Initial Rotational Stiffness Research Articles

Seismic performance of light steel-natural timber composite beam-column joint in low-rise buildings

Current timber structures or steel-timber composite structures are made of thick steel and glued laminated timber (glulam) with beams and columns connected by high-strength bolts used in high-rise and large-span structures. However, there is no high strength requirement for low-rise buildings in villages and towns. The composite action of thin-walled steel and fast-growing timber is selected to constitute the structural members together, which are connected using plain bolts for a structural system suitable for residential houses in villages and towns. Thin-walled steel can be used to minimize the initial defects and material variability of fast-growing timber. To meet the requirements of the light steel-fast-growing timber composite structural system, a fully bolted joint is designed in this paper. The quasi-static tests of seven joints are carried out to analyze their seismic performance. The results show that the seismic performance of joints can meet the requirements of low-rise residential buildings in villages and towns. The finite element simulation of the test specimens is also carried out, and the modeling approach is described in detail to analyze similar structures further. Finally, the component-based expression was used to propose a simplified spring model to calculate the joints' initial rotational stiffness and ultimate capacity and compared with the experimental results for practical applications.

Experimental investigation and analytical modeling of steel beam-to-CFDST column connection

In this paper, a prefabricated connection between concrete-filled double-skin steel tubular (CFDST) column and steel beam with flush endplates and bidirectional bolts was developed. To investigate the effects of the endplate thickness, axial compression ratio, bolt diameter, concrete fill degree, and shape of the inner tube on the seismic performance of the connection, a series of pseudo-static tests were performed on six specimens. It was observed that the bending deformation of endplates, warpage of bolts, local buckling of beam flanges, and cracking of weld seams were typical failure modes. An increase in the endplate thickness and the replacement of the circular inner tube by the square inner tube significantly improved the ultimate strength of the connection. The ultimate strength of the connection was not sensitive to the axial compression ratio and bolt diameter, and it decreased as the concrete fill degree increased. The displacement ductility coefficients of the specimens were greater than 6.21. Higher ductility and accumulated energy dissipation were obtained by increasing the endplate thickness, axial compression ratio, bolt diameter, and replacing the circular inner tube with the square inner tube. The ductility and accumulated energy dissipation decreased as the concrete fill degree increased. Based on the component method, an analytical model of the initial rotational stiffness of the connection was developed. The mean and standard deviation of the ratios of predicted values to test values were 0.95 and 0.06, respectively.

Moment–rotation curve characteristics and initial rotational stiffness calculation method of angle connections

SummaryDue to recent advances in computational power, high efficiency and high precision semi‐rigid calculation methods of steel connections are necessary. In this paper, four connection experiments were designed to study the mechanical behavior of the top and seat angle connections. In the experiment, a monotonic load was applied at the end of the beam to study its moment–rotation characteristics. In addition, this paper proposed a second derivative method to determine the yield point, the starting point of the plastic strengthening stage, and the initial rotational stiffness of the connections according to the moment–rotation curve. Loading test experiments (EX) results and finite element analysis (FEA) results showed that the compression side angle stiffener has little effect on the initial rotational stiffness. Nevertheless, it can delay the top and seat angle connection in entering the elastoplastic stage and the starting point of the plastic strengthening stage. The results also showed that the tension side angle stiffener could significantly increase the initial rotational stiffness, but makes the angle connection enter the yield stage earlier. When the connection's top and seat angles have no stiffener, the elastoplastic deformation range on the curve is smaller. Finally, based on the theory of Plates and Shells, this paper proposed the calculation method for the deformation stiffness of the key components and the initial rotational stiffness of the connection. Results from the theoretical calculation method showed high calculation accuracy and high calculation efficiency, as compared with the EX and the FEA results.

