Investigation of the appropriate thread depth for bioabsorbable screws.

The relatively low strength of bioabsorbable screws is a critical clinical issue. A shallower thread depth will increase a screw's strength, but the pull-out strength of the screw will decrease proportionally with the thread depth. We sought to provide further clarification of the relationships between (i) the thread depth and the pull-out strength, and (ii) the minor diameter and the shearing and bending strengths in bioabsorbable screws made of uncalcined and unsintered hydroxyapatite particles and poly-L-lactide (u-HA/PLLA). Seven types (thread depth from 0.1-0.7 mm) of screws with a major diameter of 4.5 mm were manufactured. Each screw type's pull-out strength was investigated using simulated bone. A shearing test and three-point bending test were both used to measure the physical strength of the screws. We then analyzed the relationships between the mechanical findings and the thread depth. The relationship between the thread depth and the pull-out strength showed a positive biphasic linear correlation with a boundary at 0.4-mm thread depth. The relationships between the minor diameter and both the shearing and bending strengths showed positive linear correlations within the range of dimensions tested. Within the scope of this study, a 0.4-mm thread depth proved to be an appropriate value that provides sufficient pull-out strength and screw strength for u-HA/PLLA screws with a 4.5-mm major diameter.

Generalisation of the yield stress measurement in three point bending collapse tests: application to 3D printed flax fibre reinforced hydrogels.

This paper describes the extrusion pressure's effect on composite hydrogel inks' filaments subjected to collapse tests. The composite considered in this work consists of an alginate-poloxamer hydrogel reinforced with flax fibres. Increased extrusion pressure resulted in more asymmetrical filaments between the support pillars. Furthermore, the material and printing conditions used in the present study led to the production of curved specimens. These two characteristics implicitly limit the validity of the yield stress equations commonly used in open literature. Therefore, a new system of equations was derived for the case of asymmetrical and curved filaments. A post-processing method was also created to obtain the properties required to evaluate this yield stress. This new equation was then implemented to identify the strength of failed hydrogels without flax fibre reinforcement. A statistical analysis showed this new equation's significance, which yielded statistically higher (i.e., 1.15 times larger) strength values compared to the numbers obtained with the open literature equations. At larger extrusion pressures, longer periods were needed for the material to converge towards its final shape. Larger extrusion pressure values led to lower yield stresses within the composite hydrogel filament: a 5 kPa increase in extrusion pressure lowered the yield stress by 19 %. In comparison, a 15 kPa increase led to a 29 % decrease in the yield stress. Overall this study provides guidelines to standardize collapse tests and analysis comparison between different materials.

Self-Adhesive Electronic Skin with Bio-Inspired 3D Architecture for Mechanical Stimuli Monitoring and Human-Machine Interactions.

Recent development of wearable devices is revolutionizing the way of artificial electronic skins (E-skin), physiological health monitoring and human-machine interactions (HMI). However, challenge remains to fit flexible electronic devices to the human skin with conformal deformation and identifiable electrical feedback according to the mechanical stimuli. Herein, an adhesive E-skin is developed that can firmly attach on the human skin for mechanical stimuli perception. The laser-induced adhesive layer serves as the essential component to ensure the conformal attachment of E-skin on curved surface, which ensures the accurate conversion from mechanical deformation to precise electrical readouts. Especially, the 3D architecture facilitates the non-overlapping outputs that bi-directional joint bending and distinguishes strain/pressure. The optimized E-skin with bio-inspired micro-cilia exhibited significantly improved sensing performances with sensitivity of 0.652 kPa-1 in 0-4 kPa and gauge factor of 8.13 for strain (0-15%) with robustness. Furthermore, the adhesive E-skin can distinguish inward/outward joint bending in non-overlapping behaviors, allowing the establishment of ternary system to expand communication capacity for logic outputs such as effective Morse code and intelligent control. It expects that the adhesive E-skin can serve as a functional bridge between human and electrical terminals for applications from daily mechanical monitoring to efficient HMI.

Substrate heterogeneities cause root growth trajectories to switch from vertical to oblique.

