Brace Stiffness Research Articles

Analysis of influence factors and stability of concrete-filled steel tube arch bridge

A structural calculation model of a fly-bird-type concrete-filled steel tube arch bridge was established by using large general finite element software. The stability of the bridge during construction and in each working condition was numerically simulated and analysed. Linear elasticity, geometric nonlinearity and material nonlinearity stability safety factors were calculated and their influences on the stability were compared. At the same time, the main influence factors of the fly-bird-type concrete-filled steel tube arch bridge stability are discussed, the influences of the wind bracing number, form and stiffness on the bridge stability are calculated and analysed, and the reasonable values or forms range and the structural stability influencing factors under different value conditions are studied.

Using model error in response history analysis to evaluate component calibration methods

SummaryThis research is part of a larger effort to better understand and quantify the epistemic model uncertainty in dynamic response‐history simulations. This paper focuses on how calibration methods influence model uncertainty. Structural models in earthquake engineering are typically built up from independently calibrated component models. During component calibration, engineers often use experimental component response under quasi‐static loading to find parameters that minimize the error in structural response under dynamic loading. Since the calibration and the simulation environments are different, if a calibration method wants to provide optimal parameters for simulation, it has to focus on features of the component response that are important from the perspective of global structural behavior. Relevance describes how efficiently a calibration method can focus on such important features. A framework of virtual experiments and a methodology is proposed to evaluate the influence of calibration relevance on model error in simulations. The evaluation is demonstrated through a case study with buckling‐restrained braced frames (BRBF). Two calibration methods are compared in the case study. The first, highly relevant calibration method is based on stiffness and hardening characteristics of braces; the second, less relevant calibration method is based on the axial force response of braces. The highly relevant calibration method consistently identified the preferable parameter sets. In contrast, the less relevant calibration method showed poor to mediocre performance. The framework and methodology presented here are not limited to BRBF. They have the potential to facilitate and systematize the improvement of component‐model calibration methods for any structural system.

Comparison of Seismic Behavior of Buckling-restrained Braces and Yielding Brace System in Irregular and Regular Steel Frames under Mainshock and Mainshock-Aftershock

Due to low stiffness of braces after yielding, the structures with buckling-restrained braces (BRBs) experience high residual drifts during an earthquake, which can be intensified by aftershocks and causes considerable damages to structures. Also, due to poor distribution of stiffness, this problem is exacerbated for irregular structures. Recently, the yielding brace system (YBS) has been introduced; which is an alternative to BRBFs to solve this problem. YBS has a secondary stiffening part in its hysteresis behavior which can prevent excessive deformations. Therefore, structures with YBS are expected to show a better peroformance in seismic sequences compared to BRBs. However, the seismic behavior of the YBS system in irregular structures has not been studied so far. On this basis, this paper investigates the seismic behavior of frames with BRB and YBS in regular and irregular structures under seismic sequences. Twenty four 4-, 8-, and 12-story frames with these two systems were designed and evaluated. First, a nonlinear dynamic analysis was conducted on the frames under mainshocks, and the maximum interstory drift and the residual interstory drift of the frames were compared. Then, using incremental dynamic analysis and fragility curves, the behavior of the frames under mainshocks was investigated. Afterwards, using incremental dynamic analysis and fragility curves, the behavior of the structures under mainshock-aftershock in three performance levels was aledso investigated. The results showed that YBS bracing, especially in low rise structures, leads to far lower maximum drifts and maximum residual drifts than BRB braces, which can reduce the probability of the occurrence of soft stories in structures.

Concept and development of a steel\u2013bamboo SI (skeleton\u2013infill) system: experimental and theoretical analysis

A steel–bamboo SI (skeleton–infill) system with steel frame as the skeleton and bamboo box as the filler is proposed, which realizes the requirements of building assembly and sustainable development. As a first step in studying the seismic behavior of the steel–bamboo SI (skeleton–infill) system, a simplified plane steel frame–bamboo infilled wall structure is tested under low-cycle reversed loading in this paper. The deformation mode, failure mode, hysteretic behavior and energy dissipation performance of the system are discussed. The test showed that the steel frame and the bamboo infilled wall were well connected and could work together. Then, the formulas for calculating the lateral stiffness of the system and the axial stiffness of the equivalent diagonal brace which replaced the infilled wall are obtained by theoretical analysis. The error between theoretical calculation and test results was about 1.3%, which proved the correctness of the proposed formula.

