Brace Axial Force Research Articles

Elastic stiffness and bearing mechanism of eccentrically braced steel frames

Eccentrically braced steel frames have great ductility and energy dissipation, but their elastic stiffness is influenced by the length of the braces. The stiffness of these frames is important for computing story drifts and link rotations, which have prescribed limits. The yield and ultimate bearing capacity of eccentrically braced steel frames can be predicted by analyzing their individual components. This paper proposes a method to calculate the elastic stiffness and bearing capacity of K-type, D-type, and V-type eccentrically braced steel frames. To calculate the elastic stiffness of these frames, the displacement of a story can be obtained by summing the deformations of the individual components. The link shear and brace axial force of a story are also considered using structural mechanics. This allows for estimating the elastic stiffness of eccentrically braced steel frames in the early design phase. Based on the virtual work principle and the ideal failure mode of these frames, the yield and ultimate bearing capacity of eccentrically braced steel frames are proposed using frame drift angle and verified by experimental results. The theoretical stiffness of these frames is compared with finite element models. The finite element analysis and experimental results show that the elastic stiffness, yield bearing, and ultimate bearing are very close with only about 10% error, verifying the high accuracy of the formula suggested in this paper.

Experimental and numerical analyses on stress concentration factors of concrete-filled welded integral K-joints in steel truss bridges

A novel fully welded concrete-filled integral K-joint incorporating longitudinal perfobond ribs welded to the inner faces of the chord is proposed to improve the fatigue behavior. To evaluate the stress concentration factor (SCF) of such joints, a 1:5 scale truss specimen was fabricated and tested to measure the SCF distribution in the fatigue prone joint. A finite element model was also developed to evaluate the SCFmax of concrete-filled welded integral K-joints and was validated against the test results. A parametric study was carried out and a comprehensive database was obtained considering the effects of brace width-to-chord thickness ratio (2γ), brace-to-chord thickness ratio (τ), the angle between braces and chord (θ) on the SCFmax. Also, the following three basic loading conditions were examined: brace axial force, chord axial force and chord in-plane bending. Based on the results of 192 numerical models, new equations to predict the SCFmax of concrete-filled welded integral K-joint were derived for design purposes. Finally, the fatigue behavior of three different designs is compared in terms of SCFmax and hot spot stress range Sh-N curves. These systems are rectangular hollow section (RHS) K-joints, concrete-filled rectangular hollow section (CFRHS) K-joints and concrete-filled welded integral K-joint. It was shown that the concrete-filled integral welded K-joint has the best fatigue behavior, followed by the CFRHS K-joint, while the RHS K-joint has the poorest fatigue behavior.

Hysteretic behavior of CHS X-joints under in-plane bending moment

In this paper, hysteretic behavior of circular hollow section (CHS) X-joints under in-plane bending moment (IPBM) is investigated. Firstly, carried out experimental study on three CHS X-joints with different brace-to-chord diameter ratio (β) and brace-to-chord angle (θ) under cyclic IPBM. Test results show that three specimens eventually failed by tearing of the chord wall in the brace/chord connection region. Before cracking, the chord wall in the connection region experienced large plastic deformation which provide significant energy dissipation; and the resistance decreases slowly after cracking due to ductile crack propagation. Test results also indicate that flexural hysteretic of the X-joints is greatly affected by the two parameters (β and θ). Specifically, either increasing β (from 0.73 to 0.89) or deceasing θ (from 90° to 70°) is benefit to ductility ratio, flexural strength and energy dissipation behavior. The test observation is further explained and confirmed by a model of load transfer mechanism (a semi-cylindrical shell constrained by the directional supports) and the finite element (FE) parameters analysis with extended range of the above two parameters. Then, a hysteretic model is proposed to simulate in-plane flexural hysteretic behavior of the CHS X-joints, and the hysteric model is verified by test and FE results. Finally, effect of chord moment and brace axial force on the in-plane flexural behavior of the X-joints was investigated by FE analysis.

Study on the brace axial force-local deformation behavior of unstiffened CHS X-joints

Numerical parametric analysis is carried out to study the force-local deformation $$(F-\delta )$$ behavior of circular hollow section X-joints under brace axial force (including compression and tension) and chord stress. An exponential model is proposed to describe the $$F-\delta $$ curves of the X-joints. Parameters of the proposed model including two intercept forces and three joints stiffness (initial stiffness and two tangent stiffness) are determined by theoretical analysis, finite element (FE) analysis and nonlinear regression. The results show that the $$F-\delta $$ behavior under brace compression is significantly different from that of brace tension. Chord stress has little effect on the initial stiffness, but has a relatively large effect on the intercept forces and the tangent stiffness. The proposed model well predicts $$F-\delta $$ behavior of the X-joints from FE results, which including strength degradation caused by chord wall buckling.

