Plane Frame Structure Research Articles

A novel family of strain-based finite elements for the analysis of the material softening of planar frames

The article presents a novel strain-based finite element family for the analysis of material softening of planar frame structures. In our case, the softening zone is described by a discrete crack, which is considered as an ‘excluded’ finite element point, i.e., the deformation quantities in the crack are considered separately from the deformation quantities of the element. They are connected to the element only through kinematic quantities, used to describe the crack opening. The criterion for crack initiation is defined as the limit axial-bending resistance of the cross-section. The advantage of the presented model is that it is not necessary to define cracks or softening zones in advance and that the solution is mesh-independent in the sense that no further densification of the mesh is needed purely on account of capturing material softening. The accuracy and efficiency of the presented finite element family is illustrated by the example of a clamped–simply supported concrete beam and a portal concrete frame. The examples demonstrate that even with a minimum number of finite elements of suitable accuracy, sufficiently accurate results are obtained for normal engineering practice.

On optimization of lightweight planar frame structures: an evolving ground structure approach

On optimization of lightweight planar frame structures: an evolving ground structure approach

A numerical assembly technique for free vibration of plane frames using a shifted and deflated Newton method

A semi-analytic method, namely the Numerical Assembly Technique (NAT) is extended to compute natural frequencies of arbitrary planar frame structures. The frame structure is systematically defined by a set of nodes, beams, bearings, springs, and external loads and the corresponding boundary and interface conditions are formulated. We consider the Timoshenko-Ehrenfest beam theory and take axial, bending and shear deformations as well as linear and rotational inertia into account. Since we use the exact solutions of the governing differential equations in the NAT, the accuracy of the results is independent from the spatial discretization. However, the resulting eigenvalue problem is non-linear and requires a numerical algorithm to solve. We consider three different representations of exact homogeneous solutions and study the numerical stability of the resulting system matrix. To solve for the eigenvalues we propose a Newton method enhanced with a shifted deflation algorithm. The stability and the efficiency of this approach is illustrated in numerical examples.

Damage and Nonlinearity Effects on Stress Wave Propagation in Planar Frame Structures: A Machine Learning Classification Approach Based on Stress Wave Amplitude Solution

Damage and Nonlinearity Effects on Stress Wave Propagation in Planar Frame Structures: A Machine Learning Classification Approach Based on Stress Wave Amplitude Solution

Component-based models of beam-column joints exposed to fire in steel framed structures against progressive collapse

This paper is supplementary research following the previous experimental and numerical studies on the progressive collapse behaviors of beam-column substructures with different joint configurations under middle-column removal scenarios induced by fire. The component-based models (CBMs) of beam-column joints exposed to fire, which include the welded web-welded flange (WW) joint, as well as the bolted web-welded flange (BW) joint, were proposed based on refined FE models established in previous studies. Subsequently, the proposed CBMs with detailed spring arrangements and constitutive parameters were incorporated into the ABAQUS software to validate the collapse responses of beam-column joints obtained from both test results and refined solid FE models. A comparison investigation with experimental data indicates that the proposed CBMs can accurately reflect the nonlinear collapse behaviors of different fire-exposed beam-column joints with relatively high computational efficiency. Moreover, the validated CBMs are further incorporated into the collapse analysis of a multi-story planar steel framed structure exposed to fire, by compiling the VUSDFLD subroutine, to realize the component deletion process. The parameter effects of fire location, joint configurations, and loading ratios on collapse behaviors and force redistributions of framed structures exposed to fire were investigated. Based on analysis results, it is shown that the component failure temperature is quite sensitive to whether the specific joint configurations are considered in the analysis of fire-resistant progressive collapse in planar framed structures, which should be paid sufficient attention to in the performance evaluation of collapse resistance. For those planar framed structures with larger loading ratios, it is recommended to increase the section of the frame column or carry out fire protection to prevent the progressive collapse of the structure.

