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An innovative buckling-restrained brace (BRB) is devised by imposing a cable stayed system (CSS) on a common BRB, namely single cross-arm pre-tensioned cable-stayed buckling-restrained brace (SPCS-BRB). Its overall external stiffness thus load-bearing capacity can be dramatically enhanced over the common BRB. A previous study conducted by the authors investigated comprehensively the elastic buckling behavior of the brace, yet experimental investigations and detailed design suggestions were not provided. Two SPCS-BRB specimens have been devised and tested. Test results revealed that both specimens possessed excellent hysteretic response with stable hysteretic curves, which fulfilled the ductility requirement specified in the AISC seismic provisions. The adopted simplified Finite Element (FE) model for experimental simulations corresponds well with the obtained test results. Moreover, additional FE analysis (FEA) has been conducted on the SPCS-BRBs subjected to monotonic and cyclic axial loads, respectively as to validate the test results further. In addition, threshold values of restraining ratios are obtained by guaranteeing the cables to remain tensioned prior to attaining ultimate failures, and ensuring maximum load resistance of the SPCS-BRBs is obtained. It is observed from the FEA that global instability failures of the SPCS-BRBs are caused by expansion of yielding at the extreme fibers of the external tube. Finally, FEA has been conducted on the load resistance of the SPCS-BRBs by considering the effect of interactive buckling and prestressing force of cables. It is found that interactive buckling could become critical in dominating the load resistance of the SPCS-BRBs when single-wave symmetric buckling mode is considered.

This paper presents the sectional strength design method of concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs). The T-CDSCW is composed of flange and web wall elements and concrete-filled steel tubes, where the former are formed by bolt-connected steel corrugated-plates and infilled concrete while the latter behave as vertical boundary elements. Load bearing capacities of T-CDSCWs are significantly improved by the favorable combination effect between bolt-connected steel corrugated-plates and infilled concrete in the wall elements. The failure mechanism and the sectional strength design of T-CDSCWs under combined axial compression and bending moment are focused analytically, experimentally and numerically, with an assumption of no consideration of overall instability of T-CDSCWs and local buckling of the steel corrugated-plates in the wall elements. An experiment of the T-CDSCW for sectional strength prediction was carried out, and a refined finite element (FE) model of the T-CDSCW was validated by the experimental results. Based on the FE model, parametric analyses of T-CDSCWs are performed to further investigate the effects of steel ratio and sectional geometry on the load-bearing capacities. It is found that T-CDSCWs under axial compression have completely different values of load-bearing capacities when they incorporate different bending direction moments. Based on experimental and numerical results, design formulas for predicting the sectional strength of T-CDSCWs under axial compression and bending moments are proposed, providing a preliminary structural design method of T-CDSCWs.

Multiple cross-arm Pre-tensioned Cable Stayed Buckling-Restrained Braces (MPCS-BRBs) can significantly enhance the elastic buckling performance and load resistance over common double-tube BRBs because of the additional cable stayed system. Previous studies conducted by the authors intended to investigate the lower limits of restraining ratios of MPCS-BRBs with pin-ended stays subjected to either monotonic or cyclic axial loads, where the initial geometric imperfection was taken to be consistent with the first order buckling mode. This study is a continuation of the previous paper, and it aims to explore interactive buckling of MPCS-BRBs with pin-ended stays in order to obtain a safe estimate of their load-carrying capacities through nonlinear Finite Element Analysis (FEA). In addition, interactive buckling of MPCS-BRBs is considered by introducing a series of asymmetric imperfections that are the mixtures of symmetric and antisymmetric imperfections during buckling analysis. The effects of different imperfections (symmetric, antisymmetric, and asymmetric) and initial pre-tensioning force of cables on the load-carrying capacities of the MPCS-BRBs with and without minor diagonal cables are explored and compared. Furthermore, a conservative design approach for those MPCS-BRBs can be established by fulfilling the corresponding lower limits of restraining ratios and optimal initial pre-tensioning force of cables based on the findings considering different types of initial geometric imperfections. Finally, such a conservative design approach is validated through nonlinear FEA for MPCS-BRBs subjected to either monotonic or cyclic axial loads. The findings in this study could provide guidance for a preliminary conservative design of the MPCS-BRBs in actual engineering applications.