Hard pans, soil compaction, soil aggregation and stones create physical barriers that can affect the development of a root system. Roots are known to exploit paths of least resistance to avoid such obstacles, but the mechanism through which this is achieved is not well understood. Here, we combined 3D-printed substrates with a high-throughput live imaging platform to study the responses of plant roots to a range of physical barriers. Using image analysis algorithms, we determined the properties of growth trajectories and identified how the presence of rigid circular obstacles affects the ability of a primary root to maintain its vertical trajectory. Results showed the types of growth responses were limited, both vertical and oblique trajectories were found to be stable and influenced by the size of the obstacles. When obstacles were of intermediate sizes, trajectories were unstable and changed in nature through time. We formalised the conditions for root trajectory to change from vertical to oblique, linking the angle at which the root detaches from the obstacle to the root curvature due to gravitropism. Exploitation of paths of least resistance by a root may therefore be constrained by the ability of the root to curve and respond to gravitropic signals.

Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory.

Static bending responses of a pressurized composite cylindrical shell made of a copper matrix reinforced with functionally graded graphene origami are studied in this paper. The kinematic relations are extended based on a new higher-order shear and normal deformation theory in the axisymmetric framework. The constitutive relations are extended for the composite cylindrical shell where the effective modulus of elasticity, Poisson's ratio, thermal expansion coefficient and density are estimated using the Halpin-Tsai micromechanical model and the rule of mixture. Some modified coefficients are employed for correction of the mentioned material properties in terms of the volume fraction and the folding degree of graphene origami, characteristics of copper and graphene nanoplatelets and thermal loads. The principle of virtual work is used to derive governing equations through computation of strain energy and external work. The static bending results including radial and axial displacements, circumferential strain and stress are presented along the longitudinal and radial directions in terms of volume fraction, folding degree and distribution of graphene origami. The results show an increase in radial displacement and circumferential strain with an increase in folding degree and a decrease in volume fraction of graphene origami. The main novelty of this work is investigating the effect of foldability parameter and various distribution of graphene origami on static results of short cylindrical shell.

Small organic osmolytes accelerate actin filament assembly and stiffen filaments.

Actin filament assembly and mechanics are crucial for maintenance of cell structure, motility, and division. Actin filament assembly occurs in a crowded intracellular environment consisting of various types of molecules, including small organic molecules known as osmolytes. Ample evidence highlights the protective functions of osmolytes such as trimethylamine-N-oxide (TMAO), including their effects on protein stability and their ability to counteract cellular osmotic stress. Yet, how TMAO affects individual actin filament assembly dynamics and mechanics is not well understood. We hypothesize that, owing to its protective nature, TMAO will enhance filament dynamics and stiffen actin filaments due to increased stability. In this study, we investigate osmolyte-dependent actin filament assembly and bending mechanics by measuring filament elongation rates, steady-state filament lengths, and bending persistence lengths in the presence of TMAO using total internal reflection fluorescence microscopy and pyrene assays. Our results demonstrate that TMAO increases filament elongation rates as well as steady-state average filament lengths, and enhances filament bending stiffness. Together, these results will help us understand how small organic osmolytes modulate cytoskeletal protein assembly and mechanics in living cells.

Automated detection and mapping of crystal tilt using thermal diffuse scattering in transmission electron microscopy.

Quantitative interpretation of transmission electron microscopy (TEM) data of crystalline specimens often requires the accurate knowledge of the local crystal orientation. A method is presented which exploits momentum-resolved scanning TEM (STEM) data to determine the local mistilt from a major zone axis. It is based on a geometric analysis of Kikuchi bands within a single diffraction pattern, yielding the center of the Laue circle. Whereas the approach is not limited to convergent illumination, it is here developed using unit-cell averaged diffraction patterns corresponding to high-resolution STEM settings. In simulation studies, an accuracy of approximately 0.1 mrad is found. The method is implemented in automated software and applied to crystallographic tilt and in-plane rotation mapping in two experimental cases. In particular, orientation maps of high-Mn steel and an epitaxially grown La0.7Sr0.3MnO3-SrTiO3 interface are presented. The results confirm the estimates of the simulation study and indicate that tilt mapping can be performed consistently over a wide field of view with diameters well above 100 nm at unit cell real space sampling.

Optimizing Building Rehabilitation through Nondestructive Evaluation of Fire-Damaged Steel-Fiber-Reinforced Concrete.

