Table 1 List of main symbols and corresponding variable names in data Tables
Variable name | Variable symbol | Variable description | Unit |
|---|---|---|---|
(in data tables) | (in equations) | ||
length_m | L | Board length measured manually with a tape | m |
\(\overrightarrow x\) | Lengthwise direction of the board | ||
width_m | w | Board width measured manually with a caliper | m |
\(\overrightarrow y\) | Crosswise direction parallel to the width of the board | ||
thickness_m | t | Board thickness measured manually with a caliper | m |
\(\overrightarrow z\) | Crosswise direction parallel to the thickness of the board | ||
massManual_kg | \(m_{board}\) | Board mass measured manually with a scale | kg |
boardDensityManual_kgpm3 | \(\rho _{M}\) | Board density measured from weight measured manually | kg m\(^{-3}\) |
boardDensityXRays_kgpm3 | \(\rho _{X\!R}\) | Board density computed from X-ray data | kg m\(^{-3}\) |
cwDensity12pc_kgpm3 | \(\rho _{CW}\) | Clear wood density of the small clear wood sample at 12 % moisture content | kg m\(^{-3}\) |
mcCWBendingTest_pc | \(u_{CW}^{test}\) | Moisture content of the small clear wood sample at the moment of the destructive bending test | % |
firstAxialFreq_Hz | \(f_{a,1}\) | Board first axial resonance frequency | Hz |
dynMoEAxial_Pa | \(E_{a,dyn}\) | Board dynamic modulus of elasticity obtained from the first axial resonance frequency | Pa |
dynEWBendFreqN_Hz | \(f_{b,N}\) | Board N\(^{th}\) edgewise transversal frequency | Hz |
dynEWBendMoEBernoulliN_Pa | \(E_{b,dyn,N}\) | Board dynamic modulus of elasticity obtained from N\(^{th}\) edgewise transversal frequency | Pa |
dynEWBendMoETimoshenko_Pa | \(E_{b,dyn}\) | Board dynamic modulus of elasticity obtained from Timoshenko bending theory | Pa |
dynEWBendShearMoE_Pa | \(G_{dyn}\) | Board dynamic shear modulus obtained from Timoshenko bending theory | Pa |
\(l_{load}\) | Distance between loading heads in the 4-point bending test | m | |
supportSpan_m | l | Span of the 4-point bending test | m |
startloadMoE_N | \(F_1\) | Load to which board static modulus of elasticity starts to be calculated | N |
endLoadMoE_N | \(F_2\) | Load to which board static modulus of elasticity ends to be calculated | N |
localStatEWBendMoE_Pa | \(E_{m,l}\) | Board static local modulus of elasticity as defined by EN 408:2012 | Pa |
globalStatEWBendMoE_Pa | \(E_{m,g}\) | Board static global modulus of elasticity as defined by EN 408:2012 | Pa |
maxLoadStatEWBend_N | \(F_{max}\) | Ultimate load in 4-point bending | N |
strenghtEWBend_Pa | \(f_m\) | 4-point bending strength of the board | Pa |