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This paper investigates the elastic buckling loads, load resistance and hysteretic responses of the multiple cross-arm pre-tensioned cable stayed buckling-restrained braces (MPCS-BRBs) with circular rigid plates as the cross-arms that are fixed to the external tube, and the circular rigid plates are considered equivalent as stays with infinite stiffness in the finite element analysis (FEA). The span and elastic buckling load efficiency of the MPCS-BRBs could be increased and improved effectively by adopting multiple cross-arms that are considered to possess infinite stiffness. Explicit expressions for the elastic buckling loads of the MPCS-BRBs are obtained in closed form through curve fitting, by adopting the FEA results on a generalized structural design parameter β that is deduced from a single cross-arm PCS-BRB (SPCS-BRB). In addition, a protocol has been proposed for the height of stays so as to achieve a convenient and generalized design guide, where the outermost point at each stay falls on the same circular arc. Furthermore, the load resistance and hysteretic responses of the MPCS-BRBs subjected to monotonic and cyclic axial loads are explored through an elastic-plastic FEA. It is found that a lower limit of restraining ratio exists, which would ensure overall instability of the MPCS-BRBs not to occur by considering an optimal initial pre-tensioning force in the cables so that they do not become slack before the MPCS-BRBs reach their ultimate failures, and ensure maximum ultimate load-carrying capacities of the braces to be obtained. The investigation and its findings on the elastic buckling loads, load resistance and hysteretic responses of MPCS-BRBs provide fundamentals and guidance for their preliminary design in actual engineering applications.

This paper presents the instability mechanism of an innovative Rhombic Grid Hyperboloid-Latticed Shell (RGHLS) under vertical load through experimental and numerical investigations. The RGHLS is only composed of bidirectional inclined primary and secondary columns without any circumferential members or lateral braces in its radial direction along its height. Therefore it would likely fail by out-of-plane multi-column interaction instability and the corresponding load-carrying capacity should be predicted. The experimental investigation of a reduced-scale test model of RGHLS was firstly performed to study its vertical load-carrying capacity and the multi-column interaction instability. A special spatial beam-string device for vertical multi-point loading of the test model has been initially designed and fabricated to precisely distribute the concentrated load to the top of the columns according to proportional distribution of loads required by designers. The experimental results revealed that the inclined columns indeed exhibited strong mutual restraining actions, and the ratio of the actual ultimate load-carrying capacity of the test model to its design load was 3.37, indicating a reasonable safety margin. In addition, FE numerical results of the test model corresponded well with the experimental results. Ultimately, additional FE numerical analyses have been conducted on the test model. Accordingly the effects of the ratio of stiffness between the secondary and primary columns, overall initial geometric imperfection, in-plane stiffness of top ring beam, and dimensions of portal columns on the load-carrying capacity and failure mode of RGHLS have been investigated extensively. As a result, the ratio of stiffness between the secondary and primary columns has been particularly recommended within a range of 0.46–0.70, so as to eliminate premature failure of X-joints prior to the instability of columns in the prototype of RGHLS.

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.

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.

The rhombic grid hyperboloid-latticed shells (RGHLSs) in the China Comic and Animation Museum (CCAM) are located on the ground floor, and they sustain enormous vertical and horizontal loads induced from upper building structures on top of them. Each RGHLS consists of numerous bidirectional inclined major and secondary columns that intertwine with one another to form a rhombic grid with X-shaped joints. Without both horizontal circumferential members and horizontal lateral braces in the radial direction of the RGHLS, as well as the existence of significant difference of compressive stiffness between major and secondary columns, the RGHLS would ultimately fail in a complicated form of in-plane and out-of-plane multi-column interaction instability in addition to its overall twist deformation under relatively low vertical loads. Currently, no design method for estimating its design strength and safety is available. Therefore, the load-carrying capacity of the RGHLS must be examined experimentally. This paper selects the RGHLS denoted by Y4 in the structure of the CCAM as the prototype, and presents an experimental investigation of its reduced scale (1:1/4) test model. A loading protocol consisting of six loading phases has been devised in order to predict the static vertical and horizontal load resistance, and horizontal hysteretic response of the RGHLS by keeping the amplitudes of the vertical load constantly as 1.0, 1.4 and 1.6 times the vertical design load of the reduced-scale test model, respectively. The experimental results obtained indicate that the test model remains elastic under 1.8 times its design loads, which is commonly adopted as static structural strength limit in practical design in China. In addition, horizontal cyclic load test indicated that the reduced-scale test model demonstrated sufficiently large horizontal load-carrying capacity as well as exhibited stable and ample hysteretic curves even under 1.6 times vertical load actions without any obvious stiffness reductions. This study comprehensively introduces the experimental test schemes and deeply analyzes the experimental results, thus forming an important basis for designing the load-carrying capacity of such RGHLSs. Ultimately, according to the experimental loading protocol, numerical simulations and analyses of the test model have been conducted by adopting ANSYS 12.1. The interaction strength design curve of the test model under a combination of vertical and horizontal loads is also proposed by carrying out additional numerical simulations of the model. The FE and experimental results have been compared, and they correspond well to one another, indicating that the results of the reduced-scale test model are accurate enough and reliable.

