12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 Duration-of-Load Effect on the Rolling Shear Strength of Cross Laminated Timber: Reliability Analysis and Duration-of-Load Strength Adjustment Factor Yuan Li Graduate Student, Dept. of Wood Science, University of British Columbia, Vancouver, Canada Frank Lam Professor, Dept. of Wood Science, University of British Columbia, Vancouver, Canada ABSTRACT: In this study, the duration-of-load (DOL) effect on the rolling shear strength of cross laminated timber (CLT) was evaluated. A stress-based damage accumulation model is chosen to evaluate the DOL effect on the rolling shear strength of CLT. This model incorporates the established short-term rolling shear strength of material and predicts the time to failure under arbitrary loading history. The model was calibrated and verified based on the test data from low cycle trapezoidal fatigue tests (the damage accumulation tests). The long-term rolling shear behaviour of CLT can then be evaluated from this verified model. As the developed damage accumulation model is a probabilistic model, it can be incorporated into a time-reliability study. Therefore, a reliability assessment of the CLT products was performed considering short-term and snow loading cases. The reliability analysis results and factors reflecting the DOL effect on the rolling shear strength of CLT are compared and discussed. The results suggest that the DOL rolling shear strength adjustment factor for CLT is more severe than the general DOL adjustment factor for lumber; and, this difference should be considered in the introduction of CLT into the building codes for engineered wood design. 1. INTRODUCTION Cross laminated timber (CLT) is a wood composite product suitable for floor and wall applications, and it consists of crosswise oriented layers of wood boards that are either glued by adhesives or fastened with aluminum nails or wooden dowels. The CLT panel usually includes three to eleven layers, as shown in Figure 1. Figure 1: Layering of CLT Rolling shear stress is defined as the shear stress leading to shear strains in a radial-tangential plane perpendicular to the grain (Fellmoser and BlaΓ, 2004). For general timber design, rolling shear strength and stiffness are not major design properties. For CLT, however, rolling shear strength and stiffness must be considered in some loading scenarios due to the existing cross layers (BlaΓ and GΓΆrlacher, 2003). For example, when a CLT floor panel is supported by columns, highly concentrated loads in the supporting area may cause high rolling shear stresses in cross layers; the same concerns may arise for designing short-span floors or beams under out-of-plane bending loads. Under out-of-plane bending loads, for example, the CLT panel capacity can sometimes be governed by the rolling shear failure in the cross layers, as shown in Figure 2 (JΓΆbstl and Schickhofer, 2007). Therefore, there is a need to evaluate the rolling shear strength properties for practical applications of CLT structures. In general, wood is stronger under loads of short-term duration and is weaker if the loads are sustained. This phenomenon is called duration of load; and, the primary relationship between the stress ratio, also known as the load ratio (i.e., the ratio between the applied stress and the short-term strength) and the time to failure is commonly referred to as the duration-of-load (DOL) effect. In fact, the DOL effect is not introduced by material deterioration, such as 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 2 biological rot; rather, it is an inherent characteristic of wood. Figure 2: Rolling shear behaviour in cross layers Although it is well known that the strength properties of wood products are influenced by the DOL effect (Barrett and Foschi, 1978; Foschi and Barrett, 1982; Gerhards and Link, 1987; Laufenberg et al., 1999; Madsen, 1992), there is very little research reported on studying the DOL effect on the rolling shear strength of CLT. Therefore, more research work is needed to quantify the DOL effect and reduce the possibility of CLT rupture under long-term loading throughout its intended service life. Li et al. (2014) performed short-term ramp loading tests and low cycle trapezoidal fatigue loading tests to accumulate damage in the research of the rolling shear DOL behaviour of CLT. In this research, basic short-term rolling shear strength distribution was first established by short-term ramp loading; the time to failure data from the low cycle trapezoidal fatigue loading tests was obtained to understand the development of deflection and damage accumulation process. The