Unequal Spans Research Articles

Effects of Soft Story Locations on the Nonlinear Time History Analysis of Multistory Reinforced Concrete Buildings

Abstract The current paper included studying the effects of soft storey locations on dynamic response of reinforced concrete (RC) buildings under the impacts of earthquakes. Soft storey is essential to provide the building with a functional space such as vehicle garages or open meeting rooms. Further analytical investigation was necessary to understand the impact of these flexible floors on the building's response during earthquakes, as conducting experimental research to address this issue is highly difficult. The research encompassed the effects of soft storey location in two types of buildings, one with equal spans and the other with unequal spans, on the nonlinear time history response. Each building consists of a 10-stories (G+9) RC residential structure subjected to earthquake effects. The analysis was carried out using program sap2000 v23. An analogous diagonal strut was used to illustrate the infill panels. The study included the effect of soft storeys on the natural period, the change in base shear with time, and the change of displacement and acceleration along time for each building. The obtained results showed that including a soft storey in the analysis for buildings having either equal or unequal spans increased the time period, displacement, and storey drift, causing a decrease in the acceleration and base shear forces. Building with the soft storey on the fifth floor (at the mid-height of the building) showed a better dynamic response compared with that using the soft storey on the ground and last floors.

Large deformation assessment of three-tower suspension bridges: An enhanced analytical model and solution algorithm

An enhanced nonlinear approach is proposed in this study to address the limitations of traditional deflection theory in analyzing large deformations of three-tower suspension bridges. In this approach, the three-tower suspension bridge is simplified as two quasi-independent bridges for analysis, and detailed considerations are given to the vertical and longitudinal deformations of the main cable, which produce the expression for the relationship between the cable's internal force and deformations. By employing the complementary energy principle and variational calculus, the nonlinear differential equations describing bridge deformations are then established. To ensure the displacement continuity at the middle tower, this paper proposes the use of Chebyshev polynomials to approximate the solutions of the differential equations, and the weighted residual method is then used to transform these differential equations into algebraic equations. On this basis, the developed nonlinear adjustment optimization algorithm enables efficient solving of the nonlinear equation and thus determination of bridge deformation under various load conditions. The accuracy and effectiveness of the proposed scheme are validated through the analysis of two suspension bridges with equal and unequal spans. Finally, the extended applications of the proposed scheme on the other type of multi-span suspension bridges are introduced for further applications.

A Hybrid Approach Based on Unequal Span Segmentation-Clustering for Short-Term Wind Power Forecasting

Because the fluctuation and uncertainty of wind power generation bring severe secure and economic challenges to power systems, wind power forecasting becomes the critical part of the management in power systems. In this paper, a hybrid approach based on unequal span segmentation-clustering is proposed to mine the variation trend information in the wind speed series for improving forecasting performance. Firstly, the wind speed series representation is proposed to accurately represent the major variation trend of the wind speed series. It reduces the influence of the non-stationary and irregular behaviors of the wind speed series on the unequal span segmentation-clustering. Secondly, the shape-position comprehensive evaluation is proposed to combine shape and position measures to evaluate the clustering of the trend segments with unequal length. It identifies the trend segments which have comprehensive similarity on both shape and position to better construct forecasting models. Thirdly, novel bayesian optimization mutation operators are proposed to optimally move or add cut points in the unequal span segmentation. It enhances the local search capability of the unequal span segmentation. By comparing different approaches using wind datasets from two wind farms, the effectiveness and advantages of the proposed approach are demonstrated.

Practical Implications of Structural Design of a Two-Span Rc Beam -Column Structure with Unequal Spans

The structural design of reinforced concrete (RC) beam-column systems with unequal spans poses unique challenges, especially when one span is significantly longer than the other. This paper explores the practical implications of designing a two-span RC beam-column structure where one span is at least three times longer than the other. The study highlights the key considerations in terms of load distribution, deflection control, reinforcement detailing, and the potential for differential settlement and vibrations. This research draws on Eurocode standards for design, provides an analysis of various load cases, and discusses practical solutions for ensuring structural integrity and serviceability.