In-plane and out-of-plane vibration analysis of laminated composite frames with warping effects

This paper addresses the free vibration analysis of a general planar frame structure, consisting of an assembly of laminated composite beam members. A mathematical model is established for the beams by introducing a novel displacement field, which encompasses the influence of shear deformation, rotary inertia, material coupling, warping phenomenon, as well as in-plane and out-of-plane deformations. By incorporating these various factors, a comprehensive representation of the beam's behavior is achieved. The continuity equations for displacements and rotations of two adjacent members are formulated to derive the equations for the entire frame structure. The assembled equations are solved using the Finite Element Method (FEM). The numerical results obtained are compared with existing results in the literature and new results from 3D models in ANSYS. The present results for torsional modes are closer to the ANSYS results than the results of previous studies. An extensive analysis is performed to investigate the impact of various parameters, including stacking sequence, frame angle, relative frame length, and anisotropy ratios on the system response.

Random vibration of the point-driven portal and multi-bay planar frames

In this study, an analytical model is presented to determine the random response of point-driven portal and multi-bay planar frame structures. Coupling effects between bending and longitudinal deformations are taken into account, with the Timoshenko-Ehrenfest beam theory being applied to model the bending deformations. With the excitation taken as band-limited white noise, expressions are derived for the mean square displacements and velocities in terms of the autocorrelation and cross-correlation components. The influence of modal cross-correlations on the overall response is shown to be dependent on the number of bays. For a lightly damped single-bay frame, the natural frequencies are generally well separated and the modal cross-correlations are small. In this situation, the velocity response displays a near symmetric distribution about the center point of the frame. Moreover, narrow zones of intensified response begin emerging as the number of responding modes increases. For frames having two or more bays, the contribution of modal cross-correlations is larger due to the increased occurrence of clusters of natural frequencies. In such cases, modal cross-correlations introduce asymmetry into the overall response distribution of the frame. Additionally, the drive-point velocity of the multi-bay frame can be severely underestimated if modal cross-correlations are ignored. The study also investigates the influence of increased damping on the response characteristics.

Development of modular and reusable AI models for fast predicting fire behaviour of steel columns in structural systems

It is important to model the local failure of structural members as well as the global responses of a structural system when it is exposed to fire. The local failure of columns such as buckling requires high-resolution models, which could be not used for modelling a structural system for its computational cost. Inspired by the hybrid simulation technique, this paper aims to develop modular AI models as a first attempt to predict the local performance of a specific steel column exposed to fires and to enable the future communication with structural system model. Two kinds of machine learning methods namely artificial neural network (ANN) and support vector regression (SVR) are utilized to train AI models based on a large numerical dataset extended from a 3D detailed shell model of columns after validation against fire test results. The excellent prediction performance of AI models is shown regarding the mean squared error (MSE), mean absolute error (MAE), coefficient of the variation of the root mean square error (cvRMSE), variance accounting for (VAL) and coefficient of determination (R2). Moreover, the capability of AI models is demonstrated in predicting fire behaviour of columns in untrained steady heating and transient heating scenarios. A further demonstration is performed within a plane-frame structure simulated with a hybrid-scale model and considering standard fire heating on columns, which shows great potential of the AI models towards further implementation in hybrid simulation.

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

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.

An Unconditionally Stable Integration Method for Structural Nonlinear Dynamic Problems

This paper presents an unconditionally stable integration method, which introduces a linearly implicit algorithm featuring an explicit displacement expression. The technique that is being considered integrates one Newton iteration into the mean acceleration method. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The objective of this investigation was to assess the accuracy and consistency of the proposed approach in contrast to the Chang method and the CR method. This is achieved by analyzing the dynamic response of three distinct structures: a three-layer shear structure model outfitted with viscous dampers, a three-layer shear structure model featuring metal dampers, and an eight-story planar frame structure. Empirical evidence indicates that the algorithm in question exhibits a notable degree of precision and robustness when applied to nonlinear dynamic problem-solving.

