Plane Steel Frames Research Articles

Limit analysis of planar steel frames, in-element plastic-hinge for uniformly distributed loads

This work calculates the collapse load and collapse mechanism of 2D frames with slender structural members and uniformly distributed loads. The search for the collapse mechanism and the collapse load is carried out using step by step method: the load factor is increased and at each step the balance and compatibility equations must be satisfied that the value of the plastic moment is not exceeded in any section. It is verified that the results are different in the cases of point loads and uniform distributed loads, both from a qualitative and quantitative point of view.

Graph recurrent neural networks-integrated real-time prediction of key displacements for fire-induced collapse early warning of steel frames

This study proposes the FRAME-Net, which can extract spatial-temporal features of discrete structures like planar steel frames, for early warning systems of fire-induced building collapse. FRAME-Net, based on graph neural networks and recurrent neural networks, seamlessly integrates feature extraction techniques, advanced graph convolution operations, and an enhanced graph long short-term memory mechanism, resolving the critical issue that the actual state of burning buildings, e.g., fire scenario, load case, material properties, etc., cannot be identified accurately and rapidly. The temperatures of steel components and easy-to-measure displacements are inputs, and hard-to-measure displacements at the top and interior of steel frames under fire can be predicted in real time. Numerical examples indicate that the trained agent accurately predicts the hard-to-measure displacements for the trained steel frame under completely unknown datasets, showcasing its potential in real-world unknown fire scenarios. Besides, the trained intelligent agent can be directly applied to untrained steel frames with different topological forms without re-training, which significantly reduces computational costs and is beneficial for swift emergency responses. Subsequently, satisfactory results predicted by the trained agent without re-training for the steel frame under the real fire test further underscores the promising generalization capability of the trained agent to adapt to unknown fire scenarios in real-world steel frames. Finally, the feasibility of the proposed framework to facilitate the implementation of the early-warning systems of fire-induced collapse is proved by comparing the predicted and actual remaining building collapse time, thereby assisting in reducing casualties during the rescue process and contributing to smart firefighting advancements.

Thermomechanical responses of steel frames under aftershock after fires

A novel advanced fiber beam-column element, which incorporates stability functions and the fiber distributed plasticity model to capture geometric and material nonlinearities, respectively, has been successfully developed to predict the nonlinear inelastic thermo-mechanical behaviors of steel frames subjected to aftershock after fires. To address the nonlinear dynamic problems resulting from aftershocks after fires, a sequential nonlinear thermal incremental-iterative solution scheme has been developed, which is based on the Newton-Raphson algorithm and Newmark-β method. In addition, a transcendental probability-based method is employed to express the statistical characteristics of aftershock intensity relative to the mainshock. The proposed method is applied to analyze three framed structures: a steel portal frame, a two-story plane steel frame, and a four-story asymmetric space steel frame. This analysis shows the accuracy, computational performance, and applicability of the proposed method. Remarkably, the results obtained from the code work, using just one or two elements per member, are in close agreement with all the results analyzed by Abaqus. This emphasizes that the proposed method effectively predicts the response of framed structures under aftershock after fires with excellent computational efficiency, significantly surpassing traditional finite element approaches in commercial software like Abaqus. The successful results of the dynamic analysis of the frames under aftershocks following fires underscore the importance of considering aftershocks after a fire incident. It is demonstrated that the occurrence of an aftershock accelerates the failure of the frame compared to the case when the frame is subjected to fire alone. This highlights the critical need to account for aftershocks when assessing the safety and structural integrity of framed structures after a fire event.

Collapse modes and mechanisms of planar multi-story large-span steel frames under fire

This paper investigates the collapse modes and mechanisms for planar multi-story large-span steel frames exposed to fire. Based on a systematic parametric analysis conducted with a wide range of parameters, including structural topological forms, fire scenarios, component sizes, load cases, fire protection levels, section temperature gradients, and wind loads. Eight potential collapse modes are identified: general inward collapse, rebalancing collapse, partial lateral collapse, heated large-span beam-induced inward collapse, restraint failure-induced collapse, overall downward collapse, unheated large-span beam-induced inward collapse, and overall lateral collapse. Simultaneously, by combining typical fire cases, corresponding structural collapse mechanisms are explored to reveal the differences in the failure sequence of locally heated components and the final structural collapse extent for different collapse modes. Furthermore, this study also analyzes the evolution laws of key horizontal and vertical displacements and velocities within the fire area for various modes, highlighting distinctions resulting from diverse collapse mechanisms. Finally, a detailed summary of various collapse modes is provided, involving reasons for inducing structural local collapse, the final extent of progressive collapse, possible areas of occurrence, and potential mode transitions as parameters change.

