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Twinning Latvia EN 1990: Basis of Structural Design 1 Content Page Codes and Literature 3 List of figures 6 List of tables 6 EN 1990 Basis of Structural Design 7 Foreword 7 General 10 Scope 10 Distinction between Principles and Application Rules 10 Structural design and structural safety 11 Assumptions 11 Requirements 13 Basic requirements for structures 13 Limiting or avoiding of potential damage 17 Reliability management 18 Design working life 19 Durability 20 Quality management 20 Principles of limit states design 21 General 21 Design situations 22 Ultimate limit states 22 Serviceability limit states 23 Limit state design 24 Basic variables 25 Actions and environmental influences 25 Classification of actions 25 Characteristic values of actions 25 Other representative values of variable actions 27 Representation of fatigue actions 28 Representation of dynamic actions 28 Geotechnical actions 28 Environmental influences 28 Material and product properties 29 Geometrical data 30 Structural analysis and design assisted by testing 30 Structural analysis 30 Structural modelling 30 Static actions 30 Dynamic actions 30 Fire design 31 Design assisted by testing 32 Verification by the partial factor method 32 General 32 Limitations 32

Twinning Latvia EN 1990: Basis of Structural Design 2

Design values 33 Design values of actions 33 Design values of material or product properties 33 Design values of geometrical data 33 Design values of the effects of actions 34 Design resistance 38

Ultimate limit states 40 General 40 Verifications of static equilibrium and resistance 41 Combination of actions (fatigue verifications excluded) 42 Partial factors for actions and combinations of actions 46 Partial factors for materials and products 46

Serviceability limit states 47 Verifications 47 Serviceability criteria 47 Combination of actions 47 Partial factors for materials 48

Annex A1 (normative) Application for Buildings 49 Field of application 49 Combinations of actions 49

General 49 Values of y factors 50

Ultimate limit states 51 Design values of actions in persistent and transient design situations 51 Design values of actions in the accidental and seismic design situations 56

Serviceability limit states 58 Partial factors for actions 59 Serviceability criteria 59 Deformations and horizontal displacements 59 Vibrations 59

Examples for Application of Annex A1 60 Example A-1: Marquee structure 60 Example A-2: Reinforced concrete slab for a roof terrace 64 Example A-3: Supporting beam 67 Example A-4: Continuous beam under bending 70 Example A-5: Reinforced concrete column and foundation subjected to normal force and bending moment 72

Annex B (informative) Management of Structural Reliability for Construction Works 90

Scope and field of application 90 Reliability differentiation 90

Consequences classes 90 Differentiation by b values 91 Differentiation by measures relating to the partial factors 92

Design supervision differentiation 92 Inspection during execution 93 Partial factors for resistance properties 93

Annex C (informative) Basis for Partial Factor Design and Reliability Analysis 94


Scope and Field of Applications 94 Symbols 94 Introduction 95 Overview of reliability methods 96 Reliability index b 100 Target values of reliability index b 110 Approach for calibration of design values 112 Reliability verification formats in Eurocodes 122 Partial factors in EN 1990 123 y0 factors 124 Examples due to the Basis of Reliability Analysis 132

Example C-1: Calculation of the failure probability by numerical integration 132 Example C-2: Reliability index for the bending capacity of a reinforced concrete joist 134 Example C-3: Reliability index for the bending capacity of a steel beam 136 Example C-4: Log Normal Distribution applied to material strengths 139 Example C-5: Gumbel Distribution applied to variable actions 140 Example C-6: Gumbel Distributions referred to different reference periods 141 Example C-7: Snow load referred to different reference periods 142 Example C-8: Determination of the design point applying the Rackwitz-Fieler-Algorithm 143 Example C-9: Design values of a reinforced concrete joist applying fixed sensitivity factors 147 Example C-10: Design value and partial factor for a snow load148 Example C-11: Combination of an imposed load with a snow load 149 Example C-12: Combination of a wind load with a snow load 151 Example C-13: Combination of a wind load with an imposed load 151 Example C-14: Combination of an imposed load with a permanent load 152

Codes and Guidelines

[89/106/EWG 88]

Council Directive 89/106/EEC on construction products from 21 December 1988 CPD (Authority paper EC, L40/1989, p. 1).

[ISO/FDIS 2394 98]

International Standard ISO/FDIS 2394 General principles on reliability for structures Final Draft 1998. International Organization for Standardization, Switzerland.

[EN 1990 02]

European Committee for Standardization (CEN): EN 1990: Basis of Structural Design. Edition April 2002.


[TC1/015 91]

Commission of the European Community: Interpretative Document Mechanical Resistance and Stability". Final Draft May 1991. Document TC1/015.

[DIN 1055-100 01]

DIN 1055-100: Grundlagen der Tragwerksplanung, Sicherheitskonzept, Bemessungsregeln. Ausgabe Mrz 2001.

[DIN 4149-1 00]

Bauten in deutschen Erdbebengebieten Teil 1: Lastannahmen, Bemessung und Ausfhrung blicher Hochbauten. Bearbeitungsstand 2000.

[DIN 18000-1 90]

DIN 18 000 Teil 1: Stahlbauten; Bemessung und Konstruktion. Ausgabe November 1990.

[DIN 1045-1 01]

DIN 1045-1: Tragwerke aus Beton, Stahlbeton und Spannbeton Teil 1: Bemessung und Konstruktion. Ausgabe Juli 2001.

Berichtigung 2 zu DIN 1045-1. Ausgabe Juni 2005.

[DIN 1054 05]

DIN 1054: Baugrund Sicherheitsnachweise im Erd- und Grundbau. Ausgabe Januar 2005.

[EN 1991-1-1 02]:

EN 1991-1-1 Eurocode 1: Actions on structures, Part 1-1: General actions: Densities, self-weight and life loads on buildings. Edition April 2002.

[EN 1991-1-3 03]:

EN 1991-1-3 Eurocode 1: Actions on structures, Part 1-3: General actions: Snow loads. Edition July 2003.

[EN 1991-1-4 05]:

EN 1991-1-4 Eurocode 1: Actions on structures, Part 1-4: General actions: Wind loads. Edition April 2005.

[EN 1991-1-5 03]:

EN 1991-1-5 Eurocode 1: Actions on structures, Part 1-5: General actions: Thermal actions. Edition Nov. 2003.

[EN 1991-1-7 05]:

EN 1991-1-7 Eurocode 1: Actions on structures, Part 1-7: General actions: Accidental actions. Draft 2005.

[EN 1991-2 03]

EN 1991-2 Eurocode 1: Actions on structures, Part 2: Traffic loads on bridges. Edition September 2003.

[EN 1992-1-1 04]

EN 1992-1-1 Eurocode 2: Design of concrete structures Part 1-1: General rules and rules for buildings. Edition December 2004.

[EN 1997-1 04]

EN 1997-1 Eurocode 7: Geotechnical design Part 1: General rules. Edition November 2004.

[EN 1998-1 06]

EN 1998 Eurocode 8: Design of structures for earthquake resistance, Part 1: Fundamentals. Edition April 2006.


Cited Literature

[BoD-doc 96]

European Convention for Constructional Steelwork: Background Documentation Eurocode 1 (ENV 1991) Part 1: Basis of Design. March 1996

[FIB-MC 90 99]

Structural Concrete Textbook on Behaviour, Design and Performance. Updated knowledge of the CEB/FIP Model Code 1990 Volume 2: Basis of Design. International Federation for Structural Concrete (fib) 1999

[Grnberg 98]

Grnberg, J.: Eurocode-Sicherheitskonzept: Lassen sich die Lastkombinationen vereinfachen? Der Prfingenieur April 1998

[Grnberg, Klaus 99]

Grnberg, J., Klaus, M.: Bemessungswerte nach Eurocode-Sicherheitskonzept fr Interaktion von Bean-spruchungen. Beton- und Stahlbetonbau 3 (1999), S. 114

[Grnberg, Klaus 01]

Grnberg, J., Klaus, M.: Diagramme fr die gezielte Querschnittsbemessung bei Interaktion von Lngskraft und Biegemoment nach DIN 1045-1. Beton- und Stahlbetonbau 8 (2001), S. 539

[Grnberg 04]

Grnberg, J.: Grundlagen der Tragwerksplanung Sicherheitskonzept und Bemessungsregeln fr den konstruktiven Ingenieurbau. Erluterungen zu DIN 1055-100. Praxis Bauwesen, Beuth Verlag 2004.

