Moment-rotation Curves Research Articles

Finite element analysis of beam-to-column joints in steel frames under cyclic loading

The aim of this paper is to present a simple and accurate three-dimensional (3D) finite element model (FE) capable of predicting the actual behavior of beam-to-column joints in steel frames subjected to lateral loads. The software package ANSYS is used to model the joint. The bolted extended-end-plate connection was chosen as an important type of beam–column joints. The extended-end-plate connection is chosen for its complexity in the analysis and behavior due to the number of connection components and their inheritable non-linear behavior. Two experimental tests in the literature were chosen to verify the finite element model. The results of both the experimental and the proposed finite element were compared. One of these tests was monotonically loaded, whereas the second was cyclically loaded. The finite element model is improved to enhance the defects of the finite element model used. These defects are; the long time need for the analysis and the inability of the contact element type to follow the behavior of moment–rotation curve under cyclic loading. As a contact element, the surface-to-surface element is used instead of node-to-node element to enhance the model. The FE results show good correlation with the experimental one. An attempt to improve a new technique for modeling bolts is conducted. The results show that this technique is supposed to avoid the defects above, give much less elements number and less solution time than the other modeling techniques.

Analytical Studies of Full-scale Steel T-stub Connections Using Delicate 3D Finite Element Methods

This study presents the development of refined three dimensional (3D) finite element (FE) models with the ability to reliably simulate the mechanical behavior of full-scale bolted T-stub connections. FE models incorporated material nonlinearity, geometric nonlinear behavior, several contact interactions between faying surfaces, and prescribed displacements for generating initial bolt pretension. These FE models were used to compare experimental test results, which verify that advanced FE modeling methods make a notable contribution to reproducing the overall behavior of connections and components accurately, including the moment-rotation curves. In addition, the FE models provide some useful information which is difficult to obtain during physical testing, i.e., the distribution of stress and strain, friction forces between shear faying surfaces, and bolt reaction forces. The validated FE models are also used for additional parametric studies so as to comprehensively understand their response mechanisms. Moreover, the observation of FE analysis results supports the statement that connection models presented herein were designed to reach the yielding of connection components when the structural beam produces its full plastic moment at the plastic hinge.

Local Buckling Influence on the Moment Redistribution Coefficient for Composite Continuous Beams of Bridges

Abstract. The present paper is concerned with the elastic design optimisation of continuous composite beams. This optimisation is based on the analysis of the beam in the inelastic range including the concrete creep and shrinkage, the tension stiffening and temperature difference effects as well as the possible local buckling instability. The finite ele-ment program PONTMIXTE (adapted to study continuous beams at real scale with short time computation) is first presented with its different sections: Pre-design (in accordance with Eurocode specifications), Non linear finite element calculation and Post-processing. In order to validate the proposed model, the numerical calculations are compared against experimental results from tests on a two-span beam in reduced scale (7.5 m length for each span) without taking into account the local buckling phenomenon avoided in the experimental test by using web-stiffeners. Next, special attention is paid to study the influence of the local buckling instability on the internal moment redistribution coefficient between hogging and sagging zones. The application concerns different 3-span beams of bridge at real scale with medium span lengths (40–60–40 m). The post-buckling behaviour represented by moment-rotation curves (M-θ) is deduced from a 3D finite element model of the cross-section developed using Castem finite element code. The M-θ curves describing the local buckling phenomenon are approximated using hyperbolic functions and implemented in PONTMIXTE using a specific rotational spring finite element. The influence of this instability on the moment redistri-bution coefficients calls the Standart predictions into question.

Unilateral contact effects in the structural response of beam-to-column connections

One of the most usual choices for the connection between the different structural members in steel structures is the bolted connection. The later provide a high level of deformation capacity for the whole structure and a level of stiffness comparable to that of fully welded connections. Top and seated angle with double web angle bolted connections are primarily used for beam-to-column joints. The most important factor for the structural response of beam-tocolumn connections is the rotational stiffness because it affects the behavior of the overall structural steel frame. For this purpose, many experimental tests have been recently conducted to obtain moment-rotation curves. Considering the moment-rotation curves obtained from experimental tests, a simplified analytical model has been suggested to predict the behavior of the connection by fitting techniques. The aim of the present paper is, from one side, the development of a moment-rotation curve for bolted top and seat angle connection with double web angle by means of a proposed theoretical model whose validity checked by comparison with experimental data, and from the other side, the determination of the appearing prying forces in the bolts by means of a simplified and reliable model.

