Lecture 1 Basics - Oct 12 - End
description
Transcript of Lecture 1 Basics - Oct 12 - End
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Practical Design to Eurocode 2
Paul Gregory
Regional Engineer
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Course Outline
Foundations
Pads, Retaining Walls, Strut & tie, Piles11th October 2012
Slabs
Serviceability, Punching Shear, Tying systems4th October 2012
Columns
Axial load, Column Moments, Buckling, Fire27th September 2012
Beams
Bending, Shear, Detailing20th September 2012
Basics
EC0, Load cases, EC1, Materials, Cover13th September 2012
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Basics
Lecture 1
13th September 2012
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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
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Each Eurocode Contains:
National front cover
Format of the Eurocodes
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Each Eurocode Contains:
National front cover
National foreword
Format of the Eurocodes
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Each Eurocode Contains:
National front cover
National foreword
CEN front cover
Format of the Eurocodes
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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
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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
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National Annex (NA)
Format of the Eurocodes
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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 columnsmin = 8 mm in text min = 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
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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
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Eurocode 0
BS EN 1990:2002
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EurocodeBasis 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 actions for the verification of both ultimate andserviceability limit states.
eg EC0 - Ultimate load can be 1.25 Gk + 1.5 Qk
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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
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Ultimate Limit State:
Loss of equilibrium (EQU)
Ed,dst Ed,stbInternal failure or excessive structural deformation (STR)
Ed RdFailure or excessive deformation of ground (GEO)
Failure caused by time dependent effects such as fatigue (FAT)
Limit State Design
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Principle: When using the partial factor method, it shall be verified that, in all relevant design situations, no relevant limit state is exceeded when design values for actions or effects of actions and resistances are used in the design models.
e.g. Ed RdEd is the design value of the effect of actions.
Rd is the design value of the corresponding resistance.
Verification by Partial Safety Factor Method
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Fd = f FrepWhere: Frep = representative value of action
= FkAnd: f = partial factor for actions
See NA to BS EN 1990: Table NA.A1.2
converts the characteristic value of action to the representative value.
Compare to
Fd = f Fk BS8110
Design Value of Action
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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 factors
can take one of four values, namely, 1.00 or 0 or 1 or 2. = 1.00 when only one variable action is present in a combination. 0Qk is the combination value of a variable action.1Qk is the frequent value.2Qk is the quasi-permanent value.
Representative Values
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Representative Values
Ref: Gulvanessian, H ICE Proceedings, Civil Engineering 144 November 2001 pp.8-13
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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
G, jGk,j + Q,1 Qk,1 + Q,i0,iQk,i Exp. (6.10)
Either
G, jGk,j + Q,1 0,1Qk,1 + Q,i0,iQk,i Exp. (6.10 a) or
G, jGk,j + Q,1Qk,1 + Q,i0,iQk,i Exp. (6.10 b)
Or (for STR and GEO) the more adverse of
The value for for the UK is 0.925
Combination of Actions
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Perm. action + leading variable action + accompanying action
Dead + live (Office) + wind
G, jGk,j + Q,1 Qk,1 + Q,I0,IQk,I Exp. (6.10)or the more adverse of
G, jGk,j + Q,1 0,1Qk,1 + Q,I0,IQk,I Exp. (6.10 a) or
G, jGk,j + Q,1Qk,1 + Q,I0,IQk,I Exp. (6.10 b)
Example: ULS Combination of Actions for the STR Limit State
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Table NA.A1.1 UK National Annex of BS EN 1990
Action 0 1 2Imposed 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 Factor
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Partial Factors for Actions (ULS)
G = 1.35 (NA 2.2.3.2 and Table NA.A1.2)Q = 1.5 (NA 2.2.3.2 and Table NA.A1.2)Relevant factors0 office areas = 0.7 (Table NA.A1.1)0 wind = 0.5 (Table NA.A1.1)
Example: ULS Combination of Actions for the STR Limit State
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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 for the STR Limit State
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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,i
Eqn (6.10a) G,j,sup Gk,j,sup G,j,inf Gk,j,inf Q,10,1Qk,1 Q,i 0,i Qk,i
Eqn (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,i
Eqn (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)
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1.0
1.5
2.0
2.5
3.0
1 2 3 4 5 6
Eqn (6.10)Eqn (6.10a)Eqn (6.10b)
Ratio Gk/Qk
F
a
c
t
o
r
,
F
(
U
l
t
i
m
a
t
e
l
o
a
d
=
F
x
G
k
)
4.5
Eqn (6.10), (6.10a) or (6.10b)?
