Brace Stiffness Research Articles

Buckling of Conventional and High-Strength Vanadium Steel Single- and Double-Angle Compression Members and Truss Subassemblies: Experimental and Computational Correlation Study

High-strength, low-alloy vanadium (HSLA-V) steel offers higher strength and toughness than conventional steel. The resulting lighter weight and more slender structural members are more susceptible to buckling in compression. This study establishes an understanding of buckling in this material and the ability to predict it analytically. A series of conventional ASTM A572 Grade 50 steel and HSLA-V (nominal Grade 80) steel angle compression members were tested at Lehigh University’s Advanced Technology for Large Structural Systems (ATLSS) laboratory. A general-purpose finite element (FE) software was used in this study to simulate the buckling and post-buckling behavior of the structural members. The objective of these simulations was to establish confidence in the ability to accurately predict buckling response. The influence of the following modeling parameters on the accuracy of the compression angle member simulation results was investigated: variation in material stress-strain relationship, residual stresses, and the shape and magnitude of geometric imperfections. For the truss subassembly simulations, the influence of the following parameters was also investigated: bracing and boundary element stiffness and design code assumptions of end conditions.

Lateral load performance of a reinforced concrete frame with pultruded GFRP box braces

Reinforced concrete buildings, which constitute most of the building stock in Turkey, should be examined in terms of earthquake resistance. Many studies have been carried out to increase the seismic resistance of reinforced concrete (RC) structures against earthquakes. In this study, a single-story, single-span RC frame stiffened with chevron steel braces was chosen as a reference frame and laterally loaded to failure. In the first step, the experimentally obtained static lateral load-deflection curve was verified by non-linear finite element (FE) analysis. Then, the uniaxial tensile properties of the selected glass fiber reinforced polymer (GFRP) materials were verified using FE analysis with the results found in the literature. In the second step, three different GFRP box braces with different axial stiffnesses were investigated and the results were compared with those of the steel chevron braces. Finally, the lateral load performance and expected buckling failure of the GFRP box braces in an RC moment frame have been presented and discussed in this study. Considering the lightweight of the GFRP sections, the lateral load capacity of the RC frame with GFRP braces was improved as much as the steel braces, and the maximum gain was about 47% more when the equal axial stiffness of steel brace was provided to GFRP brace. Ductility and story drift of the considered braced moment frames are presented.

Analytical and finite element analyses of flexural and torsional buckling of I-columns with discrete braces

The present study investigates the buckling strength of braced thin-walled columns under bending and torsional modes. Unlike the well-known bending modes, the torsion buckling modes of braced columns are not adequately assessed in design and are often overlooked. In order to control the buckling behaviour, the effects of elastic discrete springs in bending and torsion are taken into account. Analytical solutions are derived for bending and torsion buckling modes in the case of simply supported struts with doubly symmetric cross sections. Further, the threshold bracing stiffness to achieve the higher buckling modes is found in both bending and torsion modes. For more general cases, the finite element approach of the model is implemented and it is able to carry out the buckling modes of columns under compression in the presence of 3D elastic springs and for any arbitrary cross sections. The analytical and the numerical results of the present models are compared to some available solutions in the literature and to finite element simulations of the commercial code Abaqus. The efficiency of the closed-form solutions and the numerical approach is successfully verified. The post-buckling of braced columns is considered at the end in the presence of elastic bending and torsion springs. The effect of braces to enhance the buckling capacity concludes the study.

Experimental investigation of a low‐prestressed self‐centering energy dissipative brace

AbstractSelf‐centering energy dissipative (SCED) braces have the potential to contribute greatly to building resiliency, because the braces can limit both maximum and residual story drifts during earthquakes. An obstacle to widespread adoption of existing SCED systems is that they require high prestressing forces, corresponding to more than half of the brace yield strength. To address this problem, a new low‐prestressed SCED (LP‐SCED) system has been proposed, which has a flag‐shaped force–deformation hysteresis but needs only a low level of prestressing force. This paper presents the results of an experimental investigation to establish the properties of the new system's key components, as well as prototypes of the full brace specimen. The tested system had a prestressing force equal to only 3∼4% of the brace yield force. The tested systems had a stable, flag‐shaped force–deformation hysteresis relationship, even after being subjected to deformations corresponding to 3.4% story drift. Eventually, when the imposed deformations were sufficiently large, the brace stiffness increased dramatically, which helps to reduce drift concentrations that may be critical in braced‐frame structures under extreme earthquakes. The yielding and damage were restricted to the mild‐steel dissipaters, which could be replaced easily after each test, and in practice, they could be replaced easily after an earthquake.

