Semi-rigid Joints Research Articles

Structural damage detection for spatial frame structures with semi-rigid joints using multiple set wireless measurements

Damage detection of a complex spatial frame structure with semi-rigid joints is a challenging task. Most existing damage detection methods consider the joint as rigid and the nonuniform cross section of the member is not considered. This assumption results to a large error in the structural damage identification. A novel generic element is proposed for the nonuniform cross-section member with semi-rigid joints at both ends in this study. The finite element model of spatial structures with semi-rigid joints is established using the proposed element. The modal strain energy-based damage index is defined and its sensitivity to the member and joint damage has been investigated using numerical and experimental study. An 8-m long bridge model with the bolted connection at joints is built in the laboratory. Dynamic responses of the bridge under random excitations are monitored using 13 wireless tri-axis accelerometers. The spatial mode shapes of the bridge are extracted using the reference-based stochastic subspace identification from multiple set wireless measurements. The numerical model is validated using experimental results. Dynamic responses of the bridge with different damage scenarios have been simulated using the validated model and the corresponding damage indices are obtained. The results show that the proposed method is reliable and accurate to analyze dynamic behavior of the spatial structure with semi-rigid joints, and structural damage can be identified accurately using the modal strain energy-based damage index.

Wind-resistance and seismic behavior of a steel frame elevator with square hollow section members and semi-rigid joints

Wind-resistance and seismic behavior of a steel frame elevator with square hollow section members and semi-rigid joints

Influence of shear connector type and degree on semi-rigid joints of composite cold-formed steel beam-to-column connections

Influence of shear connector type and degree on semi-rigid joints of composite cold-formed steel beam-to-column connections

Seismic performance and skeleton curve model of prefabricated coral aggregate concrete-filled aluminum tube joint

Corrosion-resistant and high load-carrying capacity coral aggregate concrete-filled aluminum tube (CCFAT) structures show promising applications in island construction. However, research on CCFAT joints related to structural safety remains scarce. To advance the engineering application of this structure, a novel prefabricated CCFAT beam-column semi-rigid joint with bolt connections is designed in this study. The seismic performance of the joint is investigated through a pseudo-static method, analyzing the effects of each parameter on failure mode, hysteresis curve, deformation characteristics, and energy dissipation performance, considering the earthquake-prone nature of islands. The primary objective of this study is to explore the influence of different parameters on the seismic performance of the CCFAT joint and establish the moment-rotation relationship of this joint. It is observed that the ultimate moment relationship between the beam and connector significantly impacts the failure mode of the joint, thus affecting its seismic performance. Hence, prioritizing the ultimate moment relationship between the beam and connector in the design phase is crucial to avoid undesirable joint failures. The skeleton curve of CCFAT joints differs significantly from that of steel and reinforced concrete structures, rendering existing joint theories inapplicable to CCFAT joints. Considering joint material, structure, and failure mode, this paper proposes a theoretical calculation method for the initial stiffness and ultimate moment of the CCFAT joints. This method is based on the component method and mechanical model, establishing an exponential three-parameter skeleton curve model for the joint. This model enables an accurate prediction of the moment-rotation relationship of the CCFAT joint, aiding in its seismic performance evaluation.

Experimental response of semi-rigid reinforced concrete beam-column joints with bolted angle dissipating connections

