Unbalanced Moment Research Articles

Effects of adjusting ring and spring stiffness on fluid dynamics of steam spring-loaded safety valve

As the most typical direct-loaded safety valves, spring-loaded safety valves are automatically opened by fluid pressure. Their stable and reliable dynamic characteristics are vital for overpressure protection in nuclear power plants. Notably, the adjusting ring structure and the spring, as important components affecting the dynamic characteristics of the valve, are among the easiest way to adjust and replace. Dynamic numerical simulation method is employed to analyze the effect of adjusting ring height and spring stiffness on the valve dynamic characteristics. This study investigates the effect of the upper and lower adjusting rings heights on dynamic characteristics and highlights the unbalanced moment created by the angular structure of valve during opening and closing processes. The superiority of graphical method is revealed by comparing three spring stiffness calculation methods for steam spring-loaded safety valve - the lift formula method, the structural parameter method, and the graphical method. When the graphical method is combined with the lift formula method, a more accurate range of spring stiffness can be determined for a particular spring-loaded safety valve.

Simplification of KDS 14 Design Method for Slab–Column Connections Subjected to Unbalanced Moment

The current KDS 14 design method yields reasonable accuracy with acceptable safety in assessing the unbalanced moment-carrying capacity of slab–column connections. However, the model requires considerable computational effort owing to the effects of various design parameters, particularly the gravity-load effect. This study proposes a method to simplify the KDS 14 model to evaluate the unbalanced moment-carrying capacity of slab–column connections. In the proposed method, the gravity-load effect is decoupled from equations used for evaluating unbalanced moment-carrying capacity components. Subsequently, the total unbalanced moment-carrying capacity is determined by establishing an interaction between the gravity shear ratio and unbalanced moment components without considering the gravity-load effect. For practical design purposes, final simplified design equations are proposed. The reliability of the simplified method is validated based on a comparison with the current KDS 14 design code using a comprehensive database encompassing interior, exterior, and corner slab–column connections. Furthermore, a parametric study based on the proposed simplified approach, current design codes, combined with finite-element (FE) analysis is performed to elucidate the effects of constituents on the unbalanced moment-carrying capacity of corner slab–column connections. The results show that the proposed simplified model and KDS design method are strongly correlated with the experimental and FE results for a range of design parameters. Meanwhile, the ACI 318 model consistently provides a lower limit for strength prediction, thus yielding overly conservative and safe results compared with the test and FE results in most cases.

Study of Unsymmetrical Magnetic Pulling Force and Magnetic Moment in 1000 MW Hydrogenerator Based on Finite Element Analysis

The large dimensions of the 1000 MW hydroelectric generator sets require high mounting accuracy. Small deviations can lead to asymmetry, which in turn triggers unbalanced magnetic pulls and moments. Therefore, symmetry is a central challenge in the installation and operation of giant hydroelectric generators. In this paper, the effects of radial eccentricity, axial offset, and rotor shaft deflection on the unbalanced magnetic pull and moment are investigated by transient finite element analysis of the asymmetric magnetic field. The results of the time-domain and frequency-domain analyses show that asymmetric operation generates unbalanced magnetic forces and moments. These forces and moments increase linearly with increasing offset or deflection rate. When the eccentricity meets the installation criteria, the unbalanced magnetic pull forces are small and within acceptable limits. This study helps to understand the relationship between asymmetry and unbalanced magnetic pulling forces in large hydroelectric generators, and provides a theoretical basis for standardizing installation deviation control.

