ2/fck) for σ2 ≤ 0.05fck

= fck (1.125 + 2.50 σ2/fck) for σ2 > 0.05fckεc2,c = εc2 (fck,c/fck)2

εcu2,c = εcu2 + 0,2 σ2/fck

32

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 <1,35

≥1,05

≥1,08

≥1,15 <1,35

Characteristic strain at

maximum force, εεεεuk (%)

≥2,5

≥5,0

≥7,5

≥2,5

≥5,0

≥7,5

Fatigue stress range

(N = 2 x 106) (MPa) with an upper limit of 0.6fyk

150

100

cold worked seismichot rolled

The UK has chosen a maximum value of characteristic yield strength, fyk, = 600

MPa, but 500 MPa is the value assumed in BS 4449 and BS 4483 for normal supply.

Reinforcement (2) – From Annex C

33

0.2%εuk

f0.2k

ft = kf0.2k

ε

σft = kfykt

εuk

ε

σ

fyk

Hot rolled steelCold worked steel

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

Reinforcement (3)(3.2.4, figure 3.7)

70

Extract from BS 8666

34

εud

ε

σ

fyd/ Es

fyk

kfyk

fyd = fyk/γs

kfyk/γs

Idealised

Design

εuk

εud= 0.9 εuk

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(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

35

Strand type

Steel Number

Nominal tensile strength (MPa)

Nominal diameter (mm)

Cross-sectional 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

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.

36

Eurocode 2

Durability and Cover

77

Nominal cover, cnom

Minimum cover, cmin

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

Axis distance, aFire protection

Allowance for deviation, ∆cdev

bond ≡φdurability as per BS 8500

10 mm

Tables in Section 5 of part 1-2

Eurocode 2 - Cover

37

Durability of Structures

Cover density and quality is achieved by:

• Controlling the maximum water/cement ratio

• Controlling the cement content.

• Annex E does not apply. The UK has produced its own tables

Exposure Classes

Table 4.1 (based on EN 206-1) provides the definitions of

exposure classes for different environmental conditions.

– XO – no risk of corrosion or attack

– XC – risk of carbonation-induced corrosion

– XS – risk of chloride-induced corrosion (sea water)

– XD - risk of chloride-induced corrosion

– XF – risk of freeze/thaw attack

– XA (DC - BS8500) – risk of chemical attack in ground

38

Minimum Cover for Durability, cmin,dur• The UK National Annex defers to BS8500 for cmin,dur

• In EC2 this can be modified by further factors

• But in the UK these are all 0 – unless justified, i.e: Values of

cdur,γ, ∆cdur,st and ∆cdur,add are taken as 0 in the UK unless

reference is made to specialist literature.

Subclause Nationally Determined

Parameter

Eurocode Recommendation UK Decision

4.4.1.2 (5) Structural classification and

values of minimum cover

due to environmental

conditions cmin,dur

Table 4.3N for structural classification

Tables 4.4N and 4.5N for values of

cmin,dur

Use BS 8500-1:2006, Tables A.3, A.4, A.5 and A.9 for

recommendations for concrete quality for a

particular exposure class and cover reinforcement c.

Cmin,dur = Cover for Durability –50 year life. Taken from BS 8500

39

Minimum Cover for Bond, Cmin,b

For bars: Cmin,b = Bar diameter

• For Post-tensioned tendons:

– Circular ducts: Duct diameter

– Rectangular ducts: The greater of:

� the smaller dimension or

� half the greater dimension

• For pre-tensioned tendons:

– 1,5 x diameter of strand or wire

– 2,5 x diameter of indented wire

Cminb= øl

Cminb= øm

ømøl

Allowance in Design for Deviation

• ∆cdev: Allowance for deviation = 10mm

• A reduction in ∆cdev may be permitted:

– quality assurance system, which includes measuring

concrete cover, 10 mm ≥ ∆cdev ≥ 5 mm

– where very accurate measurements are taken and non

conforming members are rejected (e.g. precast

elements), 10 mm ≥ ∆cdev ≥ 0 mm

• RECAP : cnom = cmin + ∆cdev

40

a Axis

Distance

Reinforcement cover

Axis distance, a, to

centre of bar (or

group of bars)

a = c + φφφφm/2 + φφφφl

Scope

Tabulated data for various elements is given in section 5

Gives several methods for fire engineering

BS EN 1992-1-2 Structural Fire Design

EC2 - Cover

(Fire will be covered in Lecture 3)

Cover Exercise (Fire and Durability)

What are the nominal cover and element size for a car park

one-way slab with 1 hour fire resistance (i.e. REI = 60)?

• Assume the max bar size in the slab is 25mm.

• Assume the concrete is C32/40 with cement type IIIB

• Assume design life 50 years and in-situ construction

41

Cover Example (pro forma)

BOND

EC2-1-1 Table 4.2 (Section 4.2)

DURABILITY

EC2-1-1 Table 4.1 (Table 4.1)

UK NA & BS 8500 (Table 4.2)

DEVIATION

EC2-1-1Cl. 4.4.1.3 (Section 4.5)

FIRE

EC2-1-2 Table 5.8 (Table 4.7)

Cminb =………………….

Durability Class ……….. . .

Cmindur = ……………….

∆Cdev =…………………

Min thickness hs=……..

Min axis distance a=…..