An inelastic beam-like model for nonlinear dynamic analyses of multi-storey buildings

This paper presents an equivalent non-uniform inelastic beam-like model for the evaluation of the nonlinear behaviour of multi-storey buildings subjected to earthquake loadings. The proposed beam can be used to model buildings with non-uniform mass and stiffness distribution. The model is characterised by a number of degrees of freedom corresponding to the number of floors of the building and is conceived to predict its nonlinear dynamic response after a proper calibration based on the results of pushover analyses performed on a nonlinear FEM model. In spite of its simplicity, the proposed equivalent model provides, with a very low computational effort, an accurate representation of the nonlinear dynamic behaviour of the building comparable to that obtained through the more demanding nonlinear 3D FEM models. The effectiveness of the proposed simplified modelling approach is here validated by means of nonlinear dynamic analyses firstly performed on a benchmark known in the literature as SAC9 building, modelled as a plane steel frame structure and secondly on a three-dimensional reinforced concrete structure, designed according to old standard structural design rules. The very good agreement with the results obtained through accurate 3D FEM frame modelling, for different earthquake loadings, on the considered benchmarks provides a first validation of the proposed inelastic equivalent beam-like model and suggests its potential use for the seismic assessment of building structures. The low computational cost related to the beam-like model could be particularly advantageous for all the seismic vulnerability approaches requiring several nonlinear dynamic analyses, as those related to large scale applications, or those expressed in terms of probability of failure generally expressed in terms of fragility curves.

Limit analysis of planar steel frames with variable section type and arbitrary loads

This work calculates the collapse load factor and the collapse mechanism of 2D frames with slender structural members of variable section type and arbitrary distributed loads. A Kinematic Direct Method (KDM) is used for calculations. The equilibrium equations necessary to carry out the analysis are obtained systematically. The search for the collapse mechanism and the collapse load factor is carried out using an optimization method where the load factor is maximized. The following types of load are used: uniformly distributed loads, trapezoidal and sinusoidal distributed loads.

Prevention of brittle failure for steel connections utilizing special devices

The present paper proposes the use of a special design procedure devoted to the prevention of brittle failure for welded steel connections. In particular, reference is made to steel frame structures made up of beam elements with I-shaped cross-sections where the connections between columns and beams are usually welded and/or bolted. The proposed new design procedure consists of four subsequent analysis steps; it is based on the identification and analytical definition of new appropriate brittle safe domains defined in the N,V,M space and on the use of suitably designed devices (LRPD), recently proposed by the authors, belonging to the class of the RBS connections. The latter are able to impose prefixed values of internal forces on selected beam element cross-sections, avoiding any modification of the elastic stiffness features of the involved beam. The main novelties of the present study consist in the introduction of new brittle safe domains for I-shaped cross-sections, in the specialization of the LRPD optimal design to the present context and in the definition of a special design strategy which allows to contextually obtain structures safe from the risk of brittle failure as well as being able to dissipate an appropriate amount of plastic strain energy. The numerical application, devoted to plane steel frames, confirms the sound reliability of the procedure and the great flexibility of the utilized LRPDs.

Seismic Performance Analysis of Semi-rigid Steel Frame Based on Panel Zone Mechanical Characteristics of the Joint Experiment Study

The panel zone, as an important part of the semi-rigid connection (SRC), can effectively affect the force transfer mechanism of the connection. This study aims to evaluate the panel zone mechanical characteristics through test on end-plate connection (EPC) and T-stub connection (TSC) under cyclic loading. Based on failure criteria, the mechanical properties of the panel zone are discussed, including the shear force, plastic energy dissipation, and failure modes. In light of the test studies, an effective and accurate numerical method in OpenSees platform for SRC with a behavior monitored by nonlinear rational springs is proposed. A 4 × 6 plane steel frame with SRC under the loading stimulation of 12 ground motions is conducted to testify the reliability of the model and analyze the panel zone behavior on the frame. The panel zones exhibit stable hysteresis characteristics and excellent ductility, and the analysis results of the effect of stiffness ratio between bolted connections and panel zone on frame energy consumption provide suggestions for structural energy dissipation design. The model conducts an accurate prediction of semi-rigid connection steel frames (SRCSFs) seismic behaviors considering the panel zone mechanical properties, and it can dramatically improve computing efficiency and is conducive to seismic design.

Strain Energy and Entropy Based Scaling of Buckling Modes.