Numerical modeling of the punching shear behavior of biaxially loaded RC footings

In this study, the punching shear behavior of footings under biaxial eccentric loads is numerically investigated. Load eccentricities usually encountered in practice were primarily investigated on flat slabs, whereby the research on footings is still limited. Since the structural behavior of thick footings is significantly different compared to that of thin ones due to fracture mechanics, further investigations are required. To gain a deep understanding of the punching shear behavior of footings under biaxial eccentric loads, a numerical investigation was conducted. A finite element model was developed and validated against multiple experimental results in terms of load-deflection behavior and crack patterns. The validated model was then employed to examine the effect of different biaxial load eccentricities, different shear spans to effective depth ratios, column sizes, and column shapes. Finally, the numerical results were used for analyzing the design approach of the latest version of Eurocode 2 (FprEC2-2023). The numerical results showed a gradual transition between a fully developed punching shear cone to a partially formed cone without shear crack formation on the less loaded side with increasing load eccentricities. Additionally, larger load eccentricities lead to significantly increased rotation of the footing accompanied by a reduction of the punching shear capacity. A more pronounced influence of the effect of unbalanced moments on the punching shear capacity was identified in footings with a larger shear span to effective depth ratio. Furthermore, the effect of column size was more pronounced in small shear spans under concentric loads, while the effect was greater in footings with a larger shear span to depth ratio under eccentric loads. However, the beneficial effect of a larger column size was more pronounced for eccentric loads compared to concentric loading. Overall, the results indicate a good agreement with the design approach of Eurocode (FprEC2) for square columns. However, in some cases, the prediction was underestimated. Modified approaches from the literature for considering the effect of load eccentricity were found to address the underestimated cases safely. The results of this study demonstrated the applicability of the new design approaches for eccentric punching shear in footings under biaxial eccentric loads.

Research on Monitoring Technology for Frame Piers of Continuous Box-Girder Bridges Constructed by the Cantilever Method

This paper focuses on the analysis of the stress state of a large-span frame pier-continuous box girder bridge with pier crossbeams anchored by pier crossbeams on the main pier of the Guangfo-Zhao Expressway. The bridge is constructed by the cantilever method, and a refined finite element model of the entire bridge is established using the finite element software Midas/FEA to analyze the stress state of the frame pier during the cantilever construction process. It is found that under the possible combined action of an unbalanced load during construction, the torsional resistance of the frame pier crossbeam does not meet the requirements of the design code. In order to eliminate the torsion of the frame piers, counterweights were used to monitor the frame piers during the construction of the box girders. In this paper, the theoretical calculation formula of the inclination angle of the end section of the frame pier crossbeam with the change of unbalanced bending moment, the calculation formula of the relationship between the horizontal displacement of the frame pier and the unbalanced bending moment, and the calculation formula corresponding to the relationship with the water tank counterweight are derived using the structural mechanics method. Two monitoring methods for the frame pier are proposed. In the construction monitoring of the bridge, the numerical fitting formula obtained by finite element numerical analysis calculation is compared with the calculated formula obtained by substituting the design parameters of the frame pier into the theoretical formula. The basic constants in both formulas are basically equal, verifying the correctness of the monitoring calculation formula proposed in this paper for the torsional resistance of the frame pier crossbeam. The applicability of the two monitoring methods is also compared and analyzed. This paper takes the main pier of Chaoyang overpass’s mainline bridge as the engineering background, which adopts the framework pier with a large-span prestressed concrete continuous box girder bridge. It analyzes the torsional state of the beam of the framework pier during the bridge construction process and conducts research on the construction monitoring of the framework pier crossbeam, providing valuable references for the construction monitoring of framework pier crossbeams in the construction of large-span framework pier continuous bridges in the future. The research results of this paper can provide assistance for the construction monitoring of similar projects. This paper’s innovation primarily resides in employing structural mechanics methods to compute the torsion of frame piers. On this basis, a simplified beam torsion calculation formula is proposed to strengthen its practical application in construction monitoring. The findings of this paper can help in the construction monitoring of similar projects.

Collar plate effect on local joint flexibility of tubular K-joints under IPB moments: Parametric study and predictive equations

This study delves into the Local Joint Flexibility (LJF) of tubular K-joints reinforced with the collar plates under in-plane bending moments (IPBMs). 348 reinforced K-joints were simulated to analyze the impacts of the loading conditions (balanced and unbalanced moments), collar plate size (like the length and thickness) alongside the joints’ parameters (θ, γ, β, ξ) on the fLJF and its proportionality (ψ). The research outcomes demonstrate that factors such as η, λ, and β play a significant role in determining ψ, whereas the influence of ξ, and γ on ψ appears to be negligible. Also, in the reinforced joints, the fLJF is decreased by 77.4 % compared to the equivalent un-reinforced joint. While the role of the collar plate on the fLJF is remarkable, the matter had not been investigated on K-joints. Therefore, following the detailed parametric study, two novel equations are proposed to safety estimate the fLJF for such scenarios.

