Moment-rotation Curves Research Articles

A hybrid approach to the transient collapse analysis of thin walled frameworks II

A new improved compound beam element (CBE2) for the transient hybrid finite element analysis is presented. The element is a combination of an elastic beam and two non-linear rotary springs whose behaviour in the elastic/plastic and deep collapse range is controlled by inputted moment-rotation curves and a load interaction curve. The formulation is based on the rigid convected coordinate procedure similar to the one used by the Belytschko-Schwer (B-S) beam element. The element stiffness matrix has been derived and its dependency on the spring behaviour explained. Two series of experiments were performed on two simple structures providing the data for the element performance evaluation. The tests performed were designed so that structural components collapse under biaxial bending and torsion. The tests results have shown, not only that CBE2 is more accurate than CBE1 but also that it does not suffer from the stability problems present in the formulation of CBE1 [1].

Local buckling in class 2 continuous composite beams

For continuous composite beams, with type of cross-section as shown, the neutral axis is shifted towards the top flange, and in negative bending the joist is subjected mainly to compressive strains, from which the local buckling of the web and low flange limit its rotation capacity, therefore keeping it from reaching its ultimate strength. The work described in this paper is aimed at providing more information on local buckling and its effect on rotation capacity in the negative moment regions of continuous composite beams. An analytical design method based on a collapse mechanism is developed, allowing us to estimate, with sufficient precision, the rotation capacity of the central support as a function of bending. This method has been justified by experimental results (Aribert, J. M. and Raoul, J., Two full-scale tests of class 3 composite beams. Proceedings of Engineering Foundation Conference on Composite Construction, ASCE, Potosi, MI, 14–19 June 1992) and by its comparison with other methods proposed in the literature (Johnson, R. P. and Climenhaga, J. J., Moment-rotation curves for locally buckling beams.

Tests on beam-column strong and weak axis connections

In the present paper, the specimens of a test series having the same beam and column cross-sections for both strong and weak axis connections are considered. Moment-rotation curves of the connections are obtained from the test results. The influence of the type of the connection on the rotational stiffness is examined. Both types of connections are compared from the viewpoint of strength and stiffness.

State-of-the-art review on the design of beam-to-column connections for pultruded frames

A review and commentary is presented on the research to understand and develop practical beam-to-column connections for pultruded frames. Experimental moment-rotation curves for isolated connections are presented and their properties used in a commentary on frame design. Current design recommendations for pinned connections are given, with reasons why research is still necessary to understand their complete structural behaviour, and that of practical semi-rigid connections. The paper introduces a new analytical method to predict the static behaviour of linear elastic plane frames having real connections, second-order deflections and shear deformable members. The beam-line method and the frame analysis are used to show the potential benefits of treating frame design as semi-rigid. Results using these analytical models are shown to provide useful information in our quest to optimize the performance of semi-rigid connections and frames.

Prediction of Mode Parameters and Moment-Rotation Curves for Crushed Thin-Walled Trapezoidal Tubes in Bending

In the context of kinematic models, a general procedure for the bending crush analysis of thin-walled members is proposed and applied to the trapezoidal and rectangular tubes in bending. The main emphasis of this study is given to the determination of collapse mode parameters and the prediction of post-collapse behaviors of the structural member. The mode shapes are determined by minimizing plastic energy rate of the members. Moment-rotation curves are obtained by differentiating the absorbed plastic energy with respect to the rotation angle. For small rotation angles the solution is modified by considering elastic buckling and plastic collapse moments. Through several examples a full range of post-collapse response of the thin-walled members is shown to be effectively calculated by the proposed method without making any recourse to experimental data.

Expanded database of semi-rigid steel connections

This paper expands the existing database of semi-rigid steel connections at Purdue University by including additional test data on header-plate and seat-angle, and double-web and seat-angle connections. The experimental moment rotation curves are also compared with several analytical models describing these curves.

