prof. dr.-ing. jürgen grünberg universität hannover twinning latvia basis of structural design...

Prof. Dr.-Ing. Jürgen GrünbergUniversität Hannover

Tw

innin

g L

atv

ia

Basis of Structural Design

Basis of Structural Design[EN1990 – 02]

Prof. Dr.-Ing. Jürgen Grünberg


Tw

innin

g L

atv

ia


Introduction of myself

Name

Date of birth

Present position

Key qualifications

Contribution to Code Writing

Jürgen Grünberg

18 May 1944

Professor of concrete structures and director of the Institute of Concrete Construction, University of Hannover

Consulting engineer for structural design, testing and supervision in structural engineering, Hamburg

Reliability analysis in structural engineeringMaterial models for RC and UHPC structuresAnalysis of young concrete during the hydration processFatigue design of concrete structuresStructural design (e.g. towers, bridges, offshore structures)

EN 1990 (in Germany: DIN 1055-100)EN 1991 (in Germany: DIN 1055-1 to 10)EN 1992 (in Germany: DIN 1045-1)


Tw

innin

g L

atv

ia


Scope:

Principles and requirements for safety, serviceability, and durability.

Direct application for buildings and civil engineering works in conjunction with EN 1991 to 1999.

Guidelines relating to safety, serviceabilty and durabilty for designing structures out of the scope of EN 1991 to 1999, to serve as reference document, e.g. for product codes.

Basis of structural design [EN 1990 – 02]

Application also for the structural appraisal of existing construction, in developing the design of repairs, alterations or in assessing changes of use.


Tw

innin

g L

atv

ia


Content:

Annex B (informative) Management of structural reliability for construction worksAnnex C (informative) Basis for partial factor design and reliability analysis


Annex D (informative) Design assisted by testing EN 1992 to 1999

EN1990 – Main text

Foreword1 General2 Requirements3 Principles of limit state design4 Basic variables5 Structural analysis and design assisted by testing

Principles andrequirements

Annex A1 (normative) Application for buildings EN 1991-1Annex A2 (not published) Application for bridges EN 1991-2

Direct application

6 Verification by the partial factor method


Tw

innin

g L

atv

ia


Topics:

1. Bases of safety concept(Principles and requirements; explanation of terms and definitions)

2. Combinations of actions(Verification by the partial factor method according to the different limit states and design situations)

3. Basis for partial factor design and reliability analysis (probabilistic analysis)



Tw

innin

g L

atv

ia


1 Bases of safety concept

To assure the structural safety the following measures are required:

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).


Tw

innin

g L

atv

ia


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

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

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.


Tw

innin

g L

atv

ia


1.2 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

published by the European Community at 21-12-1988


Tw

innin

g L

atv

ia


1.2 Basic requirements for structures

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 :

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:

structural resistance,

serviceability,

and durability.

To assure 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.

A structure shall not be damaged by events such as

explosion, impact, and the consequences of human errors,

to an extent disproportionate to the original cause.


Tw

innin

g L

atv

ia


1.3 Limiting or avoiding of potential damage

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

• from insufficient knowledge and wrong activities of persons, e.g. the users of the

structure who have not been informed about the loading limits

• 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),

In spite of these two strategies –

• Measures to avoid human errors

• Measures to warrant a sufficient safety margin

errors cannot be excluded completely !

There is a remaining risk.


Tw

innin

g L

atv

ia


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;

• tying the structural members together.

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

1.3 Limiting or avoiding of potential damage


Tw

innin

g L

atv

ia


1.4 Principles of limit state design

Serviceability criterion (permissible stresses,

crack widths, deformations)

Design value of resistance (stabilising actions, material strengths,

cross area resistances)

Resistance

Design value of action effects (stresses, crack widths,

deformations)

Design value of action effects (destabilising actions,

internal forces)

Action effects

Rare or characteristicFrequent

Quasi-permanent

Persistent and transientAccidental

Seismic

Design situations

Stress limitationCrack propagation

Deformations Vibrations

Loss of static equilibriumFailure by strength limitation

Loss of stabilityFailure by fatigue

Verification criteria

Functioning of the structureComfort of people

Appearance of construction

Safety of peopleSafety of the structure

RequirementsServiceabilityUltimateLimit state


Tw

innin

g L

atv

ia


1.5 Representative values

Characteristic values of actions ( Fk ):

Action codes (EN 1991)

Characteristic values of material properties ( Xk ):

construction specific design codes (EN 1992 to EN 1999)

according material codes (EN 206 etc.)