Failure mode discrimination and theoretical prediction method for unequal span bonded prestressed concrete substructures against progressive collapse

Unequal-span prestressed concrete (USPC) structures have unequal spans on the left and right sides and are configured with prestressed steel strands on both spans. However, research on the progressive collapse resistance of these structures is lacking. The strength of the asymmetry of the USPC structure varies depending on the span ratio and reinforcement configuration, resulting in two distinct failure modes in progressive collapse. A parametric analysis was conducted using finite element software to determine how the resistance to progressive collapse and failure modes of USPC structures under middle column failure are affected by variables such as the span ratio, reinforcement configuration, and proportion of prestressing. Accordingly, a discrimination criterion for determining the failure modes of USPC structures was proposed. A theoretical approach for predicting the ultimate displacement and resistance of the progressive collapse of USPC structures was presented for different failure modes. This theoretical approach proposes an innovative stiffness combination and tension path method to establish displacement coordination and force equilibrium conditions, respectively. The theoretical prediction method was deemed valid after comparing it with finite element simulation results.

Identification of Damage in Planar Multistory Reinforced Concrete Frames Developing a Beam-Sway Plastic Mechanism Using the “M and P” Technique

The effectiveness of a recently proposed methodology for the identification of damage in planar, multistory, reinforced concrete (RC) moment frames, which develop a plastic yield mechanism on their beams, is showcased here via the examining of a group of such existing multistory frames with three or more unequal spans. According to the methodology, the diagram of the instantaneous eigenfrequencies of the frame in the nonlinear regime is drawn as a function of the inelastic seismic roof displacement by the performance of a sequence of pushover and instantaneous modal analyses with gradually increasing target displacement. Using this key diagram, the locations of severe seismic damage in an existing moment frame can be evaluated if the instantaneous fundamental eigenfrequency of the damaged frame, at an analysis step within the nonlinear area, is known in advance by “the monitoring and the identification of frequencies” using a local network of uniaxial accelerometers. This is a hybrid technique because both procedures, the instrumental monitoring of the structure and the pushover analysis on the frame (M and P technique), are combined. A ductile, five-story, planar RC moment frame with three unequal spans is evaluated in this paper by the M and P technique. The results show that the seismic roof displacement, the lateral stiffness matrix, and, finally, the damage image of this existing frame, are fully compatible with the eigenfrequencies identified by the monitoring and are calculated with high accuracy.

Sensitivity Analysis of Structural Parameters of Unequal-Span Continuous Rigid Frame Bridge with Corrugated Steel Webs

To investigate the effect of structural parameters of bridges with unequal spans on the bridge alignment, the finite element model simulating the full-scale bridge was developed, considering the construction process. For ease of finite element modeling and investigation, the section of composite beam with corrugated steel web was first converted into the section composed of the same material. For this purpose, an equivalent method of replacing corrugated steel webs with concrete webs was proposed based on theoretical derivation. After equivalent replacement, the influences of material bulk density, internal prestress, pipe friction coefficient, and pipe deviation coefficient on the main beam at the maximum cantilever stage were analyzed, and the influences of external prestress on the main beam after bridge construction were analyzed. The results show that the most sensitive parameter to structural response is bulk density, subsequently the external prestress, internal prestress, pipe friction coefficient, and pipe deviation coefficient. Among them, the bulk density, internal prestress, and external prestress are all sensitive parameters, while pipe friction coefficient and pipe deviation coefficient are non-sensitive parameters.

Vibration analysis of multi-span continuous beam bridges with unequal spans subjected to moving loads

Vibration analysis of multi-span continuous beam bridges with unequal spans subjected to moving loads

Comparative Analysis of Equal and Unequal Grounding Grid Configurations by Compression Ratio and Least Square Curve Fitting Techniques

The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power system to maintain reliable operation. With equal conductor spacing grounding grid design, the distribution of the current in the grid is not uniform. Hence, unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing. This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors: the least-square curve fitting technique and the compression ratio technique with equal grid configuration for both square and rectangular grids. Particle Swarm Optimization (PSO) is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids. Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration. Simulation results are obtained by the MATLAB software developed. Percentage of improvement in ground potential rise, step voltage, touch voltage, and grid resistance with variation in compression ratios are plotted.

