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ОБЩИЕ ПРОБЛЕМЫ СТРОИТЕЛЬНОЙ НАУКИ И ПРОИЗВОДСТВА
УДК 693
M. Holicky, J. Markova
Czech Technical University in Prague, Klokner Institute
IMPLEMENTATION AND APPLICATION OF EUROCODES
Technical and editorial problems may be encountered during the implementation of Eurocodes into the systems of national standards. The main technical problems to be solved include specification of the target reliability levels of different types of construction works, definition of characteristic values, partial and combination factors and load combination rules for structures and geotechnical design. It is expected that in the next generation of Eurocodes further harmonisation and reduction of NDPs on the basis of technical assessment will be provided.
Present generation of Eurocodes encompass a suite of 58 Parts which represents a great achievement in European harmonization of structural codes. The key role in the design of new and existing structures represents the concept of reliability differentiation of construction works and the selection of target reliability level. Recommended target reliability level, expressed commonly by reliability index b = -Ф-1(р), where Ф denotes the standardized normal distribution function and p the failure probability, are provided in several documents.
Load combination rules for verification of geotechnical design (ULS of type GEO) give three alternative approaches leading in some cases to considerably different results. For example, resulting dimensions of common footing may have differences about 20 to 40 %.
Other technical problems of implementation include lack of guidance for application of different design situations. For example a structure under fire should be verified according to the accidental design situation for which alternative combination factors are indicated in EN 1990. During subsequent repair the structure should comply with the requirements for the transient design situation, for which, up to now, there are no explicit rules for existing structures provided by Eurocodes.
Another problem is a unified definition of the characteristic values for variable actions, particularly for imposed and climatic actions, when 0.98 fractile for time dependent components should be supplemented by probabilistic specification of resulting action effect (for example, for imposed load and wind).
System of Eurocodes constitutes a great achievement in harmonization of European standards for structural design. In national implementation, it is strongly recommended to specify a unique (unambiguous) variant chosen from recommended options. Terminology and translation should be adapted to the sense of the original English version. Other manner of translations may be confusing or misleading.
Key words: bases of design, target reliability, partial factors, national choice.
1. Introduction. Present generation of Eurocodes encompass a suite of 58 Parts which represents a great achievement in European harmonization of structural codes. The Eurocodes were developed with technical support of European and international scientific organizations including fib, JCSS, IABSE, RILEM, and standardization committees CEN and ISO. The scientific bases of structural design were developed by the JCSS in the document Probabilistic Model Code [1], and have been updated continuously. The International standard ISO 2394 [2] constitute general design rules relevant to the verification of wide majority of buildings and civil engineering works. The context of structural reliability is developed furthermore through standards for risk assessment, such as the standard ISO 13824 [3] and the JCSS Guideline on Risk Assessment [4].
Most European countries have already implemented Eurocodes into their system of national standards. They have developed National Annexes with selected Nationally
© Holicky M, Markova J., 2012
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Determined Parameters (NDPs) supplemented in some cases also by non-contradictory information (NCCI). However, current existence of more than 1600 NDPs in Eurocodes and possibility for their national choice adversely influences intended harmonization of European standards for structural design.
Joint Research Centre (JRC) has prepared a database for collection of NDPs of CEN Member States. It is foreseen to analyse NDPs with intention for their further harmonization and considerable reduction. However, presently about half of CEN countries are filling up the JRC database only what makes considerable obstacle for analyses of NDPs. It is partly caused by slow implementation process in some countries, by technical problems including lack of experience mostly caused by non-regular attendance of meetings of the technical committee CEN/TC 250 and its subcommittees SC1 to SC9 and also by economic problems. Implementation of Eurocodes is running against several imperfections of Eurocodes as inaccuracies or faults, ambiguousness of interpretation of provisions and presence of alternative procedures. Despite that most problems were removed during translations and preparation of National Annexes, several questions of technical and editorial character remains still open.
