Moment-rotation Curves Research Articles

A Macro-model for Nonlinear Analysis of 3D Reinforced Concrete Shear Walls

Architectural limitations in many situations make it necessary for the RC shear walls to be extended in plan in different directions at a single location that makes them a 3D configuration. Analysis of such walls is very challenging. In this research about 450 cases of 3D shear walls are considered with different shapes and heights. L, T and H-shape walls are studied. They are nonlinearly analyzed in Abaqus using a micro-model, i.e. the finite element modeling and analysis. A meso-modeling approach using fiber elements is also examined in Opensees. It is shown that the meso-model is both accurate enough and much faster than the micro modeling approach. To go further, a macro-model is developed in bending in which the nonlinear behavior is assumed to be concentrated at the base of the wall using a rotational spring. The axial force, shape of the cross section, percentage of the longitudinal reinforcement and the aspect ratio of the wall are recognized to be the main parameters defining characteristics of the rotational spring. Using regression, semi-analytical formulas are suggested for rapid determination of the moment-rotation curve of the rotational spring. Comparison with micro-model and experimental results confirm the good accuracy of the developed macro-model.

Experimental and numerical assessment of beam-column connection in steel moment-resisting frames with built-up double-I column

Built-up Double-I (BD-I) columns consist of two hot rolled IPE sections and two cover plates which are welded by fillet welds. In Iran, this type of column is commonly used in braced frames with simple connections and sometimes in low-rise Moment Resisting Frames (MRF) with Welded Flange Plate (WFP) beam-column detailing. To evaluate the seismic performance of WFP connection of I-beam to BD-I column, traditional and modified exterior MRF connections were tested subjected to cyclic prescribed loading of AISC. Test results indicate that the traditional connection does not achieve the intended behavior while the modified connection can moderately meet the requirements of MRF connection. The numerical models of the connections were developed in ABAQUS finite element software and validated with the test results. For this purpose, moment-rotation curves and failure modes of the tested connections were compared with the simulation results. Moreover to avoid improper failure modes, some improvements of the connections were evaluated through a numerical study.

Experimental and analytical behavior of stiffened angle joints

The application of rib stiffeners is common on steel connections, with regard to the stiffened angle connection, experimental results about the influence of stiffeners under monotonic and cyclic loading are very limited. Consequently, this paper presents the experimental investigation on four types angle connections with or without stiffener under static loading and another four type stiffened angle connections subjected to cyclic loading. The static experimental result showed that the rib stiffener weld in tension zone of the connection greatly enhanced its initial rotational stiffness and flexural strength. While a stiffener was applied to the compression zone of the connection, it had not obvious influences on the initial rotational stiffness, but increased its flexural strength. The moment-rotation curves, skeleton curves, ductility, energy dissipation and rigidity were evaluated under cyclic loading. Stiffened top-and-seat angle connections behaved as semi-rigid and partial strength, and rotation of all stiffened angle connections exceeded 0.04rad. The failure modes between monotonic and cyclic loading test were completely different and indicated certain robustness.

Analysis of the Behaviour of Semi Rigid Steel End Plate Connections

The analysis of steel-framed building structures with full strength beam to column joints is quite standard nowadays. Buildings utilizing such framing systems are widely used in design practice. However, there is a growing recognition of significant benefits in designing joints as partial strength/semi-rigid. The design of joints within this partial strength/semi-rigid approach is becoming more and more popular. This requires the knowledge of the full nonlinear moment-rotation behaviour of the joint, which is also a design parameter. The rotational behaviour of steel semi rigid connections can be studied using the finite element method for the following three reasons: i) such models are inexpensive; ii) they allow the understanding of local effects, which are difficult to measure accurately physically, and iii) they can be used to generate extensive parametric studies. This paper presents a three-dimensional finite element model using ABAQUS software in order to identify the effect of different parameters on the behaviour of semi rigid steel beam to column end plate connections. Contact and sliding between different elements, bolt pretension and geometric and material non-linearity are included in this model. A parametric study is conducted using a model of two end-plate configurations: flush and extended end plates. The studied parameters were as follows: bolts type, end plate thickness and column web stiffener. Then, the model was calibrated and validated with experimental results taken from the literature and with the model proposed by Eurocode3. The procedure for determining the moment–rotation curve using finite element analysis is also given together with a brief explanation of how the design moment resistance and the initial rotational stiffness of the joint are obtained.

