Lecture-Introduction to EC2

Practical Design to Eurocode 2

Course Outline 24th September

1st October

Basics EC0, EC1, Materials, Cover Beams Bending, Shear, Detailing

Jenny Burridge

Charles Goodchild

Columns 8th October

Axial load, Column Moments, Buckling

Jenny Burridge

Slabs 15th October

22th October

Serviceability, Punching Shear Foundations Pads, Piles, Retaining Walls

Charles Goodchild

Paul Gregory

1

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

2

Background & Basics

Setting the scene 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

Eurocodes are being/ will be used in: • EU countries • EFTA Countries • Malaysia • Singapore • Vietnam • Sri Lanka • Others?

6

3

The Eurocodes •

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

Eurocode Hierarchy These

EN 1990 Basis of Design

+ NA

Structural safety, serviceability and durability

affect concrete design

EN 1991 Actions on Structures EN 1992 EN 1993 EN 1994 EN 1995 EN 1996 EN 1999

+ NA

EN 1997 Geotechnical Design

Concrete Steel Composite Timber Masonry Aluminium EN 1998 Seismic Design

+ NA

+ NAs

Actions on structures

Design and detailing

+ PDs

+ NA

Geotechnical & seismic design 8

4

Format of the Eurocodes Each Eurocode Contains: • National front cover

Format of the Eurocodes Each Eurocode Contains: • National front cover • National foreword

5

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)

6

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)

7

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

Features of the Eurocodes • 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

8

Eurocode 0 BS EN 1990:2002 Basis of structural design

Eurocode (EC0)

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.

9

Limit State Design Limit states are conditions beyond which some design criterion is violated. Generally the structure shall be verified at: – Ultimate Limit State: Any condition that concerns the safety of people or structure – 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)

10

Verification by Partial Safety Factor Method

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

Design Value of Action Fd Where:

= γf ⋅ Frep

Frep = representative value of action = ψ ⋅ Fk

And:

γf = partial factor for actions See NA to BS EN 1990: Table NA.A1.2

ψ

converts the characteristic value of action to the representative value.

Compare to Fd = γf ⋅ Fk

BS8110

11

Representative Values of Variable Actions 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 ψ factors, 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

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

12

Combination of Actions 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 Either Σ γG, j⋅Gk,j

+ γQ,1⋅ Qk,1

+ ΣγQ,i⋅ψ0,i⋅Qk,i

Exp. (6.10)

Or (for STR and GEO) the more adverse of ΣγγG, j⋅Gk,j

+ γQ,1⋅ ψ 0,1⋅Qk,1 + ΣγQ,i⋅ψ0,i⋅Qk,i

Exp. (6.10 a)

or Σ ξ⋅ γG, j⋅Gk,j + γQ,1⋅Qk,1

+ ΣγQ,i⋅ψ0,i⋅Qk,i

Exp. (6.10 b)

The value for ξ for the UK is 0.925

Eurocode – ULS (GEO/STR) Design values of actions, ultimate limit state – persistent and transient design situations (Table A1.2(B) Eurocode) Comb’tion expression reference

Unfavourable

Favourable

Leading variable action

Eqn (6.10)

γG,j,sup Gk,j,sup

γG,j,inf Gk,j,inf

γQ,1 Qk,1

Eqn (6.10a)

γG,j,sup Gk,j,sup

γG,j,inf Gk,j,inf

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

Eqn (6.10b)

0.925x1.35Gk

1.0 Gk

Permanent actions

Accompanying variable actions Main(if any)

γQ,i Ψ0,i Qk,i γQ,1Ψ0,1Qk,1

1.5 Ψ0,1 Qk 1.5 Qk,1

Others

γQ,i Ψ0,i Qk,i

1.5 Ψ0,i Qk,i 1.5 Ψ0,i Qk,i

13

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

Action Imposed loads in buildings, Category A : domestic, residential Category B : office areas Category C : congregation areas Category D : shopping areas Category E : storage areas Category F : traffic area, < 30kN Category G : traffic area, 30– 160 kN Category H : roofs Snow load: H ≤ 1000 m a.s.l. Wind loads on buildings