The need for "simplification" and "shortening" of Eurocodes is a real problem for which satisfactory answers have not yet been found. The main difficulty of the problem is the feeling that what is too simple may be wrong, and what is exact is often too complex and may be unusable in practice.
The following critical review is based on the previous studies provided in [5—7] and includes only limited number of general problems noted during application of Eurocodes in the Czech Republic. Similar difficulties to those presented here may be encountered in other countries including Russia, where the concept of limit states in conjunction with the partial factor method has been used for a long time. Presented experience and technical findings included in the following text are expected to provide valuable recommendations for majority of countries implementing Eurocodes, and for their future revisions and improvements.
2. Selected technical problems
2.1. Target reliability level. The key role in the design of new and existing structures represents the concept of reliability differentiation of construction works and the selection of target reliability level. Recommended target reliability level, expressed commonly by reliability index p = -^(p), where ®(p) denotes the standardized normal distribution function andp the failure probability, are provided in several documents [2, 5, 6]. In EN 1990 [8] the target reliability index p is given for two reference periods (1 year and 50 years) as shown in Tab. 1. However, no explicit link between the target reliability level and the design working life is provided in [8].
Tab. 1. Reliability classification in accordance with EN 1990 [8]
Reliability class Consequences of structural failure Reliability index ß for reference period Examples of buildings and civil engineering works
1 year 50 years
RC3 - high High 5,2 4,3 Granstands, public buildings
RC2 - normal Medium 4,7 3,8 Residences and offices
RC1 - low Low 4,2 3,3 Agricultural buildings
Table 1 is not easy to understand for common user and, in fact, may be misinterpreted. It should be underlined that a couple of p values (for 1 year and 50 years) given in Tab. 1 for each reliability class corresponds to the same reliability level. Practical application of these values depends on the time period considered in the verification, which may be linked to available probabilistic information concerning time variant basic variables (imposed load, climatic actions, seismic actions, etc.).
For example, for a building in reliability class 2 and the design working life of 50 years the reliability index p = 3,8 should be used provided that probabilistic models of basic variables are available for this period. The same reliability level is achieved when the reference period of 1 year and p = 4,7 are applied using the theoretical models for one year. Note that it could be sufficient to provide a set of values of reliability index p in Table 1 (taken from EN 1990 [8]) for a reference period of one year and apply a relationship given in Annex C [8] for other reference periods.
A more detail recommendation concerning reliability levels is provided by ISO 2394 [2] where the target reliability indices are indicated for the whole design working life (without any limitation) and related not only to the consequences, but also to the relative costs of safety measures (see Tab. 2).
Tab. 2. Target reliability index p (life-time, examples) in accordance with ISO 2394 [2].
Relative costs of Consequences of failure
safety measures small some moderate great
High 0 1,5 2,3 3,1
Moderate 1,3 2,3 3,1 3,8
Low 2,3 3,1 3,8 4,3
ISO 2394 [2] seems to recommend the reliability indices lower than those given in EN 1990 [8] even for the "small relative costs" of safety measures. ISO 2394 [2] recommends indices for "life-time", thus related to the design working life.
However, a clear link between the design working life and the target reliability level is not apparent from the both documents [2, 8]. Thus, it is not clear which target reliability index should be used for a given design working life different from 50 years (say 100 years applied commonly for bridges). Obviously, it is desired to clarify the link between the design working life and the reliability index and to provide guidance for specification of the target reliability level for a given design working life. It appears that the results of probabilistic optimization should be supplemented by practical recommendations.
2.2. Partial factor method. In accordance with the partial factor method accepted in EN 1990 [8] the design values of the basic variables, Xd and Fd, are usually not introduced directly into the design expressions. They are commonly expressed in terms of their representative values X and F , which may be:
rep rep' J
the characteristic values Xk and Fk, i.e. values with a prescribed or intended probability of being exceeded, for example for actions, material properties and geometrical properties; the nominal values X and F , which may be treated as characteristic values for mate-
nom nom' J
rial properties and design values for geometrical properties.
