International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Duration-of-load effect on the rolling shear strength of cross laminated timber : reliability analysis… Li, Yuan; Lam, Frank Jul 31, 2015

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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 Blaß, 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 (Blaß and Görlacher, 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 (Jöbstl 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: 𝑖𝑖𝑖𝑖 𝜎𝜎(𝑡𝑡) > 𝜏𝜏0𝜎𝜎𝑠𝑠  𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡= 𝑎𝑎(𝜎𝜎(𝑡𝑡) − 𝜏𝜏0𝜎𝜎𝑠𝑠)𝑏𝑏 + 𝑐𝑐(𝜎𝜎(𝑡𝑡)− 𝜏𝜏0𝜎𝜎𝑠𝑠)𝑛𝑛𝑑𝑑 𝑖𝑖𝑖𝑖 𝜎𝜎(𝑡𝑡) ≤ 𝜏𝜏0𝜎𝜎𝑠𝑠                         𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡 = 0 where 𝑑𝑑 is the damage state variable (𝑑𝑑 = 0 in an undamaged state and 𝑑𝑑 = 1 in a failure state); 𝑡𝑡 is the time; 𝜎𝜎(𝑡𝑡) is the applied stress history; 𝜎𝜎𝑠𝑠  is the short-term strength; 𝜏𝜏0  is a ratio of the short-term strength 𝜎𝜎𝑠𝑠; thus, the product 𝜏𝜏0𝜎𝜎s  is a threshold stress below which there will be no accumulation of damage; and, 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝜏𝜏0  and 𝑛𝑛 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 specimens’ 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 𝑎𝑎 , is expressed approximately by the ramp rate Ks , the strength 𝜎𝜎s  and model parameters, τ0 and b. 𝑎𝑎 ≅Ks (1 + b)[𝜎𝜎s − τ0𝜎𝜎s](1+b) then, the predicted number of cycles to failure in the trapezoidal tests can be expressed as follows: Nf =log(K1 + K0 − 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 =α2K1− 1        K1 = α1 where α1 and α2 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 τ0) and the developed ramp rolling shear strength were assumed to be lognormally distributed. The lognormal distributed rolling shear strength 𝜎𝜎𝑠𝑠  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 𝜎𝜎(𝑡𝑡) 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 𝑏𝑏 39.857 2.219 𝑐𝑐 3.483 × 10−8 2.466 × 10−8 𝑛𝑛 6.754 0.117 𝜏𝜏0 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 𝑁𝑁𝑖𝑖  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 𝑁𝑁𝑖𝑖th cycle, because only 𝑁𝑁𝑖𝑖  value as whole number (in Table 1) with rolling shear failure was measured in the tests. However, as the 𝑁𝑁𝑖𝑖  increases, this error becomes trivial because the 𝑁𝑁𝑖𝑖  value is much larger. For example when 𝑁𝑁𝑖𝑖 = 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 𝑁𝑁𝑖𝑖  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(𝑁𝑁𝑖𝑖 ) values. Figure 7 shows the cumulative distributions of the experimental and the simulated Log( 𝑁𝑁𝑖𝑖 ) 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:  1.25𝐷𝐷𝑛𝑛 + 1.50𝑄𝑄𝑛𝑛 = 𝜙𝜙𝑅𝑅𝑅𝑅(0.05)𝑇𝑇𝑉𝑉  (1) where 𝐷𝐷𝑛𝑛  is the design dead load which is normally computed using average weights of materials, and 𝑄𝑄𝑛𝑛  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, 𝜙𝜙 is the performance factor applied to the characteristic strength (i.e., 𝑅𝑅𝑅𝑅(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 𝑅𝑅𝑅𝑅(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. 𝑇𝑇𝑉𝑉  is the ratio between load capacity and shear strength (in 𝑘𝑘𝑁𝑁/𝑀𝑀𝑀𝑀𝑎𝑎), which will be introduced in the next paragraph; therefore, 𝑅𝑅𝑅𝑅(0.05)  is not dependent on the ratio 𝑇𝑇𝑉𝑉  used. 𝑇𝑇𝑉𝑉  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 𝑇𝑇𝑉𝑉  values are shown in Table 4.  Table 4: Summary of the calculated 𝑇𝑇𝑉𝑉  values (in 𝑘𝑘𝑁𝑁/𝑀𝑀𝑀𝑀𝑎𝑎) for five-layer CLT  Five-layer CLT 𝑇𝑇𝑉𝑉  from layered beam theory 𝑇𝑇𝑉𝑉  from gamma beam theory 𝑇𝑇𝑉𝑉  from shear analogy theory 11.24 11.90 11.76  From Equation (1), the performance factor 𝜙𝜙 will affect the reliability index 𝛽𝛽; with a given 𝜙𝜙, the performance function G for the calculation of the reliability index 𝛽𝛽 is: 𝐺𝐺 = 𝑅𝑅 − (𝐷𝐷 + 𝑄𝑄) 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 𝑅𝑅𝑅𝑅(0.05)  in Equation (1); 𝐷𝐷  is the random dead load; and, 𝑄𝑄  is the random live load. Then, the ratio of the design dead load to the design live load is defined as: 𝑟𝑟 =𝐷𝐷𝑛𝑛𝑄𝑄𝑛𝑛= 0.25 therefore, the performance function G is:  𝐺𝐺 = 𝑅𝑅 −𝜙𝜙𝑅𝑅𝑅𝑅(0.05)𝑇𝑇𝑉𝑉(1.25𝑟𝑟+1.50)(𝑑𝑑𝑟𝑟 + 𝑞𝑞) (2) where the random variables d and q are: 𝑑𝑑 =𝐷𝐷𝐷𝐷𝑛𝑛     𝑞𝑞 =𝑄𝑄𝑄𝑄𝑛𝑛 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 𝛽𝛽 and the performance factor 𝜙𝜙. 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 𝛽𝛽 − 𝜙𝜙 relationship is slightly different; this small difference comes from the different term 𝑇𝑇𝑉𝑉  in Equation (2), and this 𝑇𝑇𝑉𝑉  is changing when different beam theories are adopted.  