Seismic Performance of RC Split-Foundation Frame Structures with Steel Braces in the Mountainous Area

Reinforced concrete (RC) split-foundation frame structures are widely used in mountainous areas. There are two grounding terminals with different heights in the split-foundation frame structures. Under the earthquake, the local damage phenomenon of the structures is severe due to the uneven stiffness distribution. It is one way to improve the seismic performance of the split-foundation frame structures to install steel braces in the upper embedding floor. According to the deformation characteristics of the upper embedding floor, three types of steel braces arrangement for the split-foundation frame structures were proposed: horizontal braces, V-type braces, and V-[Formula: see text] braces. Then based on the ratio of lateral stiffness of steel braces and concrete frame columns, the section of steel brace was designed. A quasi-static test was carried out to analyze the influence of steel braces on the failure mode of the RC split-foundation frame. The reasonable seismic waves were selected to carry out the nonlinear dynamic time history analysis. Then the seismic response and failure mode of the split-foundation frame structures with different braces arrangements were compared. On this basis, fragility analysis was carried out, and the earthquake-induced collapse resistance capacity of split-foundation frame structures with steel braces was preliminarily evaluated. The results show that the horizontal steel brace can improve the phenomenon of damage concentration of the split-foundation frame structures. Furthermore, setting V-shaped braces can significantly reduce the damage degree of the upper embedding end columns and change the phenomenon of locally severe damage of the split-foundation frame structures. Moreover, according to the design method proposed in this paper, setting steel braces can improve the seismic collapse resistance capacity of the split-foundation frame structures.

Brace stiffness for parallel semi-rigid columns

Proposed in the paper is an analytical method of determining the ideal brace stiffness for a structural system consisting of parallel semi-rigid columns with horizontal tie bracing at mid-height. Based on a newly proposed unbraced frame model, the ideal brace stiffness of the parallel column system can be obtained from buckling of an equivalent unbraced frame with column height being half of the original one. The influence of column stiffness interaction associated with semi-rigid connections, column sizes, and applied loads is theoretically considered in the determination of the ideal brace stiffness, which makes the proposed method applicable to systems with nonidentical columns. For a system with the same columns and end connections, the minimum ideal brace stiffness in elastic analysis can be achieved with the end-fixity factor being 0.392. In addition, a simple expression is presented to quantify the effect of the semi-rigid connection on the ideal brace stiffness of the system. Good agreements between analytical and finite element analysis results of presented examples indicate the proposed method can accurately evaluate the ideal brace stiffness of a semi-rigid parallel column system.

Lateral-Torsional Buckling Analysis for Doubly Symmetric Tubular Flange Composite Beams with Lateral Bracing under Concentrated Load

Tubular flange composite beams are increasingly applied in modern bridge structures. In order to investigate the overall stability behavior of doubly symmetric tubular flange composite beams with lateral bracing under concentrated load, the analysis of elastic lateral-torsional buckling is conducted by the energy variation method. The analytical solution of critical moment of doubly symmetric tubular flange composite beams with lateral bracing is obtained. Meanwhile, the simplified calculation formula of critical moment is fitted by 1stOpt software based on 26,000 groups of data, and the accuracy is verified by the finite element method. It is found that, the critical moment rises obviously with increasing lateral bracing stiffness, and adding lateral bracing to doubly symmetric tubular flange composite beams is beneficial to improve the overall stability in engineering practice. Finally, the influence of several parameters including concrete strength, span, steel ratio of flange and height-thickness ratio of web are studied. The results show that the concrete strength and the web height-thickness ratio have a weak influence on critical moment of elastic lateral-torsional buckling, while the influence of span-depth ratio and flange steel ratio is very significant.

Seismic performance of suspended‐floor structures with viscous dampers considering acceptable interstory drift

SummaryNumerical studies of suspended‐floor structures were conducted, and viscous dampers were applied to improve their seismic performances. The following issues were analyzed under 20 earthquake records: seismic responses of the primary structure and suspended floors, the distributions of the damping coefficient c0, and the interstory stiffness of the suspended floors. There was a significant reduction in the roof drift and the base shear force of the cores after replacing the steel bars with viscous dampers. The suspended‐floor structures with viscous dampers exhibited an optimal c0. The suspended‐floor structure with a triangular distribution of c0 showed a smaller seismic response than the one with a uniform distribution of c0. Under the design‐based earthquake, there was complete damage of nonstructural components in the y‐direction. Hence, applications of diagonal steel braces within the 1st to 10th floors were suggested to increase the lateral stiffness of the suspended floors in the y‐direction. The application of diagonal steel braces reduced the story drift Sd of the suspended floors, resulting in slight damage to nonstructural components under the design basis earthquake (DBE) hazard level. However, the roof floor, which contains electrical and mechanical components, exhibited an increase in Sd after the application of the diagonal steel braces. With increasing stiffness of the diagonal brace, the story drift profile of the suspended floors tended to be uniform, and the suspended‐floor structures with the uniform distribution of c0 exhibited seismic performances closer to those of the suspended‐floor structures with the triangular distribution of c0.

