Nonlinear Frame Analysis Research Articles

Simplified Modeling of Unstiffened End-plate Connections in Nonlinear Analysis of Steel Frames at Elevated Temperatures

Simplified Modeling of Unstiffened End-plate Connections in Nonlinear Analysis of Steel Frames at Elevated Temperatures

The α-generalized implicit method associated with Potra–Pták iteration for solving non-linear dynamic problems

Generally, direct time integration procedures are used for solving the equations of motion in transient analysis of structures with large displacements. In this context, we propose an algorithm that combines the α-Generalized implicit integration method with the Potra–Pták two-step iterative scheme. The free Scilab program develops a computer code for the non-linear dynamic analysis of plane frames with large displacements and rotations. The FEM corotational formulation discretizes the structures considering the Euler-Bernoulli beam theory. The null-length connection element described by the axial, translational and rotational stiffnesses simulate the behavior of the beam-column connection. Jacobi’s method and the Scilab’s spec function determine the natural frequencies. The developed program is used for modal and transient dynamic analyses of frame problems available in the literature. The numerical results show that the Potra-Pták scheme obtains approximate solutions with fewer cumulative iterations until convergence and shorter processing time compared to the standard Newton-Raphson scheme. Further-more, the results show that the type of beam-column connection affects the vibratory behavior of the structure as well as the values of its natural frequencies.

Nonlinear finite element analysis of steel moment-resisting frames with shear fuse under seismic loading

Nonlinear finite element analysis of steel moment-resisting frames with shear fuse under seismic loading

Non-linear Finite Element Analysis and Performance Evaluations of Frames Strengthened by Non-uniform Concrete Brace Facade

Non-linear Finite Element Analysis and Performance Evaluations of Frames Strengthened by Non-uniform Concrete Brace Facade

Nonlinear analysis of plane frames considering hyperelastic models through the finite element positional method

Nonlinear analysis of plane frames considering hyperelastic models through the finite element positional method

Mechanical Properties of Window Frames Exposed to High Temperature (II)

This study compares the dropout time obtained through a thermal analysis program with the results of a real experiment to estimate the time when a window in contact with outside air is dropped because of a fire in the compartment space. Nonlinear analysis of PVC and Al6063-T5 window frames on glass with a fire resistance of 1 h showed that the maximum strain over time was approximately 11.04% for the PVC frames and 9.55% for the Al6063-T5 frames. By comparing this over time, it was calculated that the front end occurred at approximately 750 s for the PVC frame and at 1,710 s for the Al6063-T5 frame. Existing real-world experiments show that the frame was deformed by melting and harmful penetration at approximately 540 s for PVC and 1,560 s for Al6063-T5; similar results are expected if the experiment is conducted until the window completely collapses.

A multi-strut model for the hysteresis behavior and strength assessment of masonry-infilled steel frames with openings under in-plane lateral loading

The analysis of masonry-infilled frames (MIFs) with openings is a complex problem in structural engineering. Previous studies have shown that when an infill panel has an opening, it behaves as four separate subpanels around the opening. Therefore, it can be conceived that a perforated masonry infill panel behaves as four inclined compression-only equivalent struts in each direction. This paper presents a multi-strut model (MSM) using the equivalent strut concept for the nonlinear analysis of masonry-infilled steel frames (MISFs) with openings. The MSM consists of two inelastic side pier struts connected to the surrounding frame joints using rigid trusses representing the subpanels above and below the opening. The model incorporates an envelope curve and a hysteretic law to define the initial stiffness, peak strength, and post-peak strength behavior of the inclined struts under reversal loads. The MSM was used to analyze the lateral load behavior of tested MISFs with openings found in the literature. It was shown that the proposed model is efficient and can predict the stiffness and capacity of MISFs with openings under both monotonic and cyclic lateral loadings.

