Bending Moment Distribution Research Articles

Seismic response of micropiles-reinforced landslide based on shaking table test

A series of shaking table tests were conducted on unreinforced and micropiles-reinforced soil landslides to investigate the seismic response of micropiles-reinforced landslide and the dynamic mechanical behaviour of micropiles in landslide under earthquake. The test results indicate that: (1) The micropiles can raise the anti-seismic performance of landslide, and it can efficiently delay the development of earthquake landslide hazards. (2) After earthquake, the flexural failure of micropile mainly occurs in the area that 1.4–4 times pile diameter above the sliding surface and the area that 1.4–3.4 times pile diameter below the sliding surface. (3) After reinforced by micropiles, the acceleration response on the slope surface of landslide can be decreased, especially the slope toe. (4) Both thrust of sliding mass and resistance of sliding bed are mainly concentrated near the sliding surface. The dynamic bending moment distributions of the three rows of micropiles present as reverse ‘S’. The maximum bending moment of the pile above sliding surface is located at the point that 3.7 times pile diameter above sliding surface, and the maximum bending moment of the pile below sliding surface is located to the point that 1.43 times pile diameter below sliding surface.

Non-constant biaxial bending capacity assessment of CFST columns through interaction diagrams

The mechanical response of concrete-filled steel tubular (CFST) columns subjected to pure compression or uniaxial bending was studied in depth over the last decades. However, the available research results on CFST columns under biaxial bending are still scarce and the lack of experimental tests for this loading situation is evident. At the same time, the design provisions in Eurocode 4 Part 1.1 for verifying the stability of CFST columns under biaxial bending make use of a simplistic interaction curve, which needs to be revised. This paper presents the outcome of a numerical investigation on slender CFST columns subjected to biaxial bending. Eccentricities differing in minor and major axis, as well as varying end moment ratios are considered in the numerical model. A parametric study is conducted for assessing the current design guidelines of EN1994-1-1. Different aspect ratios, member slenderness, reinforcement ratios and load eccentricities are studied, covering both constant and variable bending moment distribution. The numerical results are subsequently compared to the design provisions of EN1994-1-1, showing that the current interaction equation results overly conservative. An alternative interaction equation is developed by the authors, leading to a more accurate yet conservative proposal.

Comparison of beam-column resistance according to European Standards

Abstract When designing slender steel beam-columns, verification of their resistance have to satisfy design criterions according to approaches given in EN 1993-1-1. Torsten Hoglund (2014) also presented proposal for verification of beam-column resistance, which is based on design approach accepted in EN 1999-1-1, together with comparisons between these two standards on simply supported members subjected to compressive force and constant or linearly distributed bending moment. In this paper, further comparisons between these two approaches with different end conditions and different distribution of internal forces are presented.

Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

Abstract The article presents the analysis of complex stress states in the concrete structure of grain silos, caused by non-centric emptying. The authors present a combination of loads from the pressure of bulk solid on the silo chamber according to Eurocode 1, Part 4 [11], which should be taken into account when emptying on large eccentricities in action assessment class 3 (AAC3) silos. For the example of a cylindrical wheat silo with a height of 25 m and a diameter of 10 m, the researchers carried out an analysis regarding the impact of the size of the eccentric discharge outlet on the distributions of forces and bending moments in a reinforced concrete wall.

Stability and Resistance of Steel Continuous Beams with Thin-Walled Box Sections

AbstractThe issues of local stability and ultimate resistance of a continuous beam with thin-walled box section (Class 4) were reduced to the analysis of the local buckling of bilaterally elastically restrained internal plate of the compression flange at longitudinal stress variation. Critical stress of the local buckling was determined using the so-called Critical Plate Method (CPM). In the method, the effect of the elastic restraint of the component walls of the bar section and the effect of longitudinal stress variation that results from varying distribution of bending moments were taken into account. On that basis, appropriate effective characteristics of reliable sections were determined. Additionally, ultimate resistances of those sections were estimated. The impact of longitudinal stress variation and of the degree of elastic restraint of longitudinal edges on, respectively, the local buckling of compression flanges in the span section (p) and support section (s) was analysed. The influence of the span length of the continuous beam and of the relative plate slenderness of the compression flange on the critical ultimate resistance of box sections was examined.