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Design values of actions, ultimate limit state persistent and transient design situations (Table A1.2(A) 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,i
Eqn (6.10) 1.10 Gk 0.9 Gk 1.5 Qk,1 1.5 0,i Qk,i
Eurocode ULS (EQU)
Note - alternative method may be used when both EQU and STR should both be checked. See note below this table A1.2(A)
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Combinations of Actions (SLS)
Characteristic combination Gk,j + Qk,1 + 0,IQk,I(typically irreversible limit states)
Frequent combination Gk,j + 1,1Qk,1 + 2,IQk,I(typically reversible limit states)
Quasi permanent combination Gk,j + 2,IQk,I(typically long term effects and appearance of the structure)
Partial Factors for Actions (SLS)
G = 1.00Q = 1.00
0 - combination value1- frequent value.2- quasi-permanent value.
Serviceability Limit State BS EN 1990 (6.5.3)
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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, mGk Qk tan c cu
Combination 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 Q = 0 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
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Load Arrangements(BS EN 1992, Cl 5.1.3) Concise: 5.4.2
EC2
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Load CasesEC2 clause 2.4.3 Combinations of actions:
Additional information is in PD 6687-1:2010
See clause 2.9 Simplified load combinations[BS EN 1992-1-1:2004, 5.1.3 (1)P]
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EC2: Load cases & combinationsEC2: Cl 5.1.3 gives one option: Concise: 5.4.2
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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
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2. Continuous single-way slab. Using the Single load combination for a three span slab in an office building 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).
Which of these expressions will lead to the most economic design?
1. Overhanging cantilever beam. Illustrate the load combinations that should be considered in the design :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
5m 5m 5m
Gk = 6 kN/m2, Qk = 4kN/m2
Load Arrangement Exercise
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l a
5m 5m 5m
6.10
6.10a
6.10b
EQU
STR
STR
Load Arrangement Exercise
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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 (1)
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a) Value using Combination from BS EN 1990 Expression (6.10)G Gk + Q Qk 1.35 x 6 + 1.5 x 4 = 14.1 kN/m2
2. 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
G Gk + Q 0Qk 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
G Gk + Q Qk 1.35 x 0.925 x 6 + 1.5 x 4 = 13.5 kN/m2Expression (6.10b) gives the most economic design
Load Arrangement Exercise Solution (2)
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Cantilever
EQU 1.1 Gk
1.5 Qk0.9 Gk
STR/GEO - 1 1.35 Gk or1.25 Gk
1.5 Qk
STR/GEO - 31.35 Gk or1.25 Gk
1.5 Qk
1.0 Gk
1.5 Qk
STR/GEO - 2
STR/GEO - 31.0 Gk
1.5 Qk
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Frame see note in BS EN 1990 Table A.1.2 (A) & UK NA
Check EQU for uplift at A 1.35 Gk,N + 1.5 Qk,W + 1.5 x 0.7 Qk,N + 1.5 x 0.7 Qk,SN - 1.15 Gk,1 - 1.15 Gk,2 1.35 Gk,N + 1.5 Qk,N + 1.5 x 0.5 Qk,W + 1.5 x 0.7 Qk,SN - 1.15 Gk,1 - 1.15 Gk,2
Qk,W Gk,N Qk, N
Qk,S
Qk,1Gk,1Qk,SN
Qk,2Gk,2
Qk,2Gk,2
Qk,2Gk,2
A B
0 = 0.7 for Qk,20 = 0.7 for Qk,10 = 0.5 for Qk,W0 = 0.7 for Qk,S
Wind as leading variable action
Wind as accompanying variable action
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EC1 Loads/Actions
BS EN 1991
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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
