Equivalent Bending Moment Research Articles

Bending deformation behavior and characterization method of flexural stiffness of composite tubes under four-point bending tests

The four-point bending test has inherent errors in measuring the flexural stiffness of tubes. The size of loading noses/supports could affect the response of equivalent bending moment on the tested tubes’ transverse section. The asymmetric axial strain distribution on the tested tubes’ transverse section depends on the tube’s thickness to diameter ratio. Based on the above phenomena, a four-point bending test with small-sized loading noses/supports and a characterization formula of tube’s flexural stiffness were proposed. The proposed methods were conducted on a thin-walled steel tube and a composite tube respectively. The errors between theoretical and experimental results were discussed.

A method for rapid estimation of residual stresses in metal samples produced by additive manufacturing

The mechanical methods for measuring residual stresses typically rely on so-called destructive techniques where some stress components can be determined based on part deflection after material removal (cutting, etching, drilling, etc.). While these methods don't provide a comprehensive representation of residual stresses within the entire part, they can be readily applied in most manufacturing labs. In this study, we propose an efficient method for determining residual stress within additively manufactured cylindrical samples of stainless steel. The method is based on the assumption of a relation between the axial component of residual stress (normal to cross-section) and the cylinder radius. The general form of this relation is proposed based on data from numerical simulations using linear, parabolic or piecewise approximations. The parameters for the proposed relation are defined using equilibrium equations for total force and moment. The proposed method relies on an experiment with a mechanical cut along the cylinder. Consequently, the deflection of the cylinder halves after the cut allows for obtaining the equivalent bending moment.

Root cause analysis of flywheel gear failure in a marine diesel engine

Engine gear failures are of significant concern across a wide range of industries. It is important to investigate each gear failure in light of its unique loading and operating conditions for root cause analysis (RCA) and further corrective actions to avoid such failures in the future. The aim of this study was to investigate the premature failure of a flywheel gear of a marine diesel engine and establish the root cause and damage mechanisms using experimental and numerical analysis techniques. A bottom-up creative approach was adopted to assess the loading conditions on the failed gear by first estimating the bending deformation of the failed securing bolt, assuming overload torque on the flywheel caused an equivalent bending moment permanently bending the bolt. Von Mises equivalent stress acting on the gear was numerically estimated as σVM = 737 MPa, which was found significantly more than the specified yield strength of gear governing material AISI 1055 (σY = 550 MPa). SEM fractography revealed a quasi-cleavage failure mechanism in the ‘case’ region near the gear root and a ductile failure mechanism inside the ‘core’ region of the flywheel gear. A crack was found to initiate from the gear root consisting of high-stress concentration under overload stresses. RCA established that the flywheel gears had failed by overload stresses, caused due to overload torque generated from sudden inertial thrust in the internal combustion (IC) engine due to excess fuel throttle opening.

Stress Classification Lines for Non-Standard Y-Tee Design in Piping System

All processes fluids in the oil and gas industry are generally transferred from one point to another via complex piping networks. The process temperature and the pressure of the fluids may vary between -21 °C to 816 °C and from atmospheric, 1.013 barg to 431 barg, respectively. Under these conditions, the entire piping networks are exposed to thermal expansion and contraction resulting in mechanical bending, potentially causing mechanical failures. The most common pipe fitting used in piping networks to divide the fluid flow into two different directions would be a standard equal tee which was designed in accordance with ASME B16.9. The equal tee, however, has distinctive flexibility characteristics compared to the pipe, which is well defined in ASME B31.3. These flexibility characteristics generate a stress intensification factor (SIF) through bending moment equations for beam-type element analysis for standard equal tee components. However, due to the limitation of SIF and flexibility characteristics for the non-standard pipe fittings, the stress evaluation could not be done using beam-type element analysis. When using finite element method (FEM) analysis, generally equivalent stresses (Von Mises or Tresca) or principal stresses would be evaluated depending on the stress categorization as explained in ASME codes and standards. In this paper, a stress evaluation method for non-standard Y-tee was developed and demonstrated against ASME VIII Div. 2 Part 5 requirement. The developed SCLs line for the non-standard Y-tee fittings provides the guides for stress assessment against design stress allowable. An optimum design for non-standard Y-tee is proposed at 45° and 60° crotch radii which resulted in lower stress value at SCL lines, hence improving the structural integrity.