Torque and bending moment acting on a flexible shaft agitated by disk turbines in a gas–liquid stirred vessel

Abstract The torque and bending moment acting on a flexible overhung shaft in a gas–liquid stirred vessel agitated by a Rushton turbine and three different curved-blade disk turbines (half circular blades disk turbine, half elliptical blades disk turbine, and parabolic blades disk turbine) were experimentally measured by a customized moment sensor. The results show that the amplitude distribution of torque can be fitted by a symmetric bimodal distribution for disk turbines, and generally the distribution is more dispersive as the blade curvature or the gas flow rate increases. The amplitude distribution of shaft bending moment can be fitted by an asymmetric Weibull distribution for disk turbines. The relative shaft bending moment manifests a “rising-falling-rising” trend over the gas flow number, which is a corporate contribution of the unstable gas–liquid flow around the impeller, the gas cavities behind the blades, and the direct impact of gas on the impeller. And the “falling” stage is greater and lasts wider over the gas flow number for Rushton turbine than for the curved-blade disk turbines.

Analysis of the temperature effect on concrete crosstie flexural behavior

The manner in which temperature affects concrete components or structures has been studied extensively for many applications, such as pavements, bridges, and frames. However, little attention has been given to the temperature effects on concrete railroad crossties. Recent research at the University of Illinois at Urbana-Champaign revealed the relationship between temperature gradient and curling on freight railroad concrete crossties, which showed that temperature gradient could change the support conditions of the crossties, affecting their flexural performance. This paper presents the results from an extensive field study of temperature effects on the flexural behavior of rail transit concrete crossties, part of a larger research program aimed at designing more efficient and resilient concrete crossties for rail transit applications. Field instrumentation was installed on light, heavy, and commuter rail systems to monitor temperature variation and corresponding concrete crosstie flexural behavior for up to 10 months at each location. A linear relationship between the temperature in the crosstie and the ambient temperature is observed. Additionally, the bending moment distribution under revenue service loading conditions is found to be directly affected by the temperature gradient between top and bottom of the crosstie. This effect is believed to be a consequence of the variation in the support condition due to curling, and is thought to be independent of the crosstie design or loading environment. A linear correlation between the temperature gradient variation in the crosstie and the flexural behavior of the crosstie is observed. A maximum difference of 38 kip-in (4.29 kN-m) for the center negative bending moment of the concrete crosstie was found due to a change in the temperature gradient from −10 °F (−5.6 °C) to 37 °F (20.6 °C), which represents 21% of the design capacity. Based on the analysis of field observations, a correction factor of 1 kip-in/°F (0.203 kN-m/°C) is recommended to account for the temperature gradient as a design variable for future rail transit concrete crossties.

Sensitivity analysis of hull girder reliability in intact condition based on different load combination methods

The paper focuses on hull girder reliability and sensitivity analysis of an oil tanker and a bulk carrier in intact condition. After a brief review of the theoretical background concerning the reliability analysis, Turkstra rule, Ferry-Borges and Castanheta, Moan and Jiao load models are applied and compared to investigate the incidence on hull girder reliability of different load combination methods for ships in full load (sagging) and ballast load (hogging) conditions. Subsequently, sensitivity analysis is carried out to investigate the incidence on the hull girder failure probability of the main parameters affecting the still-water and vertical wave bending moment stochastic processes, namely the maximum still-water bending moment reported in the loading manual, the ship voyage duration, the shape parameter of the long-term Weibull distribution of vertical wave bending moment and the mean wave period. Two reference ships, namely the ISSC oil tanker and bulk carrier, are assumed as test case for reliability and sensitivity analysis, that are performed by Monte Carlo simulation based on a dedicated programme developed in Matlab MathWorks. Obtained results are discussed and some suggestions are provided to improve the effectiveness of reliability analysis.

Behavior and design considerations of steel plate shear wall with self-centering energy dissipation braces

An innovative steel plate shear wall with self-centering energy dissipation braces (SPSW-SCEDB) is proposed, and the mechanical behavior is explained. The system has excellent self-centering capability when the remaining restoring force of the braces is greater than or equal to the compressive force of the wall plate. On the basis of capacity design principles, the distribution equations of bending moment, axial force, and shear force along the beam are developed and then verified by cyclic loading analysis. The effects of the SPSW–SCEDB parameters on the bending moment distribution are investigated using an orthogonal experiment and the sequence of plastic hinge appearance in the beam is also analyzed. Results indicate that to satisfy the strength and residual deformation requirements of the system, the initial force of the brace and the thickness of the wall plate should be sufficiently large, and the brace activation force should be controlled to ensure that the plastic hinge in the beam appears before the in-span plastic hinge. The design procedure of the SPSW-SCEDB is presented.