The representative values X and F should be divided and/or multiplied, respectively.
rep rep
by the appropriate partial factors to obtain the design values Xd and Fd. Considering the representative values X and F by their characteristic values X and F , the design values X
rep rep k k d
and Fd can be expressed as
X/Ym (6)
Fd = Yf Fk (7)
where ym denotes the partial factor of materials properties, and yf the partial factor of action. Both partial factors ym and yf are in most cases greater than 1.
As described in the following sections, both partial factors ym and yf should include model uncertainties, which may significantly affect the reliability of a structure. As stated in EN 1990 [8], design values for model uncertainties may be incorporated into the design expressions through the partial factors YEd and ym applied as follows:
ed = y ede {y g; Y pp; Y qiqki; y v v0iqia; ad..); (8)
Rd = R { Xk' Ym; ai-)/y
Rd ■
(9)
Here ^ denotes a conversion factor appropriate to the material property. The factor y, which takes account of reductions in the design values of variable actions, is applied as y or to simultaneously occurring accompanying variable actions. The following simplifications may be made to Eqn. (8) and (9).
a) On the loading side (for a single action or where linearity of action effects exists):
E = E (YF/rep,,. «d>. (1°)
b) On the resistance side the general format is given in Eqn. (9), and further simplifications may be given in the relevant material-oriented documents.
The relation between individual partial factors in Eurocodes is schematically indicated in Fig. 1. The partial factor yF may be split into the load intensity uncertainty factor y and model uncertainty factor yEd. Similarly, the partial factor yM may be split into the material property factor ym and resistance model uncertainty factor yRi.
Generally, it holds that
Yf = Yf YEd; (11)
Ym = Ym Y*d. (12)
Numerical values of both factors of model uncertainty depend on particular conditions and should be derived from previous experience and available experimental data. The factor of load effect gEd may be expected within the interval from 1,05 to 1,15. The resistance factor gRd depends on the construction materials and behaviour of the structural member. For example, uncertainty of the bending capacity of a steel beam will be lower (about 1,05) than uncertainty of a welded connection capacity (about 1,15).
Fig. 1. Partial factors in EN 1990 [8]
2.3. Partial factors for permanent actions. Consider a permanent load G having a normal distribution. It is assumed that the characteristic value Gk of the mean (xG:
Gk = G
Then the design value Gd is given as
Gd = ^ - aF x p x ^ = »g (1 + °,7 x P x VP.
In equation (14) »G denotes the mean, aG the standard deviation, VG the variation and aE = - 0,7 the sensitivity factor of actions as recommended in EN partial factor gG of G can be then determined from the ratio
Yg
G/ G
Taking into account equation (13) and (14) it follows from (15) that
Yg = (1 + 0,7 x p x Vg)
Fig. 2 shows the variation of the partial factor yg with the reliability index coefficients of variation VG. If VG = 0,1 and p = 3,8, then the partial factor yg = 1 if VG = 0,03 (a safe value for self-weight and massive structures), then yg = 1,08
(self-weight) G is equal to
(13)
(14)
coefficient of 1990 [8]. The
(15)
(16)
P for selected 27. However, . Obviously, a
single partial factor y = 1,35 recommended in [8] is a conservative value. A series of realistic values y > 1,05 are provided in [9] e.g. for self-weight of different materials (concrete, steel, soil). Similar values of partial factors were also recommended in original Czech standards.
2,5
Yg
1,5
0,5
0 1 2 3 4 5
P
Fig. 2. Variation of the partial factor gG with the reliability index b for selected values of the coefficient of variation
2.4. Partial factors for variable actions. A similar procedure as in the case of the permanent load G can be used for estimation of the partial factors gQ for variable loads Q. Assuming the Gumbel distribution, the characteristic value of action is usually defined as 0,98 fractile of annual extremes (or extremes related to a certain basic reference period) and is given as
a = ^ (1 - V0 (0,45 + 0,78 ln(-ln(0,98)))).