Creep-Fatigue Life Property of P91 Welded Piping Subjected to Bending and Torsional Moments at High Temperature

Abstract In recent years, the role of thermal power plants has shifted from providing a baseload to providing supplemental supply to compensate for fluctuations in the output of renewable energy sources. Thus, the operation of these plants involves frequent startup and shutdown cycles, which lead to extensive damage caused by creep and fatigue interactions. In addition, the piping utilized in thermal plants is subjected to a combined stress state composed of bending and torsional moments. In this study, a high-temperature fatigue testing machine capable of generating such a bending-torsional loading was developed. Creep-fatigue tests were conducted on P91 steel piping with weldment. The results clarified that the creep-fatigue life was reduced by the superposition of the torsional and bending moments and that it was further reduced by a holding load. It was shown that the creep-fatigue life of piping with weldment can be estimated accurately using the equivalent bending moment, which is composed of the torsional and bending moments. It was also confirmed that crack occurred in the heat-affected zone (HAZ) of the welded part, which has been often observed in actual thermal power equipment. From the finite element analysis, it was identified that cracking was initiated in the HAZ due to the accumulation of creep strain and increase in the hydrostatic pressure component during a holding load.

Stochastic analysis for bending capacity of precast prestressed concrete bridge piers using Monte-Carlo simulation and gradient boosted regression trees algorithm

The use of precast prestressed concrete bridge piers is rapidly evolving and widely applied. Nevertheless, the probabilistic behavior of the bending performance of precast prestressed concrete bridge piers has often been overlooked. This study aims to address this issue by utilizing actual precast bridge piers as the engineering context. Through the implementation of the Monte-Carlo simulation and Gradient Boosted Regression Trees (GBRT) algorithm, the stochastic distribution of the bending performance and their critical factors are identified. The results show that the normal distribution is the most suitable for the random distribution of bending performance indicators. The variability of the elastic modulus of ordinary steel bars, initial strain of prestressed steel hinge wires, and constant load axial force has little effect on the bending moment performance, while the yield stress of ordinary steel bars, elastic modulus of concrete, compressive strength of unrestrained concrete, and elastic modulus of prestressed steel hinge wires have a greater impact on the bending performance. Additionally, the compressive strength of unrestrained concrete has a significant influence on the equivalent bending moment of the cross-section that concerns designers.

DEVELOPMENT OF A 50-LITRE BATCH CAPACITY INDUSTRIAL MIXER

This work focused on the development of a 50- litre batch capacity industrial mixer using locally sourced material. The essence is to produce an industrial liquid mixer that is relatively cheap and easily affordable. The design is simplified in such a way that limits operational hazards. The development of the machine involved the use of simple fabrication techniques and methods for each component part so as to eliminate unnecessary complexity, for ease of maintenance. The electric motor capacity is 0.5hp. Calculation results gave the volume of vessel as 70. 372 liters, the total tension on the belt as 1033.063N, the force acting on the impeller as 197.867N, the power required to drive the 2 impellers as 22.694Watts (0.0304hp), the belt length as 254.435mm, the minimum length of the shaft as 760mm, the equivalent bending moment acting on the shaft as 142.603Nm, the equivalent twisting moment acting on the shaft as 71.371Nm, the shaft diameter as 20.5mm. Performance testing shows that the machine performed well as expected. The highly homogeneous product obtained during testing proves the viability of the machine and is indicative of the overall efficiency of the machine.

Failure mechanism and design method for box girder bridge with interior hinged supports under eccentrically vertical loads

This paper presents the study to uncover the response, failure mechanism and design method of overturning of box girder bridges with interior hinged supports under eccentrically vertical loads. The effect of girder rotation after girder detaches from support is considered theoretically with the proposed equivalent inertia bending moment (EIBM) applied to Euler-Bernoulli beam theory. Horizontal displacement is found under eccentrically vertical loads when girder rotates during the analyses. The static ultimate overturning vertical load (SUOVL) of girder bridges is found to decrease while the number of spans increases, which is opposite compared with rigid body assumption method used in the previous studies. Both theoretical and numerical analysis shows that girder bridges with interior hinged supports are unfavorable to resist eccentrically vertical load. In the paper, a spatial frame model is proposed to model girder bridges under eccentrically vertical loads. The theoretical results are validated with the finite element model. Structure responses including reactions and bending moment considering the effect of girder rotation are analyzed. Finally, structure parameters including bearing spacing, boundary condition and horizontal curved radius are studied to find their effect on overturning stability, based on which to provide an efficient way to enhance the overturning stability of box girder bridges. The results provide a more general and clear idea of how a box girder bridge behaves under heavy eccentrically vertical loads when girder is detached from supports.

