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1
Reinforced Concrete
Structures 1 - Eurocodes
RCS 1
Professor Marwan SADEKhttps://www.researchgate.net/profile/Marwan_Sadek
https://fr.slideshare.net/marwansadek00
Email : [email protected]
If you detect any mistakes, please let me know at : [email protected]
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PLAN – RCS1
M. SADEK
Ch 1 : Generalities – Reinforced concrete in practice
Ch 2 : Evolution of the standards – Limit states
Ch 3 : Mechanical Characteristics of materials – Constitutive relations
Ch 4 : Durability and Cover
Ch 5 : Beam under simple bending – Ultimate limit state ULS
Ch 6 : Beam under simple bending – serviceability limit state SLS
Ch 7 : Section subjected to pure tension
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3
Selected ReferencesFrench BAEL Code (91, 99)
Règles BAEL 91 modifiées 99, Règles techniques de conception et de calcul des ouvrages et constructions en béton armé, Eyrolles, 2000. J. Perchat (2000), Maîtrise du BAEL 91 et des DTU associés, Eyrolles, 2000. J.P. Mougin (2000), BAEL 91 modifié 99 et DTU associés, Eyrolles, 2000.….
EUROCODES H. Thonier (2013), Le projet de béton armé, 7ème édition, SEBTP, 2013. Jean-Armand Calgaro, Paolo Formichi ( 2013) Calcul des actions sur lesbâtiments selon l'Eurocode 1 , Le moniteur, 2013. J. M. Paillé (2009), Calcul des structures en béton, Eyrolles- AFNOR, 2009. Jean Perchat (2013), Traité de béton armé Selon l'Eurocode 2, Le moniteur,2013 (2ème édition) Manual for the design of concrete building structures to Eurocode 2, TheInstitution of Structural Engineers, BCA, 2006. A. J. Bond (2006), How to Design Concrete Structures using Eurocode 2, Theconcrete centre, BCA, 2006.https://usingeurocodes.com/
M. SADEK
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4
In addition to Eurocodes, the references that are mainly used to prepare this course material are : Thonier 2013
Perchat 2013
Paillé 2009
Some figures and formulas are taken from
Cours de S. Multon - BETON ARME Eurocode 2 (available on internet)
Cours béton armé de Christian Albouy
M. SADEK
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5
CHAPTER 2
Evolution of the STANDARDS – LIMIT STATES
M. SADEK
1. Introduction – Design standards
2. Eurocodes
3. EC0 / Semi –probabilistic methods
4. Limit states
5. Actions – Eurocode 1
6. Combinations of Actions (SLS- ULS)
Annexes
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Design standards / History
M. SADEK
Admissible stresses : BA45, BA60, CCBA68
( Safety factor applied on the resistance of materials, + use of linear elastic model)
Limit states : BAEL 83, BAEL 91, modifiée 99
other: ACI, BS, SIA
Eurocodes (EC2 –Reinforced & Prestress Concrete) : limit state
concept used in conjunction with a partial factor method
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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The EUROCODES
The EN Eurocodes are a series of 10 European Standards, EN
1990 - EN 1999, providing a common approach for the design of
buildings and other civil engineering works and construction
products
Three official languages (English, French, German)
These european standards « EUROCODES » are intended to
harmonize the design regulations inside the European union.
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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The clauses of EUROCODES are composed of the Principles and
Application Rules :
The Principles, identified by the letter (P) comprise the general
statements and definitions for which there is no alternative, as well
as requirements and analytical models for which no alternative is
permitted unless specifically stated.
The Application Rules are generally recognized rules which
comply with the Principles and satisfy their requirements.
NOTE :The Eurocodes are applicable for the design of new structures, but the principles, the basicrequirements and the application rules of EN1990 are applicable for the structural appraisal ofexisting construction, in developing the design of repairs and alterations or in assessing changesof use.