Numerical analysis of self-centering energy dissipation brace with arc steel plate for seismic resistance

A self-centering energy dissipation brace (SEDB) with an arc steel plate was designed to improve the seismic performance of a structure and reduce the residual structural deformation after an earthquake. Seven groups of self-centering energy dissipation brace models of arc steel plates with different configurations were established based on ABAQUS software. A method for calculating the internal forces, stiffness, yield displacement and yield load of a brace was derived and shows agreement with theoretical values. This brace shows a favorable hysteretic performance that corresponds to its full, flag-shaped hysteretic curve. The stiffness transition of various stages is smooth and stable. The maximum residual deformation of the component is 3.75 mm and decreases as prepressing of the disc springs is increased. The component's reset performance can be fully utilized to satisfy specific needs. The advised values for designing the energy dissipation components of an arc steel plate are described as follows: 1/250 of a radian, width of 50–80 mm and thickness of 20 mm. The damping force, damping displacement and brace stiffness of the SEDB can be adjusted by the structural parameters of the arc steel plate to satisfy the engineering requirements.

Force Development Prediction Model for Constrained Lithium-Ion Pouch Cells

Mechanical stability of lithium-ion battery modules is crucial for the safety of electric vehicles. This is challenging to ensure as cells show irreversible thickness growth over lifetime. Therefore, mechanical bracing of cells and the consequent force on the module housing increases over lifetime. Furthermore, both too low and too high mechanical pressure on cells have been shown to have negative impact on their lifetime due to layer delamination and lithium plating, respectively [1]. Consequently, an integrated design should realize medium cell pressures over the entire lifetime. Thus, in order to properly design a module for a specific cell in a given installation space a force prediction model is necessary which may consider the potential addition of pressure pads. Unfortunately, both a comprehensive modeling technique as well as automotive module force development data over lifetime are unavailable in literature. Cell thickness growth is mainly attributed to solid electrolyte interface (SEI) growth on anode particles with consequent cycling [2]. Slightly grown particles cause the macroscopic electrode to expand upon mechanical reorganization of the microstructure caused by the cyclic swelling. Thus, cell thickness growth correlates directly with loss of active lithium to the SEI and – in the limited case – to the capacity loss of the cell [2]. A novel one-dimensional mechano-electrochemical model is presented which considers the cell stack in force equilibrium with its bracing module. For this, a fixed bracing stiffness and an aging-dependent cell stack stiffness is considered where the cell stack may consist of cells with or without pressure pads. Care is taken to implement the aging anode lithiation degrees in the graphite anode affected by lithium loss influencing the reversibility of SOC dependent swelling. The experimental data required for the model are the module dimensions, stiffness data of components and the cell thickness growth of cells over aging. The latter is measured in a constant-force cell aging experiment where the cell thickness evolution is measured. Based on this, the model may predict force development of the module over lifetime and can thus a priori validate designs or considered pressure pads. For model validation, automotive modules with and without pressure pads are aged in representative as well as accelerated aging conditions. The force development is determined at several points during aging by correlating 3D-deformations of module capping plates to a reference experiment. Such measurements of force development over lifetime in automotive modules have not been reported yet. Both accelerated and representative aging conditions show similar force evolution as correlated to capacity loss but not to energy throughput. Crucially, the predictions of the model are validated by the force evolution in the modules in both cases. As designed modules with pressure pads show significantly attenuated force development which is also successfully predicted by the model. Remaining errors exist at higher pressures which have to be investigated in detail in the future. The presented model is a powerful tool to quantitatively validate module and pressure pad designs as well as predict force evolution in given bracing conditions.