theory of the damage accumulation model is one of the key tools to investigate the DOL behaviour in wood-based products (Foschi, 1989; Gerhards and Link, 1987). A stress-based damage accumulation model was developed by Foschi and Yao (1986) to consider the DOL effect on the strength properties of dimensional lumber (Foschi and Barrett, 1982; Foschi, 1989). The Foschi and Yao model considers the damage accumulation rate as a function of stress history and the already accumulated damage state as follows: ππππ ππ(π‘π‘) > ππ0πππ π πππππππ‘π‘= ππ(ππ(π‘π‘) β ππ0πππ π )ππ + ππ(ππ(π‘π‘)β ππ0πππ π )ππππ ππππ ππ(π‘π‘) β€ ππ0πππ π πππππππ‘π‘ = 0 where ππ is the damage state variable (ππ = 0 in an undamaged state and ππ = 1 in a failure state); π‘π‘ is the time; ππ(π‘π‘) is the applied stress history; πππ π is the short-term strength; ππ0 is a ratio of the short-term strength πππ π ; thus, the product ππ0ππs is a threshold stress below which there will be no accumulation of damage; and, ππ, ππ, ππ, ππ0 and ππ are random model parameters. The Foschi and Yao model was adopted in the current DOL research of CLT rolling shear capacity. In this study, by analysing the measured data from the trapezoidal fatigue loading tests (Li et al., 2014), the stress-based damage accumulation model was calibrated and verified. This verified model can then be used to quantify the rolling shear DOL effect of CLT under other loading conditions. As the damage accumulation model is a probabilistic model, it can be incorporated into a time-reliability study. Therefore, a reliability assessment of the CLT products was performed considering short-term and snow loading cases. The reliability analysis results and factors reflecting the DOL effect on the rolling shear strength of CLT are compared and discussed. 2. EXPERIMENTAL TESTS AND DAMAGE ACCUMULATION MODEL 2.1. Introduction of Specimens and Test Results The detailed information in this section can be found in the literature (Li et al., 2014). Five-layer Spruce-Pine-Fir (SPF5) CLT plates were studied; they were denoted as SPF5-0.4 for convenience. The CLT beam specimens in a short span-depth ratio of 6.0 were sampled for the short-term ramp tests and the trapezoidal fatigue loading tests. The pair sampling method was adopted to assure random matching formula; in one plate replicate, specimens were selected in a staggered way for the ramp tests, and the corresponding specimens for the trapezoidal tests were cut from the same panel (Li, 2015). 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 3 Figure 3: Loading setup The ramp loading setup, the same as that of the trapezoidal tests, is shown in Figure 3. The ramp tests were displacement controlled until specimensβ failure; the speed was 2 mm/min (around 3.9 kN/min). The short-term rolling shear failure load was recorded, when the first rolling shear crack occurred in the cross layer at an inclined angle, as shown in Figure 5. In the trapezoidal fatigue loading protocol using load control method as shown in Figure 4, the uploading and unloading rate was 37.5 kN/min; this was higher than the short-term ramp loading rate. Furthermore, the ramp tests adopted the displacement control method with a constant deformation rate, so the stress rate was different from one beam to another, while the loading rate for trapezoidal cases is given in terms of stress. Figure 4: Trapezoidal fatigue loading protocol The constant load level in the plateau part was chosen as the 25th percentile of the short-term ramp rolling shear failure loads. The load was cyclically applied until the first rolling shear crack was observed with careful examination in the cross layer, defined as rolling shear failure. Two types of the trapezoidal fatigue loading tests were performed with different load duration in the plateau part. The first one, i.e., the trapezoidal short-plateau test, includes the constant loading part with a duration of 0.5tm, where tm is the duration in the uploading segment shown in Figure 4. The second type, i.e., the trapezoidal long-plateau test, has a longer plateau part which is equal to 2.0tm. The number of cycles to rolling shear failure Nf was recorded when the first rolling shear crack was observed within that Nf th cycle. The basic short-term rolling shear strength distribution can be established by the ramp tests. The time to failure data from the trapezoidal tests can be obtained to understand the development of deflection and damage accumulation process, and it can be adopted in the damage accumulation modeling process. Less than 25% of the specimens failed in the first uploading although the 25th percentile failure