Vierendeel steel truss arches are often used in lighting zones of the spatial roof to obtain good permeability and lighting effects. They are different from conventional steel truss arches in terms of failure mechanism and strength design because they have only transverse tubes without diagonal tubes between chords. The chords of the Vierendeel truss arch undertake axial, bending and shear actions while the transverse tubes only resist the bending action. Hence, their structural design against strength is different from conventional steel truss arches. However, this aspect is not well analyzed in literature. This study analyzed the in-plane instability mechanism, failure mode and corresponding strength of the Vierendeel truss arch under a uniform radial load, a full-span uniform vertical load, a half-span uniform vertical load and their combinations. The global in-plane elastic buckling load of the arch under a uniform radial load is derived firstly and an interaction design formula for predicting the global in-plane strength of the arch under a uniform axial compression is proposed. It is found that the chords of the arch may fail in fully sectional plastic moment mode. Transverse tubes may fail because of the end moments. Slender enough arches may also undergo global failure. Strength design equations for local chord failure and for global failure of arches are developed. All of the equations proposed for predicting global in-plane elastic buckling, global in-plane ultimate strength and chord local strength of the arch agree quite well with the finite element results.

A new type of BRBs, namely a triple-truss-confined BRB (TTC-BRB) is proposed, and its hysteretic response is investigated experimentally and numerically in this paper. The TTC-BRB is formed through introducing an additional structural system of rigid trusses to the outside of a common BRB to effectively increase its external restraining flexural stiffness and its overall load-carrying capacity, especially when it is utilized as a long-span and a heavily axially loaded brace. The TTC-BRB may be adopted innovatively as diagonal braces in mega-frame structures of high-rise buildings and in long-span spatial structures. A total number of two TTC-BRB specimens have been designed and the hysteretic responses of the two TTC-BRB specimens are experimentally investigated under a combination of standard and fatigue loading protocols. The obtained experimental results indicate that both the TTC-BRB specimens have excellent hysteretic responses as well as being able to attain stable and ample hysteretic curves under cyclic loads, with both cumulative ductility and total accumulated cycles of loading, being well above the requirements specified respectively in the AISC seismic provisions and the Chinese code GB50010 for seismic design of buildings. The experimental results obtained are compared with those obtained by numerical analysis from a simplified FE model consisting of BEAM188 element, indicating that the FE model provides good correlations with the experimental results. Moreover, relevant failure mechanism and design suggestions of the TTC-BRB specimens are discussed and provided based upon the FE results. At last, as a mega brace, the influence of its self-weight, length and imperfection are investigated numerically to reveal the performance of the TTC-BRBs under cyclic loads.

This paper proposes a new type of buckling-restrained braces (BRBs), namely shuttle-shaped buckling-restrained braces (SS-BRBs). The proposed SS-BRB is composed of a circular steel tube as the inner core, and a shuttle-shaped thin-walled steel tube as the external restraining member. The space between them is filled by a steel-plate isolation system. The shuttle-shaped restraining member of the SS-BRB significantly improves load-carrying efficiency and saves material in its strength design. Moreover, the SS-BRB is more aesthetically appealing and can be utilized as an exposed BRB in long-span or spatial structures. In terms of the concept of restraining ratio of a BRB, no design method of an SS-BRB is available currently because it concerns the solution of the elastic buckling load of an SS-BRB. Therefore, the elastic buckling load of a pin-ended SS-BRB is initially studied by adopting the equilibrium method and is further verified through finite element (FE) method. The lateral displacement function of an SS-BRB, and the longitudinal stress at the extreme fiber of the external restraining member are derived by considering an initial geometric imperfection that is consistent with the first order overall buckling shape of the SS-BRB. A correction factor considering shear deformation has been incorporated for a more accurate prediction. The lower limit of the restraining ratio for a load-bearing type of SS-BRBs is further obtained based on yielding of the extreme fiber of the restraining member. Furthermore, the proposed formula has incorporated a strain hardening factor for the SS-BRB that experiences strain hardening of the core after its initial yielding. The proposed formulas have been validated through FE numerical analysis. The findings in this paper provide fundamentals to develop the design method for an energy-dissipation type of SS-BRBs.