Welded Interior Box-Column to I-Beam Connections

This paper deals with experimental investigations to study the ultimate load behavior of I-beam to box-column connections stiffened externally. Specimens representative of interior columns in a steel building frame were fabricated with connections stiffened by T-sections butt-welded at the junction of the beam and column flange. They were tested to failure under static and fluctuating loads applied separately. Ultimate load-carrying capacity and typical load-deflection and moment-rotation responses obtained experimentally are presented; the results for those specimens tested under static loading are compared with the corresponding results using the elasto-plastic finite-element method. Close agreement is observed between the experimental and theoretical moment-rotation curves. Results show clearly that these connections satisfy the basic criteria: sufficient strength, sufficient rotation capacity, and adequate stiffness for a moment connection. The proposed connections are capable of developing load-carry...

A Backpropagation Neural Network Model for Semi‐rigid Steel Connections

Abstract: The analysis of semirigid steel structure connections based on exact theoretical modeling, which is demanding and time consuming if all the nonlinear parameters of the problem are taken into account, can be avoided provided that enough experimental measurements exist and an appropriate predictor can be constructed from them. A supervised learning backpropagation neural network approach is proposed in this paper for the construction of this model free predictor. A number of experimental momentrotation curves for single‐angle and single‐plate beam‐to‐column connections are used in this paper to train the neural network. The trained network provides us with an estimator for the mechanical behavior of the steel structure connection element.

Toward design office moment-rotation curves for end-plate beam-to-column connections

A semi-analytic method to model moment-rotation curves for unstiffened extended end plate connections is presented. Two physically based parameters; connection initial stiffness and connection moment capacity, and one experimentally based parameter are used in a three-parameter power model. Good correlation between the proposed model and experimental results is shown. The proposed method is then simplified, resulting in moment-rotation curve modeling suitable for design office environments.

First-order computation of the statistics of joint moments in partially restrained steel structures

The flexibility of connections affects the performance of steel frame structures. Therefore, it must be considered in order to analyze the structure accurately. This flexibility is best described by the moment-rotation ( M- θ) curve of the connection which is modeled quite well by the Richard model. This model characterizes the M- θ relation by four parameters. The variation in the four parameters governing the M- θ curves for similar connections is mainly due to differences in fabrication and field conditions. This results in the moment predicted by the Richard M- θ model being a random variable. For a specific value of joint rotation, the probability distribution of the moment is dependent on the four parameters which define the model. This distribution should be determined in order to account for the variability in joint behavior in the analysis of flexible steel frames, and to assess the reliability of the structures. In this study, the distribution of the moment is found from the distributions of the four parameters which completely characterize the Richard model. Statistical simulation is used to generate values of the four parameters from their respective distributions. These values are used to calculate values of the moment for a range of values of rotation. The results are used to compute the statistics of the moment and to fit an appropriate probability distribution to its value. Finally, in order to provide a practical means of estimating the mean value and variance of the moment, a first-order Taylor series approximation is used and its results are compared to those of the simulation.

Performance of composite connections: Major axis end plate joints

Abstract The results of a series of five tests on composite beam-to-column connections are reported. The steelwork part of the connection used an end plate, welded to the beam and bolted to the column flange. For comparison, a sixth test was on a bare steel connection of the same type. Increasing the amount of reinforcement caused a rise not only in moment resistance but also in the rotation capacity of the composite connection. A similar result was obtained by replacing a flush end plate by an extended one. Increase in the depth of the steel section decreased rotation capacity. Plastic analysis of the composite connections, with forces in tension bolts predicted by Annex J of Eurocode 3, provides satisfactory prediction of moment resistance. Good rotation capacity in hogging bending is associated with a plastic neutral axis for the composite beam being in the top flange of the steel section. Large deformation of the lower part of this section by local buckling is the preferable failure mode, because no sudden drop in resistance occurs. A simple spring model can be used to predict satisfactorily a bilinear approximation of the moment-rotation curve, provided account is taken of the deformation of the shear connection.