Analysis of the Behaviour of Semi Rigid Steel End Plate Connections

The analysis of steel-framed building structures with full strength beam to column joints is quite standard nowadays. Buildings utilizing such framing systems are widely used in design practice. However, there is a growing recognition of significant benefits in designing joints as partial strength/semi-rigid. The design of joints within this partial strength/semi-rigid approach is becoming more and more popular. This requires the knowledge of the full nonlinear moment-rotation behaviour of the joint, which is also a design parameter. The rotational behaviour of steel semi rigid connections can be studied using the finite element method for the following three reasons: i) such models are inexpensive; ii) they allow the understanding of local effects, which are difficult to measure accurately physically, and iii) they can be used to generate extensive parametric studies. This paper presents a three-dimensional finite element model using ABAQUS software in order to identify the effect of different parameters on the behaviour of semi rigid steel beam to column end plate connections. Contact and sliding between different elements, bolt pretension and geometric and material non-linearity are included in this model. A parametric study is conducted using a model of two end-plate configurations: flush and extended end plates. The studied parameters were as follows: bolts type, end plate thickness and column web stiffener. Then, the model was calibrated and validated with experimental results taken from the literature and with the model proposed by Eurocode3. The procedure for determining the moment–rotation curve using finite element analysis is also given together with a brief explanation of how the design moment resistance and the initial rotational stiffness of the joint are obtained.

Numerical simulation of beam-to-column joints with flange cleats

Although the effect of semi-rigid steel beam-to-column connections on the behaviour of steel frames and their substantial economic benefits are recognized nowadays, many structural analyses still consider connections as either fixed or pinned. For that reasons, there is need to be able the generate moment-rotation responses of semi-rigid connections that can be used for analysis and design proposes. Characteristic of the joints can be found using FEM models. The objective of the analysis was to find moment-rotation curves for beam-to-column joints with flange cleats and compare them to curves obtained from experimental studies. Numerical elastic-plastic 3D finite models was performed in order to establish a numerical analysis method for evaluating deformation of connections. For all joints there were obtained the FE results lightly underestimates results achieved from experiments. Some differences in the initial value of stiffness and resistances indicate the need for further work on improving FEM models. The inclusion of dimensional deviations of the IPE nad HEB sections, variability in the values of the prestressing forces of the bolts and the not centric positions of the bolts in the holes in the FEM model may contribute to increasing the degree of compliance of the results from experimental and numerical analyzes.

Numerical modelling of innovative DST steel joint under cyclic loading

This paper addresses the numerical simulation of an innovative double split Tee beam-to-column joint fitted with a dissipative friction damper, recently proposed at the University of Salerno. The innovative connection prevents damage to all other structural components with the exception of one component of the connection that is specially designed to dissipate the input energy of a seismic hazard by means of the slippage of a friction material. The main topics herein presented are the development of a strategy for the numerical modelling of complex friction problems and a detailed numerical model of the overall beam-to-column joint equipped with the friction device. The joint is subjected to both monotonic and cyclic loading conditions. The numerical modelling was developed using the Finite Elements Method (FEM) with Abaqus Software. Sliding force–displacement curves are obtained for two damper materials and an estimation of their wearing is presented. To evaluate the accuracy of the numerical model, moment–rotation curves of the joint are compared with the experimental curves. The FE results show good correlations and confirm the potential interest of this novel joint typology to achieve easily replaceable details in case of a seismic event.

Rotational behavior of degraded traditional mortise-tenon joints: experimental tests and hysteretic model

ABSTRACTThis article presents the results of an experimental study on the rotational behavior of degraded Chinese traditional mortise-tenon joints with different degradation types and different degradation degrees. Six joint specimens degraded through artificially simulated method, were tested by reversed cyclic loading, from which the moment-rotation curves were obtained. The results indicated that the rotational behavior of these joints is semi-rigid, the hysteretic curve shapes of degraded joints are same to that of joint without degradation. The maximum moment, yield moment, and initial rotational stiffness of degraded joints decreases as the degraded degree increases, whose empirical degradation relationships were obtained based on the test data. A hysteretic model for degraded traditional mortise tenon joints was proposed. Experimental results were used to validate the proposed hysteretic model. Good agreement between predictions and tests was observed.

Analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams

This work aims at studying the mixed-mode delamination process in Moment-Loaded Double Cantilever Beam (MLDCB) specimens. The delamination problem is addressed both analytically and numerically, while considering the interfaces as an assemblage of two sublaminates partly bonded together by an elastic interface. Such interface is modeled as a continuous distribution of elastic-brittle springs acting along the normal and/or tangential direction depending on the interfacial mixed-mode condition. The Timoshenko’s beam theory is here applied to determine the governing equations of the differential problem and the associated boundary conditions, whose solution is not straightforward. The Generalized Differential Quadrature (GDQ) method is then applied as numerical tool to solve directly the differential equations of the problem in a strong form. The capability of the proposed numerical approach is first exploited through a comparative evaluation of the results with the analytical predictions resting on a suitable change of variables for delamination test specimens. The local and global response is determined, in terms of interfacial stresses, internal forces and displacements, as well as in terms of compliance, energy release rate, mode mixity angle, and moment-rotation curves. A further check of the proposed numerical method is performed with respect to a Finite Fracture Mechanics (FFM) criterion, which is able to join both stress- and energy-based approaches. A good agreement between results confirms the good feasibility of the GDQ method when studying delamination phenomena occurring within composite materials or laminated joints, usually subjected to mixed-mode conditions.

Experimental investigation on bending and shear performance of two-way aluminum alloy gusset joints

Two-way aluminum alloy gusset joints (AAGJs) are considered to be employed in cable-stiffened aluminum alloy single-layer reticulated shell structures meshed with quadrilateral grids. In this study, a series of experiments on six AAGJs with and without shear connectors were conducted to investigate their semi-rigid behavior. Two joints were subjected to pure bending moments and others to shear loads, then their corresponding failure modes were investigated which were mainly beam rupture, beam web buckling, and bolt failure. The moment-rotation curves, shear load-rotation curves, and strain-load curves were also obtained, indicating that AAGJs are typical semi-rigid joints. Shear connectors can optimize the load transferring path and improve ductility under bending moment while enhancing shear performance significantly. A simplified theoretical AAGJ model was also established and parameterized according to the experimental results.

Monotonic and cyclic tests on beam-column joints of industrial pallet racks

Pallet racks are characterized by boltless beam-column connections and the extensive use of thin-walled cold-formed steel members. Due to the great number of beam-end connector types and member geometries, a reliable evaluation of their structural behavior, especially under seismic loads, requires a thorough modeling of beam-column joints, whose moment-rotation curves can be reliably assessed only through experimental tests. In this paper, the authors present results of monotonic and cyclic tests on four different types of industrial rack joints. Tested joints differ from one another in the type of beam-connector, which is obtained by folding the beam end or is welded to the beam-end section with different welding layouts. Moreover, joints differ in the number of tabs and the relative thickness of the upright and the beam-end connector. Experimental results from cyclic tests allows for moment-rotation curves of joints to be accurately identified, confirming that they are significantly different from traditional steel framed buildings due to pinching in hysteresis loops. Obtained curves can be used for reliable modeling of joints in seismic analyses of steel pallet racks. As producers of steel rack structures are interested in reducing the total welding length of beam-end connectors for time efficiency and cost saving, the influence of the welding layout of beam-end connectors on the structural response and failure mode of joints has also been investigated. Finally, some joints have also been equipped with additional bolts to evaluate their influence on the bearing capacity, initial elastic stiffness and dissipated energy per cycle.

Combination of mechanical and informational modeling to predict hysteresis behavior of I beam‐to‐CFT column connection

SummaryThe behavior of beam‐to‐column connections is significantly complicated because it depends on the material, nonlinear relationship between different members, and contact of connecting elements. Their hysteretic response exhibits highly inelastic characteristics and continuous variation in stiffness, strength, and ductility. Therefore, accurate hysteretic models of bolted connections are essential to accurate seismic assessment and design. Composed (Hybrid) modeling approach is presented to represent the complex hysteretic behavior of I beam‐to‐concrete‐filled‐tube (CFT) column bolted connection. For the purpose in this study, experimental evaluation of I beam‐to‐CFT column connection with bolted end‐plate under cyclic loading is done. It must be mentioned to make the connection easily applicable practically and also prepare the column flanges continuity, a connection with the bolts penetrated into the CFT column are used since using the stiffeners in hollow sections is not easily applicable. In the composed mechanical–informational modeling framework, the conventional mechanical model is complemented by information‐based model components. Finally, moment–rotation curves of composed model have been compared with experimental results. Comparison showed that the composed model has a good agreement with experimental results. A newly designed specimen for validation purpose of the composed modeling was made and experimented. Composed model was well applied to predict the behavior of new connections. The presented results show that the composed model has a good ability to predict of hysteretic behavior.