Accelerated building construction is a challenge and opportunity for modern construction techniques such as prefabricated building. However, insufficient connection detail for precast structures resulted in serious damages (even collapse) in past earthquake, which significantly hit the further development of prefabricated building. With satisfactory seismic performance and minimal residual displacement, self-centering joint is an excellent alternative with respect to traditional prefabricated joint. In self-centering system, bolted connections are sufficiently utilized as energy dissipation system. However, the information about connection details is quite limited. Thus, a comprehensive experimental study was conducted to characterize the seismic behavior of semi-rigid reinforced concrete (RC) beam-column joints with bolted angle dissipating connections, namely, semi-rigid joints. Ten full-scale semi-rigid joints were tested under cyclic loading, taking the connection detail as variable. The main configurations of semi-rigid joints based on Eurocode 3 were angle thickness, angle stiffener, bolt diameter, column bolt gauge, rows of beam bolts, and grouting of beam bolts. The test results showed that, by adopting the ductile connection concept, it was possible to produce high ductility and abundant energy dissipation, control damages within the connection zone, and even achieve equivalent monolithic behavior through mobilizing a sufficient rigidity. Feasibility of replacing the damaged connection with a new one with the identical or higher capacity thus obtaining the equivalent or better performance with respect to the original tested joint is also evaluated. Finally, a theoretical model was proposed to evaluate the initial stiffness and bearing capacity of the joints. A good correlation was achieved as comparing to the test results. This research provides significant insight into the performance of precast semi-rigid joints and offers essential data for further investigation of developing design-oriented procedures.

Study on the Mechanical Properties and Design Method of Frame-Unit Bamboo Culm Members Based on Semi-Rigid Joints

The frame-unit bamboo culm structure system offers a novel approach to bamboo structure, combining advantages like reduced construction times and simplified joint designs. Despite its benefits, there is limited research on its mechanical properties and computational methodologies. This study conducted bending performance tests on simply supported frame-unit bamboo culm structures, revealing that the bending stiffness of the structure increases with the number of bolts in the edge joints, though with diminishing efficiency. Based on the experimental observations, a calculation model for this type of structure was established, proposing formulas to describe the stiffness relationships between the corner joints, edge joint, and the overall structure. Numerical simulations calculated the stiffness of the edge joint as a function of the number and placement of bolts, indicating that positioning bolts closer to the outer side enhances edge joint stiffness. By inputting the various rotational stiffness values of corner joints into the simulations and stiffness formulas, consistent total stiffness values were obtained, validating the proposed stiffness relationship formulas. The average stiffness values of the corner joints were derived from these formulas and experimental data, and the rotational stiffness of other types of corner points can also be obtained using this method. Furthermore, a finite element computational method tailored for this structural system was introduced, converting the actual structure into a beam element model for calculation. The equivalent joint forces can be distributed to various components of the actual structure, resulting in the internal force distribution of bamboo culms and bolts in the actual structure, thus achieving the design of the components. The calculated displacement values obtained from this method are close to the displacement values in the experiment, proving the feasibility of this method.

Experimental investigation of aluminium alloy gusset joints’ dynamic response to lateral impact loads: Evaluating the influence of gusset plate bending stiffness

The traditional aluminium alloy gusset plate (AAG) joint is commonly regarded as a representative semi-rigid joint characterized by limited stiffness. This deficiency in stiffness significantly hampers its capacity for load transmission and resistance against progressive collapse in spatial grid structures. Notably, the dynamic response characteristics of semi-rigid joints, especially when subjected to short-term, highly intense loads such as impacts and explosions, deviate substantially from those of rigid joints. This research examines the dynamic failure behavior of six distinct traditional AAG joints with varying degrees of stiffness when subjected to impact loads. The first group comprises three specimens where the variance in AAG joint stiffness is achieved by altering the gusset plate’s diameter. The second group comprises three specimens aiming to manipulate the AAG joint’s stiffness by modifying the gusset plate’s thickness. The study yielded comprehensive data, including stress profiles, displacement patterns, acceleration time history curves, and failure modes of AAG joints. The experimental findings revealed that both groups of AAG joints under lateral impact loads exhibited brittle failure. The predominant failure modes included the rupture of the H-shaped aluminium alloy beam, distortional buckling of the beam, and warping of the thinner gusset plate. It is evident from the stress, displacement, and acceleration time history curves that the AAG joint adheres to the characteristics of a typical semi-rigid joint, and the diameter and thickness of the gusset plate exert significant influence on the AAG joint’s dynamic response. Subsequently, the six test conditions were simulated using ANSYS/LS-DYNA software. This simulation considered the stress distribution, impact force time history curves, and strain energy time history curves of AAG joints. It facilitated a detailed discussion of the failure mechanism underlying AAG joints when subjected to lateral impact loads.