ψ0

ψ1

ψ2

0.7 0.7 0.7 0.7 1.0 0.7 0.7 0.7 0.5 0.5

0.5 0.5 0.7 0.7 0.9 0.7 0.5 0 0.2 0.2

0.3 0.3 0.6 0.6 0.8 0.6 0.3 0 0 0

Example: ULS Combination of Actions 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 factors ψ0 – office areas = 0.7

(Table NA.A.A1.1)

ψ0 – wind = 0.5

(Table NA.A.A1.1)

14

Example: ULS Combination of Actions 1.35 Gk

+

1.5 Qk,1

+ 0.75Qk,w

Exp. (6.10)

Or the more adverse of +

1.35Gk

1.05 Qk,1

+ 0.75Qk,w

Exp. (6.10 a)

Qk,1

+ 0.75Qk,w

Exp. (6.10 b)

or 1.25Gk

+

1.5

Factor, F (Ultimate load = F x Gk)

Eqn (6.10), (6.10a) or (6.10b)? 3.0

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

2.5

2.0

1.5

1.0 1

2

3

4

4.5

5

6

Gk/Qk

Ratio Gk/Qk

15

Eurocode – ULS (EQU)

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

Permanent actions Unfavourable

Favourable

Leading variable action

Accompanying variable actions

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

Main(if any) Others

Eurocode – SLS Partial Factors for Actions (SLS) γG = 1.00 γQ = 1.00 Combinations of Actions (SLS) Characteristic combination (typically irreversible limit states) Frequent combination (typically reversible limit states)

Gk,j + Qk,1 + Σψ0,I⋅Qk,I Gk,j + ψ1,1⋅Qk,1 + Σ ψ2,I⋅Qk,I

Quasi permanent combination Gk,j + Σ ψ2,I⋅Qk,I (typically long term effects and appearance of the structure) ψ0⋅ - combination value ψ1⋅- frequent value. ψ2⋅- quasi-permanent value.

16

EC2: Load cases & combinations EC2: Cl 5.1.3 gives one option:

Concise: 5.4.2

EC2 NA – additional load cases

17

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

Concise: 5.4.2

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

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

γQj.Qkj

Alternate spans loaded

Adjacent spans loaded

All spans loaded

UK NA: Arrangement of Actions NA gives additional options:

Concise: 5.4.2

Alternate spans loaded 1.5 Qk 1.35 Gk or 1.25 Gk 1.5 Qk 1.35 Gk or 1.25 Gk

All spans loaded

1.5 Qk 1.35 Gk or 1.25 Gk

18

Eurocode (EC0) 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.

Load Arrangement Exercise 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

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).

5m

5m

5m

19

Load Arrangement Exercise

(pro forma)

Span γGGk + γQQk

Q1

Cant γGGk + γQQk

a) EQU b1) STR b2) STR

l

a

γGGk

Q2

γQQk

n

(6.10) (6.10a) (6.10b)

5m

5m

5m

EC1 – Loads/Actions BS EN 1991 Actions on Structures

20

Eurocode 1 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

21

Eurocode 1 UK NA - Extracts Category

Example Use

qk (kN/m2)

Qk (kN)

Char. value of udl

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

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

22

BS EN 1991 1-3 (NA)

Snow loads

BS EN 1991 1-4 (NA) Wind speeds vb,map

23

Eurocode 2

BS EN 1992 Design of concrete structures Materials

Eurocode 2: Context Date

UK

CEB/fib

1968

CP114 (CP110 draft)

Blue Book (Limit state design)

1972

CP110 (Limit state design)

Red Book

1975 1978 1985

Treaty of Rome Model code BS8110

1990 1993 2004 2005 2006 2010

Eurocode 2

Eurocode 2 (EC) Model Code EC2: Part 1-1(ENV) (CEN)

BS110/EC2 EC2

EC2: Part 1-1 (EN) UK Nat. Annex. PD 6687 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 [?] 51

24

Eurocode 2: Design of Concrete Structures

• 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: relationships BS EN 1997 GEOTECHNICAL DESIGN

BS 8500 Specifying Concrete

BS EN 206 Concrete

NSCS

BS EN 13670 Execution of Structures

DMRB?