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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
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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
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BS EN 1991 1-3 (NA)
Snow loads
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BS EN 1991 1-4 (NA)
Wind speeds
vb,map
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Eurocode 2
BS EN 1992
Design of concrete structures
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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: Concrete StructuresBS EN 1992
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1. General2. Basis of design3. Materials4. Durability and cover to reinforcement5. Structural analysis6. Ultimate limit state7. Serviceability limit state8. Detailing of reinforcement and pre-stressing tendons General9. Detailing of member and particular rules10. Additional rules for precast concrete elements and structures11. Lightweight aggregated concrete structures12. Plain and lightly reinforced concrete structures
Eurocode 2 Contents
BS EN 1992-1-1: General Rules and Rules For Buildings
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A. (Informative) Modification of partial factors for materialsB. (Informative) Creep and shrinkage strainC. (Normative) Reinforcement propertiesD. (Informative) Detailed calculation method for pre-stressing steel
relaxation lossesE. (Informative) Indicative Strength Classes for durability Use BS8500F. (Informative) Reinforcement expressions for in-plane stress
conditionsG. (Informative) Soil structure interactionH. (Informative) Global second order effects in structuresI. (Informative) Analysis of flat slabs and shear wallsJ. (Informative) Examples of regions with discontinuity in geometry
or action (Detailing rules for particular situations) Alternative J in PD 6687
Eurocode 2 - AnnexesBS EN 1992-1-1: General Rules and Rules For Buildings
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BS8110 vs EC2
Differences 1EC2:
1. Laid out to give advice on phenomena rather than by member type as in BS8110
2. Derived design formulae not included in code (contained in Non-contradictory complimentary information NCCI)
3. Design based on cylinder strength rather than cube strength
4. Higher strength concrete up to C90/105,
5. Applicable for ribbed reinforcement fy 400MPa 600MPa (Info on plain and mild steel given in PD 6687)
6. Reinforcement partial factor for material m = 1.15 but fy to BS4449 500MPa effect negligible
7. Effects of geometric imperfections (notional horizontal loads) considered in addition to lateral loads
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BS8110 vs EC2
Differences -2
EC2:
8. Cover related to requirements for durability, fire and bond also subject to allowance for deviations due to variations in execution
9. Variable strut inclination method for shear
10. Punching shear checks at 2d from support
11. Rules for determining anchorage and lap lengths.
12. Serviceability checks
13. Decimal point replaced by comma
14. Units of stress MPa
15. 1/1000 expressed as
16. Axes changed from x, y to y, z
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Eurocode 2
Materials
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fcm = fck+ 8(MPa)
fctm = 0.30 fck(2/3) C50/60= 2.12 In(1+(fcm/10)) > C50/60
fctk;0,05 = 0,7fctm5% fractile
fctk;0,95 = 1,3fctm95% fractile
Ecm = 22[(fcm)/10]0,3(fcm in MPa)
Strength classes for concretefck (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
fctk,0,05(MPa)
1 1 1,3 1,5 1,8 2,0 2,2 2,5 2,7 2,9 3,0 3,1 3,2 3,4 3,5
fctk,0,95(MPa)
2,0 2,5 2,9 3,3 3,8 4,2 4,6 4,9 5,3 5,5 5,7 6,0 6,3 6,6
Ecm(Gpa)
27 29 30 31 32 34 35 36 37 38 39 41 42 44
c1 () 1,8 1,9 2,0 2,1 2,2 2,25 2,3 2,4 2,45 2,5 2,6 2,7 2,8 2,8cu1 () 3,5 3,2 3,0 2,8 2,8 2,8c2 () 2,0 2,2 2,3 2,4 2,5 2,6cu2 () 3,5 3,1 2,9 2,7 2,6 2,6