(17)
The design value Qd related to the working life described by period ratio N is given as
Qd = »q (1 - Wq (0,415 - 0,78ar ln(N)+ 0,78ln(-ln(F1(-a£P)))). (18)
In Eqn. (17) and (18) |Q denotes the mean, wQ the coefficient of variation of extreme values of Q determined for the basic reference periods (for 1 or 5 years), N denotes the ratio of the working design life, for example 50 years, and the basic reference period. As an example, the period ratio N = 10 (= 50/5) is considered below. Finally, aE = - 0,7 is the sensitivity factor of Q and aT is the time-sensitivity factor given by the ratio w'Q / wQ, where w'Q denotes the coefficient of variation of the time-dependent component of Q and wQ denotes the coefficient of variation of the total Q. When Q depends on time-dependent components only, w'Q = wQ and aT = 1. Note that the reliability index p in Eqn. (18) is related to the design working life (for example to 50 years) and not to the basic reference period (for example to
1 or 5 years). The partial factor yQ of Q is given as
Yq = Qd/ Qk (19)
The partial factor yQ of a variable action Q defined by Eqn. (19) depends on five parameters. In addition to wQ, aE p (used also in the case of time-invariant basic variables), the partial factor of variable actions yQ depends also on the period ratio N and on the time-sensitivity factor aT. Fig. 3 shows the variation of yQ with the coefficients of variation wQ for selected values of p assuming a Gumbel distribution of Q, and the period ratio N = 10 (the design working life 10 times greater than the basic reference period) and the time-sensitivity factor aT = 1 (no time-independent components).
It should be noted that the time-variant component may have a considerably lower variability than the total action Q, and, therefore, a reduced coefficient of variation should be considered in Eqn. (20) for estimating time-variant effects (aT < 1). Consequently, the predicted design value Qd and the partial factor y would decrease. Without going into details, it ap-
2
1
pears that the value yQ = 1,5, which is recommended in EN 1990 [8], is a reasonable approximation corresponding to the reliability index p = 3,8, the coefficient of variation wQ = 0,3 (that may be considered as a reduced coefficient of variation of the extremes of Q) and to the period ratio N = 10 (the design working life being 10 times of the basic reference period).
The factor yQ = 1,5 appears to be conservative for VQ < 0,3 and unsafe for VQ > 0,3. Note that yQ = 1,4 is given in Russian code [13] for snow and wind actions (yQ = 1,4 for snow and yQ = 1,2 to 1,3 for wind actions in original Czech standards).
Yq 1.8
1.6
1.4 1.2
ß= 4,3
3 ,8
ß= 3,3
0.2
0.4
0.6 0.8
WQ
Fig. 3. Variation of yQ with the coefficients of variation wQ for selected values of p assuming a Gumbel distribution of Q, period ratio N=10 and aT = 1
yq wQ = 0 .8
WQ = 3.5 /
WQ = 0.3
ß
1.6
1.4
1.2
Fig. 4. Variation of yQ with the reliability index b for selected values of the coefficients of variation wg assuming a Gumbel distribution of Q, ratio N = 10 and aT = 1
2.5. Load combination rules. Two alternative procedures are given in EN 1990 [8] for verification of EQU. The first procedure is based on separate verification of EQU and application of STR (if needed), the second approach is based on combined verification and appears to be in some cases less safe.
Load combination rules for verification of Ultimate limit states (ULS) of type strength (STR) described in EN 1990 [8] by expression (6.10) and its modification (6.10a) and (6.10b) offer two alternatives which may lead to significant differences in load effects (commonly about 15—20 %). This problem is well known and already thoroughly analysed in [6, 7]. As a result of these investigations it is strongly recommended to specify in national
2
0
2
2
3
4
4.5
5
implementation a unique (unambiguous) variant, similarly as in recently revised Russian standard [9].