This paper proposes Multiple cross-arm Pre-tensioned Cable Stayed Buckling-Restrained Braces (MPCS-BRBs) with pinned connections between stays and external tube. By adopting pin-ended stays, the additional bending moment that would be exerted on those connections can be effectively released instead of fixed connections. This eliminates premature strength failures at those connections and simplifies the tensioning process of the cables, thus making the pin-ended stays to be a very practical option in engineering applications. Comparative studies have been conducted on the elastic buckling, load resistance and cyclic behaviors of the MPCS-BRBs with and without additional minor diagonal cables through Finite Element Analysis (FEA). Explicit expressions for the elastic buckling loads of the two types of MPCS-BRBs are obtained in closed form through curve fitting based on a generalized structural design parameter β of the external restraining system. It is found that the elastic buckling performance of the MPCS-BRBs with additional minor diagonal cables could be enhanced dramatically as compared to those not possessing the minor diagonal cables. At last, by ensuring the major cables not to become slack before reaching ultimate failures of the MPCS-BRBs, the load resistance and cyclic behaviors subjected respectively to monotonic and cyclic axial loads are explored through an elastic-plastic FEA. Corresponding lower limits of restraining ratios are attained, where they would provide fundamentals and guidance for preliminary design of the MPCS-BRBs in actual engineering applications.

Buckling restraining braces (BRBs) have functions of both high load-carrying capacity and good energy-dissipation performance. Therefore, they are widely used in high-rise buildings and large-span space structures as lateral resistant axially-loaded members. But, in actual engineering applications, BRBs may be subjected additionally to external lateral loads so that the external restraining system (ERS) should be strengthened against the adversely lateral load effects in addition to the effects imposed by the core bending. Therefore, this paper investigates the instability mechanism and design method of BRBs considering additional symmetrical lateral load effects. First, the formula for predicting the lower limit of the restraining ratio of uniform-section BRBs is derived, based on considering the combined effect of an axial compression load of the core and a symmetrical external lateral load. Then, taking the double-tube BRB (DT-BRB) as an example, a finite element (FE) model is established with the FE software ANSYS to investigate the influence of the key parameters on the elastic buckling performance, elastic-plastic ultimate load-carrying capacity and hysteretic behavior. The FE numerical investigations of the key parameters covering the common application variation in the length and section size, the lateral load types and amplitudes, have been carried out, focusing on the effect of the parameters on the outcomes of the proposed lower limit of the restraining ratio. Finally, the design procedure for the DT-BRB is established according to the lower limit of the restraining ratio, which is used as a preliminary fundamental structural design guide in actual application.

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.

Buckling behavior and hysteretic performance of a new type of buckling-restrained brace (BRB), namely core-separated buckling-restrained brace (CSBRB), are theoretically and experimentally investigated. The material utilization efficiency of the CSBRB is significantly improved compared with common BRB, since its cross-section spreads outwards by spacing two cores, thus improving the flexural rigidity of the restraining system. On the basis of the elastic buckling loads of pin-ended CSBRBs, a design procedure involving two design parameters, namely normalized slenderness and buckling factor, is firstly established. Then, hysteretic behavior of CSBRBs is investigated by FE nonlinear analysis to obtain the critical normalized slenderness. Finally, test results of four specimens with different normalized slenderness values are presented to reveal the hysteretic characteristics and the energy-dissipation abilities, concluding that a CSBRB with adequate restraining rigidity can provide stable hysteretic performance. The test results coincide well with the results obtained from refined FE numerical analyses.

Grid Cylindrical-Lattice Shells (GCLSs) have found their wide application in high-rise buildings and TV towers as the outer cylindrical frame of tube-in-tube structures subjected mainly to axial compression. This paper presents the elastic buckling behaviour of Grid Cylindrical-Lattice Shells (GCLSs) under axial compression. Because of a lack of lateral braces in the radial direction of the GCLS along its height, the GCLS tends to fail by two buckling modes under axial compression, namely global flexural buckling and circumferential multi-wave buckling. First, the fundamental three-story GCLS is investigated by using the energy method. The restraining action of the ring beam on the columns in the two buckling modes is explored separately, and this exploration leads to the radial rotational restraint stiffness, tangential rotational restraint stiffness and translational restraint stiffness of the ring beams, denoted by βr, βt and α, respectively; in addition, the corresponding elastic buckling loads of the three-story GCLS in the two buckling modes are separately derived. Then, based on the three key parameters, simple fitting formulas are developed to separately predict the elastic buckling loads of the multi-story GCLS in the two buckling modes. This outcome provides fundamentals for further establishing load-carrying capacity design of GCLSs under axial compression.