Fire incidents pose significant threats to the structural integrity of reinforced concrete buildings, often necessitating comprehensive rehabilitation to restore safety and functionality. Effective rehabilitation of fire-damaged structures relies heavily on accurate damage assessment, which can be challenging with traditional invasive methods. This paper explores the impact of severe damage due to fire exposure on the mechanical behavior of steel-fiber-reinforced concrete (SFRC) using nondestructive evaluation (NDE) techniques. After being exposed to direct fire, the SFRC specimens are subjected to fracture testing to assess their mechanical properties. NDE techniques, specifically acoustic emission (AE) and ultrasonic pulse velocity (UPV), are employed to assess fire-induced damage. The primary aim of this study is to reveal that AE parameters-such as amplitude, cumulative hits, and energy-are strongly correlated with mechanical properties and damage of SFRC due to fire. Additionally, AE monitoring is employed to assess structural integrity throughout the loading application. The distribution of AE hits and the changes in specific AE parameters throughout the loading can serve as valuable indicators for differentiating between healthy and thermally damaged concrete. Compared to the well-established relationship between UPV and strength in bending and compression, the sensitivity of AE to fracture events shows its potential for in situ application, providing new characterization capabilities for evaluating the post-fire mechanical performance of SFRC. The test results of this study reveal the ability of the examined NDE methods to establish the optimum rehabilitation procedure to restore the capacity of the fire-damaged SFRC structural members.

Influence of Test Method on the Determination of Tensile Strength Perpendicular to Grain of Timber for Civil Construction.

Tensile perpendicular to grain is an important mechanical property in the design of joints in timber structures. However, according to the standards, this strength can be determined using at least two different methods: uniaxial tensile and three-point static bending. In this context, the present paper aims to investigate the influence of these test methods on the determination of tensile strength perpendicular to grain of wood used in civil construction timber. Three wood species from Brazilian planted forests (Pinus spp., Eucalyptus saligna, and Corymbia citriodora) were used in this investigation. Twelve specimens of each species were used for each test method investigated. Moreover, a statistical analysis was performed to propose an adjustment to the equation of the Code of International Organization for Standardization 13910:2014 for the three-point bending test. Tensile strength values perpendicular to grain obtained from the uniaxial tensile test were significantly higher than those determined by the three-point bending test. It is proposed that the tensile strength perpendicular to grain can be determined more precisely with adoption of coefficient 5.233 in the term [(3.75·Fult)/b·Lh] of the equation specified by the Code of International Organization for Standardization 13910:2014 for the three-point bending test.

Thermal Annealing Effect on Elastoplastic Behaviour of Al/Cu Bimetal during Three-Point Bending.

This paper presents the results of experimental studies on the effects of temperature and time of annealing on the elastoplastic properties of bimetallic aluminium-copper sheets. Mechanical tests were carried out on flat samples previously heated to temperatures of 250, 350, 450, and 500 °C for 40, 90, and 150 min. At the beginning of the tests, the elastic constants and internal friction energy were determined after thermal exposure using the impulse vibration exposure method. Further tests were carried out on the same samples using the three-point bending test. Based on the tests, the following quantities were determined and analysed: elasticity angles, translocations of the neutral axes of the cross-sections of samples, and changes in the values of bending moments plasticizing the extreme layers of bimetallic Al/Cu samples resulting from thermal interactions. The final part of this paper presents the results of measurements of the thickness of diffusion zones at the interface and their effect on the stability of the joint after annealing. The studies that were conducted indicate the dominant influence of the thermal factor on the properties of the Al/Cu bimetal above the temperature of 350 °C, which leads to the weakening of its strength and the degradation of the structure at the metallic phase boundary.

Study on the Flexural Performance of Ultrahigh-Performance Concrete-Normal Concrete Composite Slabs.

In recent years, there have been an increasing number of examples of using ultrahigh-performance concrete (UHPC) as a pavement layer to form an ultrahigh-performance concrete-normal concrete (UHPC-NC) composite structure to improve the bearing capacity of bridges. In order to study the flexural performance of this kind of structure, this research studied the flexural performance of UHPC-NC composite slabs, with UHPC in the compression zone, using experiments, numerical simulation, and theoretical analysis. The results showed the following. Firstly, after the UHPC-NC interface had been chiseled, there was no obvious slip between the two materials during the test, and the composite plate was always subjected to synergistic stress. Secondly, the composite slabs in the compression zone of the UHPC were all subjected to bending failure, and the cooperative working performance of each part under the bending load was good, indicating that the composite slab had a unique failure mode and a high bearing capacity. Thirdly, increasing the thickness of the UHPC significantly improved the flexural capacity of the composite plate, and the maximum increase was about 15%. Increasing the reinforcement ratio of the tensile steel rebars also had an increasing effect, with a maximum increase of about 181%. Finally, the proposed formula for calculating the flexural capacity of composite slabs with UHPC in the compression zone could accurately predict the bearing capacity of said slabs. The calculated results were in good agreement with the experimental values, and the error was small.