Nominal Cover governed by …………………= ………..mm

Eurocode 2

Structural Analysis

42

Structural Analysis (5.1.1)

• Common idealisations used:

– linear elastic behaviour

– linear elastic behaviour with limited redistribution

– plastic behaviour

– non-linear behaviour

• Local analyses are required where non-linear strain distribution is

not valid:

– In the vicinity of supports

– Local to concentrated loads

– In beam/column intersections

– In anchorage zones

– At changes in cross section

Soil/Structure Interaction (5.1.2)

• Where soil/structure interaction has a significant effect on the structure use EN 1997-1

• Simplifications (see Annex G) include:

– flexible superstructure

– rigid superstructure; settlements lie in a plane

– foundation system or supporting ground assumed to

be rigid

• Relative stiffness between the structural system and the ground > 0.5 indicate rigid structural system

43

Second Order Effects (5.1.4)

• For buildings 2nd order effects may be ignored if they are

less than 10% of the corresponding 1st order effects

• Two alternative methods of analysis are permitted:

– Method A based on nominal stiffnesses (5.8.7)

– Method B based on nominal curvature (5.8.8)

• Linear elastic analysis may be carried assuming:

– uncracked sections (concrete section only)

– linear stress-strain relationships

– mean value of the modulus of elasticity

• Linear elastic analysis may be used for both ULS and SLS

• For thermal deformation, settlement and shrinkage

effects at ULS a reduced stiffness corresponding to

cracked sections may be assumed.

Linear Elastic Analysis (5.4)

44

• In continuous beams or slabs which are mainly subject to flexure and

for which the ratio of adjacent spans is between 0.5 and 2

δ ≥ 0,4 + (0,6 + 0,0014/εcu2)xu/d

≥ 0,7 for Class B and C reinforcement

≥ 0,8 for Class A reinforcement

where δ is (distributed moment)/(elastic moment)

xu is the neutral axis depth after redistribution

• For column design the elastic values from the frame analysis should

be used (not the redistributed values).

Linear Elastic Analysis with Limited Redistribution (5.5)

• Additionally x/d is traditionally limited to

a min of 0.45 to avoid brittle failure

0

5

10

15

20

25

30

35

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

x /d

% r

ed

ist

fck =70 fck =60 fck =50

Redistribution Limits for Class B & C Steel

45

0

5

10

15

20

25

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

x /d

% r

ed

ist

fck =70 fck =60 fck =50

Redistribution Limits for Class A Steel

• Beam: Span ≥ 3h otherwise it is a deep beam

• Slab: Minimum panel dimension ≥ 5h

– One-way spanning

• Column: h ≤ 4b and L ≥ 3h otherwise it should be considered as a wall

• Ribbed or waffle slabs need not be treated as discrete

elements provided that:

• rib spacing ≤ 1500mm

• rib depth below flange ≤ 4b

• flange depth ≥ 1/10 clear distance between ribs or 50mm -transverse ribs are provided with a clear spacing ≤ 10 h

Idealisation of the structure (5.3)

46

b

b1 b1b2 b2

bw

bw

beff,1beff,2

beff

beff = Σ beff,i + bw ≤ b

Where beff,i = 0,2bi + 0,1l0 ≤ 0,2l0 and beff,I ≤ bi

l3

l1 l

2

0,15(l1 + l2 )l =0

l0 = 0,7 l2 l0 = 0,15 l2 + l3l0 = 0,85 l1

l0, is the distance between points of zero moment.

It may be taken as:

Effective Flange Width (5.3.2.1)

leff = ln + a1 + a2

• The design moment and reaction for monolithic support

should generally be taken as the greater of the elastic

and redistributed values (≥ 0,65 the full fixed moment).

leff

ai ln

h

t

ln

leff

a = min {1/2h; 1/2t }i

• Permitted reduction, ∆MEd = FEd.supt/8

Effective Length of Beam or Slab (5.3.2.2)

47

Geometric Imperfections (5.2)

• Deviations in cross-section dimensions are normally

taken into account in the material factors and should

not be included in structural analysis

• Imperfections need not be considered for SLS

• Out-of-plumb is represented by an inclination, θl

θl = θ0 αh αm where θ0 = 1/200

αh = 2/√l; 2/3 ≤ αh ≤ 1

αm = √(0,5(1+1/m)

l is the height of member (m)

m is the number of vert. members

ei

N

Hi

N

l = l0 / 2

ei

N

l = l0Hi

N

ei = θi l0/2 (for walls and isolated columns ei = l0/400)

Hi = θiN for unbraced members

Hi = 2θiN for braced members

or

UnbracedBraced

Isolated Members (5.2)

48

Na

Nb

Hi

l

iθ

iθNa

Nb

Hi

/2iθ

/2iθ

Bracing System Floor Diaphragm Roof

Hi = θi (Nb-Na) Hi = θi (Nb+Na)/2 Hi = θi Na

Structures (5.2)

Partial factors for Hi

It is not clear how the notional force

Hi should be regarded, i.e. as a

permanent action, a variable action,

an accidental action. However by

inference if should be the same as

for the constituent axial loads N,

NEd, Na and/or Nb.

i.e. γHi = (1.35Gk + 1.5Qk )/(Gk + Qk)

But TCC’s Worked Examples says “As

Hi derives mainly from permanent

actions its resulting effects are

considered as being a permanent

action too.” and γHi = γG = 1.35 was used.

Documents

Lecture-Introduction to EC2