Fatigue Design of Aluminium Structures according to the new Eurocode 9 Univ. Prof. Dr.-Ing. Dipl. Wirt.-Ing. (NDS) Martin Mensinger SIA * Dr.-Ing. Christina Radlbeck ** * Technische Universität München, Chair of Metal Structures, Germany
[email protected] ** Technische Universität München, Chair of Metal Structures, Germany
[email protected] Abstract: The preliminary document of the Eurocode 9 (EC 9, EN 1999), Design of Aluminium, was adopted in May 1998 as ENV 1999. Currently work is under way for the conversion to a full European Norm EN 1999 (1) consisting of Part 11: ‘General structural rules’, Part 1-2: ‘Structural fire design’, Part 1-3: ‘Additional rules for structures susceptible to fatigue’, Part 1-4: ‘Supplementary rules for cold-formed sheeting’ and Part 1-5: ‘Supplementary rules for shell structures’. According to the European Committee for standardization (CEN) national standards are to be replaced by Eurocodes as from 31.03.2010. In this paper, the innovative concepts and procedures according to the EC 9 are presented. Since lightweight and hence an R-ratio of 0.4 to 0.5 make aluminium an adequate material for structures with dynamic loading, such as bridges, it is focused on fatigue design. Thereby three separate fatigue design procedures are distinguished: traditional safe-life design, based on evaluation of S-N curves, damage tolerant design, and design assisted by testing. Key Words: aluminium, bridges, Eurocode 9, fatigue, innovative design concepts 1 Introduction The Eurocode 9 on design together with EN 1090-3 on execution are in many ways pioneer documents for the design of aluminium structures: They provide to the engineering community a comprehensive tool to deal with a variety of structural shapes, joints, and loading cases. A broad range of wrought and cast alloys for structural components, along with characteristic values for the material properties, and for connecting devices (bolts, rivets) in both aluminium and steel is considered. In addition marginal structural problems are covered, in detail especially welded and adhesively bonded joints. Also biaxial bending, interaction effects as well as rules for fatigue design never have been clearly addressed in national aluminium codes before. First results even prove that the design procedures included in EC 9 provide more economic results than national standards, such as DIN 4113 for Germany (see Figure 1 and [1, 2]). Since the EC 9 gives extensive advice considering not only analysis, but also material and manufacturing characteristics, it resembles rather an instruction manual than a design standard. Although not expressly stated, it is anticipated that the EC 9 will serve other applications besides buildings, like “structural engineering works”. Thereby also bridges are covered. 1,8 1,6
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■ Xi (EC 9dead loads)/ Xi (DIN 4113H-loads); ■ Xi (EC 9live loads)/ Xi (DIN 4113H-loads) Figure 1: Static system of a traffic sign bridge with unit loads and ratio of maximum applicable forces Xi according to the EC 9 –Part 1 [3] and DIN 4113 [4,5] of the traffic sign bridge
2 Aluminium in Bridges Indeed, aluminum structures as primary load carrying as well as secondary elements offer excellent properties for bridge structures. As main advantage, there is to mention its lightweight (1/3 steel) together with high strength values. According to the type of alloy, strength values within the range of steel are yielded. In general, this results in a weight reduction of 50 to 60% when using aluminum instead of steel [6]. This allows for equal (sometimes even lower) initial costs of the structure although material costs in general are much higher for aluminum (Figure 2). Other advantages are presented by its functionality because of various alloys and extruded profiles, natural corrosion resistance, formability, workability and flexibility. In addition transport and (dis-)assembly are simplified and aluminium structures can be nearly completely prefabricated (Figure 6). In bridge rehabilitation these properties become significant with rapid and easy installation of repair parts and the possibility to keep original piers, etc. In very large structures reduction of the dead load of the structure itself significantly reduces overall cost, as it reduces the weight of other primary parts as well, such as pylons, cables, anchorages. The benefits of aluminum get even more obvious by considering the whole life cycle. Thereby durability, low if any maintenance cost and no loss of quality during recycling are the main characteristics (Figure 2).
Discounted Costs [€]
Wood Steel Reinforced Concrete Aluminium
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Figure 2: Comparison of four bridge systems made of different materials (for details see [7]) Since 1995 in North America as well as in Europe and also in Japan, new initiatives were taken to develop and promote aluminium bridge designs. In Europe, particularly in Norway and Sweden, approximately 80 bridge decks have been built from aluminium since 1990, replacing timber or concrete. And also in the Netherlands there is a renewed interest in aluminium bridges. Although long-span aluminium bridges are interesting because of weight reduction, the number of these bridges is rather small. However, bridges with typical spans up to 20 m, which are found in large numbers. In general aluminium is often used for pedestrian bridges (Figure 3), temporary / movable bridges (Figure 4 and 5) and renovation of bridge decks (Figure 6). Especially for the latter two application areas fatigue design is an important issue.
