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.

Experimental study of ultra-high-performance fibre-reinforced concrete (UHPFRC)-encased CFST short columns under axial and eccentric compression

This study presents a comprehensive experimental programme and analysis of ultra-high-performance fibre-reinforced concrete (UHPFRC)-encased concrete-filled steel tube (CFST) columns subjected to axial and eccentric compression. Twelve short columns were tested, with six of them utilising UHPFRC encasement while the other six employing normal strength fibre-reinforced concrete (FRC) encasement for comparison purpose. The study focused on the effects of load eccentricity ratio, concrete encasement type, and steel tube configuration. Key findings from the test results including failure modes, load-deflection behaviour, moment-curvature relationships and curvature ductility were examined. The findings showed that UHPFRC-encased CFST columns exhibited significantly enhanced strength and bending capacity, while FRC-encased columns showed remarkable ductility. A notable shift in failure mode was observed with increasing load eccentricity ratio, transitioning from crushing of concrete to compression, and then to balanced failure. Furthermore, applicability of prevalent design codes such as EC4, AIJ, and ACI 318 in calculating the peak loads of UHPFRC- and FRC-encased CFST columns was assessed. The plastic stress distribution methods in EC4 and AIJ overestimated peak loads, while ACI 318's strain compatibility approach accurately predicted FRC-encased columns but not UHPFRC-encased columns. To address this, modifications of the parameters α and β were incorporated into the ACI design method to reflect the relative brittle nature of UHPFRC, resulting in accurate predictions.

Response and Fracture of EMT Carbon Steel Round-Hole Tubes with Different Hole Orientations and Different Hole Diameters under Cyclic Bending

This paper aims to investigate the response and fracture of EMT carbon steel round-hole tubes (EMT carbon steel RHTs) under cyclic bending loads. The study considers four different hole orientations (0°, 30°, 60°, and 90°) and five distinct hole diameters (2, 4, 6, 8, and 10 mm). The results reveal that hole orientation and diameter exert a minimal impact on the moment-curvature relationship, leading to the formation of stable loops. The ovalization-curvature graphs demonstrate a trend of asymmetry, serration, and growth with an increasing number of bending cycles. Additionally, larger hole orientations or smaller notch diameters result in reduced ovalization. Furthermore, the double logarithmic coordinates of the controlled curvature–number of cycles required to induce fracture reveal five parallel lines for different hole diameters when the hole orientation is fixed. Finally, in adopting the formulas for smooth tubes and for 6061-T6 aluminum alloy round-hole tubes (6061 aluminum alloy RHTs), this study adjusts the related material parameters. These modifications effectively describe the controlled curvature–number of cycles required to induce fracture for EMT carbon steel RHTs with different hole orientations and diameters under cyclic bending, demonstrating reasonable agreement with the experimental results.

Investigation of Linear and Nonlinear Behaviour of Reinforced Concrete Column Exposed to Corrosion Effect for Different Damage Limit Levels

The high performance of reinforced concrete structural elements under the effects of lateral loads such as earthquakes is of great importance in terms of minimizing the loss of life and property that may occur due to earthquakes. One of the parameters affecting the earthquake behavior of a reinforced concrete structure is the corrosion effect. The aim of this study is to investigate the behavior of reinforced concrete columns exposed to different corrosion levels for different durations within the damage limits. In this direction, it is aimed to perform linear and nonlinear analysis of reinforced concrete columns in 5 different corrosion scenarios. In the study, nonlinear analyzes of the column were made using ANSYS software, the data obtained were determined for different damage limit levels and compared with the section analysis. Because of the study, moment-curvature relations, lateral load-horizontal displacement relations, bending ductility and plastic rotation capacity of the reinforced concrete column were determined for each corrosion scenario.

A new method for rapidly capturing the strength and full nonlinear response of partially interacting steel–concrete composite beams

A semi-analytical procedure is presented for predicting the complete flexural response of partially interacting steel–concrete composite beams up to failure. The governing equation of the Euler–Bernoulli beam theory is solved wherein concrete, steel and the shear connectors joining the concrete slab to the steel beam are assumed to have nonlinear stress-deformation relationships. The adopted constitutive relationship for the connectors allows for partial or full composite action. The solution is applicable to beams and one-way slabs subjected to concentrated or uniform load and/or their combination. The governing equation is numerically solved by satisfying the equilibrium and compatibility requirements along the member. For the reinforced concrete part of the composite beam, a nonlinear moment–curvature relationship is developed that accounts for concrete nonlinearity in compression and for cracking and tension-stiffening in tension as well as for steel reinforcement nonlinearity. The steel profile is assumed to have a bilinear elasto–plastic strain-hardening moment–curvature relationship. Comparison of the proposed model results with the corresponding experimental load–deflection curves and interfacial shear–slip curves of several beams tested by others shows good agreement. The relative simplicity, efficiency and easy application of the present solution make it possible to accurately predict the failure load, interfacial slip and full nonlinear response of partially interacting composite beams.

