Scale Modeling of Tests with Combined Thermo-Structural Loading
Standard methods for fire resistance testing require large-scale assemblies and are typically conducted on specialized furnaces at considerable cost. This research focused on developing a scaling methodology for a reduced-scale fire resistance test that reduces the size of the test article while maintaining the same thermal and structural response exhibited in the large-scale test. The developed scaling methodology incorporates uniform geometric scaling, Fourier number time scaling, and furnace boundary condition matching. The scaling laws were experimentally validated with fire exposure tests on gypsum wallboard samples at three scales (full-scale, 1/2-scale, and 1/6-scale). Next, these scaling laws were demonstrated for wood with combined thermo-structural loading. Dimensional lumber boards at ½-scale and ¼-scale were subjected to combined bending and thermal loading. Samples were placed in static three-point bending with the loading scaled to have structural similitude, while simultaneously, the bottom surface was exposed to a scaled fire exposure. Analytical modeling of wood pyrolysis demonstrated that, due to char kinetics as the heating rate is increased in the tests, equivalently less char is formed in the reduced-scale tests. Therefore, we developed a char timescale correction factor, calculated from both model predictions and measured charring rates, which modified the previous Fourier number time scaling laws. Finally, we investigated the effect of multi-orientation materials with a similar set of combined thermo-structural three-point bending tests on plywood samples. The stacking sequence of laminated wood significantly impacts the composite mechanical behavior of the material, especially when scaling down thermo-mechanical tests on plywood. A consequence of the different stacking sequences is that the data from the reduced-scale test cannot be directly scaled to predict the behavior of the larger-scale tests. Thus, modeling becomes essential to extrapolating the data from the reduced-scale test to predict the behavior of the larger-scale test. Reduced cross-sectional area models incorporating classical lamination theory were used to predict the mechanical response of the composite samples as the char front increased.