Increase In Bending Stiffness Research Articles

Comparison of Bending Stiffness between String of Pearls Plate-Bone Substitute Constructs with and without Bending Tees in a Fracture Gap Model

Abstract Objective The aim of this study was to compare the bending properties of String of Pearls plate-bone substitute constructs with and without bending tees in the nodes over a simulated fracture gap. It is hypothesized that the constructs with tees will have higher bending stiffness. Study Design Acetal polymer tubes and 12-hole, 3.5-mm String of Pearls plates were used to create plate-bone substitute constructs simulating stabilization in a bridging fashion over a 45-mm gap. Twenty-four constructs were made with 12 containing tees in the nodes over the fracture gap. Single-cycle load-to-failure 4-point bending was performed in mediolateral and craniocaudal planes. Bending stiffness was compared with a t-test (p < 0.05). Results All plate-bone substitute constructs had a permanent loss of structural integrity via plastic deformation of the plate. The bending stiffness (mean ± standard deviation) of the craniocaudal group was 59.11 ± 1.98 N/mm with tees and 59.25 ± 1.69 N/mm without tees (p = 0.88). In the mediolateral group, the bending stiffness was 43.17 ± 0.75 N/mm with tees and 41.09 ± 0.91 N/mm without tees (p = 0.0042). Conclusion In 4-point bending, the plate-bone substitute constructs with tees had equivalent bending stiffness in the craniocaudal plane and increased bending stiffness in the mediolateral plane. However, with a small absolute difference in values, the clinical significance is unclear. Future studies for cyclic bending, torsional, and axial compression tests should be performed to further investigate the value of tees in the nodes over a comminuted or gap fracture repaired in a bridging fashion.

Nonlinear dynamics of a flexible rod partially sliding in a rigid sleeve under the action of gravity and configurational force

We investigate various methods of analyzing systems with moving boundaries, using as an example a flexible rod sliding in an ideal frictionless sleeve in the field of gravity. Special attention is paid to the configurational force acting on the rod at the sleeve opening and thus determining the rod’s dynamics. The non-material kinematic description used in simulations is based on the re-parametrization of the Lagrangian arc length coordinate. The variational formulation uses the energy expressions written for the entire rod, comprising the free segment and the one inside the sleeve. A novel finite element scheme is efficient for highly flexible rods, which may undergo complete ejection. A simplified two degrees of freedom model, which accelerates simulations, shows a good agreement as the bending stiffness increases. An analytical study using Hamiltonian mechanics exploits the separation of variables into fast oscillations and slow axial motion. The adiabatic invariant approach leads to approximate closed-form solutions for the slow dynamics and yields the maximum injection depth of the rod into the sleeve.

The Effect of Carbon Nanofibers on the Mechanical Performance of Epoxy-Based Composites: A Review.

This review is a fundamental tool for researchers and engineers involved in the design and optimization of fiber-reinforced composite materials. The aim is to provide a comprehensive analysis of the mechanical performance of composites with epoxy matrices reinforced with carbon nanofibers (CNFs). The review includes studies investigating the static mechanical response through three-point bending (3PB) tests, tensile tests, and viscoelastic behavior tests. In addition, the properties of the composites' resistance to interlaminar shear strength (ILSS), mode I and mode II interlaminar fracture toughness (ILFT), and low-velocity impact (LVI) are analyzed. The incorporation of small amounts of CNFs, mostly between 0.25 and 1% by weight was shown to have a notable impact on the static and viscoelastic properties of the composites, leading to greater resistance to time-dependent deformation and better resistance to creep. ILSS and ILFT modes I and II of fiber-reinforced composites are critical parameters in assessing structural integrity through interfacial bonding and were positively affected by the introduction of CNFs. The response of composites to LVI demonstrates the potential of CNFs to increase impact strength by reducing the energy absorbed and the size of the damage introduced. Epoxy matrices reinforced with CNFs showed an average increase in stiffness of 15% and 20% for bending and tensile, respectively. The laminates, on the other hand, showed an increase in bending stiffness of 20% and 15% for tensile and modulus, respectively. In the case of ILSS and ILFT modes I and II, the addition of CNFs promoted average increases in the order of 50%, 100%, and 50%, respectively.

