Time-Temperature Profile across a Lumber Section Exposed to Pyrolytic Temperatures

Transcription

1 FIRE AND MATERIALS, VOL. 18, (1994) Time-Temperature Profile across a Lumber Section Exposed to Pyrolytic Temperatures D. Shrestha Robbins Engineering, Inc., PO Box , Tampa, FL , USA S. Cramer Department of Civil and Environmental Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA R. White USDA, Forest Service, Forest Products Laboratory, Madison, WI 53705, USA This paper presents a closed-form solution with empirical adjustments to predict the time-temperature profile across a lumber section when the exposure history of its surace is known. The formulation is based on the two-dimensional heat-conduction equation that includes the effects of moisture evaporation and pyrolysis of wood. The kinetic constants and adjustment factors needed in the model were estimated from the temperature profile test data of dimension lumber and other published sources. This technique offers a simple practical means to estimate the internal temperatures of structural lumber exposed to high temperatures, and has been effectively implemented in the analyses of protected wood assemblies exposed to fire situations. INTRODUCTION Structural analysis of an assembly requires prior knowledge of the strength and stiffness properties of the components that constitute it. Material properties are normally defined at ambient temperatures. When the assembly is analyzed at high-temperature conditions these properties become a function of the severity and duration of exposure. Hence, these properties must be established for each time step of the analysis. Wood members exposed to heat fluxes resulting in a temperature of 100 C (212 F) or higher for sufficiently long durations undergo thermal degradation, leading to a reduction in their strength and stiffness and, possibly, physical properties. The reductions in the strength and stiffness properties are related to the thermal response of the section, which is a function of exposure conditions and physical/thermal properties of the section. A wood member exposed to a heat source develops a unique time-temperature profile across the cross-section until the section reaches thermal equilibrium. Hence, fire-endurance modeling of a wood assembly requires the capability of predicting the thermal response of the components with sufficient accuracy. Thermal response analysis of a wood section at elevated temperature is complex and requires the solution of nonlinear transient heat transfer equations. Researchers have used different numerical techniques with different assumptions to predict the thermal response of a wood section. 1 7 An assembly will have at least several components exposed to different degrees of severity during fire exposure. It is computationally cumbersome and often impractical to use such techniques to evaluate the thermal response of each component of the assembly at each time step of the analysis process. Hence, an efficient and reliable method to predict the thermal response and the resulting effects in the properties of the components is highly desirable, even at the expense of some flexibility and accuracy. CCC /94/ by John Wiley & Suns, Ltd. The objective of this paper is to introduce a novel technique for solving an idealized two-dimensional heat transfer problem that includes the thermal degradation and moisture effects of the section. The model is then calibrated with the time-temperature profile of 51 mm 102 mm (2 in 4 in) lumber sections exposed to varied conditions so that the model can be readily used. This technique is unique and has potential application in fire-endurance modeling of structural assemblies where it is essential to estimate the thermal response of several different components simultaneously and at every incremental time step. BACKGROUND Wood is a cellulosic material primarily composed of hemicellulose (approximately 25% by weight), cellulose (50%) and lignin (25%). It undergoes thermal degradation when exposed to a heat source. In general, when wood is heated it becomes dehydrated and emits water vapor up to a temperature of 150 C (302 F); hemicellulose decomposes at C ( F), cellulose at C ( F) and lignin at C ( F). 8 Schaffer 9 has tabulated thermally induced changes of dry wood in an inert atmosphere. The pyrolysis mechanism of a wood slab heated on one surface has been described as a pyrolysis front propagating into the solid wood, leaving behind the residual char. 1 3,5 Pyrolysis of wood is generally modeled by assuming the decomposition of wood or its constituents to follow certain variations of the first-order Arrheniustype equation: 2 4,6 8,10,11 (1) Received 16 August 1993 Accepted 16 September 1993