[GRUSIBAU 81]

DIN Deutsches Institut fr Normung e.V.: Grundlagen zur Festlegung von Sicherheitsanforderungen fr bauliche Anlagen. 1. Auflage. Berlin / Kln: Beuth Verlag GmbH 1981

[Knig, Hosser, Schobbe 82]

Knig, G., Hosser, D., Schobbe, W.: Sicherheits-anforderungen fr die Bemessung von baulichen Anlagen nach den Empfehlungen des NABau eine Erluterung. Der Bauingenieur 57 (1982), Seite 69 bis 78

[Schobbe 82]

Schobbe, W.: Konzept zur Definition und Kombination von Lasten im Rahmen der deutschen Sicherheitsrichtlinie. Ernst & Sohn 1982

[Schuller 81]

Schuller, G. I.: Einfhrung in die Sicherheit und Zuverlssigkeit von Tragwerken. W. Ernst & Sohn 1981

[Spaethe 92]

Spaethe, G.: Die Sicherheit tragender Baukonstruktionen. Springer 1992


List of figures

Fig. 1: Action model (load arrangement) 14 Fig. 2: Structural model 15 Fig. 3: Material Law 15 Fig. 4: Representative values of a variable action 28 Fig. 5: Predominant action effect EQd,1 = E (Qk,1; gQ,1)

in non-linear structural analysis 36 Fig. 6 Relation between individual partial factors 39 Fig. 7: Limit state of static equilibrium

(here: safety against lifting off) 42 Fig. 8: Interface at the joint between foundation and subsoil and

load transfer 54 Fig. 9: Example for structural design of a foundation subjected

to second order effects 55 Fig. 10: Overview of reliability methods 96 Fig. 11: Limit state equation in the original x-space 103 Fig. 12: Limit state equation in the standardized y-space 103 Fig. 13: Distribution density of the random variable u1 104 Fig. 14: Transformation relations according to FORM 108 Fig. 15: Linearization of the limit state equation in the design

point 109 Fig. 16: Gumbel distribution, at the design point xd (yd)

approximated by a Standard Normal Distribution 113 Fig. 17: Sensibility factors fixed with respect to the limit state

expressed in standardized y-coordinates 114 Fig. 18: Sensibility factors in case of two simultaneous actions116 Fig. 19: Partial factors for variable actions 123 Fig. 20: Borges-Castanheta-Model 125 Fig. 21: Distribution densities of a single variable action Q2,

in accordance to the significant time intervals 126 Fig. 22: Determination of the maximum value Emax 126 Fig. 23: Combination factors y0,i for variable actions Qi 130

List of tables

Table 1: Indicative design working life 19 Table 2: Systematics of verification procedure 21 Table 3: Single actions for buildings 49 Table 4: Recommended values of y factors for buildings 50 Table 5: Recommended values for partial factors gF 57 Table 6: Relation between b and Pf 100 Table 7: Reliability index and failure probability 105 Table 8: Target reliability index b for Class RC2 structural

members 1) 111 Table 9: Design values for various distribution functions 117 Table 10: Partial factors depending on the variation coefficients 124 Table 11: Expressions for yo in case of two variable actions 124 Table 12: Basic time intervals T1 for single actions 128 Table 13: Assembly of combination factors y0,i 131


EN 1990 Basis of Structural Design

Foreword

This document (EN 1990: 2002) has been prepared by Technical Committee CEN/TC 250 Structural Eurocodes. Conflicting national standards shall be withdrawn at the latest by March 2010.

[EN 1990 02], Foreword

Background of the Eurocode programme

In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.

Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them.

In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN).

CEN:

European Committee for Standardization

Comit Europen de Normalisation

This links de facto the Eurocodes with the provisions of all the Councils Directives and/or Commissions Decisions dealing with European standards.

[89/106/EWG 88]

The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts:

EN 1990 Eurocode 0 : Basis of Structural Design

EN 1991 Eurocode 1 : Actions on structures

EN 1992 Eurocode 2 : Design of concrete structures

EN 1993 Eurocode 3 : Design of steel structures

EN 1994 Eurocode 4 : Design of composite steel and concrete structures

EN 1995 Eurocode 5 : Design of timber structures

EN 1996 Eurocode 6 : Design of masonry structures

EN 1997 Eurocode 7 : Geotechnical design

EN 1998 Eurocode 8 : Design of structures for earthquake resistance

EN 1999 Eurocode 9 : Design of aluminium structures

Responsibility of Member States

Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.


Status and field of application of Eurocodes

The Member States of the EU and EFTA recognise that EUROCODES serve as reference documents for the following purposes:

- as a means to prove compliance of building and civil engineering works with the

essential requirements of Council Directive 89/106/EEC,

particularly Essential Requirement N1 Mechanical resistance and stability

and Essential Requirement N2 Safety in case of fire ;

[89/106/EWG 88]

[TC1/015 91]

- as a basis for specifying contracts for construction works and related engineering services

- as a framework for drawing up harmonised technical specifications for construction products (ENs and ETAs)

The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards.

CPD Council Directive 89/106/EEC on construction products

The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature.

Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.

National Standards implementing Eurocodes

The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN,

which may be preceded by a National title page and National foreword

and may be followed by a National annex.

The National annex may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters (NDP), to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e. :

values and/or classes where alternatives are given in the Eurocode, i.e. values of g- and y-factors or establishing reliability classes,

values to be used where a symbol only is given in the Eurocode,

country specific data (geographical, climatic, etc.), e.g. snow map, wind zones, earthquake zones ,

the procedure to be used where alternative procedures are given in the Eurocode, i.e. concerning ground structure interaction,

decisions on the application of informativ annexes, i.e. treating them as normative in the Member State,

references to non-contradictory complementary information to assist the user to apply the Eurocode.

A wide field of interpretation! Therefore, see Guidance Paper L


Links between Eurocodes and products harmonised technical specifications (ENs and ETAs)

There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works.

Furthermore, all the information accompanying the CE Marking of the construction products which refer to Eurocodes should clearly mention which Nationally Determined Parameters have been taken into account.

Intended users of EN 1990

EN 1990 is intended for use by :

committees drafting standards for structural design and related product, testing and execution standards ;

clients (e.g. for the formulation of their specific requirements on reliability levels and durability) ;

designers and constructors;

relevant authorities.

EN 1990 may be used as a guidance document for the design of structures outside the scope of EN 1991 to EN 1999, for :

assessing other actions and their combinations ;

modelling material and structural behaviour;

assessing numerical values of the reliability format. See [EN 1990 02], annexes B and C, for example

Numerical values for partial factors and other reliability parameters are recommended as basic values that provide an acceptable level of reliability.

They have been selected assuming that an appropriate level of workmanship and of quality management applies.

When EN 1990 is used as a base document by other CEN/TCs the same values need to be taken.

National Annex for EN 1990

This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made.

Therefore the National Standard implementing EN 1990 should have a National annex containing all Nationally Determined Parameters to be used for the design of buildings and civil engineering works to be constructed in the relevant country.

National choice is allowed in EN 1990 through clauses :

- A1.1(1)

- A1.2.1(1)

- A1.2.2 (Table A1.1)

- A1.3.1(1) (Tables A1.2(A) to (C))

- A1.3.1(5)

- A1.3.2 (Table A1.3)

- A1.4.2(2)


General [EN 1990 02], Section 1

Scope [EN 1990 02], 1.1 Scope

EN 1990 establishes the Principles and requirements for

safety,

serviceability

and durability

of structures, describes the basis for their design and verification and gives guidelines for related aspects of structural reliability.

Clause (1)

(as referred to [TC1/015 91])

It is based on the limit state concept

used in conjunction with a partial factor method.

EN 1990 is intended to be used in conjunction with Eurocodes EN 1991 to 1999 for the structural design of new structures, i.e. buildings and civil engineering works, including

geotechnical aspects,

structural fire design,

situations involving earthquakes,

execution and temporary structures.