Bending performance of laminated veneer lumber timber beams strengthened in the compression side with near-surface mounted CFRP plates

This study investigated the bending behavior of timber beams that were strengthened using carbon fiber-reinforced polymer (CFRP) plates. Fourteen laminated veneer lumber (LVL) timber beams, each measuring 60 mm×200 mm x 2400 mm, were subjected to four-point bending tests. The objective was to investigate the effect of using CFRP plates as near-surface mounted (NSM) strengthening in the compression zone on the bending behavior of the LVL timber beams. In this experiment, two beams were left unstrengthened while the remaining beams were strengthened with varying lengths, depths and numbers of CFRP plates. The beams load-midspan deflection relationship, ultimate load capacity, stiffness, failure mode, and strain profile distribution were analysed based on experimental results. The use of CFRP plates in the compression zone of LVL beams has been found to improve their strength and stiffness. The test result showed timber beams strengthened with CFRP plates with a reinforcement ratio ranging from 1.67 % to 5.00 % experienced a significant increase in bending strength of 4.24–28.85 % and an increase in bending stiffness of 16.48–62.51 %. These results indicate that NSM CFRP plates can effectively strengthen timber materials, offering improved bending performance and durability.

Effect of increased shoe longitudinal bending stiffness on ankle and foot biomechanics in jump-cut movements of low and high degrees

Lateral ankle sprains are the most common injuries in indoor and court sports, with ankle inversion being a primary injury driver. Stabilising the ankle during multidirectional changes is crucial for injury prevention. Conversely, increased shoe stiffness has been hypothesised to influence the magnitude of ankle inversion and may raise the risk for ankle injuries. Therefore, the purpose of this study was to investigate the influence of shoe longitudinal bending stiffness on ankle biomechanics during indoor and court sport-specific cutting movements. Biomechanical data from 19 participants were collected using a motion capture system and force plate. A jump-cut protocol with two different cutting directions after landing was performed in indoor shoes with and without carbon plate inserts of varying stiffness. Ankle kinematics and kinetics were analysed with statistical parametric mapping and repeated measures analysis of variance. A significant increase in ankle inversion during the 180° cut and a reduction in forefoot inversion (foot torsion) for stiffer footwear conditions during both the 45° and 180° cut were observed. While dorsiflexion moments differed during the last 10% of ground contact, ankle inversion moments did not significantly diverge between shoe conditions. Furthermore, a noteworthy correlation between footwear longitudinal bending stiffness and torsional stiffness was identified. In conclusion, increased bending stiffness significantly affected ankle and foot kinematics. The ankle compensated for restricted mobility and higher demands during high-degree jump-cuts, while foot torsion played a more prominent role in low-degree cuts. The heightened ankle inversion during high-degree cuts may induce an elevated risk for lateral ankle sprains. Further longitudinal studies are necessary to comprehensively understand injury incidence and the role of shoe stiffness in injury prevention.

Construction of Reconfigurable and Polymorphic DNA Origami Assemblies with Coiled-Coil Patches and Patterns.

DNA origami nanodevices achieve programmable structure and tunable mechanical and dynamic properties by leveraging the sequence-specific interactions of nucleic acids. Previous advances have also established DNA origami as a useful building block to make well-defined micron-scale structures through hierarchical self-assembly, but these efforts have largely leveraged the structural features of DNA origami. The tunable dynamic and mechanical properties also provide an opportunity to make assemblies with adaptive structures and properties. Here the integration of DNA origami hinge nanodevices and coiled-coil peptides are reported into hybrid reconfigurable assemblies. With the same dynamic device and peptide interaction, it is made multiple higher-order assemblies (i.e., polymorphic assembly) by organizing clusters of peptides into patches or arranging single peptides into patterns on the surfaces of DNA origami to control the relative orientation of devices. The coiled-coil interactions are used to construct circular and linear assemblies whose structure and mechanical properties can be modulated with DNA-based reconfiguration. Reconfiguration of linear assemblies leads to micron scale motions and ≈2.5-10-fold increase in bending stiffness. The results provide a foundation for stimulus-responsive hybrid assemblies that can adapt their structure and properties in response to nucleic acid, peptide, protein, or other triggers.

