Non-Destructive Evaluation of Reclaimed Timber Using Visual Grading, Dynamic Excitation, Mechanical Testing, and X-ray CT-Based Modelling

Non-Destructive Evaluation of Reclaimed Timber Using Visual Grading, Dynamic Excitation, Mechanical Testing, and X-ray CT-Based Modelling Johannes A. J. Hubera,b, Tom Svilansc, Maarja Kaunistee, Niels H. Vonkf, Olof Bromane, Eero Tuhkanene, Wendy Wuytsd, Alar Juste, Martin Tamkec, Mette Ramsgaard Thomsenc aWood Science and Engineering, Luleå University of Technology, Forskargatan 1, Skellefteå, 93194, Sweden bWood K Plus - Kompetenzzentrum Holz GmbH, Klagenfurter Straße 87–89, St. Veit an der Glan, 9300, Austria cCentre for Information Technology and Architecture (CITA), Royal Danish Academy, Philip de Langes Allé 10, Copenhagen, 1435, Denmark dOmtre AS, Follumveien 100, Hønefoss, 3515, Norway eTallinn University of Technology, Ehitajate tee 5, Tallinn, 19086, Estonia fTNO - Building Materials and Structures, Molengraaffsingel 8, Delft, 2629JD, The Netherlands Abstract This study evaluates the suitability of multiple non-destructive methods for characterising the mechanical properties of reclaimed structural timber. Visual grading, dynamic excitation, and X-ray computed tomography (CT) were combined with global and zone-wise flatwise bending tests on 56 reclaimed timber beams. The comparison highlights the practical performance, predictive accuracy, and limitations of each method for material reuse. Dynamic excitation provided the strongest nondestructive prediction of global bending stiffness and strength, whereas visual gradEmail addresses: [email protected] (Johannes A. J. Huber), [email protected] (Tom Svilans), [email protected] (Maarja Kauniste), [email protected] (Niels H. Vonk), [email protected] (Olof Broman), [email protected] (Eero Tuhkanen), [email protected] (Wendy Wuyts), [email protected] (Alar Just), [email protected] (Martin Tamke), [email protected] (Mette Ramsgaard Thomsen) Preprint submitted to Preprint server November 24, 2025 ing showed limited discriminatory power for this heterogeneous material. CT-based analyses, using density evaluation and data-driven indicators from finite element and meshless continuum models, captured spatial stiffness variations linked to knots and fibre disturbances and delivered predictive capability comparable to mechanical non-destructive tests. However, absolute accuracy was constrained by moisture uncertainty, defect-induced artefacts, and the global nature of the mechanical reference tests. The results show that combining established non-destructive techniques with CT-derived indicators provides a robust basis for assessing reclaimed timber and offers a viable path toward more reliable structural reuse. The study establishes an empirical reference for future work on advanced CT-based modelling and multi-modal indicators for circular construction. Keywords: strength grading, computational modelling, sustainable construction, material passport, structural reuse 1. Introduction 1.1. Reclaimed Timber in Circular Construction The construction sector today faces a dual challenge: to meet growing global infrastructure needs while drastically reducing carbon emissions. Timber, as a renewable and carbon-sequestering material, offers distinct environmental advantages, especially when sourced from reclaimed streams such as deconstructed buildings, industrial off-cuts, or packaging waste. By extending the life-cycle of wood products and reducing reliance on virgin resources, reclaimed timber can play a vital role in mitigating the climate impact of construction [1, 2, 3]. Reuse strategies minimise environmental burdens, enable the substitution of more carbon-intensive materials, and advance the sector towards circular economy principles [4, 5]. 2 Cascading use forms the core of circular timber strategies: high-quality wood is first directed to the most demanding applications, and only downgraded to lowervalue uses or energy recovery as its performance diminishes [6]. A growing body of research and practice shows that reclaimed timber can undergo multiple cycles of reuse, with dedicated design-for-disassembly, reverse logistics, and digital material tracking now supporting this transition [7, 8]. Across Europe, numerous initiatives are integrating reclaimed timber into new construction and engineered products, ranging from building-scale applications to hybrid and laminated systems [9, 10, 11, 12, 13, 14]. Laboratory work and case studies have demonstrated that engineered products such as cross-laminated timber (CLT) and glulam made with reclaimed stock can achieve performance levels comparable to those made from new timber, provided that variability is managed appropriately [15, 16, 17, 18]. Despite these promising advances, widespread structural reuse remains limited by significant technical and economic barriers [4, 19]. Major obstacles include the lack of consistent, piece-specific data on material properties, the absence of robust grading methods for heterogeneous reclaimed stock, and logistical challenges around disassembly, storage, and re-certification [8]. Without reliable information, the structural potential of reclaimed timber cannot be confidently assessed, leading to conservative downgrading and loss of value. Most reclaimed timber is therefore relegated to nonstructural applications or processed into composite boards, rather than used in new load-bearing structures. Inspection and preparation of reclaimed timber remains a manual, labour-intensive process. Each piece must be examined to ensure freedom from fasteners and debris, accurate geometric measurement, and adequate mechanical integrity, steps essential both for safety and for efficient integration into new products. This manual approach is costly and slow, and does not scale to the growing volumes of post-consumer timber 3 generated each year [20]. 1.2. Non-Destructive Evaluation Methods for Timber A broad range of non-destructive evaluation (NDE) techniques has been developed to assess the properties of timber for structural applications. Traditional methods such as visual grading remain foundational, but their reliability can be limited, especially for reclaimed stock with hidden or internal defects. More advanced approaches, like dynamic excitation, ultrasonic and stress-wave timing, as well as local penetration or drilling resistance tests, provide additional information on mechanical properties and can support more nuanced grading decisions [21, 22, 23, 24]. In practice, multi-method combinations are increasingly used, as single-method approaches often correlate more strongly with stiffness than with ultimate strength [24]. Among advanced NDE techniques, X-ray computed tomography (CT) provides the most comprehensive internal characterisation of timber, yielding volumetric density fields from which wood physical properties [25, 26], anatomical features [27], and fibre orientation [28, 29] can be inferred. CT is used in sawmilling to map internal features and optimise cutting strategies [30], and CT-derived density and fibre deviation fields are increasingly employed in computational models to predict mechanical properties such as stiffness and strength [31]. These internal datasets complement surface-based computer-vision measurements [32] and provide a benchmark for developing and validating industrially feasible sensing and modelling approaches. While CT is not intended for routine grading of reclaimed timber, it offers a reference framework against which simpler scanning modalities and model-based indicators can be evaluated. Such high-resolution, spatially resolved data enable more precise allocation of material within engineered products, for example by placing stronger regions in higher4 stress zones and weaker regions in low-stress zones [33]. Automated matching and conservative grading workflows are being developed for industrial use of reclaimed timber [34], though current approaches still rely on cautious strength assumptions in the absence of documentation. Further progress requires refined classification protocols, improved performance criteria, and automated data processing pipelines. Digital material passports and transparent supply chain documentation are emerging as scalable solutions [35, 4, 34]. 