Characteristic values of actions

The characteristic values of permanent actions Gk

generally are their mean values.

The characteristic values of variable actions Qk

generally are their 98 %-quantiles for the reference period of 1 year.


Tw

innin

g L

atv

ia


Other representative values of variable actions

… shall be defined as products of a characteristic value Qk

and a combination factor i ( 1,0 ).

1. Combination value: Qrep,0 = 0 Qk

The factors 0 are chosen such, that the failure probabilities for the action effect resulting from combination of actions and from a single action are adequate.

2. Frequent value: Qrep,1 = 1 Qk

with a limited duration or frequency of being exceeded within the reference period.

3. Quasi-permanent value: Qrep,2 = 2 Qk

determined as the value averaged on the reference period.

In case of fatigue other representative values may be considered.


Tw

innin

g L

atv

ia


Comparison of representative values of a variable action

Q

Design value Qd = Q Qk

Characteristic value Qk

Combination value 0 Qk

Frequent value 1 Qk

Quasi-permanent value 2 Qk

t


Tw

innin

g L

atv

ia


Characteristic values for material properties

… generally are defined as quantiles of a statistical distribution, for instance:

• as 5 %-quantiles of material strength parameters,

• as mean values of structural stiffness parameters,

• as upper nominal values for determination of indirect actions.

1.5 Representative values


Tw

innin

g L

atv

ia


1.6 Design values

Design values of actions

Frep represents either Gk, Qk or Qrep.

d Ed f rep F repF F F

Design values of material properties

ork k

dRd m M

X XX

k

dM

XX

The conversion factor takes into account volume and scale effects,effects of moisture and temperature, etc.


Tw

innin

g L

atv

ia


Relations between individual partial factors

Uncertainty of representative values of actions

Model uncertainties

Uncertainty of material properties

Actions and action effects

Structural resistances

f

Ed

Rd

m

F

M

1.6 Design values


Tw

innin

g L

atv

ia


Design values of geometrical data

or

Nominal values anom

Deviations a ( e.g. in case of geometrical imperfections )

d noma a d noma a a

Design values of action effects

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).

General format:

d d,1 d,2 d,1 d,2 d,1 d,2E E F ,F ,...,a ,a ,...,X ,X ,...

1.6 Design values


Tw

innin

g L

atv

ia


Applying partial factors, the following formats can be derived:

1. General format:

d Ed g,1 k,1 g,2 k,2 q,1 rep,1 q,2 rep,2E E G , G ,..., Q , Q ,...

2. Formats for combination of actions in non-linear analysis:

2.1. The action effect Ed increases more than the leading action Qk,1:

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

2.2. The action effect Ed increases less than the leading action Qk,1:

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 , Q ,...

3. Format only to be used in linear-elastic structural analysis:

d G,1 Gk,1 G,2 Gk,2 Q,1 Qrep,1 Q,2 Qrep,2E E E ... E E ...


Tw

innin

g L

atv

ia


EQd,1

Q1

HQd,1 > Q,1 HQk,1

(Arch structure)

NQd,1 = Q,1 NQk,1

(Suspension bridge)

linear

a) above proportionality

b) below proportionality

Qk,1 Qd,1 = Q,1 Qk,1

NQk,1

HQk,1

1.6 Design values

Formats for combination of actions in non-linear analysis

Predominant action effect EQd,1 = E (Qk,1; Q,1) in non-linear structural analysis


Tw

innin

g L

atv

ia


Design values of resistances

The resistances (R) depend on the geometrical data (a) and the material properties (X).

General Format:

d d,1 d,2 d,1 d,2R R a ,a ,... X ,X ,...

1.6 Design values


Tw

innin

g L

atv

ia


1. Format applying divided partial factors:

k,1 k,21 2 nom,1 nom,2

Rd m,1 m,2

d1 X X

R R , ,...,a ,a ,...

2. Format applying integrated partial factors:

k,1 k,2d 1 2 nom,1 nom,2

M,1 M,2

X XR R , ,...,a ,a ,...

3. Format applying on partial factor R for structural resistance:

Rd 1 k,1 2 k,2 nom,1 nom,2

R M,1 M,2

R1R R X , X ,...,a ,a ,...

• Application: e.g. non-linear structural analysis of reinforced concrete structures

Applying partial factors, the following formats can be derived:


Tw

innin

g L

atv

ia


1.7 Verification of limit statesby the partial factor method

It shall be verified that,

in all relevant design situations,

no relevant limit state is exceeded

when the design values for actions or action effects and resistances are used in the design models.

