Bending Moment-curvature Relationship Research Articles

Bridging Behavior of Palm Fiber in Cementitious Composite

This study addresses the growing need for sustainable construction materials by investigating the mechanical properties and behavior of palm fiber-reinforced cementitious composite (FRCC), a potential eco-friendly alternative to synthetic fiber reinforcements. Despite the promise of natural fibers in enhancing the mechanical performance of composites, challenges remain in optimizing fiber distribution, fiber–composite bonding mechanism, and its balance to matrix strength. To address these challenges, this study conducted extensive experimental programs using palm fiber as reinforcement, focusing on understanding the fiber–matrix interaction, determining the pullout load–slip relationship, and modeling fiber bridging behavior. The experimental program included density calculations and scanning electron microscope (SEM) analysis to examine the surface morphology and diameter of the fibers. Single fiber pullout tests were performed under varying conditions to assess the pullout load, slip behavior, and failure modes of the palm fiber, and a relationship between the pullout load and slip with the embedded length of the palm fiber was constructed. A trilinear model was developed to describe the pullout load–slip behavior of single fibers, and a corresponding palm-FRCC bridging model was constructed using the results from these tests. Section analysis was conducted to assess the adaptability of the modeled bridging law calculations, and the analysis result of the bending moment–curvature relationship shows a good agreement with the experimental results obtained from the four-point bending test of palm-FRCC. These findings demonstrate the potential of palm fibers in improving the mechanical performance of FRCC and contribute to the broader understanding of natural fiber reinforcement in cementitious composites.

Method of strain analysis of pipelines under landslides: An improved semi-analytical method for softening bending moment-curvature

The accurate description of the elastic‒plastic stress‒strain of a pipeline is used to evaluate the risk that the pipeline will undergo failure during a landslide. This paper proposes a complete set of refined semi-analytical methods (SAMs) for pipeline elastic-plastic strain to accurately evaluate the safety of pipelines. First, a concise model for the calculation of landslide thrust is established based on the pipe-soil interaction mechanism as load boundaries of the SAMs. Secondly, the plastic softening bending moment-curvature relationship (BMCR) is derived to establish a difference equation for the deformation of the pipeline during the plastic stage based on the principle of internal force balance of the pipe section, and then the bending plastic strain is calculated accurately. Finally, the axial strain is fully calculated considering the interaction between axial force and bending of the pipeline. The comparison of the results of small-scale landslide tests, large-scale landslide tests, and SAM calculations shows that the improved SAM has good applicability, with 20% better accuracy than traditional methods. In conclusion, the SAM proposed in this paper can effectively guide the design and evaluation of the strain-based design pipeline.

Study on the influence of bending curvature on the bending characteristics of unbonded flexible pipes

Unbonded flexible pipes are widely used in offshore oil and gas development as key equipment for offshore oil and gas transportation. Their biggest advantages are their flexibility and easy bending, making them more adaptable to the complex marine environment and the movement of offshore floating oil and gas platforms. These platforms also bring challenges to the structural design and analysis of flexible pipes. The mechanical response of each spiral strip layer used to construct the flexible pipe is the most complex response in the bending process. To analyze the bending performance of flexible pipes, this study focuses on the derivation of the explicit relationship between the bending curvature and the minimum critical curvature of a flexible pipe in the partial slip process of a spiral strip layer. An interlayer friction coefficient is introduced in the theoretical derivation, and complete expressions of the bending moment and bending stiffness for the non-slip, partial slip, and complete slip stages of the spiral strip layer are established. The expressions explain the hysteresis phenomenon of the bending characteristics of flexible pipes under a bending load. The results show that the hysteresis present when analyzing the bending moment-curvature relationship and the bending stiffness-curvature relationship of flexible pipes is mainly caused by the nonlinearity of the bending moment-curvature relationship of the tensile armor layer, while the bending moment-curvature relationship of all other layers is linear and the bending stiffness remains constant. The contribution of the carcass layer, pressure armor layer and anti-wear layer to the bending moment and bending stiffness is very small. The minimum critical curvature is the key variable affecting the slippage of the spiral strips of the tensile armor layer. The minimum critical curvature has a linear relationship with the interlayer friction coefficient and a nonlinear relationship with the helix angle.