Analysis and comparison on the mechanical behaviors of original bolt-column (OBC) joint and improved bolt-column (IBC) joint

In this study, OBC joint is improved by incorporating one web, two flanges, and two additional bolts, putting forward a novel semi-rigid joint referred to as IBC joint. Finite element models of both OBC and IBC joints are established and the former is validated based on previous research. Subsequently, a total of 84 numerical models is utilized to investigate and compare the mechanical behaviors of OBC and IBC joints, taking into account different thicknesses of side plate and flange as wll as various loading conditions. The numerical results indicate that: (I) in comparison to OBC joints, the IBC joints exhibit significant enhancements in strong axis bending performance and axial tensile performance, including average enhancement ratios of 48%, 67%, 44%, and 19% in initial strong axis bending stiffness, ultimate strong axis bending moment, initial tensile stiffness and ultimate tension, respectively; (II) compared to OBC joints, the IBC joints demonstrate reduced capacity in axial torsional resistance and axial compressive performance, with mean decline ratios of 54%, 39%, 14%, and 7% in initial torsional stiffness, ultimate torque, initial compressive stiffness and ultimate compression, respectively; (III) OBC joints have better weak axis bending performance compared to IBC joints, but this gap decreases remarkably with increasing thicknesses of side plate and flange; (IV) the initial out-of-plane shear stiffness and ultimate out-of-plane shear of the IBC joint exhibit average enhancement of approximately 20% and 10%, respectively, when compared to those of the OBC joint; (V) regarding in-plane shear performance, the initial stiffness of IBC joints exceeds that of OBC joints by an average ratio of 61%, while IBC joints with flange thickness over 10 mm demonstrate significant improvement in ultimate capacity; (VI) The mechanical performance of OBC and IBC joints shows varying degrees of improvement with an increase in the thicknesses of side plate and flange.

Exact closed-form dynamic stiffness matrix of damaged frames comprising Timoshenko–Ehrenfest beams

The present work proposes the extension of an exact distributional model for cracked beams to include the local influence on axial deformation on shear deformable beams. Axial, shear and flexural concentrated flexibilities are taken into account to model the damaged sections. Shear deformability is accounted for by adopting the Timoshenko–Ehrenfest model and exact closed-form solution of the mode shapes for multiple cracked beams are derived. On this ground, the final achievement of the work consists in the original formulation of the Dynamic Stiffness Matrix (DSM) with multiple cracked sections in exact closed form. The closed-form expression of the DSM allows the assemblage of the global DSM of a structure to conduct the free vibration analysis of damaged framed structures as well as for the study of frames with semi-rigid joints. This approach has the advantage to avoid any numerical procedure for the construction of the DSM as well as the introduction of further degrees of freedom (dofs) in correspondence of the damaged sections, keeping the size of the problem the same as in the intact configuration. Natural frequencies of the frames are determined by means of the Wittrick–Williams algorithm (W–W), then the mode shapes and modal forces are subsequently obtained in closed form. The proposed approach is validated with results available in literature for two portal frames characterized by the presence of cracks and semi-rigid joints, respectively. Finally, the potentiality of the approach, also in view of practical applications, is demonstrated analysing a multi-storey frame with semi-rigid connections.