Theoretical study on the rotation angle and bearing capacity of beam-to-column composite connections in prefabricated steel frames

To study the rotation mechanisms of the steel column, end-plate, and end-plate stiffener of extended end-plate joints, cyclic loading tests were carried out on two extended end-plate joints, one of which contained a composite slab. The deformations of these three components during test loading were described using digital images, and their bearing capacities and rotation angles in the elastic stage, yield stage, and strengthening stage were deduced by the component method. The results showed that the failure modes of the extended end-plate joints were yielding of the end-plate, bolt fracture, and end-plate stiffener buckling, and the composite joint experienced local crushing of the composite slab. The composite slab improved the initial rotational stiffness and bearing capacity of the composite joint. The joint rotation angle of the extended end-plate connection was mainly composed of three parts: shear deformation of the panel zone, relative deformation between the end-plate and the column flange, and yield deformation of the end-plate stiffener. The composite slab had a constraining effect on the deformation of these three parts. In addition, by defining the moment–rotation curves of three components, a simplified three-rotation spring model was established to simulate the joint-loading process. The results showed that the model could simulate the test joint-loading process accurately, and is conducive to promoting seismic performance analyses of prefabricated steel frames.

Artificial neural network and regressed beam-column connection explicit mathematical moment-rotation expressions

Steel flush endplate beam-column connections behavior is commonly described by the moment-rotation, M -φ, relationship, which is characterized by two essential terms; resistant moment, M j, Rd , and initial rotational stiffness , S j, init . A great amount of concerted effort has been invested worldwide to either experimentally or analytically describe these properties due to geometrical and material variations. However, these methods are either costly, laborious, or time-consuming. Therefore, acknowledging the wealth of literature information, this paper formulates a set of practically convenient mathematical M -φ expressions by means of artificial neural network (ANN) and multi-linear regression (MLR) approaches utilizing the MATLAB software. Differing from most existing machine learning variants, the paper offers explicit expressions for maximum moment, M max , and S j, init , which can be characterized through a simplistic insertion of input parameters in terms of beam depth, beam width, thickness of beam flange , thickness of beam web, column depth, column width, endplate depth, endplate thickness, and bolt capacity. The computed M max and S j, init can then be adopted to express the currently defined continuous M -φ relationship. By statistical evaluation, it is witnessed that the mean-absolute-percentage error (MAPE) and correlation coefficient ( R 2 ) of both ANN and MLR methods are of remarkable prediction vitality. Also, ANN outperforms slightly MLR model in the prediction of both M max and S j, init although both approaches agree closely with the source data. Therefore, both approaches are of high reliability in predicting M max and S j, init as well as in characterizing the M -φ relationship of the flush endplate beam-column connections for further engineering analysis and design purposes. • Equation for continual M-φ relation for flush endplate beam-column behavior. • Continuous M-φ relation is produced simply by plugging in connection properties. • M-φ relation is defined only by maximum moment M max & stiffness S j,init . • M max & S j,init are defined by connection geometrical & material expressions. • Proposed ANN & regression models predict statistically well the observed M-φ curve.

Behaviour of castellated beam-to-column end-plate connection under monotonic load

The development of plastic hinges in a steel frame structure with steel beam-to-column end-plate connection joints by strengthening the end-plate area is a widely used design concept. This study explores the realization of this design concept with a beam web opening and without end-plate stiffening. The factors that impact the mechanical properties and failure modes of these joints are the end-plate thickness, opening diameter, opening position, and opening type. These parameters are tested for monotonic loading of six beam-column joints, and 220 finite element models are parametrically analysed. Additionally, the development of plastic hinge of the beam based on the development trend of maximum strain of each component section is studied. The initial rotational stiffness, ductility, bearing capacity, deformation capacity, and failure mode are used as the evaluation criteria to assess the behaviour of this joint. The research indicates that a castellated steel beam-to-column end-plate connection can realize the occurrence of plastic hinge and exhibit good ductility and load-bearing performance. This study highlights the premise that the beam web opening and end-plate thickness parameters must be within a specific range to achieve accurate results; additionally, the division method of the interval of parameters is described. The influence of end-plate thickness on the working mechanism of the connection is clarified, and the mechanical properties and failure modes of connections under different parameter intervals are studied. This study proposes a method for calculating the initial rotational stiffness of the connection to achieve good accuracy by considering the participation of the components on the beam in the rotation of the connection.