Mitigation of Railway-Induced Ground Vibration by Soft Support Elements and a Higher Bending Stiffness of the Track

The mitigation of train-induced ground vibrations by track solutions is investigated by calculations and measurements. The calculation by a wavenumber domain method includes the correct vehicle–track interaction and the correct track–soil interaction. Some theoretical results for elastic elements and an increased bending stiffness of the track are presented where the force transfer of the track and the vehicle–track interaction are calculated for the high-frequency dynamic mitigation, and the force distribution along the track is calculated for the low-frequency mitigation which is due to the smoother impulses from the passing static loads. Measurement results for the ground vibration near isolated and un-isolated tracks are given for several under-sleeper pads, for under-ballast mats, and for several under-ballast plates and ballast troughs. The elastic elements yield a resonance frequency of the vehicle–track–soil system and a high-frequency reduction of the dynamic axle loads which depends mainly on the softness of the pads or mats and which can be improved by a higher sleeper mass. In addition, all troughs and most of the soft elements show a low-frequency reduction which is attributed to the scattered impulses of the static axle loads. Besides this main contribution of the article, the problem of a soft reference section on a different soil is discussed and recommendations for better ground vibration measurements of mitigation effects are given.

Enhancing heat transfer in laminar channel flow by tuning the mass distribution of a flexible reed

Recent studies have leveraged wall-mounted flexible reeds to augment heat transfer efficiency in channel flows. In this study, we demonstrate that tuning the reed's mass distribution can substantially elevate this heat transfer enhancement. Numerical simulations incorporating the fluid–structure–thermal interaction are performed to investigate the impact of mass distribution on the reed dynamics and the associated heat transfer augmentation. The results indicate that the mass distribution of the reed significantly affects its motion mode, which, in turn, critically modulates the heat transfer characteristics. The maximum thermal efficiency factor is obtained when the reed's mass is concentrated at its distal end. Furthermore, the enhancement effect of tuning reed's mass distribution on heat transfer efficiency is closely related to the bending stiffness γ. Within the range of bending stiffness considered in this study (0.02–0.14), the effect of tuning the reed's mass distribution on the thermal efficiency factor exhibits a trend of increase–decrease–increase as the bending stiffness increases. At high bending stiffness, simply tuning the reed's mass distribution can increase the channel heat flux and reduce energy loss, thereby achieving the goal of enhancing the thermal efficiency factor. At γ = 0.14, allocating the reed's mass at its distal end resulted in a notable enhancement, with a thermal efficiency factor surge of 11.1%.

Cilostazol Stimulates Angiogenesis and Accelerates Fracture Healing in Aged Male and Female Mice by Increasing the Expression of PI3K and RUNX2.

Fracture healing in the aged is associated with a reduced healing capacity, which often results in delayed healing or non-union formation. Many factors may contribute to this deterioration of bone regeneration, including a reduced 'angiogenic trauma response'. The phosphodiesterase-3 (PDE-3) inhibitor cilostazol has been shown to exert pro-angiogenic and pro-osteogenic effects in preclinical studies. Therefore, we herein analyzed in a stable closed femoral fracture model whether this compound also promotes fracture healing in aged mice. Forty-two aged CD-1 mice (age: 16-18 months) were daily treated with 30 mg/kg body weight cilostazol (n = 21) or vehicle (control, n = 21) by oral gavage. At 2 and 5 weeks after fracture, the femora were analyzed by X-ray, biomechanics, micro-computed tomography (µCT), histology, immunohistochemistry, and Western blotting. These analyses revealed a significantly increased bending stiffness at 2 weeks (2.2 ± 0.4 vs. 4.3 ± 0.7 N/mm) and an enhanced bone formation at 5 weeks (4.4 ± 0.7 vs. 9.1 ± 0.7 mm3) in cilostazol-treated mice when compared to controls. This was associated with a higher number of newly formed CD31-positive microvessels (3.3 ± 0.9 vs. 5.5 ± 0.7 microvessels/HPF) as well as an elevated expression of phosphoinositide-3-kinase (PI3K) (3.6 ± 0.8 vs. 17.4 ± 5.5-pixel intensity × 104) and runt-related transcription factor (RUNX)2 (6.4 ± 1.2 vs. 18.2 ± 2.7-pixel intensity × 104) within the callus tissue. These findings indicate that cilostazol accelerates fracture healing in aged mice by stimulating angiogenesis and the expression of PI3K and RUNX2. Hence, cilostazol may represent a promising compound to promote bone regeneration in geriatric patients.

