Nonlinear Finite Element Model Research Articles

Landing cushioning analysis of new generation heavy airborne armored vehicles

Purpose The purpose of this study is to ensure the successful implementation of a landing cushion for the new generation armored vehicles with significantly enhanced quality. Furthermore, to introduce a high-precision landing cushioning analysis model. Design/methodology/approach To accurately analyze the cushioning performance of the new generation armored vehicles, a nonlinear finite element dynamics model considering the complex travel system was established. The model considered the influence of various nonlinear factors to measure the dynamic response difference between the proposed and traditional models. The cushioning performance of airbags under different landing conditions and their various influence factors were analyzed. Findings The travel system has a large influence on the key points of the vehicle, whose rear end of the upper deck has a larger acceleration fluctuation compared with the traditional model. The increase in the body material stiffness is helpful to reduce this fluctuation. The established nonlinear finite element model can effectively analyze the landing cushioning performance of airborne armored vehicles. The area of the external airbag vent has a large influence on the cushioning performance, and the cushioning system has excellent cushioning performance under various operating conditions. Practical implications This study introduces the travel system, which is ignored by traditional analytical models. The interactions between various types of complex structures are included in the analysis process in its entirety, leading to valuable new conclusions. Quantitatively reveals the analytical errors of traditional simulation models in multiple dimensions and the reasons for their formation. Based on a high-precision simulation model, it is verified that the designed airbag cushioning system has an excellent cushioning effect for the new generation of heavy airborne armored vehicles. Originality/value The novelty of this work comes from the need for smooth landing with low overload for a new type of large-load airborne armored vehicle and provides a high-precision model that quantifies the traditional analytical modeling errors and error principle.

3D nonlinear finite element investigation of laminated bamboo plate strengthened prestressed concrete slab

Due to environment and recycling concerns, interest in applying natural fiber reinforced polymer (NFRP) as an alternative for glass/carbon FRP to strengthen concrete structures has been increasing. This study developed a 3D nonlinear finite element (FE) model for laminated bamboo (LB) plate strengthened prestressed concrete slab. By involving temperature load on defined temperature sensitive material, the proposed model provided good simulation of prestressing process. The accuracy of the developed model was confirmed through comparisons with experimental data, representing peak load discrepancies of only 6.5% and 8.2% for un-strengthened and strengthened slabs, respectively. The parametric study examined the impact of LB plate dimensions and tensile strength, alongside the use of FRP wraps, on concrete slab performance. The results show that the 15 mm thick LB plate can enhance the slab’s peak load by 83.2%. Variations in LB plate tensile strength by up to 10% do not significantly affect the performance of the strengthened prestressed concrete. The increases of the peak load for strengthened cases with LB plate width of 150 mm, 300 mm and 460 mm were 29.4%, 41.9% and 50.2%, respectively. It also shows that FRP end wraps can increase the performance of thick LB plate strengthened prestressed concrete slab.

Finite Element Modelling and Simulation of Tunnel Gates of Dam Structures in ABAQUS Using Reduced-Integrated 8-Node Hexahedral Solid-Shell Element

Tunnel gates used for water regulation are very important and critical parts of dam safety. This is because they are exposed to the hydrostatic pressure of the total height of the water in the reservoir. In this case study, a nonlinear finite element modelling and simulation of the diversion tunnel gate of the Gokdere Bridge Dam in Adana, Turkey, are performed to investigate the performance and capacity of the structure before collapse. The maximum water level in the reservoir is 85 meters. A 3D finite element modelling of the gate structure was created, considering the details of the construction project. Both the concrete structure and the anchorages between the concrete of the first and second phases of the gate structure and the steel profiles in the gate supports are modelled to obtain composite behavior, bond stresses, and a more accurate load and stress distribution. For the nonlinear finite element modelling in ABAQUS, C3D8R reduced-integrated 8-node hexahedral solid elements with concrete damage and tension stiffening are used. For the simulation, linear and nonlinear capacity analyses of the gate structure are performed, and the stresses, strains, deformations, and crack propagation in concrete and steel are investigated. It is found that nonlinear analysis and finite element modelling of anchors for capacity and load transfer are important in the simulation of gate structures to prevent tunnel collapse. It is suggested that dam monitoring and control systems and the use of multiple gates are recommended when a problem occurs in the operation of a gate in the diversion tunnel gates of a dam structure.