COMPARASION PLASTIC BEHAVIOR OF BOX GRIDER BRIDGE WITH MULTIPLE BOX AND CELLULAR BOX CROSS SECTIONS

This study compares plastic deformation behavior in box girder bridges with multiple boxes and cellular box cross-sections. The cross-section's shape significantly influences the girder's post-yield behavior despite being designed to have the exact yield moment. Steel's stress-strain relationship undergoes linear behavior until the yield stress is reached, followed by strain hardening. This study aims to assess the impact of strain hardening on the plastic behavior of girder box bridges.Two types of box girder sections, multiple box and cellular box, are designed with equivalent yield moments. The analysis is conducted with and without strain hardening calculations to evaluate plastic moment, inelastic area length, shape factor, and moment-curvature relationship. The design and analysis follow RSNI T-03-2005 standards using SAP 2000 v.15.Results indicate that multiple box sections exhibit more prominent plastic moments and inelastic area lengths than cellular box sections. Strain hardening calculations show significant increases in plastic moments for both section types. Graphical comparisons highlight the differences in moment-curvature relationships between models with and without strain hardening. Understanding the impact of strain hardening on plastic behavior provides valuable insights for designing and assessing box girder bridges, ensuring structural safety and performance under load conditions.

Moment redistribution in continuous reinforced concrete beams: Experimental study and analytical investigation

This paper presents the results of experimental and analytical studies carried out on continuous reinforced concrete (RC) beams to determine moment redistribution in statically indeterminate RC structures. For this purpose, continuous RC beams were produced with varying tensile reinforcement ratio at the intermediate support, which are shown as the parameters that affect moment redistribution the most in the literature. One of the main goals of this study is to check if the formulations in the design code provisions and in the literature give a safe estimate, and in order to perform this check, a dataset consisting of the experimental results of 141 beams in the literature has been used for validation and the moment redistribution ratios of this dataset have been estimated with all these formulations. The obtained results have been compared using various statistical indices such as the mean value (MV), standard deviation (SD), coefficient of variation (COV), the root mean square error (RMSE), mean absolute percentage error (MAPE). In particular, the formulations in the literature that take into account many parameters affecting the moment redistribution have been found to give better results than the formulations in the design code provisions. The results of this study confirm that elastic moment redistribution, which occurs in the process from the moment when the concrete cracks until the tensile reinforcement yields and constitutes a significant part of the total moment redistribution, is also important. Moreover, the properties of continuous RC beams related to their general behaviors, such as load-displacement relationships, ductility and moment-curvature relationships have been also investigated in detail.

Flexural Response of Functionally Graded Rubberized Concrete Beams.

Recycling rubber and/or steel fiber components of waste tires in construction applications is a venue for maximizing the recycling rate of these items. Additionally, it supports the move towards producing sustainable construction materials and conserving natural resources. Previous research explored the viability of employing recycled waste rubber particles as an alternative for natural aggregate. Despite the adverse effect of rubber on the mechanical properties of concrete (e.g., lower compressive strength), it produces several advantages, including excellent dynamic and ductility properties, which can be utilized in structural members critical to dynamic loads, e.g., blasts, earthquakes, and impacts. In an effort to expand the adoption of waste rubber in concrete beams and to eliminate key concerns associated with the degradation of their flexural behavior, the functionally graded (FG) beams concept was utilized. The present investigation comprised the testing of five beams using a four-point bending configuration. Plain concrete, rubberized concrete (RuC), and steel-fiber reinforced rubberized concrete (SFRRuC) beams were cast along with FG beams arranged in two layers. The top layer of the FG beams comprised plain concrete, while the bottom layer consisted of RuC or SFRRuC. Experimental findings indicated that the flexural behavior of the FG beam with layers of SFRRuC and plain concrete exceeded the flexural strength, displacement ductility ratio, and toughness performances of the plain concrete beam by 9.9%, 12.9%, and 24.4%, respectively. The moment-curvature relationship was also predicted for the tested beam and showed an excellent match with the experimentally measured relationship.