Performance of rocking foundations on unsaturated soil layers with variable groundwater levels

An emerging foundation design scheme, termed a rocking foundation, has the potential to limit loads transmitted to the superstructure, with the potential trade-off of increased settlements and rotations at the foundation level. These soil deformations can be significant for foundations with low vertical bearing capacity factors of safety. In this study, a set of dynamic centrifuge tests was performed to assess the response and to develop design considerations for a rocking foundation embedded in soil with varying degrees of saturation. Foundation design procedures dependent on degree of saturation are developed to predict moment capacities and initial rotational stiffness. Experimental data were used to validate the reliability of these procedures, regardless of the degree of saturation in the underlying soil. As the degree of saturation reduced, the moment capacity of the foundation increased, potentially increasing the load transmitted to the superstructure. Further, foundation settlements and rotations in the saturated soils can be reduced by lowering the water table depth in the underlying soil layer, which is beneficial to the performance of rocking foundations. Consequently, the degree of saturation of the supporting soil should be considered in the foundation design to predict the foundation settlement–rotation response and to assess properly the superstructure ductility demands.

Rotating performance of Temcor joints for aluminum single-layer reticulated shells

The Temcor joints for the aluminum alloy single-layer reticulated shell has been widely used in the spatial structures due to simplefabricationmethod and construction convenience. The rotational performance of Temcor joints for the aluminum alloy single-layer reticulated shell has been experimentally investigated in this research. Four types of Temcor joints with various section heights were examined in this study. The failure mode, the moment-rotation curves and the stress distribution of the components and Gusset plates of Temcor joint were discussed. The results show that the failure was the section fracture caused by the weakened section of bolt holes in the lower flange of component end within the joint. The initial rotational stiffness of the joints was effectively improved by increasing their section heights. The maximum stress was observed at the outermost bolt, while the stress decreased with the distance from the center of gusset plate. This has thereby explained the failure of the joint region.

Behavior of exposed column-base connections with four internal anchor bolts under seismic loading

Laboratory experiments were conducted to define the response to earthquake loading of the exposed column-base connections common in low-rise steel frame structures. Six full-scale column-base connections with four internal anchor bolts were prepared and tested to failure under major- and minor-axis cyclic loading. The parameters varied were the size and thickness of the base plate and the diameter of the anchor bolts. The data were used to calibrate a finite element simulation, and that was used to predict the influence of other design parameters on the initial rotational stiffness of a connection. Linear regression was used to model the response surface of the initial rotational stiffness and the bending capacity of the connections under minor-axis loading. A three-parameter power function model was derived which acceptably predicted the experimental results.

Numerical simulation and mechanical model of steel beam-to-column joints retrofitted by haunches

Within the retrofitting of steel structures, welding haunches to retrofit weak panel zones in beam-to-column joints are deemed to provide reliable cyclic behavior based on previous tests. Also, the force transferring mechanism in haunched beam sections is substantially changed under the influences of the haunch and panel zone. For the investigation of the behavior of the haunched beam section and the haunch, finite element models (FEMs) were established with considerations of material and geometry nonlinearities and then verified against previous tests. The force distributions were obtained and also predicted by mechanical models. Results showed that the moment resistance and initial rotational stiffness increased by 34.3%–76.9% and 51.6%–83.3% through retrofitting. Moreover, a noticeable difference in force distributions was observed in the haunched beam section. The direction of the shear force within the shear plate was reversed and its value could be even greater than the beam load. After the yielding of panel zones, the force redistribution appeared and subsequently led to increased forces in the shear plate and haunch flange. Furthermore, the comparisons among mechanical models indicated that the AISC model might underestimate the contributions of both the haunch flange and the shear plate in the elastic stage, and the plane-section-assumption model showed better agreements. However, without considering the force redistribution in the post-yielding stage, the above two models underestimated forces by 8.8%–32.0% and 9.7%–64.2%, respectively, and the simplified model was proposed with better predictions concerning the impact of the force redistribution to provide a greater safety margin in design.

