lecture-introduction to ec2
DESCRIPTION
Introduction to EC2TRANSCRIPT
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
Each Eurocode Contains:
• National front cover
• National foreword
Format of the Eurocodes
6
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
7
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
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]
for fck≥ 50 MPa otherwise 1,75
εcu3 (0/00) =2,6+35[(90-fck)/100]4
for fck≥ 50 MPa otherwise 3,5
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.