Three-dimensional mechanical characteristics analysis of double-shoulder tool joint under complex loads

Taking a new type of special threaded drill pipe joint as the research object, a 3D nonlinear finite element model of the double-shoulder tool joint (DSJ) including the engage and retract groove structure is established by considering the factors of structural asymmetry and contact of each engaging surface. ABAQUS/Explicit finite element method (FEM) is used to study the stress and contact pressure distribution characteristics of the critical structure of DSJ under complex loads. The accuracy of the finite element model was verified by combining with the physical test, and the connection strength and sealing performance of DSJ are evaluated. The results show that the stress concentration occurs at the key structure of DSJ under the make-up torque. The geometry size and structural discontinuity at the transition fillet of the double-shoulder structure have a significant effect on the stress and contact pressure distribution on the shoulder. Under axial tension, the stress level and stress concentration area of the whole joint and the key structure change, especially in the thread section. The sealing performance on the shoulder decreases significant, while that of the thread section increases slightly. The test results are consistent with the finite element simulation results, and this joint shows good mechanical properties, which can meet the design requirements of drilling tool manufacturers and provide data support for its optimal design and application.

The impact of disc degeneration on the dynamic characteristics of the lumbar spine: a finite element analysis

The dynamics of disc degeneration was analyzed to determine the effect of disc degeneration at the L4-L5 segment on the dynamic characteristics of the total lumbar spine. A three-dimensional nonlinear finite element model of the L1-S1 normal lumbar spine was constructed and validated. This normal model was then modified to construct two degeneration models with different degrees of degeneration (mild, moderate) at the L4-L5 level. Modal analysis, harmonic response analysis, and transient dynamics analysis were performed on the total lumbar spine when experiencing following compressive loading (500 N). As the degree of disc degeneration increased, the vibration patterns corresponding to the first three orders of the model’s intrinsic frequency were basically unchanged, with the first order being in the left-right lateral bending direction, the second order being in the forward-flexion and backward-extension direction, and the third order being in the axial stretching direction. The nucleus pulposus pressure peaks corresponding to the first order intrinsic frequency for the harmonic response analysis are all on the right side of the model, with sizes of 0.053 MPa, 0.061 MPa, and 0.036 MPa, respectively; the nucleus pulposus pressure peaks corresponding to the second order intrinsic frequency are all at the rear of the model, with sizes of 0.13 MPa, 0.087 MPa, and 0.11 MPa, respectively; and the nucleus pulposus pressure peaks corresponding to the third order intrinsic frequency are all at the front of the model, with sizes of 0.19 MPa, 0.22 MPa, and 0.22 MPa, respectively. The results of the transient analysis indicated that over time, the response curves of the healthy model, the mild model, and the moderate model all exhibited cyclic response characteristics. Intervertebral disc degeneration did not adversely affect the vibration characteristics of the entire lumbar spine system. Intervertebral disc degeneration significantly altered the dynamics of the degenerative segments and their neighboring normal segments. The process of disc degeneration gradually shifted the load from the nucleus pulposus to the annulus fibrosus when the entire lumbar spine was subjected to the same vibratory environment.

Estimating nonlinear wind-induced response of roof cable nets by aeroelastic experiments and ML modeling

The paper examines the structural engineering challenges related to the assessment of the wind-induced vertical displacements of lightweight, hyperbolic-paraboloid cable-supported membrane roofs. Analysis and comparisons are conducted using three distinct methods for calculating the roof vertical, out-of-plane displacements. Finite-element model (FEM) analysis is employed using: (i) estimated static nodal forces obtained from wind pressure coefficients determined by aerodynamic wind tunnel tests on a rigid building model, and (ii) loads found from wind pressure coefficients, estimated through machine learning (ML) methods, and (iii) measured roof response found from aeroelastic wind tunnel tests on a flexible model. The study examines three different roof geometries (square, rectangular and circular) and two distinct membrane curvatures for each geometry. Furthermore, wind directionality (three mean-wind incidence angles) and Reynolds number effects (seven mean wind velocities) are studied. Comparisons show that the non-linear FEM analysis, based on estimated static wind loads, underestimates the roof displacements at the roof center, compared to the direct measurements on the aeroelastic model. The main contribution of the study consists of a novel application of ML models, and Artificial Neural Networks (ANNs) in particular, which are employed to correct roof displacement estimations, found by simplified aerodynamic test pressure measurements on rigid roof models. The goal is to better describe the complex fluid-structure interaction of the roof membranes, which can only be achieved by direct aeroelastic tests that are difficult to design and execute. Finally, the study demonstrates that ANNs can be used not only for preliminary design of the full-scale structure but also for construction of wind tunnel scale models.