Numerical Study on Performance of Prefabricated RCS Joint under Normal Temperature and Fire

To study the mechanical behavior and fire resistance of the prefabricated reinforced concrete column and steel beam (RCS) joints with endplate, this paper presented a numerical investigation on the joints under normal temperature and fire. The full 3D solid finite element models were implemented in ABAQUS. The simulated results show that under normal temperature, the yield moment and initial rotation stiffness increase with the increase of the endplate thickness, the failure mode changes from deformation of the endplate to yield of the extensional part. Increasing the thickness of stiffeners and changing the form of stiffeners can effectively improve the yield moment of the joint, but the initial rotational stiffness keeps invariant basically. Under fire condition, the load ratio has a significant effect on the fire resistance of the prefabricated RCS joint; the thickness of the endplate and stiffener, the stiffener form have less influence on the fire resistance of the joint.

Experimental static and seismic behaviour of glulam beam-to-column connection with screwed-in threaded rod joints

To evaluate the static and seismic behaviour of glulam beam-to-column connections with screwed-in threaded rods, nine specimens grouped in three were tested under both monotonic and reversed cyclic loads. The failure modes, moment resistance, initial rotation stiffness, ductility, and energy dissipation capacity of the developed connections were investigated. The results indicated that the developed beam-to-column connections showed superior structural performance. Furthermore, with the introduction of a steel bracket, the hybrid screwed-in threaded rod connection features larger stiffness, higher load-carrying capacity, remarkable ductility, and better energy dissipation capacity. The main failure modes included the yielding of steel brackets, as well as the yielding or rupture of the threaded rods, which indicated a ductile behaviour. The connection specimens with steel columns showed larger stiffness than those with glulam columns, which is reasonable for the bigger compressive deformation of glulam columns.

I-beam-to-CHS-column moment resisting joints using passing-through plates

Conventional connections of I-beam-to-CHS-column are prone to local distortion of the tube-wall in presence of bending moment that reduce its resistance and rigidity, and limit the use of these connections in multi-storey portal frames. Elements passing-through the CHS column may be a good solution to increase the resistance and stiffness of connections between I-beams and tubular members. Passing-through I-beam-to-CHS-column joints develop important stiffness and resistance, although the profile cross-section dimensions variability raises the problem of slot clearance. An alternative consists in using passing-through plates and connect the flanges and the web of the I-beam outside the CHS-column. The plates dimensions are known with a good accuracy and the slot clearance can thus be reduced.This paper presents an experimental campaign performed on 14 passing-through plates-to-CHS-column joints tested under two loading configurations: equal hogging bending moments and opposite hogging/sagging bending moments. The first loading case is representative of gravity loads whereas the second loading case occurs under seismic actions, for instance. The main parameters investigated are the tube-wall thickness, the welding type, full and partial penetration butt welds or fillet welds, and the dimensions of the web/flange plates. The behaviour of these connections is compared to that of conventional directly welded I-beam-to-CHS-column joints. Cyclic tests have been performed for the second loading configuration (opposite bending moments). To reproduce the effect of upper storeys, one cyclic test has been performed with an additional constant compressive force acting on the column. Based on the test results, an analytical model is suggested for the evaluation of the bending resistance for both loading cases and the initial rotational stiffness for the symmetric loading case only. The load transfer mechanism between the different components of the joint, tube-wall, flange and web plates, is addressed.

Initial rotational stiffness of end-plate connections based on the theory of plates and shells

With current developments in the optimization design of the building structure, and due to the need for the optimization design to carry out multiple iterative calculations, the accuracy and efficiency of these structural calculations are increasingly required. However, the traditional calculation method of the initial rotational stiffness (Rini) of the beam-to-column connection has certain limitations, and the efficiency of the finite element calculation method is poor. To establish an accurate method for predicting the initial rotational stiffness of major- and minor-axis end-plate connections, the theory of plates and shells and the finite difference method (FDM) are used to analyze the connection following the base on component method. In this study, boundary condition equations were established first based on the theory of plates and shells, for components that undergo significant lateral deformation, namely, the end-plate, column flanges, and column web. Then, the FDM was employed to solve these equations to determine the deformation of these components. Considering the deformation compatibility conditions as well as the force equilibrium conditions, the bolt load at the unit moment was calculated. Finally, based on the stiffness of each of connection components and the bolt load, the Rini of an end-plate connection was calculated. A comparison of the Rini values calculated by the proposed method and those obtained from the experiment (EX), finite element analysis (FEA), and Eurocode 3 (EC3) indicated that the proposed method is more accurate.