Cyclic behavior and numerical modelling of a semi-rigid frame

It is clear that semi-rigid frames exhibit completely non-linear behaviour under cyclic loading due to gradual yielding of connection components. The current study presents the experimental results from the test of a semi-rigid frame specimen, comprising a single storey and one bay, and the analysis results obtained from a finite element model of the specimen. In this study, semi-rigid joints with header plates are used for beam-tocolumn connections. The initial stiffness and moment-carrying capacity of the connection, designed as a semi-rigid and partial strength connection type, were determined in accordance with Eurocode 3. In the modelling of the semi-rigid beam-to-column connection behaviour, four-parameter non-linear representation of the moment—rotation curve obtained using the Ramberg-Osgood formula was employed. Loading of the test specimen consisted of quasi-static cycles with displacement control. The cyclic response of the specimen is characterized by a stable hysteretic behaviour. When comparing the envelope of the hysteresis loops from the cyclic test of the specimen with the pushover curve achieved by non-linear finite element analysis, the model gives a good prediction of the ultimate strength and initial stiffness of the frame.

Seismic behaviour of beam-to-column partial-strength joints for steel–concrete composite frames

The paper presents a large experimental campaign carried out on ten steel–concrete composite beam-to-column sub-assemblages employing monotonic and cyclic loading test protocols. Structural members (beams, columns and slabs) were defined through the design of a full-scale 3D prototype frame subjected to PSD testing campaign; main design hypothesis was to dissipate seismic energy in the joints designed as partial-strength. Testing programme on beam-to-column sub-assemblages was executed in order to assess seismic performance varying structural details at beam-to-column connection level and material qualities. Different mechanical connecting systems between concrete slab and column, two end-plate configurations, weak and strong column web panel, two steel qualities and different concrete strengths. The analysis of sub-assemblages performance was realized in two steps: a first step in which the joints behaviour was assessed, characterizing response at local level (e.g. moment–rotation curves); a second step in which the response was assessed at global level (e.g. force–displacement curves). The structural behaviour (i.e. resistance, plastic deformation and stiffness) was evaluated at three stages–identified as initial, service and maximum load–in order to monitor the evolution of sub-assemblage response increasing solicitation level. Moreover, seismic behaviour of specimens–in terms of dissipated energy, ductility, over-strength and equivalent viscous damping–was also executed. Comparison between experimental results was made in order to identify those parameter suitable for improved and reliable seismic behaviour of steel–concrete composite partial-strength joints.

Performance of the PR connections under combined Axial-tension and moment loading

The inherent moment capacity of bolted top-seat angle connections with double web angles (TSDW), categorized as partially restrained (PR) connections according to AISC-LRFD specifications, can be considered in analyses of semi-rigid connections especially when an accurate analysis of such fames is desired. However, in some cases, developed internal forces in the frame elements may affect the connection behavior, considerably. Axial tension force is one of such internal forces that may be imposed on frame connections in some cases such as construction imperfections, seismic loading or under large deflections of the catenary action during the progressive collapse of the semi-rigid frames. This study aims at the effects of the axial tension force on the performance of the bolted TSDW angle connections using nonlinear finite element method (FEM). The obtained results show that the axial tension force reduces the connection moment capacity and stiffness, considerably. Based on the obtained moment-rotation curves, affected by this particular loading type, equations are proposed to estimate the reduction rate of the connection stiffness and moment capacity.

Engastamento parcial de ligações viga-pilar em estruturas de concreto armado

Neste trabalho são apresentados os resultados experimentais de ensaios em ligações viga-pilar de concreto armado realizados na Escola de Engenharia de São Carlos - USP. Os referidos resultados experimentais concentram-se nas rotações relativas entre os elementos viga e pilar, importantes para a determinação da relação momento-rotação das ligações e da caracterização do comportamento semi-rígido das mesmas. Os dados experimentais foram obtidos a partir de ensaios de ligações viga-pilar de extremidade. A influência da resistência à compressão do concreto e da taxa de armadura transversal na região dos nós de pórtico sobre as rotações relativas foi analisada. Os resultados experimentais foram confrontados com o modelo teórico proposto por Ferreira [1] para ligações com engastamento parcial, permitindo uma avaliação da porcentagem de engastamento alcançada pelas tipologias de ligações monolíticas abordadas neste trabalho.

Analytical models for the initial stiffness and plastic moment capacity of an unstiffened top and seat angle connection under a shear load

This study was conducted to propose analytical models that can predict the initial stiffness and plastic moment capacity of an unstiffened top and seat angle connection. These analytical models were developed by considering the moment-rotation curves, plastic hinge lines, and failure modes of an unstiffened top and seat angle connection. In the development of these analytical models, the effects of the prying action and the moment-shear interaction of a top angle were also considered. Application feasibility of these analytical models was verified by comparing these models’ results with those obtained from using the Chen-Kishi and Faella models, as well as the Nethercot experimental test data. Four tests were conducted to obtain the moment-rotation curves and failure modes of an unstiffened top and seat angle connection under shear.

