Restraint Stiffness Research Articles

Axial compression behavior of mechanized filament-wound GFRP-steel tubed concrete stub columns

Filament-wound is presently the prevailing and efficient process in the field of molding, known for its ability to achieve optimal molding effects. This technique offers numerous advantages, including high precision, a high fiber content. Traditional FRP-steel tubed concrete stub columns (FSTCSCs) are fabricated by longitudinally wrapping FRP sheet, which results in low production efficiency. This paper introduces a mechanized filament-wound FSTCSC, which can achieve overall molding and effectively improve production efficiency. This paper presents an examination of the axial compression performance of mechanically wound FSTCSC. Two variables were considered including FRP wrapping angle and concrete strength. The experimental results reveal that fiber fracture of mechanized filament-wound FSTCSC is a gradual process, with damage starting from the outermost layer. When GFRP undergoes fracture, a higher wrapping angle results in enhanced restraint stiffness but reduced ductility. Moreover, the validated finite element model is used to analyze the parameters such as the wrapping angle and the thickness of GFRP tube, and it is found that adjusting both upward and downward wrapping angles plays a role in boosting the peak load carrying capacity. Furthermore, five models for predicting ultimate strengths were evaluated using test results, followed by the provision of recommendations for practical design.

Local Stability Analysis of a Composite Corrugated Steel Plate Pipe-Arch in Soil

The straight part of the corrugated steel plate (CSP) pipe-arch structure in soil may cause local buckling instability due to insufficient load-bearing capacity. Recently, composite CSP pipe-arch has been widely utilized to enhance structural stability, and their stability needs to be thoroughly investigated. This paper studies the local buckling stability problem of the straight part of composite CSP pipe-arch in soil by simplifying the soil support and introducing the inter-layer bonding effect. Based on elastic stability theory, a theoretical mechanical model of composite CSP pipe-arch was proposed. The Rayleigh–Ritz method and the semi-combined composite structure stiffness approximation were used to derive the critical buckling conditions for the straight part of the composite CSP pipe-arch. Through numerical calculation and influencing factors analysis, it is concluded that the critical buckling load of the straight part of the composite CSP pipe-arch structure is affected by the elastic modulus, thickness, Poisson’s ratio, rotational restraint stiffness and side length of the straight part of the material. In particular, it is found that as the inter-layer bonding coefficient increases, the critical buckling load is improved, while the critical buckling wave number is mainly influenced by the width of the straight part, elastic modulus, and inter-layer bonding coefficient. Additionally, we discussed the coupling effect of several key parameters on the stability of the structure. The results of this study offer theoretical foundations and guidance for the application of composite CSP pipe-arch in soil engineering, such as culverts, tunnels, and pipeline transportation.

Design method of prestressed anchor bolt system for wind turbine foundation

SummaryThe prestressed anchor bolt system is a reasonable connection mode between the upper steel tower and the bottom concrete foundation for multi‐megawatt wind turbines. This prestressed anchor bolt connection with forged flanges has a similar form to the prestressed high‐strength bolt connection with forged flanges between steel tubes for the tower. However, their mechanical performances have a great difference because of the influence of the stiffness of the anchorage zone in the concrete foundation. Based on the Petersen's method, the engineering calculation method of the prestressed anchor bolt system for wind turbine foundation is derived. The tensile force of the anchor bolt, the anchorage stiffness and clamping force of the base are all deduced according to the theories of mechanics of materials. The numerical models of the segment foundation with the unfavorable anchor bolt and the overall foundation with all anchor bolts are developed for researching the influence of the spatial effect of adjacent segments on the restraint stiffness of the concrete foundation. The numerical analyses of four engineering cases designed by engineering calculation method are carried out for verifying the effectiveness of engineering calculation method. The analysis results show the spatial effect of adjacent segments can be neglected and the Petersen's method can be directly applied for the design of the prestressed anchor bolt system for wind turbine foundation in engineering practice. The engineering calculation method meets the accuracy requirements in engineering practice and can be used to design the prestressed anchor bolt system of wind turbine foundation.