Linearly Implicit Algorithm with Embedded Newton Iteration of Velocity and its Application in Nonlinear Dynamic Analysis of Structures

With the application of energy dissipation and damping techniques such as viscous dampers and viscoelastic dampers in seismic engineering, dynamic equilibrium equations of overall structures involve nonlinear damping force. Therefore, numerical integration methods with explicit velocity expressions are more favorable. Based on the average acceleration method, a novel linearly implicit algorithm with explicit expression of velocity is proposed in which once Newton iteration is embedded. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The nonlinear stability of the proposed algorithm is also examined using a single-degree-of-freedom shear-type structure. The dynamic response analysis of a three-storey shear structure model equipped with viscous dampers, a three-storey shear structure equipped with metal dampers, and an eight-storey planar frame structure, are carried to investigate the accuracy and stability of the proposed method with respect to the Chang method and the CR method. The results show that the proposed algorithm exhibits higher accuracy and finer stability for nonlinear dynamic problems.

A New Method for Analyzing Dynamic Characteristics of Generalized Planar Frame Structures Under Complex Conditions

This paper presents a novel method for analyzing the vibration characteristics of planar frame structure composed of straight beams with arbitrary shapes. The method is based on the first-order shear theory, which takes into account the shear deformation and cross-sectional rotational inertia of the beams. On the one hand, an improved Fourier series method (IFSM) is employed to approximate the displacement function of the straight beam, and the displacements are determined by using the Rayleigh–Ritz method. On the other hand, the displacements of the curved beam are obtained by using the finite element method (FEM), which are then combined with the IFSM for the analysis of coupled nodes of straight and curved beams. This results in a computational method for calculating the vibration characteristics of complex planar frame structures with concentrated masses, straight and curved beams, arbitrary boundary conditions, and any connection form of nodes. The applicability of the proposed method is demonstrated through numerical examples, including planar frame structure with arbitrary shapes composed of straight beams, different cross-sectional shapes, and combinations of beam with various cross-sectional shapes, as well as planar frame structures with straight and curved beams. The results of the proposed method are validated by comparing them with those obtained from literature or finite element software ABAQUS. The numerical examples show that the proposed method combining the IFSM with FEM has the advantages of high accuracy, good convergence, and strong applicability for calculating the vibration characteristics of planar frame structures.

Random vibrations of laminated planar frames

In this study, the normal mode method is used to determine the response of a generalized laminated planar frame structure subjected to random loading conditions. The model, which is based on the Timoshenko–Ehrenfest beam theory, accounts for the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy. The free vibration analysis of the frame is formulated and solved, and the orthogonality condition derived. Following this, the normal mode method is applied to determine expressions for the mean square longitudinal, transverse and rotational displacements in terms of the excitation spectral density. Although the proposed model is capable of analyzing a wide range of problems, the numerical analysis conducted in this paper is centered on investigating the response of inclined two-member and three-member frames excited by a point force, whose spectrum is band-limited white noise. It is shown that in cases where the modal cross-correlation is negligible and the boundary conditions are symmetric, the spatial response of the mean square displacements are nearly symmetric about the center point of the frame. Contrarily, as the influence of the modal cross-correlation on the overall response increases, the featured spatial symmetry vanishes. An interesting characteristic of frame structures, is that the spacing between the natural frequencies is dependent on the frame angle. Consequently, modal cross-correlations can have a much greater effect on certain frame angles compared to others, even when the damping is fairly low. The study also investigates the effects of bending-extension material coupling on the random response of asymmetrically laminated cross-ply frames. The numerical results presented in this work are verified with independent finite element simulations conducted in the software package, Ansys® Parametric Design Language (APDL).

The Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

AbstractThe Numerical Assembly Technique (NAT) is extended to investigate arbitrary planar frame structures with a focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and coupling conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this improvement by investigating the condition number of the system matrix and also by the use of variable precision arithmetic.

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.