Experimental study on flexural behavior of the BFRC-concrete composite beams

Three specimens of composite beams were tested under a four-points bending test to study the effect of BFRC height on the flexural behavior of the composite beam. The numerical software MATLAB was used to numerically study the bending moment-curvature (M-φ) relationship of the composite beams. The finite element software (ABAQUS) was used to simulate the flexural behavior of the composite beams, and the parameter analysis is carried out to study the effect of strength and height of BFRC, strength and ratio of steel reinforcement on the flexural performance of BFRC-concrete composite beams. The study results show that the flexural capacity of the composite beam is higher than that of the normal concrete beam. With the increase of the height of the BFRC, the flexural capacity increases, and the bottom crack propagation is significantly inhibited. The BFRC height has a negligible effect on the ductility of the composite beam. The results illustrate the assumption of the plane section is valid, and the bonding behavior between steel bar and BFRC as well as the co-working between BFRC and ordinary concrete are perfect. Based on the experimental results, formulae are developed for predicting the cracking, yield, and ultimate moment bearing capacity of the composite beam, and a simplified formula is also developed for predicting the ultimate bearing capacity of composite beam with a balanced reinforcement ratio. The prediction results are consistent well with the test results, and the simulation results exhibit a good agreement with the test results of composite beams.

Stiffness Estimation of Girder Bridges Using Influence Lines Identified from Vehicle-Induced Structural Responses

The influence line is an important static property in bridges. The shape and magnitude of the girder bridge influence line contain stiffness information for the bridge supports and beam. This research sought to directly identify the rotational stiffness of bridge supports and the flexural stiffness of beams from extracted influence lines, which provides a quantification method for bridge damage and performance degradation. The paper first reviews the influence line identification method from vehicle-induced bridge responses. Then, the complete theoretical formulations of the deflection, rotation, and strain influence line for a general girder bridge are derived. Based on these derivations, the rotational stiffness at two supports and the equivalent flexural stiffness value of the beam are identified. Next, a certain span of a continuous girder bridge is converted to an equivalent simply supported system, and the flexural stiffness distribution of the beam is estimated based on the bending moment-curvature relationship and Betti’s law. The paper then presents a three-span continuous girder bridge verification example. The stiffness estimation results under different test conditions combined with the bridge influence line identification algorithm are presented to verify the reliability of the proposed method. This stiffness estimation method can be applied to baseline-free bridge performance evaluations based on vehicle-induced bridge responses.

A calculation approach for sandwich panels with facings made of UHPFRC and pre-tensioned CFRP reinforcement

Sandwich panels are widely applied in construction industry, e.g. for modern building envelopes. They show low self-weight and high load-bearing capacity as well as sufficient physical properties, but are usually limited to relatively short spans. In contrast, thin concrete shell structures show high stiffness as well as load-bearing capacity even for long spans. Combining both construction methods and applying non-corrosive high-strength materials enables multifunctional, light elements with long spans, high load-carrying capacities and additional physical properties.In this paper, sandwich panels with flat and folded plate facings made of ultra-high performance fibre reinforced concrete (UHPFRC) and carbon fibre reinforced polymer (CFRP) prestressing strands are investigated. For a reliable bond strength and to account for spatial facings, a special production method was developed. For the prediction of the flexural behaviour, a new calculation approach is derived step-by-step which accounts for non-linear behaviour. Theoretical bending moment–curvature relationships are derived for UHPFRC cross-sections with CFRP prestressing strands and incorporated in differential equations of sandwich theory to account for cracking and residual stresses in facings. As additional merit of this approach, the tensile strength of UHPFRC is derived from material samples. Spring models to consider stiffness of shear connectors and core material are applied. The non-linear calculation approach covers typical failure mechanisms. Non-linear load-deformation relationships are calculated and compared to experimental test data of prestressed sandwich panels.

Shape-Sensing of Beam Elements Undergoing Material Nonlinearities.