Seismic performance improvement of tension-only-braced frames with Energy-Dissipative Rocking Columns

Steel braced frames consisting of strong beams, weak columns, and tension-only braces (BTFs) have been extensively used in low-rise steel buildings, since it is prefabricated rapidly and is cost-efficient. However, BTFs are vulnerable to soft story failure due to the negligible post-yielding stiffness of tension-only braces. A novel device of Energy-Dissipative Rocking Column (EDRC) is proposed to improve the seismic performance of BTFs. An EDRC consists of dual hinge supported steel column branches and replaceable steel strip dampers between them. Firstly, the effectiveness of EDRCs were verified through nonlinear time history analyses on benchmark multi-story BTFs using a suite of far-field ground motion records. Secondly, systematic parametric studies are conducted to quantify the effect of key influencing factors such as stiffness ratio of EDRC to BTF and bending stiffness of column branches on the seismic performance improvement of BTF-EDRC systems. The results show that the maximum inter-story drift and inter-story drift concentration under earthquakes as well as the residual drift after earthquakes can be significantly mitigated by coupling with EDRC. It is found that the maximum inter-story drift ratio can be reduced by 50% when the stiffness ratio of EDRC to BTF reached 1.0. The most effective stiffness ratio of EDRC to BTF for mitigating the inter-story drift concentration and residual drift ratio falls in a range of no more than 0.2 and 0.4, respectively.

Study on Synthesis Stiffness of Inner Supported Deep Excavation in Soft Soil Area

The horizontal displacement of retaining structure is particularly associated with synthesis stiffness of support system. The synthesis stiffness of support system is highly interrelated with three parts including the retaining wall, the inner brace and the soil at bottom of excavation. In order to estimate the lateral movement of retaining wall, a synthesis stiffness formula is been proposed. The proposed model concludes a variety of factors, such as horizontal flexural rigidity of retaining wall, compressional stiffness of inner brace, average vertical support spacing, average horizontal support spacing, depth of wall penetration and stiffness of the soil below final excavation depth. Comparing with the Clough synthesis stiffness, more factors is been considered. Comparing with the MVSS synthesis stiffness, the factor of soil below final excavation is been defined exactly. After that, finite element method is employed to calculate the maximal lateral displacement of the retaining wall. And a good relationship is established between maximal horizontal displacement and synthesis stiffness formula. Finally, the calculations are used to compare with the observed data from several deep excavations, the result validates the applicability of proposed model. The research provides a new method for describing the comprehensive stiffness of support system of foundation pit. It is convenient to estimate the maximum horizontal displacement of the retaining structure at the design stage and to select the support system quickly.

Investigation of dielectric elastomer human energy harvesting to reduce knee joint torque deviation due to bracing.

IntroductionThe use of a smart electromechanical material, dielectric elastomer, is investigated for the development of an active bracing technique, which modifies the stiffness and damping of the knee brace during energy harvesting so as to reduce knee joint torque deviation during late swing in braced walking.MethodsThe bracing technique considered involves a dielectric elastomer energy harvesting cycle, which activates only when the knee flexor muscles are contracting eccentrically during late swing. The brace reduces the leg extension deviation during late swing in braced walking by transforming a portion of the mechanical stored energy into electrical energy, reducing the required internal work performed within the body.ResultsSimulated behavior of the dielectric elastomer brace worn across the knee joint demonstrates that when properly activated, the dielectric elastomer brace’s reduction in stiffness and increase in damping minimize the added energy expenditure of knee joint bracing during late swing.ConclusionsThe modeling results demonstrate the effective application of a soft, circumferential, dielectric elastomer energy harvesting knee brace, which utilizes the changes in the dynamic behavior of the knee joint occurring during energy harvesting in order to reduce the added demand placed on the knee joint under braced conditions.

