Restraining Ratio Research Articles

Seismic performance of shuttle-shaped double-restrained buckling-restrained brace: Experimental investigation and numerical analysis

To solve the problems of excessive cross-section size and self-weight and buckling instability of super-long buckling-restrained brace, a new lightweight shuttle-shaped double-restrained BRB (SDR-BRB) is proposed in this study. Firstly, cyclic loading experiments are conducted on three SDR-BRB specimens to investigate their failure mode and seismic performance. Then, a finite element model considering geometric, material, and contact nonlinearity is established and verified by experimental results. Finally, the effect of the restraining ratio on the hysteretic performance of SDR-BRB is studied by parameter analysis, and the restraining ratio requirement of the energy-dissipation type of SDR-BRB that meets the ductility requirements is obtained. The results show that SDR-BRB has stable and plump hysteretic curves, excellent energy-dissipation capacity, and low cycle fatigue performance, exhibiting obvious strain-strengthening characteristics. The restraining ratio is an important factor affecting the overall stability and failure mode of SDR-BRB, and it is recommended that the restraining ratio requirements of the SDR-BRB should be 2.25. The above research can provide a design reference for the practical engineering application of SDR-BRB.

The Effect of Buckling Restraint on Axial Strain Life Fatigue Data

Abstract Focused on the common problem of easy specimen buckling in the axial strain–controlled fatigue testing of thin automobile steel sheets, a strain fatigue test method for thicknesses less than 2.5 mm is proposed. Because of the unrestrained grip end of specimens between the anti-buckling device and the testing machine fixture, specimens were prone to buckling in this area. In addition, if the designed specimen sizes were unreasonable, buckling may have occurred in the width and thickness directions of the gauge length of the specimen. Both situations can lead to invalid tests. This paper adopted a testing machine fixture and an anti-buckling plate as a mortise-and-tenon structure for the anti-buckling method; the upper and lower fixtures of the testing machine were cut in straight grooves, and the left and right anti-buckling plates were designed to be connected with a mortise and tenon. This is equivalent to narrowing the width of the unrestrained part of the specimen’s grip end to avoid buckling failure due to plane strain. The factors affecting the stiffness of fatigue specimens are also discussed herein. In order to avoid common instability in the thickness and width directions of the gauge length and unconstrained part of the specimen’s grip end at a strain ratio of Re = −1 during testing, six recommended specimen sizes are given on the premise of ensuring maximum specimen stiffness. When using the anti-buckling device, the recommended specimen sizes and test points of this study (i.e., the lower limits for yield strength and thickness of strain control testing) are 110 MPa and 0.5 mm, respectively, with which continuous and smooth stress–strain curves that result in accurate and reliable experimental data can be obtained.

Experimental & numerical investigation of all-steel assembled cruciform buckling-restrained braces

In this paper, an all-steel assembled cruciform buckling-restrained brace is proposed for the first time. It is mainly composed of 26 main components, including one external restraint steel tube, eight internal restraint steel tubes, one inner core, and 16 high-strength bolts for connection. Four BRB specimens were designed in the test stage, and all specimens were subjected to displacement-controlled axial cyclic load. As a result, hysteretic performance, energy dissipation, and ductility were summarized and analyzed for each specimen. In addition, 50 nonlinear finite element models are established using the large-scale commercial finite element software ABAQUS for numerical simulation analysis. The results of the experiment and numerical simulation show that: (1) A new type of all-steel assembled cruciform buckling-restrained braces (BRB) with stable hysteretic performance has been successfully designed, and a corresponding simplified but refined three-dimensional nonlinear finite element model that can be in good agreement with the test results has been established. (2) The traditional concept of restraining ratio has been disassembled into the concept of internal and external restraining ratios in this BRB configuration. (3) The concept of restraining length ratio of this BRB configuration and related design standards are proposed.

Seismic performance of triple-truss-latticed buckling-restrained braces: Tests and numerical simulations

Buckling-restrained braces (BRBs) have been proven to be excellent seismic-resistant members in the past few decades. In this study, an innovative type of BRB, namely triple-truss-latticed buckling-restrained brace (TTL-BRB), is proposed to accommodate the high hysteretic performance requirements. The TTL-BRB comprises three separated steel tubes as cores and a triple-truss-latticed member as the restraining system. Cyclic experiments were conducted on two TTL-BRB specimens to investigate their hysteretic performance, such as hysteretic curves, skeleton curves, equivalent viscous damping ratio, and strain distribution. The test results revealed that both specimens exhibit plump hysteretic curves and stable load-carrying responses under cyclic loads, indicating that the composition of TTL-BRB enables it to achieve an excellent energy-dissipation capacity. Furthermore, a FE model considering geometric and material nonlinearities was developed, which accurately predicted the hysteretic performance of specimens in experiments. Moreover, a parametric study was performed to investigate the effect of restraining ratios on the failure modes of TTL-BRBs. Through the 72 FE model results, the restraining ratio requirements for global and local buckling designs in the statistical sense were given, providing valuable design references for engineering applications of the TTL-BRBs.