Dynamic Stress Analysis of a Composite Electromagnetic Track

The firing of an electromagnetic gun is shown to result in the armature moving along the guide rail, which can cause extrusion, wear, planing and other problems, which set limits on its application. The track properties can be adjusted by changing its composition, so as to obtain good electrical conductivity, corrosive resistance, and strength. For simplicity, the composite track is presented as an elastic foundation beam, and the general solution of composite track deflection at dynamic load is obtained by using the two-dimensional Fourier integral transformation, on this basis, the bending moment distribution and expression for dynamic stress are obtained. The characteristics of dynamic stress distribution and factors that influence them are analyzed, the effect of the proportion of the composite layer and its parameters on the dynamic stress of the track is discussed.

A simplified procedure for estimating nonlinear seismic demand of tall piers

More than 40% of the bridges in mountainous areas of Southwest China are constructed with piers having a height of over 40 m. The seismic response of such tall pier structures is usually estimated by nonlinear response history analysis and/or adaptive pushover procedures; while providing satisfactory results, these methods can be quite time consuming and computational demanding. Therefore, this paper proposes a simplified procedure for estimating the nonlinear seismic response of tall piers. The influence of plastic deformation at the base on dynamic properties (natural periods and mode shapes) of a linearized system for the tall piers is first investigated, using a numerical model of the prototype bridge, based on an equivalent linearization technique. Using these results, a simplified procedure is proposed to predict the distribution of seismic shear force and bending moment along the pier height, as well as the curvature ductility ratio at the pier base. The efficiency of the proposed procedure is verified with numerical examples of tall piers subjected to recorded ground motions, through comparing the seismic demands determined by this method with rigorous nonlinear response history analysis. The results show that the proposed method can efficiently estimate the distribution of both shear force and bending moment along the height of the tall pier; the curvature ductility ratio at pier base can be predicted with errors around 10%.

Prototype Loading Tests on Full-Ring Segmental Lining of Rectangular Shield Tunnel

A series of full-scale loading tests are performed for a prospective subway tunnel with a rectangular shape including two reliability tests: one stagger-jointed three-ring reliability test, and one ultimate failure test on a single ring. Comprehensive measuring programs are designed to record the deformation of both lining structure and joints and the stresses of concrete, bolts and reinforcements. Experimental results show that in both the single-ring and three-ring loading cases, the long sides of tunnel cross section bend inwards while the short sides of tunnel cross section bend outwards. The inner part of joints opens while the outer part of joints closes at places experiencing positive moment and vice versa. Joint’s rotational stiffness varies at different locations. Concrete cracking and crushing are the chief damage modes, and they are closely related to the distribution of bending moment. Stagger-jointed fabrication significantly increases the overall rigidity of lining system, which thereby greatly reduces the deformation of both concrete lining and joints in comparison with the single-ring case. It is shown that the routinely-used uniform rigidity model is conservative and the preliminary design can be optimized by applying an effective rigidity ratio (ERR) of 0.5.

Dynamic Response Evaluation of Long-Span Reinforced Arch Bridges Subjected to Near- and Far-Field Ground Motions

This study assessed the structural performance of reinforced concrete (RC) arch bridges under strong ground motion. A detailed three-dimensional finite element model of a 400 m RC arch bridge with composite superstructure and double RC piers was developed and its behavior when subjected to strong earthquakes examined. Two sets of ground motion records were applied to simulate pulse-type near- and far-field motions. The inelastic behavior of the concrete elements was then evaluated via a seismic time history analysis. The concept of Demand to Capacity Ratios (DCR) was utilized to produce an initial estimate of the dynamic performance of the structure, emphasizing the importance of capacity distribution of force and bending moment within the RC arch and the springings and piers of the bridge. The results showed that the earthquake loads, broadly categorized as near- and far-field earthquake loads, changed a number of the bridge’s characteristics and hence its structural performance.