A new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

Collapse performance of post-tensioned steel frames considering influence of infill walls

The aim of this paper is to study the effect of infill walls on load resisting behaviors of post-tensioned (PT) steel frames against collapse. Three planar PT steel frames are simulated using finite element (FE) method, one of which has no infill wall while the other two are installed with infill walls. The applied loads, lateral displacements, failure patterns, stress developments in infill walls, resisting mechanisms, as well as re-centering capabilities of three PT steel frames are studied and the role that infill walls play is discussed. Parametric analyses are conducted to investigate influences of magnitude of PT forces and critical material properties. Results indicate that infill walls work as compressive struts, significantly increasing initial stiffness, resistance and story drifts of PT steel frames, and play as energy dissipation devices during the collapse process. The existence of opening makes the stiffness distributed discontinuously throughout infill walls, greatly changing the failure pattern and increasing story drifts of PT frames. The resistances of infilled PT steel frames increase with increasing PT forces, bed joints strength and masonry unit strength in the initial stage. A design scheme is also developed to precisely predict the collapse resistance of infilled PT steel frame structures.

A convolutional neural network-based architecture for health monitoring of joint damages in a steel plane frame structure under temperature variability

A convolutional neural network-based architecture for health monitoring of joint damages in a steel plane frame structure under temperature variability

Modelling Initial Geometric Imperfections of Steel Plane Frames Using Entropy and Eigenmodes

The article introduces an innovative approach to modelling initial geometric imperfections in steel plane frames. Initial imperfections are introduced using the analysis of normalised deformations of elastic buckling modes. The scale of these modes is assessed by applying Shannon entropy and potential energy analysis. The presented case study demonstrates a decreasing scale of the elastic buckling modes. The entropy computed from the deformation reveals a new perspective on buckling modes and provides a more profound understanding of steel frame behaviour. The case study results indicate that anti-symmetric buckling modes exhibit higher entropy than symmetric buckling modes. This entropy-based analysis enables the differentiation between symmetric and anti-symmetric buckling modes, which is particularly valuable when the critical buckling loads of sway and non-sway buckling modes are closely aligned or overlap.

Stability Calculation of the Plane Steel Frame Structures Using Tangent Modulus Theory

This paper considers the phenomenon of the instability of steel plane frame structures in the elastic–plastic domain. The numerical analysis uses finite element method, where the corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. The tangent modulus concept is applied when buckling occurs in the plastic range. Thus, the stiffness matrices for nonlinear material behavior are also derived. The procedure for determining effective length factors of compressed columns, which implies a global stability analysis of entire frames, is established too. It means that the proposed approach is based on the assumption that the collapse of the structure occurs when the most loaded columns reach their stability limit. So, the presented procedure enables the calculation of the real critical load of plane frame structures in the elastic–plastic domain and determines the corresponding effective length factors.

Numerical formulation for advanced non-linear static analysis of semi-rigid planar steel frames

Numerical formulation for advanced non-linear static analysis of semi-rigid planar steel frames

Optimal Design of Planar Steel Frames Using the Hybrid Teaching–Learning and Charged System Search Algorithm

In this study, a novel effective algorithm called HTC which results from a hybridization process between the teaching–learning-based optimization (TLBO) and charged system search (CSS) algorithms is proposed and utilized to optimize planar steel frames. Among the features of the proposed algorithm, simplicity and low number of setting parameters can be mentioned. The main goals of this hybridization process are to establish a balance between exploration and exploitation, increase the rate of convergence, and avoid getting trapped in the local optimal point. Moreover, the purpose of optimizing steel frames is to calculate their minimum weight by choosing suitable sections as well as considering the stress and displacement constraints in accordance with the requirements of the AISC design regulations using the load and resistance factor design (LRFD) method. To evaluate the performance of the HTC algorithm, standard benchmark steel frames are examined, and the results of the proposed algorithm are compared with other metaheuristic optimization methods. According to the outcomes of the comparison, the proposed algorithm has better performance than the other methods.

Vibration data‐driven machine learning architecture for structural health monitoring of steel frame structures

AbstractA vibration data‐based machine learning architecture is designed for structural health monitoring (SHM) of a steel plane frame structure. This architecture uses a Bag‐of‐Features algorithm that extracts the speeded‐up robust features (SURF) from the time‐frequency scalogram images of the registered vibration data. The discriminative image features are then quantised to a visual vocabulary using K‐means clustering. Finally, a support vector machine (SVM) is trained to distinguish the undamaged and multiple damage cases of the frame structure based on the discriminative features. The potential of the machine learning architecture is tested for an unseen dataset that was not used in training as well as with some datasets from entirely new damages close to existing (i.e., trained) damage classes. The results are then compared with those obtained using three other combinations of features and learning algorithms—(i) histogram of oriented gradients (HOG) feature with SVM, (ii) SURF feature with k‐nearest neighbours (KNN) and (iii) HOG feature with KNN. In order to examine the robustness of the approach, the study is further extended by considering environmental variabilities along with the localisation and quantification of damage. The experimental results show that the machine learning architecture can effectively classify the undamaged and different joint damage classes with high testing accuracy that indicates its SHM potential for such frame structures.

