Inference on stiffness and strength of existing chestnut timber elements using Hierarchical Bayesian Probability Networks

Abstract

The assessment of the mechanical properties of existing timber elements could benefit from the use of probabilistic information gathered at different scales. In this work, Bayesian Probabilistic Networks are used to hierarchically model the results of a multi-scale experimental campaign, using different sources of information (visual and mechanical grading) and different sample size scales to infer on the strength and modulus of elasticity in bending of structural timber elements. Bayesian networks are proposed for different properties and calibrated using a large set of experimental tests carried out on old chestnut (Castanea sativa Mill.) timber elements, recovered from an early 20th century building. The obtained results show the significant impact of visual grading and stiffness evaluation at different scales on the prediction of timber members’ properties. These results are used in the reliability analysis of a simple timber structure, clearly showing the advantages of a systematic approach that involves the combination of different sources of information on the safety assessment of existing timber structures.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. 1.

    JCSS (2006) JCSS Probabilistic Model Code, Part 3: Resistance Models – 3.5 Properties of Timber. Probabilistic Model Code. Joint Committee on Structural Safety

  2. 2.

    Cavalli A, Togni M (2013) How to improve the on-site MOE assessment of old timber beams combining NDT and visual strength grading. Nondestruct Test Eva 28(3):252–262

    Article  Google Scholar 

  3. 3.

    Bonamini G, Togni M, Uzielli L (1995) The strength and stiffness of large ancient timber beams: experimental assessment of the effectiveness of combined visual grading and non-destructive testing. In: 1st international conference on science and technology for the safeguard of cultural heritage in the Mediterranean Basin, Catania

  4. 4.

    Feio A, Machado JS (2015) In-situ assessment of timber structural members: combining information from visual strength grading and NDT/SDT methods - A review. Const Build Mater. doi:10.1016/j.conbuildmat.2015.05.123

    Google Scholar 

  5. 5.

    Faggiano B, Grippa MR, Marzo A, Mazzolani FM (2011) Experimental study for non-destructive mechanical evaluation of ancient chestnut timber. J Civ Struct Health Monitor 1(3):103–112

    Article  Google Scholar 

  6. 6.

    Sousa HS, Sørensen JD, Kirkegaard PH, Branco JM, Lourenço PB (2013) On the use of NDT data for reliability-based assessment of existing timber structures. Eng Struct 56:298–311. doi:10.1016/j.engstruct.2013.05.014

    Article  Google Scholar 

  7. 7.

    Calderoni C, De Matteis G, Giubileo C, Mazzolani FM (2010) Experimental correlations between destructive and non-destructive tests on ancient timber elements. Eng Struct 32(2):442–448

    Article  Google Scholar 

  8. 8.

    Bertolini C, Brunetti M., Cavallero P, Macchioni N (1998) A non destructive diagnostic method on ancient timber structures: some practical application examples. In: WCTE98, 5th world conference on timber engineering, Montreaux

  9. 9.

    Vega A, Dieste A, Guaita M, Majada J, Baño V (2012) Modelling of the mechanical properties of Castanea sativa Mill. structural timber by a combination of non-destructive variables and visual grading parameters. Eur J Wood Wood Prod 70(6):839–844. doi:10.1007/s00107-012-0626-7

    Article  Google Scholar 

  10. 10.

    Isaksson T (1999) Modelling the variability of bending strength in structural timber. Report TVBK-1015, Dept. of Structural Engineering, Lund University

  11. 11.

    Denzler JK (2007) Modellierung des Größeneffektes bei biegebeanspruchtem Fichtenschnittholz. Ph.D. dissertation, Technische Universität München

  12. 12.

    Fink G, Deublein M, Kohler J (2011) Assessment of different knot-indicators to predict strength and stiffness properties of timber boards. In: Proceedings of the 44th meeting, international Council for Research and Innovation in Building and Construction, Working Commission W18, Timber Structures, Alghero, Italy, CIB-W18, Paper No. 44-5-1

  13. 13.

    Fink G, Kohler J (2014) Model for the prediction of the tensile strength and tensile stiffness of knot clusters within structural timber. Eur J Wood Wood Prod 72(3):331–341. doi:10.1007/s00107-014-0781-0

    Article  Google Scholar 

  14. 14.

    Madsen B (1992) Structural behaviour of timber, chapter 6: Duration of load. Timber engineering LTD, Canada. ISBN 0-9696162-0-1

  15. 15.

    Barrett JD, Foschi RO (1978) Duration of load and probability of failure in wood. Part 1: modelling creep rupture. Can J Civil Eng 5(40):505–514

    Article  Google Scholar 

  16. 16.

    Gerhards CC (1979) Time-related effects on wood strength: a linear cumulative damage theory. Wood Sci 11(3):139–144

    Google Scholar 

  17. 17.

    Deublein M, Schlosser M, Faber MH (2011) Hierarchical modeling of structural timber material properties by means of Bayesian Probabilistic Networks. In: Faber M, Köhler J, Nishijima K (eds) Applications of Statistics and Probability in Civil Engineering. Taylor & Francis Group, London, pp 1377–1385

    Google Scholar 

  18. 18.