Experimental study of mechanical properties of beam-column joint of a replaceable energy-dissipation connector-precast concrete frame

A type of replaceable energy-dissipation connector - precast concrete frame is proposed, in which the replaceable energy dissipation connectors are assembled on the upper and lower sides of the beam end with a direct load-transfer path. The connectors can induce plastic deformation of the frame concentrated in the connectors themselves, while the main structural members, such as beams and columns, can remain elastic under strong earthquakes. Additionally, the seismic rehabilitation of the frame could be easily achieved by replacing the damaged connectors. Pseudo-static tests on an exterior beam-column joint of the frame were conducted, including the initial working condition and the seismic rehabilitation working condition. The test results revealed that a stable hysteretic property could be obtained in the joint, while a high energy-dissipation capacity was also confirmed. Plastic deformation was concentrated in the connectors, while a few cracks could be seen in the concrete components. The seismic rehabilitation working condition revealed that the initial stiffness and the hysteretic property could remain the same as those of the initial working condition. The formula for the initial rotational stiffness of the joints is derived at the end of the paper, indicating that the calculated results of the test specimens are consistent with the test results. • A new type of beam-column joint named replaceable energy dissipation connectors-fabricated concrete frame (REDC-PCF). • Construction and rehabilitation method of the REDC-PCF. • Construction of the REDC with buckling-restrained devices. • Stable hysteretic property and high low-cycle fatigue performance on the REDC-PCF.

Component method based rotation performance and design method for the connection in ATLS modular house

The assembled-type light-steel (ATLS) modular house is an off-site prefabricated construction technique, which has been widely adopted for hotels, dormitories, schools and hospitals where repetitive units are preferred. This paper mainly presents the numerical and theoretical studies on the bending behavior and design method of the semi-rigid connection in ATLS modular house. Elaborated finite element model (FEM) was developed and its accuracy was validated by the good consistency between the experimental results and the FEM in terms of failure modes and load–displacement curves. Parameters including vertical load on the column, column thickness, bolt diameter, bolt length have been considered to conduct the parametric analysis to reveal their influence on the initial rotational stiffness, ultimate flexural capacity and M-θ model of the connection in ATLS modular house. The parametric analysis quantified the influence of each parameter on the initial rotational stiffness and the ultimate flexural capacity in different loading direction. Furthermore, theoretical analysis on the initial rotational stiffness and ultimate flexural capacity as well as the moment–rotation design model were performed based on the component method and the comparison between the theoretical value and finite element analysis demonstrates the reasonability of the theoretical analysis. Finally, the M-θ design model is proposed and validated to describe the semi-rigid characteristic of the connection in ATLS modular house, which will provide useful guidelines for the design of ATLS modular house.

Hysteretic performance of stainless steel double extended end-plate beam-to-column joints subject to cyclic loading

This paper focuses on the hysteretic performance of stainless steel beam-to-column joints with double extended end-plate connections under cyclic loading. Six full-scale joint specimens were fabricated, including three interior column joints and three exterior column joints. Two stainless steel grades — austenitic grade EN 1.4301 and duplex grade EN 1.4462, and one carbon steel grade Q345B were considered. A4-80 stainless steel bolts and grade 10.9 high strength steel bolts were employed to assemble the joint specimens. The cyclic loading tests were conducted using the loading protocol set in Chinese standard JGJ/T 101. The force versus displacement (F-Δ) hysteresis curves were recorded, and the failure modes, the ductility, the strength and stiffness degradation, and the energy dissipation capacity of the tested joints were analysed and discussed in detail. Empirical hysteresis models were developed and calibrated against the recorded hysteretic curves and energy dissipation capacities of the tested joints. The experimental results involving the initial rotational stiffness values and the moment resistances were further utilised to evaluate the accuracy of current design provisions codified in EN 1993-1-8, ANSI/AISC 358 and GB 51022. The comparison shows that the development of accurate design guidance accounting for the pronounced strain hardening of stainless steels is warranted.