1.3. Performance Assessment of Timber Performance, in the context of reclaimed timber, encompasses mechanical, physical, and aesthetic attributes. While strength traditionally dominates grading efforts, stiffness and, to a lesser extent, density are often more critical, as they govern deflections, vibrations, and dynamic behaviour that must remain within serviceability limits. For virgin sawn timber, properties are commonly determined by strength grading according to established standards [36], utilising either visual inspection or automated systems. These automated procedures employ a range of technologies to determine predictors, so-called indicating properties (IPs), such as resonance frequency, slope of grain, knot-area-ratio, or any feature measurable non-destructively. Statistical models, typically regressions, are then used to relate these IPs to the underlying grade-determining properties: strength, stiffness, and density [37]. Grading outcomes are traditionally captured in strength classes [38], which require characteristic values for strength and density - defined as the fifth percentile value of a defined population of timber, often from a single region and processed at a specific sawmill - but mean values for stiffness. Calibration of these systems requires destructive testing of large, representative samples to establish the relationship be5 tween IPs and grade-determining properties, and to determine thresholds of IPs for the targeted strength classes. These calibrations are speciesand source-specific and must be regularly updated to maintain reliability. A fundamental limitation of this approach is that after classification, the detailed information contained in the IPs is lost. Strength classes express only statistical properties of the graded population, not the true, individual performance of each piece. Moreover, the relationships between the three grade-determining properties strength, stiffness, and density are fixed within each strength class, defined by predetermined correlation tables. As a result, the specific variation and correlation present in the original data are no longer accessible at the level of individual elements, precluding more nuanced or tailored piece-specific assignment of structural roles. In Europe, strength is the central focus of grading, but this perspective can be restrictive. Stiffness may be a more reliable and predictable performance measure which is less sensitive to localised defects, since it can be assessed repeatedly, both locally and globally per specimen, and by various non-destructive experiments, such as static loading or dynamic excitation. The known correlation between stiffness and strength can be exploited in both directions, enabling strength to be predicted from stiffness and vice versa. Notably, in New Zealand, grading systems have adopted a stiffness-driven approach, in which a minimum modulus of elasticity (MoE) is set as the criterion for grade assignment, and strength is inferred accordingly [39]. This approach reflects the greater stability and assessability of stiffness, using MoE as a reliable proxy for modulus of rupture (MoR) and thereby simplifying the grading process. Uncertainty in material properties is not unique to timber and is inherent to all construction materials. Building codes address this by requiring safety factors in structural calculations [40]. However, the heterogeneity characteristic of renewable 6 materials, and especially reclaimed timber, tends to amplify these uncertainties, often resulting in overly conservative designs and inefficient resource use. 1.3.1. Limitations of Conventional Grading for Reclaimed Timber Conventional grading is ill-suited to reclaimed timber, due to the diversity of dimensions, species, and conditions encountered in reclaimed stock. Additional complexity arises from contaminants such as embedded metal fasteners, surface treatments, and the effects of long-term environmental exposure, which can alter microstructure and performance [12]. Ageing and prior load history, particularly the effects of duration-of-load (DoL), further complicate the assessment, as DoL typically reduces strength more than stiffness, while other ageing mechanisms remain less well-understood [41, 42, 43]. Existing non-destructive assessment standards, designed with new timber in mind, are limited in scope, often focusing on moisture content (MC) or basic geometry and cannot reliably account for factors such as cracks, hidden defects, or historical loading [21]. Machine strength grading, dependent on species and provenance, is also poorly suited to reclaimed timber with unknown or mixed heritage. Even recent advances in NDE, including ultrasound, stress wave analysis, Pilodyn [22], and resistograph methods [23], have shown limited correlation with the true mechanical properties of aged timber in destructive tests [24]. Recent standards such as the Norwegian NS 3691 series and Italy’s UNI 11119 attempt to address some of these issues, offering guidance on terminology, contamination assessment, and visual grading for specific species [44, 21, 24, 14]. Nevertheless, their applicability to the heterogeneous reality of reclaimed stock is still restricted, and calibration for broader use remains incomplete. Practical challenges include managing irregular dimensions, accurately evaluating 7 the three-dimensional structure of knots, and addressing geometric features such as wane without default rejection. Uniform MC must be ensured, and hardwood species, which are frequently encountered in historic structures, require appropriate characterisation, which is rarely provided by conventional systems [12]. Reclaimed timber thus exposes the limitations of grading systems designed for homogeneity and scale. Effective reuse requires individual assessment rather than batch classification, demanding flexible, accurate, and efficient grading protocols to unlock its structural potential. 1.4. Objective This study aims to advance the structural reuse of reclaimed timber by systematically benchmarking non-destructive methods for assessing the mechanical and physical properties of individual beams. Recognising the inherent variability of reclaimed material, particular emphasis is placed on capturing both global (whole-beam) and local (section-wise) variations in properties, enabling a more precise and spatially resolved characterisation. Specifically, this work seeks to: •apply established non-destructive assessment techniques, such as visual grading and dynamic excitation, together with advanced data-driven models based on X-ray computed tomography, •perform experimental validation through both non-destructive measurements targeting intra-beam property variation and destructive mechanical testing, •critically compare the accuracy, practicality, and predictive value of these methods for characterising the spatially varying properties of reclaimed timber elements intended for structural reuse. 