Enhancing bending performance in 3D woven spacer composites with lightweight biomimetic integrated double‐spacer structure

AbstractThree‐dimensional woven spacer composites (3DWSCs) with lightweight and excellent mechanical properties have promising application in communication, transportation, aerospace and other fields. However, traditional single‐layer 3DWSCs exhibit insufficient strength, especially when dealing with high thickness, as the pile yarns tend to buckle. In this study, inspired by the structural features of the Thalia dealbata, 3D woven integrated double‐layer glass fiber/epoxy resin spacer composites by mimicking were fabricated. Innovative integrated double‐layer structure design effectively improves the performance and failure mode of 3DWSCs under bending loads. Compared to single‐layer 3DWSCs, the resulting double‐layer 3DWSCs exhibited a 41.79% increase in peak bending load, a 46.85% increase in bending stiffness, and a 99.38% increase in energy absorption. In addition, the double‐layer 3DWSCs showed a low density of 0.52–0.55 g/cm3. This work introduces bioinspired double‐layer 3DWSCs with characteristics of lightweight and superior bending performance, potentially offering novel ideas for the design of high‐performance composites.Highlights Inspired by the structural features of the Thalia dealbata, a 3D integrated woven double‐layer glass fiber/epoxy resin spacer composites by mimicking were fabricated. 3D woven double‐layer spacer composites are lightweight (0.52–0.55 g/cm3) and can effectively improve the bending properties of single‐layer structures. Based on the analysis of the fracture morphology, the significant improvement of the fracture pattern of the single‐layer structure by the double‐layer structure is effectively demonstrated. This study introduces novel design strategies for multi‐layer lightweight composite materials and holds broad applications.

Numerical, Theoretical, and Experimental Analysis of LVL-CFRP Sandwich Structure.

Optimization of structural elements via composition of different components is a significant scientific and practical point-of-view problem aimed at obtaining more economical and environmentally friendly solutions. This paper presents the results of a static work analysis of small-size laminated veneer lumber (LVL) beams reinforced by a Carbon Fiber Reinforced Polymer (CFRP) sheet. The nominal dimensions of LVL beams were 45 × 45 × 850 mm, and 0.333- and 0.666-mm thick reinforcement layers were used. The reinforcement was applied on opposite sides of the cross section obtaining a sandwich-type structure. An epoxy resin was used as a bonding layer. The bending tests were conducted in the so-called four-point bending static scheme in edgewise and flatwise conditions. The results of experimental tests confirmed the validity of this combination of materials. The highest load-bearing capacity was obtained for configuration, where CFRP sheets with a thickness of 0.666 mm were placed on the sides of the core, parallel to the direction of loading and the veneer's grain in the core. The increase in this case was up to a maximum of 57% compared to the core alone. The highest bending stiffness increase, 182% compared to the core alone, involves placing two layers of sheets perpendicular to the direction of loading, i.e., on the upper and lower surfaces. The presented novel sandwich structure can be competitive against traditional steel and reinforced concrete elements in civil engineering and can be utilized as beams or slabs.

Parathyroid hormone stimulates bone regeneration in an atrophic non-union model in aged mice