The use of in situ strain measurements to reconstruct the deformed shape of structures is a key technology for real-time monitoring. A particularly promising, versatile and computationally efficient method is the inverse finite element method (iFEM), which can be used to reconstruct the displacement field of beam elements, plate and shell structures from some discrete strain measurements. The iFEM does not require the knowledge of the material properties. Nevertheless, it has always been applied to structures with linear material constitutive behavior. In the present work, advances are proposed to use the method also for concrete structures in civil engineering field such as bridges normally characterized by material nonlinearities due to the behavior of both steel and concrete. The effectiveness of iFEM, for simply supported reinforced concrete beam and continuous beams with load conditions that determine the yielding of reinforcing steel, is studied. In order to assess the influence on displacements and strains reconstructions, different measurement stations and mesh configurations are considered. Hybrid procedures employing iFEM analysis supported by bending moment-curvature relationship are proposed in case of lack of input data in plastic zones. The reliability of the results obtained is tested and commented on to highlight the effectiveness of the approach.

Variation of the 90° Redundant-hole Diameter Effect on the Response and Failure of Round-hole 6061-T6 Aluminum Alloy Tubes under the Cyclic Bending

This paper presents an experiment and an analysis for examining the variation of the 90° redundant-hole diameter effect on the cyclic bending mechanical behavior and fracture failure of round-hole 6061-T6 aluminum alloy tubes. In this investigation, a round-hole 6061-T6 aluminum alloy tube with a 6 mm hole diameter was drilled to obtain a 90° redundant hole but with different hole diameter of 2, 4, 6, 8, or 10 mm. It can be observed that from the first bending cycle, the bending moment-curvature curve describes a stable loop. The diameter of the 90° redundant hole has little effect on the bending moment-curvature relationship. However, when the number of bending cycles increases, the ovalization-curvature curve shows an increasing, asymmetrical, ratcheting, and bow-like tendency. The diameter of 90° redundant-hole shows a significant influence on the ovalization-curvature relationship. In addition, five non-parallel straight lines corresponding to five different 90° redundant hole diameters were discovered for the controlled curvature-number of bending cycles necessary to cause failure relationship on the double logarithmic coordinates. Finally, a formula was presented to simulate the above relationship. It is found that the experimental and analytical data were in good agreement.

Investigation on springback behaviours of hexagonal close-packed sheet metals

In this study, a novel analytical method for predicting bending and springback behaviours of hexagonal close-packed (HCP) sheet metals is presented. The proposed analytical approach is developed by using the Cazacu-Barlat 2004 asymmetric yield function and isotropic plastic hardening rule. This model can be used to determine bending moment-curvature relationships and springback of HCP metals under uniaxial and plane strain loading conditions. Furthermore, to capture the nonlinearity in unloading and to improve springback prediction, the variable elastic modulus approach is implemented in the proposed model. The proposed new model reveals that reverse effects of the back force on springback behaviours cannot be found under the plane strain condition, which could not be found by using any existing models. Moreover, the analytical model is implemented into Abaqus via UMAT subroutine for its application in complex cases, and a numerical model is then developed as a showcase. The proposed methods are validated by using those experimental results available in literature. The results show considerable improvements by considering the plane strain condition and nonlinear unloading.

Analysis of Structural Concrete Bar Members Based on Secant Stiffness Methods

In this paper, the behavior of structural concrete linear bar members was studied using numerical model implemented in a computer program written in MATLAB. The numerical model is based on the modified version of the procedure developed by Oukaili. The model is based on real stress-strain diagrams of concrete and steel and their secant modulus of elasticity at different loading stages. The behavior presented by normal force-axial strain and bending moment-curvature relationships is studied by calculating the secant sectional stiffness of the member. Based on secant methods, this methodology can be easily implemented using an iterative procedure to solve non-linear equations. A comparison between numerical and experimental data, illustrated through the strain profiles, stress distribution, normal force-axial strain, and moment-curvature relationships, shows that the numerical model has good numerical accuracy and is capable of predicting the behavior of structural concrete members with different partially prestressing ratios at serviceability and ultimate loading stages.