Fatigue behavior of bird-beak SHS X-joints under cyclic brace axial forces

This paper presents an experimental investigation on the fatigue behavior of bird-beak X-joints under brace axial force. Two square bird-beak and two diamond bird-beak specimens were fabricated by using 80% partial joint penetration (PJP) welds. Static loading was firstly carried out to measure the hot spot stresses at weld toes, by which stress concentration factors (SCFs) were extrapolated and subsequently the critical locations were identified. A cyclic axial loading was then implemented on the brace end. The fatigue behavior investigated includes crack initiation, crack propagation, failure mode, fatigue life and stiffness degradation. The results show that the SCFs calculated from test data could well predict the location of crack initiation. Furthermore, the through-thickness crack lives ( N 3 ) of all are found to be greater than the fatigue lives derived from the IIW (International Institute of Welding) design S N curves, which indicates that these curves for conventional joints can be conservatively used for estimating the fatigue life of bird-beak SHS X-joints. • High-cycle fatigue tests for square and diamond bird-beak SHS X-joints under cyclic brace axial force were conducted. • Fatigue crack propagation and failure mode of bird-beak SHS X-joints under cyclic brace axial force were investigated. • Variations of crack length and joint stiffness with number of load cycles were revealed. • Comparisons between experimental fatigue data and IIW fatigue design curves were carried out.

Stress concentration factors of bird-beak SHS X-joints under brace axial forces

ABSTRACT Bird-beak joints are a new type of welded square hollow section (SHS) joints and their fatigue behaviors are of the most attentions recently. The stress concentration factors (SCFs) of both square and diamond bird-beak X-joints under brace axial forces were systematically investigated in this research by using experimental and numerical methods. Four specimens including two square bird-beak X-joints and two diamond bird-beak X-joints were tested. Elastic strain distributions within crown and saddle areas were measured, and the strain concentration factors (SNCFs) at specified hot spots were obtained by using the quadratic extrapolation approach. Refined finite element models, whose accuracies have been validated by experimental data, were developed to parametrically simulate the stress concentrations at weld toes of such innovative joints. The influences of three non-dimension parameters (i.e., brace/chord width ratio β , chord wall slenderness ratio 2 γ , and brace/chord wall thickness ratio τ ) on SCFs of bird-beak X-joints were revealed. Comparison also shows that the saddle areas commonly contain the highest SCFs within whole joint, and that square bird-beak X-joints provide lower stress concentrations than diamond ones in case of identical non-dimensional parameters. Based on numerous results from parametric analysis, design formulas were finally proposed to calculate the SCFs at typical hot spots of both square and diamond bird-beak X-joints subjected brace axial forces.

Gusset design considering buckling forces in frame and brace action directions: Test and finite element analysis of a self-centering braced frame for verification

A steel dual-core self-centering brace (DC-SCB) has been developed to combine both energy dissipation and self-centering properties into a single member for seismic resistance. A strong gusset-weak brace design assures the seismic response of the DC-SCB in earthquakes. In this work, in-plane cyclic tests and finite element analyses were conducted on single story steel frames with the DC-SCB to investigate the performance of corner gusset plates due to the brace axial force (which acts in the direction of the brace) combined with the force from the frame action (which acts in a direction near perpendicular to the brace axial force). Different configurations of gusset plates were used for analyses to develop a design method to consider effects from brace forces and frame action forces. The yielding and buckling forces of a gusset plate in the frame action direction are verified based on a proposed column strip model and buckling coefficient varied with gusset thickness. It is shown to be consistent with the behavior from the tests and finite element analyses with errors in strength of up to 13% for the range of gusset configurations considered.

SCF of bird-beak SHS X-joints under asymmetrical brace axial forces

This research investigated the stress concentration factor (SCF) superposition of bird-beak square hollow section (SHS) X-joints under asymmetrical axial brace forces. Three typical non-dimensional parameters (i.e., β = 0.6, 2γ = 20, τ = 0.5) were employed for tubular joints. Finite element models of conventional, square bird-beak, and diamond bird-beak SHS X-joints were constructed by accurately considering the geometries of welds, and the structural hot spot stresses at weld toes were obtained using the extrapolation method. Numerical results show that, in case of single-side brace axial force, the stresses on the unloaded brace side of bird-beak X-joints are obviously higher the values at the corresponding locations of conventional X-joints, and as a result the SCF errors induced by the existing superposition formula of conventional joints are significant for bird-beak joints. The mechanism was revealed to be the interactions between adjacent walls of the chord by further investigating the compatible deformations of these joints. A modified superposition formula, in which a new load case considering both single-side brace axial force and reversed chord in-plane bending has been employed, was introduced as the solution. The SCF variations with non-dimensional parameters under the new load case were also identified by conducting parametric analysis. The proposed superposition approach gives reasonable predictions of SCF of bird-beak SHS X-joints under asymmetrical brace axial forces.