Numerical study on existing RC circular section members under unequal impact collision

Traffic accidents and derailed train-related incidents have occurred more often than ever in recent years, resulting in some economic damage and casualties. Reinforced concrete (RC) constructions often involve derailed train and vehicle accidents. Rarely are such side collisions studied in previous studies. To do this, high-fidelity simulation-based finite-element (FE) models are created in this paper to accurately simulate the collision of circular RC members with a derailed train. The reinforced concrete member structure is common in high-speed railway stations. The impact energy of the impact body is significant, causing structural member failure. It analyses the dynamic behavior of reinforced concrete members under unequal span impact loads. Numerical implementations of impact issues are discussed from the perspective of geometric, contact, and material properties. The reliability and precision of the ABAQUS code to solve impact issues are verified by comparing failure modes, impact, and deflection time history experimental outputs. By analysing the impact response characteristics, used the control variables to study the failure process and mode (including the characteristics of impact and reaction forces, deflection time history curve, impact force–deflection curve, and bearing reaction force–deflection curve). The reinforcement ratio, impact velocity, concrete strength, and slenderness ratio significantly affect shear crack pattern and development. Changes in impact velocity and slenderness ratio also affect member failure modes.

Study on Dynamic Characteristics of an Improved Composite Box Girder with Corrugated Steel Webs

Composite box girders with corrugated steel webs (CBGCSWs) are used worldwide owing to their light self-weight, high efficiency of prestressing application, and reasonable distribution of shear force and bending moment. An improved composite box girder with corrugated steel webs (ICBGCSWs) has been recently introduced to further reduce the dead weight and improve its durability. Because the innovative ICBGCSW has emerged as a new structure, very few studies have been conducted on its dynamic characteristics. In the present study, a theoretical analysis was first conducted. By comprehensively considering the shear lag effect and the shear deformation of CSWs, the element stiffness matrix of ICBGCSW was derived based on the principle of stationary potential energy. The natural frequencies and mode shapes in vertical bending vibration were calculated via a self-developed software program. The proposed method was verified by comparing the results with finite-element analysis and experimental results. Then, sensitivity studies were performed to investigate the influences of the shear lag and shear deformation on the natural frequencies of vertical bending vibration. Finally, vibration frequencies of the continuous ICBGCSW were calculated, and a general formula for calculating the fundamental frequency of simply supported girders, continuous girders with equal spans, and continuous girders with unequal spans was proposed. The proposed method, being able to consider both the effects of shear lag and shear deformation of the box girder, delivered very good performance in studying the dynamic characteristics of the ICBGCSW, whereas the proposed general formula of fundamental frequency could serve as a good reference for the bridge design in practice.

Construction monitoring of cable stayed bridge with unequal span and single tower and single cable plane

In order to improve the efficiency of bridge construction, a bridge construction monitoring method based on MIDAS civil finite element software is designed in this paper. Taking the construction monitoring of the main bridge of Huangshuihe bridge on Tonghai road in Xining City as an example, the monitoring parameters of the top deflection of the main tower and the simulation of temperature change during construction are described in detail. The effectiveness of the method is verified by the comparative analysis of theoretical data and measured data.

Radial Force and Vibration Analysis of Modular Fault‐Tolerant Permanent Magnet Motor with Unequal Span Windings