Punching and lateral cyclic behavior of concrete slab-column connections reinforced with steel sheets

During an earthquake, slab-column structures with high gravity-shear ratios often experience increased local shear stress and deformation in the connection area, leading to reduced unbalanced moment capacity and drift capacity of the connections. This study aims to create a new and more efficient method of enhancing the unbalanced moment capacity and deformation capacity of reinforced concrete slab-column structures through using steel sheets as punching reinforcement. Tests were conducted to evaluate the effects of the thickness, extension length, and layout of this new type of punching reinforcement on the unbalanced moment capacity and deformation capacity of the connections when subjected to vertical and horizontal cyclic loads. The results indicated that as the steel sheet thickness increased, the unbalanced moment capacity of SC-2 and SC-3 rose by 24 % and 48 % respectively, while the drift capacity improved by 20 % and 40 % compared to SC-1. Furthermore, the failure mode shifted from stress-induced punching to drift-induced punching. Compared to SC-1, a cruciform layout with an additional diagonal arrangement of sheets increased the unbalanced moment capacity and drift capacity by approximately 17 % and 20 %, respectively. The extension length of the sheets reduced from 600 to 420 had negligible effect on the unbalanced moment capacity and deformation capacity. Utilizing experimental data, this study compared the relationship between the drift capacity and gravity shear ratio of connections reinforced with different shear reinforcements. The underlying causes for the observed lower drift capacity of the specimens are analyzed, and design recommendations for optimizing the steel sheets are subsequently proffered. After thoroughly analyzing the experimental results, a simplified calculation methodology for assessing the shear strength of steel sheets was developed, taking inspiration from the shear strength calculation approach outlined in ACI 318–19. The efficacy of this simplified approach was subsequently validated by comparing the experimental results with those predicted by current design codes. Furthermore, by comparing the experimental results with the predicted values, the relationship between the punching failure mode of connections and their punching strength was discussed.

Packaging machine vibration reduction by dynamic balancing

In this article vibrations transmitted to the frame of a packaging machine are reduced through dynamic balancing. It is known that unbalanced inertial forces and moments result in undesirable vibrations that negatively affect the performance and durability of machines. These shaking forces and shaking moments must be completely balanced to eliminate the vibrations. Balancing generally increases other dynamic characteristics like driving torque, bearing reactions in joints and the overall mass of the mechanism and can lead to a more complex mechanism. Instead of a complete balance of shaking force and moment, these can be minimized through optimization techniques. In this work, an optimization procedure is formulated to determine the masses and locations of counterweights that provides the minimum shaking force and moment of a packaging machine sealing head, thus reducing the vibrations transferred to the frame.

Thick-shell finite element analysis of reinforced concrete flat plates with non-uniform connection stresses

This paper presents the application of a thick-shell nonlinear finite element analysis procedure to estimate the punching shear resisting performance of reinforced concrete slab-column connections under variable connection shear stress conditions. In the analyses performed, varied connection shear stress conditions stem from slabs being supported by columns with different cross-section aspect ratios, being subjected to different distributions of gravity loading, being constructed with different planar reinforcement ratios in orthogonal directions, as well as the application of unbalanced bending moments. Forty-eight isolated slab-column connection specimens presented in the literature were modelled and analyzed using a thick-shell finite analysis procedure. All numerical results were developed using a predefined set of material models and analysis parameters, a consistent meshing procedure, and are shown to provide meaningful agreement with experimental data without the need for case-specific model calibration or the adoption of specialised failure criteria. The results show that thick-shell modelling methods can be suitable for estimating the punching shear response of slabs subjected to non-uniform shear stress development in connection regions, and can provide similar levels of precision to that obtained for the analysis of idealised slab-column connections typically used for design procedure and model development.