Experimental study on the axial compression performance of pultruded GFRP tubes for emergency bridges

Glass fiber reinforced polymer (GFRP) tubes exhibit significant potential in the design and construction of emergency bridges owing to their high strength-to-weight ratio. Axial compression tests were conducted on 13 pultruded GFRP tubes with varying slenderness ratios (11.9, 14.3, 21.4, 28.6, and 35.7) and diameter-thickness ratios (37.2, 46.5, and 86.2). Furthermore, a nonlinear finite element model was applied to analyze the failure characteristics and load-bearing capacity of the GFRP tubes when subjected to axial loads. A modified Perry formula was proposed based on this analysis. The results indicate that the GFRP tubes are prone to experiencing brittle failure. With the slenderness ratio increases from 11.9 to 35.7, the failure mode tends to change from crushing to local buckling to global buckling. The modified Perry formula displays a high degree of agreement with experimental results, with an average error of 9.38%, and offers a more precise prediction of the capacity of composite tubes. The findings have practical implications for the design of composite truss bridges.

Experimental and numerical investigations of high-strength cold-formed steel multi-limb built-up section columns

This paper investigates the buckling behaviour and load-carrying capacity of G550 high-strength cold-formed steel multi-limb built-up section columns under axial compression. Each built-up section consists of multiple lipped and unlipped channel sections connected by self-tapping screws. The C3U1 section is formed by three C-sections (i.e. lipped channel section) and one U-section (i.e. unlipped channel section), while the C2U2 section is formed by two C-sections and two U-sections. The experimental programme involved tensile coupon tests, measurements of initial geometrical imperfection, and column tests on ten C3U1 and ten C2U2 multi-limb built-up section columns. The numerical modelling programme was then performed, with the nonlinear finite element models created and validated against the experimental results. The applicability of the codified Effective Width Method and Direct Strength Method for predicting the strengths of G550 high-strength cold-formed steel multi-limb built-up section columns, as specified in the American Specification and Australian Standard, was then evaluated. The evaluation results showed that the codified Effective Width Method led to rather conservative and less accurate failure load predictions for G550 high-strength cold-formed steel multi-limb built-up section columns, while the codified Direct Strength Method provided accurate and consistent failure load predictions and thus applicable to the design of G550 high-strength cold-formed steel multi-limb built-up section columns. Concerning the lack of design guidelines specifically for multi-limb built-up sections, a modified Direct Strength Method was thus proposed as an alternative design method and shown to provide accurate failure load predictions.

The Investigation of Various Flange Gaps on Wind Turbine Tower Bolt Fatigue Using Finite-Element Method

Upon careful examination, numerous wind turbine collapses can be attributed to the failure of the tower bolts. Nowadays, the Schmidt–Neuper algorithm is extensively accepted in wind turbine tower bolt design. It is not advisable to utilize the finite-element method, notwithstanding the effect of the flange gap. To quantitatively investigate the influence of flange gaps on bolt fatigue, a nonlinear finite-element model of a flange segment incorporating bolt pretension and contact elements is herein proposed. Three distinct types of flange gaps are defined intentionally. It is possible to determine the nonlinear relationship between the wall load and bolt internal force. The fatigue damage of bolts was thus computed using the obtained nonlinear curve. Comparing with the results with those of Schmidt–Neuper method revealed the bolt fatigue damage is susceptible to a specified flange gap.

Dynamic response of concrete beams reinforced with GFRP and steel bars under impact loading

This study explores the dynamic response of concrete beams reinforced with hybrid glass fiber-reinforced polymer (GFRP) and steel bars under impact loading. A detailed three-dimensional nonlinear finite element model of concrete beams is developed, considering the strain rate effects for concrete, GFRP and steel bars. The accuracy of the numerical model is validated against experimental results available in existing literature. Based on the simulation results, the impact responses of hybrid GFRP-steel RC beams are discussed and compared with steel-RC and GFRP-RC beams. The study results reveal that increasing the effective reinforcement ratio of hybrid GFRP-steel RC beams enhances impact performance, with values above 1% found to be crucial for mitigating severe damage and deflection. Hybrid GFRP-steel RC beams with an effective reinforcement ratio ranging from 1.04% to 1.30% demonstrated enhanced impact resistance compared to GFRP-RC and steel-RC beams. Additional parameters affecting the impact response of hybrid GFRP-steel RC beams, such as impact location, configuration of tensile longitudinal bars, impact velocity and drop weight inclination angle, are explored.