Influence of mean period of ground motion on inelastic drift demands in CBFs designed to Eurocode 8

The influence of mean ground motion period, Tm, on the inelastic drift response of steel Concentrically Braced Frame (CBF) structures designed to Eurocode 8 is investigated. Incremental dynamic analysis is performed for a set of case study frames with varying structural characteristics at four different seismic intensity levels. From the results of these analyses, regression models for predicting both global and inter-storey drift are developed. It is shown that that both global and inter-storey drift tend to increase nonlinearly as the ratio of fundamental structural period to mean ground motion period, T1/Tm, decreases below unity. The rate of this increase is dependent on the ground motion intensity, represented by the EC8 behaviour factor q. The first mode participation factor, relative storey stiffness and column-to brace stiffness are also shown to influence inter-storey drift response. The values of drift predicted by the developed regression models are compared to values predicted by design codes as well as other predictive models developed in previous studies. It is observed that design codes can under predict drift at lower T1/Tm values.

Experimental investigation of combined vibrations for a hydrofoil-rod system at low Reynold numbers

A hydrodynamic tunnel experimental investigation and analysis of vibration characteristics for a hydrofoil in a transient regime is considered. Tests are performed for NACA 0017 models with a non-uniform section at an angle of attack AOA = 5o and Reynolds numbers up to Re = 7.0 × 106. This study is related to a project design of experiments in a complex facility that involves several parameters. The analysis focuses on the vibrations of a hydrofoil for different values of the bracing stiffness kh, the torsional stiffness ka, and the locations of the elastic axis ā and of the center of gravity xa. The structural bracing response is investigated via measurements of the displacement of the free tip section of the hydrofoil using a three-axis acceleration sensor, and the torsional response of the structure is analyzed via measurements of displacements with single-axis acceleration sensors. The hydrofoil is made of reinforced plastics without flexibility, and elastic functions are provided by a spring support mechanism combined with a torsional structure. The study shows that an increase of the velocity V∞ results in different behaviors of the bracing and torsional amplitudes. Another notable result of the study is that the emergence of transition occurs simultaneously with additional peaks and changes of vibration amplitudes.

The Effects on the Bracing Stiffness of Timber Structures of the Stiffness of Its Members

The design of slender structures is often associated with a number of assumptions made by engineers in checking on the stability of the structure. Not seldom, these assumptions are rather uncertain. In the present paper the effects of the stiffness of different members on the bracing stiffness of timber structures is studied. Both full-scale laboratory testing and FE-modelling are employed here in the investigation. In particular, two different bracing approaches are analysed, those of (1) cross bracing (wind trusses) and (2) diaphragm action (through use of steel sheeting) in the plane of the roof. In addition, the effects of the connections and the number of fasteners used in the structure are evaluated. The stiffness of the connections is obtained by means of an FE-updating approach, i.e. that the relevant parts included in the FE-model are calibrated to ensure that the FE-results match the laboratory results. The findings obtained indicated, (1) that the connections can have a significant effect on the stiffness of the bracing systems, (2) that the cross bracings close to the mid-span of the structure are less effective than those close to the supports, (3) that the lateral stiffness obtained using a diaphragm approach is closely related to the number of fasteners between the steel sheet and the timber parts in the roof that are employed, and (4) that the two different bracing approaches used provide about the same lateral stiffness of the roof. Finally, it should be emphasized that FE-models can markedly overestimate the stiffness of timber structures. If the connections are not modelled accurately, the engineers involved are advised to seek safe sided assumptions regarding them.

Experimental and numerical investigations on out-of-plane ultimate resistance of parallel twin-arch under uniform radial load

Studies on out-of-plane buckling of parallel twin-arch with lateral braces are lacking in contrast to free-standing arches, although they have been widely used in the engineering practice. This paper deals with experimental investigations into out-of-plane ultimate resistance of fixed circular parallel twin-arch under uniform radial load. Seven parallel twin-arch consisting of two steel tubular arch ribs connected by lateral braces are tested under symmetric radial loading. A loading frame comprising a reaction beam, sliding supports and distribution beams is used to apply five-point radial loads over the full span of the arch ribs. Initial out-of-plane imperfections are generated by a push rod before loading. The test results show that all of the specimens fail in an out-of-plane symmetric C-shaped buckling mode, and the lateral displacements are much larger than the vertical displacements. It is also found that the stiffness of the lateral braces have great effects on the ultimate resistance of the parallel twin-arch. The ultimate resistance increases as the cross-section diameter of lateral braces increase. A finite element model is also developed. Comparisons of the FE results for the out-of-plane elasto-plastic behaviour of parallel twin-arch with the experimental ones indicate that the finite element model can predict the elasto-plastic out-of-plane buckling response of parallel twin-arch very well.