The average 𝛽𝛽 in Figure 8 is then calculated from the 𝛽𝛽 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 𝜙𝜙 = 0.834 which is around 0.9 at a target reliability index 𝛽𝛽 = 2.80. For the short-term bending strength of lumber in the Canadian design code, the performance factor is 𝜙𝜙 = 0.9 . Therefore, the obtained 𝜙𝜙 in Figure 8 for CLT is close to the 𝜙𝜙 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 𝛽𝛽 − 𝜙𝜙 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:  𝐺𝐺 = 1 − 𝑑𝑑 (3) where 𝑑𝑑  is the damage parameter from the damage accumulation model. If 𝐺𝐺>0, the sample will survive. If 𝐺𝐺 <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 𝐾𝐾𝐷𝐷  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 𝛽𝛽 − 𝜙𝜙 relationship. The first case is curve one without considering the DOL effect, based on the average 𝛽𝛽 − 𝜙𝜙 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 𝛽𝛽 = 2.8  (consistent with the literature) (Foschi, 1989), the performance factor for curve one is defined as 𝜙𝜙𝐼𝐼, and 𝜙𝜙𝐼𝐼𝐼𝐼  is the factor from curve two. Then the strength adjustment factor 𝐾𝐾𝐷𝐷  for the rolling shear strength is defined as:  𝐾𝐾𝐷𝐷 =𝜙𝜙𝐼𝐼𝐼𝐼𝜙𝜙𝐼𝐼 (4) For example, Table 5 shows the relationship between the reliability index 𝛽𝛽  and the performance factor 𝜙𝜙  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 𝛽𝛽 𝜙𝜙𝐼𝐼 𝜙𝜙𝐼𝐼𝐼𝐼  𝐾𝐾𝐷𝐷  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 𝐾𝐾𝐷𝐷  is shown in Table 5. 𝐾𝐾𝐷𝐷  is around 0.466 to 0.617 when the reliability index 𝛽𝛽 = 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 𝐾𝐾𝐷𝐷  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). “Duration of load and probability of failure in wood, part 1: Modeling creep rupture.” Canadian Journal of Civil Engineering, 5(4), 505-514. Barrett, J.D. (1996). “Duration of load: the past, present and future." International COST 508 Wood Mechanics Conference, Germany. Blaß, H.J., and Görlacher, R. (2003). “Brettsperrholz. Berechnungsgrundlagen.” Holzbau Kalender, Karlsruhe, Bruder, 580-598. Bodig, J., and Jayne, B.A. (1982). “Mechanics of wood and wood composites.” Van Nostrand Reinhold Company, New York, USA. Canadian Standard Association (CSA). (2009). “Engineering Design in Wood. Standard CSA O86-09.” Canadian Standards Association, Mississauga, ON, Canada. Chen, Y. (2011). “Structural performance of box based cross laminated timber system used in floor applications.” Ph.D. Thesis, Dept. of Wood Science, University of British Columbia. European Committee for Standardization. (2004). “Eurocode 5: Design of timber structures. Part 1-1: General – Common rules and rules for buildings.” EN 1995-1-1, Brussels, CEN. Fellmoser, P., and Blaß, H. J. (2004). “Influence of RS modulus on strength and stiffness of structural bonded timber elements.” CIB-W18/37-6-5, Edinburgh, U.K. Foschi, R.O., and Barrett, J.D. (1982). “Load duration effects in western hemlock lumber.” Journal of the Structural Division, ASCE, 108(7), 1494-1510. Foschi, R.O., and Yao, F.Z. (1986). “Another look at the three duration of load models.” In Proceedings of IUFRO Wood Engineering Group meeting, Florence, Italy, paper 19-9-1. Foschi, R.O. (1989). “Reliability-based design of wood structures.” Structural Research Series, Dept. of Civil Engineering, University of British Columbia, Canada, Report No. 34. Gerhards, C.C., and Link, C.L. (1987). “A cumulative damage model to predict load duration characteristics of lumber.” Wood and Fiber Science, 19(2), 147-164. Jöbstl, R.A., and Schickhofer, G. (2007). “Comparative examination of creep of glulam and CLT slabs in bending.” CIB-W18/40-12-3, Bled, Slovenia. Kreuzinger, H. (1999). “Platten, Scheiben und Schalen - ein Berechnungsmodell fur gangie Statikprogramme.” Bauen Mit Holz,1, 34-39. Laufenberg, T.L., Palka, L.C., and McNatt, J.D. (1999). “Creep and creep-rupture behaviour of wood-based structural panels.” Project No. 15-65-M404, Forinteck Canada Corp.. Li, Y., Lam, F., Li, M., and Foschi, R.O. (2014). “Duration-of-load effect on the rolling shear strength of cross laminated timber: duration-of-load tests and damage accumulation model.” Proc. of WCTE 2014, Quebec City, Canada. Li, Y. (2015). “Duration-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). “Structural behaviour of timber." Timber Engineering Ltd., Vancouver, British Columbia, Canada. 

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