Odnos momenta savijanja i zakrivljenosti kao pokazatelj seizmičke otpornosti stupova starijih mostova

Odnos momenta savijanja i zakrivljenosti kao pokazatelj seizmičke otpornosti stupova starijih mostova

A novel identification method for obtaining bending moment–curvature relations of wood stems based on digital image correlation and SDOF analysis

Bending moment–curvature relations (M-χ) are useful in many beam modelling approaches. It allows describing in a simple way the mechanical behaviour at the cross-section scale and can be used to model continuous beams as single degree of freedom systems dedicated to perform stochastic analysis. This paper focused on tree mechanical charaterisation and presents an identification method for obtaining bending moment–curvature relationships up to failure from Digital Image Correlation (DIC) and experimental three points bending tests. Due to wood intrinsic variability, the proposed identification method has been validated from a Finite Element (FE) model which aims at simulating precisely the bending response of a cylindrical stem. The refined FE model has been developed based on the geometry and the boundary conditions of the experimentally tested stems. M-χ curves are derived from the FE model and used within a Single Degree Of Freedom (SDOF) approach. At the stem scale, the prediction of the SDOF model (Force-Displacement) is compared to the FE model and lead to a good agreement. Then the approach is used to characterise fresh European beech samples allowing deriving their mechanical properties (longitudinal Young modulus, modulus of elasticity and modulus of rupture).

Finite element analysis of the bending moment-curvature of the double-layered graded concrete beam

The use of functionally graded concrete in structural member provides a beneficial prospect since it promises the increase of beam stiffness with less of construction cost. In structural analysis, concrete stiffness plays role in determining the performance of beam elements in resisting deflection due to the working loads. In this study, the behaviour of the graded concrete beam is continuedly investigated. The bending moment-curvature relationship of the graded concrete beam is conducted numerically to understand the level of ductility and the failure mode compared with the conventional beam. A singly reinforced graded concrete beam is modelled using a non-linear simulation program, Strand7. The result of the analysis is then evaluated in accordance with the Eurocode. The graded concrete beam is expected to exhibit a reliable behaviour of bending moment – curvature so that the graded concrete beam is possible for advanced application as structural elements.

Friction models for evaluating dynamic stresses in non-bonded flexible risers

This paper addresses friction models used for evaluating dynamic stresses in non-bonded flexible risers. A review of the most commonly used methods to model friction between layers in such structures was performed. Four models for calculating friction under dynamic contact pressure and constant shear interaction stick stiffness conditions were then formulated to enable stress calculation of cross-sections exposed to variable tension and bending loads. The friction models were implemented into a computer code used for numerical studies. A sensitivity study was carried out to determine the optimum shear interaction stick stiffness parameter, K0, with respect to representing the plane surfaces remain plane assumption. This was followed by an investigation of the performance of the developed models with respect to the tendon axial force next to the outermost fibre position. The proposed friction models were also verified against full scale tests in terms of bending moment-curvature data. As the test data indicated less bending stiffness in the stick domain than that can be obtained by the plane surfaces remain plane assumption, a method to estimate the parameter K0 was proposed, which accounted for the shear deformation of the plastic layers. The initial strain concept was further applied to deal with the significant hysteresis observed in the test data for low internal pressures pointing the way forward with respect to dealing with this effect in stress analysis. Furthermore, a friction model comparison study was carried out for investigating the static friction effect on the axial force at the outermost fibre position and the bending moment-curvature relationship.

Helical wire stress analysis of unbonded flexible riser under irregular response

A helical wire is a critical component of an unbonded flexible riser prone to fatigue failure. The helical wire has been the focus of much research work in recent years because of the complex multilayer construction of the flexible riser. The present study establishes an analytical model for the axisymmetric and bending analyses of an unbonded flexible riser. The interlayer contact under axisymmetric loads in this model is modeled by setting radial dummy springs between adjacent layers. The contact pressure is constant during the bending response and applied to determine the slipping friction force per unit helical wire. The model tracks the axial stress around the angular position at each time step to calculate the axial force gradient, then compares the axial force gradient with the slipping friction force to judge the helical wire slipping region, which would be applied to determine the bending stiffness for the next time step. The proposed model is verified against the experimental data in the literature. The bending moment–curvature relationship under irregular response is also qualitatively discussed. The stress at the critical point of the helical wire is investigated based on the model by considering the local flexure. The results indicate that the present model can well simulate the bending stiffness variation during irregular response, which has significant effect on the stress of helical wire.