The EUROCODES
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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9M. SADEK
EUROCODES establish fundamental requirements in order to reach an appropriate
level of performance in terms of structural reliability mainly :
The structural SAFETY OF PEOPLE
The SERVICEABILITY and FUNCTIONING of the structure
The STRUCTURAL INTEGRITY in accidental situations
The DURABILITY, with regard to environmental conditions
The EUROCODES
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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LIST OF EUROCODES
Nb of StandardsBasis of structural design EC 0 2ACTIONS EC 1 10CONCRETE EC 2 4STEEL EC 3 20COMPOSITE EC 4 3TIMBER EC 5 3MASONARY EC 6 4GEOTECHNIC EC 7 2EARTHQUAKE EC 8 6ALUMINIUM EC 9 5
NOTA : The 10 Eurocodes constitute a group of 59 parts ( 30 until 2005)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Links between EUROCODES
Structural safety, service-
ability and durability
Actions on structures
Design and detailing
Geotechnics & Earthquake
EN 1991
EN 1990
EN 1992 EN 1993 EN 1994
EN 1995 EN 1996 EN 1999
EN 1997 EN 1998
The EUROCODES
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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12M. SADEK
Typical Layout
• National Title Page
• National Foreword
• EUROCODE – MAIN TEXT
• NORMATIVE ANNEXES
• INFORMATIVE ANNEXES
• NATIONAL ANNEX
(Professional rules)
European STANDARD
French Standard
NATIONAL STANDARDS IMPLEMENTING EUROCODES
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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13M. SADEK
EUROCODE 2 French Standard NF EN 1992
DESIGN OF CONCRETE STRUCTURES:
EN 1992-1-1 : General rules, and rules for buildings (2005)
FNA - French National Annex (2007)
Professional recommendations (2007)
EN 1992-1-2 : Structural fire design
EN 1992-2 : Reinforced and prestressed concrete bridges
EN 1992-3 : Liquid retaining and containing structures
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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14M. SADEK
The EUROCODES for the design of RC buidings
EUROCODE Part D’EUROCODE TITRE ET/OU OBJET
EN 1990 – Basis of structural designMain part
Fundamental requirements. Design principle at Limit states using the partial factor method.
AnnexeA1 Combinations of actions – application for buildings
EN 1991 : Eurocode 1 – Actions on structures
Part 1-1 Densities, self-weight, imposed loads for buildings
Part 1-2 Actions on structures exposed to fire.
Part 1-3 General actions - Snow loads
Part 1-4 General actions - Wind actions
Part 1-5 General actions - Thermal actions
Part 1-6 General actions - Actions during execution.
Part 1-7 General actions - Accidental Actions
EN 1992 : Eurocode 2 – Design of concrete structures Part 1-1 General rules, and rules for buildings
Part 1-2 Structural fire design
EN 1997 : Eurocode 7 – Geotechnical design Part 1 General rules - Design of foundation
EN 1998 : Eurocode 8 – Design of structures for earthquake resistance
Part 1 General rules, seismic actions and rules for buildings.
Part 5 Foundations, retaining structures and geotechnical aspects
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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15M. SADEK
L’EUROCODE 0 : BASIS OF STRUCTURAL DESIGN
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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16M. SADEK
L’EUROCODE 0 : BASIS OF STRUCTURAL DESIGN
Several factors are likely to affect the safety of a construction
• Definition of the applied actions (Actions)
• Properties of the materials
• Definition of the internal forces (Effect of actions)
• Methods and design assumptions
• Execution method / qualification of employees
Safety
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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17M. SADEK
Origin of Probabilism
A limit state could be reached due to combined effect of several random factors
of uncertainties. The basic idea of probabilism is to limit the probability of
reaching a limit state by taking into account the random character of :
Uncertainty in material property
Uncertainty in representative values of actions
Model uncertainty in actions and action effects (internal forces M,
N, T ..)
Model uncertainty in structural resistance
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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18M. SADEK
L’EUROCODE 0 : BASIS OF STRUCTURAL DESIGN
SEMI-PROBABILISTIC Method in conjunction with Partial factor
of safety (Actions, resistance, effects)
LIMIT STATE CONCEPT
The design method at « Limit State » apply the partial factor ofsafety on the material Resistance and on the Actions (and theireffect)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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19M. SADEK
Check using the PARTIAL FACTOR METHOD
Fd : design value of the Action
Fk : Characteristic value of the Action
Frep : Representative value of the Action
f : partial factor for the Action accounting for model uncertainties and
dimensional variations
ψ = ψ0, ψ1 ou ψ2 (factors of combinations)
1) Design values of actions (Fd)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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20M. SADEK
2) Design Value of the effect of the action (Ed)
ad : Design values of geometrical data
Sd : Partial factor associated with the uncertainty of the action and/or
action effect model
Check using the PARTIAL FACTOR METHOD
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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21M. SADEK
Check using the method of partial factors
3) Design value of a material property (Xd)
Xk : Characteristic value of a material property
: mean value of the conversion factor that take in account the scale
effect, humidity, temperature ..