Strengthening CHS T-joints subjected to brace axial compression using through-bolts

T-joints of circular hollow steel sections (CHS) with large brace-to-chord diameter ratios usually fail in an outward chord deformation (ovalization) mode when subjected to brace axial compression. In this paper, a new technique is presented for increasing the joint capacity using radial through-bolts to laterally brace the chord member and delay the joint failure. Strengthened CHS T-joint specimens were experimentally tested to scrutinize the effect of changing the number and spacing of the through-bolts on the gained strength and stiffness of the joint. This strengthening technique showed significant joint's strength enhancement even by using only one through-bolt where the joint capacity increased by at least 35%. Numerical analysis using the finite element method was carried out to examine the effect of a wider range of parameters such as the class of chord member section and the pattern/spacing of the through-bolts on the failure load of the joint. It is concluded that strengthening of CHS T-joints subjected to brace axial compression forces using through-bolts is an effective and practical strengthening technique. The investigation also revealed that increasing the number of closely spaced bolts increased the joint capacity; but, an odd number of the through bolts is recommended especially for large-spaced bolts. Based on the outcomes of the experimental and analytical investigation, a bolt spacing is proposed in order to get the maximum gain in strength and stiffness for CHS T-joints strengthened using transverse through bolts.

Tests to Determine Stress Concentration Factors for Square Bird-Beak SHS Joints under Chord and Brace Axial Forces

AbstractBird-beak joints are a type of welded square hollow section (SHS) joint, the static strength of which is higher than that of conventional joints. Experimental analyses were conducted on the stress concentration factors (SCFs) of square bird-beak joints to obtain more information regarding their fatigue behavior. Twelve specimens, i.e., three conventional joints and nine square bird-beak joints, are separately tested by considering chord and brace axial force load cases. Both conventional and square bird-beak joints tested have a T-shape and are simply supported at their chord ends. Elastic strain distributions near the crown and saddle areas are measured, and strain concentration factors (SNCFs) at potential hot spots are calculated using an extrapolation approach. Quadratic extrapolation is suggested for the square bird-beak joints because linear extrapolation may underestimate SNCFs by up to 35%. Furthermore, critical locations are identified for square bird-beak joints subjected to chord and br...

The Response of the Bi-Directional Beam String Structure under Vertical Seismic Considering Supporting Frame

This paper using time time-procedure analysis method to analyze seismic response on a 80 m × 80 m bidirectional beam string structure model. Under vertical seismic action, we respectively compared to the seismic performance under the structure have or no supporting frame and have the same supporting frame but different support conditions. Under vertical seismic action, the axial force of brace is almost the same considering or unconsidering the supporting frame, while the upper beam vertical displacement is increased and the surrounding of the roof even increased several times considering supporting frame; the boundary conditions for the sliding hinge support bidirectional beam string structure which under vertical seismic ( middle seismic ) action the brace axial force and winding beam vertical displacement are nearly same with the fixed hinged support, while the horizontal displacement of the winding beam is larger than the fixed hinged support; the change of support conditions affect the order of the various modes of the structure but no affect the structural vibration modes.

Ultimate strength of gusset plate connections with fillet welds

Braced frames are commonly used as lateral-load resisting systems in seismic design. The braces are connected to the beams and columns by gusset plate connections. Fillet welds are commonly used to connect the gusset plates to the beams and columns. And the fracture of the interface welds were observed in the past research and earthquakes. This paper focused on the ultimate strength of interface weld connection between gusset plate and frame elements when the brace is in tension. Pilot experimental study was conducted with four specimens and proved that the evaluation recommended by AIJ works well. A verified finite element analysis model was developed to conduct a parametric study. The studied parameters are the brace angle, gusset plate size, and eccentricity of brace. From the parameter study, it is confirmed that the tensile brace axial force is primarily transferred to the interface weld within an extension Whitmore region, which is named as the effective region in the AIJ evaluation. And the extension Whitmore region is affected by the gusset plate geometrical constraint. A revised extension Whitmore region is suggested by considering the aforementioned parameters. The AIJ evaluation using the revised extension Whitmore region is also compared with the UFM, and showed better evaluation for the rectangular shape gusset plate.