Load combination rules for verification of geotechnical design (ULS of type GEO) give three alternative approaches leading in some cases to considerably different results. For example resulting dimensions of common footing may have differences about 20 to 40 %.
3. Other technical problems
Other technical problems of implementation include lack of guidance for application of different design situations. For example a structure under fire should be verified according to the accidental design situation for which alternative combination factors are indicated in EN 1990 [8]. During subsequent repair the structure should comply with the requirements for the transient design situation, for which, up to now, there are no explicit rules for existing structures provided by Eurocodes.
Another problem is a unified definition of the characteristic values for variable actions, particularly for imposed and climatic actions, when 0,98 fractile for time dependent components should be supplemented by probabilistic specification of resulting action effect (for example for imposed load and wind, [9, 10]).
Concerning imposed load provided in EN 1991-1-1 [9], a more detail guidance on the specification of the load intensity from recommended intervals is needed. Clarification of when the partitions and parapets are acting as barriers and should be exposed to horizontal loads is to be provided.
The document on accidental loads EN 1991-1-7 [11] should be further elaborated and supplemented by other sources of accidental loads (explosion of various chemicals). The procedure of risk assessment should be provided by appropriate risk criteria.
4. Editorial problems
The formal editorial problems including terminology and translation cause significant difficulties in many countries, particularly in those countries (including the Czech Republic and Russia) where the concept of limit states in conjunction with the partial factor method have been used for a long time. Eurocodes were developed much later, and, consequently, are based on new scientific basis available at that time. Unfortunately, in those days available documents on partial factor methods (as earlier versions of recently revised standard [2]) have not been taken into account.
New terminology and translation of English versions of Eurocodes cause sometimes difficulties and misunderstanding. Translations to different European languages may be in some cases confusing and misleading and should be prepared with help of experts on structural design. To avoid future ambiguity it is recommended to adopt the terminology and adapt the translation to the sense of the original English versions. For facilitation of national implementation of European standards, several Czech technical vocabularies have been prepared which are focused on loading, reliability of structures and material oriented structures.
5. Evolution of eurocodes
Further evolution of Eurocodes proposed in document [12] includes simplifications and clarification of provisions, revision of serviceability criteria (imperfections, deflections, vibrations), incorporation of the latest results of research including structural glass, FRP polymers, membrane structures, guidance for existing structures, re-consideration of the status of certain clauses or annexes, improvement of the liaison with other European standards, evaluation of contents with regards to mainly first two basic requirements of the Construction Product Directive (CPR). The basis of design rules will be transferred from several parts of EN 1991 and EN 1993 to Annexes A3 to A5 of EN 1990 [8].
It is foreseen to reduce the number of NDPs on the basis of analysis of JRC database and review possible need for changes in the National Annexes in comparison to recommended values provided in Eurocodes.
ВЕСТНИК 10/2012
It is proposed to develop requirements for robustness of structures, for design of fatigue, for application of non-linear approach and to introduce criteria for displacement and vibration of structures in EN 1990 [8].
6. Conclusions
(1) System of Eurocodes constitutes a great achievement in harmonization of European standards for structural design.
(2) The main technical problems of implementation with regards to the basis of design include specification of the target reliability level, definition of the characteristic values, partial and combination factors and load combination rules for various types of structures and geotechnical design.
(3) In national implementation, it is strongly recommended to specify a unique (unambiguous) variant chosen from recommended options.
(4) Terminology and translation should be adapted to the sense of the original English version. Other manner of translations may be confusing or misleading.
(5) Next generation of Eurocodes should be drafted with regards to the need for further harmonization and reduction of NDPs, for simplification and user-friendly applications.
Acknowledgements
This study was partly conducted within the GACR project P105/12/589.