Buckling mechanism and modified direct strength method of CFS built-up beams with multi-box cross section

A comprehensive study on the buckling mechanism of the Cold-Formed Steel (CFS) box beam composed of C- and U-shaped channels is conducted in order to improve the accuracy of the Direct Strength Method for calculating the bending capacity of CFS beams. Experimental tests involving four-point bending are carried out on six CFS box beams with varying screw spacing and stiffener numbers. In addition, numerical analyses are performed by finite element method. Based on the investigation of experiments and parameter analysis, an elastic constraint model for web buckling is proposed and the buckling coefficient are derived by the application of a generalized variational principle. The experiments reveal an interaction between local buckling in the upper flange under compression and the web. When the upper flange in compression buckles before the web, it leads to a reduction in the lateral constraint stiffness of the flange on the web, consequently, resulting in web buckling. An elastic constraint model for web buckling is proposed, incorporating the constraint effects of the upper flange's elastic support on the web. The critical buckling stress and buckling coefficient of the model are derived using the generalized variational principle. According to the experimental and numerical analysis results, the relative restraint stiffness of the flange on the web shows effects on the buckling coefficient. As the screw spacing and the length of the pure bending area decrease, as well as the number of stiffeners increases, the relative restraint stiffness increases. Subsequently, this leads to an increase in the buckling load and ultimate displacement of the CFS beam. Considering the interaction between the buckling of flange and web, the Direct Strength Method in AISI-2016 is modified for the CFS built-up box beam composed of C- and U-shaped channels. The applicability and correctness of the proposed modified Direct Strength Method is approved through the application of multi-box CFS beams composed of 2C-2 U and 3C–2 U channels. Compared with the Effective Width Method in current Chinese code and Direct Strength Method in AISI-2016, the proposed modified DSM exhibits the highest accuracy in predicting the bending capacity of the CFS box beam. It is shown that the proposed method can be effectively employed to calculate the flexural capacity of CFS beams with multi-box under local buckling control.

Resistance Behaviours of Clamped HFR-LWC Beam Using Membrane Approach

Beam-like members sustaining the combined action of transverse load and membrane force exhibit a special load response to progressive deflection. A theoretical model is therefore developed to depict the resistance behaviours of clamped reinforced concrete (RC) beams observed in tests. The support-induced membrane effects are simulated by a longitudinal spring and a rotational spring. The load responses to progressive deflection are obtained using the membrane approach, and the prediction accuracies of proposed method are validated by a series of four-point bending tests on hybrid fibre reinforced-lightweight aggregate concrete (HFR-LWC) beam. It is illustrated that the bearing capacities of clamped HFR-LWC beam are significantly enhanced by the membrane effect. Ultimate load of the clamped beam ranges from 64.0 to 184.0 kN, and the larger bearing capacity compared with simply supported beam is obtained. An ultimate load of 1.85 to 5.31 times the yield line value is achieved, and thereby, the ultimate resistance of the clamped beam might be seriously underestimated using yield line approach. A strong support constraint is beneficial for increasing the load-carrying capacity of clamped HFR-LWC beam, although the large longitudinal restraint stiffness would inevitably gives rise to brittle failure. The relative errors between predicted load and measured value are less than 7.23%, indicating that the presented model is a promising tool to estimate the ultimate load of clamped beam-like member.

Analytical model of compressive arch action for one-way RC beams and two-way framed substructures under column removal scenarios

This paper proposes a direct analytical model to evaluate compressive arch action (CAA) of reinforced concrete (RC) beam-column sub-assemblages under middle column removal scenario (MCRS), incorporating bending curvature of the double-span beam, and different horizontal and rotational restraint conditions at the beam ends. Based on the proposed approach, the structural engineer can easily obtain the CAA peak capacity and the corresponding CAA displacement by hand calculations. Unlike the previous models in which the accuracy highly relies on pre-assumed CAA displacement, this prediction approach directly derives the CAA displacement and CAA capacity through force equilibrium, geometric relationship, compatibility and boundary conditions, incorporating various horizontal restraint conditions, span-to-depth ratio and section profile of the bridging beam. Comparison with existing test results in available literature indicates that this model not only gives good predictions of peak capacity, displacement and maximum axial beam force in CAA, but also incorporates the effect of horizontal restraint stiffness and working stress of compression reinforcement. Besides, a further simplified explicit model is proposed to enhance usability in practical design, and sensitive studies are conducted to study how the simplification affects the prediction accuracy of vertical CAA capacity and displacement. Thereafter, the proposed model is extended to substructures with orthogonal beams in X- and Y- directions to predict CAA capacity under different column removal scenarios such as interior, penultimate, edge and corner column removal cases.