Numerical-Computational Model for Dynamic Nonlinear Analysis of Frames With Semi-Rigid Connection Considering the Damping Effect

Objective: the scope of this work is to present a numerical-computational model for transient dynamic nonlinear analysis of frames with geometric nonlinearity and semi-rigid connection. Methodology: the equation of motion, which describes the structural dynamical system, is solved by the a-Generalized direct integration method associated with the standard Newton-Raphson method. The structures are discretized through the co-rotational formulation of the Finite Element Method considering the Euler-Bernoulli beam theory. The semi-rigid connection of structural members (beam-column and beam-support) is simulated by a connection element with zero length, which is described in terms of axial, translational and rotational stiffness. Results and conclusion: From the numerical results of three structural systems (bi-fixed beam, L-shaped frame, and single-story frame) obtained with the free Scilab program, it is concluded that the definition of the type of connection is an important factor to be considered in the analysis of frames subjected to dynamic loads. Furthermore, structural damping, which is a measure of energy dissipation, drives the structure from a vibrating state to a resting state. Research implications: Structural Engineering has been designing systems that cannot be analyzed and dimensioned without dynamic effects being considered. lack of knowledge of the levels and characteristics of the dynamic response can lead to system failure during the application of repetitive loading due to accumulation of structural damage. In this sense, the numerical model can represent a valuable engineering tool when it comes to the dynamic analysis of plane metallic structures with geometric nonlinearity.

Nonlinear inelastic analysis of space semi-rigid steel frames subjected to static load using plastic-zone method

A new hybrid element based on plastic-zone method is proposed for static nonlinear analysis of space semi-rigid steel frames. Four zero-length nonlinear rotational springs are added to the beam ends to model both in- and out-of-plane connection rotational behavior with appropriate semi-rigid connection models. The von Mises yield criteria are applied to govern material plasticity along the member length and throughout the cross-section using Newton–Cotes integration points. The modified generalized displacement control method is used to solve the system of nonlinear equilibrium equations. Some numerical examples are investigated to show the reliability and visual illustration of the proposed hybrid element.

Seismic Response and Recentering Behavior of Reinforced Concrete Frames: A Parametric Study

The inelastic response of reinforced concrete (RC) frames under seismic loading is influenced by mechanical and geometrical properties and by the reinforcement arrangement of the beam–column members. In this paper, the seismic response and recentering behavior of RC frames is investigated numerically via cyclic pushover analysis and described by means of three synthetic behavioral indexes, namely a recentering index, a hardening index, and a ductility index. A fiber–hinge formulation is used to describe the inelastic behavior of the RC elements, and the versatile pivot hysteresis model is implemented at the material level to capture the possible pinching effects ascribed to the weak transverse reinforcement and to poor construction details that might be observed in the existing RC structures. This model is first validated against the experimental results from the literature and then applied, within a wide parametric study, to a set of 80 RC frame scenarios featured by various combinations of axial load levels and reinforcing details. As the output of this parametric study, practical design abacuses are constructed to describe the trends of the above-mentioned behavioral indexes, which are usefully related to specific mechanical and loading features of the analyzed RC frames. The reliability of the obtained results and the usefulness of the constructed abacuses in anticipating the overall cyclic behavior of a generic RC building, depending on the actual mechanical parameters of the RC sections at each story level, is finally demonstrated through a nonlinear time history analysis of an eight-story RC frame, representative of the substandard RC frames built in the 1970s in Italy.

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

An effective geometric nonlinear analysis approach of framed structures with local material nonlinearities based on the reduced-order Newton-Raphson method

The P-Δ effect is essential to be considered in the quasi-static pushover or horizontal seismic analysis of high-rise framed structures. Owing to the presence of the P-Δ effect, however, the geometric stiffness varies with the members’ internal variables (such as axial force and relative lateral displacement). Using a conventional nonlinear analytical process, each iteration has to update the structural effective stiffness even though the material remains elastic. Consequently, it requires a tremendous amount of computational effort in the material and geometric (double) nonlinear analysis of large-scale frames. To alleviate this disadvantage, this study presents an efficient and accurate nonlinear analysis approach for the high-rise framed structure considering the P-Δ effect. Assuming an invariant (time-independent) vertical load of each storey after the gravity analysis, the structural geometric stiffness induced by the P-Δ effect is then constant. Accordingly, the conventional double nonlinear system could be converted into an equivalent material nonlinear one whose effective stiffness contains material and geometric components. After that, a reduced-order Newton-Raphson method is employed to simplify the iterative analysis of the global system into that of a reduced subsystem comprised by yielding elements. Four application cases demonstrated the accuracy and reliability of the presented geometric nonlinear analysis approach. Predictably, the presented strategy will considerably improve the efficiency of double nonlinear analysis of the tall framed structure with local material nonlinearities.