Pushover Analysis of Steel Seismic Resistant Frames with Reduced Web Section and Reduced Beam Section Connections

The widespread brittle failure of welded beam-to-column connections caused by the 1994 Northridge and 1995 Kobe earthquakes highlighted the need for retrofitting measures effective in providing ductility to connections. Researchers presented the reduced beam section (RBS) as a viable option to prevent brittle failure at the connection weld. More recently, an alternative connection known as a reduced web section (RWS) has been developed as a potential replacement, and initial studies show ideal performance in terms of rotational capacity and ductility. This study performs a series of non-linear static pushover analyses using a modal load case on three steel moment-resisting frames (MRFs) of 4-storeys, 8-storeys and 16-storeys. The frames are studied with three different types of connections; fully-fixed moment connections, RBS connections and RWS connections, in order to compare the differences in capacity curves, inter-storey drifts and plastic hinge formation. The seismic-resistant connections have been modelled as non-linear hinges in ETABS, and their behaviour have been defined by moment-rotation curves presented in previous recent research studies. The frames are displacement controlled to the maximum displacement anticipated in a 2 in 50 earthquake. The study concludes that RWS connections perform satisfactorily when compared with frames with fully-fixed moment connections in terms of providing consistent inter-storey drifts in low to mid-rise frames, without significantly compromising the overall strength capacity of the frames. The use of RWSs in taller frames causes an increase in inter-storey drifts in the lower storeys, as well as causing a large reduction in strength capacity. Frames with RWS connections behave comparably to frames with RBS connections and are deemed a suitable replacement.

Numerical analysis of aluminium alloy gusset joints subjected to bending moment and axial force

A test series was carried out and reported in a companion paper on the semi-rigid behaviour of aluminium alloy gusset (AAG) joints subjected to bending moment and axial force. This paper presented the results of an extensive numerical analysis program devoted to the investigation of the bending behaviour of AAG joints. The analysis was developed by means of finite element (FE) models implemented in the non-linear code ABAQUS. The procedure was accurately calibrated on the basis of the available experimental results. It is indicated that the FE models could be used effectively to describe the mechanical performance of AAG joints, including the failure modes, deformation process and bending moment-rotation curves. Furthermore, the shear connector, the thick plate and the advanced contact of bolts and bolt holes could improve the bending behaviour of AAG joints. According to the deformation process of AAG joints, a four-line model was proposed to simulate the bending moment-rotation relationship. To develop a further understanding, the effects of the member height, axial force, bolt pretension force, bolt gap and material nonlinearity on the bending behaviour of AAG joints were investigated.

NON-LINEAR POST-BUCKLING LARGE DISPLACEMENT ANALYSIS FOR PLANE STEEL NON-PRISMATIC MEMBERS FRAMES WITH FLEXIBLE CONNECTIONS

Although the joints constitute a small proportion of the total weight of the structure, but they have a comparatively large work ratio, thus the accounted is represent a large percentage of the total cost of framing. In addition, the contact region deformation is sometimes responsible for a significant proportion of the total deviation of the structure and often has a large impact on the distribution of internal distribution of the forces. All real structures show nonlinear behavior when loads and deformations become large enough and the tapered members are also used in several locations in the structural applications such as aerospace structures, bridges, as well, in many mechanical components. It is used to try to meet the architectural requirements for the shape of buildings and to achieve a suitable division of strength and weight. So, the nonlinear post-buckling behavior of plane steel frame under loads was a major research topic. A general formulation of Eulerian is used to analyze the plane frames and it is clear that this method of analysis are be good to use within theory of beam-column. This study is shown that a polynomial modeling of the non-linear moment-rotation curve of steel connection gives excellent results with the exact non-linear moment-rotation curve with a difference not more than (1%) and the effect of the flexible connections must be considered in the analysis because it has significant effect on the behavior of the steel structures and the new modified tangent stiffness matrix which takes into account the two types of non-linearities at the same time (i.e. geometry and connection) and non-prismatic members efficient in giving accurate results of analysis of different types frames with difference not more than (0.5%) compere with the other finite element methods for analysis

Experimental and numerical research on gear-bolt joint for free-form grid spatial structures

The nodal connection system for the free-form grid spatial structures should both implement complex-shaped curvature and fulfil the required loading capacity, whilst also meeting various important requirements, such as quick and easy assembly at the construction site. A novel joint system named gear joint with the above advantages, developed for free-form grid spatial structures, is presented in this paper. First, a series of tests was carried out considering different bolt diameters, tooth heights, tooth numbers and ball thicknesses. The different failure modes and whole moment-rotation (M-Ф) curves of gear bolt joints were obtained, and the joint stiffness and strength were investigated. Second, a three-dimensional finite element (FE) model of the joint was established. The comparison between computation and experiments highlights the degree of accuracy of the proposed FE model. The stiffnesses, strengths, rotation behaviours, and failure modes of the new joint system were carefully compared and discussed. Based on the results, the influence rules of the parameters on the mechanical behaviour of the new joint were obtained. Finally, based on the power-function model, the formulae for predicting the M-Ф curves of the joints were established. The M-Ф curves have preferable accuracy compared with the experimental curves.