Clause (2)

(i.e. direct application)

EN 1990 also gives guidelines for the aspects of structural reliability relating to safety, serviceability and durability :

for the design of structures where other materials or other actions outside the scope of EN 1991 to 1999 are involved.

Clause (3)

to serve as a reference document for other CEN TC's concerned with structural matters.

EN 1990 also is applicable for

the structural appraisal of existing construction,

in developing the design of repairs

and alterations or in assessing changes of use.

Clause (4)

Distinction between Principles and Application Rules

[EN 1990 02], 1.4 Distinction between Principles and Application Rules

Depending on the character of the individual clauses, distinction is made in EN 1990 between Principles and Application Rules.

Clause (1)

The Principles are identified by the letter P following the paragraph number. They comprise :

Clause (2)

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.

Clauses (3) and (4)

It is permissible to use alternative design rules, provided that they accord with the relevant Principles and are at least equivalent with regard to the structural safety, serviceability and durability to be expected when using the Eurocodes.

Clause (5)


Structural design and structural safety

Structural design of buildings and civil engineering works means:

The design of the structure in the whole as well as of their structural members (slabs, columns, walls, footings) has to be performed with respect to the approved rules of engineering.

These rules are based on the sum of experiences in engineering, and they are well developed in practical application.

They are generally recognized by all persons involved in building, as they are clients, architects, civil engineers in structural design and execution.

[Spaethe 92]

To assure the structural safety the following measures are required: [EN 1990 02]

1. Measures to avoid human errors (Assumptions and preconditions for structural design),

2. Measures to warrant a sufficient safety margin between action effect and structural resistance (Basic requirements for design and execution of structures),

3. Measures to prevent potential causes of failure and/or reduce their consequences (Limiting or avoiding of potential damage).

See Section 1 General 1.3 Assumptions

See Section 2 Requirements 2.1 Basic requirements

In the following these measures are described in detail.

Assumptions [EN 1990 02], 1.3 Assumptions

Design which employs the Principles and Application Rules is deemed to meet the requirements provided the assumptions given in EN 1990 to EN 1999 are satisfied (see Section 2).

Clause (1)

The general assumptions for structural design according to EN 1990 are :

1. The choice of the structural system and the design of the structure is made by appropriately qualified and experienced personnel.

2. Execution is carried out by personnel having the appropriate skill and experience.

3. Adequate supervision and quality control is provided during execution of the work, i.e. in design offices, factories, plants, and on site

4. The construction materials and products are used as specified in EN 1990 or in ENs 1991 to 1999 or in the relevant execution standards or reference material or product specifications.

5. The structure will be adequately maintained.

6. The structure will be used in accordance with the design assumptions.

Clause (2)

See also [EN 1990 02],

2.2 Reliability management, Clause (5),

2.5 Quality management, Clause (1)

These general assumptions are in the range of principles!

They are the preconditions for the safety concept and strongly connected with the basic requirements for structures.


Education

Failure analysis has shown that most of the collapse situations are generated by persons involved in building.

One possible reason for that may be the lack of knowledge.

Teaching, further studying as well as training on the job have to contribute to reduction of danger risk.

Communication

The powerful increasing of science leads to the development of specialising in all subject areas.

More and more experts are working on multidisciplinary tasks developing more and more complex.

Therefore, information and communication between the persons involved in building gain in importance increasingly.

Coordination

Because of economic necessities the special activities are divided onto different experts in design as well as onto different companies for execution.

Problems often arise at the interfaces in the design process and in the sequence of construction work.

Therefore, the coordination between these separate activities is of eminent importance.

Sense of responsibility

Human errors, as a consequence of carelessness, lack of attention or negligence, pose a potential danger.

Therefore, sense of quality and of responsibility have to be crucial task of education.

Building inspection

Only a few human errors are unavoidable and unrecognisable.

The most important procedures to detect errors and mistakes are controlling and inspection.

Controlling also induce psychological effects on the quality of workmanship.

Quality assurance

Effective strategies of controlling have to face systematically those problems which are of dominant importance for structural safety or which have the risk of errors appearing most frequently.

These procedures are most essential for quality assurance or for quality management respectively.

Human errors are not covered by the safety margins defined in the design codes!


Requirements [EN 1990 02], Section 2

Basic requirements for structures [EN 1990 02], 2.1 Basic requirements for structures

The basic requirements for structures are established in

the Interpretative Document Mechanical Resistance and Stability" associated to the Construction Product Directive

as well as in some basic codes as they are ISO 2394 or GRUSIBAU in Germany.

[TC1/015 91], [89/106/EWG 88], [GRUSIBAU 81], [ISO/FDIS 2394 98]

A structure shall be designed and executed in such a way that it will, during its intended life, with appropriate degrees of reliability and in an economical way

Clause (1)

sustain all actions and influences likely to occur during execution and use, and

remain fit for the use for which it is required.

To reach a sufficient reliability, a structure shall be designed to have adequate:

Clause (2)

structural resistance

serviceability,

and durability.

See [EN 1990 02], 2.4

To assure an adequate structural resistance the following events are not allowed to occur

collapse of the entire structure or of one structural element,

or large deformations exceeding the limits of failure.

In the case of fire, the load-bearing capacity of the structure shall be assured for the required period of time.

Clause (3)

A structure shall be designed and executed in such a way that it will not be damaged by events such as:

Clause (4)

explosion,

impact, and

the consequences of human errors,

The events to be taken into account are those agreed for an individual project with the client and the relevant authority.

to an extent disproportionate to the original cause.

The basic requirements should be met: Clause (6)

by the choice of suitable materials,

by appropriate design and detailing, and

by specifying control procedures for design, production, execution, and use relevant to the particular project.

The provisions of Section 2 should be interpreted on the basis that due skill and care appropriate to the circumstances is exercised in the design, based on such knowledge and good practice as is generally available at the time that the design of the structure is carried out.

Clause (7)

see [EN 1990 02], 1.3


The dimensions of the structure as well as the material properties have to be designed in such a way that, during its intended life, the following inequality is satisfied with a high probability:

E R (or C)

or

Z R (or C) E 0 (1)

where E Action effect (as a function of place and time)

R Structural resistance

C Serviceability criterion (i.e. permissible deformation)

Z Safety margin (or safety zone)

Z > 0 The structure is sustainable (stable) or usable (for the use intended)

Z = 0 The structure has reached the ultimate limit state (ULS) or the serviceability limit state (SLS)

Z < 0 The structure fails (collapse or large deformation) or looses its fitness for use

The satisfaction of inequality (1) would be trivial if the design engineer would not have to meet the opposite requirements of economy and low material consumption.

The intention of economical building forces the structural engineer to keep the safety margin as small as possible.

[Spaethe 92]

The engineers responsibility consists in balancing carefully the requirements for safety and for economy.

The quantities of R (or C) and E are not known precisely during the design process, because the resistances R (criteria C) do not appear before the execution whereas the actions E even do not appear before the use of the structure.

Therefore, engineers have to make decisions during the design process which are connected with a lot of risks.

To reduce these risks they need devices which enable them to judge reliably the structural behaviour in the future.

The most important resource is the structural analysis which is composed of

Assumption about the actions to be expected concerning

their magnitudes design value and

their distribution action model (load arrangement)

Fig. 1: Action model (load arrangement)


Analysis of the action effects (internal forces) and of their

transmission through the structure down to the foundation by means of

Structural models (stability systems) based on the available methods of structural analysis, as they are linear-elastic analysis, plastic analysis or other methods of non-linear analysis

see [EN 1990 02], 1.5.6 Terms relating to structural analysis

Fig. 2: Structural model

Calculation of the structural resistances resulting from the cross area dimensions in combination with the material properties (strength, material law) of the structural members and the subsoil concerning

- their magnitudes design values and

- their distribution resistance model

Fig. 3: Material Law

Between the theoretical model imagination during the design process and the real structure during its execution and its working life, there are the following deviations:

Systematic deviations (model uncertainties)

of the action models,

of the structural models,

of the resistance models

The model uncertainties depend on the insufficiencies of the calculation procedures.