Seven pinned double-rectangular tube assembled buckling-restrained brace (DRT-ABRB) specimens are investigated by axial cyclic loading tests in this study. The core member of the specimen is a single flat-plate, with two rectangular tubes assembled to form the external restraining member by high-strength bolts. Each rectangular tube is composed of external channel steel and an external cover plate. The influence of end detailing of DRT-ABRBs on the energy dissipation is explored in the tests, which demonstrates that, compared with the end strengthening measure using an external hoop, the counterpart with a bench ribbed stiffener provides better energy dissipation capacity. In addition, the gap between the bench ribbed stiffener and the external channel steel should be controlled in design. All DRT-ABRBs studied exhibits excellent energy dissipation capacity, which proves the effectiveness of the DRT-ABRB end detailing proposed.

As inspired from a double-arm pre-tensioned cable stayed column (PCSC), a concept of a double-arm pre-tensioned cable stayed buckling-restrained brace (DPCS-BRB) is put forward through adding the core inside PCSC. But a previously published paper only limited into the DPCS-BRBs that have pin-ended stays and their practical application is limited undoubtedly. Therefore, this paper focuses on DPCS-BRBs with fix-ended stays and investigates into their structural performance and design through theoretical derivation and Finite Element Analysis (FEA). With fix-ended stays in the DPCS-BRBs, flexural rigidity and deformations of the stays must be considered in both elastic and elastoplastic FEA of DPCS-BRBs. The design method in obtaining the lower limit value of restraining ratios should be re-established by considering the fix-ended stays. Firstly, this study explores elastic buckling behavior of DPCS-BRBs, focusing on explicit formula prediction of the elastic buckling load under either symmetric and antisymmetric buckling mode by using energy method. The obtained theoretical formulas are then validated through FEA. And then, the static load-carrying behavior and hysteretic performance of DPCS-BRBs are investigated by employing elastoplastic FE models that were validated by experimental tests conducted previously by the authors. Finally, because the possible existence of asymmetric imperfection interaction between two possible aforementioned buckling modes would lead to reduction in the load-carrying capacity, therefore, interactive buckling must be considered for establishing conservative design method of DPCS-BRBs, particularly where prestressing force of cables is involved. The research outcomes attained would provide structural design guidance in engineering applications of DPCS-BRBs with fix-ended stays.

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.

This paper investigates the flexural buckling behaviour of axially loaded concrete-infilled double steel corrugated-plate-walls with T-section (T-CDSCWs). The T-CDSCW is composed of flange and web wall elements and vertical boundary elements. The wall element consists of two bolted-connected steel corrugated-plates with concrete infilled. The composite effect of the components in the wall element improves the load-bearing capacities of the T-CDSCW efficiently and leads to a thinner wall. Therefore, the failure mode of the T-CDSCW may be governed by global instability. With the web breadth relatively less than the flange breadth, the first-order elastic buckling mode of the T-CDSCW is flexural buckling about the asymmetric axis. The design issue of the flexural instability of the axially loaded T-CDSCW is investigated experimentally and numerically in this paper. The load-bearing and deformation behaviours were investigated by an experiment of the axially loaded T-CDSCW, based on which refined finite element (FE) models of T-CDSCWs are established and validated. The FE buckling analysis is carried out to investigate the elastic buckling behaviour of the T-CDSCW and propose the elastic flexural buckling load and the borderline between flexural and flexural-torsional buckling. Then, the inelastic flexural instability of the T-CDSCW is investigated by the FE nonlinear analysis, and influences of initial geometric imperfection are discussed. The normalized flexural slenderness ratio derived from elastic flexural buckling load delineates flexural instability pretty well and bases the design formulas of strength reduction factor. The design formulas proposed in this paper help to understand the axial load-bearing behaviour of the T-CDSCW.

The contact interaction between the core and external restraining members is a vital factor that affects the overall performance of buckling-restrained braces (BRBs) significantly. In this study, refined finite element (FE) model was employed to evaluate the contact force between the core and external restraining members and to investigate the BRB performance. Moreover, the influences of strength and stiffness of external restraining member, core length, and other geometric parameters on the BRB performance were also studied. On the basis of numerical results obtained in the study, the recommended values of core width-to-thickness ratio, core thickness and gap were proposed. By considering the core plasticity and the lateral restraint of external restraining member, some formulas for predicting the half-wave length of core buckling as well as contact force were also proposed while the core buckled in multi-wave form. These formulas were numerically verified and could be references in the design of BRB.