2 212 D. SHRESTHA, S. CRAMER AND R. WHITE where ρ = local density of the pyrolyzing solid, A = rate constant or frequency factor, E = activation energy, T = absolute temperature, and R = universal gas constant. The kinetic constants A and E are established through thermogravimetric analysis of the specimen, where the weight loss of the specimen is recorded as a function of time and temperature. A wide variation occurs in the kinetic constants reported in different publications. Roberts 8 compared the kinetics data from several different sources and indicated the range of the published data as E = kj mole 1 ( Btu mole 1 ), A = to s 1 for small samples (thinner than 1.6 mm (1/16 in)) and E = kj mole 1 ( Btu mole 1 ), A = to s 1 for large samples (thicker than 93 mm (3/8 in)). White 11 measured E = kj mole 1 ( Btu mole 1 ) and A = s 1 from the thermogravimetric analysis on small samples of various species of wood. Fredlund 7 found E = kj mole 1 (22-25 Btu mole 1 ) and A = s 1 from the in-situ tests on large samples of three different species of wood. These wide variations in the kinetic data of wood reflect the complexities associated in establishing these data, and hence in modeling the pyrolysis of wood. Roberts' has discussed the influence of structural effects, heat transfer mechanism, kinetic constants, heat of reaction and variations of thermal properties in a pyrolysis model of wood. Odeen 13 and White and Schaffer 14 have observed the effects of moisture in the thermal response of wood subjected to elevated temperatures. Tinney 10 concluded that one or more break points, where the kinetic constants and the thermal properties of the specimen change, improved correlation between observed and predicted temperature profile and weight loss data. Kung 2 suggested that the variations of the thermal properties and the convective heat transfer of volatiles were essential in any refined model. He presented a onedimensional pyrolysis model of a wood slab which included transient conduction, internal convection, variable thermal properties and endothermicity. He assumed wood to pyrolyze following a first-order Arrhenius-type decomposition producing volatile pyrolysates and residual char, and neglected the effects of moisture. Atreya 3 further advanced Kung's model by incorporating a moisture zone that vaporizes and follows a first-order Arrhenius-type equation. The crack formation in the charred layer was related to the outward mass flux of volatile gases. Parker 5 advanced Atreya's model by including char shrinkage and variations in thermal properties with respect to the degree of char and temperature. In addition, different constituents of wood (hemicellulose, cellulose and lignin) were allowed to have different kinetic constants and heat of reaction. Springer and Do 4 presented a two-dimensional heat transfer model to compute temperature distribution across a section and mass loss of a wood specimen. They assumed a mass of wood to comprise an active part which can pyrolyze and an inactive part which cannot pyrolyze any further at the given temperature. At any instant the mass loss is assumed to be due to pyrolysis of active wood and vaporization of water. Both of these reactions are assumed to follow a first-order Arrheniustype equation. Fredlund 7 assumed wood material to be composed of four distinct phases: active wood which pyrolyzes producing a gaseous volatile, charcoal which oxidizes on the surface, and water in liquid and vapor phases. He developed a two-dimensional finite-element formulation to predict temperature and distribution of pore pressure across a lumber section by assuming local thermodynamic equilibrium and total energy content per volume to be equal to the energy content of individual phases. HEAT TRANSFER MODEL A number of models with different complexities and features have been put forward to model pyrolysis of wood or cellulosic materials. The models are based on some variation of the conservation of energy equation, and the solution technique on some form of numerical methods. Numerical methods generally require much computational effort and tend to be computationally prohibitive for a large assembly of wood members. Fireendurance modeling of a wood assembly requires the evaluation of the thermal response and strength/stiffness