Numerical Analysis of the Ultimate Bearing Capacity of Strip Footing Constructed on Sand-over-Clay Sediment

This paper analyzes the bearing capacity of two-layered soil medium using finite element (FE) software ABAQUS/CAE 2023. Although geotechnical engineers design foundations for layered soil, majorly current geotechnical studies emphasize single homogenous soil. So, this research has significant novelty as it focuses on layered soil and adds to the current literature. A nonlinear FE model was prepared and analyzed to determine the ultimate bearing capacity of two-layered soil (sandy soil over clayey soil). The Drucker–Prager and Mohr–Coulomb models were used to represent sandy soil and clayey soil layers, respectively. Strip footing material properties were considered isotropic and linearly elastic. This study performed parametric studies to understand the effects of thickness, unit weight, and the modulus of the elasticity of sandy soil on the ultimate soil bearing capacity. Additionally, it also analyzed the effect of the cohesive strength of clayey soil on layered soil bearing capacity. Results showed that an increase in sandy soil layer thickness strengthens the layered soil, and thus, improves the bearing capacity of soil. Increasing the sandy soil layer thickness over footing width (h1/B) ratio from 0.15 to 2.0 improved the ultimate bearing capacities with elastic settlements of 350 mm and 250 mm by 145.62% and 101.66%, respectively. Additionally, for a thicker sandy soil layer, an increase in the unit weight and modulus of the elasticity of sandy soil led to higher ultimate bearing capacity. Furthermore, it was concluded that an increase in clayey soil’s cohesive strength from 20 kPa to 30 kPa resulted in a 24.31% and 3.47% increase in soil bearing capacity for h1/B = 0.15 and h1/B = 2.0, respectively. So, the effect of cohesion is prevalent in the case of a thicker clayey soil layer.

Marginal integrity in minimally invasive molar resin composite restorations: Impact of polymerization shrinkage

ObjectivesThis study utilized non-linear finite element (FE) models to explore polymerization shrinkage and its impact on marginal integrity in molars following both selective caries removal (SCR) and conventional treatment. Specifically, we performed 2D in silico simulations to study residual stresses post-resin polymerization shrinkage and their influence on the marginal integrity of various restoration types. MethodsInitially, FE models were developed based on a cohesive zone framework to simulate crack propagation along the bonded interfaces between restoration and tooth structure in SCR-treated molars with class I and class II restorations. The modeled resin composite restorations first underwent polymerization shrinkage and were then subjected to various occlusal loading conditions. Stress magnitudes and distributions were identified to evaluate the margin integrity and predict the mechanism and location of interfacial failure. Results and discussionThe FE models computed polymerization shrinkage stresses of less than 1 MPa, exerting a minor influence on the composite/tooth interface. Occlusal loading, however, significantly impacted the load-bearing capacity of the composite/tooth (c/t) interface, potentially jeopardizing the restoration integrity. Especially under bi-axial occlusal loading, interfacial debonding occurred in the vertical cavity walls of the class I restorations, increasing the risk of failure. Notably, SCR-treated teeth exhibited better margin integrity than restored teeth after complete caries removal (NCR).These findings provide valuable insights into the mechanical behavior of SCR-treated teeth under different loading conditions and highlight the importance of considering the load scenarios that may lead to failure at the c/t interface. By investigating the factors influencing crack initiation and delamination, this novel research contributes to the optimization of restorative treatments and aids in the design of more resilient dental restorations.

Computational assessment of carbon fabric reinforced polymer made prosthetic knee: Mechanics, finite element simulations and experimental evaluation.