Enhanced rational horizontal tying force method for practical robustness design of building structures

Under the backdrop of the rational horizontal tying force method recently developed at Imperial College London, which focuses on the tying resistance of floor systems based on constant tying forces and its planar interaction with the surrounding structure alone, this paper presents relevant enhancements to the original method. These enhancements involve simplified mechanics-based models quantifying i) the residual flexural resistance arising from the curtailed reinforcement in tying via beams, ii) the additional flexural resistance from transverse beam in one-way tying via floor systems and iii) the planar restraint stiffness from the surrounding structure, including the influence of the compressive ring mobilised within the affected floor system under tensile membrane action. Following a detailed exposition of the formulation of the models, the paper presents several studies which demonstrate the effectiveness of the enhanced tying force method. Importantly, the method addresses resistance and stiffness mechanisms not covered in the current prescriptive tying requirements within a practical application framework that is still comparable in simplicity to such requirements, thereby further promoting the rational horizontal tying force method as a potential replacement for the prescriptive tying requirements in the next generation of robustness design codes.

Quantifying the effect of end support restraints on vibration serviceability of mass timber floor systems: Testing

Design of mass timber floor systems is commonly governed by vibration serviceability due to high stiffness-to-weight ratio and low inherent damping of timber. Research and design practice have shown that static deflection under a concentrated load and fundamental natural frequency can be effective and robust indicators for vibration performance of mass timber floors. These design parameters are normally calculated by assuming simply supported conditions in existing design methods. However, such an assumption deviates from actual floor supports, especially in platform-framed buildings, and in-situ end support restraints have been widely recognized as a significant factor affecting the vibration performance. The purpose of the study is to quantify the influence of end support restraints on vibration serviceability of mass timber floors in platform construction through a comprehensive experimental program and analytical treatment. This paper is the first part and focus specifically on the experimental work on cross-laminated timber (CLT) panels. In particular, extensive laboratory tests have been conducted on different CLT floor panels with various end support restraints induced by top loads, self-tapping screws and steel angle brackets. The fundamental natural frequency and mid-span deflection under a concentrated load were measured for each end support configuration. The rotational restraint stiffness was determined by comparing results of restrained supports to those of simple supports and represented as end fixity factors. The analysis of test results shows that the CLT floor-to-wall connection exhibited inherent non-linear behaviour and such characteristic was more significant for higher top loads. Compared with screws and brackets, the top loads dominated the partially restrained effect but such dominance gradually diminished for lower-level top loads. In addition, support wall thickness notably impacts the support restraint. It was then suggested that the clear span could be used to determine deflection and frequency in the design, but further investigation is needed.

Natural Frequency Maximization of Beam with an Internal Sliding Joint of Translational Restraint

The natural frequency variation of a uniform Euler–Bernoulli beam with an internal sliding joint of the translational restraint is studied intensively such that the optimal design of the connecting point is pursued for maximization of a natural frequency of the system. First, the compatibility conditions at the linkage are presented in detail, and the dynamic characteristic equation of the beam system is accordingly derived. Next, the influences of both the translational restraint stiffness and the position of the sliding joint upon the natural frequency and mode shape are described comprehensively. Then, the optimal position and the corresponding minimum translational stiffness of the internal joint are explored exclusively for maximizing a natural frequency of the beam structure. In this context, the essential requirements for the optimization of the internal sliding joint are presented, respectively, in two different ways to reveal their mechanical implications. It turns out that the optimal joint location can be determined readily from the corresponding mode shape of the equivalent continuous beam. Afterward, numerical results are provided with two classical beams of a single internal sliding joint to demonstrate the variations of their dynamic characteristics as well as to offer significant physical insight into the vibratory behaviors of the beam system with maximization of a natural frequency of interest.