The low‐speed and high‐torque modular fault‐tolerant permanent magnet motor has the strong fault‐tolerant ability, and can make the motor output torque act on the load directly, and the system has the highest transmission efficiency, which is especially suitable for ship propulsion. In the electric ship direct‐drive propulsion system, the motor is the core of the power system. Because the motor is directly connected with the load, the intermediate buffer mechanism is canceled, so the smooth operation of the motor is put forward to higher requirements. Especially in some fault‐tolerant operations, the unbalanced radial force generated by the asymmetric operation may cause the motor to vibrate greatly, which will reduce the operational life of the motor and even bring new faults. In serious cases, the whole transmission system will be damaged. Therefore, it is necessary to study the vibration of the fault‐tolerant motor under different operating conditions. In this paper, the module combined stator fault‐tolerant permanent magnetic synchronous motor for ship direct‐drive propulsion is taken as the research object. Based on the Maxwell tensor method, the radial force wave expressions of the motor during regular operation and fault‐tolerant operation are derived, and the harmonic order and frequency, which have a significant influence on vibration are summarized. The radial force of the motor under different operating conditions with different control strategies is calculated by the finite element method, and the harmonic components are analyzed by the two‐dimensional Fourier transform. On this basis, the vibration of the motor and the mechanical strength of the rotor support frame are analyzed. The research results of this paper provide some reference for the subsequent vibration reduction strategies of fault‐tolerant motors. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Investigation into fault tolerant capability of new modular low‐speed and high‐torque direct‐drive permanent magnet motor based on unequal span winding

Investigation into fault tolerant capability of new modular low‐speed and high‐torque direct‐drive permanent magnet motor based on unequal span winding

Free vibration behaviour of thin-walled concrete box-girder bridge using Perspex sheet experimental model

Purpose: Curved box-girder bridges offers an excellent solution to the problems associated with traffic congestion. However, owing to their complex geometry, they are subjected to shear lag, torsional warping and cross-sectional distortion, which must be assessed in their study and design. Furthermore, the dynamic behaviour of curved bridges adds to the complexity of the issue, emphasizing the importance of studying free vibration. The purpose of this study is to numerically model the concrete curved box-girder bridge considering torsional warping, distortion and distortional warping effects and to identify key parameters that influence the free vibration response of the box-girder bridge by validating it with experimental and analytical studies. Design/methodology/approach: The concrete bridge is numerically modelled by means of computationally effective thin-walled box-beam finite elements that consider torsional warping, distortion and distortional warping, which are prominent features of thinwalled box-girders. The free vibration analysis of the concrete curved box-girder bridge is performed by developing a finite element based MATLAB program. Findings: The identification of critical parameters that influence the free vibration behaviour of curved thin-walled concrete box-girder bridges is one of the main findings of the study. Each parameter and its effect has been extensively discussed. Research limitations/implications: The study limits for the preliminary design phase of thin-walled box-girder bridge decks, where a complete three-dimensional finite element analysis is unnecessary. The current approach can be extended to future research using a different method, such as finite element grilling technique on multi-span curved bridges having unequal span.

Quantitative assessment of resistant contributions of two-bay beams with unequal spans

Following the sudden removal of an internal column from a steel-frame composite-floor system, the two-bay beams connected to the failed column play a key role in the internal force redistribution and rebalancing of the remaining structure. Moreover, the span–depth ratios of the adjacent two-bay beams have a significant influence on the collapse-resistant performance of the structure. To date, studies on structural progressive collapse of beams with unequal spans have been limited. In this study, based on the results of static loading tests on composite beam–column assemblies with cover-plate joints under three different span ratios, the finite element modeling method was validated and numerical models of the beam–column assemblies with three unequal spans were established. The influence of the unequal span of two-bay beams on the internal force development and load-resisting mechanisms of the composite beam–column assemblies were analyzed in detail. To gain deeper insight into the load-resisting mechanisms, the contributions of the flexural and catenary mechanism resistances to the total resistance of two-bay beams were quantitatively separated using the energy equilibrium theory, and it was found that the resistant contributions of the catenary mechanism, in general, account for less than a half of the structure’s resistance capacity. Moreover, theoretical formulas for the different resistant contributions of two-bay beams were proposed as recommendations for structural progressive collapse design and practical engineering applications. The analysis of results demonstrated that the span–depth ratios of two-bay beams determined the resistant contribution coefficients for the flexural mechanism, whereas the span ratios of two-bay beams determined the resistant contribution coefficient for the catenary mechanism, whereas the beam depth had little influence thereon.