References
1. Probabilistic model code. JCSS. 2008. http://www.jcss.byg.dtu.dk/publications.
2. ISO 2394. General principles on reliability for structures. ISO. Geneva, 1998.
3. ISO 13824. General principles on reliability for structures. ISO. Geneva, 1998.
4. Guideline on Risk Assessment. Principles, System Representation & Risk Criteria. JCSS. 2008. http://www.jcss.byg.dtu.dk/publications.
5. Gulvanessian H., Calgaro J.-A., Holicky M. Designer's Guide to EN 1990, Eurocode: Basis of Structural Design. Thomas Telford, London, 2002, 192 pp. (Russian translation published by MGSU, Moscow, 2011).
6. Holicky M. Reliability analysis for structural design. ISBN 978-1-920338-11-4, SUN MeDIA, Stellenbosch, South Africa, 2009, 199 p.
7. Holicky M., Markova J. Calibration of partial factors for design of concrete structures. ICASP 2011, Curych.
8. EN 1990. Basis of structural design. CEN, 2002.
9. EN 1991-1-1. Action on structures - Part 1-1 General actions — densities, self-weight, imposed load for buildings. CEN, 2002.
10. EN 1991-1-4 Action on structures - Part 1-4 Wind actions. CEN, 2005.
11. EN 1991-1-7 Action on structures - Part 1-7 Accidental actions from impact and explosion. CEN, 2006.
12. Calgaro J.A. The Eurocodes and Construction Industry. Medium-Term Strategy. 2008—2013. CEN/TC 250, 2010.
13. Construction Norms and Rules 2.01.07—85. Collection of Rules: Loads and Actions. Construction Rules 20.13330.2011.
Поступила в редакцию в августе 2012 г.
About the authors: Holicky Milan — Ph.D., Prof., Deputy Director, Klokner Institute, Czech Technical University in Prague (CTU), Solinova 7, 166 08 Prague 6, Czech Republic, [email protected]; +420 2 2435 3842;
Markova Jana — Assoc. Prof., researcher, Klokner Institute, Czech Technical University in Prague (CTU), Solinova 7, 166 08 Prague 6, Czech Republic, [email protected]; +420 2 2435 3501.
For citation: Holicky M., Markova J. Implementation and Application of Eurocodes. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 10, pp. 11—19.
М. Голицки, Я. Маркова
Чешский технический университет
ВВЕДЕНИЕ ЕВРОКОДОВ В СОСТАВ НАЦИОНАЛЬНЫХ СТАНДАРТОВ И ИХ ПРИМЕНЕНИЕ
Введение Еврокодов в состав систем национальных строительных стандартов может сопровождаться проблемами как лингвистического, так и технического характера. Основные технические проблемы представляют собой определение необходимых уровней надежности различных видов строительных конструкций, числовых значений всевозможных параметров, частичных и комбинированных коэффициентов, правил сочетаемости нагрузок на конструкции, а также требований к геотехническому проектированию. Следующее поколение Еврокодов будет характеризоваться более высокой степенью гармонизации и сокращением численности параметров, значения которых будут устанавливаться на внутринациональном уровне.
Ключевые слова: основы проектирования, требования к надежности, частичные коэффициенты, национальный выбор.
Об авторах: Голицки Милан — кандидат технических наук, профессор, заместитель директора Института Клокнера, Чешский технический университет в Праге (ЧТУ), 166 08, Прага-6, ул. Солинова, д. 7, Республика Чехия, +420 2 2435 3842, [email protected];
Маркова Яна — доцент, научный сотрудник Института Клокнера, Чешский технический университет в Праге (ЧТУ), 166 08, Прага-6, ул. Солинова, д. 7, Республика Чехия, +420 2 2435 3501, [email protected].
Для цитирования: Holicky M., Markova J. Implementation and application of Eurocodes // Вестник МГСУ. 2012. № 10. С. 11—19.