Simplified analytical model for prediction of collapse resistance of restrained steel beam-column substructure exposed to fire

This paper provides a simplified analytical model for the restrained steel beam-column substructure under a fire-induced progressive collapse scenario, which is applied to predict the collapse resistance of substructures under fire. The simplified model is formulated for axially and rotationally restrained two-span steel beam-column substructures under column-loss scenarios and involves rigid and semi-rigid connections. The response characteristics of restrained substructures exposed to fire under column-loss scenarios in each response stage are elaborately analyzed. A “negative” catenary stage, in consideration of the unique negative axial force effects induced by the temperature thermal expansion, was first introduced in the five-stage simplified model for restrained substructures exposed to fire against progressive collapse. Subsequently, the explicit calculation formulas for determining the vertical loads and deflection of both rigid and semi-rigid joint substructures exposed to fire were derived in a quantified way, based on rigid-plastic mechanisms and restraint coefficient methods. In addition, the corresponding numerical simulation analysis on a restrained two-span steel beam-column substructure with different end constraints and fire conditions was carried out to verify the applicability and reliability of established theoretical formulas. Comparisons of vertical load-deflection relationships between the calculation formulas and corresponding numerical simulation shows good accuracy. For more accurate prediction results, the error analysis was further conducted, and several theoretical formulas were modified, which were verified to be accurate and reliable after correction. With derived resistance functions, the resistance of steel beam-column substructures in fire-induced progressive collapse scenarios can be predicted.

Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis

The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.

Effect of joint stiffness on the load-carrying capacity of single-layer cylindrical reticulated shell with improved bolt-column (IBC) joint

To enlarge the application of single-layer reticulated shells, this study proposes an innovative semi-rigid joint based on the original bolt-column (OBC) joint, referred to as the improved bolt-column (IBC) joint. The mechanical behavior of the IBC joint under the pure load and the coupling effect of bending and axial force is investigated using numerical tests. Then, the practical analytical model of IBC joint is developed based on a three-parameters power model and component method. Subsequently, a mechanical model considering joint stiffness is developed to establish semi-rigidly connected single-layer cylindrical reticulated shell. A total of 456 numerical models of shells are conducted to examine the impact of different kinds of joint stiffness on the load-carrying capacity of shells systematically. The results demonstrate that (i) weak axis bending stiffness and axial stiffness significantly affect the load-carrying capacity of shells by approximately 19 % and 14 % on average respectively; (ii) strong axis bending stiffness and torsional stiffness have relatively minor effects on the critical load of shells, with average decline ratios of only 5 % and 6 % respectively; (iii) out-of-plane shear stiffness and in-plane shear stiffness exhibit negligible impacts on the load-carrying capacity of shells, with an average effect not exceeding 1 %. Finally, the findings of numerical simulation considering all stiffness of IBC joint reveal insights into both varying laws of load-carrying capacity and failure modes for shells. It is observed that the mean critical load can reach up to 59 % of the one of rigidly-connected shells, which is significantly higher than those observed in shells with pinned joints.

Rotational Stiffness Investigation and Parametric Analysis of a Novel Assembled Joint in Lattice Shells

Although there are currently many types of lattice shell joints with different characteristics, assessing the flexural capacity of lattice shell joints is always a great challenge. In this paper, a fan-shaped assembled joint and a welded joint for comparison were subjected to bending tests to investigate the flexural behavior and rotational stiffness of the assembled joint. The strain distribution, load–displacement curve, moment–rotation curve, and damage modes of key parts were analyzed to determine the vulnerable parts of the joints. Our test results show that, with an initial rotational stiffness of about one third of that of the welded joint, the assembled joint specimen exhibits the obvious characteristics of a semi-rigid joint. The finite element analysis results were in good agreement with the experimental results. The results of our parametric analysis show that the rotational stiffness and ultimate moment of the assembled joint increase with increases in the spacing of the bolts and the number of bolts. The performance of the high-strength bolts had a significant influence on the flexural stiffness of the assembled joints. The spacing of the bolts and the number of bolts for the assembled joint are suggested to be greater than the height of the member section and more than three, respectively. The proposed theoretical formula can approximately simulate the initial rotational stiffness of the joint. More in-depth investigations are required in the future for assessing the mechanical behavior of FSA joints subjected to combined bending–compression loads.