properties of individual members simultaneously, and repeatedly at incremental time steps. This has led to the development of a semi-empirical solution technique to predict the thermal response of structural lumber exposed to a heat source. A series solution is first generated by approximating and simplifying different terms of a fundamental heat transfer equation. The solution is then adjusted with correction factors based on different test data to yield a readily usable solution for conditions within the range of these data. Different assumptions made in the development of an idealized heat transfer model are: (1) A unit mass of wood constitutes active wood undergoing pyrolysis, inactive char, and moisture that evaporates. (2) The pyrolysis reaction and moisture evaporation are represented by single-step first-order Arrhenius-type reactions. (3) The thermal and physical properties of wood are constant. (4) The outward flow of the gaseous volatiles generated during the pyrolysis process is neglected. (5) Cracking of the surface is ignored. (6) Energy contents of the accumulated vapors and gaseous volatiles are ignored. From the fundamentals of conservation of energy, the transient heat conduction equation 7,15 can be approximated by assuming constant thermal properties as where k is the thermal conductivity along the x- and y -directions, ρ the mass density, c the heat capacity, T the temperature at any point in the domain at time t, and Q(t) is the net exothermic effect associated with the pyro- (2)

3 TIME-TEMPERATURE PROFILE 213 lysis of active wood (Q a (t)) and vaporization of moisture present (Qw(t)). Assuming wood to be composed of an active part which undergoes pyrolysis to produce volatile gases, an irreducible part which produces charcoal, and liquid water which poduces water vapor, the original mass density can be expressed as a sum of the individual components as (3) where ρ is the mass density with respect to original volume and the subscripts a, c, and w refer to wood, charcoal, and water, respectively. If we assume the mass flow is prevented, i.e. the volatile pyrolysis products and water vapor generated remain at the same point where the phase transformation takes place, 7 there will be no internal convection, and the internal heat generated due to pyrolysis and moisture evaporation for a temperature rise of T are, respectively, given by Consider a rectangular homogeneous section at room temperature T o, suddenly exposed to a uniform heat source inducing a constant surface temperature T s on the sides of the section as shown in Fig. 1. The transient thermal state of the section can be expressed by Eqn (2) with boundary conditions for (7) where b and d are the width and depth of the section, respectively. The temperature, T, of Eqn (2) can be expressed in a series form using the transformation given by (8) which transforms the boundary conditions represented by Eqn (7) to where L v and L g are latent heat of vaporization and heat of reaction, respectively. The above equations represent the stored energy of the active wood or moisture present, and endothermic energy associated with the generation of volatile pyrolysates or vaporization of water. The differential terms represent the generation of volatile pyrolysis products and water vapor, and can be represented by first-order Arrhenius-type reaction 3,4,7 as (4) (9) while the heat equation expressed by Eqn (2) transforms to Representing T' with a double Fourier series Eqn (10) leads to (10) (11) where the constants are as defined in Eqns (1) and (3). Assuming the phase transformation occurs at a fixed temperature, Eqn (5) reduces to (6) where the subscripts c and o refer to the residual char and original material, respectively. (5) (12) We can also represent Q(t) with a double Fourier series: (13) and by using the orthogonality relationship 16 in Eqn (13), followed by substitution of the result in Eqn (12), we get where (14) Figure 1. A rectangular section exposed to a constant temperature. and C mn is the integration constant. The heat generation term Q(t) in the integrand in Eqn (14) includes the effects of pyrolysis of wood and evaporation of moisture present and these effects are expressed in Eqn (4). The evaluation