Flexural design of restraining panels in buckling-restrained steel plate shear walls considering high-order buckling modes

Buckling-restrained steel plate shear wall (BRSPSW) is one kind of excellent energy dissipating member. The inner steel plate in BRSPSW usually works with high-order buckling modes to resist lateral force under the buckling restrained effect of outer restraining panels. However, current design of the restraining panels is commonly based on simplified uniform-loaded plates without considering the effect of the high-order buckling modes, which may result in unsafe designs. In this paper, the high-order buckling modes in BRSPSW and their influence on the flexural design of the restraining panels were studied. Finite element (FE) models that can accurately simulate the out-of-plane interaction behavior of BRSPSW were developed and verified by existing test results. The numerical results show that the high-order buckling of the steel plate leads to a series of inclined strip-shaped stress regions on restraining panels. When the parameters of BRSPSW are varied in common range, the positive and negative bending moments of the restraining panel under the strip-shaped force are 9.6 and 2.8 times those under the uniform force, respectively. The differences between the bending moment of the restraining panels under strip-shaped force and that under uniform force become larger as the spacings of the strip-shaped stress regions increase. Furthermore, the spacings of the strip-shaped stress regions increase with the decrease of the height-to-thickness ratio of the steel plate and the increase of the gap between the steel plate and the restraining panel. Two fitting formulas of the positive and negative moment amplification factors considering the effect of the high-order buckling modes are proposed to design the restraining panels safely. Additionally, a simplified model and bending moment equations of the restraining panels in BRSPSW are suggested. To avoid the excessive negative bending moments occurring at side supports of the restraining panel, the ratio of cantilever length to middle span is suggested to be not more than 0.4.

Investigation of Offshore Wind Turbine Structure Deflection Using Experimental Work, Numerical, and Theoretical Approach

Electrical energy from offshore wind turbines is an important source of clean, renewable energy production. One of the reasons for the low efficiency of wind turbines is the change in the flow angle of attack, denoted by the symbol (α), as a result of the deflection of the structure. The study aims to know the values of the maximum deflection of the proposed structure under the environmental conditions of the Arabian Gulf water area. Our research adopted a novel approach to extracting results; the characteristics of sea waves were extracted from the experimental work after fixing five sea waves, knowing the displacement of the top of the structure, and using the numerical approach in the ANSYS-Fluent program to know the average wind and wave forces. Two simulations were performed. The first included the five cases of sea wave characteristics without rotating wind turbine blades. The second was for the fifth case only with the wind turbine blades rotating at a speed of (20.5 rpm), assuming that the structure was exposed to a constant wind speed (12 m/s) for the two simulations. The study also included obtaining the maximum deflection value of the structure. Then, the equations of the theoretical approach were developed based on the Euler-Bernoulli bending moment equation, and the forces extracted from the simulations were entered into the theoretical equations to extract the maximum deflection values of the structure. Reading the experimental work resulted in the highest displacement of the top of the structure in the fifth case (0.178 m). The result of the second simulation had the highest value of the structure deflection (0.201 m). In comparison, its value came in the theoretical approach (0.160 m), which adopted the forces of the second simulation.

Development of a fatigue strength testing machine

A profound engineering design and modeling of fatigue strength machine for testing the failure which occurs when a metallic material is subjected to cyclic stresses is presented. The main goal is developing a locally made fatigue strength machine that can be used in material science laboratory. A major direction in this development of the machine is the ability to thread on the path of technology transfer and dominance by concentrating on the building of indigenous capacity. In carrying out the machine development, engineering design formulae were applied and Computer Aided Design modeling was developed. The developed fatigue strength testing machine had a designed machine capacity of 18875Nmm that sustained a motor power of 5.93kw.The machine shaft diameter determined to be 9.88mm developed an equivalent torque and bending moment of 45799.8Nmm and 40890Nmm respectively. The machine designed critical speed of 23.52rad/s had belt tensions on the tight and slack sides to be 139.02N and 44.65N respectively. The fabricated machine has the ability to record low and high fatigue cycles.