m : Partial factor for a material property
(ex : 1.5 the concrete, 1.2 pour the steel)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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22M. SADEK
Semi – Probabilistic Method
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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23M. SADEK
INDICATIVE DESIGN WORKING LIFE
DESIGN WORKINGLIFE CATEGORY
Indicative design
working life (years)
FNA EXAMPLES
1 10 10Temporary structures
2 10-25 25 Replaceable structural parts, e.g. gantry girders,
3 15-30 25Agriculture and similar structures
4 50 50 Buildings structures and other common structures
5 100100 Monumental building structures, bridges and other civil
engineering structures
The design working life should be specified. Table 2.1 of EN 1990 proposes:
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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24M. SADEK
PRINCIPLE OF
LIMIT STATE DESIGN
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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25M. SADEK
PRINCIPLE OF LIMIT STATE DESIGN
A limit state is a condition of a structure beyond which it no
longer fulfills the relevant design criteria.
Ultimate Limit State (ULS)
Serviceability Limit State (SLS)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Ultime Limit State (ULS)
M. SADEK
Maximum capacity of the structure (people and structural safety)
Exceeding ULS Immediate Collapse
Based on Eurocodes, We distinguish the following ULS:
1. Loss of static equilibrium of the structure or any part (EQU)
2. Internal failure or excessive deformation of the structure or structural
members (STR)
3. Failure or excessive deformation of the ground (GEO)
4. Fatigue failure (FAT)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Ultime Limit State (ULS)
M. SADEK
1. Loss of static equilibrium (EQU)
Ex : Sliding or Overturning of a retaining Wall : earth pressure,
friction …
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Ultime Limit State (ULS)
M. SADEK
2. Structural failure (STR)
2.a) Résistance of materials:
Failure of one or several structural elements even if the global
equilibrium is ok (beam subjected to bending or shear..)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Ultime Limit State (ULS)
M. SADEK
2. Structural failure(STR)
2.b) Elastic instabilities : Buckling of columns, lateral torsional
buckling of beams
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Serviceability Limit State - SLS
M. SADEK
The SLS are associated with conditions of normal use. They concern
the functioning of the structure, confort of people.
Strain, vibration, cracking..
We distinguish the following SLS:
1. Stress limitation (Steel & Concrete)
2. Crack control (crack width)
3. Deflection control
Other : Vibration, Thermal or sound insulation…
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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31M. SADEK
1. Stress limitation in Steel and Concrete: In order to limit the
longitudinal cracks, micro cracks or high creep ..
Serviceability Limit State - SLS1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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32M. SADEK
2. Crack Control : Cracks should not be unsightly or wide
enough to lead to durability problems. It depends on several
parameters (steel-concrete bond, minimum cover..)
Definition of Exposure Classwmax 0.4, 0.3 ou 0.2 mm
Serviceability Limit State - SLS1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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33M. SADEK
3. Deflection control (Appropriate limiting values of deflection)
Serviceability Limit State - SLS1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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ACTIONS (LOADS)
Eurocode 1
M. SADEK
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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ACTIONS (Loads)(EN 1991 – Part 1)
M. SADEK
Forces induced by the applied loads and/or imposed deformation
to a construction.
Different sources :
Permanent load
Variable Load (Live load)
Climate load
Imposed deformation : Temperature variation,
soil settlement ..
Earthquake, Fire
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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ACTIONS (Loads)
M. SADEK
Fk : Characteristic value of an Action
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Classification of Actions
M. SADEK
1. Permanent Loads
2. Variable loads
3. Accidental loads
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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38M. SADEK
1. Permanent loads (characteristic value Gk : low variability ,
represented by mean value, see Annex A for densities)
Self Weight of the structure
Weight of equipments : cladding, machines in industries
Weight, earth pressure, liquid pressure (constant level)
…
NOTE: In some cases, the variation in permanent load should be taken in account
(when the difference becomes significant)
Ex : asphalt pavement layer (± 20 %)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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39M. SADEK
2. Variable loads
imposed loads (or Live load) in a building or a bridge (Q)
Climatic Action : Wind (W), Snow (S))
Uniform or differential variation of temperature (T ou T)
Moving loads (Trucks, trains ..)
..