Research on Multi-Core Curvature Sensing Measurement Based on PPP-BOTDA.

To address the issue of spatial resolution limitations in traditional Brillouin optical time-domain analysis systems due to phonon lifetime constraints, we employed pre-pumped pulse technology. Additionally, to mitigate the double-peak phenomenon observed in pre-pumped Brillouin optical time-domain analysis systems, we implemented a two-sided band interference method to reduce the linewidth of the double-peak fitting. We conducted bending measurements on three eccentric cores and intermediate cores spaced 120° apart. Our results demonstrate that the system described in this paper can achieve a spatial resolution of 30 cm, with bimodal linewidths of 23.1 MHz and 16.0 MHz. Using the parallel transmission frame algorithm, we determined the curvature of a seven-core fiber with a curvature diameter of approximately 10 cm to be 20.67 m-1, with an error margin of 3.2%.

Investigating Additive Manufacturing Possibilities for an Unmanned Aerial Vehicle with Polymeric Materials.

Fused filament fabrication, also known as fused deposition modeling and 3D printing, is the most common additive manufacturing technology due to its cost-effectiveness and customization flexibility compared to existing alternatives. It may revolutionize unmanned aerial vehicle (UAV) design and fabrication. Therefore, this study hypothesizes the 3D printing possibility of UAV using a simple desktop printer and polymeric material. The extensive literature analysis identified the acceptable prototyping object and polymeric material. Thus, the research focuses on applying polylactic acid (PLA) in manufacturing the flying wing-type UAV and develops a fabrication concept to replicate arial vehicles initially produced from a mixture of expanded polystyrene and polyethylene. The material choice stems from PLA's non-toxicity, ease of fabrication, and cost-effectiveness. Alongside ordinary PLA, this study includes lightweight PLA to investigate the mechanical performance of this advanced material, which changes its density depending on the printing temperature. This proof-of-concept study explores the mechanical properties of printed parts of the wing prototype. It also considers the possibility of fragmentation in fabricated objects because of the limitations of printing space. The simplified bending tests identified significant reserves in the mechanical performance regarding the theoretical resistance of the material in the wing prototype, which proves the raised hypothesis and delivers the object for further optimization. Focusing on the mechanical resistance, this study ignored rheology and durability issues, which require additional investigations. Fabricating the wing of the exact geometry reveals acceptable precision of the 3D printing processes but highlights the problematic technology issues requiring further resolution.

Silk Fibroin Film Decorated with Ultralow FeCo Content by Sputtering Deposition Results in a Flexible and Robust Biomaterial for Magnetic Actuation.

Magnetically responsive soft biomaterials are at the forefront of bioengineering and biorobotics. We have created a magnetic hybrid material by coupling silk fibroin─i.e., a natural biopolymer with an optimal combination of biocompatibility and mechanical robustness─with the FeCo alloy, the ferromagnetic material with the highest saturation magnetization. The material is in the form of a 6 µm-thick silk fibroin film, coated with a FeCo layer (nominal thickness: 10 nm) grown by magnetron sputtering deposition. The sputtering deposition technique is versatile and eco-friendly and proves effective for growing the magnetic layer on the biopolymer substrate, also allowing one to select the area to be decorated. The hybrid material is biocompatible, lightweight, flexible, robust, and water-resistant. Electrical, structural, mechanical, and magnetic characterization of the material, both as-prepared and after being soaked in water, have provided information on the adhesion between the silk fibroin substrate and the FeCo layer and on the state of internal mechanical stresses. The hybrid film exhibits a high magnetic bending response under a magnetic field gradient, thanks to an ultralow fraction of the FeCo component (less than 0.1 vol %, i.e., well below 1 wt %). This reduces the risk of adverse health effects and makes the material suitable for bioactuation applications.

Experimental and Numerical Investigation of the Flexural Behavior of Reinforced-Concrete Beams Utilizing Waste Andesite Dust.