By reason of the increasing capability of computers, the model uncertainties may be reduced but not be eliminated.

e

s


Stochastic deviations (variations of the mechanical parameters)

of the actions (load parameters),

of the geometrical data (dimensions) and

of the material properties.

The structural behaviour in reality only can be predicted by means of a probabilistic analysis.

To this end, stochastic models are needed on the basis of random sampling. Often the extent of sampling is not sufficient.

The variations of material and subsoil properties are influenced by the natural composition, the manufacturing and the assembly in site.

The variations of the structural geometry predominantly result from execution.

The variations of actions result from their alterations from place to place as well as from their variation in time.

The quantities of these variations are different with respect to their source (permanent actions, variable actions, accidental actions or seismic actions).

In fact, the variations of permanent actions are subjected to the same influences as the material properties, but they are significantly lower.

Reliability analysis of structures:

The influence of stochastic variations on the safety or reliability of a structure only can be analysed by means of stochastic methods.

In practise, however, simplifications are necessary which must be derived from these methods or theories.

See [EN 1990 02], Annex C

Parameter controlled safety concept:

The mechanical quantities are treated as basic variables to be identified by characteristic values.

The model uncertainties and the parameter variations are covered by partial factors.

See [EN 1990 02], Sections 3, 4, 6; Annex A1

These parameters are combined linearly and then allocated to structural models close to reality.

The action effects resulting from structural analysis have to be compared with the resistances by means of inequality (1), in order to prove structural stability.


Limiting or avoiding of potential damage

In spite of these two strategies

Measures to avoid human errors See [EN 1990 02], 1.3 Assumptions

Measures to warrant a sufficient safety margin See [EN 1990 02], 2.1 Basic requirements, Clauses (1) to (4)

errors cannot be excluded completely!

There is a remaining risk.

Furthermore, actions are possible which have not been considered in design, as they are resulting

from errors which were not detected although systematic inspections were performed,

from the stochastic coincidence of extreme events,

from exceeding the loading limits during the working life,

from hazards which are caused by persons or nature (e.g. explosions)

from insufficient knowledge and wrong activities of persons, e.g. the users of the structure who have not been informed about the loading limits

Controlling and inspection are limited to the period of design, construction and execution for most of the buildings and civil engineering works.

Exceptions are bridges, large dams and nuclear power plants.

The collapses of hall structures which occurred recently in Germany and Poland may highlight the importance of inspections with certain intervals during the working life of structures which are used by the public.

To assure structural safety, the third strategy is to reduce the consequences of failure and, especially, to avoid injuring and even killing of people.

Therefore, potential damage shall be avoided or limited by appropriate choice of one or more of the following :

avoiding, eliminating or reducing the hazards to which the structure can be subjected;

selecting a structural form which has low sensitivity to the hazards considered ;

selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage ;

avoiding as far as possible structural systems that can collapse without warning ;

tying the structural members together.

[EN 1990 02], 2.1 Basic requirements, Clause (5)

See also 2.2 Reliability management, Clauses (5) and (6)


Reliability management [EN 1990 02], 2.2 Reliability management

The reliability required for structures within the scope of EN 1990 shall be achieved:

Clause (1)

a) by design in accordance with ENs 1990 to 1999 and See also [EN 1990 02], 1.3 and 2.1

b) by appropriate execution and quality management measures. See 2.2(5) and Annex B

Different levels of reliability may be adopted inter alia : Clause (2)

for structural resistance; See [EN 1990 02], Annex C

for serviceability.

The choice of the levels of reliability for a particular structure should take account of the relevant factors, including :

Clause (3)

See also [EN 1990 02], Annex B

the possible cause and /or mode of attaining a limit state;

the possible consequences of failure in terms of risk to life, injury, potential economical losses ;

See also [EN 1990 02], 2.1: Limiting or avoiding of potential damage

public aversion to failure; Especially with respect to the use of public buildings like concert halls or large bridges

the expense and procedures necessary to reduce the risk of failure.

The levels of reliability that apply to a particular structure may be specified in one or both of the following ways:

Clause (4)

by the classification of the structure as a whole; [EN 1990 02], Annex B

by the classification of its components.

The levels of reliability relating to structural resistance and serviceability may be achieved by suitable combinations of:

Clause (5)

a) preventative and protective measures, e.g.

- implementation of safety barriers,

- active and passive protective measures against fire,

- protection against risks of corrosion such as painting or cathodic protection, etc.);


b) measures relating to design calculations:

- representative values of actions,

- the choice of partial factors;

See also [EN 1990 02], 2.1 Basic requirements: Parameter controlled safety concept

c) measures relating to quality management; See also [EN 1990 02], 1.3 Assumptions

d) measures aimed to reduce errors in design and execution of the structure, and gross human errors;



e) other measures relating to the following other design matters:

- the basic requirements,

- the degree of robustness (structural integrity),

- durability, including the choice of the design working life,

- the extent and quality of preliminary investigations of soils and possible environmental influences,

- the accuracy of the mechanical models used,

- the detailing;

f) efficient execution, e.g. in accordance with execution standards referred to in EN 1991 to EN 1999;

See also [EN 1990 02], 1.3 Assumptions

g) adequate inspection and maintenance according to procedures specified in the project documentation.

See also [EN 1990 02], 1.3 Assumptions

The measures to prevent potential causes of failure and/or reduce their consequences can, in appropriate circumstances, be interchanged to a limited extent provided that the required reliability levels are maintained.

Clause (6)

See also [EN 1990 02], 2.1 Basic Requirements, Clause (5)

Design working life [EN 1990 02], 2.3 Design working life

The design working life should be specified Clause 1

Indicative categories and according values are given in Table 1. These values may also be used for determining time-dependent performance (e.g. fatigue-related calculations).

See [EN 1990 02], Table 2.1

Table 1: Indicative design working life

Design working life category

Indicative design working life (years)

Examples

1 10 Temporary structures (1)

2 10-25 Replaceable structural parts, e.g. gantry girders, bearings

3 15-30 Agricultural and similar structures

4 50 Building structures and other common structures

5 100 Monumental building structures, bridges, and other civil engineering structures

1) Structures or parts of structures that can be removed with a view to being re-used should not be considered as temporary.

The level of reliability depends on a specified reference period which should be

- established equally to the design working life in case of permanent design situations, or

- considered in relation to the design working life in case of transient or accidental design situations.



Durability [EN 1990 02], 2.4 Durability

The structure shall be designed such that deterioration over its design working life does not impair the performance of the structure below that intended,

having due regard to its environment and the anticipated level of maintenance.

Clause (1)

In order to achieve an adequately durable structure, the following should be taken into account:

the intended or foreseeable use of the structure;

the required design criteria;

the expected environmental conditions;

the composition, properties and performance of the materials and products;

the properties of the soil;

the choice of the structural system;

the shape of members and the structural detailing;

the quality of workmanship, and the level of control;

the particular protective measures;

the intended maintenance during the design working life.

Clause (2)

The environmental conditions shall be identified at the design stage so that their significance can be assessed in relation to durability and adequate provisions can be made for protection of the materials used in the structure.

Clause (3)

The degree of any deterioration may be estimated on the basis of calculations, experimental investigation, experience from earlier constructions, or a combination of these considerations.

Clause (4)

Quality management [EN 1990 02], 2.5 Quality management

In order to provide a structure that corresponds to the requirements and to the assumptions made in the design, appropriate quality management measures should be in place. These measures comprise:

definition of the reliability requirements,

organisational measures and

controls at the stages of design, execution, use and maintenance.

Clause (1)


Principles of limit states design [EN 1990 02], Section 3

General [EN 1990 02], 3.1 General

The bearing capacity of a structure will be verified with respect to the approved rules of engineering, considering the requirements for durability, by facing of

the design values of resulting action effects and resistances

as defined for limit states and the according design situations.

Limit states

A structure does not meet any longer the requirements of design if it exceeds a limit state.

A distinction shall be made between ultimate limit states and serviceability limit states.

Clause (1)

An ultimate limit state is exceeded by collapse or similar kinds of structural failure

A serviceability limit state is exceeded when the requirements of use established for the structure or one of its elements are not fulfilled any longer.