Effectiveness of shock absorber device for damage mitigation of curved viaduct with steel bearing supports

This paper presents a numerical evaluation of the effectiveness of shock absorber devices installed between roller bearing and stopper in reducing viaduct damage. The effectiveness of thickness and types of shock absorber devices on mitigating viaduct damage is investigated accordingly. The thickness of shock absorber devices is from 0cm to 8cm, with increment of 2cm. The viaduct seismic performance is evaluated for five cases based on the thickness of shock absorber devices. In addition, three cases are studied based on the different design parameters of shock absorber devices. The three cases include viaducts with strain hardening, elastic, and strain softening shock absorber devices. Moreover, the pounding forces between roller bearing and stopper, pier damage, displacement of superstructures, relative displacement between two decks, and bending moment–curvature relationship at the pier base are evaluated. Results show that the application of thick shock absorber devices on viaducts can significantly mitigate viaduct damage. The strain softening shock absorber devices plays a more important role in reducing viaduct damage.

Effectiveness of Stoppers and Shock Absorber Devices in Mitigating Earthquake Damage to Curved Viaducts with Steel Bearing Supports

Viaducts with steel bearings are subject to damage during earthquakes. Damage to conventional steel bearings could cause viaduct decks to collapse. This study attempts to prevent large displacements by installing steel stoppers at both sides of roller bearings. Shock absorber devices (SADs) are also installed between roller bearings and stoppers to reduce pounding forces. The study then explores the effectiveness of different stopper gaps and SADs installed between roller bearings and stoppers in mitigating viaduct damage. The effectiveness of stoppers without and with SADs is also investigated. The pounding forces between roller bearings and stoppers, the displacements on the tops of piers, the displacements of superstructures, and the bending moment–curvature relationship at pier bases are evaluated accordingly. Numerical results reveal that earthquake damage to viaducts with small stopper gaps is not significant. The application of SADs is also found to significantly mitigate viaduct damage.

Análisis del comportamiento a flexión de muros de adobe reforzados con geomallas

Rammed earth is a widely used building material in many regions of the world. Due to the high seismic risk in those areas, earthen constructions require suitable and efficient reinforcement techniques from a technological and socioeconomic point of view. This paper analyzes the bending behavior of geogrid reinforced adobe walls from an experimental and analytical point of view. The experimental bending moment-curvature relationships are analytically approached. The results show how geogrid reinforcement improves the performance of adobe masonry in terms of strength and ductility. Thus, a better seismic performance is achieved.

A model for the biaxial dynamic bending of unbonded flexible pipes

An analytical model is given to investigate the behavior of unbonded flexible pipes under biaxial dynamic bending. The stick-slip conditions of each wire are studied in the framework of incremental analysis by an operator splitting of the time step into a stick-state prediction and a slip-state correction step. The tension gradient is calculated using the classical return-mapping algorithm and the obtained tension gradients are integrated numerically to find the axial tension by imposing appropriate boundary conditions. From the axial tension the bending moments with respect to the principal bending axes of the pipe are obtained. Poisson's effect, bending induced tension in the wire, shear deformations of the supporting plastic layer and the changes of the effective torsion and curvature increments of the wire after slip occurs are taken into account in the model. The results of bending moment–curvature relationship from this model are compared with the test data from simple bending and good correlations are found. The comparison of the biaxial bending moment results between this model and the available model also shows good agreement.

A finite element analysis for unbonded flexible risers under bending loads

As the exploitation of oil and gas resources advances into deeper waters and harsher environments, the design and analysis of the flexible risers has become the research focus in the offshore engineering filed. Due to the complexity of the components and the sliding between the adjacent layers, the bending response of the flexible risers is highly non-linear. This paper presents the finite element analysis of the flexible risers under bending loads. The detailed finite element model of the flexible riser is established in ABAQUS software. This finite element model incorporates all the fine details of the riser to accurately predict its nonlinear structural behavior. Based on the finite element model, the bending moment-curvature relationships of a flexible riser under various axisymmetric loads have been investigated. The results have been compared with the analytical ones obtained from the literature and good agreements have been found. Moreover, the stress of the tendon armors has been studied. The non-linear relationship between the armor tendons' stress and the bending loads has been obtained.