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.

This paper studies the load-carrying capacity of concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs) under axial compression and biaxial bending. T-CDSCWs are composed of flange and web walls and boundary elements. The T-section is mono-symmetric and exhibits different interaction curves of load-carrying capacity when subjected to axial load and different direction bending. Based on the finite element (FE) model established by the previous study, the local buckling of the steel corrugated-plates is considered in the load-carrying capacity. Subsequently, this paper investigates the behaviours of T-CDSCWs under axial compression and uniaxial bending, including stress distribution, load–displacement curves, and interaction curves. Based on the numerical results, the pure moment capacity is found to be evaluated by reducing the plastic moment capacity, and the interaction equations of N–positive Mx, N–negative Mx, and N–My are proposed in the bilinear, linear, and parabolic form. For biaxial bending, the shape of the interaction curves is almost exclusively related to the axis compression ratio. Accordingly, this paper proposes the interaction equations of Mx–My subjected to certain axial compression. Moreover, the local buckling of steel corrugated-plates has no significant influence on the shape of the interaction curves no matter the bending direction. The global stability of T-CDSCWs is not involved in the study, and with the interaction equations obtained above, the global stability design of T-CDSCWs can be investigated by introducing the magnification factor of the bending moment caused by the secondary effect.

Pre-compression loads are conducted in BRBs if the installation of frames and BRBs are performed simultaneously. In this paper, the load-carrying and energy-dissipating behavior of BRBs under pre-compression are investigated by subassemblage tests and additional finite element (FE) analyses. A total of five specimens were tested, in which two specimens were tested by cyclic pure compression loads and three specimens were tested by hysteresis loads; four of them maintained stable load-carrying behavior during loading process. The load-carrying and energy-dissipating behavior of the specimens were satisfactorily simulated using a refined FE model with a combined isotropic and kinematic hardening rule of the core material, and the compression strength adjustment factor and the stress enhancement coefficient were well predicted by the FE analytical results with a relative error less than 3.0%. The FE analytical results of BRBs with different pre-compression strains are presented, indicating that the pre-compression in a BRB would aggravate the stress enhancement of the core material in both tension and compression, yet it would hardly influence the value of the compression strength adjustment factor.

A new type of core-separated buckling-restrained braces, namely a core-separated battened buckling-restrained brace (B-BRB) has been proposed. Its load-carrying capacity and hysteretic response are investigated theoretically and experimentally in this paper. The B-BRB has a remarkable advantage over a common buckling-restrained brace (BRB), in which the newly formed cross-section of the B-BRB is spread outwards by spacing two cores, hence resulting in higher material utilization efficiency in its structural design. In addition, the two independent all-steel BRBs, each having a single plate core simply in-filled in a narrow hollow section, are connected by longitudinally distributed battens rather than continuous plates. Based on the elastic-plastic FE analysis of a B-BRB under monotonic compressive load, its ultimate resistance and failure modes are investigated numerically, considering the effect of its overall initial geometric imperfection. An interaction formula between normalized slenderness ratio and buckling factor of the B-BRB is proposed for predicting its ultimate load-carrying capacity. Consequently, the hysteretic response of the B-BRB is explored through elastic-plastic FE analysis. The maximum normalized slenderness ratios of the B-BRBs required for a load-bearing type and an energy-dissipation type are proposed in their strength designs, respectively. Ultimately, hysteretic responses of five B-BRB specimens have been experimentally investigated. The experimental results are compared with the FE numerical analysis, which considers plate local buckling of all components of the B-BRBs. The comparison has verified the rationality of the proposed design method.