n 2,0 1,75 1,6 1,45 1,4 1,4c3 () 1,75 1,8 1,9 2,0 2,2 2,3cu3 () 3,5 3,1 2,9 2,7 2,6 2,6
Concrete properties(Table 3.1)
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Design Strength Values(3.1.6)
Design compressive strength, fcdfcd = cc fck /c
Design tensile strength, fctdfctd = ct fctk,0.05 /c
cc (= 0.85 (flexure) and 1,0 (shear)) and ct (= 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
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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 coef. of thermal expansion = 10 x 10-6 K-1
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Creep(3.1.4)
01,02,03,04,05,06,07,0100
50
30
1
2
3
5
10
20
t 0
(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 - = 1,8
h0 = 2Ac/u where Ac is the cross-section area and u is perimeter of the member in contact with the atmosphere
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Shrinkage(3.1.4)
Shrinkage Strain, cs, is composed of two components: Drying Shrinkage Strain, cd, develops slowly Autogenous Shrinkage Strain, ca, develops during the hardening of the
concrete.
Drying shrinkage, cdcd(t) = ds(t,ts)kh cd,0 (EC2, Exp (3.9)
Autogenous shrinkage, caca(t) = as(t)ca() (EC2, Exp (3.11)
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Annex B Creep and Shrinkage
Creep 0 is the notional creep coefficient (in Figure 3.1 the notation
used is (,t0)) (t,t0) is the creep at any time, t after time of loading, t0
Shrinkage cd,0 is the basic drying shrinkage strain cd,(t) = ds(t,ts)kh cd,0 (Section 3)
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fcd
c2
c
cu2 c0
fck
For section analysis
Parabola-rectangle
c3 cu30
fcd
c
c
fck
Bi-linear
fcm
0,4 fcm
c1
c
cu1 c
tan = Ecm
For structural analysis
Schematic
c1 () 0,7 fcm0,31cu1 () =
2,8 + 27[(98-fcm)/100]4 fcm)/100]4
for fck 50 MPa otherwise 3.5
c2 () = 2,0 + 0,085(fck-50)0,53for fck 50 MPa otherwise 2,0
cu2 () = 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 0
f forc cd c2 c cu2 c3 () = 1,75 + 0,55 [(fck-50)/40]
for fck 50 MPa otherwise 1,75
cu3 () =2,6+35[(90-fck)/100]4for fck 50 MPa otherwise 3,5
Concrete Stress Blocks(3.1.5 and 3.1.7)
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As
d
fcd
Fs
x
s
x
cu3Fc
Ac
= 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
= 0,8 for fck 50 MPa
Rectangular Concrete Stress Block (3.1.7, figure 3.5)
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Confined Concrete(3.1.9)
c2,c cu2,c
c
c
fck,c
fcd,c
0
A 2 3 ( = 2)
1 = fck,c
fck
cu
fck,c = fck (1.000 + 5.0 2/fck) for 2 0.05fck= fck (1.125 + 2.50 2/fck) for 2 > 0.05fck
c2,c = c2 (fck,c/fck)2cu2,c = cu2 + 0,2 2/fck
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Reinforcement (1)(3.2.1 and 3.2.2) EC2 does not cover the use of plain 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
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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
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0.2% uk
f0.2kft = kf0.2k
ft = kfykt
uk
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)
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ud
fyd/Es
fyk
kfyk
fyd = fyk/skfyk/s
Idealised
Design
uk
ud= 0.9 ukk = (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 (4) Design Stress/Strain Curve (3.2.7, Figure 3.8)
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Prestressing Steel (1)(3.3.1 and 3.3.2)
Unlike EN 10080 the harmonised standard for prestressing steel, EN10138, 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.
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
Adequate ductility is assumed if fpk/fp0,1k 1.1 the mean density of prestressing tendons may be taken as 7850
kg/m3
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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.