A prosthetic knee is designed to replace the functionality of an anatomical knee in transfemoral amputees. The purpose of a prosthetic knee is to restore mobility and compensate amputees for their impairment. In the present research numerical modelling and simulation of a carbon fabric reinforced polymer made polycentric prosthetic knee with four-bar mechanism was performed. Virtual prototyping with computer-aided design and computer-aided engineering software ensured geometric and structural stability of the knee design. The linkage mechanism, instantaneous centre's location and trajectory were investigated using multibody dynamics and analytical formulations. Computational simulations with a non-linear finite element model were employed with joints, contact formulations and an orthotropic material model to predict the displacement, stress formulated and life of the knee prosthesis under static and cyclic loading conditions. Finite element analysis assessed the strength and durability of knee in accordance to standards. Maximum Principal stress of 155 MPa and life expectancy of 3.1 × 106 cycles were determined for the composite knee through numerical simulations ensuring a safe design. Experimental testing was also conducted as per standards and the percentage error was estimated to be 2.52%, thereby establishing the validity of the finite element model deployed. This type of simulation-based approach can be implemented to efficiently and affordably design and prototype a prosthetic knee with desired functioning criteria.

Structural behaviour of asymptotic geodesic hybrid timber gridshells

Asymptotic geodesic gridshells are a novel structural system that is fabricated from straight and flat planks. The planks are elastically bent and twisted around their slender dimension to achieve the desired geometry, while the tall dimension creates structural stiffness. This system combines the geometric features of asymptotic and geodesic curves to create a hybrid tri-hex network on doubly curved surfaces, and provides a stable grid to resist its self-weight and external loads. To comprehensively explore the structural capabilities of asymptotic geodesic gridshells, a full-scale timber gridshell prototype was designed and built. Loading tests, including local and one shell asymmetrical loading, were carried out to examine the structural behaviour of the gridshell. A nonlinear finite-element model was developed and subsequently validated using experimental data. The evaluation of the timber gridshell revealed its high performance under uniformly distributed loads, and the simulation indicated a viable live load capacity of 7.0 kN/m². In a parametric study, the influence of the polar array layout, the joint rotation stiffness, and the support condition on the structural performance of the hybrid gridshell are analysed. Parameters influencing the achievable span are discussed regarding strength, stiffness and buckling behaviour for future design considerations.

Development of a Novel Lightweight Utility Pole Using a New Hybrid Reinforced Composite—Part 1: Fabrication and Experimental Investigation

This paper is the first part of a two-part paper that discusses the development of a novel lightweight and cost-effective hybrid 3D composite material and its and utilization for constructing utility poles. The main objective was to generate a material/pole with a comparable performance to the commercially available poles made of 2D fiber-reinforced polymer (FRP) and examine its feasibility. The novel hybrid composite was configured using a recently developed and marketed 3D E-glass fabric–epoxy composite reinforced with wood dowels, referred to as 3D dowel-reinforced FRPs (3D-drFRPs) hereafter. Firstly, the compressive and flexural properties of the 3D-drFRPs are evaluated. Then, the development of the 3D pole is discussed followed by the fabrication details of two 3D-drFRPs using the standard test method, and their responses are compared. For the second part, robust finite element (FE) models were developed in an LS-DYNA environment and calibrated based on the experimental results. A sophisticated nonlinear FE model was used to simulate the performances of ASTM standard-size compression and three-point bending specimens and tapered 2D and prismatic 3D poles. Moreover, the responses of equivalent 2D and 3D poles were simulated numerically, as the task could not be accommodated experimentally due to our laboratory’s deficiencies. The integrity of the numerical simulation results was validated against experimental results, confirming the accuracy of the developed model. As an example, the stiffness values for the 3-pt bending specimens and the 3D poles obtained through the simulations were very close to the experimentally obtained results, with small margins of errors of 3.2% and 0.89%, respectively. Finally, a simplified analytical calculation method was developed so practicing engineers can determine the stiffnesses of 3D-DrFRP poles very accurately and quickly.

3D non-linear finite element modeling of one-way RC slab strengthened with concrete overlay

Reinforced concrete (RC) slabs often require strengthening due to deterioration, increased loads, or design changes. Concrete overlay is a commonly used technique for strengthening, but predicting the behavior of overlays can be challenging. To address this challenge, this study presents a three-dimensional non-linear finite element model using Abaqus/CAE to analyze the structural performance of one-way reinforced concrete (RC) slabs strengthened with concrete overlays. The model considers three different bonding conditions at the interface: friction, epoxy, and shear connectors. The predictions of the model were compared to experimental results, and it was found that the model accurately captures the load–deflection response, cracking behavior, and interfacial slip in the strengthened slabs. Additionally, the model accurately predicts the new structural capacity of the strengthened slabs, showing good agreement with experimental data. These findings offer valuable insights into the effectiveness of concrete overlays as a traditional strengthening technique for RC slabs. Moreover, the developed finite element model provides a useful tool for optimizing the design of these overlays.