For the selected design situations and the relevant limit states the individual actions for the critical load cases should be combined using the

characteristic values or other representative values in combination with

partial factors (F; M) and other factors (e.g. combination factors i).

However, actions that cannot occur simultaneously should not be considered together in combinations.


Tw

innin

g L

atv

ia


1.7 Verification of limit states

Verification formats for Ultimate Limit states (ULS)

The following ultimate limit states shall be verified as relevant:

a) EQU: Loss of static equilibrium of the structure or any part of itconsidered as a rigid body

b) STR: Internal failure or excessive deformation of the structure, one of its members or the foundation, where the strength of construction materials governs

c) GEO: Failure or excessive deformation of the soil where the strengths of the soil or rock are significant in providing resistance

d) FAT: Fatigue failure of the structure or structural elements(Note: For fatigue design see EN 1992 to EN 1999)


Tw

innin

g L

atv

ia



Verification formats for Ultimate Limit states (ULS)

• Limit state of static equilibrium (EQU)(e.g. overturning, buoyancy, lifting off)

Verification of a structure considered as a rigid body:

stb,ddst,d EE

Ed,dst Design value of the effect of

destabilising actions

Ed,stb Design value of the effect of

stabilising action (= gravity resistance)


Tw

innin

g L

atv

ia


• Limit state of structural failure (STR) (rupture, excessive deformation)

Verification of a structural cross area, member or joint:

dd RE

Ed Design value of the effect of actions (internal forces, stresses)

Rd Design value of the structural resistance (bearing capacity)


• Limit state of static equilibrium involving the resistance of anchoring structural members

Furthermore, the limit state of structural failure has to be verified with respect to the anchoring structural member

G,STR,sup G,EQU,sup d,dst d,stb d,anch/ E E R


Tw

innin

g L

atv

ia


dd CE

Ed Design value of the effects of actions

(e.g. deformation, stress)

Cd Limiting design value of the effects of actions

specified in the serviceability criterion (e.g. limiting values of deformations, stresses, etc.)


Verification formats for Serviceability Limit states (SLS)


Tw

innin

g L

atv

ia


2 Combinations of actions

2.1 Single actions for buildings

AEdSeismic actions

AdAccidental actions

Qk,

Qk,H

6. Indirect actions, caused by uneven settlements

Gk,H4. Fluid pressure, permanent 5. Fluid pressure, variable

Gk,E3. Earth pressure Qk,T4. Thermal actions

Qk,W3. Wind loadsPk2. Prestressing

Qk,S2. Snow and ice loads

Qk,N1. Imposed loads, life loadsGk1. Self-weights

QkiVariable actionsGkj; PkPermanent actions


Tw

innin

g L

atv

ia


• Generally, the self-weights of the structure and of the fixed equipment, as permanent loads, may be united to one common single action Gk.

• In case of a limit state of static equilibrium, the permanent actions have to be subdivided into their unfavourable and their favourable parts ( Gk,dst,j and Gk,stb,j).

• Generally, all the imposed loads and life loads within one building

coming from different categories of use appearing there

are assembled to one multi-component action QN,k.

2.1 Single actions for buildings


Tw

innin

g L

atv

ia


2.2 Ultimate Limit States (ULS)

Persistent and transient design situations (fundamental combinations)

• General format

(special formats in non-linear structural analysis, see 1.6)

G,j k,j p Q,1 k,1 Q,i 0,i k,id kj 1 i 1

E E G P Q Q

• Format used only in linear-elastic structural analysis

Leading variable action effect:

G,j Gk,j p Pk Q,1 Qk,1 Q,i 0,i Qk,idj 1 i 1

E E E E E

Q,1 0,1 Qk,1 Q,i 0,i Qk,i1 E Max. 1 E


Tw

innin

g L

atv

ia


Alternatively for STR and GEO limit states,

the less favourable of the following formats may be applied:

• Alternative format, general

d G,j k,j P k Q,i 0,i k,ij 1 i 1

E E G P Q

a)

d G,j j k,j P k Q,1 k,1 Q,i 0,i k,ij 1 i 1

E E G P Q Q

b)

• Alternative format, used only in linear-elastic structural analysis

d G,j Gk,j P Pk Q,i 0,i Qk,ij 1 i 1

E E E E

a)

b) d G,j j Gk,j P Pk Q,1 Qk,1 Q,i 0,i Qk,ij 1 i 1

E E E E E

j Reduction factor for unfavourable permanent actions Gk,j

(j = 0,85 indicative)