Optimization of VEDs for Vibration Control of Transmission Line Tower

This paper investigates the optimization of viscoelastic dampers (VEDs) for vibration control of a transmission line tower. Considering the stiffness of the steel brace connected to a VED, the mechanical model of the VED-brace system was established. Subsequently, the additional modal damping ratio of the transmission line tower attached with VEDs was obtained analytically. Furthermore, the finite element model of a two-circuit transmission line tower with VEDs was built in ANSYS software, and the influences of installation positions and parameters of VEDs on the additional modal damping ratio were clarified. In addition, the control performance of VEDs on the transmission line tower subjected to wind excitations was emphatically illustrated. The results show that the stiffness of the steel brace connected to a VED has a significant effect on the maximum additional modal damping ratio of the VED-brace system provided for the transmission line tower and the optimal parameters of the VED. Meanwhile, the installation positions of VEDs dramatically influence the additional modal damping ratio. Moreover, the increase of the brace stiffness and the loss factor is beneficial to improve the control performance of VEDs. Besides that, the VEDs present superior control performance on the top displacement of the transmission line tower as well as the transverse bending vibration energy.

Study on prediction method of initial stiffness of self-centering energy dissipation braces

The self-centering energy dissipation (SCED) brace is an innovative structural component of seismic-resistant systems that provides a flag-shaped response with good energy dissipation and self-centering capacity. The initial stiffness of the SCED brace is a crucial parameter for brace design and a braced frame system. The current use of SCED braces is limited by the significant discrepancy between the actual and theoretically predicted initial stiffnesses. In this paper, the sources resulting in the inaccurate prediction are identified as the accuracy of the theoretical governing equations and the practical fabrication tolerances of the braces. The accuracies of the governing equations with different levels of complexity are analyzed and compared based on a typical SCED brace. To investigate the reduction effect of fabrication tolerances on the effective axial stiffness, a large number of numerical simulations are conducted on an axially loaded tube member with different tolerance characteristics, including the fundamental length tolerance, contact surface nonuniformity, and load level. According to the trends of the effective axial stiffness, a valid stiffness reduction factor is defined. It can provide good estimates of the reduced axial stiffness under different tolerance parameters. Additionally, the stiffness reduction factor is incorporated into a refined governing equation of an experimental SCED brace to verify the accuracy of the predicted initial stiffness when the effect of the fabrication tolerances is considered. It is shown that the modified governing equation estimates well the actual initial stiffness. Moreover, this prediction equation can be easily extended to other types of SCED braces once the tolerance parameters have been determined.

Effects of Brace Stiffness and Nonlinearity of Viscous Dampers on Seismic Performance of Structures

In the applications of supplemental dampers for seismic hazard mitigation, the supporting braces for the dampers are considered an important component for ensuring an efficient energy dissipation in the structure. Despite their importance, studies on the effects of the brace stiffness and the velocity exponent in the case of nonlinear viscous dampers are rather limited. In this paper, a numerical time-stepping method is developed for computing the seismic response of the structure with supporting braces and nonlinear viscous dampers. Using the proposed method, effects of the parameters of the nonlinear damper-brace systems are investigated, using first a single-story structure, followed by multi-story buildings. Results indicated that the design parameters for the dampers and supporting braces may be combined in numerous ways to satisfy a given set of structural performance objectives, but the brace stiffness can be minimized to achieve design efficiency in the range of velocity exponent commonly used for seismic applications of nonlinear viscous dampers. Results also indicated that for a set brace stiffness, if the dampers are optimally designed, the velocity exponent has an insignificant effect on the structural seismic performance objectives considered in this paper.