    Sousa HS, Branco JM, Lourenço PB (2015) Use of bending tests and visual inspection for multi-scale experimental evaluation of chestnut timber beams stiffness. J Civil Eng Manag. doi:10.3846/13923730.2014.914083

    Google Scholar 

  19. 19.

    UNI (2004) UNI 11119:2004 Cultural heritage - wooden artifacts - load-bearing structures - on site inspections for the diagnosis of timber members. UNI Milano

  20. 20.

    Sousa HS, Branco JM, Lourenço PB (2013) Effectiveness and subjectivity of visual inspection as a method to assess bending stiffness and strength of chestnut elements. Adv Mat Materials Res 778:175–182. doi:10.4028/www.scientific.net/AMR.778.175

    Article  Google Scholar 

  21. 21.

    CEN (2010) EN 408:2010 - Timber structures - Structural timber and glued laminated timber - Determination of some physical and mechanical properties, European Committee for Standardization, Brussels

  22. 22.

    Solli KH (2000) Modulus of elasticity - local or global values. In: WCTE2000, 6th world conference on timber engineering, Whistler

  23. 23.

    Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers, Inc., San Mateo

    MATH  Google Scholar 

  24. 24.

    Jensen FV (2001) Bayesian Networks and Decision Graphs. New York Springer

  25. 25.

    Aguilera PA, Fernández A, Fernández R, Rumí R, Salmerón A (2011) Bayesian networks in environmental modelling. Environ Model Softw 26(12):1376–1388. doi:10.1016/j.envsoft.2011.06.004

    Article  Google Scholar 

  26. 26.

    Weber P, Medina-Oliva G, Simon C, Iung B (2012) Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas. Eng Appl Artif Intel 25(4):671–682. doi:10.1016/j.engappai.2010.06.002

    Article  Google Scholar 

  27. 27.

    Czomch I, Thelandersson S, Larsen H (1991) Effect of within member variability on bending strength of structural timber. In: Proceedings of the CIB-W18 Meeting 24, Paper 24-6-3, Oxford

  28. 28.

    Köhler J (2007) Reliability of Timber Structures. Ph.D. dissertation, Department of Civil, Environmental and Geomatic Engineering, Zurich, ETH Zurich

  29. 29.

    Hugin (2008) Hugin Researcher, Aalborg, Hugin Experts A/S

  30. 30.

    Brites RD, Lourenço PB, Machado JS (2012) A semi-destructive tension method for evaluating the strength and stiffness of clear wood zones of structural timber elements in-service. Constr Build Mater 34:136–144. doi:10.1016/j.conbuildmat.2012.02.041

    Article  Google Scholar 

  31. 31.

    Kloiber M, Drdácký M, Machado JS, Piazza M, Yamaguchi N (2015) Prediction of mechanical properties by means of semi-destructive methods: a review. Constr Build Mater 101:1215–1234. doi:10.1016/j.conbuildmat.2015.05.134

    Article  Google Scholar 

  32. 32.

    Piazza M, Riggio M (2008) Visual strength-grading and NDT of timber in traditional structures. J Build Appraisal 3(4):267–296

    Article  Google Scholar 

  33. 33.

    CEN (2009) EN 338:2009. Structural timber - Strength classes. CEN European Committee for Standardization, Brussels

  34. 34.

    JCSS (2001) JCSS Probabilistic Model Code, Part 2: Load Models. Probabilistic Model Code, Joint Committee on Structural Safety

  35. 35.

    Ranta-Maunu A (2004) Theoretical and practical aspects of the reliability analysis of timber structures. In: WCTE 2004 conference, Lahti

  36. 36.

    Faber MH, Sørensen JD (2003) Reliability based code calibration – the JCSS approach. In: ICASP9, vol. 2. San Francisco, pp. 927–935

  37. 37.

    Hansen PF, Sørensen JD (2002) Reliability-based code calibration of partial safety factors. In: Joint Committee of Structural Safety, JCCS-Workshop on Code calibration

  38. 38.

    Köhler J, Fink G (2012) Reliability Based Code Calibration of a Typical Eurocode 5 Design Equations. In: WCTE 2012 conference, vol. 4. Auckland, pp 99–103

  39. 39.

    CEN (2004) EN 1995-1-1:2004, Eurocode 5: design of timber structures. Part 1-1: General common rules and rules for buildings, CEN European Committee for Standardization, Brussels

  40. 40.

    CEN (2002) EN 1990:2002, Eurocode 0: Basis of Structural Design, European Committee for Standardization, Brussels

Download references

Acknowledgments

The financial support of the Portuguese Science Foundation (Fundação de Ciência e Tecnologia, FCT), through Ph.D. Grant SFRH/BD/62326/2009, is gratefully acknowledged. The authors acknowledge also the support of Augusto de Oliveira Ferreira e Ca., Lda. (offer of specimens).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hélder S. Sousa.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sousa, H.S., Branco, J.M., Lourenço, P.B. et al. Inference on stiffness and strength of existing chestnut timber elements using Hierarchical Bayesian Probability Networks. Mater Struct 49, 4013–4028 (2016). https://doi.org/10.1617/s11527-015-0770-8

Download citation

Keywords

  • Structural reliability
  • Bayesian Probabilistic Networks
  • Existing timber structures
  • Bending stiffness
  • Bending strength