Table 2: Systematics of verification procedure [DIN 1055-100 01], Table 1

Limit state Ultimate Serviceability

Requirements Safety of people

Safety of the structure

Comfort of people

Functioning of the structure

Appearance of the construction works

Verification criteria

Loss of static equilibrium

Material failure

Stability failure

Fatigue

Stress limitation

Crack occurrence

Deformations

Vibrations

Design situations

Persistent and transient

Accidental

Earthquake

Rare or characteristic

Frequent

Quasi-permanent

Action onto the structure

Design values of action effects

(destabilising actions, internal forces)

Design values of action effects

(stresses, crack widths, deformations)

Reaction of the structure

Design values of resistances

(stabilising actions, material strengths)

Serviceability criteria

(permissible stresses, decompression, crack widths, deformations)

Verification of one of the two categories of limit states may be omitted provided that sufficient information is available to prove that it is satisfied by the other.

Clause (2)

Limit states should be related to design situations which should be classified as persistent, transient or accidental.

Clause (3), (4); see [EN 1990 02], 3.2

Verification of limit states that are concerned with time dependent effects (e.g. fatigue) should be related to the design working life of the construction.

Clause (5)

See also [EN 1990 02], 2.3


Design situations [EN 1990 02], 3.2 Design situations

A structure has to be investigated in those design situations that can occur in the limit states to be considered.

The relevant design situations shall be selected taking into account the circumstances under which the structure is required to fulfil its function.

Clause 1

Design situations shall be classified as follows:

persistent design situations, which refer to the conditions of normal use

transient design situations, which refer to temporary conditions applicable to the structure, e.g. during execution or repair;

accidental design situations, which refer to exceptional conditions applicable to the structure or to its exposure, e.g. to fire, explosion, impact or the consequences of localised failure;

seismic design situations, which refer to conditions applicable to the structure when subjected to seismic events.

Clause (2)

The selected design situations shall be sufficiently severe and varied so as to encompass all conditions that can reasonably be foreseen to occur during the execution and use of the structure.

Clause (3)

These design situations are related to certain verification criteria and the according formats for the calculation of the design values of the structure (Table 2).

[DIN 1055-100 01], Table 1, see above

Ultimate limit states [EN 1990 02], 3.3 Ultimate limit states

The limit states that concern:

- the safety of people, and / or

- the safety of the structure

shall be classified as ultimate limit states.

Clause (1)


In some circumstances, the limit states that concern the protection of the contents should be classified as ultimate limit states.

Clause (2)

Contents within a structure

States prior to structural collapse, which, for simplicity, are considered in place of the collapse itself, may be treated as ultimate limit states.

Clause (3)

e.g. large deformations

The following ultimate limit states shall be verified where they are relevant (Table 2):

Loss of equilibrium of the structure or any part of it, considered as a rigid body;

failure by excessive deformation, transformation of the structure or any part of it into a mechanism , rupture, including supports and foundations;

loss of stability of the structure or any part of it;

failure caused by fatigue or other time-dependent effects.

Clause (4)


Mechanism = kinematical chain

Note: Different sets of partial factors are associated with the various ultimate limit states. Failure due to excessive deformation is structural failure due to mechanical instability.

see [EN 1990 02], 6.4.1


Serviceability limit states [EN 1990 02], 3.4 Serviceability limit states

The limit states that concern (Table 2):

- the functioning of the structure or structural members under normal use;

- the comfort of people;

- the appearance of the construction works.

Clause (1)


A distinction shall be made between reversible and irreversible serviceability limit states.

Clause (2)

The verification of serviceability limit states should be based on criteria concerning the following aspects:

Clause (3)

a) deformations

- that affect the appearance,

? the comfort of users or

? the functioning of the structure (including the functioning of machines or services),

? or that cause damage to finishes or non-structural members ;

b) vibrations

- that cause discomfort to people, or

- that limit the functional effectiveness of the structure;

c) damage that is likely to adversely affect

- the appearance,

- the durability or

- the functioning of the structure.


Limit state design [EN 1990 02], 3.5 Limit state design

The design has to be performed in the following steps:

1. Establishing of action models and structural models applying the design values of geometrical data.

[EN 1990 02], 5.1.1

Design for limit states shall be based on the use of structural and load models for relevant limit states.

Clause (1)

Possible deviations from the assumed directions or positions of actions shall be taken into account.

Clause (8)

Structural and load models may be either physical models or mathematical models.

Clause (9)

2. Assessment of representative values for single actions as well as for material properties.

[EN 1990 02], Section 4

3. Calculation of design values

Design values of actions are determined by combining linearly the representative values of single actions .

[EN 1990 02], Section 6

The requirements of 3.5(1)P should be achieved by the partial factor method, described in section 6.

Clause (4)

In case of linear analysis, the representative values of single action effects should be calculated separately. Hence the design values of action effects are determined by linear combination with the partial factor method.

4. Structural analysis on the basis of the chosen models. [EN 1990 02], 5.1

The verifications shall be carried out for all relevant design situations and load cases.

Clause (3)

The selected design situations shall be considered and critical load cases identified.

Clause (6)

For a particular verification load cases should be selected, identifying compatible load arrangements, sets of deformations and imperfections that should be considered simultaneously with fixed variable actions and permanent actions.

Clause (7)

5. Verification of the limit states [EN 1990 02], 6.4 and 6.5

The design values of the action effects on the structure are not allowed to exceed the design values of the structural resistance or the design values of serviceability criteria.

It shall be verified that no limit state is exceeded when relevant design values are used in these models, for

- actions,

- material properties or

- product properties and

- geometrical data.

Clause (2)

As an alternative, when agreed with the client and the relevant authority, a design directly based on probabilistic methods may be used.

Clause (5)

For a basis of probabilistic methods, see Annex C.


Basic variables [EN 1990 02], Section 4

Actions and environmental influences [EN 1990 02], 4.1 Actions and environmental influences

Classification of actions [EN 1990 02], 4.1.1

Actions shall be classified by their variation in time as follows:

permanent actions (G), e.g. self-weight of structures, fixed equipment and road surfacing, and indirect actions caused by shrinkage and uneven settlements;

variable actions (Q), e.g. imposed loads on building floors, beams and roofs, wind actions or snow loads;

accidental actions (A), e.g. explosions, or impact from vehicles.

Clause (1)

Certain actions, such as seismic actions and snow loads, may be considered as either accidental and/or variable actions, depending on the site location, see EN 1991.

Clause (2)

Actions caused by water may be considered as permanent and / or variable actions depending on the variation of their magnitude with time.

Clause (3)

Actions caused by fluid pressure, the magnitude of which is limited by geometrical or hydrological conditions, may be considered as permanent, too.

See [DIN 1055-100], 6.1 (9)

Actions shall also be classified

by their origin, as direct or indirect,

by their spatial variation, as fixed or free, or

by their nature and / or the structural response, as static or dynamic.

Clause (4)

An action should be described by a model, its magnitude being represented in the most common cases by one scalar which may have several representative values.

Clause (5)

See also [EN 1990 02], 5.1

Characteristic values of actions [EN 1990 02], 4.1.2

The characteristic value Fk of an action is its main representative value and shall be specified:

as a mean value, an upper or lower value, or a nominal value (which does not refer to a known statistical distribution), see EN 1991;

in the project documentation, provided that consistency is achieved with methods given in EN 1991.

Clause (1)

The characteristic value of a permanent action shall be assessed as follows:

if the variability of G can be considered as small, one single value Gk may be used;

if the variability of G cannot be considered as small, two values shall be used: an upper value Gk,sup and a lower value Gk,inf.

Clause (2)

The variability of G may be neglected if G does not vary significantly during the design working life of the structure and its coefficient of variation is small. Gk should then be taken equal to the mean value.

Clause (3)


Note : This coefficient of variation may be in the range of 0,05 to 0,10 depending on the type of structure.

In cases when the structure is very sensitive to variations in G (e.g. some types of prestressed concrete structures), two values should be used even if the coefficient of variation is small.

Then Gk,inf is the 5% fractile and Gk,sup is the 95% fractile of the statistical distribution for G, which may be assumed to be Gaussian.