4 214 D. SHRESTHA, S. CRAMER AND R. WHITE of the integrand" leads to (15) where the terms X a and X w are defined in Eqn (6). The integration constant C mn can be evaluated from Eqns (11) and (14) using the boundary condition of Eqn (9) and an orthogonal property. (16) Substitution of Eqns (14)-(16) in Eqn (11) leads to the solution of T' which can be transformed to T using the transformation relation of Eqn (8). Hence, the temperature T at any point within the section is given by was derived based on a number of simplified assumptions. Hence, the model needs to be calibrated before it can be readily used. For this purpose, a series of temperature profile tests were conducted at the USDA, Forest Products Laboratory, Madison (FPL). Alternatively, the model can be calibrated with other numerical models. However, the accuracy of any model used for calibration may need to be further established. Additional difficulties lie in model comparisons as the models have different features and complexities. A rigorous comparison of the presented model to other more complex models was beyond the scope of this study. A brief description of the- FPL test facility 18 and the temperature profile test procedures are presented here. The tests were conducted in a tension/furnace apparatus. The interior of the furnace was lined with mineral fiber blankets and had interior dimensions of 991 mm wide, 1829 mm long, and 1219 mm high (39 in 72 in 48 in). The furnace was provided with one observation window, a 229 mm 508 mm (9 in 20 in) (17) Some of the simplifications made in the deduction of this equation were uniform properties across the section, exposure of all sides of the section to a constant temperature, uniform distribution of moisture across the section, and a single-step global representation of the pyrolysis and vaporization process by Arrhenius-type reactions. However, the properties across a wood section are not uniform and they change as the section is heated, the exposure temperature is not always constant, and the pyrolysis and vaporization processes are also not uniform across the section. Furthermore, temperature gradients inside the section and the pressure gradient created by the vaporization of hygroscopic water force moisture toward the center of section, causing a localized increase in moisture. 14 Higher temperatures produce charred or partly charred layers, which serve as an insulative layer. At the same time, they result in outflow of pyrolysis gases which would have a cooling effect on the interior as heat is transferred out of the specimen through the char layer. Localized moisture is evident from moisture moving to the interior and reducing the effect of moisture vaporization as it recondenses. Therefore, it is recognized that the model presented in Eqn (17) is a simplification of true behavior. EXPERIMENTAL WORK AT FPL As discussed in the preceding sections, the closed-form solution to predict temperature of a rectangular section opening on each end of the furnace for positioning specimens, and a removable lid. Eight diffusion-flame natural gas burners, located at the bed, supplied the necessary heat to maintain the furnace at any desired temperature condition. The flow of natural gas was controlled so that the furnace temperature followed a predefined time-temperature curve. A thermocouple attached on the surface of the specimen was used to control the furnace temperature. The temperature profile tests were conducted on 2134 mm (84 in) long southern pine lumber of 51 mm x 102 mm (2 in x 4 in) nominal dimensions at 100 C, 200 C, 250 C, 275 C, and 300 C (212 F, 392 F, 482 F, 527 F, and 572 F) constant temperatures, and at a simulated plenum temperature. The latter temperature followed a prescribed time-dependent path of 65 C, 93 C, 188 C, 260 C, and 327 C (149 F, 199 F, 370 F, 500 F, and 621 F) at 10, 20, 30, 45, and 60 min, respectively, and was derived from various ASTM E standard fire tests of protected truss assemblies. Twenty thermocouples (36 gage, type K ) were used to monitor the temperatures on the surface and across the section of a specimen. Figure 2 shows a schematic representation of the thermocouple locations and the test setup. A 64 mm 38 mm 495 mm (2.5 in 1.5 in 19.5 in) block was removed from each end of the test specimens and thermocouple holes were drilled into the open faces. The rectangular blocks were then glued in their original positions with phenol-resorcinol two-part epoxy.

5 TIME-TEMPERATURE PROFILE 215 Figure 2. A schematic representation of the temperature profile test. Figure 3. Time-temperature profile across a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 100 C (21 2 F). Figure 4. Time-temperature profile across a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 200 C (392 F).

