Bending Moment Research Articles

Structural behavior of RPC beams subjected to flexural and torsional effects

This research is concerned with the behavior of reactive powder concrete beams (RPC) under the combined effects of bending and torsion moments, with three main parameters: torsional to bending moments ratio (T/M), longitudinal reinforcement ratio ( ), and transverse reinforcement ratio ( ). 12 rectangular reinforced RPC beams with dimensions of (1500 200 150) mm were tested. The outcome demonstrated that increasing the longitudinal reinforcement ratio from =0.009 to =0.016 improved the ultimate capacity significantly by 34.16%, and 35.54% in cases of (T/M) =0, and 0.5 respectively, also it significantly improved moment-deflection response in the case of (T/M) = 1, and well improved torque-rotation response in cases of (T/M)=0.5, and 1. Increasing the transverse reinforcement ratio from = 0.0042 to =0.0075 improved the ultimate capacity significantly by 49.22% in case of pure torsion and slightly improved it in other cases. Also it significantly improved moment- deflection response in case of (T/M) = 1 and improved torque -rotation response in cases of (T/M)=1and ꝏ.

Behavior of large SCFST column with different confinement effects under pseudo-static loading

In this study, tests of twenty-four square concrete filled steel tubular (SCFST) columns with different structural sizes by the pseudo-static method were conducted to investigate the influence of the confinement effects. In addition, the structural size and the confinement effect are respectively represented by column width and width-to-thickness ratio. The experimental results, including the failure mode, the lateral load-displacement curves and the indices of the seismic performance were recorded and analyzed. The mode of failure is typical compressive flexure pattern. As the structural size increases or the confinement effect decreases, the nominal flexure strength of SCFST column decreases. Compared of the nominal flexural strength of small column, the influence of confinement effect is more significant on that of large column. The displacement ductility coefficient, the mean energy dissipation factor and the relative stiffness decrease with the increasing column width. Then enhanced confinement effect has no obvious influence on the displacement ductility coefficient of the SCFST column. When the confinement effect increases, the energy dissipation capacity of the SCFST column increases. Finally, the modified calculated method considering size effect is established, and this method is applicable to predict the bending moment of the SCFST column with different confinement effects and structural sizes.

Free vibration and buckling analysis of functionally graded beams using the DMCDM

In this paper, the Dual Mesh Control Domain Method (DMCDM) is used to carry out the free vibration and buckling analysis of two-constituent Functionally Graded Beams (FGBs) with through-thickness material variation. The material composition (modulus and density) is varied continuously through the beam thickness according to a power-law. The Euler-Bernoulli beam model consisting of the displacements and bending moment as the primary nodal degrees of freedom (i.e., mixed model) and the Timoshenko beam model with the displacement degrees of freedom (i.e., displacement model) are formulated as eigenvalue problems using the DMCDM. The numerical examples presented consider typical beam boundary conditions and various power-law exponents and slenderness ratios. The accuracy of this method is demonstrated by comparing the numerical results with those available in the literature.

Residual strength of a casing with corrosion semi-ellipsoid defect in high-sulfur gas wells

There are few studies on the residual strength of semi-ellipsoid defect casing considering the bending moment load in high sulfur gas well. In this paper, a numerical model of a casing with corrosion defects exposed to bending moment is proposed. The effect of the defect positions along the circumference on the residual strength of the casing with bending moment is investigated. Parametric studies highlight that defect size have significant effect on the residual strength of the casing, and the circumferential defect and the axial defect can change the critical internal pressure and the critical axial load. This finding has a significant guidance for residual intensity evaluation of a casing with defect.

Bivariate reliability analysis for floating wind turbines

Abstract Wind turbines are designed to withstand extreme wind- and wave-induced loads, hence a reliability study is vital. This study presents a bivariate reliability approach, suitable for accurate assessment of critical forces and moments, occurring within the wind turbine’s critical mechanical parts, such as the drivetrain. A ecently developed bivariate modified Weibull method has been utilized in this study. Multivariate statistical analysis is more appropriate than a univariate one, as it accounts for cross-correlations between different system components. This study employed a bivariate modified Weibull method to estimate extreme operational loads acting on a 10-mega watt (MW) semi-submersible type floating wind turbine (FWT). Longitudinal, bending, twisting, and cyclic loads being among typical load types that FWTs and associated parts are susceptible to. Furthermore, environmental loads acting on an operating FWT being impacted by incoming wind’s stochastic behavior in terms of wind speed, direction, shear, vorticity, necessitates accurate nonlinear extreme load analysis for FWT critical parts such as the drivetrain. Appropriate numerical methods were used in this study to model dynamic, structural, aerodynamic, and control aspects of the FWT system. Bending moments acting on the FWT drivetrain have been obtained from SIMPACK (Multibody Simulation Method), given realistic in-situ environmental conditions. For a 5-year return period of interest, a bivariate modified Weibull method offered robust assessment of FWT’s coupled drivetrain’s bending moments.