Seismic Performance Assessment of a Cable-Damper Stopper Equipped for Coal-Fired Thermal Power Plants: Theoretical and Numerical Analyses

ABSTRACT A new cable-damper stopper equipped for Coal-Fired Thermal Power Plants (CFTPPs) was proposed in our previous paper, where a series of shaking table tests were carried out to investigate its seismic performance, so this paper aims to reveal the working mechanism of the stopper from the theoretical and numerical simulation aspects. The stopper is composed of three main components, i.e. a steel cable, a steel block and a viscous damper. First, the nonlinear restraint stiffness of the steel cable to the boiler was derived; second, the critical damping of the stopper, which makes the vibration of the boiler decay exponentially with no oscillation, was derived; third, an iterative method was proposed to globally tune the CFTPP structure, which makes it possible to obtain the optimal parameters of the cable-damper stopper, including the diameter of the steel cable and damping coefficient of the damper. Finally, finite element models were built and time history analyses were conducted to verify the proposed optimization approach. Firstly, the finite element models were proved valid through the comparison between the results of the simulations and the experiments. Then, based on the results of the simulations, the theoretical procedure was validated. The results revealed that the proposed cable-damper stopper reduced the seismic responses of displacements of the top floor and the boiler significantly, about 30.18% and 60.01% respectively compared with their counterparts of CFTPPs without stoppers.

Behaviour of axially-restrained slender steel tubes exposed to fire

The behaviour of axially-restrained slender steel tubes exposed to fire was studied. Fire tests and corresponding finite element (FE) simulations were conducted on four specimens with varying slenderness ratios and axial restraint stiffness. The accuracy of FE simulation was validated against the test results. Both the test and numerical results showed that the axially-restrained slender steel tubes buckled at much lower temperatures than steel columns. Continuous temperature elevation was then required to complete their buckling, because the steel maintains considerable stiffness at the buckling temperature. Parametric analysis was conducted based on FE simulations to investigate the effect of the slenderness ratio, axial restraint stiffness, and peak temperature on the behaviour of axially-restrained slender steel tubes exposed to fire. Empirical equations were established for the buckling temperature and post-fire residual lateral displacement using response surface methodology. These equations demonstrated a strong ability to fit the experimental data and predict the responses for new scenarios.

Buckling and critical temperatures of restrained H-section steel columns in fire considering dynamic effect

In this paper, a parametric analysis on the buckling and critical temperatures of restrained H-section steel columns in fire, considering the dynamic effect, is presented. The developed finite element model of steel columns was verified by test results. Then, the buckling and critical temperatures of steel columns, obtained by static and explicit dynamic analyses, were compared. Moreover, the effects of rotational and axial restraint stiffness ratios, as well as load ratios, were studied. It was found that as the rotational restraint stiffness ratio increased, the buckling and critical temperatures both rose, and the rotational restraint stiffness ratio affected the critical temperature more than the buckling temperature. Besides, when the axial restraint stiffness ratio and load ratio rose, the buckling and critical temperatures dropped significantly. Finally, by combining the findings of the research and existing calculation formulas in literatures, new simplified formulas for buckling and critical temperatures were proposed, respectively. The prediction results of the proposed calculation formulas agreed well with the parametric analysis results. The proposed formulas were further verified by test data. According to the comparative results, the proposed formulas could well predict the buckling and critical temperatures of steel columns in fire.

Identification of vertical restraint stiffness of foundation for continuous-beam bridges

With the progress of engineering technology, the natural frequency of structures can be easily obtained by dynamic testing. If the relationship between the fundamental frequency and the constraint stiffness is analysed, the constraint stiffness of the foundation can be identified. To this end, the vertical vibration of piers is first carried out, and a dynamic identification method for constraint stiffness is proposed. Relying on a project example of a bare pier, the vertical fundamental frequency of the test pier is measured by the pulsation method. Then finite-element software is used to establish a test pier model. The stiffness identification is simulated in the completion stage by adding elastic support and concentrated mass on the top of the model pier. The results show that the difference between the identification results of the bare pier and the calculated value according to the empirical formula is only 2.97%. The error of the identification results obtained by simulating the completion stage is less than 2.34%, and decreases with the increase of the constraint stiffness of the pier top. This method is highly accurate and therefore suitable for identifying the vertical restraint stiffness of the foundation of constant section piers of continuous beam bridges.