load was applied, due to the use of a significantly higher rate of uploading resulting in the increase of apparent short-term strength. In the modeling process, past research has shown that short-term strength property of wood increases under higher loading rate. Madsen (1992) observed a 15% increase in shear strength when the loading rate was increased by a factor of ten. Based on this information, a 15% increase in short-term rolling shear strength was assumed in the damage accumulation modeling process to account for the difference between the loading rates used in ramp and fatigue tests (Li, 2015). Table 1: Test results Group SPF5-0.4 Ramp loading rolling shear failure load (kN) Mean 19.39 COV 12.6% 25th% tile 17.79 5th% tile 14.75 No. of cycles to rolling shear failure (Nf) in trapezoidal short-plateau test Mean 66.1 STDV 76.5 Maximum cycles 281 No. of cycles to rolling shear failure (Nf) in trapezoidal long-plateau test Mean 15.2 STDV 18.5 Maximum cycles 88 Figure 5: Failure mode in the ramp loading test The ramp and the trapezoidal test results are shown in Table 1. In the short-term ramp loading tests, rolling shear failure was the major failure 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 4 mode, as shown in Figure 5. The short-term 5th and 25th percentile rolling shear capacities in Table 1 were obtained based on fitted Lognormal distributions. In the trapezoidal fatigue loading tests, the trapezoidal long-plateau test showed smaller number of cycles to rolling shear failure compared to the Nf in the short-plateau test. 2.2. The Damage Accumulation Model The theory for the damage accumulation model is one of the key tools to investigate the DOL behaviour in wood-based products. The Foschi and Yao model has been applied in the DOL investigation on the strength property of dimensional lumber (Foschi, 1989); this model was adopted in the current DOL research of CLT rolling shear capacity. In a ramp loading case, the model parameter ππ , is expressed approximately by the ramp rate Ks , the strength ππs and model parameters, Ο0 and b. ππ β Ks (1 + b)[ππs β Ο0ππs](1+b) then, the predicted number of cycles to failure in the trapezoidal tests can be expressed as follows: Nf =log(K1 + K0 β 1K1)log(K0)+ 1 where K0 and K1 are determined by analysing the damage accumulated in the first two cycles of the trapezoidal fatigue loading: K0 =Ξ±2K1β 1 K1 = Ξ±1 where Ξ±1 and Ξ±2 are the damage accumulated in the first cycle and in the first two intact cycles. Based on the equal rank assumption (Barrett, 1996), the relationship between the number of cycles to rolling shear failure (Nf from Table 1 in the logarithm scale) and the stress ratio applied is shown in Figure 6, where the data points are related to the results in Table 1. The figure shows that, under the same stress ratio, the time to failure was shorter in the trapezoidal long-plateau test, since more damage is accumulated in this test category for each loading cycle. The cumulative distribution of the measured number of cycles to rolling shear failure (Nf from Table 1 in the logarithm scale) is shown as data points in Figure 7. The model calibration procedure was based on the algorithm developed by Foschi (1989). The random parameters (i.e., b, c, n and Ο0) and the developed ramp rolling shear strength were assumed to be lognormally distributed. The lognormal distributed rolling shear strength πππ π was based on the maximum cross layer rolling shear stresses evaluated from the finite element model with consideration of the influence of higher loading rate, which used each individual ramp rolling shear failure load (from Table 1) as the load input; the short-term rolling shear strength was then corrected with a 15% strength increase due to the higher uploading rate (in trapezoidal tests) for modeling purpose, as given in Table 2. The applied stress history ππ(π‘π‘) was evaluated by finite element models as well. Table 2: Summary of the finite element evaluation results on the rolling shear strength Five-layer CLT Rolling shear strength (MPa) Mean COV 5th percentile 2.02 12.2% 1.56 Table 3: Calibration results Model parameters in SPF5-0.4 Mean STDV ππ 39.857 2.219 ππ 3.483 Γ 10β8 2.466 Γ 10β8 ππ 6.754 0.117 ππ0 0.194 0.247 Then, by employing a nonlinear function minimization procedure using the quasi-Newton method, the mean and standard deviation of the lognormal distribution for each model parameter were estimated. The damage accumulation model was calibrated against the trapezoidal long-plateau test data, as shown in Figure 6 and Figure 7. Table 3 shows the model calibration results. In Figure 6 and Figure 7, at the lower