This paper proposes a new type of buckling-restrained brace (BRB), the so-called corrugated-web connected buckling-restrained brace (CWC-BRB), which is a core-separated BRB. The external restraining system of the CWC-BRB is composed of two all-steel external tubes connected by either single or double sinusoidal corrugated webs. Each of the two cores of the CWC-BRB has a single steel plate section and an extended projection at each end of the CWC-BRB, and the two core projections at each end are connected by a core stiffener. The external restraining systems, corrugated webs, two cores and core stiffeners form a firm and robust I-section CWC-BRB, and the flexural stiffness and load-carrying capacity of the proposed steel CWC-BRB are much larger than those of ordinary single-cored steel BRBs. The elastic buckling load of the CWC-BRB is derived by considering the shear deformation of the corrugated webs in the external restraining system. The ultimate load-carrying capacity under monotonic axial compression of CWC-BRBs and their hysteretic and low-cycle fatigue performance under repeated compressive-tensile cyclic loads are investigated using a shell element FE model. In addition, the effect of the restraining ratio or normalized slenderness ratio on the load resistance and failure mode of a CWC-BRB is explored. To further investigate the hysteretic performance and corresponding failure modes of CWC-BRBs and to validate the FE model, experimental studies are reported on four CWC-BRB specimens: two having a single sinusoidal corrugated web and other two having double sinusoidal corrugated webs. It is shown that the FE model provides excellent correlations with experimental results.

The external restraining members in an Assembled Buckling-Restrained Brace (ABRB) are mainly connected by high-strength bolts. Because of the bolts’ longitudinal discrete layout, the stiffness reduction of the external restraining members should be considered, and a significant increase in the local stress of the external member between two bolts must be considered as well. Thus, this study first uses theoretical derivation and numerical verification to investigate the stress state of BRB subjected to core single-wave overall deformation and core multi-wave buckling deformation, respectively. Based on the unique mechanical characteristics of the pinned ABRBs, a design method applicable for the pinned ABRB with a flat core is put forward, considering the external restraining stiffness reduction coefficient and the additional local influence of contact force when the core deforms in a multi-wave form. Finally, six ABRB FE models are presented to verify the rationality of the design method being safe and reliable to predict the ABRB’s overall buckling failure and bending failure in the ECSR of BRBs. This design method also considers the influence of a series of design parameters, including the gap between the core and external members, pinned connector length, extended core length, length, strength, stiffness and imperfection of the external restraining members, bolt dimensions and layout, etc.

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.

This paper deals with elastic shear buckling behavior of infill panels in sinusoidally corrugated steel plate shear walls, and fitting equations predicting the shear buckling loads are presented. Firstly by using finite element analyses (FEA), the previous formulae for bending rigidities of sinusoidally corrugated plates are revised, then pure shearing model are established to study the effects of key parameters on elastic shear buckling of sinusoidally corrugated infill panels, such as the aspect ratio, corrugation ratio, corrugation depth to plate thickness ratio and corrugation repeating number. Based on extensive FEA numerical results, fitting equations with good accuracy are proposed to estimate elastic shear buckling loads of sinusoidally corrugated panels, which are improved much compared with the solutions in previous studies. It is found that, the formulae for bending rigidities of corrugated plates revised in this paper are accurate compared with the previous ones. For sinusoidal corrugated infill panels, only global buckling and local buckling can be observed in the lowest buckling mode of eigenbuckling analysis, while interaction buckling is not obvious. The parameter of corrugation repeating number has a significant influence on elastic shear buckling loads, whereas it was neglected in previous studies.

This paper reports experimental and numerical investigations used to develop a simple and accurate design method for the in-plane strength of circular steel I-section arches having a sinusoidal corrugated web under a uniform vertical load over the entire span. In deference to a flat web that can resist both shear and normal stresses, a sinusoidal corrugated web can resist only shear stresses, since its axial and bending stiffnesses are quite small. Tests are carried out to investigate the global in-plane elasto-plastic behaviour and strength of a circular steel I-section arch with a sinusoidal corrugated web under symmetric loading. A finite element model is also developed, validated by the test results, and then used to further investigate the global in-plane elasto-plastic behaviour and strength of the steel arches. Based on the test and finite element results, a design equation for predicting the global in-plane strength of circular steel I-section arches with a sinusoidal corrugated web subjected to a uniform vertical load over the entire span is proposed. It is found from the finite element results that in addition to an in-plane global failure mode, a circular steel I-section arch with a corrugated web may also fail in an elasto-plastic web shear buckling mode. Hence, elasto-plastic shear buckling of the sinusoidal corrugated web in arches must also be considered in their design.