8 2. Materials and Methods 2.1. Specimens and Experimental Programme A total of 56 reclaimed timber elements, hereafter referred to as specimens, were used in this study (see Fig. 1). The material was supplied by the company Omtre AS from storage facilities in Hønefoss, Norway. Each specimen was first subjected to X-ray computed tomography (CT) scanning at the Division of Wood Science and Engineering, Luleå University of Technology (LTU), Skellefteå, Sweden. CTderived data were used to generate numerical models for non-destructive evaluation of internal structure and mechanical properties. Following scanning, all specimens underwent dynamic excitation testing, visual grading, and flatwise bending experiments at Tallinn University of Technology (Taltech), Estonia. This combination of methods enabled a systematic comparison between non-destructive indicators and destructive reference values for the same material. The specimens had nominal cross-sectional dimensions of 49 ×98mm2and lengths between 1904 mm and 2862 mm. The timber originated from temporary use during the construction of student apartments at Kringsjå, Norway, and can be considered cut-offs from that process. The material was originally graded as strength class C24 [38], which was visibly imprinted on the surface. Before delivery to storage, remaining metal fasteners were removed. At Omtre’s facility, the timber was kept under shelter from precipitation but without heating or climate control, thus exposed to outdoor humidity and temperature conditions. Storage duration was approximately two years before the start of the present study. 2.2. Evaluated Properties To assess the suitability of reclaimed timber for structural reuse, three key properties were considered: stiffness, density, and strength. These quantities vary spatially 9 l r t Figure 5: Density isosurfaces representing earlywood–latewood layering. Local density gradient orientations align with the radial (r) direction, while the longitudinal (l) and tangential (t) directions follow from the principal continuity direction and its orthogonal complement. Let Iσ(x)denote the density field smoothed with a Gaussian kernel of standard deviation σ. The GST is defined as J(x) = gω∗∇Iσ(x)∇Iσ(x)⊤,(1) where gωis a Gaussian kernel with scale ωproviding spatial regularisation, ∗denotes convolution and ∇is the gradient operator. The symmetric tensor J(x), positive semi-definite 3×3matrix that characterises the local distribution of gradient orientations in the image. Its eigendecomposition J vi=λivi, λ1≥λ2≥λ3,(2) yields three orthonormal eigenvectors vi. In regions where the eigenvalues are well separated, v1corresponds to the direction of steepest density increase and was used as the radial material direction. The direction of highest continuity, v3, was used to approximate the longitudinal material direction, i.e. the fibre orientation. The tangential direction follows from the cross product of these two vectors. This produced a continuous orthotropic material coordinate system F(§)at voxel resolution, including in knot-affected regions, without requiring explicit knot segmentation. 16 2.4.3. Stiffness Tensor Assignment A spatially varying orthotropic stiffness tensor CF, aligned with F(§), was assigned following L1from [31]: CF(x) = ρCT(x) ρ02 κ(x)C0(3) where ρ0and C0are the reference density and stiffness tensor for Norway spruce at 12% MC [54]. To account for the different mechanical character of knots, a penalisation factor κ= 0.5was applied where ρCT >900 kg/m3, and κ= 1 otherwise [32]. 2.4.4. Body of Properties The fields ρCT(x),B(x)F(x)and CF(x)were integrated into the BoP, a single volumetric data structure using OpenVDB grids [55, 56]. This enabled consistent data exchange with simulations, efficient sampling along arbitrary beam sections, and a compact, vendor-neutral storage format. All subsequent FE and CM computations queried material values via the BoP. 2.4.5. 3D Finite Element Model Geometry was extracted from B(x)using marching cubes [57], converted to a triangular surface mesh and decimated using Open3D [58] to a 10mm surface resolution. A quadratic tetrahedral mesh (max element size 7.5 mm) was generated in Gmsh [59]. FE analyses (static bending and eigenfrequency) were conducted in CalculiX [60]. For each element, the local CFand Fwere retrieved from the BoP using a custom UMAT subroutine. Element density was set to the specimen-level mean ρCT. For the bending analysis, nodes were embedded along the specimen centreline at 10mm spacing, to query deflections. A simply supported pure bending configuration 17 was imposed. End sections were kinematically coupled to end nodes. One end node was fixed in translation, the other allowed translation only along x. Rotations were locked except about yand opposite moments Mwere applied at the end nodes. The mid-span deflection wFE,mid and the deflection profile wFE(x)were extracted at the centreline. The apparent global stiffness from midpoint bending was computed as EFE,w =ML2 8IzwFE,mid ,(4) with second moment of area Izfrom nominal specimen dimensions. A local curvaturebased stiffness profile EFE,κ(x)was derived by assuming an inhomogeneous Euler–Bernoulli beam under constant moment M: EIz(x)κ(x) = M, (5) where EIz(x)and κ(x)are the locally varying bending stiffness and curvature, respectively. Since κ≈d2w/dx2, EIz(x) = Md2w(x) dx2−1 , EFE,κ(x) = EIz(x) Iz ,(6) where wFE(x)was used for deflections and the second derivative was obtained via a Savitzky-Golay filter [61]. In the eigenfrequency analysis, the first 20 eigenfrequencies were computed. The lowest mode dominated by longitudinal deformation defined f0,FE. A dynamic stiffness EFE,dyn was calculated as EFE,dyn = (2L f0,FE)2ρCT.(7) 2.4.6. Meshless Continuum Model This model performs direct cross section-wise continuum mechanical evaluations of the BoP on a regular grid, combined with Euler–Bernoulli beam theory, to obtain 18 stiffness profiles along the specimen length and is based on work outlined in Huber [51], Huber et al. [31]. A structured grid with 1 ×1mm2cross-sectional resolution and 10mm spacing along xwas used. BoP fields were linearly interpolated to each grid point. At each point, CFwas rotated from the local to the global coordinate system: C†(x) = T⊤ FCFTF,(8) where C†(x)is the rotated tensor and TFthe corresponding 6×6transformation matrix [62, 31]. The compliance tensor S=C−1 †gave the uniaxial and shear stiffness components: Ex=1 S11 , Gxy =1 S44 .(9) For each cross section, the neutral axis yn, the bending stiffness around the neutral axis EIz(x), the axial stiffness EA(x)and the shear stiffness GAy(x)were computed by numerical integration over B(x)[51]: yn=RR Exy dy dz RR Exdy dz ,(10) EIz(x) = ZZ Ex(y−yn)2dy dz, (11) EA(x) = ZZ Exdy dz, (12) GAy(x) = ZZ Gxy dy dz, (13) Corresponding sectional geometric quantities A(x),Iz(x)and mean density were evaluated analogously. Section-equivalent stiffness profiles ECM,EI (x),ECM,EA(x), and Gy.CM,GA(x), based on bending, axial, and shear stiffness, respectively, were then obtained: ECM,EI (x) = EIz(x) Iz(x), ECM,EA(x) = EA(x) A(x), GCM,GA(x) = GAy(x) A(x).