Punching performance of flat slabs with openings accounting for the influence of moment transfer and shear reinforcement

The arrangement of openings adjacent or near to slab-column connections is very common practice in flat slab design due to a number of advantages for technical installations. Such location is however conflicting with the most critical region of the slab, where punching shear failures may develop and typically govern the design at ultimate limit state. This requires in many cases arranging shear reinforcement to enhance the performance of the connections both in terms of resistance and deformation capacity. Such shear reinforcement is in addition particularly useful when unbalanced moments are transferred from the slab to the columns, which is a phenomenon typically detrimental for the punching shear resistance of inner connections. Despite the practical relevance of this case, there is currently no experimental evidence on the response of shear-reinforced slab-column connections with adjacent openings and moment transfer. Design is thus performed on the basis of simplified rules, modifying the resistance of connections without openings. In the present study, a comprehensive test programme addressed at this issue is presented in an effort to improve the current state-of-knowledge. Five slabs representing several practical cases and potential arrangements of shear reinforcement were tested. The experimental results are investigated in detail and compared to codes of practice, highlighting a number of deficiencies of current simplified rules. The phenomena is finally investigated on the basis of the mechanical model of the Critical Shear Crack Theory, showing a general frame for modelling and design of such detail.

Investigating punching shear in slabs with unbalanced moments and openings

The impact of openings and moment transfer on punching shear resistance was investigated by conducting tests on nine interior slab-column connections measuring 2,400 mm square and 150 mm thick. The connections were subjected to different unbalanced moment orientations with eccentricities of 250 mm and 500 mm, and without shear reinforcement. The openings, located on the faces of the rectangular supports, had widths of either 200 mm × 200 mm or 200 mm × 300 mm. The study analysed ultimate loads, vertical displacements, flexural reinforcement strains, and concrete strains. The experimental punching strength was compared to theoretical predictions according to ACI 318:19, fib MC 2010:13, for different levels of approximation and the 2nd generation of Eurocode 2 prEN 1992-1-1:21. Observations are provided regarding the code’s calculation for slabs with openings.

Reduced area approach for predicting punching shear resistance of biaxial hollow slabs with openings

Due to the inclusion of hollow plastic spheres in bubbled slab systems, the shear resistance is greatly reduced. Also, the existence of the opening in the vicinity of columns takes away part of the concrete responsible for resisting shear forces and unbalanced moments, which in turn further reduces the punching shear capacity of the slab-column connection. In this study, experimental and theoretical investigations had been carried out on bubbled slabs with 2000 × 2000 × 230 mm dimensions. The investigated parameters were the size, position, distance of opening relative to the column stub, and the location of bubbles relative to the critical shear perimeter. A new calculation approach for determining punching shear resistance for bubbled slabs was developed. The proposed modification for calculating the effective critical perimeter showed an appropriate range of agreement of the punching shear strength, which is calculated by the methods adopted by (ACI 318, Eurocode 2, BS 8110, and AS 3600) codes, in comparison to the experimental data. The average ratios of the test results to the calculated punching shear capacity determined according to the proposed approach are between 1.007 and 1.417 with a standard deviation of 0.039–0.186 and a coefficient of variation of 0.038–0.131.

Control structures for rail vehicles using active steering technology

ABSTRACT In this study, an analytical method based on a linear single bogie model was used to investigate the mechanism of active steering for three control structures: wheelset yaw control (WYC), wheelset lateral control (WLC), and bogie yaw control (BYC). The results revealed that the WYC structure reduced both circumferential and axial wear, whereas the WLC and BYC structures mainly reduced circumferential wear, and BYC was ineffective when the primary lateral stiffness was low. Moreover, the impact of external forces on the control quantity was investigated by using a nonlinear full-vehicle model, with the wheelset unbalanced moment having the largest impact. Subsequently, the adaptation of the WYC and BYC structures to two control modes, namely, force and displacement control, was analysed. The results showed that for the WYC, the displacement control mode was favoured, whereas for the BYC, the force control mode was the sole alternative. Finally, the control efficiency was determined, with the WYC being recommended for low primary longitudinal stiffness and BYC for higher stiffness.

