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Duration of load effects of solid wood; Methods and models

Duration of load effects of solid wood; Methods and models. COST Action E55 Joint 3rd MC/WG meeting Graz, Austria 2007. Staffan Svensson Dept. Civil Engineering Technical University of Denmark nss@byg.dtu.dk. kg. kg. kg.

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Duration of load effects of solid wood; Methods and models

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  1. Duration of load effects of solid wood; Methods and models COST Action E55 Joint 3rd MC/WG meeting Graz, Austria 2007 Staffan Svensson Dept. Civil Engineering Technical University of Denmark nss@byg.dtu.dk

  2. kg kg kg The effect of long-term load on load carrying capacity of structural timber and engineered wood products Knots and natural variation of wood reduces the load carrying capacity of wood to between a half and a quarter. Long-term effects may reduces the load carrying capacity another half for structural timber to a third for EWP. All wood based products are effected by long-term load.

  3. kg F Traditional DOL-test procedure, sampling Short-term (En 408) Grading into two mechanically equivalent sub-samples (MOE) Long-term

  4. F fm [MPa] E [MPa] Relative difference of short-term strength for samples matched on modulus of elasticity S. 1 Simulation 2 x 100 specimen S. 2

  5. kg F F S time tf Traditional test procedure, direct results F R d

  6. Traditional test procedure, results after equal rank matching Si/Ri = SLRi Equal rank

  7. kg Drawbacks of traditional constant load until failure test. • Time consuming • Space consuming • Information limited • One-to-one matching of specimens submitted to different test procedure It should also be stressed that the type of DOL experiments described are quite expensive relative to the information obtained due to the need for extensive specialized equipment, a large testing area and considerable manpower. But perhaps the worst drawback of the experimental method is that it does not in itself provide an understanding of the basic mechanism that creates the observed DOL phenomenon. (quote from Madsen 1992)

  8. Demand for other DOL test procedures? Requirements for new test procedures: Reduction of test duration Reliable results Provide an understanding of the basic mechanism that creates the observed DOL phenomenon

  9. F Deflection Failure Failure Short-term 2dp Long-term dp Dt Time F Duration of deformation (DOD) test procedure Short-term Long-term

  10. F F RSt RLt Time F DOD test procedure, direct results Short-term R Effects of long-term loading may be found as mean values and deviations from hole samples. Long-term

  11. DOD and DOL comparison DOD Test series SLR = ratio of mean failure load acc. def. step test and mean of maximum load short-term test tf = Dt DOL Test series SLR = ratio of S and mean of maximum load short-term test tf = median of tf,i

  12. Madison curve, linear regression in log(t) Regression models, Madison curves Fitted M. Parameters (ML) A = 0.915 B = 0.054 s = 0.019 Madison curve, Hyperbolic Fitted M. Parameters (ML) A = 0 B = 0.947 C = 0.033 s = 0.016

  13. Arrhenius type models 1-Par Gerhards Fitted M. Parameters (ML) B = 52.79 s = 0.579 In Arrhenius empirical relation the natural logarithm of rate (of a reaction) is proportional to the activation energy, under isothermal conditions. In the damage accumulation model proposed by Gerhards the natural logarithm of damage rate is proportional to the ratio of applied load, S(t), and short-term capacity, R0 as: 2-Par Gerhards Fitted M. Parameters (ML) A = 37.27 B = 40.24 s = 0.334

  14. Phenomenological type models Origin from general functional relation: Wood B & F 1 B & F 2 F & Y F & Y Fitted M. Parameters (ML) B = 13.76 C = 0.371 D = 3.956 s = 0.368

  15. Fracture mechanics type models Nielsen’s model The fracture mechanics approach is based on the hypothesis that the material contains ultra cracks and that damage is accumulated when the cracks grow. Failure will initiate when ultra cracks, in a material region, connect and form propagating micro cracks. LFM model Fitted M. Parameters (ML) A = 0.981 / 1 / n = 172 / 0.161 / t = 11712 / 7528 / s = 0.301 / 0.304/

  16. Strain energy type models Reiner and Weisenberg’s material reliance Bach’s material reliance Fridley’s impeding failure Energy models postulate that there is limit for the energy input or a defined fraction of the energy input, where energy inputs on or above this limit are failure states. Fitted M. Parameters (ML) Wcr = 17.21 E = 0.001 h = 407.8 Ek = 0.005 hk = 2.42 s = 0.009

  17. Deformation kinetics type models On an ultra (molecular) level of a material with molecule chains as in wood, three distinct responses to excitation on a molecule level may occur. One response is a change of bond length between and within the molecules. If no locking of the deformed state takes place this response is energetic elastic. A second response is straightening or bundling of molecule chains. If no locking of the deformed molecules takes place this response is entropy elastic. The third response is breaking and re-bonding of bonds between molecules. This response is not elastic. Deformation kinetics when applied to long-term effects on wood, describes the third response type. Failure as a result of long-term loading is determined by localized strain deformation i.e. strain limit (Caulfield 1985). In Van der Put (1989) the definition of material failure is when the rate of bond breaking exceeds the re-bonding. Fish (1983) uses cease in change of entropy,DS = 0 as a failure criterion

  18. Deformation kinetics type models cont. Caufield (Gerhards) Fitted M. Parameters (ML) A = 37.27 B = 40.24 s = 0.334 Fish Fitted M. Parameters (ML) A = 0.175 B = 30.16 s = 0.356 Van der Put Fitted M. Parameters (ML) A = 0.797 B = 35.21 C = 38.91 s = 0.335

  19. Comparison in time domain

  20. Model calibration traps Model redundancy to test Fitted M. Parameters (ML) Wcr = Fixed, cf. graph E = 0.015 – 0.371 h = 4830 - 102000 Ek = 0.066 -2.01 hk = 28.7 - 856 s = 0.009

  21. Test results are dominating kmod = 0.75, 0.76, 0.77 for Gerhards’, Nielsen’s Foschi’s models

  22. Conclusions Sampling methods influence the test results from DOL – tests. A models feature can be constrained by the test results on which it has been calibrated. A model is never better than the test it has been calibrated/verified against. A good model is a model that can be verified in different test types.

  23. The questions Is it possible to find the best model for predicting the effect of long-term load on structural timber as long as the only reference for calibration is a traditional DOL-test? Is the test results from a traditional DOL-test a good enough tool for determine the modification factors in the structural codes, or is other test types needed to for better utilization of timber and increased reliability of timber structures?

  24. Thank you for your attention

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