This paper is concerned with the out-of-plane elastic buckling behavior of planar truss arch with continuous or discrete lateral bracings. Firstly, planar truss arches with continuous lateral bracings are studied, and a closed form solution of out-of-plane elastic buckling load is obtained theoretically. As for planar truss arches laterally restrained with discrete bracings, two key parameters, namely lateral bracing threshold stiffness and out-of-plane elastic buckling load of an arch segment between two adjacent bracings, are investigated by the finite element method, respectively. Besides, it is found from finite element results that, if the planar truss arch is manufactured by using intersecting joints between web members and chord tubes and is laterally restrained on top chord tubes, the out-of-plane buckling of bottom chord tubes will fully be prohibited. However, the gusset-plate connections between chord tubes and web members cannot prevent the planar truss arch from the out-of-plane buckling due to their weak stiffness, even though the arch is laterally fully restrained on top chord tubes.

As a new kind of non-uniform member, the asymmetrically double tapered column with tubular cross-section is composed of two tapered parts with different lengths. This kind of column is more effective and economic to resist combination of axial load and transverse load, with both its ends hinged and transverse load applied at the largest cross-section. Some classic non-uniform members such as stepped or tapered members have been investigated thoroughly, but there is not any available design method for asymmetrically double tapered columns so far. In this study, the elastic buckling behaviors of asymmetrically double tapered columns with solid circular and tubular cross-section are studied respectively. Bessel functions and fitting processes are used to derive explicit formulas of the critical load. Subsequently, the ultimate bearing capacity of asymmetrically double tapered tubular columns subject to axial load is studied. And the results obtained by the design formula proposed herein correlate well with these obtained by using finite element numerical analysis. Finally, a P–M interaction formula for predicting in-plane strength of double tapered tubular columns under axial load and uniaxial bending is suggested. Employment of a detailed nonlinear finite element analysis demonstrates the accuracy of the interaction formula.

Although several studies of the out-of-plane strength and design of steel arches with a solid web section have been reported, little research of the out-of-plane strength and design of spatially trussed arches has been reported in the open literature or design codes. In deference to the steel arch with a solid web section, the shear deformations play important parts in the out-of-plane inelastic buckling behavior of spatially trussed arches. In addition, global out-of-plane inelastic buckling of a spatially trussed arch is associated with local buckling of its components such as chord and diagonal web tubes and hence local component buckling influences the out-of-plane strength of the arch. This paper investigates the out-of-plane inelastic strength and design of spatially trussed circular arches with a rectangular lattice section under general loading using a three-dimensional nonlinear inelastic numerical approach. Methods for the out-of-plane inelastic strength and design of spatially trussed arches under uniform compression or under uniform bending are developed, based on which interaction equations for the design of spatially trussed steel arches under general loading against their out-plane failure are proposed. These interaction equations provide good lower bounds for the out-of-plane strength of spatially trussed arches.

Multi-tube latticed steel columns without diagonal tubes and the ones with diagonal tubes are two common types of prismatic latticed columns used nowadays. Instability behavior of prismatic multi-tube latticed steel columns is studied in this paper. The focus on the problem is based on the derivation of shear stiffness for multi-tube latticed steel columns. Formulas are established to express the elastic buckling loads as well as the modified slenderness ratios, in which the effect of shear deformation is taken into account. Cases are analyzed via finite element method ANSYS to calculate the ultimate load-carrying capacity of the latticed columns for comparison with the design method in different design codes for compressive members. Formulas to estimate the design resistance for axial compressive prismatic multi-tube latticed steel columns are proposed and detailed design suggestions for the component steel tubes are presented as well.

A beam-column model has been presented on the analysis of the elasto-plastic interaction buckling behaviour between local and overall flexural buckling modes in a cold-formed thin-walled box beam-column with plate (local) and column (overall) imperfections. The beam-column is modelled as an assemblage of a series of locally buckled short struts, each being equal to half the local buckle wavelength of the perfect column. A material and geometric nonlinear finite strip method developed by the author 1–5 is employed to calculate the moment-curvature-thrust relationships of the locally buckled short strut in the elasto-plastic range. With the help of the developed M - P - θ relationships of the short strut, the strength of the locally buckled beam-column is predicted by employing Little's beam-column approach. An experimental program on the cold-formed thin-walled box columns was carried out. The comparison of the experimental and theoretical results is satisfactory.