tail when ππππ is small, the model output in calibration and test results seemed to be slightly different; however, this is due to the small difference has been magnified by the logarithm scale. Also, the other reason for the small difference between the fitting and the test data at the lower tail is that, in the lower tail of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 5 distribution when the calibration was performed at the time basis, there was uncertainty of how to define the specific time to failure point within that ππππth cycle, because only ππππ value as whole number (in Table 1) with rolling shear failure was measured in the tests. However, as the ππππ increases, this error becomes trivial because the ππππ value is much larger. For example when ππππ = 100, this error is only less than 1/100=1%. Figure 6: Relationship between stress ratio and number of cycles to failure (in logarithm to base 10) Figure 7: Cumulative distributions of number of cycles to failure (in logarithm to base 10) In general, the fitting was also quite acceptable in the upper tail; therefore, it is a viable option to investigate the DOL behaviour based on the measured number of cycles to failure, which is also in time scale basis. After calibrating the model by the trapezoidal data, the relationship between the stress ratio and the number of cycles to failure can be predicted. For example, with the calibrated parameters in Table 3, simulated ππππ values were produced and compared to the trapezoidal short-plateau test data. These model calibration and verification results are shown in Figure 6, giving the relationships between the stress ratio and the predicted Log(ππππ ) values. Figure 7 shows the cumulative distributions of the experimental and the simulated Log( ππππ ) values. In Figure 6 and Figure 7, the model verifications agreed well with the test data. 3. RELIABILITY ANALYSIS 3.1. Reliability Analysis of Short-Term Rolling Shear Strength of CLT This section introduces the reliability analysis on the limit state of the short-term rolling shear strength of CLT products, without considering the DOL effect. The objective of this analysis is to evaluate the relationship between the reliability index and the performance factor in the design codes. To clarify, the reliability analysis with consideration of the DOL effect will be addressed in the next section. First, based on the ultimate strength limit state design equation from the design code: 1.25π·π·ππ + 1.50ππππ = πππ π π π (0.05)ππππ (1) where π·π·ππ is the design dead load which is normally computed using average weights of materials, and ππππ is the design live load which, in the case of snow plus associated rain for example, is taken from the distributions of annual maxima and corresponds to loads with a 1/30 probability of being exceeded (i.e., 30 years return); and, ππ is the performance factor applied to the characteristic strength (i.e., π π π π (0.05)). This characteristic rolling shear strength is chosen to be the parametric 5th percentile rolling shear stress value evaluated by Lognormal fitting (Foschi, 1989); the π π π π (0.05) is calculated with consideration of the influence of higher loading rate (consistent with the model calibration process in Section 2.2), as obtained from the finite element evaluation results on the rolling shear strength corrected with the expected 15% strength increase due to the higher loading rate for modeling purpose, as shown in Table 2. ππππ is the ratio between load capacity and shear strength (in ππππ/ππππππ), which will be introduced in the next paragraph; therefore, π π π π (0.05) is not dependent on the ratio ππππ used. ππππ in Equation (1) is defined as the ratio between the sectional rolling shear load capacity 00.20.40.60.811.21.40 0.5 1 1.5 2 2.5 3STRESS RATIOLOG(Nf)LOG(Nf) - STRESS RATIODATA TEST-SHORTMODEL-TEST-SHORT-VERIFYDATA TEST-LONGMODEL-TEST-LONG-CALIBR00.10.20.30.40.50.60.70.80.910 0.5 1 1.5 2 2.5 3CDFLOG(Nf)CDF OF LOG(Nf)DATA TEST-SHORTMODEL-TEST-SHORT-VERIFYDATA TEST-LONGMODEL-TEST-LONG-CALIBR12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 6 calculated from different beam theories (i.e., the layered beam, the gamma beam and the shear analogy theory) and the shear stress value. For each theory, the relationship between the sectional capacity and the shear stress is introduced in the literature (Bodig and Jayne, 1982; Eurocode 5, 2004; Kreuzinger, 1999); the calculated ππππ values are shown in Table 4. Table 4: Summary of the calculated ππππ values (in ππππ/ππππππ) for five-layer CLT Five-layer CLT ππππ from layered beam theory ππππ from gamma beam theory ππππ from shear