Threshold stiffness of lateral bracing in systems of parallel compression members

This paper explores the stiffness requirements for bracing components used in systems of parallel compression members or sub-assemblages. While rudimentary closed form equations are available to compute the threshold brace stiffness for single column systems, determining the stiffness of bracing components in multi-member systems is more complex. With the goal of developing useful multi-member stiffness models, the presented formulation is based on an equilibrium analysis of a single arbitrary column within a braced n-member system of interest. The resulting recursive relationship associated with tie-brace deformation is expanded, together with the brace-to-column shear connections and boundary conditions representing the anchor bracing, to generate a system of brace stiffness equations. Reformulating the equations as an eigenvalue problem, the minimum eigenvalue is the basis for subsequent equations derived to compute the required tie-brace stiffness in terms of the number of parallel members, and the stiffness of the shear connectors and the components of the system anchorage. Two approximations of the theoretically exact solution are also developed, providing useful alternatives for estimating system bracing requirements. Error analysis indicates that both approximate expressions sufficiently determine threshold bracing stiffness for structural systems with multiple parallel members with one or more brace points. An illustrative example is presented to demonstrate the use of the approximate expressions, and subsequent results are compared with both the derived theoretical solutions and results from finite element analyses.

Hysteretic and seismic performance of dual self-centering variable friction damper braces

A novel dual self-centering variable friction damper (DSC-VFD) brace was introduced to achieve greater post-yield stiffness and a better energy dissipation capability. To evaluate its hysteretic response with a novel flag shape, a new uniaxial material with different loading and unloading stiffnesses was developed based on the OpenSees platform in this study. The actual initial stiffness of the DSC-VFD brace was significantly lower than the theoretical value because of the tube length and pin diameter tolerances. The initial stiffness modification coefficients of the DSC-VFD brace were defined, and their calculation equations were established. Because of the uneven gap openings along the friction plates, the matrix displacement method was applied to determine the different gap openings under the tension and compression stages. Then, the hysteretic response of the DSC-VFD brace was calculated with the user-defined model; the model results were in good agreement with the experimental result, verifying the reliability of the proposed model. Simulation models were used to study the crucial parameters for the hysteretic response of the DSC-VFD brace. Finally, nonlinear dynamic analyses of a four-story braced frame were conducted to study the seismic performance of the DSC-VFD brace with a novel flag shape. The results showed that the DSC-VFD brace with a larger post-yield stiffness provided stable self-centering behavior and an effective energy dissipation capability. The high loading stiffness and energy dissipation ability effectively decreased the deformations of the braced structures and improved their seismic responses.

Analytical and experimental studies on a two-level yielding rocking steel frame with buckling-restrained columns (TYRSFB)

The lower post-yielding stiffness of a buckling-restrained brace (BRB) was improved by constructing a two-level yielding BRB by setting an additional unit with a certain stiffness after the yielding of a traditional BRB. In this paper, a pinned steel rod with an initial gap is added at the outside of each buckling-restrained column (BRC) in a rocking steel frame with BRCs (RSFB) to improve the stiffness, lateral carrying capacity and ductility of the RSFB after BRCs yielding, which is named as a two-level yielding RSFB (TYRSFB). This paper studies the seismic performance of the TYRSFB and determines the influence of key constructional parameters of steel rods on structural performance. First, the top force–displacement curves of the TYRSFB are derived. Then, quasi-static tests and numerical simulations are conducted on the TYRSFB and RSFB, and the results show that the proposed TYRSFB can achieve the anticipated seismic performance. Moreover, the numerical simulation results are basically consistent with the calculation results of the proposed theoretical formulas. Finally, parametric studies based on the theoretical formulas and numerical models show that changing the value of the distance between steel rods and the central column, the initial gap, the ratio of the cross-sectional area and the length between the steel rod elastic and energy dissipating portions will influence the structural lateral carrying capacity, ductility and failure mode.

Towards optimal slip force and stiffness distribution in designing friction dampers

The considerable capacity of friction dampers in energy dissipation makes them a good choice for vibration control of structures. The slip force of friction dampers and also the stiffness of the corresponding bracing system are the major parameters that must be chosen carefully in the design procedure of these dampers. This paper presents an innovative approach to determine these parameters using the data extracted from a series of analyses conducted on three different structures, subjected to five different earthquake records. For this purpose, 900 time-history analyses are conducted. The responses extracted from these analyses are used to compare the effect of different slip forces and to choose the optimum case. Also, a stiffness calibration method is proposed to determine the bracing system stiffness. Finally, two multi-functional optimization methods are introduced to find a single value for optimal slip force. It is shown that between 56 to 74% of the input energy can be dissipated by friction dampers, using this design approach. Additionally, up to 20, 45, 64, and 62% reductions in maximum displacement, velocity, acceleration, and base shear are achieved respectively for the structures studied in this research.