Structural Characteristics of Composite Mortars and their Evolution with PET Substitution Level for Several Specimens’ Ages

This present study aims to investigate the evolution of structural response of PET-Mortar composite test with a short-beam specimen in three-point bending tests, with composite mortar ages and volumetric polymer rate and this, based on compression strength tests. The ultimate PET-mortar composite structural responses are calculated at the mid span of the short-beam by the mean of mechanics-of-materials theory basis. According to this theory, the distribution of bending moments and shear forces at any point of the composite short-beam specimen doesn’t depend on material mechanical properties especially the young modulus of modified mortar composite; so, the structural response analysis has been limited to investigate the evolution of ultimate deflection with several volumetric PET rates and composite mortar ages. In the other hand, we present a comparative study between experimental test results of splitting tensile and compressive strengths with the ones predicted by codale previsions (ACI-363 and B.S) codes in terms of PET mortar ages and volumetric PET rates in order to recommend the most suitable design code for PET-mortar composite applications in construction industries.

A comprehensive study on composite risers: Material solution, local end fitting design and global response

Two up-to-date composite riser solutions, specifically, the thermoset and thermoplastic based ones are studied in a global-local framework to examine their technical feasibility for offshore applications. At the local scale, the riser pipe body with multi-layered structure is homogenized through an analytical approach, obtaining equivalent material properties of the riser string model for the global analysis. The metal-composite interface (MCI) end fittings between the riser body and standard connector are examined using finite element (FE) simulations to understand their load-transfer mechanisms for both solutions. At the global scale, an in-house analysis code is performed to study the risers' static and dynamic response in a certain sea condition due to top-tension, current drag and vortex induced vibration (VIV). The analyzed parameters include the resulting riser deflection, axial stress, tension and bending moment distributions. Following that, an integrated analysis utilizing the global results and the local failure envelopes is performed to determine if the maximum stress states of the riser exceed the equivalent structural strength boundary. It is concluded that composite risers exhibit a larger safety margin than traditional steel riser under the same sea condition.

Cyclic Experimental Behavior of CFST Column to Steel Beam Frames with Blind Bolted Connections

This paper aims to investigate the seismic behavior of blind bolted end plate composite frames between square or circular concrete filled steel tubular (CFST) columns and steel beams. Two composite frames were tested under a constant axial load on the CFST columns and a lateral cyclic load on the frame. Each specimen composed of CFST columns and steel beams was selected to represent a plan frame in an assembly building. Failure pattern of the type of frames was analyzed to comprehend the structural response. The seismic resistance ability of the blind bolted CFST frames was also estimated in terms of hysteretic curves, ductility and energy dissipation etc. The effect of column section type and end plate type on the type of semi-rigid CFST frames was studied. The test results showed that at the same steel ratio of the column section, the bearing capacity and energy dissipation of square CFST frame were higher than those of circular CFST frame at ultimate state. Strain response of main members in each CFST frame was also estimated. The internal force analysis of the test CFST frames with semi-rigid connections was discussed and evaluated the effect of the bending moment distribution. It was concluded that the novel typed CFST frames exhibited excellent seismic performance and structural internal force redistribution. The experimental studies will be useful for design and application of the blind bolted CFST frames in fabricated steel structure building.

Optimization of Structural Performance of the Toroidal Field Coil System of a Tokamak

The toroidal field (TF) coils of a tokamak are subjected to very high operational electromagnetic loads. The shape of a TF coil plays an important role for structural performance since an arbitrary shape is subjected to considerable bending. To mitigate this issue, the TF coils were designed with special “bending free” (constant tension) shapes derived analytically using a thin filament approximation. However, this approximation ignores the stiffnesses of the TF coil case, the central support, and the intercoil structures. This issue was pointed out by other authors and is studied in this paper using FEA. Based on the 2015 EU DEMO baseline design, a finite element model of a constant tension “Princeton D” TF coil was developed. Electromagnetic and structural modeling of the initial and the developed designs were conducted and the in-plane bending in the windings was analyzed. It was shown that a coil case can significantly change the bending moment distribution in the winding pack and even introduce additional bending to a “bending free” shape. On the other hand, such a shape imposes additional constraints on the magnet system design making the usage of these shapes questionable. An alternative strategy of TF coil case reinforcement is discussed.

