Investigation on the influence of point loads on the deflection behaviour of G+5 frame structure

Abstract Nowadays, multi-storey structure portal frames are most commonly used worldwide. Multistory frames are used in structural systems in all metropolitan cities, future cities, and important businesses. The present study the effect of various point loads varying from 22 to 32 kN in steps of 2 were applied on the center of horizontal beams of the frame structure. The deflection behaviour in form of deflection, reaction, beading moments under point loading were discussed analytically according to stiffness matrix method and the results are validated with the help of simulation using STAAD Pro software. Results revealed that the analytical method using manual calculations in excel sheet provides approximately similar results as obtained by the costly simulation technique using STAAD Pro software. Therefore, the implementation of this excel sheet can be recommended for standard analysis of portal frame structures based on the outcomes of this study.

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Static Elastic-Plastic Analysis of a Pipe Structure by the Transfer Matrix Method

Journal of Pressure Vessel Technology ◽

10.1115/1.4047680 ◽

2020 ◽

Vol 143 (1) ◽

Author(s):

Masayuki Arai ◽

Shoichi Kuroda ◽

Kiyohiro Ito

Keyword(s):

Transfer Matrix ◽

Transfer Matrix Method ◽

Stiffness Matrix ◽

Matrix Method ◽

Frame Structure ◽

Pipe System ◽

Curved Pipe ◽

Elastic Plastic ◽

Complex Problems ◽

Element Method

Abstract Pipe systems have been widely used in industrial plants such as power stations. In these systems, the displacement and stress distributions often need to be predicted. Analytical and numerical methods, such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM), are typically adopted to predict these distributions. The analytical methods, which can only be applied to problems with simple geometries and boundary conditions, are based on the Timoshenko beam theory. Both FEM and BEM can be applied to more complex problems, although this usually requires a stiffness matrix with a large number of degrees-of-freedom. In FSM, although the structure is modeled by a beam element, the stiffness matrix still becomes large; furthermore, the matrix size needed in FEM and BEM is also large. In this study, the transfer matrix method, which is simply referred to as TMM, is studied to effectively solve complex problems, such as a pipe structure under a small size stiffness matrix. The fundamental formula is extended to a static elastic-plastic problem. The efficiency and simplicity of this method in solving a space-curved pipe system that involves an elbow are demonstrated. The results are compared with those obtained by FEM to verify the performance of the method.

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Modeling, Analyses, and Optimization of Planar Active Frame Structures Composed of Piezoelectric Beams

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455419501463 ◽

2019 ◽

Vol 19 (12) ◽

pp. 1950146 ◽

Cited By ~ 1

Author(s):

Ke Wu ◽

Houfei Fang ◽

Bingen Yang

Keyword(s):

Vibration Control ◽

Stiffness Matrix ◽

Shape Control ◽

Frame Structure ◽

Distributed Model ◽

Frame Structures ◽

Transverse Shear Strain ◽

Governing Equations ◽

Element Stiffness Matrix ◽

Ant Lion

Frame structures are widely used in engineering applications, especially in space structures. For special use such as shape and vibration control of such structures, piezoelectric patches are usually placed on the beam surfaces to form active frame structures. To perform shape control or vibration control tasks, modeling methods for the formed active frame structures need to be studied. This paper develops a new distributed model of an active frame structure composed of multilayer piezoelectric beam components. First, the governing equations of a beam, bonded with piezoelectric patches, are developed via the generalized Hamilton principle, by considering the transverse shear strain. Then, the analytical solutions of the governing equations and the generalized element stiffness matrix are derived through the distributed transfer function formulation. Finally, the analytical solution of the entire system is obtained by the technique for assembling element stiffness matrix. In numerical simulations, buckling and vibration of an active frame structure are both studied. In addition, a novel Improved Ant Lion algorithm is proposed for optimal design of the frame structures. The optimization examples confirm that the proposed algorithm is more efficient than other existing popular algorithms such as Genetic Algorithm (GA) and Ant Lion Optimization (ALO) algorithm.