NONLINEAR ANALYSES OF COMPOSITE PREFLEX STEEL BEAMS ENCASED IN CONCRETE

In the present study, a nonlinear three-dimensional finite element analysis has been used to predict the load-deflection and moment-rotation behaviors of composite encased beams consisting of preflex steel sections using the finite element computer program (ANSYS V. 10). Composite encased beams are analyzed and a comparison is made with available experimental moment-rotation curves, good agreement with the experimental results is observed. Camber of steel section is introduced on the steel section of the composite beams encased in concrete. It is found that using of preflex section can increase the ultimate load capacity of the composite encased beam by relatively (15%) and also it is found that rotations are nearly (65% to 80%) the rotations of the same beam without preflex steel section. Parametric studies have been carried out to study the increasing of the moment-carrying capacity due to the use of encased concrete for the laminated partially encased beams; meanwhile the slip along the composite partially encased beams length is studied. The strain distributions along the steel section and encased concrete depth are also examined. Poisson’s ratio of concrete, the effect of cambering of steel-section and the effect of mesh refinement are also investigated.

Steel spot-welded hat sections with perforations subjected to large deformation pure bending

Steel spot-welded hat-type sections are used extensively in the automotive industry to manufacture vehicle structures. The main objective when designing a crashworthy vehicle is to protect the occupants in the event of a collision by dissipating crash energy via large plastic deformation and ensuring the survival space is not encroached. In rollover crashes, the components in the roof structure will be subjected to large deformation bending as the roof frame collapses and kinetic energy is dissipated. This paper presents a procedure whereby the energy absorbed by a spot-welded hat section under large deformation bending may be determined. The results are shown to compare well with experiments of spot-welded hat sections with seven different geometries and four different perforation sizes. The perforations were introduced into the compression flange of the sections. The range of section and perforation geometries investigated was designed to cover the full range typical to the automotive industry. The theoretical large deformation bending moment–rotation curves and energy absorbed are determined from a rigorous yet relatively simple three stage process, which includes elastic, in-plane plastic and plastic collapse mechanism components.

Generalised component-based model for beam-to-column connections including axial versus moment interaction

A generalised component-based model for semi-rigid beam-to-column connections including axial force versus bending moment interaction is presented. The detailed formulation of the proposed analytical model is fully described in this paper, as well as all the analytical expressions used to evaluate the model properties. Detailed examples demonstrate how to use this model to predict moment–rotation curves for any axial force level. Numerical results, validated against experimental data, form the basis of a tri-linear approach to characterise the force–displacement relationship of the joint components. The relationship of the present development to key prior studies of this topic is also explained.

Behavior of Khorjini connections in fire

Beam-to-column connections have been shown to have great influence on structural behavior at ambient and elevated temperatures. When steel-framed structures are subjected to fire, the load-bearing capacity is decreased and the behavior of the joints is of particular concern. In this paper, the behavior of a semi-rigid Khorjini connection is studied at elevated temperatures. Four experimental tests are carried out on this kind of connection at elevated temperatures, and the results are presented as temperature–rotation and moment–rotation curves. Then, finite-element models are developed and compared with the experimental tests. Good agreement was achieved between the model and experiment, confirming that the finite-element method is capable of predicting the behavior of these connections at elevated temperatures.

Mechanical modeling of the nonlinear response of beam-to-column joints

A methodology for the estimation of the complete moment–rotation curve of structural beam-to-column joints is presented in this paper. The methodology is based on the component method and is materialized through appropriate mechanical models that are analyzed nonlinearly. The cases examined in this work include bolted connections with end-plates and with angles. Significant consideration is devoted to the reliable simulation of the tensile joint components that have the form of equivalent T-stubs, by application of a recently developed incremental T-stub model, for the calculation of their nonlinear force–displacement laws. The proposed methodology is evaluated against experimental tests and advanced finite element models in terms of stiffness, strength and rotational capacity, and its performance is found to be very satisfactory.

Open cross-section beams under pure bending II. Finite element simulation

Starting from the set of bending tests of U sections performed in our laboratory and described in Part I. Experimental investigations [Pastor MM, Roure F. Open cross-section beams under pure bending. I. Experimental investigations. Thin-Walled Struct 2008;46(5):476–483.], a numerical model has been developed. It reproduces the actual testing conditions and also the building of hinges in pure bending, as well as producing the moment–rotation curves of the section and a complete information about the stresses and strains of the beam along the whole loading process. Once the model has been validated, a parametric study has been done for the U sections. The influence of several parameters on the ultimate strength in bending of the section has been analysed: thickness ( t), width ( b), depth ( c w) and position of the point of application of the load ( y).