(14) 19 2.4.7. Model-based Indicating Properties IPs, i.e. predictors for regression models, were derived from both modelling approaches, at the global specimen level and at zone level (aligned with the mechanical test zones, see Section 2.7). Scalar FE-based quantities were used directly as global IPs. For spatially varying quantities, arithmetic means were taken over the full specimen to receive global IPs, or the corresponding mechanical zones for zone-wise IPs. A summary of the IPs is provided in Table 1. Table 1: Model-derived indicating properties (IPs) from CT-based modelling. Global IPs represent arithmetic means over the full specimen length; zone IPs represent arithmetic means over the mechanically tested zones. Source Global IP Zone IP EFE,w EFE,w – f0,FE f0,FE – EFE,dyn EFE,dyn – EFE,κ(x)EFE,κ EFE,κ,i ECM,EA(x)ECM,EA ECM,EA,i ECM,EI (x)ECM,EI ECM,EI,i Gy,CM,GA(x)Gy,CM,GA Gy,CM,GA,i ρCT(x)ρCT ρCT,i 2.5. Visual Grading Visual grading was performed only on the specimens selected for destructive bending tests and was carried out at the specific longitudinal zone used in the mechanical testing (Section 2.7). This ensured that the visual classification corresponded directly to the material volume governing the measured bending strength. However, 20 since only one zone per evaluated specimen was graded, this value was also used globally for the specimen. Grading followed the general procedure of EN 1611-1 [63], which specifies inspection of knots, slope of grain, cracks, wane, distortions, decay, and other surface irregularities. Each specimen was examined on all faces under uniform lighting. Knots and cracks were measured manually using a ruler and caliper, and checks and surface defects were documented photographically for subsequent analysis. Three regional standards were applied: INSTA 142 [64], NS 3691-3 [65], and UNI 11119 [44]. INSTA 142, harmonised with EN 1912 [66] and EN 14081 [67], assigns grades T0, T1, T2, and T3 corresponding to indicative strength classes C14, C18, C24, and C30 [38]. NS 3691-3 extends this framework to reclaimed timber, including criteria for contamination (e.g. embedded metal, coatings), end-grain integrity, and visual indicators of ageing or prior loading. UNI 11119 defines the classes III (lowest grade), II, and I (highest grade), primarily for historic timber and provides empirically derived ranges for bending strength and stiffness. All grading was performed by trained personnel. Ambiguous cases were checked by a second grader, and disagreements were resolved by consensus. For each specimen, the three standards yielded a set of visually inferred equivalent bending strengths, denoted σf,vis,INS,σf,vis,NS, and σf,vis,UNI, obtained by mapping the assigned visual class to the characteristic bending strength specified in the respective standard. 2.6. Dynamic Excitation Longitudinal dynamic excitation was applied to estimate the stiffness and strength of each specimen using a hand-held mobile timber grader (MTG 960,Brookhuis, the Netherlands). The method determines a dynamic modulus of elasticity, EDE,dyn, as 21 an IP, which serves as input to regression models predicting the grade-determining properties: static modulus of elasticity EDE and bending strength σf,DE, following EN 14081 [68]. Each specimen was excited longitudinally by an internal impactor, and the vibration response was recorded by an integrated accelerometer. A Fast Fourier Transform (FFT) converted the signal to a frequency spectrum (resolution 4 Hz), from which the fundamental frequency f0was identified as the lowest peak. For specimens with intact ends, four impacts (two per end) were performed, and the average f0was used for subsequent analysis. Density at the time of measurement (ρDE) was determined gravimetrically from mass and geometric dimensions, while MC was determined from repeated measurements at both specimen ends using a handheld capacitive meter (FMW-T,Brookhuis, the Netherlands). The correction of ρDE to the 12% MC reference state (ρ12,DE) followed EN 384 [69] and is given by: aMC,DE =MCDE −12 100 , ρ12,DE =ρDE 1 + aMC,DE 2(15) where MC is in percent. The dynamic IP of the MTG is computed as: EDE,dyn = (2L f0cMTG)2ρ12,DE (16) where Lis the specimen length in mm, cMTG a dimensionless correction factor, f0is in Hz, and ρ12 in kg/m3. The details of the internal computation, including cMTG, are proprietary to Brookhuis, though similar formulations have been published [70, 71]. The MTG software uses regression relationships to infer EDE and σf,DE from EDE,dyn. For this study, strength categories were defined with a bin width of one to allow continuous, specimen-wise estimation, in contrast to the broader grading classes defined in EN 338 [38]. 22 2.7. Zone-wise Flat-wise Bending Test Four-point bending tests were conducted in accordance with EN 408 [72] to determine the stiffness and strength of the reclaimed timber specimens. Tests were performed in flatwise orientation, i.e. bending about the weak axis, which was necessary due to the relatively short specimen lengths. All tests were carried out using a universal testing machine (walter+bai LFM Series) equipped with a 600 kN load cell. To capture intra-member variability, each specimen was tested non-destructively in two or three longitudinal zones, depending on its length, positioned near the start (x1), midspan (x2), and end (x3) of the beam (Figure 6). Each zone was loaded within the elastic range, remaining below the proportionality limit, to obtain the local modulus of elasticity EFB,i for zone i. Following these non-destructive measurements, 15 specimens were selected and tested to failure in one of the previously tested zones (chosen at random) to determine the flatwise bending strength σf,FB. The remaining specimens were kept within the elastic range for subsequent analyses. 270270 810 1 1 (3)2 2(4) 3 (5) 4 (6) 5 6 405 LVDTGLO TESTING OF THE LAMELLA 405 810 1 1 (3)2 2 3 405 405 270270 405 405 Figure 6: Section-wise four-point bending test setup. The support span Liand loading-point distance awere both 270mm, and the loading rate was 0.15 mm/s. Midspan deflection was measured using an LVDT with 23 5µm resolution. The MC at testing, MCFB, was recorded for 28 specimens, including all 15 that were loaded to failure, using the oven-dry method on a cut-off section. A malfunction in the instrumentation intended to measure differential deflections between the loading points prevented the calculation of local modulus of elasticity within the pure bending region. Consequently, only global zone-wise moduli could be determined. These represent average bending stiffness over the entire test span and include shear contributions. The global modulus of elasticity for each zone was calculated using Equation 17, based on the most linear portion of the load–deflection curve in accordance with EN 408: EFB,i =3a L2 i−4a3 2bih3 i2∆wi ∆Fi−6a 5G bihifor i= 1,2,3(17) where Liand aare in mm, biand hiare the specimen width and height in zone i,∆Fi is the applied load increment in N, and ∆withe corresponding midspan deflection increment in mm. The shear modulus Gwas assumed as 650 MPa following EN 408. To quantify the sensitivity to this assumption, a shear-free modulus EFB,G∞,i was also computed by setting G→ ∞, consistent with common practice in strength class estimation. For global comparisons, zone-wise stiffness values were averaged to a single specimen-level mean (zone index iomitted). For specimens tested to failure, the bending strength σf,FB was calculated as: σf,FB =3Ff,i Li 2bih2 i ,(18) where Ff,i is the maximum load in N at failure. The failure zone was recorded, but as only one zone was tested per specimen, the resulting strength value was taken as the specimen-level bending strength. Adjustments to reference MC and specimen size followed EN 384 [69]. For stiffness 24 and strength, the corrected values were computed with MCFB at testing (%) as σf,FB,adj =σf,FB(1 + 0.02 aMC,FB), aMC,FB = (MCFB −12)/100,(19) EFB,adj,i = 1.3EFB,i(1 + aMC,FB)−2690 MPa.(20) 2.8. Comparisons All measured quantities and derived variables used are summarised in Table 2. Table 2: Overview of all measurement modalities with measured quantities and derived variables. Profiles dependent on the longitudinal coordinate use (x), and corresponding zone-wise values (used where applicable) carry subscript i. Zone-wise stiffness variables of models were omitted for readability. FB = flat-wise bending; DE = dynamic excitation; FE = finite element; CM = meshless continuum model. Method Measured Quantities Derived Variables CT-based models ρCT(x),B(x),F(x)ρCT(x): sectional mean density, EFE,w: mid-point based bending stiffness, EFE,κ(x): curvature-based stiffness profile, EFE,dyn: dynamic stiffness from eigenfrequency, ECM,EI (x),ECM,EA(x),GCM,GA(x): sectional stiffness profiles (bending, axial, shear) Dynamic excitation f0,ρ12,DE,MCDE EDE: static bending stiffness, σf,DE: bending strength Visual grading INSTA 142, NS 3691-3, UNI 11119 σf,vis,INS,σf,vis,NS,σf,vis,UNI: visual equivalent strength estimates Bending tests dimensions bi,hi, Load–deflection curves, Ff,i (subset), MCFB (subset) EFB,G: global bending stiffness, EFB,G,adj: adjusted global bending stiffness (subset), EFB,G∞: shear-free bending stiffness, σf,FB: adjusted bending strength (subset), 25 f , vis, INS f , vis, NS f , vis, UNI E DE E FB, G , adj E FB, G f , FB, adj FB -0.11 0.43 0.14 0.41 0.43 0.31 0.50 0.43 0.36 0.38 0.43 0.61 0.08 0.43 0.14 Spearman Rank Coefficient ( rs ) Figure 11: Spearman rank correlation coefficients (rs) between visual grading categories and experimentally measured values. Higher absolute values indicate stronger monotonic association. 