UAV-based operational modal analysis method using improved homography-based perspective rectification method

In this paper, a new dynamic photogrammetry method using an unmanned aerial vehicle (UAV) is proposed and the UAV-based operational modal analysis method is established. The presented dynamic photogrammetry method can measure the dynamic displacements of structure using one or two cameras. However, it is difficult to use fixed cameras or handheld cameras to measure the dynamic responses for some outdoor structures, because it is hard to reach for measurement or maintenance sometimes. Therefore, UAV is an effective alternative and the homography-based perspective rectification method can be used to correct the UAV images. However, the presented methods use only four calibration points. Additionally, there is still obvious signal drift in the extracted dynamic responses. In this paper, a new time varying homography matrix, calculated using n calibration points, is proposed here for the first time to correct the perspective distortion for image at different time and the relative displacements are used to eliminate the influence of UAV in-plane motion. The influence analysis of UAV vibration and the method to eliminate the UAV vibration are the novelty of this paper. And then, the UAV-based operational modal analysis method is proposed. The proposed method is verified using a plane frame structure in laboratory. The results show that the proposed method can effectively eliminate the vibration of UAV and identify the structural modal parameters. Under the impulse excitation and white noise excitation, when the calibration points n is larger than 60, the relative errors of natural frequency and damping ratio are less than 0.4% and 5.45%, respectively. And the MAC values are all greater than 0.99. Meanwhile, the influence of the number of adopted calibration points on modal parameters identification is considered in the experiment and the advised value is given.

Hybrid Test of Precast Concrete Frame with Energy-Dissipation Cladding Panel System

To investigate the influence of an energy-dissipation cladding panel system (EDCPS) on the dynamic responses of a precast concrete (PC) frame structure, a six-story, three-span planar frame structure with an EDCPS (called “damping structure”) and a counterpart planar bare frame structure (called “bare frame structure”) were designed. The middle span and bottom two stories of the frame were selected as the test substructures, whereas the rest were considered using the numerical substructure. Hybrid tests were conducted on the two structures under four earthquake levels. The test results indicated that the damage evolution characteristics of the PC frame were not affected by the introduction of EDCPS. The dampers in the EDCPS successfully yielded and dissipated seismic energy under the four earthquake levels. Moreover, the maximum inter-story drift ratio of the damping structure was reduced by 12.59%, 17.68%, and 10.34% under the design-basis earthquake, maximum considered earthquake, and very rare earthquake, respectively, exhibiting a satisfactory damage-control effect. The cladding panels remained intact under the four earthquake levels, indicating that this structure effectively prevents damage to the cladding panels. Finally, a numerical simulation method is recommended according to the damage characteristics of the damping structure and is validated against the test data.

非線形オイルダンパーを有する平面骨組モデルのダンパー減衰性能のばらつきに対する地震時応答上限値の簡易評価法

A new uncertainty analysis method is developed for planar frame structure models equipped with oil dampers of linear and nonlinear force-velocity relationships. The structural analysis software SNAP® is collaborated with previously proposed uncertainty analysis method called NURP to obtain the maximum structural response when the damper characteristics are varied. In order to consider the uncertainties in the input, the critical double impulse is employed in addition to standard design ground motions, and we proposed the practical solution to use it in the structural analysis software. The validity of the proposed uncertainty method for frame structure models is investigated by comparing the result with maximum response derived by genetic algorithms. As a simplified method to evaluate the maximum value of the frame structure response, a method that uses a shear model equivalent to the frame structure model is also proposed.

Experimental investigation on reinforcing effects of engineered cementitious composites (ECC) on improving progressive collapse performance of planar frame structure

This paper experimentally investigates the progressive collapse performance of planar frame structure with engineered cementitious composites (ECC) under middle column removal scenario. One normal concrete specimen and two ECC specimens were used for experiments. Quasi-static vertical loading was imposed onto the middle column, and structural response was analyzed for the specimens with different concrete and reinforcement ratio. Furthermore, the impact of ECC on the behavior of planar frame structure to resist progressive collapse was evaluated. Experimental results indicated that ECC specimens exhibited multi-cracking behavior with limited crack width, and their progressive collapse performance including ductility, horizontal reaction, bending moment and rotation capacity of plastic hinge can be improved significantly in three stages of resisting mechanisms. The resistance force and energy absorption can be reinforced over several times in elastic stages while the reinforcing effects can not continue in compressive arch stage and catenary stage. The ultimate resistance in catenary stage is largely determined by the reinforcement ratio. Finally, the ECC is proved to be highly effective in reinforcing progressive collapse resistance, which provides a basic insight into the application of ECC building structure in engineering.