Behaviour and design of spatial triple-truss-confined BRBs with a longitudinal shuttle shape

For several decades, innovative studies on the external restraining system of the buckling-restrained brace (BRB) have focused on the design and application of BRBs. This paper presents a Spatial Triple-Truss-Confined BRB (STC-BRB) with a longitudinal shuttle-shape and investigates its buckling behaviour, static strength and seismic design. The STC-BRB could significantly improves the material utilization and particularly enhance the architectural aesthetics when it is used as an exposed design externally. The overall elastic buckling performance, load resistance and hysteretic responses of the STC-BRB are investigated numerically by adopting a finite element model (FEM) validated by previously conducted test results of a truss-confined BRB (TC-BRB). A design method regarding the lower limit of the restraining ratios of the STC-BRBs is recommended. First the overall elastic buckling performance of the STC-BRB is comprehensively investigated by using a beam element FEM, leading to an explicit expression for the overall elastic buckling load of the STC-BRB, which is further adopted to define a restraining ratio of the STC-BRB design. Consequently the load resistance of STC-BRBs under monotonic axial compression is numerically analyzed. Accordingly a lower limit of the restraining ratio of the STC-BRBs is recommended for monotonic axial load resistance design, such that the core reaches the fully sectional yield, along with a plasticity strain amplitude of 2% without a global instability of the STC-BRBs. Finally, the hysteretic responses of STC-BRBs subjected to axially compressive-tensile cyclic loads are studied numerically, and the corresponding lower limit of the restraining ratio of STC-BRBs is proposed in the design as an energy-dissipating device. The two lower limits of the restraining ratios of the STC-BRBs obtained in this study form fundamentals for the preliminary static and seismic design of STC-BRBs.

Load-carrying performance and design of BRBs confined with longitudinal shuttle-shaped-trusses

This paper presents load-carrying performance and design method for a Shuttle-Shaped Truss-Confined Buckling-Restrained Brace (SSTC-BRB). Such external restraining system (ERS) innovation through adopting longitudinally variable cross-sectional trusses in the BRB significantly enhances axial load-carrying efficiency of SSTC-BRB that could carry very large axial applied load for over long BRB design when used on exposed purpose externally. Firstly, the elastic buckling performance of the SSTC-BRB is comprehensively investigated by adopting a beam element Finite Element (FE) model, and this leads to an explicit expression of the elastic buckling load of the SSTC-BRB that is adopted to define the restraining ratio of the SSTC-BRB for its strength and stiffness design. Consequently, the load resistance of SSTC-BRBs under monotonic axial compression is numerically analyzed. Accordingly, the lower limit of restraining ratio of the SSTC-BRBs subjected to monotonic axial load is recommended for their load resistance design, where the core could be fully yielded with the plastic strain amplitude reaches 2% without global instability of the SSTC-BRBs. Finally, the hysteretic responses of SSTC-BRBs subjected to axial compressive-tensile cyclic loads are studied numerically, and the corresponding lower limit of restraining ratio of SSTC-BRBs is proposed for their energy-dissipation design. Those two lower limits of restraining ratios of the SSTC-BRBs obtained in this study provide fundamentals for preliminary static and seismic designs of SSTC-BRBs.

Global buckling prevention of reduced-core-length buckling-restrained braces: theoretical and numerical investigations

An economic type of buckling-restrained braces (BRBs) to allow long spans and large capacities, the reduced-core-length BRBs (RCL-BRBs) are formed by sequentially assembling ordinary BRBs (yield portions) and ordinary braces (elastic portions) with high-strength bolts. This paper presents design recommendations for the global stability of the RCL-BRBs via theoretical and numerical investigations. In the analysis, the interaction between the yield and elastic portions of the RCL-BRBs is considered. First, the RCL-BRBs were classified into six types according to their compositions (the yield portion at one end, mid-span or both ends) and joint types (rigid or semi-rigid joint). Second, formulas for predictions of the elastic buckling loads of the RCL-BRBs were theoretically derived, and were verified by performing finite element (FE) eigenvalue buckling analyses. To investigate the nonlinear behavior of the RCL-BRBs, FE models considering both geometrical and material nonlinearities were built and calibrated with existing hysteretic tests of the RCL-BRBs. Then, a parametric study was conducted to investigate the effects of the geometrical parameters on the global stability behavior of the RCL-BRBs. Finally, based on the numerical results, the restraining ratio design requirements corresponding to the different types of RCL-BRBs were proposed to prevent their global buckling under axial compressive loads. Moreover, recommendations on the connection types between the yield and elastic portions of the RCL-BRBs are provided by analyzing a number of numerical examples.