Figure 3: Pedestrian Bridge, Germany [7]
Figure 4: Riekerhaven bridge in Amsterdam, Netherlands [8]
Figure 5: The floating road, various lovcations [9]
Figure 6: Forsmo Bridge, Norway 3 Fatigue Design according to Eurocode 9 (EN 1999-1-3) In the following the main concepts and procedures are presented. In total three separate fatigue design procedures are distinguished: (a) traditional safe-life design, based on evaluation of S-N curves, (b) damage tolerant design, and (c) design assisted by testing.
3.1 Safe-Life-Design In safe-life design it was decided to group the different structural details in three slope value groups (m=7 or 4,3 or 3,4 in the main cycle range from 105 to 5⋅106 cycles), the first covering practically parent material, the other two all welded details. Together with assuming a higher cycle range as the reference point for estimation of design S-N curves this approach allows for a closer fit to actual test data in the cycle range of primary interest for aluminium applications and thus more economical design [10]. An equidistant mesh of standardised values for the design curves, i.e. the value ΔσC [N/mm²] at 2⋅106 cycles, has been conceived, introducing a logical pattern in case of necessary reductions due to corrosion or thickness effects (Figure 7). The mean stress effect was also taken into account in design by introducing a bonus factor (Figure 8). logs Standard Values 60 N/mm²
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Figure 7: Equidistant design value mesh [11]
Figure 8: Concept for enhancement by the Bonus factor f(R) [4]
3.2 Damage Tolerant Design This method is introduced as a complementary option to safe-life design, in case that the latter with the linear damage accumulation leads to values larger than unity. Of special importance is the fact that in the case of aluminium complete information about the crack propagation behaviour of the material and its welded joints is available [12], [13], allowing for respective quantitative establishment of inspection intervals. 3.3 Design by Testing For acceptance of a safe life design, the life to failure determined by test, adjusted to take account of the number of test results available, should be Tm ≥ F·TL with TL: design life (in cycles), Tm: the mean life to failure determined by test (in cycles), and F: factor dependent upon the effective number of test results available – to be defined. In practice only estimates for the mean and standard deviation of the population, i.e. xm and s respectively, may be calculated for a sample size n, Figure 9. Accordingly correction factors expressing the confidence intervals of both the mean and the variance (or standard deviation) have to be applied. The multiplier K (infinite sample size) thus becomes k (limited sample size) and includes a theoretical value k1 of the distribution belonging to a specific probability of survival, a correction for the confidence interval of the standard deviation k2 and the mean k3 respectively. These depend on the standard deviation s, sample size n and, naturally, on the desired level of confidence α. The factors k1, k2 and k3 can be expressed by the normal, chi-square (standard deviation) and t-Student (mean) distributions respectively for a given probability of survival and confidence level, Fehler! Verweisquelle konnte nicht gefunden werden.10.
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In most practical applications the assumptions can be made that: (1) the standard deviation value is known from previous experience, i.e. based on a sufficiently large sample size – this allows k2 to be set to unity, (2) sufficient knowledge of the underlying distribution is available or no significant deviation from the normal distribution exists and (3) in the correction for the confidence interval for the mean the t-distribution may be replaced by the normal distribution.
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Figure 9: Test data distributions [11]
Figure 10: Probability, confidence margins [11]
For more specimens all tested to failure we have k = k1 + k2 + k3 = z(1-α/2) + z(1- α/2) / √n. In the case of more specimens simultaneously tested until failure of first specimen and in order to estimate k, we may assume that the resulting life of the first specimen – relating to TL – from the expression Tm ≥ F·TL will lie on the upper boundary of the respective distribution, and the required or design life – relating to Tm from expression Tm ≥ F·TL - will be at the lower boundary of the distribution. The lower boundary will be derived from xm–k1·s, with k1 according to Figure 10. The upper boundary will be derived correspondingly from the expression xm+k4·s. The appropriate value of k4 is calculated from the assumption that if the probability of survival of one specimen, failing at the corresponding life, is P, then the probability of survival of n specimens at the same level will be Pn. To be on the safe side a sufficiently low value for Pn = c will be defined, and k4 is calculated from the normal distribution at c1/n probability for corresponding values n. The factor k is calculated from k = k1 + k2 = z(1-α/2) + zp. Expression Tm ≥ F·TL may be transformed to logTL = logTm – logF and by comparison to the expressions in 9 we get logF = ks or F = 10ks. The factor F can be obtained from Figure 11 for the two options of testing. The value of the standard deviation has to be estimated. Previous experience with similar structural cases provides more reliable values. Data available for various aluminium welded structural details give a range of different standard deviation values slogΔσ. These may be transformed by the respective average regression line slope of m = 4 to values slogN for the life range up to the constant amplitude fatigue limit of N = 5x106. The values F for the testing option of more specimens simultaneously tested until failure of first specimen are based on a probability of survival of 95% and a confidence level of 0,95 for the normal distribution and a standard deviation value of slogN=0,18. In the case of first sample to fail a probability of survival value of Pn=5% is assumed.