3.2.2. Stiffness Profiles Figures 12–16 compare the experimentally determined zone-wise bending stiffness with the model-derived profiles, shown both at full resolution and as zone averages. Each plot also includes the density-projection averages along the weak and strong axes to enable direct visual comparison with density variations and features such as knots. The figures shown here are exemplary; full profiles for all specimens are available in the published dataset [77]. Across all specimens, local reductions in bending stiffness coincide with knots and other high-density inclusions, while increases align with clearwood or broader-scale density rises. Knots emerging on the flat face consistently produced larger stiffness reductions than knots on the side faces, consistent with bending about the weak axis. This behaviour is reflected in the model-specific responses: the bending-related profile ECM,EIzemphasised stiffness drops at knots on the flat surface, whereas the axial-profile ECM,EA responded to knots on all faces, resulting in more uniform sensitivity. The FE-based global estimate EFE,w closely matched the mean of the full FE stiffness profile EFE,κ(x), as expected. The FE-derived profile was smoother than the 32 CM-based profiles due to Savitzky–Golay filtering and consistently underestimated stiffness, as noted earlier. In contrast, the dynamic-excitation estimate EFE,dyn deviated more strongly from the bending-derived FE predictions, although it followed the same tendency toward underestimation, while the experimental EDE,dyn tended to overestimate stiffness. Specimen 1 presents a clear case with distinct knots and regular geometry (Figures 12 and 13). All stiffness estimates show broadly consistent variation along the beam, although the bending-related FE predictions deviate more strongly in magnitude. Both CMand FE-based profiles capture the principal stiffness reductions around knots and follow similar spatial patterns. Specimen 6 contains two diffuse high-density regions (Figures 14 and 15), likely corresponding to compression wood or moisture pockets. These features increased the modelled stiffness locally, most visibly in the rightmost zone average. The CM-based predictions retained good agreement with the experimental trend, while EDE,dyn showed substantial overestimation in this specimen. Specimen 49 includes several small, sharp density inclusions (Figures 16 and 17), presumably related to metal remnants in former nail holes, as indicated by distinct spikes in the density projection. These inclusions generate gradient fields similar to those around knots, leading both models to interpret them as local disturbances in fibre orientation and therefore as stiffness-reducing features. In the CM profiles, these effects remain localised, whereas the smoothing in the FE-based profiles spreads the influence over a larger region. The wrongly inferred apparent fibre disturbance may also explain why EFE,dyn deviates less strongly here than in the other specimens. 33 0 250 500 750 1000 1250 1500 1750 2000 Beam length (mm) 1 2 3 4 5 6 7 8 E (GPa) E FB, G , i E FE, mean E FE, in zone i E FE, w E FE, dyn Figure 12: Specimen 1: experimental zone-wise stiffness EFB,G,i compared with the FE stiffness profile EFE,κ(x), its zone averages, and global FE estimates EFE,w and EFE,dyn. Density projection averages along the strong and weak axes are shown below. 0 250 500 750 1000 1250 1500 1750 2000 Beam length (mm) 2 3 4 5 6 7 8 9 E (GPa) E FB, G , i E DE, dyn E CM, EIz mean E CM, EIz in zone i E CM, EA Figure 13: Specimen 1: experimental zone-wise stiffness EFB,G,i compared with meshless model profiles ECM,EIz(x)and ECM,EA(x), including zone averages. Density projection averages along the strong and weak axes are shown below. 34 0 250 500 750 1000 1250 1500 1750 2000 Beam length (mm) 2 4 6 8 10 12 E (GPa) E FB, G , i E FE, mean E FE, in zone i E FE, w E FE, dyn Figure 14: Specimen 6: experimental zone-wise stiffness EFB,G,i compared with the FE stiffness profile EFE,κ(x), its zone averages, and global FE estimates EFE,w and EFE,dyn. Density projection averages along the strong and weak axes are shown below. 0 250 500 750 1000 1250 1500 1750 2000 Beam length (mm) 0 2 4 6 8 10 12 14 16 E (GPa) E FB, G , i E DE, dyn E CM, EIz mean E CM, EIz in zone i E CM, EA Figure 15: Specimen 6: experimental zone-wise stiffness EFB,G,i compared with meshless model profiles ECM,EIz(x)and ECM,EA(x), including zone averages. Density projection averages along the strong and weak axes are shown below. 35 0 500 1000 1500 2000 Beam length (mm) 0 2 4 6 8 10 12 E (GPa) E FB, G , i E FE, mean E FE, in zone i E FE, w E FE, dyn Figure 16: Specimen 49: experimental zone-wise stiffness EFB,G,i compared with the FE stiffness profile EFE,κ(x), its zone averages, and global FE estimates EFE,w and EFE,dyn. Density projection averages along the strong and weak axes are shown below. 0 500 1000 1500 2000 Beam length (mm) 2 0 2 4 6 8 10 12 E (GPa) E FB, G , i E DE, dyn E CM, EIz mean E CM, EIz in zone i E CM, EA Figure 17: Specimen 49: experimental zone-wise stiffness EFB,G,i compared with meshless model profiles ECM,EIz(x)and ECM,EA(x), including zone averages. Density projection averages along the strong and weak axes are shown below. 36 3.2.3. Zoneand Specimen-wise Predictions The statistical heatmaps (Figures 18–23) summarise the regression performance of the model-derived IPs against the experimental targets at both zone and specimen level. They complement the local stiffness profiles by quantifying how well each predictor captures the variation in bending stiffness and bending strength across the dataset. For the zone-wise regressions, the achievable R2values of the model-based IPs were generally modest and the errors comparatively high. This behaviour is expected: the zone averages of the experimental bending stiffness are influenced by shear effects and global-span bending, whereas the CT-derived predictors represent localised material features. The homogenisation inherent in zone averaging therefore reduces the attainable correspondence. Even so, the zone-level CMand FE-based predictors outperform ρCT alone and show appreciable explanatory power for bending strength, indicating that local structural information contained in the density and orientation fields is effectively exploited. At the same time, residual discrepancies suggest that additional local factors such as moisture variation, microstructural defects, or measurement of global rather than local stiffness during testing would need to be resolved to further investigate and increase the predictive performance. At the specimen level, the regression performance improves. Dynamic excitation remains the best non-destructive predictor of both stiffness and strength, with EDE and σf,DE yielding similar results because they differ only by a scaling factor. The comparatively moderate R2values for stiffness reflect the use of global bending-test values, which are less sensitive to local curvature in the pure-bending region. The non-standard flatwise orientation used in the bending tests may contribute additional scatter. 