Design and numerical analysis of new earthquake-resilient semi-rigid joints

A calculation method for the design of a new earthquake-resilient semi-rigid joint was proposed, and its accuracy was verified through cyclic loading tests. Finite element model analysis was performed to investigate the energy dissipation capacity of the new joint. The deformation characteristics, energy dissipation capacity, and stiffness of energy dissipators with different shapes and lengths were compared. Subsequently, the computational method was improved. The parametric analysis results revealed the excellent seismic performance of the joint; the energy dissipator dissipated more than 75% of the energy. Furthermore, we assessed the influence of the area, shape, and length of the energy dissipators on their energy dissipation capacity. Increasing β (the ratio of the flange to web area in the energy-dissipating core area) and γ (the slenderness ratio of the energy-dissipating core area) resulted in an initial rise in the energy dissipation capacity followed by a decrease. The recommended values for β and γ are 0.67 and 7.71–9.21, respectively.

Experimental and numerical study on seismic performance of steel semi-rigid joints equipped with SMA bars and friction dampers

To reflect and inherit the characteristics of ancient Chinese architecture and regional culture, the Chinese antique building (CAB) imitating ancient Chinese timber building has been constructed using contemporary steel materials. These buildings mostly deploy steel rectangular-shaped beams and circular cross-sectional columns, which normally exhibit typical premature yielding fractures at the beam ends under seismic actions, as well as weak energy dissipation capacity and significant residual deformation. A steel semi-rigid joint equipped with SMA bars and friction dampers was proposed to improve the seismic performance and recoverability of CABs. The proposed joint aims to achieve the purpose of "self-centering during minor to moderate earthquakes" and "high energy-dissipating capacity under severe earthquakes" for CABs. Compared to simple semi-rigid joints, the energy dissipation of joints with friction dampers improved, while the joints equipped with the shape memory alloy (SMA) bar-friction damper coupling devices exhibited significant increases in yield displacement, strength, and overall stiffness, along with remarkable reduction in residual deformation. Based on the test observations, a numerical model was constructed to parametrically optimize the structural design of the damage-controllable steel semi-rigid joints equipped with SMA bars and friction dampers. The research results shall provide a theoretical basis for the proposed joint in engineering applications of steel antique buildings.

Resilient joints with SMA bar-shear friction damper (SSFD) device in steel modern Chinese traditional-style buildings: Seismic performance evaluation and optimized design

To inherit and protect ancient Chinese architectural culture, modern building materials and techniques have been combined in the modern Chinese traditional-style building (MCTB) with similar exterior forms to ancient Chinese timber architecture. However, the typical joint in MCTB exhibits weak energy dissipation capacity and significant residual deformation under seismic actions, resulting in a problematic post-earthquake repair behavior. A semi-rigid friction-damped joint with resilient function has been proposed to improve the seismic performance and recoverability of MCTBs. Low-cyclic loading was conducted on four specimens of full scale. The results indicated that the yielding failure of four specimens primarily occurred in the vulnerable regions designed with replaceable angles. Compared with semi-rigid joints, the yield displacement, overall strength, initial stiffness, and cumulative energy dissipation of the specimen with the shape memory alloy (SMA) bar-shear friction damper device was significantly increased, and the residual deformation was significantly reduced, indicating that the device has a significant enhancement effect on the seismic and repairable performance of the structure. Based on the experimental results, a three-dimensional model was established using ABAQUS finite element software to optimize the design of joints and determine the optimal structural system that meets the requirements of MCTB.

Damage and failure of semi-rigid steel joints during progressive collapse

Ductile metal materials during a ductile failure will suffer from micro-void damage, simulation of which can contribute to the prediction of the macro fracture of steel structure. In this paper, the Gurson-Tvergaard-Needleman (GTN) constitutive model which describes the aggregate failure of metal voids is selected as the constitutive relation to investigating the damage evolution and fracture of semi-rigid joints in steel structures during a progressive collapse. During the process, specific parameters of the GTN model of steel are confirmed based on the combined results of the test and numerical simulation. The progressive collapse of two kinds of semi-rigid joints of steel pipe-to-H shaped steel were simulated by a nonlinear finite element method. A comparison between the simulation and test results verified that the GTN constitutive model can accurately simulate the fracture failure of the steel semi-rigid joints. Besides, a simplified joint failure model based on concentrated plastic hinge theory is proposed. Considering the damage and fracture of semi-rigid joints and the collision contact among different components, the progressive collapse of the semi-rigid steel frame structure is simulated by explicit dynamic analysis based on a finite particle method. Afterwards, the dynamic response of the structural progressive collapse can be predicted more accurately.