A machine-learning-based model for seismic performance assessment of interior slab-column connections

Slab-column connections are the most critical components in flat plate systems under seismic actions due to their brittle failure mode. Finite element analysis (FEA) can be adopted as an extension of experimental testing to potentially lead to the development of modern design codes by providing significant information on the punching shear failure process of connections. However, the available concrete constitutive models in FEA packages fail in simulating the hysteretic response of the connections under cyclic loads. Moreover, it is shown that the available design code recommendations and empirical models are not accurate tools for assessing the seismic performance of these connections (e.g., unbalanced moment and/or drift capacity). In an effort to overcome these limitations, a dataset of previously tested experiments is compiled to predict the ultimate load and drift of the connections using the multi-variate non-linear regression model. Additionally, there is a need to develop a new constitutive material model for seismic performance assessment of the connections to capture the complete hysteretic response of the connection using numerical FEA. Consequently, a deep neural network is trained over the accumulated dataset and integrated into the OpenSees source code to determine the seismic performance of the connections. For data augmentation, a generative neural network model of autoencoders known as Generative Adversarial Networks (GANs) is constructed to generate synthetic data. The proposed material model is found to have significantly improved precision in capturing the hysteretic response of flat plates. The developed models showed higher accuracy than the design code estimations and empirical models.

Optimal design of chain equilibrator based on genetic algorithm

In order to satisfy the overall structure requirements of a self-propelled gun, the mechanism of a chain equilibrator is utilized. According to the working principles and action procedures of the chain equilibrator, the drawing method and the analytical method are used respectively in the design process. In the existing design schemes, the stepwise quadratic programming methods are widely used to solve the unbalanced moment optimization models. However, this type of conventional methods relies heavily on the initial value and gradient, and exhibit the poor ability of global optimization. In this paper, we propose a multi-population genetic algorithm to obtain the optimal solution of unbalanced moment model for improving the design of chain equilibrator. Finally, the results of numerical examples show the superiority of the proposed method in the global search ability than that of stepwise quadratic programming, which is suitable for the design of chain equilibrator. The comparative experiments and analysis show that the drawing method has low design efficiency and is difficult for optimization, whereas the analytical method exhibits the highest design efficiency.

Aero-Engine Rotor Assembly Process Optimization Based on Improved Harris Hawk Algorithm

Multi-stage disc rotor assembly is an important part of the aero-engine rotor manufacturing process. To solve the problem that excessive unbalance of assembly affects the vibration of the whole machine, this paper presents an optimization method for aero-engine rotor assembly balance based on an improved Harris Hawk algorithm. Firstly, the assembly sequence model of the single-stage disc blade and the phase assembly model of a multi-stage disc of the engine rotor is established. Secondly, by using the initial population generation based on dynamic opposing learning and the escape energy function of the non-linear logarithmic convergence factor, the search mechanism of the whale optimization algorithm is introduced in the global exploration, and the adaptive weight strategy and mutation strategy of the genetic algorithm is introduced in the development to improve the algorithm. Then, the effectiveness of the algorithm is verified by experiments and compared with particle swarm optimization, genetic algorithm, and Harris Hawk algorithm, the unbalance of the optimal blade assembly sequence is reduced by 91.75%, 99.82%, and 83.39%, respectively. The algorithm comparison and analysis are carried out for all disc-blade assembly optimization of the rotor. The optimal unbalance of the improved Harris Hawk optimization algorithm is reduced by 79.71%, 99.48%, and 54.92% on average. The unbalance of the algorithm in this paper is the best. Finally, the improved Harris Hawk algorithm is used to find the best assembly phase, and the optimized unbalanced force and moment are reduced by 84.22% and 98.05%, respectively. The results of this study prove that the improved Harris Hawk algorithm for aero-engine rotor assembly balance optimization can effectively reduce the unbalance of rotor disc blade assembly and rotor unbalance and provide a powerful solution for solving engine vibration.