analogy theory 11.24 11.90 11.76 From Equation (1), the performance factor ππ will affect the reliability index π½π½; with a given ππ, the performance function G for the calculation of the reliability index π½π½ is: πΊπΊ = π π β (π·π· + ππ) in which, R is the random variable related to the rolling shear load-carrying capacity (based on the observation from the short-term ramp loading tests in Table 1) corrected with the expected strength increase due to the higher loading rate for modeling purpose, which is consistent with the term π π π π (0.05) in Equation (1); π·π· is the random dead load; and, ππ is the random live load. Then, the ratio of the design dead load to the design live load is defined as: ππ =π·π·ππππππ= 0.25 therefore, the performance function G is: πΊπΊ = π π βπππ π π π (0.05)ππππ(1.25ππ+1.50)(ππππ + ππ) (2) where the random variables d and q are: ππ =π·π·π·π·ππ ππ =ππππππ the calculation of the random variables d and q can be found in the literature (Foschi, 1989). Two site snow loads from Halifax and Vancouver were investigated in the reliability analysis. The snow load information comes from the statistics on the maximum annual snow depth, the snow duration and the ground-to-roof conversion factors provided by the National Research Council of Canada (Foschi, 1989; Li, 2015). The objective of this reliability analysis, adopting the First Order Reliability Method (FORM), is to evaluate the relationship between the reliability index π½π½ and the performance factor ππ. Figure 8 gives the results under the Halifax snow load case. Figure 8: Curves between the reliability index and the performance factor (Five-layer/Halifax) From the above results in Figure 8, under different beam theories, the obtained π½π½ β ππ relationship is slightly different; this small difference comes from the different term ππππ in Equation (2), and this ππππ is changing when different beam theories are adopted. The average π½π½ in Figure 8 is then calculated from the π½π½ values in the three beam theories, to get an average estimation over the error from the different assumptions; it is also given in Table 5. In Figure 8, it shows that the ππ = 0.834 which is around 0.9 at a target reliability index π½π½ = 2.80. For the short-term bending strength of lumber in the Canadian design code, the performance factor is ππ = 0.9 . Therefore, the obtained ππ in Figure 8 for CLT is close to the ππ in the code for lumber. 3.2. Reliability Analysis of CLT Rolling Shear Strength under Thirty-Year Snow Load This section will introduce the reliability analysis on the limit state of CLT products under a thirty-year snow load, considering the DOL effect on the rolling shear strength to evaluate the π½π½ β ππ relationship. A Monte Carlo simulation procedure, incorporating the verified damage accumulation model in Section 2.2, was used to 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 7 determine the probability of the rolling shear failure of a single bending CLT beam specimen under load for a prescribed service life (Foschi, 1989). Then, based on the previous results from the short-term rolling shear strength reliability analysis (without considering the DOL effect), the DOL adjustment factor for rolling shear strength can be obtained with one safety margin. The Monte Carlo simulation was used to determine the probability of rolling shear failure for a service life ranging from one year to thirty years. Based on the verified model, a sample size of NR=1000 replications was chosen. Then, these simulated samples were tested under the thirty-year snow loading history as introduced in the literature (Foschi, 1989). Consistent with the procedure in Section 3.1, the snow loads from Halifax and Vancouver were considered. Dead load was also included in the service life. Then, the performance function G is: πΊπΊ = 1 β ππ (3) where ππ is the damage parameter from the damage accumulation model. If πΊπΊ>0, the sample will survive. If πΊπΊ <0, the sample will fail. Figure 9: The factor determination procedure (curve one-without DOL effect; curve two-with DOL effect) The DOL strength adjustment factor πΎπΎπ·π· can then be derived, after performing the Monte Carlo simulation. The basic determination procedure for this factor is shown in Figure 9, with two cases displayed for the π½π½ β ππ relationship. The first case is curve one without considering the DOL effect, based on the average π½π½ β ππ relationship in Figure 8. The second curve in Figure 9 includes the performed Monte Carlo simulation results with the DOL effect taken into account. With the Monte Carlo simulation results (the dots in curve two), curve two is