This paper presents an experimental study on the out-of-plane inelastic buckling strength of fixed circular steel arches under symmetric and non-symmetric loading. A test loading arrangement that allows for lateral deflections to develop freely under vertical loading is described. A finite element (FE) model consisting of the tested steel arch and the loading system is established for carrying out supplementary numerical investigation on the inelastic out-of-plane buckling strength of the fixed steel arches. The FE numerical model is validated by the experimental results. From the experimental results and supplementary FE investigation, it is found that the out-of-plane inelastic buckling strength of fixed steel arches is influenced significantly by the magnitude and distribution of initial out-of-plane geometric imperfections, as well as the out-of-plane elastic buckling modes and the in-plane loading patterns. It is also found that the out-of-plane buckling strength of a fixed steel arch under non-symmetric loading is lower than that under symmetric loading. Based on the experimental and FE results, a lower bound interaction equation is developed for predicting the out-of-plane inelastic buckling strength in the design of fixed circular steel arches against their out-of-plane failure.

The Concrete-infilled Double Steel Corrugated-plate Wall (CDSCW) consists of a corrugated part and two vertical boundary elements. The corrugated part is composed of two steel corrugated plates (SCPs) and infilled concrete, where high-strength bolts connect the two SCPs. The two vertical boundary elements are concrete filled steel tubulars. Obviously, owing to the corrugation configuration of SCPs as well as the positive interactive effect among SCPs, infilled concrete and vertical boundary elements, a CDSCW can attain high axial load-bearing efficiency and good seismic performance. This paper presents the experimental seismic performance of CDSCWs by exerting horizontal cyclic loads under constant axial compressions. Eight specimens were tested, with axial compression ratio, shear span to depth ratio and eccentricity of in-plane compressive load as the main research variables. The experimental results indicated all the specimens subjected to compression-bending failure with failure modes closely related to their axial compression ratios. There was a significant negative correlation between the axial compression ratio and the ductility of CDSCW specimens. In addition, the shear to span depth ratio had an important influence on the ductility of CDSCW specimens. Moreover, the experiment showed that the sectional axial strain distribution of CDSCW specimens conformed to the plane section assumption before reaching their peak load-bearing capacities, and most of the steel fibers except the ones near the neutral axis could be considered as plastic when the CDSCW specimens subjected to in-plane combined compression-bending-shear loads. Based on this, the formulae for estimating the load-bearing capacity of the CDSCW specimens under the combination of constant axial compressions and horizontal cyclic loads are established. The comparison between the formula values and the experimental results proves that the formulae are accurate and conservative. The conclusions of the experimental investigation provide fundamentals for the establishment of CDSCW seismic design method.

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.

Truss-confined buckling-restrained braces (TC-BRBs) are composed of conventional double steel tube BRBs and additional installation of external truss-confining systems. The truss-confining systems make TC-BRBs fulfil the need of the long-span bracing and enable economic and rational design. The previous experimental and numerical investigation of TC-BRBs suggested that the lower limit of the restraining ratio to ensure a stable cyclic behaviour was an empirical value of 3.0 for preliminary and conservative design. This paper aims to propose more rigorous design formulas for estimating the lower limit of the restraining ratio based on the numerical and theoretical analyses of typical TC-BRBs, triple- and quadruple-TC-BRBs (TTC- and QTC-BRBs). First, the formulas of the elastic buckling load of TC-BRBs are derived. Then, the load-carrying behaviour of TC-BRBs with the initial geometric imperfection is investigated with consideration of the most disadvantageous bending direction. The internal force variation of the external restraining members is discussed with increasing the restraining ratio, and it is found that the failure of TC-BRBs is governed by the compressive chord at the mid span. Furthermore, according to the criterion that the external restraining members do not fail before the core reaches the required axial displacement, the rigorous formulas for predicting the lower limit of the restraining ratio are derived. The formulas assure more rational and economic design of the load-carrying capacity of TC-BRBs.