Development of Cold-Formed Steel Portal Frames with PRY Sections

A series of column, beam, and connection tests for portal frames which consisted of closed cold-formed steel PRY sections as columns and rafters were carried out. Firstly the compressive and the flexural strengths of the PRY sections were investigated, and secondly the structural behavior of the connections including the moment-rotation relation, the yield and the ultimate moment capacities of the connections were studied. The connection test specimens consisted of column-base, column-to-rafter, and rafter-to-rafter connections. The main testing parameters of the connection tests were the thickness and the shape of mild steel connectors, which were important for the proposed attachment system of wall panels. The connection test results were compared with those achieved by using advanced analysis procedures. The semi-rigid connection concept was considered appropriate for the analyses of the portal frames using the secant stiffness of the connections, which were estimated from the measured moment-rotation curves of the connections tested. Simple formulae for the shear resistances of the screwed connections were also proposed after calibrated with test results. The performance of the portal frame with PRY sections was investigated through the full scale tests.

Reinforced concrete columns strengthened with angles and battens subjected to eccentric load

The aim of the work is, on the one hand, the presentation of a theoretical fiber model able to predict the moment–curvature behaviour of RC columns confined by means of angles and battens and, on the other hand, the validation of the proposed model by means of the comparison between analytical results and experimental evidence coming from 13 specimens tested under axial force–moment interaction. The analytical model is able to account for many parameters often neglected in current design practice, such as the influence of both hoops and battens on concrete confinement, the buckling of longitudinal bars and the influence of the structural detail aimed at assuring the continuity through the concrete floor slab which affects the angle behaviour. The proposed model has been used for predicting the load carrying capacity of both unstrengthened and strengthened columns, obtaining a good degree of accuracy. In addition, the comparison in terms of moment–rotation curves has been performed, showing the model accuracy in predicting the structural response in the whole deformation range.

Influence de la connexion partielle sur le voilement local des poutres mixtes continues selon l'Eurocode 4

ABSTRACT Today, composite structures form a growing sector, and its practice highlights that it can be competitive compared to steel or concrete structures. The calculation of composite sections with the hypothesis of a partial connection is introduced each time when the full resistance of a composite section has no need to be used. This requires to study the influence of the partial connection on the local buckling of continuous beams and to search for an analytic model that allows to value, with a sufficient degree of precision, the capacity of cross-sections rotations at the intermediate supports according to the evolution of the moment. A model is therefore proposed in this paper, based on the theorem of the plastic limit, to allow to estimate with a good precision the rotation capacity of class 2 cross-sections according to Eurocodes 3 and 4: a failure mechanism for the local buckling based on plastic hinges is introduced for assessing moment-rotation curves on supports. A comparison with experimental data is given at the end of this paper.

Discrete and continuous treatment of local buckling in stainless steel elements

Cross-section classification is an important concept in the design of metallic structures, as it addresses the susceptibility of a cross-section to local buckling and defines its appropriate design resistance. For structural stainless steel, test data on cross-section capacity have previously been relatively scarce. Existing design guidance has been developed based on the limited experimental results and conservative assumptions, generally leading to unduly strict slenderness limits. In recent years, available test data for stainless steel cross-sections have increased significantly, enabling these slenderness limits to be re-assessed. In this paper all available stainless steel test data have been collected and additional moment–rotation curves have been presented. The study covers both cold-formed and welded plated elements as well as CHS. Following analysis of the test results, new slenderness limits for all loading conditions have been proposed and statistically validated. In addition to re-assessment of the current slenderness limits, a new approach to the treatment of local buckling in structural elements–the Continuous Strength Method–has been outlined. The Continuous Strength Method (CSM) is based on a continuous relationship between cross-section slenderness and deformation capacity and is applied in conjunction with accurate material modelling. The method enables more rational and precise prediction of local buckling than can be achieved with the traditional cross-section classification approach, thus allowing better utilization of material and more economic design.

Análise teórico-experimental de ligações parafusadas com enrijecedores de alma em perfis de aço formados a frio

Nesse trabalho, são apresentados estudos teórico-experimentais para avaliação do comportamento de uma tipologia, não padronizada, de ligação viga-coluna parafusada, utilizando seções transversais em perfis de aço formados a frio. O programa experimental consistiu na realização de quatro ensaios em quatro diferentes configurações de ligações viga-coluna e, para efeito de comparação, agrupadas em dois grupos: sem enrijecedores (SE) e com enrijecedores (CE) de alma soldados nos flanges da coluna. Os resultados experimentais permitiram determinar as curvas momento-rotação e rigidezes, bem como os momentos últimos e seus respectivos mecanismos de colapso. Verificou-se, também, que ao considerar a semicontinuidade - através dos enrijecedores de alma - entre as vigas separadas por uma coluna, o mecanismo de colapso muda e as ligações ficam mais resistentes e rígidas.