37 Among the CT-based indicators, ECM,EA and ECM,EI show the best specimenwise performance and exceed the predictive ability of both ρCT and, marginally, ρFB. This demonstrates that the structural signal in the 3D density field, and in particular the orientation information extracted from its gradients, enhances predictive capability beyond bulk density alone. Notably, for bending strength, these CM-based IPs perform similarly to the elastic mechanical estimates. The FE-based IPs, in contrast, show weak correlations except for the frequency-derived EFE,dyn, which retains partial predictive value despite the systematic stiffness underestimation noted earlier. To contextualise these trends, the Appendix includes pairgrid visualisations (Figures A.26–A.27 and A.28–A.29) that show all pairwise relationships among experimental variables and between model-based predictors and experimental targets. These provide a compact qualitative counterpart to the heatmaps. For clarity, σf,DE was omitted from the pairgrids because it differs from EDE only by a scaling constant, and the variable EFB,G∞was omitted due to the results differing little from EFB,G. E FB, G , adj E FB, G E FB, G f , FB, adj FB E FE, , i E CM, EA , i E CM, EI , i Gy , CM, GA , i CT, i E FB, G , adj E FB, G E FB, G f , FB, adj FB 1.00 0.98 0.98 0.68 0.36 0.17 0.30 0.29 0.24 0.25 0.98 1.00 1.00 0.62 0.25 0.16 0.26 0.24 0.19 0.18 0.98 1.00 1.00 0.64 0.25 0.16 0.25 0.24 0.19 0.17 0.68 0.62 0.64 1.00 0.62 0.37 0.56 0.60 0.54 0.49 0.36 0.25 0.25 0.62 1.00 0.69 0.81 0.79 0.82 0.90 R² (regression) Figure 18: Zone-level coefficients of determination (R2) for linear regressions between predictors (columns) and target variables (rows). Higher values indicate stronger explanatory power. 38 E FB, G , adj E FB, G E FB, G f , FB, adj FB E FE, , i E CM, EA , i E CM, EI , i Gy , CM, GA , i CT, i E FB, G , adj E FB, G E FB, G f , FB, adj FB 0 320 327 1504 1958 2008 1921 1936 2002 1987 248 0 49 1245 1771 1824 1732 1748 1804 1825 210 41 0 1026 1474 1514 1439 1452 1498 1515 6660667677 42 46 46 36 029 23 24 22 16 RMSE (regression) Figure 19: Zone-level root-mean-square errors (RMSE) from linear regressions between predictors (columns) and target variables (rows). Lower values indicate higher predictive accuracy. E FB, G , adj E FB, G E FB, G f , FB, adj FB E FE, , i E CM, EA , i E CM, EI , i Gy , CM, GA , i CT, i E FB, G , adj E FB, G E FB, G f , FB, adj FB 1.00 0.99 0.99 0.83 0.60 0.41 0.54 0.53 0.49 0.50 0.99 1.00 1.00 0.79 0.50 0.41 0.51 0.49 0.44 0.42 0.99 1.00 1.00 0.80 0.50 0.40 0.50 0.49 0.44 0.42 0.83 0.79 0.80 1.00 0.79 0.61 0.75 0.77 0.73 0.70 0.60 0.50 0.50 0.79 1.00 0.83 0.90 0.89 0.91 0.95 Pearson r Figure 20: Zone-level Pearson correlation coefficients (r) between predictors (columns) and target variables (rows). Higher absolute values indicate stronger linear association. 39 f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB f 0, FE E FE, dyn E FE, w E FE, E CM, EA E CM, EI Gy , CM, GA CT f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB 1.00 0.30 0.41 0.25 0.24 0.30 0.38 0.10 0.11 0.61 0.16 0.25 0.26 0.16 0.16 0.11 0.10 0.30 1.00 0.58 0.51 0.51 1.00 0.75 0.65 0.61 0.33 0.66 0.56 0.59 0.67 0.65 0.61 0.54 0.41 0.58 1.00 0.98 0.98 0.58 0.70 0.34 0.41 0.23 0.34 0.23 0.24 0.45 0.44 0.37 0.39 0.25 0.51 0.98 1.00 1.00 0.51 0.66 0.23 0.27 0.07 0.22 0.18 0.20 0.33 0.32 0.25 0.24 0.24 0.51 0.98 1.00 1.00 0.51 0.68 0.23 0.27 0.07 0.22 0.18 0.20 0.33 0.32 0.25 0.23 0.30 1.00 0.58 0.51 0.51 1.00 0.75 0.65 0.61 0.33 0.66 0.56 0.59 0.67 0.65 0.61 0.54 0.38 0.75 0.70 0.66 0.68 0.75 1.00 0.56 0.62 0.21 0.46 0.36 0.36 0.64 0.66 0.62 0.60 0.10 0.65 0.34 0.23 0.23 0.65 0.56 1.00 0.97 0.42 0.83 0.71 0.73 0.82 0.80 0.84 0.90 0.11 0.61 0.41 0.27 0.27 0.61 0.62 0.97 1.00 0.41 0.84 0.70 0.70 0.85 0.84 0.87 0.94 R² (regression) Figure 21: Specimen-level coefficients of determination (R2) from linear regressions between predictors (columns) and target variables (rows). Higher values indicate stronger explanatory power. f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB f 0, FE E FE, dyn E FE, w E FE, E CM, EA E CM, EI Gy , CM, GA CT f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB 0101 89 105 105 101 87 115 115 73 107 101 101 112 111 114 115 2170 01667 1821 1824 11428 1535 1626 2062 1469 1679 1615 1495 1530 1619 1755 1770 1486 0 319 324 1486 1356 1863 1768 1781 1650 1786 1773 1708 1716 1820 1798 1679 1354 247 0 41 1354 1055 1693 1647 1811 1659 1700 1680 1579 1592 1669 1691 1397 1128 209 34 0 1128 875 1410 1370 1502 1377 1412 1396 1314 1325 1389 1407 80666055675665566 85666507675666666 58 36 49 54 54 36 43 0 10 45 24 32 31 26 27 24 20 50 33 40 46 46 33 36 9 0 40 20 28 28 21 22 19 13 RMSE (regression) Figure 22: Specimen-level root-mean-square errors (RMSE) from linear regressions between predictors (columns) and target variables (rows). Lower values indicate higher predictive accuracy. 40 f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB f 0, FE E FE, dyn E FE, w E FE, E CM, EA E CM, EI Gy , CM, GA CT f 0, DE E DE E FB, G , adj E FB, G E FB, G f , DE f , FB, adj 12, DE FB 1.00 0.55 0.64 0.50 0.49 0.55 0.61 0.32 0.33 0.78 0.40 0.50 0.51 0.39 0.40 0.34 0.32 0.55 1.00 0.76 0.71 0.71 1.00 0.86 0.81 0.78 0.58 0.81 0.75 0.77 0.82 0.81 0.78 0.74 0.64 0.76 1.00 0.99 0.99 0.76 0.83 0.58 0.64 0.48 0.58 0.48 0.49 0.67 0.66 0.61 0.62 0.50 0.71 0.99 1.00 1.00 0.71 0.82 0.48 0.52 0.27 0.47 0.43 0.45 0.58 0.57 0.50 0.48 0.49 0.71 0.99 1.00 1.00 0.71 0.82 0.48 0.52 0.27 0.47 0.42 0.44 0.58 0.57 0.50 0.48 0.55 1.00 0.76 0.71 0.71 1.00 0.86 0.81 0.78 0.58 0.81 0.75 0.77 0.82 0.81 0.78 0.74 0.61 0.86 0.83 0.82 0.82 0.86 1.00 0.75 0.79 0.46 0.68 0.60 0.60 0.80 0.81 0.78 0.77 0.32 0.81 0.58 0.48 0.48 0.81 0.75 1.00 0.99 0.65 0.91 0.84 0.85 0.91 0.89 0.92 0.95 0.33 0.78 0.64 0.52 0.52 0.78 0.79 0.99 1.00 0.64 0.92 0.84 0.84 0.92 0.92 0.93 0.97 Pearson r Figure 23: Specimen-level Pearson correlation coefficients (r) between predictors (columns) and target variables (rows). Higher absolute values indicate stronger linear association. 3.3. Methodological Limitations Several methodological aspects are inherent to the applied approaches and influence both the accuracy and interpretability of the model-derived indicators. The CT-derived density and orientation fields depend on calibration stability, segmentation thresholds, and gradient-based orientation inference; cavities and metallic inclusions can distort these gradients and propagate into the FEand CM-based stiffness estimates. The absence of spatially resolved moisture information in the CT data further affects the absolute scaling of densityand stiffness-related quantities. The FE discretisation is currently based on a sequence of processing and meshing steps that may accumulate geometric deviations, including the smoothing of sharp edges and approximation of local surface irregularities. Mesh generation failed for specimens with severe internal cavities, introducing a bias toward less-degraded material. The curvature-based FE stiffness EFE,κ relies on numerical differentiation of displace41 [4] B. S. Byers, D. Raghu, A. Olumo, C. De Wolf, C. Haas, From research to practice: A review on technologies for addressing the information gap for building material reuse in circular construction, Sustainable Production and Consumption 45 (2024) 177–191. URL: https://www.sciencedirect.com/science/ article/pii/S2352550923002920. doi:10.1016/j.spc.2023.12.017. [5] C. Grüter, M. Gordon, M. Muster, F. Kastner, P. Grönquist, A. Frangi, S. Langenberg, C. De Wolf, Design for and from disassembly with timber elements: strategies based on two case studies from Switzerland, Frontiers in Built Environment 9 (2023). doi:https://doi.org/10.3389/fbuil.2023.1307632, publisher: Frontiers. [6] M. Hudert, S. Pfeiffer, Rethinking Wood: Future Dimensions of Timber Assembly, in: Rethinking Wood, Birkhäuser, 2019. URL: https://www. degruyter.com/document/doi/10.1515/9783035617061/html?lang=en. doi:10.1515/9783035617061. [7] R. N. Passarelli, Design for Disassembly and Reuse of Timber in Construction: Identification of Trends and Knowledge Gaps, in: L. Bragança, M. Cvetkovska, R. Askar, V. Ungureanu (Eds.), Creating a Roadmap Towards Circularity in the Built Environment, Springer Nature Switzerland, Cham, 2024, pp. 57–67. URL: https://doi.org/10.1007/978-3-031-45980-1_6. doi:10. 