BackgroundNon-union formation still represents a major burden in trauma and orthopedic surgery. Moreover, aged patients are at an increased risk for bone healing failure. Parathyroid hormone (PTH) has been shown to accelerate fracture healing in young adult animals. However, there is no information whether PTH also stimulates bone regeneration in atrophic non-unions in the aged. Therefore, the aim of the present study was to analyze the effect of PTH on bone regeneration in an atrophic non-union model in aged CD-1 mice.MethodsAfter creation of a 1.8 mm segmental defect, mice femora were stabilized by pin-clip fixation. The animals were treated daily with either 200 mg/kg body weight PTH 1–34 (n = 17) or saline (control; n = 17) subcutaneously. Bone regeneration was analyzed by means of X-ray, biomechanics, micro-computed tomography (µCT) imaging as well as histological, immunohistochemical and Western blot analyses.ResultsIn PTH-treated animals bone formation was markedly improved when compared to controls. This was associated with an increased bending stiffness as well as a higher number of tartrate-resistant acid phosphatase (TRAP)-positive osteoclasts and CD31-positive microvessels within the callus tissue. Furthermore, PTH-treated aged animals showed a decreased inflammatory response, characterized by a lower number of MPO-positive granulocytes and CD68-positive macrophages within the bone defects when compared to controls. Additional Western blot analyses demonstrated a significantly higher expression of cyclooxygenase (COX)-2 and phosphoinositide 3-kinase (PI3K) in PTH-treated mice.ConclusionTaken together, these findings indicate that PTH is an effective pharmacological compound for the treatment of non-union formation in aged animals.

Study of the Tensile and Bending Stiffness Behavior of Antistatic and Antibacterial Knitted Fabrics

Abstract The influence of fabric treatments, fabric structure and yarn composition on the strength, elasticity and bending stiffness behavior of developed antistatic knitted fabrics was investigated for daily wear clothing. 1×1 rib knit fabrics showed higher elongation and strength than half-Milano rib knit fabrics, with high elongation in the wale direction of the fabrics. An increase in antistatic polyester content causes an increase in the tensile strength of the fabrics. Fabric treatments were found to be highly influential with respect to the properties of the knitted fabrics developed. Dyed and softened fabrics showed lower stiffness, while the antibacterial finished group showed increased bending stiffness.

Simulation and Experiment Analysis of Driveshaft

A driveshaft is a small spring coil less than 1mm in diameter, composed of several stainless-steel wire filaments. In intervention, the driveshaft is used to transmit force and motion to the inside body through the existing micro channels (such as arteries, veins, and gastrointestinal tract). The performance of the driveshaft determines the efficiency, stability, and accuracy of force and motion transitions, the ability to pass through tortuous microchannels, and the damage to healthy tissues. To determine the influence of fabrication parameters (filament, wire diameter, and outer diameter) on the mechanical properties (such as bending stiffness and natural frequency) of the driveshaft, a simulation was established in ABAQUS to calculate the deformation displacement under 0.0098N and first-order natural frequency. Then, the bending stiffness is calculated. The results show that the bending stiffness and the first-order natural frequency of the driveshaft increase with the increase of the filament number and wire diameter, and with the outer diameter of the driveshaft increases, the bending stiffness increases, while the first-order natural frequency decreases. Finally, the simulation model is verified by measuring the deformation displacement in the experiment. This study provides a methodology for designing and selecting the driveshaft in Interventional therapy.

Simulating performance of tow reinforced hybrid-molded composites

A critical milestone to the adoption of 3D tow reinforced hybrid-molded structures is the development of design guidelines and analysis techniques for accurate performance modelling. The cross-sectional dimensions of the tow bundle leads to fiber length discrepancies between the inner fibers and the outer fibers which manifest as tow spreading and local fiber waviness. The effects of simulating the resulting fiber orientations and effective elastic properties is investigated by modelling a representative beam in tension and bending load cases and comparing to previous experimental results. Accounting for fiber waviness in tension demonstrated greatly improved part stiffness predictions. Spread tow bundles improved predicted strength and stiffness over simulations where tow was constrained to a uniform cross section. Increased tow reinforcement increased bending stiffness, but failure behavior was significantly influenced by the overmolding material.

The structural design and earthquake resistance assessment of composite steel–concrete frame structures with welded dissipative fuses

Mitigation of earthquake damage to buildings is a major task in structural engineering. A reliable reinforced concrete structure with composite joints is crucial to create a high-performance structural system. The paper develops and investigates alternative dissipative systems with welded fuses in reinforced concrete structures, particularly, composite steel–concrete frame structures. This paper discusses the findings of an experiment on the mechanical properties of three types of plate flanges with different geometric parameters and power factors under different cyclic loadings. Sample ductility, dissipation, and durability made it clear that increasing the plate’s cross-sectional area leads to increased bending stiffness coefficient and reduced intensity of stiffness degradation during cyclic loading. The tensile strength is twice the yield in the case of sagging, while these values are very close in the case of hogging. Samples with a high power factor have low dissipative properties, thereby contributing to the rapid wear of non-replaceable parts. Plates with a 10 × 100 mm2 cross-section have a sufficiently high resistance and the ability to dissipate the seismic vibration energy. The findings can be used in the design of residential and industrial buildings with reinforced concrete structures with welded fuses. Further research involves studying the effect of other plate parameters on improving the composite structure’s plastic parameters.