An Adaptive Section Discretization Scheme for the Nonlinear Dynamic Analysis of Steel Frames

The paper presents an adaptive section discretization scheme for the inelastic response analysis of structural members with cross sections that can be decomposed into rectangular and circular subdomains. Each subdomain can consist of a different material. As long as the largest strain in a subdomain does not exceed the specified trigger strain values, the subdomain contribution to the section response is determined by the numerically exact cubature rule for the subdomain. Once the largest strain reaches the trigger value for a subdomain, it is discretized with a fiber mesh and the numerical evaluation of its contribution to the section response is determined with the midpoint integration rule. The fiber mesh with the midpoint integration rule remains in effect for the activated subdomain until the end of the response history. The paper applies the adaptive discretization scheme to the thin-walled sections common in metallic structures and investigates the effect of different trigger strain values on the accuracy and computational efficiency of the inelastic response analysis of wide-flange steel sections and multistory steel frames under static and dynamic excitations.

Comparative Nonlinear Analysis of Composite Frames with Concrete Filled Steel Tube Columns Having Different Properties

In this study, the nonlinear analysis and seismic appraisal of composite frames having concrete filled steel tube columns (CFSTs) were investigated. The case study composite frames were made of the square columns surrounded by steel tube outside and infilled with concrete, and also steel I beams. These frames were taken as 4, 6 and 8 stories with three equal bays. Then, the nonlinear pushover analysis was applied to examine the influence of variation in the width-thickness ratio, slenderness ratio, yield strength of the steel tube and compressive strength of the concrete within the columns of each frame. Thus, a total of seventy-two different composite frame models with CFST columns and steel beams were examined in accordance with the response parameter of the base shear-top displacement. The obtained results were discussed comparatively as per the lateral capacity and initial stiffness. It was observed that the material and dimensional properties of the CFST columns influenced significantly the seismic behavior of the composite frames.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

An advanced computational method for nonlinear inelastic thermo-mechanical analysis of spatial steel frames in fires

A novel advanced computational method incorporating the stability functions and the distributed plasticity model into the fiber beam-column element is proposed for the first time to predict the nonlinear inelastic thermo-mechanical behavior of spatial steel frames in fires. The space spread of plasticity is captured by tracing the uniaxial temperature-stress–strain relation of each fiber on sections at integration points. The element stiffness matrix is integrated via the Gauss-Lobatto numerical integration scheme. The nonlinear material behavior is captured by adopting the distributed plasticity model with the force-based interpolation function whereas the geometric nonlinearity of P-δ and P-Δ effects are considered by using the stability functions and a geometric matrix, respectively. The shear deformation and residual stresses which normally exist in steel frames are also considered. For the implementation, a nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson and Gaussian Elimination algorithm is also developed to address the nonlinear problems due to thermal expansion and material degradation. By taking advantage of the computational benefits of stability functions and the force-based interpolation function, the proposed method offers a novel computational framework for nonlinear structural analysis in a fire with excellent computational efficiency. The reliability and accuracy of the proposed program are verified by comparing the obtained results with results from test data, existing studies, and Abaqus. In addition, the computational performance of the proposed numerical program is about 10 times more effective than the Abaqus commercial software, thus would offer an extremely valuable tool for practical fire resistance designs.