1007/978-3-031-45980-1_6. [8] S. Litleskare, W. Wuyts, Planning Reclamation, Diagnosis and Reuse in Norwegian Timber Construction with Circular Economy Investment and Operating Costs for Information, Sustainability 15 (2023) 10225. URL: https: 48 //www.mdpi.com/2071-1050/15/13/10225. doi:10.3390/su151310225, number: 13 Publisher: Multidisciplinary Digital Publishing Institute. [9] W. Dong, C. M. Rose, J. A. Stegeman, Cross-laminated secondary timber: Validation of non-destructive assessment of structural properties by fullscale bending tests, Engineering Structures 298 (2024). URL: https://www. sciencedirect.com/science/article/pii/S014102962301444X. [10] A. Pronk, S. Brancart, F. Sanders, Reusing Timber Formwork in Building Construction: Testing, Redesign, and Socio-Economic Reflection, Urban Planning 7 (2022) 81–96. URL: https://www.cogitatiopress.com/urbanplanning/ article/view/5117. [11] M. Lebossé, G. Halin, F. Besancon, A. Fuchs, Incorporating BIM Practices into Reuse Process of Timber - Propositions of a digital workflow and tool for reclaiming structural pieces of wood, in: eCAADe 2022: Co-creating the Future - Inclusion in and through Design, Ghent, France, 2022, pp. 205–214. URL: https: //hal.science/hal-03819849. doi:10.52842/conf.ecaade.2022.1.205. [12] D. Bergsagel, F. Heisel, Structural design using reclaimed wood – A case study and proposed design procedure, Journal of Cleaner Production 420 (2023) 138316. URL: https://linkinghub.elsevier.com/retrieve/pii/ S0959652623024745. doi:10.1016/j.jclepro.2023.138316. [13] P. Asa, C. El Feghali, C. Steixner, Y. Tahouni, H. J. Wagner, J. Knippers, A. Menges, Embraced Wood: Circular construction method for composite long-span beams from unprocessed reclaimed timber, fibers and clay, Construction and Building Materials 416 49 (2024) 135096. URL: https://www.sciencedirect.com/science/article/ pii/S095006182400237X. doi:10.1016/j.conbuildmat.2024.135096. [14] M. Kauniste, A. Just, E. Tuhkanen, T. Kalamees, Assessment on strength and stiffness properties of aged structural timber, Journal of Sustainable Architecture and Civil Engineering 34 (2024) 62–74. doi:10.5755/j01.sace.34.1. 35534. [15] C. M. Rose, D. Bergsagel, T. Dufresne, E. Unubreme, T. Lyu, P. Duffour, J. A. Stegemann, Cross-laminated secondary timber: experimental testing and modelling the effect of defects and reduced feedstock properties, Sustainability 10 (2018) 4118. [16] C. U. Chúláin, D. F. Llana, P. Hogan, P. McGetrick, A. M. Harte, Bending characteristics of clt from recovered spruce, in: World Conference on Timber Engineering, volume 2023, 2023, pp. 888–894. [17] W. Dong, C. M. Rose, J. A. Stegemann, Cross-laminated secondary timber: Validation of non-destructive assessment of structural properties by full-scale bending tests, Engineering Structures 298 (2024) 117029. [18] N. H. Vonk, J. Niederwestberg, R. W. A. Oorschot, J. D. de Jong, Upcycling of single-use pallet wood to cross laminated timber, Accepted for publication in the 1st International Conference on Net-Zero Built Environment (2024). [19] M. Ramsgaard Thomsen, P. Nicholas, G. Rossi, A. E. Daugaard, A. Rech, Extending the Circular Design Framework for Bio-Based Materials, Design for Rethinking Resources - UIA World Congress of Architectur 2023 (UIACPH2023) (2023) 609. Publisher: Springer Nature Swizerland AG. 50 [20] W. Wuyts, A. Tomczak, K. Nore, L. Huang, T. Haavi, REUSE OF WOOD - learning about the benefits and challenges of highand low-tech diagnostic methods through action research in Norway, in: Proceedings of the World Conference On Timber Engineering 2023: Timber for a Livable Future, Oslo, Norway, 2023. doi:10.52202/069179-0539. [21] M. Piazza, M. Riggio, Visual strength-grading and NDT of timber in traditional structures, Journal of Building Appraisal 3 (2008) 267–296. URL: http://link. springer.com/10.1057/jba.2008.4. doi:10.1057/jba.2008.4. [22] D. J. Cown, Comparison of the pilodyn and torsiometer methods for the rapid assessment of wood density in living trees, New Zealand Journal of Forestry Science 8 (1978) 384–391. [23] F. Rinn, F.-H. Schweingruber, E. Schär, Resistograph and x-ray density charts of wood. comparative evaluation of drill resistance profiles and x-ray density charts of different wood species, Holzforschung 50 (1996) 303–311. doi:10.1515/hfsg. 1996.50.4.303. [24] M. Piazza, M. Del Senno, Proposals and criteria for the preliminary evaluation, the design and the execution of works on ancient load bearing timber structures, Wooden Handwork/Wooden Carpentry, European Restoration Sites (2021) 263– 277. [25] O. Lindgren, Medical CT-Scanners for Non-Destructive Wood Density and Moisture Content Measurements, Ph.D. thesis, Luleå University of Technology, 1992. [26] L. Hansson, J. Couceiro, B.-A. Fjellner, Estimation of shrinkage coefficients 51 in radial and tangential directions from CT images, Wood Material Science & Engineering 12 (2017) 251–256. doi:10.1080/17480272.2016.1249405. [27] F. Longuetaud, F. Mothe, B. Kerautret, A. Krähenbühl, L. Hory, J. Leban, I. Debled-Rennesson, Automatic knot detection and measurements from Xray CT images of wood: A review and validation of an improved algorithm on softwood samples, Computers and Electronics in Agriculture 85 (2012) 77–89. URL: http://dx.doi.org/10.1016/j.compag.2012.03.013. doi:10.1016/j. compag.2012.03.013, publisher: Elsevier B.V. [28] M. Hu, A. Olsson, S. Hall, T. Seifert, Fibre directions at a branch-stem junction in Norway spruce: a microscale investigation using X-ray computed tomography, Wood Science and Technology 56 (2022) 147–169. doi:10.1007/ s00226-021-01353-y. [29] M. Hu, A. Olsson, O. Abdeljaber, J. Huber, Determining growth surfaces and fiber orientation in Norway spruce sawn timber using X-ray computed tomography and optical scanning, Construction and Building Materials 482 (2025) 141734. URL: https://linkinghub.elsevier.com/retrieve/pii/ S0950061825018859. doi:10.1016/j.conbuildmat.2025.141734. [30] A. Rais, E. Ursella, E. Vicario, F. Giudiceandrea, The use of the first industrial X-ray CT scanner increases the lumber recovery value: case study on visually strength-graded Douglas-fir timber, Annals of Forest Science 74 (2017) 28. URL: https://annforsci.biomedcentral.com/articles/10. 1007/s13595-017-0630-5. doi:10.1007/s13595-017-0630-5. [31] J. A. Huber, O. Broman, M. Ekevad, J. Oja, L. Hansson, A method for generating finite element models of wood boards from X-ray com52 puted tomography scans, Computers & Structures 260 (2022) 106702. URL: https://doi.org/10.1016/j.compstruc.2021.106702https: //linkinghub.elsevier.com/retrieve/pii/S0045794921002248. doi:10.1016/j.compstruc.2021.106702. [32] M. Lukacevic, G. Kandler, M. Hu, A. Olsson, J. Füssl, A 3D model for knots and related fiber deviations in sawn timber for prediction of mechanical properties of boards, Materials & Design 166 (2019) 107617. URL: https://doi.org/10.1016/j.matdes.2019.107617https: //linkinghub.elsevier.com/retrieve/pii/S0264127519300541. doi:10.1016/j.matdes.2019.107617. [33] M. Tamke, S. Gatz, T. Svilans, M. Ramsgaard Thomsen, Tree-to-Product: Prototypical workflow connecting Data from tree with fabrication of engineered wood structure - RawLam, in: Proceedings of WCTE2021, Santiago, Chile., 2021, pp. 2754–2763. URL: https://www.proceedings.com/61811.html. [34] S. M. Haakonsen, A. Tomczak, B. Izumi, M. Luczkowski, Automation of circular design: A timber building case study, International Journal of Architectural Computing 0 (2024) 1–17. doi:10.1177/14780771241234447. [35] S. Çetin, D. Raghu, M. Honic, A. Straub, V. Gruis, Data requirements and availabilities for material passports: A digitally enabled framework for improving the circularity of existing buildings, Sustainable Production and Consumption 40 (2023) 422–437. URL: https://www.sciencedirect.com/ science/article/pii/S2352550923001665. doi:https://doi.org/10.1016/ j.spc.2023.07.011. 