Theoretical and experimental study on overall stability for the thin-walled double cantilever photovoltaic stent under uniform pressure

As an important part of the solar-energy system, the bearing capacity design is crucial to the photovoltaic stent structure. It consists of thin-walled steel components, which are prone to bending and torsional buckling after being stressed. However, it is rare to conduct a comprehensive analysis and experimental research on the lateral-torsional buckling (LTB) behavior of the photovoltaic stent. In this study, Rayleigh-Ritz method is utilized to analyze the stability of the Z-shaped thin-walled Double Cantilever Photovoltaic Stent (DCPS) under uniform pressure, and the theoretical formulas for its critical load are derived. In addition, the stability failure experiment and Finite-Element (FE) simulation of the thin-walled DCPS under uniform pressure are carried out. Through mutual verification of the theoretical derivation, experimental data and FE modeling results, the failure modes of the DCPS under uniform pressure is studied, the effects of different influencing factors on the bearing capacity of the structure are studied through the parametric analysis, and the theoretical formula of torsional restraint stiffness Kr is given based on laboratory test data. The research results can provide a reference for the design of photovoltaic structures.

Frequency Variation of Beam with an Internal Hinge of Rotational Restraint

The frequency variation problem of a classical beam with a rotationally restrained internal hinge arbitrarily located is studied intensively. The characteristic equations of the natural vibration are derived rigorously upon the corresponding boundary conditions and the compatibility conditions at the interconnecting point such that the effects of both the rotational restraint stiffness and the hinge position on the natural frequencies and mode shapes are described comprehensively. In the context, the critical locations of an internal hinge are investigated extensively to obtain the extreme values of a natural frequency of the beam system, and the associated requirements are explored in depth. It appears that the essential conditions for obtaining the critical points with regard to the maximum or minimum frequency come, respectively, from the same compatibility relation of the rotational flexibility in view of the opposite criteria. Numerical results are provided with two representative uniform beams to show the variations of their dynamic characteristics and to gain new insights into the transition conditions in the two distinct cases.

Numerical study on the fire behaviour of restrained steel-concrete composite beams

An elaborate solid-shell finite element model was developed to investigate the fire behavior of restrained steel-concrete composite beams. The model was validated against experimental results in literatures. Parametric studies were also performed to study the parameters including restraint stiffness, load ratio, span, exposure length, embedding depth, steel beam height and protective layer on the fire behavior of restrained composite beam. The analysis results show that the mechanical response of restrained composite beams goes through four phases: elastic, elasto-plastic, rapid plastic deformation and plastic catenary action phase. With the decrease of restraint stiffness, the increase of load and span, the failure mode of the restrained composite beam changes from overall lateral instability to a sharp increase in deformation rate, and the code BS476-20 and ISO834 underestimate the fire resistance of restrained composite beams. The negative bending moment at the beam end increases sharply and reaches the peak value within a short fire time. Therefore, reinforcement shall be provided at the top of the concrete slab near the support section. Furthermore, the difference in fire resistance of restrained composite beams is mainly reflected in the plastic catenary action phase. When the load ratio is less than 0.5, the fire resistance of restrained composite beams can be improved by reducing the fire range, beam height and span, and increasing the axial restraint stiffness. When the load ratio is 0.7, the fire resistance of restrained composite beam is hardly affected by the axial restraint stiffness and span, while with the exposure length reducing from 5 m to 4 m, embedded depth increasing from 0 mm to 50 mm, and the protective layer increasing from 0 mm to 10 mm, the fire resistance of the composite beams increases by 114 min and 160 min and 76 min, respectively.

Analytical solutions for thermal effects of suspension bridges based on a surrogate model with longitudinal restraint stiffness

Ambient temperature variation has a significant influence on the deformation of main cables and the internal force of towers of long-span suspension bridges. Currently, the finite element method (FEM) is mainly used for these calculations. This paper intends to present an analytical solution of the thermal effects on suspension bridges. First, three typical temperature patterns are defined. Then, a surrogate model is established by replacing the longitudinal restraint stiffness of the main cable and the tower lateral stiffness with a set of equivalent horizontal springs. The stiffnesses of the suspended cables are formulated according to the energy conservation principle, while the tower lateral stiffnesses are obtained by incorporating the pure bending and Euler buckling solutions, namely considering the effect of the axial force placed on the tower top. Following the force equilibrium conditions, two governing equations are built, which can calculate the variations in the longitudinal displacement of the tower top caused by the temperature variation. After that, some other significant thermal effects, such as the horizontal force of the main cable, the sag of the main cable and the bending moment of the tower bottom, are obtained. Finally, the analytical solution is verified through the field test data of the Tsing Ma Bridge in Hong Kong and the FEM results of four typical examples. The proposed surrogate model offers a quick and easy approach for thermal effect analysis with acceptable accuracy. It is helpful to clarify the mechanical nature of temperature effects to facilitate the preliminary bridge design.