Numerical method for predicting first crack load on hollow-cored beams subjected to point load at Midspan

Predicting the initial crack load in concrete is important to detect early warning of a problem. In this study, a model for predicting the first crack load on a hollow-cored rectangular beam point loaded at mid-span was developed by combining a numerical method and an experimental approach. The modulus of rupture was introduced into the governing moment-curvature relationship. Experimentally, flexural testing with point loads at mid-span was performed on fifteen (15) beams made up of three (3) beam types at 1 kN intervals for a span of 750mm using the Universal Testing machine. The beams were simply supported by roller points. The dimensions of the beams were kept constant and later varied while investigating the following hollow diameters: 0, 30, 60, 75, and 105mm. Numerically, the beams were designed as a beam element point loaded at mid-span with a span of 700mm centers, and the support conditions were defined as pinned support. Governing equations relating failure load with the modulus of rupture, stiffness matrix, shape functions, and moment of inertia were developed. The equation for predicting the first crack load, incorporating the modulus of rupture, was derived. The moment of inertia was calculated by discretizing the hollow-cored beam section using an isoparametric geometric transformation. The experimental results were used to validate the numerical model. 90.55% agreement between experimental and numerical results was observed. The overall average percentage difference between the two methods recorded is 9.45%. This shows that at about 91% confidence level, both approaches are the same and can be applied with confidence in the prediction of the first crack load on hollow- cored reinforced concrete beams.

CFRP-steel composite beams with seawater sea sand concrete cores subjected to bending

A redesign was attempted for the concrete-filled double-skin tube subjected to bending, and by adjusting the core tube position and applying carbon fiber-reinforced polymer (CFRP) sheets or steel bars in the tensile region, it was hoped to delay the cracking of the concrete in the tensile region. Epoxy mortar was used to modify the interface. Seawater and sea sand has been successfully applied from reinforced concrete beams to concrete-filled steel tube beams, benefiting from the corrosion-resistant properties of CFRP and epoxy mortar. The four-point bending test parameters included the type of core tube, the number of CFRP layers, and the diameter of the steel bars. The beams with FRP sheets exhibited better flexural capacity and residual stiffness, while the brittle fracture of FRP led to major crack in concrete. The beams with steel bars exhibited better initial stiffness and the cracks in concrete were more uniform in width. When the layers of CFRP or the diameter of the steel bars was increased, the flexural capacity of the composite beams increased by 11.0%-13.6% and 7.0%-9.1%, respectively. The enhancements provided by the core tubes were small, and the design of the composite beams should be considered from various perspectives. The moment-curvature relationships, ultimate states, and flexural stiffness were defined by considering concrete cracking, FRP fracturing, and steel buckling. Several formulas for calculating flexural stiffness in the code were evaluated in combination with the test data.

Analysing the influence of ground granulated blast furnace slag and steel fibre on RC beams flexural behaviour

This study examines the effect of Ground Granulated Blast Furnace Slag (GGBS) and steel fibers on the flexural behaviour of RC beams under monotonic loading. Various percentages of GGBS were used to substitute cement, namely 0%, 20%, 40%, 60%, and 80% and fibers were added to the concrete mix as 0%, 0.5%, 1%, and 1.5% of the volume of concrete. The load–deflection behaviour of GGBS-incorporated RC beams with fibers was compared with the control RC beam. Beams were tested under load control for 28 days and 180 days. The ultimate load of the GGBS-incorporated RC beam up to 40% cement replacement was found to higher than that of the control beam. The strength of concrete is reduced by 28% and 19% when cement was partially replaced by 80% of GGBS at 28 and 180 days, respectively, compared to control concrete without fibres. Further, the analytical load–deflection response of GGBS-incorporated RC beams was determined by using several codes of practice, namely, ACI 318-11(2011), CSA A23.3-04 (2004), EC-04 (2004), and IS 456 (2000). The Codal provisions were primarily based on the effective moment of inertia, Young’s modulus, and modulus of rupture, stiffness, and cracking. Average load–deflection plots obtained from experiments were compared with the computed load–deflection of analytical studies. It was found that the analytically predicted load–deflection behaviour is comparable with the corresponding average experimental load–deflection response. Moment curvature relations were also developed for RC beams.