-
Eurocode 2
Durability and Cover
-
Concrete Cover
The Nominal Cover, Cnom, the cover specified on the drawings, is defined as:
Cnom = Cmin + Cdev
Cmin = max{Cmin,b; Cmin,dur; 10mm}
Bond durability
-
Durability of Structures
Cover density and quality is achieved by:
Controlling the maximum water/cement ratio
Controlling the cement content.
but 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
-
Minimum Cover for Durability, cmin,dur The UK National annex provides a table for cmin,dur
In EC2 this can be modified by further factors
But in the UK these are all 0
ie: Values of cdur,, 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
-
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= lCminb= m
ml
-
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
-
Fire
BS EN 1992 1-2
Tabular Data
Simplified Methods
Axis Distance a is specified (not cover). This is distance from the face to the centre of the main bar.
(Fire will be covered in Lecture 3)
a AxisDistance
-
Cover Example (Fire and Durability) What are the nominal cover and element size for a car
park slab with hour fire resistance?
Assume the max bar size in the slab is 20mm.
Assume the concrete is C28/35 with cement type IIIB
Assume design life 50 years and in-situ construction
-
Cover Example
BOND
EC2-1-1 Table 4.2 (4.2)
DURABILITY
EC2-1-1 Table 4.1 (Table 4.1)
BS8500-1:2006 Table A.4 (Table 4.2)
DEVIATION
EC2-1-1Cl. 4.4.1.3 (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
-
Cover Example
BOND
EC2-1-1 Table 4.2 (4.2)
DURABILITY
EC2-1-1 Table 4.1 (Table 4.1)
BS8500-1:2006 Table A.4 (Table 4.2)
DEVIATION
EC2-1-1Cl. 4.4.1.3 (4.5)
FIRE
EC2-1-2 Table 5.8 (Table 4.7)
Cminb = 20mm
Durability Class = XD3
Cmindur = 45mm
Cdev = 10mm
Min thickness hs= 60mm
Min axis distance a= 10mm
Nominal Cover governed by durability = 55mm
-
Eurocode 2
Structural Analysis
-
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 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 affect 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
-
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)
-
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 0,4 + (0,6 + 0,0014/cu2)xu/d 0,7 for Class B and C reinforcement 0,8 for Class A reinforcement
where 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)
-
05
10
15
20
25
30
35
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60x /d
%
r
e
d
i
s
t
fck =70 fck =60 fck =50
Redistribution Limits for Class B & C Steel
-
05
10
15
20
25
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60x /d
%
r
e
d
i
s
t
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 1500mmrib depth below flange 4bflange 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)
-
bb1 b1 b2 b2
bw
bw
beff,1 beff,2
beff
beff = beff,i + bw bWhere beff,i = 0,2bi + 0,1l0 0,2l0 and beff,I bi
l3l1 l2
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)
-
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, ll = 0 h m where 0 = 1/200h = 2/l; 2/3 h 1m = (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 = i l0/2 for walls and isolated columns ei = l0/400
Hi = iN for unbraced membersHi = 2iN for braced members
or
Unbraced Braced
Isolated Members(5.2)
-
Na
Nb
Hi
l
i
iNa
Nb
Hi
/2i
/2i
Bracing System Floor Diaphragm Roof
Hi = i (Nb-Na) Hi = i (Nb+Na)/2 Hi = i Na
Structures(5.2)
-
lx (> ly)
ly
ly/4 ly/4
ly/4
ly/4
= lx - ly/2
= ly/2
= ly/2 A
B
B
A Column strip
B Middle strip
Negative moments Positive moments Column Strip
60 - 80%
50 - 70%
Middle Strip
40 - 20%
50 - 30%
Note: Total negative and positive moments to be resisted by the column and middle strips together should always add up to 100%.
Equivalent Frame Analysis Annex I
Eurocode 2MaterialsDurability and CoverStructural Analysis