calculated using the exponential regression fitting method. In Figure 9, at the target reliability index level π½π½ = 2.8 (consistent with the literature) (Foschi, 1989), the performance factor for curve one is defined as πππΌπΌ, and πππΌπΌπΌπΌ is the factor from curve two. Then the strength adjustment factor πΎπΎπ·π· for the rolling shear strength is defined as: πΎπΎπ·π· =πππΌπΌπΌπΌπππΌπΌ (4) For example, Table 5 shows the relationship between the reliability index π½π½ and the performance factor ππ in the five-layer CLT products, for both curve one and curve two. Table 5: Reliability results for the strength adjustment factors in the five-layer CLT Five-layer Reliability results π½π½ πππΌπΌ πππΌπΌπΌπΌ πΎπΎπ·π· Halifax 3.0 0.758 0.354 0.467 2.8 0.834 0.388 0.466 2.5 0.961 0.444 0.463 Vancouver 3.0 0.794 0.496 0.625 2.8 0.855 0.528 0.617 2.5 0.953 0.580 0.609 Then, from Equation (4), the derived DOL rolling shear strength adjustment factor πΎπΎπ·π· is shown in Table 5. πΎπΎπ·π· is around 0.466 to 0.617 when the reliability index π½π½ = 2.80. The factor difference comes from the different snow load in each location, and the average factor from the two cities is 0.541. In the Canadian design code, for lumber, the factor πΎπΎπ·π· is 0.8. Therefore, the results suggest that the DOL strength adjustment factor for rolling shear strength in CLT products seems to be very different from that in lumber. Specifically, the CLT rolling shear DOL strength adjustment factor was found to be more severe compared to the general DOL factor for lumber. 4. CONCLUSIONS The stress-based damage accumulation model theory was adopted to evaluate the DOL effect on the rolling shear strength of CLT. This model was calibrated and verified based on the collected test results; the model predictions fitted the measured data well. 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 8 As the developed DOL model is a probabilistic model, a time-reliability study of the CLT products was performed. The reliability results provided further information about the DOL effect on the rolling shear behaviour of CLT. The predictions of the time to failure from this model and this investigation process elucidated the DOL effect and provided guidance for the evaluation of the CLT DOL effect. The DOL adjustment factors on the rolling shear strength of CLT were discussed, and it is suggested that this adjustment factor for CLT is more severe than the general DOL adjustment factor for lumber. Therefore, when CLT is introduced into the building codes for engineered wood design, the DOL adjustment factor on the rolling shear strength should be considered. This study considered the DOL effect only for CLT beam specimens under concentrated load cases; therefore, different loading patterns, such as uniformly distributed loading on CLT two-dimensional panels, may influence CLT DOL behaviour. This influence needs more investigation in the future research. Since the rolling shear failure was defined at the time point when the first rolling shear crack was observed, the derived adjustment factor for CLT could be relatively conservative based on this failure definition. Therefore, further research on the rolling shear failure mechanism and its impact on the structural performance of CLT systems are suggested. 5. ACKNOWLEDGEMENT The authors would like to thank NSERC strategic network for engineered wood-based building systems for supporting this research; special thanks also go to Dr. Ricardo O. Foschi for his advice and guidance in the research. 6. REFERENCES Barrett, J.D., and Foschi, R.O. (1978). βDuration of load and probability of failure in wood, part 1: Modeling creep rupture.β Canadian Journal of Civil Engineering, 5(4), 505-514. Barrett, J.D. (1996). βDuration of load: the past, present and future." International COST 508 Wood Mechanics Conference, Germany. BlaΓ, H.J., and GΓΆrlacher, R. (2003). βBrettsperrholz. Berechnungsgrundlagen.β Holzbau Kalender, Karlsruhe, Bruder, 580-598. Bodig, J., and Jayne, B.A. (1982). βMechanics of wood and wood composites.β Van Nostrand Reinhold Company, New York, USA. Canadian Standard Association (CSA). (2009). βEngineering Design in Wood. Standard CSA O86-09.β Canadian Standards Association, Mississauga, ON, Canada. Chen, Y. (2011). βStructural performance of box based cross laminated timber system used in floor applications.β Ph.D. Thesis, Dept. of Wood Science, University of British Columbia. European Committee for Standardization. (2004). βEurocode 5: Design of timber structures. Part 1-1: General β Common rules and rules for buildings.