Shear Analogy Research Articles

Evaluation of bending and shear properties of mixed softwood & hardwood cross-laminated timbers

The current version of PRG-320 Standard for Performance-Rated Cross-Laminated Timber (CLT) that governs CLT manufacturing and design, limits production to softwood species. As a result, the growing demand for CLT production could strain the supply of softwood lumber in the US within the next decade. The inclusion of hardwood in CLT production alongside softwood could be a potential solution to this problem. This paper investigates the bending and shear test results of three- and five-layer mixed species CLT beams manufactured using various combinations of yellow-poplar and southern pine. The beams were evaluated for bending strength, bending stiffness, shear strength, and shear stiffness, as well as quality control testing of moisture content, specific gravity, resistance to shear by compression loading and resistance to delamination. The experimental values for all CLT groups, adjusted according to the Allowable Stress Design (ASD) to ensure stress limits are not exceeded, were greater than those calculated using the shear analogy method. The only exceptions were bending stiffness values for the groups with all layers of southern pine and those with outer layers of southern pine and inner layers of yellow-poplar (see Table 1 for layups codes), where the differences remained within a minor range of 4 %. Although, wood failure percentages in resistance to shear by compression loading fell below the maximum value of 80 %, and face delamination percentages in resistance to delamination were above the minimum value of 5 % according to the corresponding standards. The mechanical properties of all CLT beams met or exceeded shear analogy values. The test results indicated that yellow-poplar could be a viable alternative to southern pine in the production of CLT due to its similar specific gravity. This suggests that mixed-species CLT can maintain or enhance structural performance while addressing material shortages. Furthermore, the use of yellow-poplar in CLT production promotes sustainable forestry practices, supports resource diversification, and encourages innovation in construction methods. These findings have significant practical implications for the timber and construction industries, contributing to cost efficiency and environmental sustainability.

Out-of-plane cross-angle bending stiffness of cross-laminated timber

The increasing use of cross-laminated timber (CLT) in construction worldwide can be attributed to its combination of sustainability, structural efficiency, biaxial strength and stiffness, short construction times, and architectural flexibility. However, when applied in free-form structures, CLT panels may exhibit irregular element geometries, resulting in deviations from their major or minor strength axes. The required out-of-plane cross-angle bending stiffness is not addressed by commonly used design methods. This study addresses this gap by examining the cross-angle bending stiffness of CLT panel segments using experimental, analytical, and numerical methods. Three different lay-ups (3-ply, 4-ply, and 5-ply) and five cross-angles (ranging from 0° to 90°) were tested under 3-point bending, demonstrating the nonlinear relation between cross-angle and out-of-plane bending stiffness. The lowest stiffness was observed for intermediate cross-angles and not when loaded along the minor strength direction. A proposed analytical model that combines the shear analogy with Hankinson's equation yielded adequate approximations. The model was verified by numerical simulations and then applied to predict the out-of-plane cross-angle bending stiffness of a wide range of CLT layups. This research provides valuable insights for working with CLT in complex geometrical designs, enhancing preliminary design.

Rolling shear properties of cross-laminated bamboo (CLB) specimens: A comprehensive study

This study explores the rolling shear properties of cross-laminated bamboo (CLB), an innovative engineering bamboo material. Two typical test methods are used for the experimental work: the modified planar shear tests (MPS) and the three-point short beam bending tests (SBB). The rolling shear strength and modulus are measured in MPS. The shear analogy method is used to calculate the rolling shear strength in SBB. Subsequently, comprehensive numerical models of MPS and SBB are developed, taking into account the material properties of bamboo and adhesives through user material and cohesive zone model. The stress-strain curves and failure propagations of the models align very well with the experimental results. Rolling shear failure was initiated at the interface between the middle layer and outside layer and extended diagonally. Parametric analysis on the cohesive strength of the MPS model shows the variation of loading curves and failure modes. The failure modes of SBB under different span-to-depth ratios are investigated by integrating the shear analogy method and numerical model.