CURVATURE DUCTILITYOF REINFORCED CONCRETE BEAM SECTIONS STIFFENED WITH STEEL PLATES

This paper presents theoretical parametric study of the curvature ductility capacity for reinforced concrete beam sections stiffened with steel plates. The study considers the behavior of concrete and reinforcing steel under different strain rates. A computer program has been written to compute the curvature ductility taking into account the spalling in concrete cover. Strain rate sensitive constitutive models of steel and concrete were used for predicting the moment-curvature relationship of reinforced concrete beams at different rate of straining. The study parameters are the yield strength of main reinforcement, yield strength of transverse reinforcement, compressive strength of concrete, spacing of stirrups and steel plate thickness. The results indicated that higher strain rates improve both the curvature ductility and the moment capacity of reinforced concrete beam sections. Moreover the section curvature ductility increases as the thickness of the stiffening plates decreases.

Nonlinear Semi-Numeric and Finite Element Analysis of Three-Point Bending Tests of Notched Polymer Fiber-Reinforced Concrete Prisms

A nonlinear semi-numeric and finite element analysis of three-point bending tests of notched polymer fiber-reinforced concrete prisms was performed. The computational and experimental results were compared in terms of the load-displacement behavior. The vertical midspan displacement and the crack mouth opening displacement results were considered. The nonlinear semi-numeric computational procedure involved the moment-curvature relation, calculated by considering the constitutive material law from the fib Model Code for Concrete Structures 2010, and considered a plastic hinge mechanism to simulate the cracked region behavior. Two sets of tensile mechanical properties were considered for the constitutive material law: back-calculated (by an inverse analysis) tensile strength properties from the experimental results, and tensile strength properties calculated by simplified expressions from the fib Model Code for Concrete Structures 2010. Other mechanical properties were determined by additional compressive tests and standard relations for the dependency of various mechanical properties on the concrete compressive strength. The nonlinear finite element analysis incorporated the Menetrey-Willam material model to simulate the fiber-reinforced concrete behavior. The nonlinear semi-numeric analysis load-displacement results based on the back-calculated tensile strength properties relatively accurately matched with the experimental results, whereas the nonlinear semi-numeric analysis load-displacement results based on tensile strength properties calculated by simplified expressions from the fib Model Code for Concrete Structures 2010 and the nonlinear finite element analysis load-displacement results showed certain shortcomings.

Experimental and Analytical Investigation of Moment-Carrying Capacities of Reinforced Concrete Frame Systems Corroded by Accelerated Corrosion Method

Technical investigations carried out after the devastating earthquakes in Turkey in the last 25 years show that one of the main causes of damage to reinforced concrete structures is reinforcement bar corrosion. The deterioration caused by reinforcement corrosion in reinforced concrete elements reduces the parameters that define the performance level of the structure, such as ductility, stiffness, bond-slip relationship, load carrying capacity, and energy absorption capacity. Therefore, determining the specified performance levels of reinforced concrete structures exposed to corrosion before any seismic activity occurs is of great importance in preventing loss of life and property. Cross-section behavior in reinforced concrete structures represents the load-bearing element behavior In order to accurately determine the section behavior, the Moment-Curvature relationship must be defined. In this study, the structural behavior of reinforced concrete frames exposed to corrosion was examined experimentally and analytically. For this purpose, 4 of the 5 reinforced concrete frame specimens constructed were corroded at different ratios using the accelerated corrosion method. After the corrosion process was completed, in the experimental part of the study, all specimens were tested under the effect of a 20% constant axial load and reversal-cyclic loading. In the analytical study, as a result of the cross-sectional analyzes carried out by taking into account the material-mechanical properties changing with the effect of corrosion, it was determined that the calculated moment values were in high predicted with the experimentally measured moment values.

Nonlinear semi-numeric analysis and simplified analysis of polymer fiber-reinforced concrete prisms under three-point bending test conditions

This paper presents a semi-numeric nonlinear analysis and a simplified analysis for evaluating the load-displacement behavior of polymer fiber-reinforced concrete elements under three-point bending test conditions. The considered elements were notched and unnotched prisms. The nonlinear semi-numeric analysis was based on the moment-curvature relation, plastic hinge approach, and virtual work method. The simplified analysis assumed multilinear load-displacement behavior of the prisms under three-point bending test conditions. It included four variants for the input tensile strength properties and crack widths considered for the serviceability and ultimate limit state. The notched polymer fiber-reinforced concrete prism three-point bending test results from a prior study were the basis for evaluating the simplified analysis, which was subsequently compared with the nonlinear semi-numeric analysis outcomes from the same investigation. Additionally, the simplified analysis and the nonlinear semi- numeric analysis were used to determine the load-displacement behavior of unnotched polymer fiber-reinforced concrete prisms with heights ranging from 25 mm to 250 mm. The results indicate that the simplified analysis provides a practical and efficient method for estimating the behavior of polymer fiber-reinforced concrete structures under three-point bending test conditions, yielding relatively accurate results with minimal computational effort compared to the more exact nonlinear semi-numeric analysis.