Fatigue Analysis of A356-TiB2 (5wt%) in-situ Nano composites

Abstract In the present work, Low-cycle fatigue (LCF) tests were performed on A356 Aluminium alloy and A356-TiB2(5wt%) in-situ nano-composites to estimate their fatigue performance. The tests were performed by strain controlled with a strain ratio of Re = -1. The cyclic stress–strain curves were determined for each imposed strain levels. The LCF and their characterization in the cyclic plastic response of both the alloy and composites were analysed. It is interesting to note that the type of cyclic deformation behaviour in Al-Mg-Si alloys seems to be influenced by the dispersed phases and TiB2 particles. The LCF values for the A356-TiB2(5wt%) composites were found to be higher than those of the A356 alloy. The separation fatigue life’s of the A356-TiB2(5wt%) in-situ nano-composite and A356 alloy was found to be 15652 and 12350 cycles respectively. This is attributed due to the presence of minute TiB2 particles which obviously affected the microstructure, hardness, tensile strength and fatigue life of the composites compared to the base alloy. It is further noted that the LCF values of the present composites were found to be higher than those of the alloys reported in the literature.

Design of Pre-Tensioned Cable-Stayed Buckling-Restrained Braces Considering Interrelationship between Bracing Strength and Stiffness Requirements

AbstractThe conventional restraining ratio approach is not suitable for a straightforward design of the pre-tensioned cable-stayed buckling-restrained brace (PCS-BRB) because of its complicated buc...

Numerical investigations on elastic buckling and hysteretic behavior of steel angles assembled buckling-restrained braces

This paper presents a numerical investigation on elastic buckling and hysteretic behavior of a steel angles assembled buckling-restrained brace (SAA-BRB). The SAA-BRB is composed of a cruciform-sectional steel core encased by an external restraining system, which consists of four steel angles connected together by high-strength bolts and spacers. It is found that the SAA-BRB may fail in a global buckling mode or in a local buckling mode. In order to predict the global and local buckling behavior of SAA-BRBs, two design parameters: the restraining ratio and segment restraining ratio are proposed. To determine these two design parameters, a simplified theoretical model of SAA-BRBs and an accurate finite element (FE) model are used to investigate the global and local elastic buckling behaviors of SAA-BRBs. Based on more than 500 FE results, explicit expressions of the restraining ratio and segment restraining ratio are obtained and validated to be sufficiently accurate for practical design applications. In addition, 20 refined FE models considering material and geometrical nonlinearities are used to carry out parametric studies for comprehensively investigating the hysteretic behavior of SAA-BRBs. Finally, the following design recommendations for fix-ended SAA-BRBs are proposed: (1) the restraining ratio should be >2.2 to prevent a SAA-BRB from the global buckling failure, and (2) the segment restraining ratio should be >6.0 to prevent a SAA-BRB from the local buckling failure.

Theoretical and numerical studies of elastic buckling and load resistance of double cross-arm pre-tensioned cable stayed buckling-restrained braces

This paper investigates the elastic buckling behaviour and load resistance of a double cross-arm pre-tensioned cable stayed buckling-restrained brace (DPCS-BRB) where an extra cross-arm is assigned within a longitudinal cable truss along its length. Naturally, the span and efficiency of the PCS-BRB can be increased and improved by adopting multiple cross-arms. Equilibrium method is utilised to derive the formula of elastic buckling load of a pin-ended DPCS-BRB, and the obtained results have been verified through FE analysis. It is found from theoretical derivations and FE analysis that there exists a single-wave symmetric and double-wave antisymmetric buckling modes in the DPCS-BRB, respectively. In addition, a negative linear correlation exists between the elastic buckling load and the initial pre-tensioning force of the cables in the DPCS-BRB. Furthermore, it has been explored through FE analysis that the optimal location of the cross-arms for achieving higher elastic buckling load as well as higher ultimate compressive load-carrying capacity is found to be a quarter length to each end of the DPCS-BRB. At last, the ultimate compressive load-carrying capacity of the DPCS-BRB is found to be directly proportional to its restraining ratio, and there exists a lower limit of the restraining ratio which ensures the core could reach its full cross-sectional yield load without overall instability of the DPCS-BRB. The investigation of the elastic buckling behaviour and ultimate compressive load-carrying capacity as well as the failure mechanism of the DPCS-BRB provides fundamentals to the further development of a comprehensive design method of the DPCS-BRB subjected to axial cyclic loads.