Design and Evaluation of a Shear Analogy Tool for Custom Cross-Laminated Timber (CLT) Panels Made from Various Wood Species

Abstract A user-friendly cross-laminated timber (CLT) design tool called SAM-CLT was developed to calculate the minimum design values for custom CLT panels. Custom panels are those made from different species not currently included in APA PRG 320 and include the use of multiple species in a panel. The tool uses the design value of hardwood and softwood lumber published in the national design specification book to design custom CLTs and the standard CLT grade lumber specification values published in PRG 320 standard. SAM-CLT was designed based on the shear analogy model and is intended to assist CLT manufacturers, construction and design companies, and researchers in designing and evaluating CLTs’ deformation when using different lumber types and thicknesses. This project included the calibration and validation of the tool, followed by examples of its use by computing the design value of the softwood, hardwood, and softwood–hardwood hybrid CLTs. The SAM-CLT tool was adjusted to match the published standard design values on PRG 320 and validated by comparing output for standard CLT layups. In the next step, SAM-CLT tool was used to calculate the minimum design value of custom CLTs made from hardwood–yellow poplar lumber and softwood–southern yellow pine lumber. Based on observed validation results of the tool and its application results to determine the design values for various CLT layups, this project concludes that SAM-CLT can be a valuable tool for designing custom CLTs, evaluating CLTs’ strength properties, and promoting heterogeneous lumber types in CLT manufacturing.

Mechanical properties of ply-lam cross-laminated timbers fabricated with lumber and plywood

The mechanical properties of four ply-lam cross-laminated timbers (CLTs) containing a plywood layer were compared with those of glued laminated timber (GLT) and CLT. The bending, out-of-plane shear, and compression strengths were highest in the GLT, followed by the ply-lam CLTs and CLT. The modulus of elasticity (MOE) values for the three studied ply-lam CLT samples were 1–2.5 GPa higher than GLT; however, the modulus of rupture (MOR) of all ply-lam CLTs was 7.3–18.8 MPa lower than GLT. The length of the plywood product is 2,440 mm, and longitudinal bonding is required to manufacture ply-lam CLTs of length > 3 m. The prediction of bending capabilities by shear analogy was compared with the bending properties when joints were included. The performances of all the pilot-scale ply-lam CLT samples exceeded the predicted bending performance standards for MOE (10 GPa) and MOR (30 MPa) All samples exceeded 10 GPa and 30 MPa, based on projected and experimental data.

Rolling Shear Strength of Cross Laminated Timber (CLT)—Testing, Evaluation, and Design

Cross laminated timber (CLT), with its typical orthogonal layering and exposure to out-of-plane bending, develops inherent rolling shear stresses. These stresses need to be checked during the ultimate limit state design process. With the ongoing revision of Eurocode 5, a discussion regarding the characteristic value of the rolling shear strength of CLT has arisen. One obstacle in the discussion is seen in the lack of harmonized regulations concerning how to determine rolling shear properties. This circumstance manifests in the greatly diverging test results of different institutions testing the rolling shear strength. The paper at hand aims to propose a candidate for such harmonized regulations. To achieve this, the most common test setups, such as the inclined shear test, three- and four-point bending tests, etc., were numerically and experimentally investigated. Within the numerical investigations, a comparison of the most common calculation methods (Timoshenko beam theory, modified γ-method, Shear Analogy Method, and Finite Element Analysis) for evaluating rolling shear stresses was included. In the experimental program, parameters such as the specimen width, number, and thickness of the cross layer(s), shear length, optional reinforcement against the stresses perpendicular to the grain, and the overall test setup were varied. It was found that the used test setups themselves and the area of the cross layer(s) (shear length, number, and thickness of the cross layer(s)) have a major impact on the rolling shear strength. In contrast, no effect was found from the calculation methods. Based on these findings and on a database of approx. 300 four-point bending rolling shear tests on CLT specimens from five well-established CLT manufacturers, a model for the regulation of the rolling shear strength of CLT is proposed, in combination with a corresponding four-point bending test setup. Afterwards, with two additionally conducted four-point bending test series, the proposed model is successfully validated. The conclusions and recommendations in respect to the test setup (four-point bending), evaluation procedure (Timoshenko beam theory), reference characteristic rolling shear strength, and the model, which allows adapting the reference rolling shear strength to individual conditions, are seen as a worthy basis for a more objective discussion on this topic.