Collapse hybrid simulation for testing steel building columns subject to boundary condition changes

AbstractThis paper develops a hybrid simulation to experimentally evaluate the ultimate behavior of steel columns subject to boundary condition changes and bending moment redistribution due to the progressive seismic collapse of building structures. The proposed experimental method combines sub‐structuring test techniques and refined finite element (FE) analysis methods in a hybrid scheme. The inelastic behavior of steel moment‐resisting‐frames (MRF) is computationally simulated while ground‐floor columns are physically tested online with the FE frame analysis. Boundary conditions at the interface node between the column test and the frame analysis are reproduced with the aid of three actuators that impose axial loads and bending deformations to the column test. Two square tubular steel columns are tested as part of a five‐storey five‐bay steel MRF designed to employ two different heights of the ground floor (i.e., 4.6 and 5.1 m, respectively). The hybrid simulation revealed that individual failures of the peripherical frame members significantly alter the distribution of the bending moment along the height of the column test, thus changing the boundary conditions at its top end. The imposed moment distribution was further influenced by local buckling initiated at the base of the column test and ground‐floor beams and could cause the top end of the upper‐storey columns of the frame to buckle. In the MRF with 4.6 m‐height ground‐floor, this resulted in a global collapse mechanism that involved the ground floor and the second storey. In the MRF with 5.1 m‐height ground‐floor, a weak‐storey collapse mechanism was formed within the ground floor. Compared to a corresponding isolated column tested as cantilever using conventional methods, the columns tested with the proposed hybrid simulation exhibited a more favorable inelastic behavior primarily due to the more realistic loads and changes of boundary conditions which are ignored in conventional test methods.

Study on Numerical Simulation of Surrounding Rock Structure Safety of Urban Underwater Shield Tunnel: A Case in Chongqing

Based on the engineering background of shield construction of a subway section in Chongqing, which needs to pass through a park and there is a lake inside this park, this paper adopts theoretical analysis methods and numerical simulation calculation methods to explore the distribution law of the seepage field and the characteristics of water pressure in lining segments during shield tunneling. The results show that, during the whole excavation of a double-track tunnel with EPB shield, the maximum vertical effective stress is about 4.24 MPa, which is located at the arch foot of the tunnel. The maximum effective stress in the horizontal direction is about 3.61 MPa, which is located on both side walls of the tunnel in the horizontal direction; after the left and right tunnels are excavated in sequence, a “double precipitation funnel-shaped” pore pressure distribution is formed around the tunnel; during the construction of the shield tunnel, the vertical displacement and horizontal displacement of the surrounding rock show an increasing trend and gradually tend to be stable values of 24.09 mm and 25.28 mm; the segment vault has settlement, the maximum settlement is 21.8 mm, the arch bottom has uplift, and the maximum uplift is 24.4 mm. The maximum horizontal displacement of the segment appears on both sides of the arch waist, and the maximum horizontal displacement decreases with the increase of excavation steps; the positive bending moment of the lining segment is mainly distributed on both sides of the arch crown, and the negative bending moment is mainly distributed on both sides of the arch bottom. The axial force of the lining segment is compressive stress, and the maximum axial force is mainly distributed on both sides of the arch waist. The maximum normal shear stress occurs on both sides of the segment arch bottom. The study conclusions provide theoretical foundation and a new guidance for long-term safety evaluation of underwater tunnel structures.