6 216 D. SHRESTHA, S. CRAMER AND R. WHITE Figure 5. Time-temperature profile across a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 300 C (572 F). Figures 3-5 show three-dimensional views of the time-temperature profile across the width of a 51 mm 102 mm (2 in 4 in) lumber section exposed to 100 C, 200 C, and 300 C (212 F, 392 F, and 592 F), respectively. Note that all the thermocouples embedded in the specimens were not at the same sections but were at two different sections 1.22 m (4 ft) apart. This is a major factor contributing to the uneven profiles. From these plots we can see that the temperature distribution across a lumber section is approximately parabolic in shape. This shape gradually flattens with an increase in the exposure time until the section is in a thermal equilibrium state. Thus, the center and surface temperatures of a rectangular section can be readily used in predicting the time-temperature profile across the section. at the center of lumber section exposed to the same degree of severity on all four faces is given by (18) From the observations of the test data it was noted that the moisture term correction factor γ w was a function of exposure temperature, and the factor γ p was a function of the gradient of the exposure temperature. Based on different trials, the correction factors that produced the most satisfactory results were APPLICATIONS AND LIMITATIONS where (19) The time-temperature profile at the center of lumber section exposed to different exposure temperatures indicate a gradual temperature rise to about 100 C (212 F), then the rate of temperature rise decreases because of the localized increase in moisture content and vaporization of water. The rate of temperature rise also increases after vaporization, which is further augmented with the exothermic effects associated with the pyrolysis of wood. A comparison of the observed and predicted temperature profile data indicated that the simplified solution needed an adjustment factor (γ w) in the moisture effect term ( TQ w) to account for localized increase in moisture content. Furthermore, the solution was derived assuming the surface to have a constant exposure temperature. When the exposure temperature was not constant, the temperature change needed to be factored with a reduction factor γ p. The final equation for the temperature rise from the preceding time step D T s = change in exposure temperature ( C) in time At (min) Note that many different forms for the factor γ p yield temperature profiles equally acceptable when compared with the test data. However, an abrupt change in the surface temperature does not induce a similar change in the center temperature. The factor γ p was selected to yield a smooth transition of the predicted center temperatures. When the exposure temperature is constant, the slope of the time-temperature curve is zero, the factor γ p reduces to 1, and the upper limit of the factor is set to 2.

7 TIME-TEMPERATURE PROFILE 217 Figure 6 shows the contributions of the different terms in the temperature rise at the center of a section exposed to 300 C (572 F) uniform temperature. The kinetic and thermal constants needed for the solution are presented in Table 1. Initially the temperature rise is due to heat conduction and is subdued at about 100 C (212 F) because of the heat absorbed in the vaporization of water present and localized increase in moisture content. The temperature rise is further augmented as wood pyrolyzes, generating heat. Figures 7-10 show the comparison between the analytical and observed time-temperaure profiles at the center of a 51 mm 102 mm (2 in 4 in) lumber section exposed to constant temperatures of 100 C, 200 C, 300 C (212 F, 392 F, 572 F) and a plenum-type temperature, respectively. These comparisons show a reasonably good prediction with a closed-form solution that is simple to implement and does not require extensive computional effort. The 300 C (572 F) temperature data were used to calilbrate the kinetic constants data and the moisture term correction factor γ w. The simulated plenum temperature data further verified and calibrated the correction factor γ p. For the temperature change at the center of a section, even terms in the summation of Eqn (18) reduce to zero. A comparision of the center temperature computed from Eqn (18) with different number of iterations for a 51 mm 102 mm (2 in 14 in) lumber section exposed to 300 C (572 F) is presented in Table 2. The summation Figure 6. Contributions of different terms in the prediction of center temperature of a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 300 C (572 F). Figure 7. A comparison of the observed and predicted center temperature profile of a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 100 C (212 F).