Tw

innin

g L

atv

ia


Accidental design situations

• General Format

dA GA,j k,j pA k d 1,1 k,1 2,i k,ij 1 i 1

E E G P A Q Q

• Format only used in linear-elastic structural analysis


dA GA,j Gk,j PA Pk Ad 1,1 Qk,1 2,i Qk,ij 1 i 1

E E E E E E

1,1 2,1 Qk,1 1,i 2,i Qk,iE Max. E



Tw

innin

g L

atv

ia


Seismic design situations

• General Format

• Format only used in linear-elastic structural analysis:

dE k,j k Ι Ed 2,i k,ij 1 i 1

E E G P A Q

dE Gk,j Pk Ι AEd 2,i Qk,ij 1 i 1

E E E E E



Tw

innin

g L

atv

ia


2.3 Serviceability Limit States (SLS)

Formats for linear-elastic structural analysis (normal case)

Rare (characteristic) combination

normally used for irreversible limit states (e.g. remaining deformations):

d,rare Gkj Pk Qk1 0i Qkij 1 i 1

E E E E E


01 Qk1 0i Qki1 E Max. 1 E

∙


Tw

innin

g L

atv

ia


Frequent combination

normally used for reversible limit states (e.g. corrosion attack on reinforcement in cracked concrete):

d,frequ Gkj Pk 11 Qk1 2i Qki

j 1 i 1

E E E E E


11 21 Qk1 1i 2i QkiE Max. E

Quasi-permanent combination

Normally used for long-term effects and the appearance of the structure (e.g. deformations of the structure):

d,perm Gkj Pk 2i Qkij 1 i 1

E E E E

2.3 Serviceability Limit States (SLS)


Tw

innin

g L

atv

ia


2.4 Fatigue Limit State (FLS)

The level of the design values of actions – including the relevant numbers of load cycles – corresponds to the Serviceability Limit State (SLS).

The level of the design values of material resistances – depending on the numbers of load cycles – corresponds to the Ultimate Limit State (ULS).

For fatigue design, the combinations of actions depend on the kind of material and, therefore, are given in EN 1992 to EN 1999.


Tw

innin

g L

atv

ia


00,50,6Temperature (non-fire) in buildings 00,20,6Wind loads

00,20,5 Sites located at altitude H ≤ 1000 m above sea level 0,20,70,7 Sites located at altitude H > 1000 m above sea level

Snow and ice loads 000

Category H:

roofs

0,30,50,7 Category G:

traffic areas,30 kN < v. weight 160 kN

0,60,7 0,7 Category F:

traffic areas, vehicle weight 30 kN

0,80,91,0 Category E:

storage areas

0,60,70,7 Category D:

shopping areas

0,60,70,7 Category C:

congregation areas

0,30,50,7 Category B:

office areas

0,30,50,7 Category A:

domestic, residential areas

Imposed loads in buildings (see EN 1991-1-1)210

Action

2.5 factors for buildings (recommended values)


Tw

innin

g L

atv

ia


1,00 -A accidental

1,00 1,30 Q Variable, unfavourable

1,00 1,00 G permanentC) Failure of the soil ground failure or loss of stability of a slope (GEO)

1,00-Aaccidental

1,001,50Qvariable, unfavourable

1,001,00G,inf favourable

1,001,35G,supPermanent, unfavourable B) Failure of the structure,

one of its members or of the foundation (STR)

1,00-A accidental

1,001,50Q variable, unfavourable

0,950,95G,infsmall deviations

1,001,05G,supin case of

0,950,90G,inf favourable

1,001,10G,sup permanent, unfavourable A) Loss of static equilibrium (EQU)

A P/T

SituationSymbolActionsUltimate Limit State (ULS)

2.6 Partial factors F applied to actions (recommended

values)


Tw

innin

g L

atv

ia


Differentiation of design values of permanent actions

Loss of static equilibrium (EQU)

The characteristic values of all the permanent actions are separated into two parts:

• all the parts acting unfavourably are multiplied by the factor G,sup;

• all the parts acting favourably are multiplied by the factor G,inf.

Failure of the structure, one of its members, or of the foundation (STR) All the characteristic values of one independent (single) permanent action Gk are multiplied by one unique factor G:

• by G,sup, if the resulting effect of Gk is unfavourable,

• by G,inf, however, if the resulting effect of Gk is favourable.