SEISMIC BEHAVIOR OF MULTI-STORIED RC BUILDING WITH RE-ENTRANT CORNER

Nowadays, buildings often feature irregular floor plans for functional, aesthetic, or economic reasons. Constructing earthquake-resistant structures in seismic areas, especially with irregular shapes like re-entrant corners, poses challenges. Such corners are common when maximizing limited space is a priority. In earthquakes, re-entrant corners in structures pose major vulnerabilities, causing stress concentration and torsion problems. The main aim of this paper is to develop finite element structural analysis models of 10, 12, and 15-storied L-shaped RC buildings with a re-entrant corner under different seismic zones using equivalent static analysis (ESA) and response spectrum analysis (RSA). This research also focuses on the overall behavior of analysis results (story drift, overturning moment, base shear, etc.) with the influence of re-entrant corner. It also investigates the performance of columns and beams near re-entrant corners as the number of stories increases in different seismic zones. For the current study, ETABS V19 is used. Models consider seismic, dead, and live loads. The Bangladesh National Building Code (BNBC) 2020 is used to examine the equivalent static analysis (ESA) and the response spectrum analysis (RSA) methods. It has been concluded from the study that re-entrant corner beams consistently exhibit the highest bending moments and torsion levels across all seismic zones. Similarly, re-entrant corner columns consistently demand the most axial force and rebar when compared to similar column types. Furthermore, the study identifies maximum stress levels in re-entrant corner slabs across all seismic zones.

Timber-concrete composites (TCC) floors subjected to hogging moment

In this paper, the structural behaviour of timber precast concrete composite (TCC) beam-to-column subassemblies subjected to hogging bending moments is investigated. Full-scale testing and analytical modelling are undertaken on timber precast concrete composite joints and beams. The composite actions were transferred via coach (lag) screw shear connectors embedded in the small grout pockets. The laboratory tests were designed to determine the influence of the size and type of timber beams (i.e., laminated veneer lumber (LVL) or glued laminated timber (GLT)), size of screw shear connectors and amount of reinforcement (in the slabs) on the structural behaviour (i.e., load-displacement, stiffness, capacity, and ductility) of the TCC beam-to-column connections. The hogging moment capacity and stiffness of the TCC floors with nominal slab thickness of 80 mm and reinforcing ratio (in the range of 0.9–1.8%) were up to 24% and 17% higher than that of the bare timber beam, respectively. The size of coach screw shear connectors (in the range of 8–16 mm) had less than 13% effect on the capacity and stiffness. An analytical model for calculating the peak load and stiffness of the TCC beams under hogging bending moment is developed. The model is shown to perform well when compared to the collected test data.

Investigation on the mechanical behavior of prestressed glulam bolted joints under combined moment and axial force

Among the different methods of strengthening glulam bolted joints, the reinforcement method that utilizes steel straps offers the advantages of low cost, convenient installation and satisfactory reinforcing effect. This research presents the results of a series of tests on glulam bolted joints with prestressed steel straps under combined bending moment and axial force, including a theoretical derivation of moment-rotation curves. The findings indicated that the existence of steel straps led to a delay in glulam splitting with a pronounced increase in bearing capacity compared with ordinary glulam bolted joints, i.e. by 46.85 %, 63.17 %, and 53.65 %, respectively. A three-line moment-rotation model was established to predict its mechanical behavior. This research provides valuable insights for the reinforcement of glulam connections under combined load and serves as a reference for future research in this field.

Investigating the effectiveness of CFRP strengthening in improving the impact performance of RC members

Rising global rail infrastructure expansion has increased accidents involving train derailments. Reinforced concrete (RC) elements require impact-resistance enhancement to prevent structural damage or failure. While extensive research has analyzed CFRP-strengthened concrete columns under dynamic loading, further understanding of CFRP's impact on RC members is needed. Considering dynamic factors, this study investigates CFRP-RC components' performance under asymmetric impact. Components wrapped in one, four, or six CFRP layers underwent high-energy asymmetric lateral impact testing to obtain deflection-time curves. Results showed that multiple CFRP layers significantly improved impact resistance by increasing plateau force, reducing maximum deflection to 42%, and shortening duration. Longitudinal-circumferential bonding conferred better reinforcement than other arrangements. However, multiple CFRP layers increased fracture susceptibility due to severe concrete damage. An equation was derived from dynamic equilibrium principles. Finite element modeling validated experimentally was used to simulate lateral impact. Impact force, deflection, and bending moment over time were compared. Impact resistance, flexural capacity, plastic deformation, and energy absorption were also examined. Internal force distribution and development were analyzed. A simplified calculation estimated maximum deflection. CFRP reinforcement methods' effects were examined. Results indicate CFRP elevates plateau impact force and average bending moment while significantly decreasing deflection and duration, greatly enhancing impact resistance and flexural bearing capacity.

Flexural behavior of high-strength RCFST column-to-column connections

This paper investigates the flexural behavior of high-strength rectangular concrete-filled steel tubular (RCFST) column-to-column connections with different configurations. Based on the tests, 35 additional finite element analysis (FEA) models were developed to perform the parametric analysis varying with the cross-sectional size effect of (D), the width-to-thickness ratio of steel tube (D/t), steel tube strength (fs,y), steel bars strength (fr,y), concrete strength (fc,r), length of steel bars (L), arrangement and quantity of steel bars, respectively. The current code underestimated the yield and plastic bending moment compared with the calculated results from GB 50010–2010, ACI 318–19, EN 1992–1-1:2004, and JSCE-SSCS-2007. Finally, the strain coordination method and the full plastic section method were proposed to calculate the yield and plastic bending moment of the connection.