Temporary Shear Brace Design Method for Steel Box Girder Viaduct in Transverse Block Construction

Transverse block of a steel box girder viaduct can decrease the shear connection between the upper part and the lower part. As a consequence, deflection and deflection difference between blocks are significant, and the performance of weld seams and finished viaduct can be affected. To decrease the deflection of steel box blocks with an open section after transverse discretization, a piecewise uniform arrangement of temporary shear braces is proposed on condition that the total shear stiffness of the shear braces remains unchanged. First, the formulas for slip, axial force and deflection with a piecewise uniform arrangement of temporary shear braces are given, and the accuracy is verified by comparing the results with finite element method. The proposed formulas are applied to two field studies and the results show good agreement with measured data. Finally, the optimal arrangement of temporary shear braces was explored by the sequential quadratic programming optimization method. The deflection and the deflection difference at welding position are reduced significantly after bracing, and the optimal shear braces arrangement is to arrange the braces more at the ends of the blocks.

An Interactive Solution for Lateral-Torsional Buckling of the Mono-Symmetric Beam-Columns with Discrete Lateral Bracings

The beam-column members are widely used in civil structures. These members are subjected simultaneously to the axial load and the bending moment. In this paper, the buckling strength and the bracing stiffness requirement of the mono-symmetric beam-columns with discrete lateral bracing have been investigated. For this purpose, a numerical method based on the finite element analysis is developed to calculate the buckling load-set of the mono-symmetric beam-columns. This proposed method is capable to consider the initial geometric imperfection. The proposed method is compared with the results of experimental and numerical studies obtained by previous researchers and the spatial finite element analysis, which it shows good agreement. Also, by using the matrix form of the energy equation, a closed form solution of the bracing stiffness requirement is suggested for an arbitrary number of bracing points. The P-M interaction curve and formula are presented for mono-symmetric beam-columns. The results show that the peak point of the curve occurs at the P = Pey and M = Peyy0, where Pey is Euler's buckling load. Finally, a parametric study is done to investigate the effects of the eccentricity and degree of mono-symmetry on the buckling strength and bracing stiffness requirement.

Cyclic experimental and analytical studies of buckling-restrained braces with various gusset connections

Five buckling-restrained braces (BRBs) with various gusset connections, including pinned gusset connection, bolted gusset connection, welded gusset connection, pinned-welded gusset connection as well as pinned-bolted gusset connection, were designed and tested under axial cyclic loading. Typical failure modes for all specimens were summarized and analyzed. The experimental results showed that all specimens exhibited stable hysteretic performance, good ductility and cumulative plastic deformation capacity. In addition, the relationship between the core plate strain demand and the effective factor was adopted to assess whether a BRB deformation satisfied the requirement of at least two times the design story drift. On the basis of Whitmore section and effective length, a formula of equivalent stiffness for a BRB with various gusset plates was suggested and verified by the experimental and numerical results. Furthermore, the finite element (FE) models of BRBs with various gusset connections were established and good consistency between the numerical and test results indicated that the FE modeling could simulate the cyclic behavior of BRB well. The elastic stiffness of gusset plate should be considered in the BRB design, and various gusset connection type and corresponding configurations provided an alternative method for designers to adjust conveniently the equivalent stiffness of brace under the premise of meeting the core plate strain demand.