Clause (4)

The self-weight of the structure may be represented by a single characteristic value and be calculated on the basis of the nominal dimensions and mean unit masses, see EN 1991-1.1.

Clause (5)

Prestressing (P) should be classified as a permanent action caused by either controlled forces and/or controlled deformations imposed on a structure. These types of prestress should be distinguished from each other as relevant (for example prestress by tendons, prestress by imposed deformation at supports, etc.).

Clause (6)

For variable actions, the characteristic value (Qk) shall correspond to either :

an upper value with an intended probability of not being exceeded or a lower value with an intended probability of being achieved, during some specific reference period;

a nominal value, which may be specified in cases where a statistical distribution is not known.

Clause (7)

Values are given in the various Parts of EN 1991. Note 1

The characteristic values of climatic actions are based upon the probability of 0,02 of its time-varying part exceeding for a reference period of one year.

This is equivalent to a mean return period of 50 years for the time-varying part.

However in some cases the character of the action and / or the selected design situation makes another fractile and / or return period more appropriate.

Note 2

For accidental actions the design value Ad should be specified for individual projects.

Clause (8)

See also [EN 1991-1-7 05].

For seismic actions the design value AEd should be assessed from the characteristic value AEk or specified for individual projects.

Clause (9)

See also [EN 1998 06].

For multi-component actions the characteristic action should be represented by groups of values each to be considered separately in design calculations.

Clause (10)

One example for multi-component actions are the traffic loads on bridges which are described by load models composed of concentrated and uniformly distributed loads combined by means of certain factors.

See [EN 1991-2 03]: Actions on bridges


Other representative values of variable actions [EN 1990 02], 4.1.3

Other representative values Qrep of a variable action shall be defined as a product of a characteristic value Qk and a combination factor yi ( 1,0), as follows:

Clause (1)

a) the combination value , represented as a product

Qcomb = y0 Qk,

used for the verification of ultimate limit states and irreversible serviceability limit states;

see section 6 and Annex C

The factors y0 are chosen in such a way that the reliability of a structure does not remain under the intended level when they are applied to the combination rules for actions.

In other words: Using the factors y0, the failure probability for the action effect resulting from combination of actions shall be adequate to that for the effect of a single action.

b) The infrequent value , represented as a product

Qinfr = y1,infr Qk,

y1,infq Qk, is used for the verification of certain serviceability limit states specifically for concrete bridge decks, or concrete parts of bridge decks.

Note 2

The infrequent value, defined only for road traffic loads, thermal actions and wind actions, is based on a return period of one year.

see [EN 1991-2 03]; [EN 1991-1-5 03]; [EN 1991-1-4 05]

c) the frequent value , represented as a product

Qfreq = y1 Qk,

used for the verification of ultimate limit states involving accidental actions and for verifications of reversible serviceability limit states;

For buildings, for example, the frequent value is chosen so, that the time it is exceeded is 0,01 of the reference period;

for road traffic loads on bridges, the frequent value is assessed on the basis of a return period of one week.

Note 1

d) the quasi -permanent value , represented as a product

Qperm = y2 Qk,

used for the verification of ultimate limit states involving accidental actions and for the verification of reversible serviceability limit states. Quasi-permanent values are also used for the calculation of long-term effects.

For loads on building floors, the quasi-permanent value is usually chosen so that the proportion of the time it is exceeded is 0,50 of the reference period.

The quasi-permanent value can alternatively be determined as the value averaged on a chosen period of time.

In the case of wind actions or road traffic loads, the quasi-permanent value is generally taken as zero.

Note

In case of fatigue, other representative values may be considered.

The design value Qd and the various representative values Qrep (Qk, Qcom, Qinfr, Qfreq and Qperm) are presented in Fig. 4.

See [EN 1990 02], Section 6


Fig. 4: Representative values of a variable action [Spaethe 92]

Representation of fatigue actions [EN 1990 02], 4.1.4

The models for fatigue actions should be those that have been established in the relevant parts of EN 1991 from evaluation of structural responses to fluctuations of loads performed for common structures (e.g. for simple span and multi-span bridges, tall slender structures for wind, etc.).

Clause (1)

For structures outside the field of application of models established in the relevant Parts of EN 1991, fatigue actions should be defined from the evaluation of measurements or equivalent studies of the expected action spectra.

Clause (2)

Representation of dynamic actions [EN 1990 02], 4.1.5

The characteristic and fatigue load models in EN 1991 include the effects of accelerations caused by the actions either implicitly in the characteristic loads or explicitly by applying dynamic enhancement factors to characteristic static loads.

Clause (1)

When dynamic actions cause significant acceleration of the structure, dynamic analysis of the system should be used.

Clause (2)

See [EN 1990 02], 5.1.3 (6).

Geotechnical actions [EN 1990 02], 4.1.6

Geotechnical actions shall be assessed in accordance with EN 1997-1. Clause (1)

Environmental influences [EN 1990 02], 4.1.7

The environmental influences that could affect the durability of the structure shall be considered in the choice of structural materials, their specification, the structural concept and detailed design.

Clause (1)

The effects of environmental influences should be taken into account, and where possible, be described quantitatively.

Clause (2)

Effects of environmental influences on concrete structures, for instance, are considered by means of exposition classes which are referred to certain corrosion attacks (such as carbonation, chlorides, seawater, frost, de-icing salt and aggressive chemicals).

See EN 206-1: Concrete Part 1: Specification, performance and conformity

Characteristic value Qk

Design value Qd = gQ Qk

Combination value Qcomb = y0 Qk

Frequent value Qfreq = y1 Qk

Quasi-permanent value Qperm = y2 Qk

Q

t

Infrequent value Qinfr = y1,infr Qk


Material and product properties [EN 1990 02], 4.2 Material and product properties

Properties of materials (including soil and rock) or products should be represented by characteristic values.

Clause (1)

see [EN 1990 02], 1.5.4.1

Characteristic values are the basis for inspection during manufacturing, execution and use.

[Spaethe 92]

When a limit state verification is sensitive to the variability of a material property, upper and lower characteristic values of the material property should be taken into account.

Clause (2)

Characteristic values of a material or product property generally are defined as fractile values of a certain statistical distribution.

Unless otherwise stated in ENs 1991 to 1999 these characteristic values should be chosen:

Clause (3)

as the 5% fractile value where a low value is unfavourable, e.g. for material resistance in the ultimate limit state,

as a mean value where action effects depend on integration of material properties over a structure, e.g. for the structural stiffness parameters in non-linear analysis,

See Clause (8)

Note: Different values should be used to take into account the duration of the load.

as the 95% fractile value where a high value is unfavourable, e.g. for material properties which indirect actions depend on,

See Clause (6)

as nominal value , where insufficient statistical data are available (or design values may be established directly).

Clause (5)

Material property values shall be determined from standardised tests performed under specified conditions.

A conversion factor shall be applied where it is necessary to convert the test results into values which can be assumed to represent the behaviour of the material or product in the structure or the ground.

Clause (4)

Note: See annex D and ENs 1992 to 1999

Where upper or lower design values of a material or product property are established directly (e.g. friction factors, damping ratios), they should be selected so that the reliability level is achieved, as required for the limit state considered.

Clause (5)

The reductions of the material strength or product resistance to be considered resulting from the effects of repeated actions are given in ENs 1992 to 1999 and can lead to a reduction of the resistance over time due to fatigue.

Clause (7)

Characteristic values of material or product properties are given in ENs 1992 to 1999 and in the relevant European product standards.

If values are taken from product standards without guidance on interpretation being given in ENs 1992 to 1999, the most adverse values should be used.

Clause (9)

Where a partial factor for materials or product is needed, a conservative value shall be used, unless suitable statistical information exists to assess the reliability of the value chosen.

Clause (10)

See also ENs 1992 to 1999


Geometrical data [EN 1990 02], 4.3 Geometrical data

Geometrical data shall be represented

by their characteristic values, or

(e.g. in case of imperfections) directly by their design values.

Clause (1)

The dimensions specified in the design may be taken as characteristic values.

Clause (2)

Where the statistical distribution of geometrical quantities is sufficiently known, they may be established as fractile values.

Clause (3)

Imperfections that should be taken into account in the design of structural members are given in ENs 1992 to 1999.