Experimental Study on the Effect of the H-shaped beam-Folded Roof Plate Joints on the Rotational Bracing Stiffness of Folded Roof Plates as Continuous Braces

Experimental Study on the Effect of the H-shaped beam-Folded Roof Plate Joints on the Rotational Bracing Stiffness of Folded Roof Plates as Continuous Braces

Effects of stiffness and configuration of brace-viscous damper systems on the response mitigation of offshore jacket platforms

We investigate the effects of a brace-viscous damper system on the dynamic response of offshore platforms. To do this, offshore jacket platforms with various distributions and three different configurations of brace-viscous damper systems - toggle, chevron, and diagonal configurations - and a wide range of brace stiffness are numerically modelled under the loading of irregular waves in ANSYS software. The dynamic response of the developed numerical model and its various brace-viscous damper configurations are validated against literature experimental and numerical results. Such a validation revealed an excellent agreement between the numerical results and the benchmark data. The results suggest that the standard deviation of the platform displacement given by a toggle configuration is less than that due to the chevron and diagonal configurations. Moreover, the maximum reduction of the base shear force is achieved by the application of the toggle configuration. Regarding the brace stiffness (area), for a reference damping coefficient of 500 N.m/s, a 54% increase in the brace area (from 42 to 91.8 mm2) results in a 21.26%, 38.61%, and 17.57% reduction in the structure displacement response for the diagonal, chevron, and toggle configurations, respectively. Using the results of the numerical simulations, we propose the spatially-optimized distribution of the brace-viscous damper system. Comparing the numerical results of this paper with those of field observations it was shown that the viscous damper with toggle configuration outperforms both the viscoelastic damper and uncontrolled platforms in terms of dynamic response.

Development and subassemblage cyclic testing of hybrid buckling-restrained steel braces

Buckling-restrained braced frames (BRBFs) are vulnerable to relatively higher post-earthquake residual drifts under high intensity ground shakings. This is primarily due to the low axial elastic and post-elastic stiffness of buckling-restrained braces (BRBs) satisfying the design force demand requirements. In the present study, a hybrid buckling restrained bracing system consisting of a short yielding core length BRB component and a conventional buckling-type brace component connected in series has been developed with an aim to increase the axial stiffness of braces. This study is focused on the experimental investigation of six hybrid bucking restrained braces (HBRBs) to investigate their overall behavior, load-resisting capacity, strength-adjustment factors and energy dissipation potential. The main parameters varied are the cross-sectional area, the yielding length of core elements as well as the detailing of buckling-restraining system of short yielding core length BRBs. Test results showed that the HBRBs with yielding core length in the range of 30% of work-point to work-point lengths withstood an axial strain of 6% without any instability and can deliver stable and balanced hysteretic response and excellent energy dissipation under reversed cyclic loading conditions.

Displacement response of submerged floating tunnel with flexible boundary under explosion load

In this study, a single-span submerged floating tunnel (SFT) is simplified as an elastic supporting beam model with movable ends. This model is used to analyze the displacement response of the SFT subjected to an underwater explosion in an ocean environment. The effects of the shock wave pressure and bubble pressure are considered simultaneously. The dynamic equilibrium equation was established based on D’Alembert’s principle. When the pipe segment of the SFT vibrates, the additional inertia force and the damping force of the surrounding water to the pipe are calculated using the Morison equation. The motion differential equation of an SFT under the load of an underwater explosion is obtained using the Galerkin method. The displacement analytical expressions of an SFT under four different stages of load are derived, and a comprehensive analysis is performed to assess the influence of key parameters, including the brace stiffness, damping, scaled distance, and bubble oscillation frequency, on the displacement of the SFT. It was observed that the key parameters mentioned above all significantly influence the displacement response of the SFT. Some reasonable suggestions for different parameters are proposed to provide a reference for the SFT design.

Effects of Brace-viscous Damper System on the Dynamic Response of Steel Frames

In this study, the effects of three different viscous damper configurations, chevron, diagonal and toggle, as well as brace stiffness on the performance of brace-viscous damper system in various steel frams under different earthquake records were investigated. A finite element software, ANSYS, is exploited to develop the numerical models. To verify the numerical simulations, their results were compared with those of the experimental studies in the literature. The results show the reduction in the base shear force given by the toggle configuration is larger than that due to the chevron and diagonal configurations. Regarding the brace stiffness (area), for a reference damping coefficient of 500 N.m/s, a 54% increase in the brace area (from 42 to 91.8 mm2) results in a 21.26, 38.61, and 17.57% reduction in the structure displacement response for the diagonal, chevron, and toggle configurations, respectively. Further, using the results of the numerical simulations, we proposed the spatially-optimized distribution of the brace-viscous damper system.