8 218 D. SHRESTHA, S. CRAMER AND R. WHITE Figure 8. A comparison of the observed and predicted center temperature profile of a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 200 C (392 F). Figure 9. A comparison of the observed and predicted center temperature profile of a 51 mm 102 mm (2 in 4 in) lumber section exposed to a constant temperature of 300 C (572 F). of the first ten odd terms has been found to be adequate to compute the center temperature. Thus, although a series solution is presented it does not require extensive computational effort. The model has direct application in situations where the thermal response of a number of individual members needs to be repeatedly evaluated. Shrestha 17 has applied this model in the fire-endurance modeling of wood trusses, where the degradation of the material properties are related to the thermal response of the individual members at incremental time steps. It should be understood that the solution is sensitive to the kinetic constants and other thermal and physical characteristics of lumber. As reviewed earlier, kinetic constants depend on the size, species, and other properties of a specimen, and methods adopted in evaluating them. However, in the analyses here we have used one set of kinetic constants (Table 1) which lie within the range of the published values. These values were selected to yield a visual best-fit between the observed and predicted data. The current model has been evaluated for a limited set of data for one type of specimen. The temperature range varied up to about 300 C (572 F), the exposure rate was either sudden or varied linearly at predefined intervals, the specimens used were 51 mm 102 mm (2 in 4 in) southern pine lumber with moisture contents at about 10%. From our limited test data available we have seen that the model performs relatively well for a narrow range of data. The components and the exposure conditions were selected to represent the conditions a metal-plate connected wood truss is likely to experience in the standard fire-endurance test of protected floor-ceiling assemblies. How this model will behave for different sections and varied conditions needs to be further evaluated as more test data become available. The

9 TIME-TEMPERATURE PROFILE 219 Figure 10. A comparison of the observed and predicted center temperature profile of a 51 mm 102 mm (2 in 4 in) lumber section exposed to a simulated plenum temperature of protected assemblies. Table 1. Values of different kinetic and thermal constants used in the model Constants Values Range and source A a 27 s 1 3.6E6-6.53E16; references 1 and 20 E a J mole ; reference 20 A w 1000 s ; references 3 and 5 E w J mole ; references 3 and 5 L g 0.0 Reference 7 L v 2400 kj kg 1 Reference 5 K a W mole 1 K 1 References 2 and 7 c w kj kg 1 K 1 T < 100 C Reference T 2 T > 100 C c a T kj kg 1 K 1 Reference 5 c c c a 1.0 to 2.0; reference 7 Char yield 25% 0.22 to 0.32; references 3 and 5 Table 2. Comparison of the center temperature predicted with a different number of iterations Center temperature ( C) computed with a different number of iterations Exposure time (min) Iteration 1 Iteration 5 Iteration 10 Iteration adjustment factors may need further modifications to improve the reliability of this model for wider applications and care should be taken before generalizing the results. SUMMARY AND CONCLUSION In recent years significant interest has been directed toward the development of analytical techniques in predicting the fire performance of wood floor/ceiling assemblies. Structural analysis of assemblies exposed to elevated temperatures requires strength and stiffness properties of the individual components as functions of exposure time and conditions. A major difficulty in the analysis of wood assemblies at elevated temperatures is in the thermal analysis of the components and subsequent estimation of their properties. Wood properties degrade with exposure to heat and the degree of degradation is related to the energy absorbed/generated in the heating process. A detailed thermal analysis of a wood section exposed to elevated temperatures is complex, requires extensive computational effort, and currently is computationally impractical to use for every member at every time interval during fire-endurance modeling. A solution technique has been presented to predict the thermal response of an idealized rectangular section exposed to a constant heat source. The technique is then calibrated with the experimental data to yield a readily usable solution. Pyrolysis and moisture effects are recognized as important factors influencing the thermal response of a wood section and are modeled by global first-order Arrhenius-type functions. The kinetic constants and modification factors required in the solution