Simplified methods to predict the robustness of steel parking-structure joints

An innovative simplified method for incorporating the behaviour of structural joints in structural analyses of steel parking-structure is proposed in this study. The method is based on the conventional mechanical modelling of joints through special springs that accommodate the arching effect and moment-axial force (M-N) interaction. The characterization of these springs in terms of stiffness and resistance is performed using analytical formulae. The accuracy of the proposed method is validated through comparisons to results from advanced numerical methods conducted on a multi-scale approach. Its implementation in sub-structure models is then demonstrated, with the main advantage of extremely reducing the modelling and computational time. Validated sub-structure models are finally employed to investigate the influence of the joint properties on the response of parking structures under vehicle collision scenarios. The results show that considering the rigid and semi-rigid joints in the research are characterised by the welded and bolted connections in the research, for a structure built in a courtyard, bolted connections (semi-rigid joints) are recommended, while for the same structure built near an urban road, welded connections (rigid joints) should be considered to enhance the overall robustness.

Seismic behavior of partially encased composite columns-steel plate shear wall structure with different semi-rigid joints

Seismic performance of partially encased concrete (PEC) column-steel plate shear wall (SPSW) structure is significantly affected by the characteristics of beam-column connections. Three component models of semi-rigid beam-column connections, including the bidirectional bolt extended end-plate connection, the flush end-plate connection, and the web double-angle steel connection, are designed according to Eurocode 3. Afterward, three 1/3-scale two-story single-span PEC column-SPSW structures with the three types of semi-rigid connections are tested under quasi-static cyclic loading. The test results indicate that all three structures satisfy the design requirement of “strong frame-weak wall plate”. The PEC-SPSW structure with the bidirectional bolt extended end-plate connections exhibits a higher bearing capacity and stiffness than the other two structures. Compared with the web double-angle connection, the adoption of bidirectional bolt extended end-plate connection increases the yield bearing capacity by 14.32% and the initial stiffness by 16.16%, but ductility decreases by 17.65%. The energy dissipation of each story of the structure with flush end-plate connections is relatively balanced. The energy dissipated by the second-story of SPSW is less than that of its first-story due to the higher rotational stiffness of the bidirectional bolt extended end-plate connections. The PEC-SPSW structures fracture at the column foot. The reliability of the initial rotational stiffness component models is verified by comparing the finite element (FE) and test results.

Structural performance of a novel combined nested bolted joint for aluminum alloy mega-latticed structures

A novel steel-aluminum joint system is first presented for aluminum alloy mega-latticed structures. This joint can be effectively applied to the connection of large-diameter tube members with complex spatial locations in space structures. The joint's finite element model is examined and validated, followed by a case study of one joint, including static analysis and an analysis of the bending moment-rotation curve. According to the moment-rotation curve, the joint is classified as a type of semi-rigid joint. Furthermore, the analysis considers key parameters that impact the joint's bending, axial, and torsional performance, such as the number of bolts per ring, the rings of bolts, and the thickness of the joint zone. Two simplified formulas for joint stiffness are proposed to evaluate the overall structural stability. Finally, a stability analysis of an aluminum alloy mega-latticed structure is conducted, incorporating this joint and the proposed simplified formulas. The ultimate load of the mega-latticed structure with the joints is found to be about 0.7 of that with ideal rigid joints with the same parameters. This paper presents a potential solution for appropriate connections in large-span aluminum alloy mega-lattice structures, thereby serving as a reference for the design of the joints in related space structures.