Comparative tests on endplate beam-to-column connections

The paper reports the results of an experimental investigation carried out on beam-to-column joints with the aim of comparing the behaviour of flush and extended endplate joints. In the experimental programme, twelve specimens of beam-column joints were tested under ‘tatic’ loads. Four specimens had a flush endplate and the other eight had an extended one. In the latter, four specimens had an extension of endplate on one side of the beam, while the other four had an extension on both sides. In the test specimens, parameters such as endplate thickness and bolt diameter were varied for a constant beam and a constant column cross-section. From the data collected, experimental moment-rotation curves were obtained and the end restraint offered by the joints was calculated. In comparison, it is observed that the flush endplate joints, though having rotations similar to the extended endplate joints, have lower load and moment carrying capacities.

Design of I-Beam to Box-Column Connections Stiffened Externally

This paper is concerned with I-beam to box-column connections stiffened externally. A design method to determine the dimensions of T-stiffeners is proposed. Connections of I-beams and box columns for a wide range of dimensions were studied by the finite-element method and found to satisfy the basic design criteria for a moment connection. The Ramberg-Osgood function was used to curve-fit the moment-rotation curves based on the geometric parameters of the connections and the results are found to agree well with those from the finite-element analyses. Finally, the design procedure and the curve-fitting parameters were compared with the experimental results of a four-way connection tested to failure.

Design Aid of Semi-rigid Connections for Frame Analysis

In this paper, a useful design aid for determining the values of the initial connection stiffness Rki, the ultimate moment capacity Mu, and the shape parameter n of a three-parameter power model describing the moment-rotation curve (M-qr) of semi-rigid connections with angles is prepared for its use in the practical design of flexibly jointed frames with angles. A set of nomographs allows the engineer to rapidly determine the M-qr curve for a given connection. Applying the design aid, numerical simulations on drift and column moment of a flexibly jointed frame with angles are illustrated.

Limit states design of semi-rigid frames using advanced analysis: Part 1: Connection modeling and classification

This paper presents a method for modeling connection moment-rotation curves which are essential for proportioning two-dimensional semi-rigid steel frame structures analyzed based on a second-order inelastic analysis. Procedures for calculating the key parameters used to describe the moment-rotation curves of various types of angle connections are presented. Design aids are generated in which salient size parameters that affect the moment-rotation behavior of the connection can be identified. Two schemes by which connections can be classified in terms of strength, stiffness and rotation capacity are presented, and their design implications are discussed. Analysis and design methodologies are provided in Part 2, a companion paper in which the ultimate strength and serviceability limit state behavior of a semi-rigid frame example are studied using an advanced analysis. The aim of these two-part papers is to advance the use of second-order plastic hinge based analysis for proportioning two-dimensional semi-rigid frames without the need of separate specification equation checks.

Limit states design of semi-rigid frames using advanced analysis: Part 2: Analysis and design

This paper presents an integrated advanced inelastic analysis method for proportioning semi-rigid steel frame structures in which the beam-to-column connections are composed of angles. The modeling of connection moment-rotation curves and their classifications have been presented and discussed in a companion paper. An approach called the second-order refined plastic hinge analysis is introduced. The method is validated by comparing the results with those obtained based on a more exact plastic zone analysis. It is shown that the refined plastic hinge analysis provides a good representation of inelastic behavior, and that it enables the full assessment of system and member inelastic behavior up to the limit state of strength. This analysis method is used to assess the adequacy of a two-dimensional semi-rigid frame, and its members and connections in resisting the factored load effects. The design is evaluated with respect to the system's strength and serviceability limit states, including conformance with the code requirements for strength and stability of individual members, and rotation capacity of connections. The inclusions of connection nonlinear effects in advanced inelastic analysis provide a straightforward task for proportioning of frame members and connections, thus avoiding the complexity of having to perform specification member capacity checks for individual frame members.