10 220 D. SHRESTHA, S. CRAMER AND R. WHITE were estimated from the data gathered from the temperature profile tests of 51 mm 102 mm (2 in 4 in) structural lumber exposed to different exposure conditions at the FPL test facility and from other published sources. The computational effort involved in this heat transfer analysis is minimal and yet the accuracy is sufficient within the limitations of this development. This technique is effective for computing thermal response and subsequent degradation of wood members of an assembly exposed to pyrolytic temperatures. The solution has been tested and calibrated for situations that normally prevail in the standard fire-resistance rating tests of protected wood floor-ceiling assemblies. As more test data become available for vaned conditions, the solution technique may have wider application in fire-endurance modeling of structural assemblies. NOTATION k ρ thermal conductivity mass density with respect to original volume c specific heat Q(t) internal heat generated t time R universal gas constant A rate constant E activation energy T temperature b d L v width of a wood section depth of a wood section latent heat of vaporization L g heat of reaction γ p temperature correction factor γ w moisture term correction factor T change in temperature in time At Acknowledgements The authors gratefully acknowledge the partial financial supports of the USDA Forest Service, Forest Products Laboratory, and the American Forest and Paper Association. REFERENCES 1. A. F. Roberts, Problems associated with the theoretical analysis of the burning of wood. Thirteenth Symposium (Int.) on Combustion, Pittsburgh, The Combustion Institute, (1971). 2. H. C. Kung, A mathematical model of wood pyrolysis. Combustion and Flame 18, (1 972). 3. A. Atreya. Pyrolysis, Ignition, and Fire Spread on Horizontal Surface of Wood, PhD thesis, Harvard University (1983). 4. G. S. Springer and M. S. Do, Degradation of mechanical properties of wood during fire. National Bureau of Standards, Center for Fire Research, Report No. NBS-GCR , Washington, DC (1983). 5. W. J. Parker, Development of a model for the heat release rate of wood A status report. Report No. NBSIR , US Dept. of Commerce, NBS, National Engineering Laboratory, Center for Fire Research, Gaithersburg, MD 20399, USA (1985). 6. W. B. Gammon, Reliability Analysis of Wood-Frame Wall Assemblies in Fire, PhD thesis, University of California, Berkeley (1987). 7. B. Fredlund, A model for heat and mass transfer in timber structures: A theoretical, numerical and experimental study. Lund University, Inst. of Science and Technology, Dept. of Fire Safety Engineering, Rep. LUTVDG/(TVBB- 1033), 254 (1988). 8. A. F. Roberts, A review of kinetics data for the pyrolysis of wood and related substances. Combustion and Flame 14, (1970). 9. E. L. Schaffer, Effect of pyrolytic temperatures on the longitudinal strength of dry Douglas-fir. ASTM, Journal of Testing and Evaluation 1, No. 4, (1973). 10. E. R. Tinney, The combustion of wooden dowels in heated air. Tenth Symposium (Int.) on Combustion, Pittsburgh, The Combustion Institute, (1965). 11. A. M. Kanury, Thermal decomposition kinetics of wood pyrolysis. Combustion and Flame 18, (1972). 12. R. H. White, Charring of Different Wood Species, PhD thesis presented to the University of Wisconsin- Madison, Madison, WI, USA (1988). 13. K. Odeen, Fire resistance of glued, laminated timber structures. Fire and Structural Use of Timber in Building, Fire Research Station Symposium, No. 3, HMSO, London, 7-15 (1970). 14. R. H. White and E. L. Schaffer, Transient moisture gradients in fire-exposed wood slab. Wood and Fiber 13 (1), (1981). 15. F. Kreith and W. Z. Black, Basic Heat Transfer, Harper and Row, New York (1980). 16. D. L. Powers, Boundary Value Problems, Harcourt Brace Jovanovich, Orlando, FL (1 987). 17. D. Shrestha, Fire Endurance Modeling of Metal-plate Connected Wood Trusses, PhD thesis presented to the University of Wisconsin-Madison, Madison, WI, USA (1 992). 18. R. H. White, Fire endurance research at the Forest Products Laboratory. Wood Design Focus 1, No. 2, 5-7 (1990). 19. American Society of Testing and Materials, Standard Test Methods for Fire Tests of Building Construction and Materials. Designation E-1 19 (88). Annual Book of ASTM Standards, 4.07, , Philadelphia, PA (1 991). 20. J. A. Havens, A. R. Walker and C. M. Sliepcevich, Pyrolysis of wood: A thermoanalytical study. J. Fire and Flammability 2, (1971).

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