Global buckling prevention of end collared buckling-restrained braces: Theoretical, numerical analyses and design recommendations

In recent years, buckling-restrained braces (BRBs) have been widely utilized in engineering structures. Generally, BRBs are diagonally installed in frame structures to serve as lateral-resistance and energy-dissipation members. To prevent the local buckling of the unrestrained portion of a pin-ended BRB, an end collared BRB (EC-BRB) was proposed by prior researchers by installing end collars at both ends of an ordinary BRB. By using this approach, the enhancement construction of the unrestrained portion could be remarkably simplified, and the end collars can provide lateral restraints to the restraining member, thus improving the global stability of the BRB member. In this paper, a design method for global buckling prevention of pin-ended EC-BRBs based on the restraining ratio requirements is provided via theoretical and numerical analyses. The equation of elastic buckling loads of EC-BRBs is firstly derived and validated by the eigenvalue buckling analyses via ANSYS, and the restraining ratios of EC-BRBs could be further calculated. Then, the restraining ratio requirements of EC-BRBs are theoretically proposed based on the magnification factor of the mid-span lateral deformation, and accordingly a recommended design procedure is provided. The design procedure is further validated by numerous finite element (FE) models subjected to hysteretic and monotonic loadings, indicating that this procedure can conservatively ensure the global stability of EC-BRBs and it is suitable for practical engineering applications.

Numerical studies of cyclic behavior and design suggestions on triple-truss-confined buckling-restrained braces

Abstract The cyclic behavior and design of a triple-truss-confined buckling-restrained brace (TTC-BRB) is investigated, especially when it is used in mega-frame high-rise buildings and long-span spatial structures as a long-span BRB. The TTC-BRB is formed by introducing an additional structural system of rigid truss frames to the outside of a common double-tube BRB in order to achieve a higher external restraining flexural stiffness as well as a high overall load-carrying capacity. An analytical method is utilized to derive a formula of the elastic buckling load of a pin-ended TTC-BRB, which is verified and modified through FE analyses. The effect of restraining ratio of the TTC-BRB on its cyclic behavior and failure mechanism is explored. The findings indicate that the TTC-BRB may have two different failure modes, namely in-plane and out-of-plane instability failures of the chord subjected to compression at the mid-span of the TTC-BRB. In addition, the load-carrying capacity of the TTC-BRB under cyclic loading is found to be proportional to the restraining ratio, and there exists a lower limit of the restraining ratio which ensures the core could reach its full cross-sectional yield load before overall instability failure of the TTC-BRB. Furthermore, in order for the TTC-BRB to be an energy dissipation type of BRBs, the lower limit requirement of the restraining ratio should be satisfied and its end constructional and strength design should be carefully carried out to avoid its premature failure. The investigation of the elastic buckling load and cyclic behavior as well as failure mechanism of the TTC-BRB provides fundamentals to the further development of a comprehensive design method of the TTC-BRB.

Elastic buckling and load resistance of a single cross-arm pre-tensioned cable stayed buckling-restrained brace

This paper proposes a new type of buckling-restrained braces (BRB), namely a pre-tensioned cable stayed buckling-restrained brace (PCS-BRB) which is formed through introducing an additional structural system of pre-tensioned cables and a number of cross-arms to the outside of a common BRB. This new system significantly improves the BRB’s overall external restraining stiffness, hence increasing the load-carrying efficiency in its structural design. Due to its aesthetically appealing structure, it can be utilised in stadiums and so forth as a laterally resistant brace. Equilibrium method is utilised to deduce formulas of elastic buckling load of pin-ended PCS-BRB. The restraining ratio and the initial pre-tensioning force of cables are investigated to explore the effect on the axial compressive load-carrying capacity of the PCS-BRB through finite element analyses in elastic-plastic range. The findings indicate that two different types of buckling modes may occur in this PCS-BRB, namely single-wave symmetric and double-wave antisymmetric buckling modes. It was found from theoretical and numerical analyses that: a negative linear correlation exists between elastic buckling load and initial pre-tensioning force of the cables; the geometric parameters of the cable stayed system possessed remarkable effect on the elastic buckling load. In addition, the post-yield behaviour and ultimate compressive load-carrying capacity of the PCS-BRB is directly proportional to the restraining ratio, and there exists a lower limit of the restraining ratio which allows the inner core to reach full cross-sectional yielding without overall instability failure of the PCS-BRB. Furthermore, there exists an optimal initial pre-tensioning force of cables to make the load-carrying capacity of the PCS-BRB to reach a maximum value. The investigation of elastic buckling and load resistance of PCS-BRB provides fundamentals to further develop a complete design method of PCS-BRB.