Flexural performance of pretensioned spun concrete piles reinforced with steel strands

The application of pretensioned spun high-strength concrete (PHC) piles in high-intensity seismic areas has been limited by insufficient horizontal load resistance and poor deformation capacity. A new type of pretensioned spun concrete pile with high-strength and high-elongation steel strands instead of steel bars has been developed. This paper presents a flexural performance evaluation of the new centrifugal spun concrete pile with steel strands (hereafter referred to as a PSC pile). An experimental study is presented first, including bending tests on six full-scale pile test specimens with three different pile diameters. The flexural performances of PHC and PSC piles are comparatively assessed. The results show that the new PSC piles have similar crack resistance, but higher ultimate bearing capacity and better deformation capacity under a flexural condition. Compared with PHC piles, which exhibit a brittle bending failure, PSC piles demonstrate a ductile bending failure. Following the experimental study, a theoretical model is developed to evaluate the flexural strength of the piles, and a simplified calculation equation for ultimate bending moment is proposed. Finally, a finite-element model is established to simulate the flexural performance of the piles; the modelling results are found to be in good agreement with the experimental results.

Comparative Analysis and Design of Bridge Pier for various Geometries along height

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

Comparative Analysis and Design of Bridge Pier for Various Geometries Along Height Comparing the Parameters Deflection and Bending Stresses

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

Thick plate bending analysis using a single variable simple plate theory

A third order single variable simple plate theory has been used for the bending deflection analysis of thick plates with simply supported edges. The plate theory used herein contains third order terms in the displacement field. The displacement field of the theory utilizes only one unknown displacement variable for the complete formulation of thick plates. All the necessary equations connected with this plate theory can be expressed in terms of a single unknown displacement variable. The governing equation, bending moment, shear force and boundary condition equations of the theory have close similarity to those of Classical Plate Theory equations. The mathematical effort needed in formulation of plates using this theory is slightly more in comparison with Classical Plate Theory. To demonstrate the usefulness of the plate theory used herein bending deflection analysis of thick plates with simply supported edges is carried out. Bending deflection results predicted using the present theory are compared with deflection results of other first order and higher order thick plate theories. Bending deflection results predicted by thick plate theory used herein are observed to be accurate.

Analysis of turbulence models fitted to site, and their impact on the response of a bottom-fixed wind turbine

This study compares a wind field recommended by the wind turbine design standards to more realistic wind fields based on measurements. The widely used Mann spectral tensor model with inputs recommended by the standard, is compared to FitMann, the Mann model with inputs fitted to measurements and TIMESR; using measured time series combined with the Davenport coherence model. The Mann model produces too low energy levels at the lowest frequencies of the wind spectra, while the wind spectra generated by FitMann approaches the measured values. TIMESR reproduces the measured spectral values at all frequencies. The different models give similar vertical coherence, while the Mann and FitMann models give lower horizontal coherence than TIMESR. Investigating the wind loads on a bottom-fixed 10-MW wind turbine, the spectra for the tower bottom fore-aft and blade root flapwise bending moment follow the shape of the wind spectra closely at low frequencies. The low-frequency range is important for the blade root and in particular the tower bottom bending moment. Thus, the TIMESR model, followed by FitMann, is assumed to give the most accurate fatigue estimates. For the specific situation analysed in this study, the FitMann model gives only 18 and 5 % lower estimates than TIMESR of the tower bottom and blade root damage equivalent bending moments, while the Mann model gives 27 % and 12 % lower estimates. The tower top yaw and fore-aft bending moments depend on the wind coherence. For the specific situation analysed in this study, the FitMann model gives 9 and 5 % higher estimates of the tower top yaw and tower top damage equivalent (bending) moments compared to TIMESR, while the Mann model gives 23 % and 18 % higher estimates. Since only measurements of the vertical coherence are available, it is not clear which model is superior for the tower top moments. However, the importance of a proper coherence model is documented.