Effect of lamination grade on bending and shear properties of CLT made from fast-growing Chinese fir

In this paper, fast-growing Chinese fir lumber were used to manufacture cross-laminated timber (CLT). Firstly, the non-destructive testing method was applied to test and analyze the distribution of the density and dynamic modulus of elasticity of fast-growing Chinese fir lumber, and Kolmogorov-Smirnov (K-S) test was applied to examine the distribution. After that, the bending and shear properties of CLT assembled with different grade of laminations were evaluated. Finally, the Shear Analogy Method was applied to predict the mechanical properties of CLT made from fast-growing Chinese fir lumber. The results showed that, the distribution of density of fast-growing Chinese fir lumber belonged to lognormal distribution, while the distribution of dynamic modulus of elasticity belonged to normal distribution. Besides, using higher grade lumbers as the longitudinal laminations of CLT could significantly improve its mechanical properties including bending and shear properties, and could avoid the damage in the longitudinal layer. Additionally, the Shear Analogy Method was appropriate to predict mechanical properties of CLT made from fast-growing Chinese fir lumber.

Cross-laminated secondary timber: Validation of non-destructive assessment of structural properties by full-scale bending tests

The demolition of buildings creates a vast quantity of secondary timber, which is currently chipped, downcycled or incinerated. This study examines a higher value use of secondary timber as lamellae for cross-laminated timber (CLT), which will address the increasing demand for wood products that is expected in the coming decades. The longitudinal vibration test method was used to determine the dynamic modulus of elasticity (dMoE) for secondary timber. Then, four-point bending tests were conducted for the secondary timber to obtain the static modulus of elasticity (sMoE) and modulus of rupture (MoR). The test results showed a good linear relationship between dMoE and sMoE, so the dMoE results could be used to predict sMoE of secondary timber. Furthermore, the static bending stiffness of cross-laminated secondary timber (CLST), sMoECL, was predicted by the dMoE from transverse vibration tests of CLST and longitudinal vibration tests of secondary timber. Four-point bending tests of CLST showed that the latter predicted sMoECL more accurately. CLST panels were also found to meet the structural requirements in relevant standards. Finally, analytical models were used to predict the bending stiffness and strength of CLST. The closest prediction came from combining the shear analogy method and bearing model for CLT. This paper demonstrates the feasibility of using secondary timber as a feedstock for CLT/CLST production.

A layered beam-based model for analyzing the stress of rolling shear for the cross-laminated timber panels under out-of-plane bending

When used as horizontal components to carry vertical loads, such as floors and beams, the design of cross-laminated timber (CLT) panels is driven by out-of-plane bending. In this case, rolling shear is always one of the major concerns that governs the performances of ultimate limit state of CLT members. Analytical models are available for predicting the shear capacity of CLT panels, but they are computational extensive and cannot provide the longitudinal distribution of shear stress which is necessary to predict where the failure will happen. In this paper, a layered beam-based analytical model, for analyzing the stress of rolling shear for transversely loaded CLT members was developed. The model deems that the shear deformations of out-of-plane bending CLT members are carried by cross layers while the deformations of bending moment are carried by parallel layers. Based on the layered beam theory, the equation that governs the stress of rolling shear and its analytical solution were derived. It was found that the shear stress distribution in CLT longitudinal direction obeys exponential law and the maximum shear stress is located at the end of the CLT member. Formulas to predict the shear capacity for 3- and 5-layer CLT panels under out-of-plane bending were obtained. The proposed method was validated by the experimental data generated by the authors and by other researchers. Comparing to the shear analogy method and Gamma method, the proposed method requires less computational work and provides similar accuracy.