乾燥収縮するコンクリート壁面の拘束度マップ

The free shrinkage deformation occurring in concrete members is generally restrained by members around one with different stiffness and shrinkage rate, and a restraining ratio which expresses degree of restraining has a major influence on state of shrinkage cracking. Therefore, in order to predict the shrinkage cracking, it is important to get the restraining ratio of concrete members in addition to free shrinkage strain of concrete. With this background, in order to prepare eventually a design material for controlling shrinkage cracking with the organized distribution of restraining ratio, an experimental and analytical study to find out the regularity of distribution of restraining ratio in concrete walls was previously performed by authors. Additionally, it was noted that the restraining ratio in a wall with drying shrinkage should be reasonably considered by dividing it into the following two areas. (1) Non edge area: the area whose restraining direction is horizontal and distribution of vertical direction of restraining ratio is linear because bending deformation is dominant and Bernoulli-Euler's hypothesis holds. The distribution of restraining ratio in this area can be calculated by replacing a concrete wall with a uniaxial model. (2) Edge area: the area whose restraining direction is turbulent and distribution of vertical direction of restraining ratio is non-linear because shear deformation is dominant and Bernoulli-Euler's hypothesis does not hold. This signifies that the distribution of restraining ratio in concrete walls can be potentially predicted by the following policy: (1) First, the distribution of restraining ratio in a concrete wall is calculated by the uniaxial model, (2) Next, the position of areas to which the value calculated at above (1) can be not applied (i.e. edge area) and the value of restraining ratio in those areas is obtained from the design material prepared previously, considering various conditions of concrete walls. In this study, the map of distribution of restraining ratio in concrete walls, which is the design material in line with above policy, was created. In particular, the distribution of restraining ratio in concrete walls with various conditions was calculated by FEM analysis. Moreover, the areas to which the value calculated by the uniaxial model can be not applied (peculiar areas) were shown by organizing that result, and restraining ratio and restraining direction in those areas were shown. The distribution of restraining ratio shown in the map has the following characteristics. (1) The peculiar areas occur at the upper and lower parts of both ends of a wall. (2) The position and largeness of peculiar area at lower part of both ends of a wall hardly changes depending on stiffness balance between members. Additionally, the area extends vertically as the shape of a wall is horizontally long. Furthermore, though the area is decoupled by columns and beams with increased number of layer and span, the position of that entire area hardly changes. (3) The average restraining ratio at the peculiar area at lower part of both ends of a wall is obtained by adding a constant value (approximately 0.4) to the restraining ratio calculated by the uniaxial model, and the average restraining direction at the area is 30° to 35° in any wall.

Strain Ratio Effects on Low-Cycle Fatigue Behavior of Gravity Cast Al-Si-Cu Alloys

The strain-controlled low-cycle fatigue properties of gravity cast Al-Si-Cu alloys for engine cylinder heads were investigated. At strain ratios of R e = −2, 0, and 0.1, the cyclic stress amplitude progressively increased from initiation to the 450th cycle, and then proceeded into a steady stage until failure. At a strain ratio of R e = −∞, the material exhibited a continuous cyclic hardening. The hysteresis loops in this alloy for the 2nd and half-life cycle were tension/compression asymmetry, which also corresponded well to the evolution of peak/valley stress. Transmission electron microscopy analysis suggested that cyclic hardening was caused by the dislocations multiplication/tangles at strain ratios of R e = −∞ and 0. Besides, the presence of dislocation cross slip contributed to cyclic stabilization observed at later stage of deformation at a strain ratio of R e = 0. Micro-analysis of specimen fracture appearance was conducted in order to obtain the fracture characteristics and crack paths for different strain ratios. It showed that the fatigue cracks initiated basically at the internal defects in the samples. Meanwhile, at strain ratios of R = −∞ and 0, the fracture surface was rough with a large number of small unequiaxed dimples and some tear ridges. Moreover, the localized pores offered a preferential crack path in the samples, where they were surrounded by silicon particles. At a strain ratio of R e = −∞, the fatigue cracks preferentially initiated at pores rather than α-Fe phases. At a strain ratio of R e = 0, where fatigue crack initiation was observed at the interface between plate-like branch of α-Fe phase and aluminum matrix.