Large deformations of piezoelectric laminated beams based on the absolute nodal coordinate formulation

Piezoelectric beams can be deformed into many patterns and have potential application prospect in the field of smart foldable structures. Knowing the large deformation actuation mechanism of such structures is the basis in the soft machine design. In this paper, using the Equivalent Single-layer model, a new flexible piezoelectric laminated beam element based on the Absolute Nodal Coordinate Formulation (ANCF) is established. This beam element contains three layers, in which the base layer is made of linear elastic material, and the top and bottom layers are both made of piezoelectric materials. The constitutive equation of the piezoelectric material is introduced to derive the elastic force and the piezoelectric force. The correctness of the new beam element are validated by comparing with the analytical solution and the results from the equivalent bending moment equation. A group of large deformation patterns of the laminated beam are given to prove the applicability of the proposed element. Results show that when various voltages are applied to the piezoelectric actuators that located in arbitrary positions of the base beam, the flexible beam can achieve the desired shape smoothly. Dynamic responses of a highly flexible pendulum with and without piezoelectric layers are also investigated. Research in this work can be helpful to the understanding of complicated coupled nonlinear mechanics of flexible or soft structures with covered smart piezoelectric materials.

Метод расчета усталостного повреждения регулярных зон крыла самолета при случайном нагружении на этапах типового полета

In accordance with the airworthiness standards, the aircraft structure must be operationally survivable, it means that structure must be able to remain efficiency in the presence of admissible damage. But, accumulating above than a certain level, damages cause fatigue failure of the structure, in the form of micro- and submicrocracks, thus reducing its strength characteristics. Currently, several approaches have been formed to ensure the safety of an aircraft structures in terms of strength. One of them is ensuring a safe resource (safe durability). This principle implies that during the specified service life of the product, no damage will occur in it, reducing the strength below the permissible level. The aircraft resource is limited “from above” by the durability of the regular zones of airframe. Therefore, predicting the durability of an aircraft wing structure at the design stage is a fundamental engineering problem to ensure its safety and economic efficiency. At the same time, the first step in dealing with aircraft fatigue damage at the design stage is the collection and assessment of the operational loads of the analog aircraft. However, at the design stage of a new aircraft model, obtaining such data is not always possible. Therefore, the purpose of this article is to develop a method for calculating fatigue damage at the stage of cracking and assessing the durability of regular zones of a transport aircraft wing, taking into account the conditions of its operation. The tasks to be solved are: to isolate the factors that determine the durability of the aircraft at flying in turbulent air; to take into account the asymmetry of loads and accumulated damage that occurs at each stage during the entire flight of the aircraft; to determine the aircraft's resource depending on the profile of a typical flight. The method is based on a standardized atmospheric turbulence model, typical flight profiles, fatigue characteristics of materials, the hypothesis of linear summation of damages and calculation based on nominal stresses. As result, comparison between the calculated integral repeatability of overloads and equivalent bending moments with the results of processing flight test data showed good agreements. Conclusions. The scientific novelty of the work lies in the fact that a method for calculating the fatigue damage of the regular wing zones, taking into account the expected flight profile of the aircraft was developed. This means that the proposed method makes it possible to carry out a preliminary assessment of the resource when designing an airplane without using data on the operational loads of an analogue airplane, and also estimate the residual resource of the airplane during its operation.

Novel Bending Test Method for Polymer Railway Sleeper Materials.

Alternative sleeper technologies have been developed to address the significant need for the replacement of deteriorating timber railway sleepers. The review of the literature indicates that the railway sleepers might fail while in service, despite passing the evaluation tests of the current composite sleeper standards which indicated that these tests do not represent in situ sleeper on ballast. In this research, a new five-point bending test is developed to evaluate the flexural behaviour of timber replacement sleeper technologies supported by ballast. Due to the simplicity, acceptance level of evaluation accuracy and the lack of in-service behaviour of alternative sleepers, this new testing method is justified with the bending behaviour according to the Beam on Elastic Foundation theory. Three timber replacement sleeper technologies—plastic, synthetic composites and low-profile prestressed concrete sleepers in addition to timber sleepers—were tested under service loading condition to evaluate the suitability of the new test method. To address the differences in the bending of the sleepers due to their different modulus of elasticities, the most appropriate material for the middle support was also determined. Analytical equations of the bending moments with and without middle support settlement were also developed. The results showed that the five-point static bending test could induce the positive and negative bending moments experienced by railway sleepers under a train wheel load. It was also found that with the proposed testing spans, steel-EPDM rubber is the most suitable configuration for low bending modulus sleepers such as plastic, steel-neoprene for medium modulus polymer sleepers and steel-steel for very high modulus sleepers such as concrete. Finally, the proposed bending moment equations can precisely predict the flexural behaviour of alternative sleepers under the five-point bending test.

Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.