Finite element-based analysis of optimally designed steel plane frames

Finite element-based analysis of optimally designed steel plane frames

Influence of soil-structure interaction modeling on the behavior of multi-story plane steel frames with shallow footing foundations

Traditionally, structural analysis is based on the hypothesis that supports are indeslocable due to simplicity. However, the conventional design in which settlements of foundation elements are disregarded can lead to physical results that are incompatible with reality. This work aims to analyze the influence of the consideration of soil-structure interaction (SSI) on the responses of steel structural elements obtained by a static second order analysis. Furthermore, it is evaluated the responses obtained by different types of procedures for the consideration of soil stiffness in the structural analysis. Solid elements considering linearly elastic material parameters and spring elements based on the Winkler theory are employed. The analyses were performed with the commercial software SAP2000. Plane steel frames models were analyzed, either considering conventional supports or taking into account the soil-structure interaction. Shallow footing foundations are considered. Three frames with the same characteristics, but with a different number of floors were analyzed, showing the influence of the height increase and the building stiffness on the SSI results. It has been shown that the consideration of the effects of soil-structure interaction on structural analysis of buildings can have a significant influence on the stress distribution, displacements and structural behavior. In addition, it is concluded that the structural capacity of steel frames can be affected by the type of support adopted and by changes on the way the model considers soil deformation.

Finite element model for advanced analysis of plane steel frames with hinged end conditions including von Mises criterion

Traditionally, the design of steel structures is carried out in two steps: first, the structural analysis is performed, and then the cross-sections and structural members are checked individually. In contrast, in the advanced analysis, the effects related to global (P-Δ) and local (P-δ) instabilities and to the degradation of material stiffness are incorporated; therefore, there is no need to verify the resistance capacity of the structural members separately, which allows a better use of the load capacity of the structural system. Generally, research developed in this area of study is based on the classical Euler-Bernoulli theory; however, in the case of short elements, an analysis that includes the shear effects and the interaction between normal and shear stresses on cross-section yielding becomes necessary. Thus, this work aims to study the behavior of plane steel frames considering the influence of shear deformations by using advanced analysis. A geometrically exact formulation for analysis of rigid-hinged and hinged-rigid elements is presented. The proposed numerical methodology is implemented in finite element software and takes into account Timoshenko’s kinematic hypothesis, the distributed plasticity approach, residual stresses, and second-order effects. To assess the plastification state of the structural elements, the von Mises yield criterion is applied. From numerical examples available in the literature, the efficiency of the software in predicting the nonlinear behavior of steel frames is assessed. It is concluded that for short beams, the adoption of the von Mises criterion during the analysis leads to lower load capacities, compared to the results obtained considering only the normal stresses in the evaluation of the plastification state of the cross-sections.

Shaking table test on seismic response of a planar irregular structure with differential settlements of foundation

The differential settlement of the foundation not only causes the degradation of the static performance of structures, but also affects the seismic performance. To investigate the seismic response of a planar irregular steel frame structure under differential settlement of foundation, we proposed a method to mimic multi-point differential settlement of foundations of scaled models steel frame structures. Four columns in the settlement location are adjusted downward to the set settlement distance, and then, the columns are fixed with nuts to achieve the effect of settlement in one location. Then a shaking table test was carried out on a scaled-down building model to analyze the dynamic responses of the structure. Eight seismic waves and three ground shaking intensities were set to represent frequent, moderate, and rare earthquakes. The seismic response, location changes, and torsion of the irregular planar structure were analyzed via shaking table tests under different seismic waves with frequent, moderate, and rare earthquake excitation, as well as changing parameters such as settlement location and settlement depth. The results show that compared with other locations, when a differential settlement of the foundation occurs in the corner location of the structure plane, the structure is more likely to be torsional and more prone to seismic damage. For the same seismic intensity and settlement depth, the settlement location at the corner of the structure face exhibited the greatest seismic response to the structure. In contrast, the settlement located near the center of the structure face had the least effect on the seismic response of the structure. The proposed method enables a fast and efficient way to understand the dynamic response of the structures with differential settlement of foundations, which will further benefit the development and optimization of the seismic strengthening scheme for these structures.