A Theoretical Calculation Model of H-Section Steel Members for Biaxial Bending Moments

A Theoretical Calculation Model of H-Section Steel Members for Biaxial Bending Moments

Full-scale experimental and structural characterization study of shield tunnel reinforcement under ground stacking loads

To investigate the internal force response characteristics and reinforcement effects of the shield tunnel segment structure in the presence of ground load disturbances in the Hangzhou Metro, full-scale tests were conducted on three-ring misaligned assembled segments using a self-developed "Shield Tunnel Segment Hydraulic Loading System." The study examined the structural characteristics of tunnel segments under the influence of different ground resistance coefficients (λ) and eccentric loads (P), and explored the reinforcement effects of the internal tension ring method from multiple perspectives. The research results indicate that under different ground resistance coefficients (λ), the sensitivity of internal force response is concentrated in the waist concrete, with a maximum bending moment reduction of 88.8%. The effective rate of bending stiffness tends to flatten, joint bending moment transfer effects strengthen, and the bearing capacity of the segments significantly increases after reinforcement, leading to a more uniform overall structural response. Under different eccentric loads (P), the bending moment of the segments after reinforcement approximates central symmetry with a reduced distribution range. The rate of change of the effective bending stiffness (η) shifts from "rapid" to "slow," and the variation of joint bending moment transfer coefficient (ζ) stabilizes. The reinforcement with steel rings significantly enhances the overall stiffness of the segments and reinforces the joint bending moment transfer effect. The reinforcement effect of the segments can be evaluated through the bending moment transfer coefficient and effective bending stiffness. After reinforcement, the bearing capacity of the segments is noticeably enhanced, and significant forces are observed at two locations in the right waist joint, where the combination of steel plates and segments exhibits optimal performance.

Evaluation of True Bonding Strength for Adhesive Bonded Carbon Fiber-Reinforced Plastics.

Carbon fiber-reinforced thermoplastics (CFRTPs) have attracted attention in aerospace because of their superior specific strength and stiffness. It can be assembled by adhesive bonding; however, the existing evaluation of bonding strength is inadequate. For example, in a single-lap shear test, the weld zone fails in a combined stress state because of the bending moment. Therefore, the strength obtained experimentally is only the apparent strength. The true bonding strength was obtained via numerical analysis by outputting the local stress state at the initiation point of failure. In this study, the apparent and true bonding strengths were compared with respect to three types of strength evaluation tests to comprehensively evaluate bonding strength. Consequently, the single-lap shear test underestimates the apparent bonding strength by less than 14% of the true bonding strength. This indicates that care should be taken when determining the adhesion properties for use in numerical analyses based on experimental results. We also discussed the thickness dependence of the adhesive on the stress state and found that the developed shear test by compression reduced the discrepancy between apparent and true strength compared with the single-lap shear test and reduced the thickness dependence compared with the flatwise tensile test.

Study on the Strength of the Brake Pad of a Freight Wagon under Uneven Loading in Operation.

The paper highlights the results of determining the strength of the brake pad of a freight wagon under uneven loading in operation. The main reasons for the uneven loading on the pad have been found. A mathematical tool for determining the strength of the pad unevenly loaded has been proposed. In the study, the pad is considered to be a rod system loaded with concentrated forces and bending moments. Sensors have been used in order to detect the load state of the brake pads. These sensors have been defined in the simulation software, and they have been placed on the working surface of the pad in the area of its interaction with the wheel. The operation of these sensors was simulated in the simulation software package. The results of the calculation have shown that the stresses in the pad are about 21.1 MPa; thus, they exceed the permissible values by 29%. Therefore, considering the uneven loading of the pad in operation, the strength of the pad is not ensured. To test the obtained results, the strength of the pad was determined using the finite element method. The Coulomb criterion was used for the calculation. It was found that the maximum stresses in the pad were about 19 MPa. These stresses were 21% higher than permissible values and occurred in the back of the pad. The study has proven that the uneven loading on the brake pad in operation can cause their destruction during braking. This may also cause traffic accidents with freight trains during their movement. The results of this study will contribute to the theoretical developments and recommendations aimed at improving the brake system of a freight wagon and rail traffic safety. It is considered that the tensometric sensors will be applied in future experimental tests for comparison and verification of the achieved results from the simulation computations.