Dynamic Response Analysis of Reinforced Column Subjected To Shock Wave Loading

This study focuses on the dynamical response of reinforced concrete members subjected to shock-wave loading, which can cause catastrophic damage to structures. The effects of high strain rate loading and lateral confinement on the member’s behavior are considered in the analysis. The Moment-Curvature (M-ϕ) relations are assessed using stress block equilibrium at yield and ultimate state, and an analytical model is developed that integrates the high strain rate material behavior to predict the peak deflection of the structural member. The study evaluates the dynamic response of the member using a simplified model based on single degree of freedom (SDOF) idealization, and the response of the member in elastic and elastic-plastic phases is modelled using the bilinear resistance function. The governing equation of motion is explained using the Newmark-Beta algorithm, and the shock spectrum predicting the maximum deflection is developed by varying the load duration and magnitude. Additionally, a Finite Element (FE) model is developed to provide a more detailed understanding of the member’s behavior under shock loading. The results obtained from the FE model are compared with the analytical deflection for extreme combinations of load duration and magnitude. The study provides valuable insights into the behavior of reinforced concrete members under extreme loads, which can help structural designers in predicting and design structures that can withstand such loading conditions. The results can also be used in the development of building codes and standards to improve the safety and resilience of structures subjected to shock-wave loading.

Response and Failure of Circumferential Sharp-Notched C2700 Brass Tubes under Cyclic Bending

This paper investigates the response and failure of circumferential sharp-notched C2700 brass tubes with four different notch depths of 0.2, 0.4, 0.6, 0.8, and 1.0 mm subjected to cyclic bending. The wall thickness is 1.5 mm for all tested tubes, and cyclic bending loads are applied until buckling failure occurs. The experimental moment-curvature relationships exhibit a stable loop from the first bending cycles. An increase in the notch depth results in the decrease of the peak bending moment. The experimental relationships between ovalization and curvature demonstrate symmetry, serrations, and a growth pattern as cycles progress, regardless of the notch depth. Regarding the curvature-number of cycles required to initiate buckling relationships, it can be observed that five notch depths correspond to five parallel straight lines when plotted on double logarithmic coordinates. Finally, this study employs the theoretical formulation proposed by Lee in 2010 to describe the aforementioned relationships. The theoretical analysis is compared with experimental data, revealing a close alignment between the two approaches.

Design Aids for Calculating Idealized Moment-Curvature Relationships of Circular Reinforced Concrete Bridge Columns

Design Aids for Calculating Idealized Moment-Curvature Relationships of Circular Reinforced Concrete Bridge Columns

Simplified Method for Nonlinear Seismic Response Analysis of Corroded Pile-Supported Wharf

Fiber-based finite element analysis (FB-FEA) has been widely recognized for its ability to reproduce experimental results and is also a reliable method for evaluating the nonlinear seismic response of pile-supported wharves (PSWs). Design practice often employs frame analysis (FA) due to its easy implementation. To precisely reproduce the nonlinear seismic response of PSW using FA, it is necessary to configure mechanical properties such as the hinge property correctly. However, it is unclear whether the hinge properties proposed in previous studies can be applied to PSWs with spun piles. In this study, a novel FA method was developed to investigate the nonlinear seismic response of PSWs with corroded spun piles considering PC bar area reduction, deteriorated material properties, the bending stiffness reduction factor, and the moment–curvature relationship of the spun pile. The nonlinear seismic response of corroded PSWs was determined by performing pushover analysis using three methods: FA using the method of the previous study (FA-1), the proposed FA method (FA-2), and FB-FEA. As regards PSW foundations, vertical pile and batter pile configurations were considered. The pushover analysis results were compared in terms of several parameters, such as the natural period, plastic hinge formation, and load capacity of the corroded PSWs. The FA-2 results agreed very well with the FB-FEA results, while the FA-1 results were less precise with respect to the natural periods and load capacities of corroded PSWs. The results indicated that the bending stiffness reduction factor, moment–curvature relationship, and axial load–bending moment (P–M) capacity of the corroded spun piles should be appropriately defined. Corrosion had greater negative impacts on the compressive axial load and bending moment capacities of the spun pile than on its tensile axial load capacity.

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.