Clause (4)

as to be applied to Second order non-linear analysis, for example

Tolerances for connected parts that are made from different materials shall be mutually compatible.

Clause (5)

Structural analysis and design assisted by testing

[EN 1990 02], Section 5

Structural analysis [EN 1990 02], 5.1 Structural analysis

Structural modelling [EN 1990 02], 5.1.1

Calculations shall be carried out using appropriate structural models involving relevant variables.

Clause (1)

See also [EN 1990 02], 3.5 (2)

These structural models should be appropriate for predicting structural behaviour with an acceptable level of accuracy.

They should also be appropriate to the limit states considered.

Clause (2)

See also [EN 1990 02], 3.5 (1)

Structural models shall be based on established engineering theory and practice (approved rules of engineering).

If necessary, they shall be verified experimentally.

Clause (3)

See above: Structural design and structural safety

Static actions [EN 1990 02], 5.1.2

The modelling for static actions shall be based on an appropriate choice of the force-deformation relationships of the members and their connections and between members and the ground.

Clause (1)

Boundary conditions applied to the model shall represent those intended in the structure.

Clause (2)

Effects of displacements and deformations shall be taken into account in the context of ultimate limit state verifications if they result in a significant increase of the effect of actions.

Clause (3)

Condition for applying second order analysis

Indirect actions shall be introduced in the analysis as follows :

in linear elastic analysis, directly or as equivalent forces (using appropriate modular ratios where relevant);

in non-linear analysis, directly as imposed deformations.

Clause (4)

Dynamic actions [EN 1990 02], 5.1.3

The structural model to be used for determining the dynamic action effects has to compass all relevant structural members, their masses, strengths, stiffnesses and damping characteristics, and all relevant non structural members with their properties.

Clause (1)


The boundary conditions applied to the model shall be representative of those intended in the structure.

Clause (2)

When it is appropriate to consider dynamic actions as quasi -static, the dynamic parts may be considered either by including them in the static values or by applying equivalent dynamic amplification factors to the static actions.

Clause (3)

In the case of ground-structure interaction, the contribution of the soil may be modelled by appropriate equivalent springs and dash-pots.

Clause (4)

Where relevant (e.g. for wind induced vibrations or seismic actions) the actions may be defined by a modal analysis based on linear material and geometric behaviour.

Clause (5)

For structures that have regular geometry, stiffness and mass distribution, provided that only the fundamental mode is relevant, an explicit modal analysis may be substituted by an analysis with equivalent static actions.

Applying the law of conservation of energy, the fundamental eigen frequency may be determined as the ratio of kinetic and potential vibration energy.

[Grnberg 06]

The dynamic actions may be also expressed, as appropriate, in terms of time histories or in the frequency domain, and the structural response determined by appropriate methods.

Clause (6)

Where dynamic actions cause vibrations of a magnitude or frequencies that could exceed serviceability requirements, a serviceability limit state verification should be carried out.

Clause (7)

Fire design [EN 1990 02], 5.1.4

The structural fire design analysis shall be based on design fire scenarios (see EN 1991-1-2), and shall consider models for the temperature evolution within the structure as well as models for the mechanical behaviour of the structure at elevated temperature.

Clause (1)

The required performance of the structure exposed to fire should be verified by either global analysis, analysis of sub-assemblies or member analysis, as well as the use of tabular data or test results.

Clause (2)

The behaviour of the structure exposed to fire should be assessed by taking into account either:

nominal fire exposures, or

modelled fire exposures,

as well as the accompanying actions.

Clause (3)

Note : See also EN 1991-1-2.

The structural behaviour at elevated temperatures, should be assessed in accordance with ENs 1992 to 1996 and EN 1999, which give thermal and structural models for analysis.

Clause (4)

See the parts 1-2 of each code family, concerning fire design

Where relevant to specific material and the method of assessment

either a uniform or a non-uniform temperature may be assumed within cross-sections and along members;

either structural members may be analysed separately or considering interaction between members in fire exposure.

Clause (5)

The mechanical behaviour of structural members at elevated temperatures should be modelled non-linear.

Clause (6)


Design assisted by testing [EN 1990 02], 5.2 Design assisted by testing

Design may be based on a combination of tests and calculations. Clause (1)

Normally, the verification of structures based on testing only, i.e. without any accompanying calculations, is not permitted!

Testing may be carried out, for example, in the following circumstances:

if adequate calculation models are not available;

if a large number of similar components are to be used;

to confirm by control checks assumptions made in the design.

See Annex D.

Design assisted by test results shall achieve the level of reliability required for the relevant design situation.

The statistical uncertainty due to a limited number of test results shall be taken into account.

Clause (2)

Partial factors (including those for model uncertainties) comparable to those used in ENs 1991 to 1999 should be used.

Clause (3)

Verification by the partial factor method [EN 1990 02], Section 6

General [EN 1990 02], 6.1 General

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 action effects and resistances are used in the design models.

Clause (1)

For the selected design situations and the relevant limit states the individual actions for the critical load cases should be combined as detailed in this section.

However, actions that cannot occur simultaneously, for example due to physical reasons, should not be considered together in combination.

Clause (2)

Design values should be obtained by using

the characteristic values or

other representative values

in combination with partial and other factors as defined in this section and in EN 1991 to EN1999.

Clause (3)

See [EN 1990 02], Annex A: A1 with respect to buildings, A2 with respect to bridges

It can be appropriate to determine design values directly where conservative values should be chosen.

Clause (4)

Design values directly determined on statistical bases shall correspond to at least the same degree of reliability for the various limit states as implied by the partial factors given in this standard.

Clause (5)


Limitations [EN 1990 02], 6.2 Limitations

The use of the Application Rules given in EN 1990 is limited to ultimate and serviceability limit state verifications of structures subject to static loading, including cases where the dynamic effects are assessed using equivalent quasi-static loads and dynamic amplification factors, including wind or traffic loads.

For non-linear analysis and fatigue the specific rules given in various parts of ENs 1991 to 1999 should be applied.

Clause (1)


Design values [EN 1990 02], 6.3 Design values

Design values of actions [EN 1990 02], 6.3.1

In general, the characteristic value Fk of an action can be transformed into a design value Fd by means of a partial factor and a y factor:

Clause (1)

d f repF Fg= (6.1a)

with

rep kF Fy= (6.1b)

where:

Fk is the characteristic value of the action (Gk or Qk).

Frep is the relevant representative value of the action.

gf is a partial factor for the action which takes account of

- the possibility of unfavourable deviations of the action values from the representative values.

y is either 1,00 or y0, y1 or y2.

However, the design value AEd of a seismic action should be determined taking account of the structural behaviour and other relevant criteria detailed in EN 1998.

Clause (2)

Design values of material or product properties [EN 1990 02], 6.3.3

The characteristic values Xk of material or product properties are transformed into a design values Xd by means of partial factors.

Clause (1)

In special cases a conversion factor h has to be introduced considering effects of load duration, moisture, temperature etc. as well as scale effects.

kd

m

XX h

g= (6.3)

Xk is the characteristic value of the material or product property

see [EN 1990 02], 4.2(3)

h is the mean value of the conversion factor

gm is the partial factor for the material or product property to take account of

- the possibility of an unfavourable deviation of a material or product property from its characteristic value;

- the random part of the conversion factor h.

Alternatively the conversion factor h may be taken into account:

- implicitly within the characteristic value itself,

- or by using gM instead of gm (see expression (6.6b)).

Clause (2)

Design values of geometrical data [EN 1990 02], 6.3.4

Design values of geometrical data such as dimensions of members that are used to assess action effects and/or resistances may be represented by nominal values:

Clause (1)

ad = anom (6.4)


Where the effects of deviations in geometrical data (e.g. inaccuracy in the load application or location of supports) are significant for the reliability of the structure (e.g. by second order effects) the design values of geometrical data shall be defined by:

Clause (2)

d noma a a= + D (6.5)

Da takes account of:

- the possibility of unfavourable deviations from the characteristic or nominal values;

- the cumulative effect of a simultaneous occurrence of several geometrical deviations.

Note: ad can also represent geometrical imperfections where anom = 0.

