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

2. The effect of long-term load on load carrying capacity of structural timber and engineered wood products kg
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. kg kg

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

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

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

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

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

10. DOD test procedure, direct resultsF
Short-term
Time F
RSt
RLt F 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
Fewell AR (1986 Testing and analysis carried out as part of the Prices Risborough Laboratory’s programme to examine the duration of load effect on timber. Western Forintek Spec. Publication No. SP-27

12. Regression models, Madison curves
Madison curve, linear regression in log(t)
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
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:
1-Par Gerhards
Fitted M. Parameters (ML)
B = 52.79
s = 0.579
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
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.
Nielsen’s model
LFM model
Fitted M. Parameters (ML)
A = / 1 /
n = / /
t = / 7528 /
s = / 0.304/

16. Strain energy type models
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.
Reiner and Weisenberg’s material reliance
Bach’s material reliance
Fridley’s impeding failure
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 = – 0.371
h =
Ek =
hk =
s = 0.009

21. Test results are dominating
kmod = 0.75, ,
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