Numerical simulation on the influence of delamination on the critical buckling load of CLT panels

This work aims to evaluate the critical buckling load of panels made of cross-laminated timber, considering finite element simulations and different analytical methods of calculating the effective bending and shear stiffness. In addition, the effect of openings, pre-cracks, and adhesive strength on the critical buckling load is analyzed. Results indicate that the approach with thin external faces is both simpler and more effective. When estimating the bending and shear stiffness, the methods that show the least difference are the γ-method and the shear analogy method, with the first of them being more conservative. The corrected Timoshenko method tends to overestimate the critical load. Moreover, using cohesive zone models embedded in finite element simulations, the critical load is reduced by an average of 10% due to the stiffness of the adhesive. Furthermore, when panels have adhesive-free edges, the critical load can be reduced by more than 50%.

The appropriacy of the analytical models for calculating the shear capacity of cross-laminated timber (CLT) under out-of-plane bending

Rolling shear, an inherent property of cross-laminated timber (CLT) due to the weak shear strength of cross layers, is always the determinant of load-bearing capacity for short-span CLT members subjected to out-of-plane bending. Many analytical models were developed to calculate the shear capacity of CLT members. Because of the difficulty to precisely model the complicated shear failure mechanisms, however, no model was universally accepted. This paper aims to study the appropriacy of the commonly used analytical models, namely, composite beam theory, shear analogy method, Gamma method, and simple beam theory, by tests and analytical calculations. A composite beam theory-based simplified method was proposed. Three-point loading tests for the short-span CLT panels with 3 and 5 layers were conducted, and the shear capacities of the test specimens were calculated using the above-mentioned analytical methods. Shear strength and modulus of cross layers of the test specimens, which were used as the inputs for calculating the shear capacities, were tested by modified planar shear method. By comparing the calculation results obtained from different analytical models and the test results as well, it can be concluded that: (1) composite beam theory, shear analogy method, and the proposed simplified method give almost the same calculation results, therefore, the proposed simplified method can be used as the replacement for the other models; (2) Gamma method is more appropriate for calculating the shear capacity in case the input shear strength is determined by planar shear test; (3) the simple beam theory that is used in CSA O86 provides significantly lower shear capacity predictions than those obtained by the other methods.

Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (Populus deltoides L.)

This study aimed to investigate the effect of layer arrangement on bending properties of CLT panels made from poplar (Populus deltoides L.). A total of 20 three-layer CLT panels with the same dimensions of 1300 × 360 × 48 mm3 (Length, Width, Thickness) were fabricated in five configurations: 0/30/0, 0/45/0, 0/90/0, 45/0/45, and 45/45/45. The apparent modulus of elasticity (MOEapp), modulus of rupture (MOR) and apparent bending stiffness (EIapp) values in major and minor axes of CLT panels were calculated using experimental bending testing. In the major axis, the highest values of MOR, MOEapp, and EIapp were obtained from the 0/30/0 arrangement, while the least values resulted from the arrangements of 90/60/90 and 90/45/90 in the minor axis. Besides, in all arrangements, the average of the experimental apparent bending stiffness values (EIapp,exp) of specimens was higher than that of the shear analogy apparent bending stiffness values (EIapp,shear). The bending and shear stress distribution values over the cross section of samples were also estimated using the finite element method. Moreover, the numerical apparent bending stiffness (EIapp,fem) values of samples were compared to experimental apparent bending stiffness (EIapp,exp) values. Based on experimental and finite element method results, in all groups of layer arrangements, the EIapp,fem values concurred well with the EIapp,exp values.

Glued timber concrete composite walls using ultra-high-performance concrete

This paper gives a short introduction of the development of cross laminated timber (CLT) concrete composite walls with a glued connection. In the composite walls, prefabricated ultra-high-performance concrete (UHPC) lamellas replace timber lamellas at the core layer of the CLT elements. To check the feasibility of gluing timber to UHPC small-scale shear, delamination and bonding tests were performed and showed promising results. The load bearing behaviour was analysed with centrically and eccentrically loaded tests on wall segments. Analytic modelling of the wall experiments using an effective bending stiffness, based on shear analogy method, showed a good correlation to the experimental results.