This paper is concerned with the optimal (or least weight) design of steel buckling-restrained braces against global buckling. First, the global buckling prevention criterion of steel buckling-restrained braces (BRB) is reconstituted to take on a symmetric expression, i.e., (Pcr/Pu−1)[Mr/(v0Pu) −1] ≥ 1, so as to provide clarity on the equal importance of the stiffness and strength requirements of the restraining member, where Pcr is the elastic buckling load, Mr the yield moment resistance, and v0 the initial imperfection of the restraining member whereas Pu is the ultimate compressive load of the core under cyclic axial loads. It is shown herein that the optimal design of the restraining member satisfies (1) the boundary of the global buckling prevention criterion, and (2) the relationship between the stiffness term Pcr/Pu and the strength term Mr/(v0Pu) in view of the maximum feasible cross-sectional height-to-thickness ratio as specified by the adopted design code recommendation. The satisfaction of these two conditions furnishes a unique optimal design of the restraining member. The optimal design can be expressed as an explicit equation in terms of the second moment of area of the restraining member. A design example is presented to illustrate the material (or weight) efficiency of all-steel BRB designs based on the proposed design equation.

This paper investigates the flexural-torsional buckling behaviour about the symmetric axis of axially loaded concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs). The T-CDSCW is composed of steel corrugated-plates, infilled concrete and intermediate bolts, among which a positive composite effect further improves load-bearing capacities effectively and thus reduces the thickness of composite walls. The failure mode of the T-CDSCW with high height and small thickness is governed by global instability, and flexural and flexural-torsional buckling may occur for the T-CDSCW under axial compression. This paper focuses on numerical and theoretical analyses of the flexural-torsional buckling behaviour. Based on the refined finite element (FE) model validated by previous experimental researches, parameter analysis is carried out to investigate the elastic and inelastic flexural-torsional buckling behaviour. The formulas of the elastic flexural-torsional buckling load are derived and prove it feasible to design flexural-torsional buckling in accordance with torsional buckling. Numerical results show that the strength reduction factor of flexural-torsional instability can be delineated well by the height-to-thickness ratio of the web and the normalized torsional slenderness ratio of the T-CDSCW. Together with the design formulas of flexural instability, the design formulas of flexural-torsional instability proposed in this paper supplements the design method of axially loaded T-CDSCWs, and provides the foundation for further investigation into global instability of T-CDSCWs under combined compression and bending.

Because fixed arches have much higher flexural–torsional buckling resistance than pinended arches, they are used for engineering structures in many cases. However, studies on their flexural–torsional buckling behaviour have rarely been reported in the open literature hitherto. This paper investigates the elastic flexural–torsional buckling of fixed circular arches subjected to uniform compression and uniform bending because they play important roles in the design of steel arches against their flexural–torsional failure. One of the major difficulties in solving the flexural–torsional buckling problem of a fixed arch is to determine its accurate buckling shapes. The flexural–torsional buckling shapes are studied using a finite element (FE) method in association with eigenvalue analyses. It is found that the flexural–torsional buckling shape of a fixed arch becomes more complicated than the case of a straight beam-column or a shallow arch when the rise-to-span ratio increases, and so the theoretical analysis requires more terms of Fourier trigonometric series to describe the buckling shapes. Based on this, analytical solutions for flexural–torsional buckling loads of fixed arches are derived both by the Rayleigh–Ritz method and by solving differential equations for buckling deformations. Comparisons with the FE results show that the analytical solutions by the Rayleigh–Ritz method are reasonably accurate and that the analytical solutions by solving the equations for buckling deformations are exactly the same as the FE results. Simple approximate formulas for buckling loads of fixed arches with box-sections are proposed based on the extensive FE results for structural designers to use. The validity of the effective length method for the fixed arches is also discussed. It is found that in the case of circular arches the effective length method should not be used because the rise-to-span ratios and boundary conditions have complicated and significant influence on the buckling load.

For steel tubular truss arches, calculations of sectional rigidity especially the torsional rigidity, as well as the effect of shear deformation on out-of-plane buckling are not available yet. This paper investigates the sectional rigidities of trusses and the out-of-plane buckling loads of pin-ended circular steel tubular truss arches in uniform axial compression and in uniform bending. Firstly the compression rigidity, flexural rigidity, shear rigidity and torsional rigidity of latticed configuration for trusses are deduced. Then the out-of-plane buckling equations for circular monosymmetric arches incorporating the effect of shear deformation are established using a static equilibrium approach. Lastly the closed form solutions for out-of-plane buckling loads of pin-ended circular truss arches in uniform compression and in uniform bending are obtained. It is found that the axial deformation of chord tubes need be taken into account in the derivation of shear rigidity and torsional rigidity of latticed configuration. Due to the curved arch profile, the effect of shear deformation on out-of-plane buckling loads of truss arches is much smaller than that on straight truss columns.