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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40M. SADEK
3. Accidental Action FA
Non common, quick
Only at ULS
Accident of a truck on a bridge
Fire
Earthquake (E)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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41M. SADEK
Characteristic values of Imposed Loads (NF-EN 1991-1-1, 6.3)The Residential, social, commercial and administration areas in buildings are classified in Four categories (Table 6.1)
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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42M. SADEK
Imposed loads in buildings (NF-EN 1991-1-1, 6.3)
qk (uniformly distributed load –general effect)
Qk (concentrated load impact on 50x50 mm²-local effect)
EC1
Example : Imposed loads on floors, balconies and stairs in buildings (Table 6.2)
FNA
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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43M. SADEK
Imposed loads in buildings (NF-EN 1991-1-1, 6.3)
Example : : Imposed loads on floors, balconies and stairs in buildings
Additional load due to partition
movable partitions with a self-weight ≤ 1,0 kN/m wall length : qk = 0,5 kN/m²
movable partitions with a self-weight ≤ 2,0 kN/m wall length : qk = 0,8 kN/m²
movable partitions with a self-weight ≤ 3,0 kN/m wall length : qk = 1,2 kN/m²
In lebanon : It is recommended to take an additional load of partitions :
150 to 200 daN/m²
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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44M. SADEK
Imposed loads in buildings (NF-EN 1991-1-1, 6.3)
Other aspects (see annexes)
Storage
Parking
Horizontal reduction factor
Vertical reduction factor
..
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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Combinations of Actions (EC0)
M. SADEK
The assessment of internal forces (N, T, M) is done on the basis of
load combination
Combination ULS
Combination SLS
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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46M. SADEK
Characteristic value of a permanent action Gk
Gk,sup Characteristic value of unfavourable Permanent action for the design of a
given element (Earth pressure on a retaining wall)
Gk,inf Characteristic value of favourable Permanent action for the design of a
given element (Earth pressure on a retaining wall) (soil Self weight on a
retaining wall)
Characteristic Value of the Action
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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47M. SADEK
Characteristic value of a single variable action Qk
Combination value, 0Qk
Frequent value, 1Qk
Quasi-permanent value 2Qk
Characteristic Value of the Action
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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48M. SADEK
Table A1.1 / EN1990 – Recommended values of factors for buildings
Characteristic Value of the Action1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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49
Combinations of Actions ULS (STR)
M. SADEK
1. Fundamental Combination
To simplify, for buildings
When considering the critical variable action
When considering leading and accompanying variable Actions
G : Partial factor for permanent actions G =1.35 if G unfavourable, 1, if favourable
Q,1 : Partial factor for variable action , Q,1 =1.5 for leading and accompanying variable Action
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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50M. SADEK
2) Accidental Combination
Combinations of Actions ULS (STR)
3) Seismic Combination
Ad : design value of an accidentel action
1,1 : if fire
AEd :design value of action due to Earthquake ground motion
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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51M. SADEK
1) Characteristic Combination :
Combinations of Actions SLS
2) Frequent Combination :
3) Quasi-permanent Combination
1. Introduction 2. Eurocodes 3. EC0/Semi probabilism 4. Limit States 5. Actions 6. Combinations of Actions
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52
Annexes
M. SADEK
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53M. SADEK
Selected Parts of ANNEX A (EC1 – part 1.1)Construction materials -Tables A1 A12
Table A.1 - Concrete and mortar
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54M. SADEK
Selected Parts of ANNEX A (EC1 – part 1.1)Construction materials -Tables A1 A12
TableA.2 - Masonry
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55M. SADEK
ANNEX A (EC1 – part 1.1)
Table A.3 - Timber Table A.4 - Metals
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56M. SADEK
ANNEXE A (EC1 – Part 1.1)Table A.7 - Stored Materials
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57M. SADEK
Extracted parts (EC1 – part 1.1 - 6.3)
Storage Areas, Parking
Reduction Factors
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58M. SADEK
Extracted from (EC1 – Part 1.1) Characteristic values of imposed load
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59M. SADEK
Extracted from (EC1 – Part 1.1 - 6.3)
Characteristic values of imposed load
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60M. SADEK
Characteristic values of imposed load
The recommended value for the horizontal reduction factor for floors and roofs :
French National Annex
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61M. SADEK
Characteristic values of imposed load
The recommended value for the vertical reduction factor for columns
and walls
N : is the number of storeys (> 2) above the loaded structural elements from the same category
French National Annex
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62M. SADEK
Reminder about Units
Length en (m)
1 m = 100 cm
(precision in R.C: 1 cm / sometimes 0.5 cm)
(in steel structures : 1 mm)
Force (N)
10 N = 1 daN = 1 kg (kgf )
1 MN = 103 kN = 100 T (Tf)
Pressure /Stress (Pa)
1 Pa = 1 N/m²
1 MPa = 106 Pa = 1 N/mm²
1 MPa = 10 bars = 100 T/m²
1 bar = 1 kg/cm²
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63M. SADEK
Exercices
Load / m² on a slab
Combinations of actions SLS , ULS
Numerical example / Determination of maximum forces
Total load / Load on columns
Load on beam (/ m)