Nonlinear Finite Element Modeling of Wooden Elements Strengthened by FRP

Nonlinear Finite Element Modeling of Wooden Elements Strengthened by FRP

Member Capacity of Cold-rolled Aluminium Alloy Channel Columns - Part II: Numerical Investigation and Design

The paper first presents the development of detailed finite element (FE) models for investigating the member capacity of cold-rolled aluminium alloy 5052-36 channel columns. The numerical non-linear FE models are developed using the commercial FE software package ABAQUS to simulate laboratory experiments and calibrated against the test results. The experimental program was performed by the authors at the University of Sydney and the detailed test results are fully described in a companion paper. The calibrated numerical FE models with actual mechanical properties and measured geometric imperfections in analyses accurately predict the experimental results and behaviours, including flexural and flexural-torsional buckling as well as local-global interaction buckling failure modes. A parametric study is subsequently performed to extend the data range by varying cross-section dimensions and member lengths. The effects of loading eccentricity positions and initial geometric imperfections are also considered in the parametric study. The experimental and numerical results are compared with design strength predictions from current Australian/New Zealand, American and European specifications for aluminium structures in the companion paper. In this paper, the Direct Strength Method (DSM) for the design of compression members as per the Australian/New Zealand standard AS/NZS 4600 for cold-formed steel structures is adopted for comparison. The DSM design rules for cold-formed steel compression members are found to provide more accurate predictions than those of current specifications for aluminium structures and therefore used to propose improved design equations for cold-rolled aluminium alloy columns. Finally, a reliability analysis is performed to evaluate the safety level of current design specifications and the proposed design rules.

Numerical investigation of shear behavior of steel fiber reinforced concrete beams without stirrups subjected to an asymmetric point load

Steel fibers have been shown in numerous studies to enhance the shear performance of steel fiber reinforced concrete (SFRC) beams effectively, and to evaluate the shear behavior of these beams, a nonlinear finite element (NLFE) analysis is required. In the present study, from recent experimental results of asymmetrical loading tests on SFRC beams without stirrups, three NLFE models have been validated and further developed to evaluate the impact that the ratio of shear span-to-depth (a/d) and the compressive strength of steel fiber concrete (SFC) have on the shear behavior and shear strength of SFRC beams without stirrups. The validation shows a good agreement between the chosen NLFE model and the reported experimental results. Applying the NLFE model to five different values of the a/d ratio (e.g., 1.0, 1.5, 2.0, 2.54, and 3.1) reveals a gradual decline in shear strength, while the ductility of the beam increases with the increase in ratio. Meanwhile, with increasing SFC compressive strength, the shear strength and ductility of SFRC beams without stirrups significantly increase for the same ratio of shear span-to-depth. Moreover, the failure mode of SFRC beams without stirrups dominantly depends on the a/d ratio.

Analytical study on flexural strengthening of narrow RC beams with hybrid anchored CFRP sheets

Premature debonding of fiber-reinforced polymer (FRP) sheets commonly occurs in purely bonded reinforced concrete (RC) beams. A hybrid strengthening method for narrow FRP-strengthened RC beams has been proposed to solve this problem. Experimental results have verified the effectiveness of the novel strengthening system in preventing the end debonding and impeding the intermediate debonding of the FRP sheet. However, the mechanism of its strengthening efficiency has not been studied deeply enough. Therefore, this paper developed a non-linear three-dimensional finite element (FE) model to study the flexural behavior of the FRP-strengthened narrow RC beams hybrid anchored with end self-locking system. The FE model was verified against the available experimental studies and showed good agreement, with a R2 of 0.97. Based on the verified model, parametric studies were performed to study further the influences of four major factors: FRP sheet length, steel rebar ratio, concrete compressive strength, and number of FRP sheet layers. The efficacy of hybrid strengthened beams was reduced with longer FRP bond lengths and higher steel rebar ratios. Conversely, increasing concrete compressive strength and FRP sheet layers to a certain degree enhanced the efficacy. Finally, an analytical model to predict the load-deflection curve of the beam was proposed.