Key Construction Steps of A Half-Through Basket-Type Tied- Arch Bridge with Unequal Spans and Multiple Arches

Half-through tied-arch bridges feature complex structures and are constructed via numerous processes. As these bridges are deigned more neoteric, their construction is also becoming more complex. The research takes a novel half-through basket-type tied-arch bridge with unequal spans and multiple arches over Sishui River, in Yanzhou, Shandong Province, China as the engineering background. On this basis, the structural characteristics and key construction steps of this type of bridges are analyzed. It is proposed to install triangular areas first and then arch ribs, and to assemble side spans before the middle span, followed by tensioning of hangers. Key construction steps are elaborated, which provides practical and technical reference for similar engineering.

Anti-collapse performance analysis of unequal span steel–concrete composite substructures

In the study, three 1:3-scale unequal span steel–concrete composite substructures with top-seat angle and double web angle connection were designed and identified as specimens GTSDWA-0.6, GTSDWA-1.0, and GTSDWA-1.4. Pseudo-static tests and refined numerical model analysis were conducted to examine the anti-progressive collapse performance of a semi-rigid steel–concrete composite substructure. The results indicated that the failure modes of the three specimens revealed that the fracture occurred in the root of the long leg of the top/seat angle in tension at the connection. With increases in the span ratio of the left and right composite beams, the bearing capacities of the composite substructures decreased, and the corresponding displacement increased. With respect to GTSDWA-0.6 and GTSDWA-1.4, the resistance due to the short composite beam corresponded to 62% and 60%, respectively, and the total resistance provided by the short composite beam exceeded that of the long composite beam. With respect to GTSDWA-1.0, the resistance due to the left and right composite beams was similar. All three specimens underwent the flexure mechanism and flexure–axial mixed mechanism stages. They resisted the external load mainly via the flexure mechanism. Moreover, the addition of stiffeners on both sides of the top and seat angles is advantageous in terms of improving the collapse resistance and ductility of unequal span composite substructures.

A deep granular network with adaptive unequal-length granulation strategy for long-term time series forecasting and its industrial applications

An accurate long-term forecasting for some time series in industrial production is substantially significant for improving the economic efficiency of industry enterprise. In this study, a granular computing (GrC)-based deep learning framework is proposed for long-term time series forecasting, which consists of two stages i.e., the adaptive data granulation and the GrC-based deep model construction. In the first stage, for automatically generating the basic information granules with unequal time span adaptively from data, a stacked sparse auto-encoders granulation network is designed, in which the starting and ending points of a granule are adaptively determined by setting a single neuron in the last hidden layer after multi-layer feature extraction. Then, the second stage sees a definition of a partially overlapping sub-block basis (POSB) matrix to extract the features of these granules, based on which a deep sparse coding feature decomposition-based long-term forecasting model is constructed to transform the unequal-length granules into a product of a POSB matrix and a coefficient matrix layer by layer to serve for forecasting. To verify the effectiveness of the proposed method, two synthetic datasets, two real-world datasets and two practical industrial datasets are employed. The experimental results demonstrate that the proposed method outperforms other data-driven ones on long-term time series forecasting, particularly in an industrial case.

Collapse resistance of composite beam-column assemblies with unequal spans under an internal column-removal scenario

To investigate the collapse performance of composite beam-column assemblies consisting of three columns and two beams with unequal spans under an internal column removal scenario, static loading tests with either unequal spans (1.4:1 or 0.6:1) or an equal span (1:1) were conducted. Experimental results, including the load-displacement responses, failure modes, internal force development and resistance mechanism, are discussed in detail. Besides, the contributions of different resistance mechanisms to the total resistance of the two-bay beams are quantitatively separated, which include the flexural resistance and catenary resistance of two-bay beams. In addition, finite element models of three specimens are validated based on the test results. Furthermore, the numerical models are used to illustrate the effect of the composite effect and unequal height-span ratio of two-bay beams on the collapse-resistant performance of the assembly. The results showed that the concrete slabs contributed to an increased collapse resistance of the composite beam-column assemblies. Decreasing the beam span resulted in a larger resistance under both mechanisms, whereas increasing the beam height increased the resistance under the flexural mechanism but contributed little to that under the catenary mechanism.