Multibody Modeling Method for UHV Porcelain Arresters Equipped with Lead Alloy Isolation Device

This paper presents a multibody modeling method for seismic analysis of UHV porcelain surge arresters equipped with a kind of seismic isolation device. An UHV arrester is modeled as a planar multibody system whose number of DOF is equal to the number of the arrester units. Joint coordinate method is adopted to construct the governing equations of motion. The seismic isolation device utilizing a number of lead alloy dampers as its core energy dissipation components is also investigated. An analytical model of this device is given by modeling each lead alloy damper as a hysteretic spring and reducing the entire device to a planar system consisting of a range of hysteretic springs. Its mechanical characteristic is derived theoretically, and the obtained moment-angle relationship is expressed as a system of differential algebraic equations. The initial rotational stiffness of the device is formulated in terms of the structural and mechanical parameters of the device. This analytic expression is used in estimating the fundamental frequency of the isolated equipment. By this modeling method, it is easy to construct the governing equations of motion for the isolated system. An UHV arrester specimen is analyzed by this proposed method. The effectiveness of the isolation device in terms of reducing the internal base moment is significant and the influence of system parameters on the effectiveness is also discussed. The proposed method shows its potential usefulness in optimal design of the isolation device.

Experimental study of moment carrying behavior of typical Tibetan timber beam-column joints

This study aimed to investigate the moment carrying behavior of typical Tibetan timber beam-column joints under monotonic vertical static load and also evaluate the influence of length ratio of Gongmu to beam (LRGB) and dowels layout on the structural performance of the joint. Six full-scale specimens were fabricated with same construction but different Gongmu length and dowels position. The moment carrying performance of beam-column joints in terms of failure mode, moment resistance, and rotational stiffness of joints were obtained via monotonic loading tests. Test results indicated that all joints are characterized by compressive failure perpendicular to grain of Ludou. Additionally, it was found that greater LRGB leads to greater initial rotational stiffness and maximum moment of the joint by an increase of restraint length for beam end; however, offsetting dowels toward column resulted smaller stiffness and ultimate bending moment of joints, particularly, offsetting Beam-Gongmu dowels toward column changed the moment-rotation curve pattern of the beam-column joint, accompanied by a hardening stiffness at last phase. Furthermore, a simplified trilinear model was proposed to represent the moment-rotation relationship of the typical Tibetan timber beam-column joint.

Moment Resisting Connection with Curved Endplates: Behaviour Study

This article provides a behaviour analysis of moment resisting joints with curved endplates. This is a new type of connection that can be used for joining steel beams to the circular hollow section (CHS) columns by means of bolts. Some researchers apply the Eurocode model without considering the differences in calculation schemes and assumptions, such as by using the general model of an equivalent T-stub in tension. Consequently, many of the existing behaviour studies are somewhat misleading, thus there is a need for further research. Apart from the absence of analytical methods that are devoted to predicting the initial stiffness and strength of the curved T-stub, other technical difficulties were encountered, such as gaps between the endplate and the column, as well as the initial pre-loading force of the bolts. In the previous studies, endplates were manufactured by rolling flat plates to the precise curvature which resulted in firm contact. In contrast, in this study, endplates were manufactured from a standard CHS tube, which led to significant initial gaps. Meanwhile, in terms of preloading force, it was found that it affected the moment resistance of the joint. This paper discusses problems associated with ongoing researches and presents experimental tests of the two connections. The obtained results were further used in the parametric finite element analysis (FEA) to determine the effect of the gaps and preloading force of the bolts on the moment resistance and initial rotational stiffness of the joint. The results indicate that the behaviour of curved plated connections is exceedingly complex and that the preloading force is the key factor, therefore, it should be controlled.