Tw

innin

g L

atv

ia


Design of structural members (footings, piles, basement walls, …) (STR)

Approach 1

Applying design values according to Limit State B (STR) as well as to Limit State C (GEO) – in two separate calculations – to the geotechnical actions as well as to the other actions on/from the structure.

involving geotechnical actions and the resistance of the ground (GEO)

Approach 2

Applying design values only according to Limit State B (STR) to the geotechnical actions as well as to the other actions on/from the structure.

Approach 3

Applying design values according to Limit State C (GEO) to the geotechnical actions and, simultaneously, design values according to Limit State B (STR) to the other actions on/from the structure.

The use of approaches, either 1 or 2 or 3, is chosen in the National Annex.


Tw

innin

g L

atv

ia


Design of structural members (footings, piles, basement walls, …) (STR)

involving geotechnical actions and the resistance of the ground (GEO)

Advantage of Approach 2:

The limit states STR and GEO are clearly separated.

So the structural and geotechnical verifications can be performed independently.

Structural verification:Applying design values only according to Limit State

B) Failure of the structure (STR) to the geotechnical actions as well as to the other actions on/from the structure.

Geotechnical verification:The limit state C) Failure of the soil (GEO)

– e.g. ground failure or loss of stability of a slope – should be verified in accordance with EN 1997.


Tw

innin

g L

atv

ia


3 Basis for partial factor design and reliability analysis

3.1 Overview of reliability methods

Historical methods

Empirical methods

First Order Reliability Method FORM (Level II)

Full probabilistic methods (Level III)

Semi-probablistic methods(Level I)

Partial factor design

CalibrationCalibration Calibration

Method a

Method bMethod c


Tw

innin

g L

atv

ia


Most of the partial factors and -factors established in the present Eurocodes are generated by calibration (c) of the partial factor method (Level ) to the traditional procedures for verification (a).

In both the Level and Level methods the measure of reliability should be identified with the survival probability Ps:

Ps = () = (1 – Pf),

is the cumulative distribution function of the standardised Normal distribution

is the reliability index


where Pf is the failure probability for the considered failure mode and within an appropriate reference period.

Pf = (– )


Tw

innin

g L

atv

ia


Relation between und Pf

If the calculated failure probability is higher than the target value n:

Pf > (– n), then the structure is considered unsafe!

Pf10-1 10-2 10-3 10-4 10-5 10-6 10-7

1,28 2,32 3,09 3,72 4,27 4,75 5,20



Tw

innin

g L

atv

ia


Target values of reliability index for structural members

1,53,0Serviceability (irreversible)

1,5 to 3,8 2)Fatigue

3,84,7Ultimate (RC 2)

50 (n = 50 years) 1) 1 (1 year)

Target reliability indexLimit state

2) Depends on degree of inspectability, reparability and damage tolerance

1)


nn

s,n n 1 s,1P P


Tw

innin

g L

atv

ia


Reliability differentiation in ultimate limit states (see Annex B)

50 (n = 50 years) 1) 1 (1 year)

Target reliability indexReliability class(Consequences Class)

4,35,1RC 3 (CC 3)

3,84,7RC 2 (CC 2)

3,34,3RC 1 (CC 1)

1)


nn

s,n n 1 s,1P P

Partial factors given in EN 1990 to 1999 are based on RC 2


Tw

innin

g L

atv

ia


Definition of consequences classes (see Annex B)

Consequences for loss of human life, or economic, social or environmental consequences

Consequences Class

Low: agricultural buildings, green housesCC 1

Medium: Residential and office buildingsCC 2

High: Grandstands, public buildings, concert hallsCC 3



Tw

innin

g L

atv

ia


Quality assurance (see Annex B)


Reliability Class

Consequences Class

Design supervision level

Inspection level

RC 1CC 1 Self-checking Self inspection

RC 2CC 2Checking by

different personsSpecified inspection

procedures

RC 3CC 3 Third party checking Third party inspection


Tw

innin

g L

atv

ia


3.2 R-E-Model

R = structural resistance

E = resulting action effect


Tw

innin

g L

atv

ia


r

e

fR,E(r,e)fR(r)

fE(e)

Distribution densities of R and E:

3.2 R-E-Model


Tw

innin

g L

atv

ia


fR(r)

fE(e)

r

e

fR,E(r,e)

If E and R are stochastically independent, then:

fR,E(r,e) = fR(r) · fE(e)

3.2 R-E-Model

Distribution densities of R and E:


Tw

innin

g L

atv

ia


r

e

fR,E(r,e)

fR(r)

fE(e)mE

mR

E

R Limit state function:

Z = r – e = 0

Failure part:

Z < 0

Failure probability:

Pf = ∫Z<0

fR,E(r,e) · de ∙ dr = ∫Z<0

fR(r) · fE(e) · de ∙ dr

3.2 R-E-Model


Tw

innin

g L

atv

ia


Distribution densities and limit state straight line (in the standardised space)

Precondition: e and r are stochastically independent and standard normally distributed

Survival part Failure part:

Pf = ∫Z<0

fR( ) · fE( ) · d ∙ d

Limit state straight line: Z = β – αR∙ + αE∙

Design point: yd

R

R

σmr

r

E

E

σme

e

βαe Ed

βαr Rd

f ( , ) =

fR ( ) fE ( ) = const.

r e

r e

r ree

r e


Tw

innin

g L

atv

ia


Sensitivity factors 2E

2R

EE2

E2R

RR

σσ

σα;

σσ

σα

Reliability index R E

2 2R E

m m

3.2 R-E-Model

Design values (in the original space)

βασmeandβασmr EEEdRRRd

Reliability parameters


Tw

innin

g L

atv

ia


3.3 Approach for calibration of design values

Resulting action effect ed and structural resistance rd are separated.

Survival part:Z > 0

Failure part: Z < 0

Design point: yd

min

max

Limit state straight line

R

E

σσ

min

R

E

σσ

max

E

E

σme

e

βαe E

βαr R

R

R

σmr

r

According sensibility factors E andR are assessed by fixed values with respect to the limit state expressed in standardized coordinates.


Tw

innin

g L

atv

ia


For limit state straight lines within the intervalR

E

R

E

R

E

σσ

maxσσ

σσ

min

Therefore, the design values can be determined as follows:

1 1d R R Rr F F 0,8

1 1d E E Ee F F 0,7

the sensibility factors are fixed by: R = – 0,8 and E = + 0,7

Then, the partial factors can be defined, each in relation to the according characteristic values:

E = ed / ek

R = rk / rd



Tw

innin

g L

atv

ia


Partial factors for variable actions (Gumbel distributions)


0,00

0,50

1,00

1,50

2,00

2,50

0,00 0,10 0,20 0,30 0,40

Wind and Snow LoadsImposed Loads

Q

VQ (VN; VS; VW)

S; W

N

E 50 = 0,7

3,8


Tw

innin

g L

atv

ia


Sensibility factors E1 and E2 in case of two simultaneous actions (e1, e2)

Survival part: Z > 0

Failure part: Z < 0

Design points: ed1; ed2

E

= 22,5

= 22,5

1,077E

E1 = 0

E2 = 0

E1 = E2

E2

E222 σ

mee

βα4,0e Edi

βαe Ed

E1

E111 σ

mee

βαe Ed

βα4,0e Edi

Limit state straight line for 1σσ

0E2

E1

Limit state straight line

for 0σσ

1E1

E2



Tw

innin

g L

atv

ia


In this case, the global sensibility factors E und R are multiplied by the

accompanying sensitivity factors Ei und Ri.

Design values on the safe side result, if

E1 = R1 = 1,0 is used for the leading value, and

Ei = Ri = 0,4 is used for the accompanying value

Design values of accompanying basic variables:

i i i

1 1di R R R Rr F F 0,32

i i i

1 1di E E E Ee F F 0,28



Tw

innin

g L

atv

ia


Combination of two actions (e1, e2)

Design value of the leading action:

1 1d E E Ee F F 0,7

Combination factor: 0 = edi / ed

Design value of the accompanying action:

1 1

i i i

N N1 1di E E Ee F ' F 0,4 '

where ‘ is the reliability index referred to the basic time interval T1

and N1 is the number of basic time intervals during the design working life



Tw

innin

g L

atv

ia


Design working life


Indicative design working life (EN 1990, 2.3)

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

Design working life category

Indicative design working life (years)

Examples

1 10 Temporary structures (1)

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


Tw

innin

g L

atv

ia


Combination factors 0,i for variable actions Qi


0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0,00 0,10 0,20 0,30 0,40 0,50 0,60

50 years5 years3 months1 month12 days3 days

0,i

VQ

Design working life: T = 50

E = 0,7

50 = 3,8N1 = 1

N1 = 10

N1 = 200

N1 = 600

N1 = 1500

N1 = 6000

prof. dr.-ing. jürgen grünberg universität hannover twinning latvia basis of structural design...

Documents

structural analysis

structural safety

design situations

design of repairs

partial factor design

annex d informative

testing en

jrgen grnberg slide