BS EN 1990 BASIS OF STRUCTURAL DESIGN

BS EN 1998 SEISMIC DESIGN

BS EN 1991 ACTIONS ON STRUCTURES

BS EN 10138 Prestressing Steels

BS EN 1992

BS EN 10080 Reinforcing Steels

DESIGN OF CONCRETE STRUCTURES

Part 1-1: General Rules for Structures Part 1-2: Structural Fire Design

BS 4449 Reinforcing Steels

NBS? Rail? CESWI?

BS EN 1994 Design of Comp. Struct.

BS EN 1992 Part 2: Bridges

BS EN 1992 Part 3: Liquid Ret. Structures

53

BS EN 13369 Pre-cast Concrete

25

Eurocode 2 & BS 8110 Compared 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

26

Eurocode 2 Concrete properties (Table 3.1) Strength classes for concrete fck (MPa)

12 16 20 25 30 35 40 45 50 55 60 70 80

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 fcm Ecm

90

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

• BS 8500 includes C28/35 & C32/40 • For shear design, max shear strength as for C50/60

Design Strength Values

(3.1.6)

• Design compressive strength, fcd fcd = αcc fck /γc • Design tensile strength, fctd fctd = 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

27

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

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

t0 1 2

(3.1.4)

N

R

S

3 5

C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75 C70/85 C80/95 C90/105

10 20 30 50 100 7,0

6,0

ϕ (∞, t 0)

5,0

4,0

3,0

2,0

1,0

0

100

300

500

700

900

1100 1300 1500

h 0 (mm) h0 = 2Ac/u where Ac is the cross-section area and u is perimeter of the member in contact with the atmosphere

28

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 Autogenous shrinkage, εca εca(t) = βas(t)·εca(∞)

(EC2, Exp (3.9)

(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)

29

Concrete Stress Blocks

(3.1.5 and 3.1.7)

For section analysis

For structural analysis

σc σc

“Schematic”

fcm

“Bi-linear”

“Parabola-rectangle”

σc f ck

fck

f cd

fcd

0,4 fcm tan

α

= E cm

α ε c1

εc1 00) = 0,7 fcm εcu1 (0/00) = (0 /

εc

ε cu1

ε c2

0

 σ c = fcd 1 −  σ c = fcd for

0,31

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

ε cu2

εc

n  εc   1 −   for 0 ≤ ε c < ε c2 ε  c2    ε c2 ≤ ε c ≤ ε cu2

)/100]4

n = 1,4 + 23,4 [(90- fck for fck≥ 50 MPa otherwise 2,0

for fck ≥ 50 MPa otherwise 3.5

εc2

ε c3

0

εcu3

εc

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

εcu3 (0/00) =2,6+35[(90-fck)/100]4 for fck≥ 50 MPa otherwise 3,5

(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

Rectangular Concrete Stress Block (3.1.7, Figure 3.5) εcu3 Ac

η fcd Fc

λx

x d

As

Fs

εs λ = 0,8 for fck ≤ 50 MPa = 0,8 −

(fck − 50 ) 400

for 50 < fck ≤ 90 MPa

η = 1,0

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

30

Change in Shape of Concrete Stress Block for high strength concretes

Strain at maximum stress increases

Stress

C90/105

up to C50/60 Ultimate strain reduces

Strain

Confined Concrete

(3.1.9) σc

σ1 = fck,c

fck,c fck fcd,c A

σ2

σ3 ( = σ2) 0

fck,c = fck (1.000 + 5.0 σ2/fck)

εcu εc2,c

εcu2,c εc

for σ2 ≤ 0.05fck

= fck (1.125 + 2.50 σ2/fck) for σ2 > 0.05fck

εc2,c = εc2 (fck,c/fck)2 εcu2,c = εcu2 + 0,2 σ2/fck

31

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

Reinforcement (2) – From Annex C Product form

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

Bars and de-coiled rods

A

B

cold worked

C

Wire Fabrics

A

400 to 600 hot rolled

B

C

seismic

k = (ft/fy)k

≥1,05

≥1,08

≥1,15