Reliability of Rotational Behavior of Framing Connections

Recent studies have pointed to the behavior of beam-column connections as having an important effect on stiffness and strength of steel frames, and considerable work has been done to develop analysis methods intended to include not only member, but also connection behavior. Design methods as outlined in the AISC Allowable Stress5 and LRFD6 Specifications authorize inclusion of connection effects under the heading of "Type 3" in the former, and "Partially Restrained" (PR) in the latter. In both analysis and design including connection effects, connection behavior must be known. For typical beam-to column connections of building frames, voluminous, if fragmentary, data are available. Attempts at rational prediction of connection behavior have been less than successful, but empirical expressions, based on test data, of the relation between the applied moment M and the resulting connection rotation q are available. Among these, the most commonly used are those of Frye and Morris. The deterministic moment-rotation curves shown in Fig.1, and others similar, are often based on one single test, and do not account for the scatter which may inevitably be expected of connection behavior, specially if field-bolted. Little is available in the way of replicate tests which might provide a database necessary for statistical prediction of connection behavior. Until such information about reliability of connection behavior is provided, its inclusion in design or analysis rests, at best, on a shaky basis. This paper reports a study the aim of which is to provide a statistical database for the purpose of establishing the degree of reliability of strength and stiffness for one connection type. To this end, nominally identical framing connection specimens from different sources were tested under identical conditions. The individual moment-rotation curves obtained from these tests form the database for probabilistic determination of the reliability with which specified behavior of these connections can be expected.

Beam Design in PR Braced Steel Frames

Recent American and European Codes allow the actual behavior of joints to be taken into account in frame design. The AISC-LRFD specifications introduce the concept of partially restrained construction and state the basic design requirements. Eurocode 3 permits "semi-continuous" frames and specifies basic criteria for the analysis of this type of structure as well as for the classification and modeling of the moment-rotation of beam-to-column joints. This consistent development in Code recommendations recognizes, on the one hand, the significant influence joint response has on the overall frame performance; on the other hand, it reflects a state of knowledge which is now sufficient to enable practicing engineers to undertake the design of partially restrained frames at the required level of reliability. Studies of the stability of this form of framework were recently carried out, the main problems related to the analysis investigated, and design methods established. The most important aspect, as to practical purposes, is the capability of approximating the moment-rotation curve of the joint. Satisfactory prediction models were proposed in the past few years, covering the most popular connection forms. Research work is currently underway to set up more refined models as well as to extend their scope.

Connection Flexibility and Beam Design in Non-sway Frames

Attention is drawn to the fact that virtually all commonly used types of steelwork beam-to-column connections function as semirigid. Representation of this behavior is best achieved by means of the connections moment-rotation (M—f) curve. For the types of connection normally used in non-sway frames, where "simple framing" is customarily employed, this means true behavior differs from that assumed in design. Beam-end moments are produced, the magnitude of which depends upon the M—f characteristics of the particular connection types used. The implications of this for the design of beams in non-sway frames is discussed. Connection behavior is reviewed and the results of a series of tests on a variety of types, conducted under identical arrangements, used to illustrate the range of M—f behavior expected. Special tests incorporating fabrication induced imperfections have been included so as to assess the likely variability of M—f data. A series of ultimate strength analyses on laterally supported beams provided with various forms of end connection are reported. The results provide quantitative indications of the ability of end restraint to reduce deflections and to increase load carrying capacity. Some results from a preliminary study of laterally unsupported beams are also presented. These suggest proper allowance for end restraint, which in this case should include both in plane and out-of-plane components, will also lead to worthwhile economies.

Derived moment rotation curves for double framing angles

Tension and compression force-deformation data obtained from laboratory tests of angle segments are used to generate moment-rotation curves for bolted double framing angle connections. These force-deformation and moment-rotation curves are analytically described by a four parameter formula which provides the basis for the analytical connection model. This connection model consists of a rigid bar and nonlinear springs representing the angle segments in either tension or compression. Design curves giving the four parameters of the moment-rotation curves are generated. These parameters are primarily a function of the angle thickness, gage length of the angle legs in flexure and the number of bolts in the connection. Comparison of these derived moment-rotation curves are made with published results of full scale tests.