53 [36] EN 14081-1:2016, Timber structures - Strength graded structural timber with rectangular cross section - Part 1: General requirements, European Committee for Standardization (CEN): Brussels, Belgium, 2016. [37] D. Ridley-Ellis, P. Stapel, V. Baño, Strength grading of sawn timber in Europe: an explanation for engineers and researchers, European Journal of Wood and Wood Products 74 (2016) 291–306. URL: http://link.springer.com/10. 1007/s00107-016-1034-1. doi:10.1007/s00107-016-1034-1. [38] EN 338:2016, Structural timber - Strength classes, European Committee for Standardization (CEN): Brussels, Belgium, 2016. [39] NZS AS 1720.1:2022, Timber Structures - Part 1: Design methods, Standards New Zealand: Wellington, New Zealand, 2022. [40] EN 1990:2023, Eurocode - Basis of structural and geotechnical design, European Committee for Standardization (CEN): Brussels, Belgium, 2023. [41] K. Crews, C. MacKenzie, Development of grading rules for re-cycled timber used in structural applications, in: World Conference on Timber Engineering, WCTE, 2008. [42] R. H. Falk, D. G. Maul, S. M. Cramer, J. Evans, V. Herian, Engineering properties of douglas-fir lumber reclaimed from deconstructed buildings, Research Paper FPL-RP-650. USDA Forest Service, Forest Products Laboratory, Madison, Wisconsin (2008). [43] A. Cavalli, D. Cibecchini, M. Togni, H. S. Sousa, A review on the mechanical properties of aged wood and salvaged timber, Construction and Building Materials 114 (2016) 681–687. 54 [44] UNI 11119:2004, Cultural heritage - Wooden artefacts - Load-bearing structures - On site inspections for the diagnosis of timber members, Ente Nazionale Italiano di Unificazione (UNI): Milan, Italy, 2004. [45] J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances, third ed ed., SPIE Press, Bellingham, WA, USA, 2015. doi:10.1117/ 3.2197756. [46] A. Katsevich, An improved exact filtered backprojection algorithm for spiral computed tomography, Advances in Applied Mathematics 32 (2004) 681–697. URL: https://www.sciencedirect.com/science/article/ pii/S019688580300099X. doi:https://doi.org/10.1016/S0196-8858(03) 00099-X. [47] J. Huber, O. Abdeljaber, J. Oja, A. Olsson, Evaluation Of Models Of Fibre Orientation In Sawn Timber Using Synchronised Computed Tomography And Optical Scanning Data, in: World Conference on Timber Engineering (WCTE 2023), World Conference on Timber Engineering (WCTE 2023), Oslo, Norway, 2023, pp. 421–427. URL: http://www.proceedings.com/069179-0057.html. doi:10.52202/069179-0057. [48] C. Luengo, D. Contributors, DIPlib: Quantitative Image Analysis in C++, MATLAB and Python, DIPlib Project, 2025. URL: https://github.com/ DIPlib/diplib, version 3.x, https://github.com/DIPlib/diplib. [49] J. M. S. Prewitt, M. L. Mendelsohn, The Analysis of Cell Images, Annals of the New York Academy of Sciences 128 (1966) 1035–1053. URL: http://doi.wiley.com/10.1111/j.1749-6632.1965.tb11715.xhttps: 55 //onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1965.tb11715.x. doi:10.1111/j.1749-6632.1965.tb11715.x. [50] M.-K. Hu, Visual pattern recognition by moment invariants, IEEE Transactions on Information Theory 8 (1962) 179–187. URL: http://dx.doi.org/10.1109/ TIT.1962.1057692. doi:10.1109/tit.1962.1057692. [51] J. A. J. Huber, Numerical Modelling of Timber Building Components to Prevent Disproportionate Collapse, Phd thesis, Luleå University of Technology, 2021. URL: https://doi.org/10.5281/zenodo.15464980. doi:10.5281/ zenodo.15464980. [52] J. Bigun, T. Bigun, K. Nilsson, Recognition by symmetry derivatives and the generalized structure tensor, IEEE Transactions on Pattern Analysis and Machine Intelligence 26 (2004) 1590–1605. doi:10.1109/TPAMI.2004.126. [53] M. Krause, J. M. Hausherr, B. Burgeth, C. Herrmann, W. Krenkel, Determination of the fibre orientation in composites using the structure tensor and local X-ray transform, Journal of Materials Science 45 (2010) 888–896. URL: https: //doi.org/10.1007/s10853-009-4016-4. doi:10.1007/s10853-009-4016-4. [54] J. M. Dinwoodie, Timber: Its nature and behaviour, 2 ed., Taylor & Francis, New York, NY, 2000. [55] K. Museth, Vdb: High-resolution sparse volumes with dynamic topology, ACM Trans. Graph. 32 (2013). URL: https://doi.org/10.1145/2487228.2487235. doi:10.1145/2487228.2487235. [56] T. Svilans, M. Tamke, M. Ramsgaard Thomsen, Integrative strategies across 56 the timber value chain, in: Proceedings of the 5th International Conference on Structures and Architecture (ICSA), 2022. [57] W. E. Lorensen, H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, ACM SIGGRAPH Computer Graphics 21 (1987) 163–169. URL: http://dx.doi.org/10.1145/37402.37422. doi:10.1145/37402.37422. [58] Q.-Y. Zhou, J. Park, V. Koltun, Open3d: A modern library for 3d data processing, 2018. URL: https://arxiv.org/abs/1801.09847. doi:10.48550/ARXIV. 1801.09847. [59] C. Geuzaine, J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in preand post-processing facilities, International Journal for Numerical Methods in Engineering 79 (2009) 1309–1331. URL: https://onlinelibrary. wiley.com/doi/abs/10.1002/nme.2579. doi:10.1002/nme.2579, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.2579. [60] G. Dhondt, The Finite Element Method for Three-Dimensional Thermomechanical Applications, 1 ed., Wiley, 2004. URL: https://onlinelibrary.wiley. com/doi/book/10.1002/0470021217. doi:10.1002/0470021217. [61] A. Savitzky, M. J. E. Golay, Smoothing and differentiation of data by simplified least squares procedures, Analytical Chemistry 36 (1964) 1627–1639. URL: http://dx.doi.org/10.1021/ac60214a047. doi:10.1021/ac60214a047. [62] S. Ormarsson, Numerical analysis of moisture-related distortions in sawn timber, Ph.D. thesis, Chalmers University of Technology, 1999. ISBN: 9171978348 ISSN: 0346718X. 57 900 1000 1100 1200 1300 1400 f 0, DE 6000 8000 10000 12000 14000 16000 18000 20000 E DE 6000 8000 10000 12000 14000 E FB, G , adj 6000 8000 10000 12000 14000 E FB, G 20 30 40 50 f , FB, adj 400 450 500 550 600 12, DE 1000 1200 1400 f 0, DE 350 400 450 500 550 FB 10000 15000 20000 E DE 5000 10000 15000 E FB, G , adj 7500 10000 12500 E FB, G 20 40 f , FB, adj 400 500 600 12, DE 400 500 FB Figure A.28: Zone-level pairwise relationships among experimental variables. Diagonal panels show univariate histograms; off-diagonal panels show scatter plots with fitted regression lines. Orange markers indicate specimens tested to failure; blue markers represent the remaining dataset. 64 900 1000 1100 1200 1300 1400 f 0, DE 8000 10000 12000 14000 16000 18000 20000 E DE 8000 10000 12000 14000 E FB, G , adj 6000 8000 10000 12000 14000 E FB, G 25 30 35 40 45 50 f , FB, adj 400 450 500 550 600 12, DE 800 1000 1200 1400 f 0, FE 400 450 500 550 FB 0.5 1.0 E FE, dyn 1e10 0.25 0.50 0.75 1.00 E FE, w 1e10 0.25 0.50 0.75 1.00 E FE, 1e10 0.5 1.0 1.5 E CM, EA 1e10 0.5 1.0 1.5 E CM, EI 1e10 468 Gy , CM, GA 1e8 300 400 500 CT Figure A.29: Zone-level pairwise comparisons of model-derived predictors (columns) against experimental target variables (rows). Diagonal panels show univariate histograms; off-diagonal panels show scatter plots with fitted regression lines. Orange markers indicate specimens tested to failure; blue markers represent the remaining dataset. 65