During the process of cutting andesite stones, the waste mud is kept in powder form once fully dried. It is difficult to store the waste that is produced as a consequence of the extensive utilization area and consumption of andesite. Thus, eliminating waste storage challenges and incorporating these wastes into the economy are crucial. For this reason, this study examined the effects of waste andesite dust (WAD) on the flexural behavior of reinforced-concrete beams (RCBs) using experimental testing and 3D finite-element modeling (FEM) via ANSYS. Thus, different rates of WAD up to 40% were used to investigate the influence of the WAD rate on the fracture and bending behavior of RCBs. While the RCB with 10% WAD had a slightly lower load-bearing and ductility capacities, ductility capacities significantly drop after 10% WAD. At 40% WAD, both the load-bearing capacity and ductility significantly reduced. Based on the experimental findings, using 10% WAD as a replacement for cement is a reasonable choice to obtain eco-friendly concrete. Moreover, the outcomes of 3D FEM were also compared with those of experiments conducted using ANSYS v19 software. The displacement values between the test and FEM findings are quite similar.

Five days of inpatient scoliosis-specific exercises improve preoperative spinal flexibility and facilitate curve correction of patients with rigid idiopathic scoliosis.

Preoperative spine flexibility plays a key role in the intraoperative treatment course of severe scoliosis. In this cohort study, we examined the effects of 5 day inpatient scoliosis-specific exercise (SSE) on the spinal flexibility of patients with adolescent idiopathic scoliosis before surgery. A total of 65 patients were analyzed. These patients were divided into a prospective cohort (n = 43, age: 15 ± 1.6 years, 36 girls and 7 boys, Lenke class 1 and 2, Cobb angle: 64 ± 11°) who underwent spinal fusion in 2020, and a retrospective cohort (n = 22, age: 15 ± 1.5 years, 17 girls and 5 boys, Lenke class 1 or 2, Cobb angle: 63 ± 10°), who underwent surgery between 2018 and 2019 and did not receive preoperative SSE. Rigid scoliosis was defined as a reduction of less than 50% in Cobb angle between the preoperative fulcrum bending and initial standing curve magnitude. In the prospective cohort, 21 patients (Cobb angle: 65 ± 11°) presented with rigid thoracic scoliosis (pre-SSE fulcrum bending: 40 ± 9°, 39% reduction), and therefore received 5-day SSE to improve their preoperative spinal flexibility (SSE group), whereas 22 patients (Cobb angle: 63 ± 12°) presented with flexible thoracic scoliosis (pre-SSE fulcrum bending: 27 ± 8°, 58% reduction), and therefore underwent surgery without preoperative SSE (non-SSE group). For patients who received 5-day preoperative SSE for 4 h every day, the International Schroth Three-Dimensional Scoliosis Therapy technique was implemented with an inpatient model. After 5 days of SSE, improvements in Cobb angle with post-SSE fulcrum-bending radiography (23 ± 7°, 66% reduction) and pulmonary function (forced expiratory volume in 1 s/forced expiratory volume: 87% before SSE and 92% after SSE, p < 0.01) were observed. At the postoperative day 5, the degree of scoliosis had reduced from 44 ± 6.6° to 22 ± 6° in the SSE group, which is 1° less than the Cobb angle obtained on post-SSE fulcrum-bending radiography. In the non-SSE group, the degree of scoliosis decreased to 26 ± 5.7°. In the retrospective cohort, the degree of scoliosis decreased to 35 ± 5°, with the group also having higher postoperative pain (Visual Analog Scale score = 7, range = 5-10) and an extended hospitalization duration (11 ± 3 days). At 2-year follow-up, curve correction was found to be maintained without adding-on or proximal junctional kyphosis. Compared with the non-SSE group, the SSE group exhibited a greater curve correction (66%) with a shorter hospitalization duration (5 ± 1 days) and a lower degree of postoperative pain (Visual Analog Scale score = 4, range = 3-8). Taken together, our findings indicate that 5 day SSE improves preoperative spinal flexibility and facilitates curve correction.

"I could 100% see myself getting hurt if I did it wrong": a qualitative exploration of exercise perceptions in people with chronic low back pain.