Effect of Eccentric Lateral Bracing Stiffness on Lateral Torsional Buckling Resistance of Wooden Beams

An energy-based solution is developed for the lateral torsional buckling (LTB) analysis of wooden beams with flexible mid-span lateral bracing offset from section mid-height and subjected to uniformly distributed or mid-span point load. The study shows that such beams are prone to two potential buckling modes; symmetric or anti-symmetric. The symmetric mode is shown to govern the capacity of the beam for low bracing stiffness while the anti-symmetric mode governs the capacity when the bracing stiffness exceeds a threshold value. Using the present formulation, the threshold bracing stiffness required to suppress the symmetric mode and maximize the critical moments is directly obtained by solving a special eigenvalue problem in the unknown bracing stiffness. The technique thus eliminates the need for trial and error in standard solutions. A parametric study is conducted to investigate the effect of bracing height, load height, and bracing stiffness on the critical moments. A large database of runs is generated and used to develop simple expressions for determining the threshold bracing stiffness required to maximize the elastic LTB resistance.

A mechanical analog thoracolumbar spine model for the evaluation of scoliosis bracing technology.

IntroductionThoracolumbar braces are used to treat Adolescent Idiopathic Scoliosis. The objective of this study was to design and validate a mechanical analog model of the spine to simulate a thoracolumbar, single-curve, scoliotic deformity in order to quantify brace structural properties and corrective force response on the spine.MethodsThe Scoliosis Analog Model used a linkage-based system to replicate 3D kinematics of spinal correction observed in the clinic. The Scoliosis Analog Model is used with a robotic testing platform and programmed to simulate Cobb angle and axial rotation correction while equipped with a brace. The 3D force and moment responses generated by the brace in reaction to the simulated deformity were measured by six-axis load cells.ResultsValidation of the model’s force transmission showed less than 6% loss in the force analysis due to assembly friction. During simulation of 10° Cobb angle and 5° axial rotation correction, the brace applied 101 N upwards and 67 N inwards to the apical connector of the model. Brace stiffness properties were 0.5–0.6 N/° (anteroposterior), 0.5–2.3 N/° (mediolateral), 23.3–26.5 N/° (superoinferior), and 0.6 Nm/° (axial rotational).ConclusionsThe Scoliosis Analog Model was developed to provide first time measures of the multidirectional forces applied to the spine by a thoracolumbar brace. This test assembly could be used as a future design and testing tool for scoliosis brace technology.

Elastic buckling of steel arches with discrete lateral braces

Lateral brace is an effective way to increase the out-of-plane stability of steel arches, and the certain bracing stiffness achieving full restraining effect is concerned. Unlike braced columns and beams, the buckling of steel arches with discrete lateral braces and the effect of bracing stiffness are not well explored. This paper deals with the bracing stiffness effect of equally-spaced lateral translational braces and rotational braces in steel circular arches pertaining to elastic out-of-plane flexural-torsional buckling. Firstly, for arches with discrete lateral translational braces in uniform compression, an analytical solution for the threshold bracing stiffness is derived by the Rayleigh–Ritz method, ensuring full restraint of the displacement at the bracing points. Then for arches with discrete rotational braces in uniform compression, the flexural-torsional buckling modes are explored using the finite element analysis (FEA), then improved predictions to the buckling load related to the bracing stiffness are obtained theoretically by assuming proper buckling shapes. Compared with the FEA results, it is found that the analytical solutions of threshold stiffness proposed for arches in uniform compression are reasonably accurate and can be used in other loading cases for arches under combined compression and bending moment conservatively.

05.30: Stability and load bearing capacity of a braced truss under upward wind loading

ABSTRACTThe paper is focused on the numerical and experimental investigation of stability of a steel truss under upward wind loading. The structure was stiffened by elastic braces situated at the top and bottom chord. Usually the lateral (translational) brace stiffness is considered. However, the rotational stiffness of braces caused by interaction between torsional stiffness of the truss top chord and bending stiffness of the roof elements (purlins, sandwich panels, trapezoidal sheet) should be taken into account. The model of real roof truss scaled by factor ¼ was investigated. In the research the linear buckling analysis results and non‐linear static analysis results for the truss shell model are presented. As a result the buckling and limit load in relation of the truss bracing stiffness was found and the threshold bracing condition necessary to provide maximal buckling resistance of the truss was obtained. The truss load bearing capacity obtained from numerical analysis was compared with the experimental test results and Eurocode 3 requirements.