Effects of other deviations should be covered by partial factors Clause (3)

Design values of the effects of actions [EN 1990 02], 6.3.2

The action effects (E) are the answers of the structure to the actions (F) depending on the geometrical data (a) and the material properties (X).

Therefore, for a specific load case the design values of the action effects (Ed) can be expressed in general terms as:

{ }d Ed d,1 d,2 d,1 d,2 d,1 d,2, ,..., , ,..., , ,E E F F a a X Xg= K (6.2)

Clause (1)

Fd,i are the design values of actions Fi to be determined applying equation (6.1).

ad,i are the design values of relevant geometrical data, e.g. the span of a beam.

Xd,i are the material properties, if relevant for structural analysis, e.g. the stiffness of a beam.

gEd is a partial factor taking account of uncertainties:

- in modelling the effects of actions, i.e. the deviations of the structural model from the structure or any structural member in reality ;

- in some cases, in modelling the actions, i.e. the deviations of the action arrangements such as concentrated or distributed loads, constant thermal actions or linear temperature gradients, etc. from the real actions.

The design values of action effects Ed may represent internal forces, stresses or deformations, e.g.:

- the design value of an acting bending moment MEd,

- the design value of a longitudinal stress within a beam sEd or

- the design value of a deflection fEd.

The index Ed identifies an action effect for a certain design situation in a limit state which depends on a combination of actions.

Introducing the partial factors gf,i for actions, equ. (6.2) may be transformed into:

See Fig. 6

{ }d Ed f,1 rep,1 f,2 rep,2 d,1 d,2 d,1 d,2, ,..., , ,..., , ,E E F F a a X Xg g g= K (6.2 *)


In most cases, the following simplification can be made : Clause (2)

{ }d F,1 rep,1 F,2 rep,2 d,1 d,2 d,1 d,2, ,..., , ,..., , ,E E F F a a X Xg g= K (6.2a)

with extended design values of actions

d,i F,i rep,iF Fg= (6.1c)

where F,i Ed f,ig g g= (6.2b)

Considering the different single actions, but disregarding the dependencies on geometrical data and material properties, equation (6.2 *), and (6.2a) respectively, will adopt the

General format for combination of actions in the limit states:

[Grnberg 04]

{ }d Ed g,1 k,1 g,2 k,2 q,1 rep,1 q,2 rep,2, ,..., , ,...E E G G Q Qg g g g g= (6.2 **)

{ }d G,1 k,1 G,2 k,2 Q,1 rep,1 Q,2 rep,2, ,..., , ,...E E G G Q Qg g g g= (6.2a *)

Gk,j characteristic values of single permanent actions Gj:

Qrep,i representative values of single variable actions Qi:

gg,j, gq,I; gG,j, gQ,I according partial factors

See [EN 1990 02], 4.1

A single action is represented by one or several characteristic values of forces or deformations from one unique origin, e.g. permanent weight G, life loads QN, snow and ice loads QS, wind loads QW, or thermal actions QDT.

Actions are independent of each other if they come from different origins and if their correlation may be neglected with respect to structural reliability.

[Grnberg 04]

The independent (single) actions relevant for buildings are assembled in the context of Annex A1.

See comment to [EN 1990 02], Annex A1

Although the solar energy, acting on the atmosphere and earths surface, is the common source of all environmental actions, such as snow and ice loads, wind loads and thermal actions, they are considered independently.

The reasons are the unimportant correlations between these actions as well as their basic periods which differ essentially.

Different kinds of use (multiple categories of use in one building) normally are partially correlated, and that is from the superior intention of the building.

The same kinds of use on different floors (i.e. only one category of use in one building) are only partly correlated, but stronger than different kinds of use.

All imposed loads or life loads within one building coming from all categories of use appearing there are assembled to a multi-component action which is treated as one single action.

Multi-component action: see [EN 1990 02], 4.1.2 (10)

This multi-component action results of a previous combination of actions according to special rules given in the action codes.

See [EN 1991-1-1 02] or [EN 1991-2 03], for instance


Where a distinction has to be made between favourable and unfavourable effects of permanent actions, two different partial factors shall be used (gG,inf and gG,sup).

Clause (3)

Unfavourable effects of a permanent action increase the effects of the leading variable action Qk,1, e.g. if an imposed load Qk,1 and self-weight are acting in the same direction. Then the characteristic value Gk, or the upper value Gk,sup respectively, has to be multiplied by the upper partial factor gG,sup, e.g. by gG,sup = 1,35.

The index sup is an abbreviation of the Latin word superior which means the higher one.

Favourable effects of a permanent action decrease the effects of the leading variable action Qk,1, e.g. if an imposed load Qk,1 and self-weight are acting in opposite directions. Then the characteristic value Gk, or the lower value Gk,inf respectively, has to be multiplied by the lower partial factor gG,inf, e.g. by gG,inf = 1,00.

The index inf is an abbreviation of the Latin word inferior which means the lower one.

Formats for combination of actions in non-linear analysis:

For non-linear analysis (i.e. when the relationship between actions and their effects is not linear), the following simplified rules may be considered in the case of a single predominant action (Qk,1):

Clause (4)

See Fig. 5

a) When the action effect increases more than the actions, the partial factors gF,i should be applied to the representative values of the actions:

{ }d G,1 k,1 G,2 k,2 Q,1 k,1 Q,2 rep,2, ,..., , ,...E E G G Q Qg g g g= (6.2-N1)

equivalent to equ. (6.2a *)

One example for application of equ. (6.2-N1) is the second order non-linear analysis of a building column where the design bending moment MEd increases more than the contributing single actions.

Another example is the second order non-linear analysis of an arch structure. Depending on one single action Q1 only, the horizontal reaction force H1 results from equ. (6.2-N1):

{ }Qd,1 Q,1 k,1 Q,1 Qk,1H H Q Hg g= > (6.2-H1)

Fig. 5: Predominant action effect EQd,1 = E (Qk,1; gQ,1) in non-linear structural analysis

EQd,1

Q1

HQd,1 > gQ,1 HQk,1

NQd,1 = gQ,1 NQk,1

linear

a) above proportionality

b) below proportionality

Qk,1 Qd,1 = gQ,1 Qk,1

NQk,1

HQk,1


b) When the action effect increases less than the action (i.e. the

leading variable action Qk,1), the partial factor gF (gQ,1) should be applied to the action effect of the representative value of the action:

Clause (4); continued

G,1 G,2 Q,2d Q,1 k,1 k,2 k,1 rep,2

Q,1 Q,1 Q,1

, , ..., , , ...E E G G Q Qg g g

gg g g

=

(6.2-N2)

The design values of each single action are divided through the partial factor according to the leading variable action.

This partial factor is applied to the resulting effect of the reduced actions.

One example is the second order non-linear analysis of a suspension bridge. Depending on one single action Q1 only, the longitudinal force of the main rope N1 results from equ. (6.2-N2) as the following:

{ }Qd,1 Q,1 k,1 Q,1 Qk,1N N Q Ng g= = (6.2-H2)

Formats for combination of actions in linear-elastic analysis:

d G,1 Gk,1 G,2 Gk,2 Q,1 Qrep,1 Q,2 Qrep,2... ...E E E E Eg g g g= + + + + + (6.2-E)

The representative values of single action effects, i.e. EGk,j and EQrep,I, are the answers of the structure to the representative values of the single actions Gk,j and Qrep,I respectively:

( )Gk,j k,jE E G= characteristic values of single permanent action effects

( ) ( )Qrep,i rep,i i k,i i Qk,iE E Q E Q Ey y= = = representative values of single variable action effects

gG,j, gQ,I according partial factors

In case of linear-elastic behaviour, the structural analysis may be carried out for each single action, as they are

- permanent loads Gk,

- imposed loads QN,k (or life loads),

- snow loads QS,k,

- wind loads QW,k,

- thermal actions QDT,k,

- ,

separately, but using the same structural model.

Applying the principle of superposition, the single action effects, e.g. internal forces, stresses or deformations, may be combined linearly.

[Grnberg 04]


In this case the combination rule (6.2-E) describes an additive superposition of the design values of single action effects:

d Gd,1 Gd,2 Qd,1 Qd,2... ...E E E E E= +