Seismic testing and performance of buckling-restrained bracing systems

This paper describes a subassemblage seismic test program performed on six buckling-restrained braces (BRBs). Two different brace core segment lengths and two different buckling-restraining mechanisms were examined. The applied loading histories included a qualifying quasi-static cyclic test with stepwise incremental displacement amplitudes and a dynamically applied seismic loading. A test was also carried out on a conventional bracing member for comparison purposes. The concrete-filled tube specimens exhibited satisfactory performance under the quasi-static loading protocol, regardless of the length of the core segment. Strain hardening and frictional responses resulted in brace axial forces significantly exceeding the core yield capacity. The steel BRB system exhibited good performance under the quasi-static and dynamic loading sequences, provided that the clearance between the brace core and the buckling-restrained mechanism was kept to a minimum. The dynamic loading protocol was less severe for low-cycle fatigue than the quasi-static loading, but higher strain rates resulted in amplified yield resistance. The conventional bracing member withstood the entire quasi-static loading history but exhibited limited energy-dissipation capacity compared with the concrete-filled BRBs.Key words: concentrically braced steel frames, bracing members, buckling, energy dissipation, friction, yielding, fracture, seismic.

埋込みの浅い鋼構造柱脚の力学的特性に関する実験的研究 : その2 軸力と曲げおよびせん断を受ける場合

This paper deals with the strength and ductility of very shallow embedded type steel column-to-footing connection subjected to cyclic reversed bending moments as well as column and vertical brace axial forces. Experimental investigation was focussed to inspect the effect on the reinforcement of the additional concrete cover upon the base plate to improve seismic resistant capability of the connection. The result showed that the connection embedded to about 0. 6 times the steel column depth exhibits the fairly well ductility, and thus the additional concrete cover contributes to stiffen the exposed column-to-footing connection, together with the longitudinal reinforcement of the concrete column stub arranged with proper separations around the base plate. An analytical model has been proposed to estimate the ultimate strength and rigidity of the connection under the complex loading conditions which simulate seismic behavior of such connection in the large scale industrial steel structure.

Fatigue Crack Growth Analyses of Offshore Structural Tubular Joint

Fracture mechanics fatigue life estimation procedures have been developed for offshore structural tubular joints through analyzing a K-joint under the North Sea environment. The objective of this study was to establish reliable procedures for estimating the remaining fatigue life of a tubular joint with cracklike defects. The analysis approach was the utilization of fracture mechanics methods for fatigue crack growth and failure analyses. In this study, the fully mixed mode stress intensity factors of weld toe surface flaws of the K-joint, which were calculated through detailed three-dimensional finite element analyses, were used for fatigue crack growth simulation. For the failure analyses, the failure assessment diagram method was used to predict the conditions for brittle fracture during fatigue crack propagation. The loading conditions considered in the analyses are the brace axial force, in and out-of-plane bending, and torsion.

Stiffness and Yield Strength of Simple V-joint of Offshore Structure

Most of offshore structures for oil exploitation are composed of deck and legs (pipe framed structure). The local failure of the leg may lead to overall collapse of the structure. Accordingly, it is very important to clarify the ultimate strength of the leg.For the analysis of the strength of the leg, an investigation on the strength of a joint has to be performed previously. However, the studies carried out so far are limited to the joints of which chord and braces exist in the same plane, such as Y (T) -joint and K (TY) -joint. While the loading condition of the K (TY) -joint is limited to brace-axial force.In the actual structures, most of joints are constructed three-dimensionally. The loads acting from the brace to the chord are not only brace-axial force but also in-plane and out-of-plane bending moments. The mechanical behavior of such three-dimensional joint may differ from the one of two-dimensional joint.In this study, simple (unstiffened) V-joint is investigated as one of three-dimensional joints, of which two braces exist in the plane perpendicular to the axis of the chord. The mechanical behavior under various loads (normal force and bending moment) are analyzed by PNM (Plastic Node Method) which is one of the very efficient and accurate FEM for elastic-plastic analysis.Based on the results, the characteristics of the stiffness and strength of the V-joint are clarified, comparing with those of the T-joint which has the same dimensions. The mechanisms which vary the stiffness and strength depending upon the loading condition are shown. One of the most important result is that the stiffness and strength of V-joint is reduced to 70 % of those of T-joint in severe loading condition. So the reinforce method by using a stiffener is discussed.

Stability Criteria for X‐Bracing Systems

Using the energy approach, stability criteria for X‐bracing systems are formulated and verified. By employing the Raleigh‐Ritz method of stationary potential energy, simple closed‐form relationships are obtained for calculating the compression brace critical load, directly for any ratio of Q/P, where Q and P represent the tension and compression brace axial force, respectively. Moreover, as a design aid, curves are generated for the effective length factor as a function of Q/P. The criteria are formulated for the general case where the tension and compression braces are different in section properties and lengths. However, the special case of equal lengths and section properties is also addressed. The analytical expressions for the effective length factor are simple and very amenable to design application. Application of the criteria will result in considerable savings in the weight of the primary bracing members and, hence, the overall cost of the structure. This renders the criteria very attractive.