PURPOSE: Traditionally, a specific "core" exercise focus has been favoured for chronic low back pain (CLBP) which contrasts holistic exercise approaches. This study aims to explore the perceptions of exercise in people with CLBP and whether exercise itself can convey implicit messages regarding its use in CLBP management in the absence of a clinical narrative. MATERIALS AND METHODS: Participants were asked about their CLBP history, views of exercise for CLBP, and current exercise behaviours through online semi-structured interviews. Then, participants watched the interviewer perform the deadlift, Jefferson curl, and bird dog and were asked if they thought each individual exercise was beneficial for CLBP, and why. Data were analysed using reflexive thematic analysis through a critical realism and social constructivism lens. RESULTS: All participants (n = 16) viewed all exercises as beneficial for health and pain relief, but perceived efficacy varied. "Core" exercises were deemed crucial for CLBP relief, while spinal flexion and external load were often perceived as potentially injurious. Distrust towards healthcare practitioners also influenced exercise perceptions. CONCLUSION: People with CLBP perceive different exercises to either relieve pain or improve health. Healthcare practitioners can influence these perceptions, highlighting the need for consideration of exercise perceptions in clinical contexts.

Exercise itself can convey implicit messages to people with chronic low back pain irrespective of an accompanying clinical narrative.'Core' exercises are perceived as beneficial whereas exercises involving spinal flexion or loading may be perceived as dangerous.Exercise for reducing pain is perceived as distinctly different from gym related exercises or other exercises for improving health.Healthcare practitioners must consider their client's exercise perceptions when using exercise as an intervention for chronic low back pain.

Reconfigurable, Transformable Soft Pneumatic Actuator with Tunable Three-Dimensional Deformations for Dexterous Soft Robotics Applications.

Numerous soft actuators based on pneumatic network (PneuNet) design have already been proposed and extensively employed across various soft robotics applications in recent years. Despite their widespread use, a common limitation of most existing designs is that their action is predetermined during the fabrication process, thereby restricting the ability to modify or alter their function during operation. To address this shortcoming, in this article the design of a Reconfigurable, Transformable Soft Pneumatic Actuator (RT-SPA) is proposed. The working principle of the RT-SPA is analogous to the conventional PneuNet. The key distinction between the two lies in the ability of the RT-SPA to undergo controlled transformations, allowing for more versatile bending and twisting motions in various directions. Furthermore, the unique reconfigurable design of the RT-SPA enables the selection of actuation units with different sizes to achieve a diverse range of three-dimensional deformations. This versatility enhances the RT-SPA's potential for adaptation to a multitude of tasks and environments, setting it apart from traditional PneuNet. The article begins with a detailed description of the design and fabrication of the RT-SPA. Following this, a series of experiments are conducted to evaluate the performance of the RT-SPA. Finally, the abilities of the RT-SPA for locomotion, gripping, and object manipulation are demonstrated to illustrate the versatility of the RT-SPA across different aspects.

Impact of fractured tibia implant fixation devices on bone stiffness during bending test.

This study focuses on evaluating the failure resistance of a previously reduced tibia with internal fixation implants as PLate (PL) or InterMedullary Nail (IMN), subjected later to a tibial lateral trauma. To replicate this type of trauma, which can be caused by a road accident, a three-point bending test is considered using experimental tests and numerical simulations. The withstand evaluation of the tibia-PL and tibia-IMN structures was conducted by following the load transfer through, the bone and the used implants. The analysis, up to tibia failure, required the use of an elasto-plastic behavior law coupled to damage. The model parameters were identified using experimental tests. Il was shown that the tibia-IMN structure provided a bending resistant load up to three-times higher than the tibia-PL. In fact, the used screws for plate fixation induced a high level of stress in the vicinity of threaded region, leading to a crack initiation and a damage propagation. However, in tibia-IMN structure the highest stress was generated in the trapped zone between the loader and the nail, promoting crack formation. From a biomechanical point of view, the structure with IMN is safer than the structure with PL, whose fixation induces earlier damage in bone.

Bending of bidirectional functionally graded nonlocal stress-driven beam.

This paper provides a comprehensive analysis, using nonlocal stress-driven integral theory, of the static behavior of a nanoscale beam of bidirectionally graded materials. After a brief explanation of the mathematical formulation of BDFGMs, the work done and strain energy expressions derived from the displacement field are discussed. Variational formulations and Hamilton's principle are used to develop the equilibrium equation. An analytical development of the nonlocal kernel for stress-driven integral theory and formulated governing equation which was nondimensionalized later. Explicit equations for displacement and moment are obtained by solving this equation using the Laplace transformation. Three different boundary conditions are examined, and differences in the maximum displacement with respect to the nonlocal parameter and the two material FGM parameters are displayed both visually and in table form. The results exhibit excellent agreement and provide a standard for further research when they are closely compared to the existing numerical data. This work contributes to the knowledge of BDFGMs under nonlocal effects generated by stress-driven integral theory and offers solutions that have been confirmed for further investigation.