Comparative Study on Various Strength Parameters of Structural Elements Made from Cross-Laminated Timber

Cross laminated timber (CLT) is an innovative and environment friendly engineered timber product with superior structural performance. CLT offers strong resistance against both in-plane and out-of-plane loading. Hence, it is widely used as floors, roofs or wall elements. Considerable experimental research on CLT under various loading conditions has been done in the recent past. This article presents a comprehensive review of various design methods to determine basic mechanical properties such as tension, compression and rolling shear strength of CLT with primary focus on Norway spruce. All relevant experimental data available from existing literature were collated and consequently been used to evaluate the performance of various methods to design CLT structures. The comparison revealed that different methods show considerable variance in predicting the capacity of CLT panels due to the variation in timber species, which affects the corresponding mechanical properties of the lamella. In addition to species, rolling shear properties can also vary considerably depending on the type of experimental technique used for testing. A predictive model has also been proposed to correlate rolling shear strength obtained from shear analogy method to that obtained using planar shear.

CLT beam analysis using classical elastic theory of layered beams

The classical elastic theory of layered beams is used for the analysis of cross laminated timber (CLT) beams. A brief introduction of the theory is given and followed by examples. The theory of layered beams offers a widely studied, well established method for the analysis the CLT beams including displacements and stresses of each layer of the beam. It is shown that the theoretical basis of the widely used Shear Analogy is the same as the theoretical basis of the theory of layered beams. The results are compared to test results and to results of the finite element calculations. It is seen that the deflections and strains are in 10 % fractals in mean in the considered cases. The theory of layered beams seems to be suitable method in the analysis of the CLT beams at the elastic phase.

Bending and shear performance of cross-laminated timber and glued-laminated timber beams: A comparative investigation

In mass timber construction, cross-laminated timber (CLT) and glued-laminated timber (GLT) usually build a load-bearing system together. Exploring the mechanical properties of CLT and GLT can provide a better understanding and inspiration for designing their members. This study presents a comparative study on the bending and shear characteristics of CLT and GLT beams under the out-of-plane and in-plane loading forms. A series of mechanical properties parameters in the major strength direction were obtained through the tests, and the bending properties were compared with theoretical results. A contribution rate model was developed to quantify the effects of the bending stiffness relationship between adjacent layers in the major strength direction. Under same loading forms, the CLT presented lower bending and shear properties in the major strength direction than the GLT, mainly due to the orthogonal structure inside the CLT. The shear analogy theory showed higher accuracy in the out-of-plane bending results, and the calculation theory that considered all layers could better predict the in-plane bending results. Furthermore, the proposed contribution rate model was consistent with the test results, and it intuitively revealed the effect of the layer stiffness on the overall stiffness for bending specimens under two loading forms.

COMPARATIVE ANALYSIS OF THE TYMOSHENKO METHOD AND THE Γ-METHOD FOR CALCULATION OF CLT PANELS STRENGTH BY BENDING.

The γ-method and the Timoshenko method are most often used for calculation the bending strength of CLT panels, the latter of which takes into account the transverse shear deformations of the transverse layers of boards, which are due to the significant difference between the modulus of elasticity and the shear modulus apply the method of Timoshenko's beams. The γ-method treats the CLT panel as a beam on flexible joints, similar to the Derevyagin system beam on plate dowels or Kubler cubes, where the transverse layers of the boards are considered as flexible joints and are not taken into account when calculating the geometric characteristics of cross sections of CLT panels. Taking into account the amount of shear for each type of panels, depending on the configuration of the cross-sectional components, is performed by introducing shear correction factors, which in turn depend on the thickness of the CLT panel layers and their distance from the center of gravity of the panel. The γ-method, like Timoshenko's method, is used in engineering practice more often than the shear analogy method. Each technique has its advantages and disadvantages, as it has a number of specific assumptions to simplify the calculations. This paper highlights the advantages and disadvantages of the γ-method and the Timoshenko method, which are the most common and are contained in many technical opinions of various manufacturers of CLT panels.