Sensitivity Analysis and Optimisation of Key Parameters for Railway Rigid Overhead System and Pantograph

This paper aims to enhance the speed of rigid overhead systems by investigating the impact of important parameters of the overhead system and pantograph on the interaction performance, specifically the contact force between the panhead of the pantograph and the contact wire of the overhead system. To accomplish this, this paper first builds a rigid overhead system model based on the finite element method. The pantograph–contact wire interaction simulation is achieved by including a three-stage lumped mass pantograph model. The Sobol sensitivity analysis method is utilised to determine the contribution of different parameters to the contact force standard deviation. Subsequently, an optimisation approach is used to minimise the contact standard deviation at various speeds by adopting five crucial parameters. The sensitivity analysis of 13 variables indicates that the span length, bending stiffness, and linear density of the conductor rail, and the masses of the pantograph head and upper frame are the most relevant variables for the contact force standard deviation. The quantification of each parameter’s contribution reveals that the increase in bending stiffness generally has a positive effect in reducing the contact force fluctuation, while the decreases in other variables are preferred. The optimisation analysis shows that the optimised contact force standard deviation decreases by 39.18%, 66.77%, and 61.02% at speeds of 90 km/h, 120 km/h, and 150 km/h, respectively, compared to the original values.

Nonlinear Vibration of Bolted Rotor Bearing System Accounting for the Bending Stiffness Characteristics of the Connection Interface

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark-[Formula: see text] numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system.

Adaptive partitioning of a gene locus to the nuclear envelope in Saccharomyces cerevisiae is driven by polymer-polymer phase separation

Partitioning of active gene loci to the nuclear envelope (NE) is a mechanism by which organisms increase the speed of adaptation and metabolic robustness to fluctuating resources in the environment. In the yeast Saccharomyces cerevisiae, adaptation to nutrient depletion or other stresses, manifests as relocalization of active gene loci from nucleoplasm to the NE, resulting in more efficient transport and translation of mRNA. The mechanism by which this partitioning occurs remains a mystery. Here, we demonstrate that the yeast inositol depletion-responsive gene locus INO1 partitions to the nuclear envelope, driven by local histone acetylation-induced polymer-polymer phase separation from the nucleoplasmic phase. This demixing is consistent with recent evidence for chromatin phase separation by acetylation-mediated dissolution of multivalent histone association and fits a physical model where increased bending stiffness of acetylated chromatin polymer causes its phase separation from de-acetylated chromatin. Increased chromatin spring stiffness could explain nucleation of transcriptional machinery at active gene loci.

Analytical solutions and optimization design for bending behavior of cross-laminated timber beams considering orthotropy and interface slip

The aim of this work was to propose analytical solutions and an optimization design method for the bending behavior of cross-laminated timber (CLT) beam, in which the orthotropy of timber and interface slip between the neighboring layers were considered simultaneously. The lamina layers of orthotropic woods were modeled based on the two-dimensional (2D) elasticity theory without transverse shear deformation assumption. By means of series expansion and solving differential equations, the general solutions for stresses and deformations in the beam were obtained with undetermined coefficients. The unknown coefficients were further determined by the transfer matrix method. The comparison study indicated the proposed solutions had higher accuracy than the Euler-Bernoulli beam solution and isotropic solution, since the proposed solutions renounced the transverse shear deformation assumption and considered the orthotropy of wood. Moreover, it was found that the interfacial stiffness has an economical upper bound above which no significant gain on the bending stiffness of CLT beam can be obtained, and an optimal configuration of geometry and material can achieve an increase of bending stiffness. We release our program for the proposed analytical solutions, at https://github.com/Njtpw/CLT-Beam.git.