Predictive model for fatigue evaluation of floating wind turbines validated with experimental data

Estimating internal forces and corresponding fatigue damage plays a central role in the definition of operation strategies of any wind turbine, particularly in offshore scenarios. Although strain gauges can be installed to monitor the internal forces at a particular section, it is not feasible to instrument a full wind farm, and new methods are needed that allow to eliminate, or significantly reduce, this type of installation. This paper presents a new physics motivated methodology that incorporates tower top accelerations, available in the monitoring systems of most modern wind turbines, to estimate the tower bending moments and fatigue life consumption, replacing more common data driven approaches based on environmental conditions and/or operation variables by analytical considerations. The expressions derived are validated by numerical simulations, and then applied to experimental data collected at a full scale floating wind turbine, with results systematically better when compared with a data driven approach, often applied in onshore wind turbines. By using a quite rare database, collected in one of the first utility-scale worldwide floating wind turbines, this method presents itself as one of the first data processing methodologies developed explicitly for floating wind turbines, while setting a theoretical background for future developments of monitoring strategies.

Study on the dynamic construction mechanics of side piles in metro station using the pile-beam-arch method

Based on the Tianhe East Station in Guangzhou Metro Line 11 engineering, this paper analyzes the formation mechanism of soil arching effect (SAE) of station by pile-beam-arch (PBA) method in the excavation process and studies the mechanics and deformation laws of side piles in different construction stages under different pile spacing conditions. The results show that the formation, development and destruction of SAE between piles are closely related to construction process. Both too large and too small pile spacings are not conducive to the development about SAE between piles; when it is located between them, the SAE between piles exerts greatly. In the form of composite lining system, supporting piles as well as SAE between piles play an effective role in supporting soil behind piles. The lateral deformation of pile body is most significant in the completion of buckle arch to the excavation of first soil layer, which is the critical construction phase to reduce lateral deformation of side pile. The axial forces of side pile increase gradually with the excavation of station, and the change is the most drastic at the excavation for first soil layer. The influence of pile spacing on vertical settlement and axial force of side piles is much greater than that of horizontal displacement and bending moment.

Determination of Optimal Cross-Section Dimensions of Rectangular Hollow Sections Under Oblique Bending: Analytical and Numerical Study.

An insignificant number of rigorous studies have been devoted to the development of analytical procedures that determine the optimal cross-section dimensions of rectangular hollow section (RHS) members subjected to oblique bending, albeit their ubiquity in numerous application fields. In response to this, an analytical procedure has been developed based on the concept of minimizing maximum effective stress in the RHS caused by an applied oblique bending moment, in order to reduce material costs without compromising strength requirements. The RHS members addressed in this study have been assumed to be produced by hollowing out rectangular solid sections at different cross-section area extraction ratios; therefore, only the wall thicknesses of the RHS members have been taken into consideration as design variables. The minimization of maximum effective stress has been achieved by establishing a functional correlation between the cross-section design variables. The proposed procedure allows specifying the optimal cross-sectional dimensions for given different cross-section area extraction ratios and bringing cost-effective use of materials. After the subtle mathematical calculations, the derived analytical expressions have been made available to practical engineering in simple math forms for use in real design applications. The analytical procedure has been validated against numerical results which have been extracted from finite element analyses carried out in Abaqus engineering software.

Study on mechanical characteristics of pipe umbrella support in shallow buried tunnels

Considering the micro-arching effect between pipe umbrella, the paper investigates the mechanical response of pipe umbrellas during tunnel excavation by simulating pipe umbrellas as Timoshenko beams on a Pasternak foundation. The finite difference method is employed to solve the deflection, bending moment, and shear force of pipe umbrellas. By analyzing and contrasting with real-world engineering monitoring data, finite element computation results, and existing theories of other researchers, the reliability of the proposed method is verified, and good agreements are observed. A new parameter δp is introduced in our method to represent the proportion of overlying load transmitted through the pipe umbrella, and influences of stiffness of the surrounding rock in front of the tunnel face, initial support stiffness, pipe umbrella design schemes, and excavation depth on the load transfer capacity of the pipe umbrella are subsequently investigated. The conclusions reveal that increases of surrounding rock stiffness, initial support stiffness, and diameter of pipe umbrellas would all enhance the stability of both the tunnel and pipe umbrellas. However, such enhancements have certain limitations. Particularly, when the excavation footage c <1 m, the pipe umbrella diameter should be specifically selected based on cases.