A Coupling Optimization Method of Vehicle Structure and Restraint System for Occupant Injury Protection in Traffic Accidents

Vehicle front-end structure has the characteristic of symmetry. The damage of occupants in the crash process is determined by the combined effect of the front-end structure and the restraint system of the vehicle. In this paper, the coupling relationship and an optimized method for the vehicle front-end structure and restraint system are studied based on vehicle crash dynamics, to reduce occupant injury. A fast solution algorithm for occupant motion response was established using a crash analytical model. Then, an occupant response database was established using the algorithm, to analyze the coupling relationship between the crash pulse and the restraint specific stiffness, with respect to the curve shape and parameters. The results showed that the combination of the concave crash pulse and upward restraint stiffness curve was the best coupling. Subsequently, a coupled optimization method of a concave pulse and upward restraint stiffness was proposed and combined with a crash analytical model and genetic algorithm (GA). The crash pulse and restraint stiffness of vehicle crash data from the NHTSA databases were optimized, as an example, to verify the effectiveness of the method. The optimal occupant acceleration was reduced by 44%. In addition, the feasibility of the optimal result is discussed, to provide a reference for occupant injury protection in traffic accidents.

Influence of H-column stiffness on the anti-collapse performance of composite frame in the minor-axis direction

This study is the first attempt to investigate the resistance mechanism in the minor axis of H-columns and aims to provide essential information for improving the reliability of the anti-collapse transmission path of spatial structures. A one-third scale composite frame extending in the minor-axis direction of the H-column, comprising a welded flange and bolted web beam–beam connection, was investigated through monotonic static loading test to clarify the resistance transmission mechanism of structures. Based on the progress in the internal force under different displacements, the minor-axis specimen experienced stages of elasticity, compression arch, and mixed mechanism. The influence of column stiffness on the resistance and internal force development in the minor-axis specimen was comparatively significant with respect to the results of the major-axis specimen. For parametric analysis, a full-scale model was developed, which confirmed the influence of column stiffness and boundary axial restraint stiffness on collapse performance of composite frames in the minor-axis direction, providing an underlying mechanism for anti-collapse design and optimization research. Furthermore, a multispan solid model was developed to reflect the attenuation law of the axial restraint stiffness provided by the external substructure (surroundings) with the appropriate number of spans, which assisted in formulating a simplified modeling process. To avoid or delay the negative impact of potential defects on the structure, local weakening strategies were applied to the minor-axis direction based on the experimental and simulation results, and the collapse resistance mechanism was verified using the developed model.

Development of design equations for ultra-high strength steel CHS columns under transient fire conditions considering thermal creep and axial restraint effects

Despite their potential for widespread structural applications, the use of ultra-high strength steel (UHSS) members in buildings is currently hindered by the lack of suitable design relationships for these components. In response to this technical gap, this paper presents design equations for Grade 1200 UHSS circular hollow section (CHS) columns under transient fire conditions. The design relationships are derived from an extensive parametric study on the in-fire behavior of UHSS tube columns using advanced finite element (FE) simulations in ABAQUS software. However, to verify the FE modeling framework, experiments are also conducted on axially-compressed UHSS tube specimens. The thermal creep of the UHSS tubes is explicitly included as a user-defined subroutine in the modeling by a robust creep model exclusively developed for the UHSS material under transient fire conditions. In addition to the utilization factor, the effects of non-dimensional slenderness, heating rate (or thermal creep), and axial restraint stiffness ratio are also studied and considered in the design equations obtained for the UHSS CHS columns. Finally, it is shown that the present design relationships can predict the columns' buckling and failure temperatures with a maximum absolute error (MAE) of 4%.