Effect of using Engineered Cementitious Composites (ECC) on failure behavior of flat slab-column connections

Load capacity and ductility are two key characteristics of the flat slab-column connection in high seismic areas. This study specifically examined the effect of strengthening layer thickness of Engineered Cementitious Composites (ECC) on punching shear strength and post punching behavior of flat slabs. The effect of the unbalanced moment, ECC thickness of the slab and the strengthening ECC layer on flat slab punching and post punching behavior were also investigated. Thirteen reinforced concrete flat slab specimens were made and examined. It was observed that the replacement of slab concrete with ECC increased the punching capacity and improved post-punching behavior without a large and sudden drop in load. In addition, the use of ECC as a strengthening layer for the flat slabs significantly increased the punching and post-punching shear strength capacities. The change in failure mechanism was observed from a sudden and abrupt failure to a ductile failure with high-energy absorption when more ECC layer thicknesses were used.

Flat Slabs in Eccentric Punching Shear: Experimental Database and Code Analysis

Eccentric punching shear can occur in concrete slab–column connections when the connection is subjected to shear and unbalanced moments. Unbalanced moments occur in all floor slabs at the edge and corner columns. As such, this problem is of practical relevance. However, most punching experiments in the literature deal with concentric punching shear at internal columns. This paper presents a developed database of 128 experiments of flat slabs under eccentric punching shear, including a summary of the testing procedure of each reference and a description of the slab specimens. Additionally, a linear finite element analysis of all the specimens is included to determine the relevant sectional shear forces and moments. Finally, the ultimate shear stresses from the database experiments are compared to the shear capacities determined with ACI 318-19, Eurocode 2 and the Model Code 2010. The comparison shows that the Model Code 2010 is the most precise in the predictions with an average tested to predicted ratio of 0.82 and a coefficient of variation of 29.63%. It can be concluded that improvements to the current design methods for eccentric punching shear are necessary.

Investigation of the performance of grouted couplers in vehicle impacted reinforced concrete ABC bridge piers

Increased dynamic impact on bridge piers caused by seismic events, blasts, and vehicular impact have become increasingly common. Recent research efforts indicate that code provisions for designing reinforced concrete members to withstand such dynamic loads are inadequate and need additional insights for this purpose. Numerous works have been undertaken to investigate reinforced concrete (RC) traditional bridge pier performance on high strain rate loading. However, little attention has been given to evaluate the performance of connections used in present day bridges including accelerated bridge constructions (ABC) to withstand vehicle impacts, and hence, is relatively unknown. In this study, the use of grouted couplers to contain the unbalanced moments resulting from vehicular impact forces exceeding the moment capacity of the reinforced concrete piers and avoiding extensive damage to the piers is investigated. A representative column, typical of those specified by state departments of transportation, is studied to determine the performance. The performance of the coupler is investigated for both dynamic and static combined stresses. Quasi-static to dynamic strain rates of steel reinforcement connected to the couplers is also evaluated. Quantifying the stresses and strains developed at coupler region from dynamic impact can help coupler manufacturers to optimize the strength properties, thus improving serviceability. This study investigated utilizing splice sleeves in mitigating the formation of plastic hinges, as well as addressing the essential properties of coupler sections required to adequately carry out this function, and will provide a useful design tool for the manufacturers, forensic structural engineers, and practitioners.

Local joint flexibility of tubular K-joints reinforced with external plates under out of plane bending moments

ABSTRACT In this research work, the Local Joint Flexibility (LJF) of steel tubular K-joints reinforced with external plates is investigated. In the first step, a finite element (FE) model was generated and verified. In the next step, a set number of 300 FE analysis was carried out to investigated the effect of the stiffener plate size (η and λ), the angle between brace and chord (θ), the joint geometry (γ, τ, ξ and β) and the loading conditions (balanced and un-balanced OPB moments) on the LJF factor (f LJF) and f LJF ratios (ψ). The results showed that the f LJF of an external plate reinforced K-joint can be down to 26% of the f LJF of the corresponding un-reinforced joint. Also, the gap factor (ξ) has effect on the f LJF. Finally, FE results were used to derive two parametric equations for determining the f LJF in the strengthened K-joints.