New moment-rotation equation for welded steel beam-to-column connections

A three-parameter tangent inverse equation is generically proposed for the non-linear moment-rotation (M-θ) relationship of semi-rigid steel beam-to-column connections. The parameters are the initial stiffness, the plastic stiffness, and a reference moment. Two commonly used welded moment connections are picked up for moment-rotation calculation and comparison between the results of the proposed model and those of a detailed nonlinear finite elements modeling. Semi-analytical equations are proposed for calculating the parameters containing basic factors affecting behavior of the connections. The coefficients of the equations are computed based on a data bank developed in this study using the finite element method. A large number of finite elements models covering the whole range of common dimensions of the above connections are analyzed. Accuracy of the finite element model is verified on the basis of the available test results from previous studies. Tensile tests for determination of material properties of weld to be used in the modeling are conducted. Comparison between the results of the semi-analytical equations and the finite element models shows that the proposed model is able to estimate the moment-rotation curves of the welded beam-to-column connections with very good accuracy.

Introducing box-plate beam-to-column moment connections

Nowadays, using high-ductility structures in the construction and use of significant buildings is highly appreciated. To use more ductile structures, effort has been made in this research to introduce box-plate beam-to-column connections. They underwent hysteretic loading and it was found from their moment-rotation curves that the bending capacity and ductility of the box-plate connection were more than ordinary rigid connection, and those of the latter were more than those of the normal typical one. It was also shown that stress concentration in box-plate connections disappears over the top and bottom flange plates.

Flexural behaviour of concrete-filled CHS X-joints with curved chord under out-of-plane bending

This paper presents experimental and numerical investigations on empty and concrete-filled circular hollow section (CHS) X-joints with curved chord under out-of-plane bending. A total of 16 specimens were fabricated by hot-rolled bending the chord members into curvature with three different radii to apply out-of-plane bending to the brace members, in which 6 specimens were tested with empty curved chord, 6 specimens were tested with concrete filled in the curved chord only, and 4 traditional empty and concrete-filled CHS X-joints with straight chord were also tested for comparison. The typical failure modes, axial load-vertical displacement curves, bending moment-chord deformation curves, bending moment-rotation curves and strain distribution curves of all specimens are reported. The effects of curvature radius of chord member and concrete filled in the chord member on the joint strength and behaviour under out-of-plane bending were evaluated. It is shown from the comparison that the ultimate strengths of the CHS X-joints with curvature radius of chord less than 12d0 under out-of-plane bending are closer to those of the traditional CHS X-joints with straight chord with the increase of the curvature radius of chord member. Whereas, the ultimate strengths of the CHS X-joints with curvature radius of chord less than 12d0 under out-of-plane bending are generally similar to those of the traditional CHS X-joints with straight chord. Furthermore, the out-of-plane flexural behaviour of CHS X-joints are improved with the increase of the β ratio. Whereas, filling the concrete in the chord member cannot enhance the ultimate strengths of CHS X-joints under out-of-plane bending. The joint strengths obtained from the experimental investigation are compared with the design strengths calculated using the current design rules for traditional CHS X-joints with straight chord under out-of-plane bending, which were demonstrated to be quite conservative. In addition, the corresponding finite element analysis was also performed and calibrated against the test results. The design equations are proposed based on the test and numerical results for empty and concrete-filled CHS X-joints with curved chord under out-of-plane bending, which were verified to be more accurate.

Semi-rigidity of cap plate and extended end plate connections

The behaviour of steel frames is highly influenced by the beam-column connections. Traditionally, Steel frames were usually designed assuming that connections are ideally pinned or fully rigid. A semi-rigid connection, however, creates a balance between the two extreme approaches mentioned above. In this research, two full scales of Extended End Plate Connections (EEPCs) were tested. Mathematical and numerical models were used to analyse the connections, and close correlations were found between these models and the corresponding tested specimens, which confirmed the confidence in the experimental results. The experimental results obtained enrich the available test data about behaviour of EEPC. In addition, the purpose of studying EEPC experimentally is to compare the stiffness and moment-rotation curve of EEPCs with that of Cap Plate Connections (CPCs), which were tested in a previous work. CPCs have not been studied sufficiently in the literature. The results obtained show that the typical CPC reduces the connection stiffness and these results will make a valuable contribution to the available test data in the research area of CPC.