Kantorovich variational method for the flexural analysis of CSCS Kirchhoff-Love plates

The Kantorovich variational method was used in this study to solve the flexural problem of Kirchhoff-Love plates with two opposite edges x=±a/2 clamped and the other two edges y=±b/2 simply supported, for the case of uniformly distributed transverse load over the entire plate domain. The plate considered was assumed homogeneous, and isotropic. The total potential energy functional for the Kirchhoff-Love plate was found as the sum of the potential energy of the applied distributed load and the strain energy functional of the plate. The symmetrical nature of the plate and the load was used to choose the deflection function as a single series of infinite terms involving the cosine function of the y coordinate variable with the unknown function being dependent on the x coordinate variable. Integration with respect to the y coordinate variable simplified the total potential energy functional to be dependent on the unknown function of x, and its derivatives. Euler-Lagrange differential equations were used to find the differential equations of equilibrium of the plate as a system of homogeneous fourth order ordinary differential equations (ODE) in the unknown function. The system of fourth order ODE was solved using the method of differential D operators, or the method of trial functions to obtain the general solution as the linear superposition of the homogeneous and particular solutions. The demands of symmetry of unknown function about the point x= 0, and the boundary conditions at the clamped edges were used to obtain all the four integration constants; thus, completely determining the deflection. Bending moment distributions were determined using the bending moment deflection relations. The deflection was determined at the centre of the plate. The bending moment values were also determined at the centre of the plate, and at the middle of the clamped edges. Expressions obtained for the deflection at the centre, and bending moment values were found to be single series of infinite terms with highly converging properties. The solutions obtained converged to the exact solutions with the use of only four terms of the series.

Design and Analysis of Wind Turbine Rotors Using Hinged Structures and Rods

Light weight and high stiffness are key design factors in ensuring cost effectiveness and reliability of wind turbines, especially for the inboard region of the rotor blades. In this study, several novel designs were developed to improve the mechanical performance of the rotor. Experiments were performed on an isolated blade incorporating the new features of a hinged structure and rods. The results validated the effectiveness of these features at alleviating the root-bending moment of the blade under varying wind loads and enhancing the stiffness of the blade. A numerical investigation was carried out to further examine the bending moment distribution, shear and axial force, and rod tension of these novel rotor designs under uniform loads. Longitudinal geometrical variations of the blade were considered in the model. Results showed that two designs realized a favorable bending moment distribution and improved the modal frequencies of the edgewise modes: bisymmetrical rods on a single-hinged structure and interveined symmetrical rods on a cantilevered structure. However, these designs have different deformation mechanisms. In addition, the first group of edgewise modal frequencies of these two designs were improved compared with the traditional rotor design. Their potential values in the application to the design of a lightweight, high-stiffness, and reliable wind turbine rotor were discussed.

Joint excitation synchronization characteristics of fatigue test for offshore wind turbine blade

In the case of the stiffness of offshore wind turbine blade is relatively large, the joint excitation device solves the problem of low accuracy of bending moment distribution, insufficient driving ability and long fatigue test period in single-point loading. In order to study the synchronous characteristics of joint excitation system, avoid blade vibration disturbance. First, on the base of a Lagrange equation, a mathematical model of combined excitation is formulated, and a numerical analysis of vibration synchronization is performed. Then, the model is constructed via MATLAB/Simulink, and the effect of the phase difference on the vibration synchronization characteristics is obtained visually. Finally, a set of joint excitation platform for the fatigue test of offshore wind turbine blades are built. The parameter measurement scheme is given and the correctness of the joint excitation synchronization in the simulation model is verified. The results show that when the rotational speed difference is 2 r/min, 30 r/min, the phase difference is 0, π/20, π/8 and π/4, as the rotational speed difference and the phase difference increase, the time required for the blade to reach a steady state is longer. When the phase difference is too large, the electromechanical coupling can no longer make the joint excitation device appear self-synchronizing phenomenon, so that the value of the phase difference develops toward a fixed value (not equal to 0), and the blade vibration disorder is serious, at this time, the effect of electromechanical coupling must be eliminated. The research results provide theoretical basis for the subsequent decoupling control algorithm and synchronization control strategy, and have good application value.