β EN 1995-1-1, Brussels, CEN. Fellmoser, P., and BlaΓ, H. J. (2004). βInfluence of RS modulus on strength and stiffness of structural bonded timber elements.β CIB-W18/37-6-5, Edinburgh, U.K. Foschi, R.O., and Barrett, J.D. (1982). βLoad duration effects in western hemlock lumber.β Journal of the Structural Division, ASCE, 108(7), 1494-1510. Foschi, R.O., and Yao, F.Z. (1986). βAnother look at the three duration of load models.β In Proceedings of IUFRO Wood Engineering Group meeting, Florence, Italy, paper 19-9-1. Foschi, R.O. (1989). βReliability-based design of wood structures.β Structural Research Series, Dept. of Civil Engineering, University of British Columbia, Canada, Report No. 34. Gerhards, C.C., and Link, C.L. (1987). βA cumulative damage model to predict load duration characteristics of lumber.β Wood and Fiber Science, 19(2), 147-164. JΓΆbstl, R.A., and Schickhofer, G. (2007). βComparative examination of creep of glulam and CLT slabs in bending.β CIB-W18/40-12-3, Bled, Slovenia. Kreuzinger, H. (1999). βPlatten, Scheiben und Schalen - ein Berechnungsmodell fur gangie Statikprogramme.β Bauen Mit Holz,1, 34-39. Laufenberg, T.L., Palka, L.C., and McNatt, J.D. (1999). βCreep and creep-rupture behaviour of wood-based structural panels.β Project No. 15-65-M404, Forinteck Canada Corp.. Li, Y., Lam, F., Li, M., and Foschi, R.O. (2014). βDuration-of-load effect on the rolling shear strength of cross laminated timber: duration-of-load tests and damage accumulation model.β Proc. of WCTE 2014, Quebec City, Canada. Li, Y. (2015). βDuration-of-load and size effects on the rolling shear strength of cross laminated timber." Ph.D. Thesis, Dept. of Wood Science, University of British Columbia. Madsen, B. (1992). βStructural behaviour of timber." Timber Engineering Ltd., Vancouver, British Columbia, Canada.
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Duration-of-load effect on the rolling shear strength of cross laminated timber : reliability analysis… Li, Yuan; Lam, Frank 2015-07
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Title | Duration-of-load effect on the rolling shear strength of cross laminated timber : reliability analysis and duration-of-load strength adjustment factor |
Creator |
Li, Yuan Lam, Frank |
Contributor |
International Conference on Applications of Statistics and Probability (12th : 2015 : Vancouver, B.C.) |
Date Issued | 2015-07 |
Description | In this study, the duration-of-load (DOL) effect on the rolling shear strength of cross laminated timber (CLT) was evaluated. A stress-based damage accumulation model is chosen to evaluate the DOL effect on the rolling shear strength of CLT. This model incorporates the established short-term rolling shear strength of material and predicts the time to failure under arbitrary loading history. The model was calibrated and verified based on the test data from low cycle trapezoidal fatigue tests (the damage accumulation tests). The long-term rolling shear behaviour of CLT can then be evaluated from this verified model. As the developed damage accumulation model is a probabilistic model, it can be incorporated into a time-reliability study. Therefore, a reliability assessment of the CLT products was performed considering short-term and snow loading cases. The reliability analysis results and factors reflecting the DOL effect on the rolling shear strength of CLT are compared and discussed. The results suggest that the DOL rolling shear strength adjustment factor for CLT is more severe than the general DOL adjustment factor for lumber; and, this difference should be considered in the introduction of CLT into the building codes for engineered wood design. |
Genre |
Conference Paper |
Type |
Text |
Language | eng |
Notes | This collection contains the proceedings of ICASP12, the 12th International Conference on Applications of Statistics and Probability in Civil Engineering held in Vancouver, Canada on July 12-15, 2015. Abstracts were peer-reviewed and authors of accepted abstracts were invited to submit full papers. Also full papers were peer reviewed. The editor for this collection is Professor Terje Haukaas, Department of Civil Engineering, UBC Vancouver. |
Date Available | 2015-05-21 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0076184 |
URI | http://hdl.handle.net/2429/53282 |
Affiliation |
Forestry, Faculty of Wood Science, Department of |
Citation | Haukaas, T. (Ed.) (2015). Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP12), Vancouver, Canada, July 12-15. |
Peer Review Status | Unreviewed |
Scholarly Level | Faculty Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
AggregatedSourceRepository | DSpace |
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