Experimental study on bending properties of cross-laminated timber-bamboo composites

Using bamboo and timber to manufacture cross-laminated timber-bamboo (CLTB) composites could utilize the advantages of two material to improve the mechanical properties and expand the raw material source of cross-laminated timber (CLT). To explore the feasibility of using engineered bamboo as CLT lamination, the rolling shear properties of two bamboo scrimbers and one bamboo plywood were evaluated. Two types of CLTB specimens, using bamboo scrimber as transverse layer or as both transverse layer and the outermost longitudinal layer, were developed in this study. The bending properties of CLTB and generic Spruce-pine-fir (SPF) CLT specimens were evaluated by dynamic tests and third-point bending tests, respectively. The shear analogy method was employed to calculate the apparent bending stiffness of CLT/CLTB specimen. The results indicated that the rolling shear modulus and strength of bamboo scrimber (group RB(F)-4.5) were 92.81% and 98.64% higher than those of bamboo plywood, respectively, and were 330.19% and 121.13% higher than those of SPF dimension lumber, respectively. The CLTB specimens, group BWBWB, had 23.69% and 60.50% higher apparent bending modulus and peak load than those of generic SPF CLT specimens. Most of the CLTB bending specimens had main failure mode of tensile failure in the bottom layer which replaced rolling shear failure in transverse bamboo scrimber layer. The apparent bending stiffness values of CLT/CLTB specimens obtained from dynamic test and shear analogy method were in good agreement with the static experimental values. The results presented in this paper can provide fundamental basis for supporting the potential engineering application of CLT panel products fabricated with bamboo scrimber.

Shear strength properties of hybrid (hinoki cypress and Japanese cedar) cross-laminated timber

In this study, the out-of-plane shear strength of hybrid cross-laminated timber (CLT) with outer layers of hinoki (hinoki cypress, Chamaecyparis obtusa) and inner layers of sugi (Japanese cedar, Cryptomeria japonica) is investigated for four different layer configurations. To investigate the influence from rolling shear properties of cross layers on the shear strength of CLT, stress analysis was conducted using the shear analogy method. The nominal shear strength, the maximum shear force divided by the cross-section of CLT, was in the 1.0–2.1 MPa range. Using the shear analogy method, the rolling shear modulus in the cross layer was determined as 72.9 MPa, which was comparable with the value obtained for laminae in previous study as well as the value confirmed by strain measurements in the present study. The magnitude of rolling shear stress in the cross layer was 0.9–1.1 times the average shear stress, which was negatively correlated with the nominal shear strength. From the regression line between the nominal shear strength and the magnitude of the shear stress in the cross layer, the mean shear strength of the cross layer was estimated to be 1.33 MPa.

Characterizing engineering performance of bamboo-wood composite cross-laminated timber made from bamboo mat-curtain panel and hem-fir lumber

During the global industrialization process of manufacturing cross-laminated timber (CLT), attempts have been made to use local wood species. For areas rich in bamboo resources but relatively short in timber resources, the use of bamboo- and wood-based composites to manufacture composite CLT (CCLT) has great potential. In the present work, two new types of 3-ply CCLT panel structures constituting bamboo mat-curtain panel and hem-fir lumber were investigated. In the major and minor strength directions, flatwise bending and shear tests were conducted to investigate their failure modes, maximum bending moment, bending stiffness, modulus of elasticity (MOE), bending strength, interlaminar shear strength, and specific bending and shear performance. Moreover, 3-ply hem-fir glued-laminated timber and CLT were used as controls. The effective MOE of each panel structure was calculated according to shear analogy theory and modified gamma theory and then was compared to the measured MOE. Based on the shear analogy theory, the effect of the thickness of layers on the MOE of the panels was investigated. Results showed that unlike other types of CCLT, the new CCLT exhibited distinct plate-like orthogonal strength characteristics. Its theoretical MOE agreed well with the measured MOE as the accuracy changed with the panel structure. By changing the panel structure of the new CCLT, if the MOE of one strength direction was reduced, the MOE in the other strength direction could increase accordingly based on the layer characteristics. The results presented in this paper can provide a guidance for future design and optimization of bamboo-wood CCLT.