Figure 11: Fatigue test factor F [11] 4 Conclusions Aluminium is an adequate material for bridges. Its main advantages are low weight (1/3 steel) and excellent corrosion resistance. In general, aluminium is used in bridge design to reduce initial and operating costs, to reduce lifetime costs, e.g. less maintenance, to simplify assembly, transport as well as construction, to enable prefabrication and finally to increase the live load on existing bridges. Thus the main application areas of aluminium are pedestrian bridges, movable/temporary bridges and the renovation of bridge decks. For the realization efficient methods for static and fatigue design are needed. The new EC 9 provides respective design procedures. EN 1999-1-1 1 includes innovative design checks yielding efficient results. Concerning EN 1999-1-3, the three fatigue design procedures, safe life design, damage tolerant design and design assisted by testing, include all necessary tools for respective applications. A quantitative correlation and harmonisation of quality characteristics of structural details with fatigue service behaviour will be a significant task of the future. Finally, it can be summarized, that the new EC 9 provides much potential for the static and fatigue design of aluminium structures. Acknowledgment Between 1978 and 2006 Prof. Kosteas was the head of the Section for Light Metal Structures at the TU München. During this time, he was deeply involved in the development of the EC 9 especially of Part 1-3 concerning fatigue design. Therefore the fatigue part of this paper is based on his work. 5 References [1] Radlbeck, C.: Ganzheitliche Analyse und Bewertung von tragenden Aluminiumkonstruktionen, Dissertation, Fachgebiet Leichtmetallbau und Ermüdung, TU München, 2006.
[2] [3] [2] [3] [4] [6] [7]
[8] [9] [10]
[11] [12]
[13]
Meyer-Sternberg, M.: Aluminium im Brückenbau, Dissertation, Fachgebiet Leichtmetallbau und Ermüdung, TU München, 2003 EN 1999-1-1: Eurocode 9 - Design of aluminium structures. Part 1: General structure rules, CEN, Brussels, May 2007. DIN 4113-1 (1980): Aluminiumkonstruktionen unter vorwiegend ruhender Belastung, Tei 1: Berechnung und bauliche Durchbildung. 1980. Deutsches Institut für Normung e.V., Beuth Verlag, Berlin. DIN 4113-1 /A1 (2002): Aluminiumkonstruktionen unter vorwiegend ruhender Belastung, Teil 1: Berechnung und bauliche Durchbildung, Änderung A1, Deutsches Institut für Normung e.V., Beuth Verlag, Berlin. EN 1999-1-3: Eurocode 9 - Design of aluminium structures. Part 3: Structures susceptible to fatigue, CEN, Brussels, May 2005. Kosteas, D.: Rehabilitation of Bridge Decks with Aluminium, Donaubrückenkonferenz, Regensburg, GER, 1998. Heitel, S.; Koriath, H.; Herzog, C. S.; Specht G.: Vergleichende Lebenszykluskostenanalyse für Fußgängerbrücken aus unterschiedlichen Werkstoffen, Bautechnik, Zeitschrift für den gesamten Ingenieurbau 85. Jahrgang Oktober 2008, Heft 10, S. 687–695, ISSN 0932-8351. aluMATTER: case study: Aluminium Bridges, published electronically: http://aluminium.matter.org.uk (June 2009). H2OLLAND architecture with wet feet: THE FLOATING ROAD, published electronically: http://www.h2olland.nl/project.asp?id=264 (June 2009). Kosteas, D.: Zum Betriebsfestigkeitsverhalten von Aluminium – On the Fatigue Service Behaviour of Aluminium, Stahlbau Spezial 67 „Aluminium in Practice“, Ed.: D. Kosteas, Verlag Ernst & Sohn, Berlin, pp. 111-130, 1998. Kosteas, D.; Radlbeck, C.: Static and Fatigue Design of Aluminium Structures according to the new Eurocode 9, ICSAS July, Oxford, UK, 2007. Jaccard, R.: Zum Bruchverhalten von Aluminium-Bauteilen – On the Fracture Behavior of Aluminium Structural Elements, Stahlbau Spezial 67 „Aluminium in Practice“, Ed.: D. Kosteas, Verlag Ernst & Sohn, Berlin, pp. 5465, 1998. Ondra, R.; Kosteas, D.: Practice-oriented Design Values for the Crack Propagation of Welded Aluminium Joints, Stahlbau Spezial 67 „Aluminium in Practice“, Ed.: D. Kosteas, Verlag Ernst & Sohn, Berlin, pp. 108-110, 1998.