Modeling methods and constitutive laws for nonlinear analysis of steel moment-resisting frames

This article presents several methods to model beams, columns, and panel zones of steel moment-resisting frames that incorporate force interaction, deterioration, and plasticity distribution. The methods combine the element classes and material types that exist in almost all structural analysis software packages. After introducing the element assemblies and the related constitutive laws, their accuracy is verified against several component experiments and a shake table test. Supplementary finite element analyses are included for panel zones to clarify their key behavioral parameters. The results showed the efficiency of the Fiber section And Spring Element (FASE) modeling method in capturing the actual response of bare beams and the columns resisting moderate-constant axial forces. In the case of composite beams, it adequately considered their asymmetric behavior when resisting positive and negative moments. The Fiber section And Truss Element (FATE) modeling method, developed for columns with high-variational axial forces, captured the axial force-bending moment interaction and the column axial shortening reported in past experiments. The proposed model for the panel zone accounted for all the shear and bending moment interaction, web shortening, and participation of flanges affecting its stiffness and strength. Ultimately, the integrity and accuracy of the proposed modeling methods in nonlinear time history analyses were verified by simulating a shake table test.

A Comparison of Formulations and Approximations for the Nonlinear Analysis of Steel Frames under Thermal Loading

The analysis of building frames under thermal loading is an important task in structural engineering. Linear analysis is generally inadequate for large temperature changes, and nonlinear analysis is essential to correctly model the behavior of the structure. Various nonlinear models are used in practice and these models usually involve some form of approximation of the nonlinear effects. In this case, it is not often clear what effects the approximations have on the analysis. This paper discusses a general approach for the nonlinear analysis of steel frames under thermal loading. In particular, we consider the role of approximations in the governing equations of the structure and the effects of the changes in material properties at high temperatures. Several examples are given in the paper that demonstrate the various effects of the approximations and assumptions on the results.

Nonlinear static analysis of cold-formed steel frame with rigid connections

Cold-formed steel (CFS) has become widely popular in mid and low-rise housing owing to efficient construction practice, technical, structural, and economic advantages over conventional structural materials. However, these sections are still not presented in seismic region because of their lack of understanding in seismic response. To address this problem, CFS frames used in residential building were analysed for lateral load capabilities. A finite element analysis of cold-formed steel frames (CFSF) with rigid connections was presented in this research. 72 types of CFS frames made from developed upright sections were simulated for nonlinear static behaviour using a commercial package. A geometrical parametric study on lateral load capabilities with respect to maximum permitted lateral deflection was presented. The performance of frames for lateral load was found to be improved significantly by increasing the thickness of uprights and provision of channel stiffeners.

Investigation of the effect of real ground motion record number on seismic response of regular and vertically irregular RC frames

Nonlinear time history analysis is an analytical method generally used in performance-based seismic design. With this method, seismic responses are obtained more realistically. Selection of ground motion records for nonlinear time history analysis is an important step since it strongly affects the analysis results. Therefore, it has always been a matter of curiosity to investigate the effect of the characteristics, content and number of the records on the analysis results. In this study, seismic responses of regular and irregular RC frames were investigated by varying the number of real ground motion records in a set. For this purpose, 13 different groups that contain three to hundred real ground motion records in size in a set have been considered and ten different earthquake record sets are obtained for each group. Ground motion selection procedure of Eurocode-8 was considered and a total of 130 sets were used for nonlinear response analysis of RC frames. Global drift ratio, maximum floor acceleration, inter-story drift ratio and six different intensity measures (IMs) were used to investigate the effect of the number of records. According to analysis results, nonlinear responses of RC frames are more stable and might be sufficient when the number of real records in a set is higher than seven according to Eurocode-8. Results indicate that if the number of real records in a set are lower than seven, conservative seismic responses can be found since the maximum rather than mean response values are used. It is observed that dispersion of seismic demands and mean to median ratios can be increased if the number of real records in a set is higher than ten. In addition, the correlation between some of IMs and seismic demands increase when the number of records in a set increased from three to seven and it remains stable from seven to hundred records. Furthermore, 7, 8, 15 and 22 records show the lowest error terms of considered engineering demand parameters for regular and irregular RC frames.