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A Simplified Transfer Matrix Method for Horizontal Seismic Response of Wall-Frame Structures Considering SSI

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1065-1069.1026 ◽

2014 ◽

Vol 1065-1069 ◽

pp. 1026-1030 ◽

Cited By ~ 1

Author(s):

Shuo Ying Zhang ◽

Ming Tao Li

Keyword(s):

Seismic Response ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Seismic Behavior ◽

Structural Parameters ◽

Frame Structure ◽

Frame Structures ◽

Elastic Parameters ◽

Efficient Tool

Based on the double member model of wall-frame structure and the corresponding transfer matrix method, the concept of frequent impedance of rigid foundation is introduced so that SSI can be taken into account. This method is more convenient and efficient compared to finite element method because of fewer structural parameters and faster calculation speed. Necessary structure parameters include 7 parameters of each storey, geometry size and total mass of foundation and elastic parameters of site soil. Totally 39 examples were calculated for 13 values of foundation mass and 3 kinds of soil, which are compared to the result of fix bottom model of upper structure. Results show that SSI does not always deduce a decrease of seismic response. Sometimes SSI may increases structural displacement evidently. The simplified method would provide structure designers an efficient tool to understand seismic behavior of wall-frame structures with various foundation and site soil.

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Elastic-Plastic Analysis of Pipe Structure by Transfer Matrix Method

Volume 2: Computer Technology and Bolted Joints ◽

10.1115/pvp2019-93169 ◽

2019 ◽

Author(s):

Masayuki Arai ◽

Shoichi Kuroda ◽

Kiyohiro Ito

Keyword(s):

Stress Distribution ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Stiffness Matrix ◽

Matrix Method ◽

Frame Structure ◽

Pipe System ◽

Elastic Plastic ◽

Simple Boundary ◽

Element Method

Abstract Pipe systems have been widely used in industrial plants such as power stations. In these systems, it is often required to predict the displacement and stress distribution. Analytical and numerical methods such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM) are typically adopted to predict the displacement and stress distribution. The analytical methods are solved based on the Timoshenko beam theory, but the problem that can be solved is limited to simple geometry under simple boundary conditions. Both FEM and BEM can be applied to more complicated problems, although this usually involves a large number of degrees of freedom in a stiffness matrix. The structure is modeled by a beam element in FSM. However, the stiffness matrix still becomes large, as does the matrix size constructed in FEM and BEM. In this study, the transfer matrix method (TMM) is studied to effectively solve complicated problems such as a pipe structure under a small size of the stiffness matrix. The fundamental formula is extended to apply to an elastic-plastic problem. The efficiency and simplicity of this method is demonstrated to solve a space-curved pipe system that involves elbows. The results are compared with those obtained by FEM to verify this method.

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Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

Advances in Mechanical Engineering ◽

10.1155/2014/614208 ◽

2014 ◽

Vol 6 ◽

pp. 614208 ◽

Cited By ~ 1

Author(s):

Jianguo Ding ◽

Wei Zhuang ◽

Pingxin Wang

Keyword(s):

Seismic Response ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Multibody System ◽

Building Design ◽

Frame Structure ◽

Industrial Building ◽

Portal Frame ◽

Portal Frame Structure

Portal frame structures are widely used in industrial building design but unfortunately are often damaged during an earthquake. As a result, a study on the seismic response of this type of structure is important to both human safety and future building designs. Traditionally, finite element methods such as the ANSYS and MIDAS have been used as the primary methods of computing the response of such a structure during an earthquake; however, these methods yield low calculation efficiencies. In this paper, the mechanical model of a single-story portal frame structure with two spans is constructed based on the transfer matrix method of multibody system (MS-TMM); both the transfer matrix of the components in the model and the total transfer matrix equation of the structure are derived, and the corresponding MATLAB program is compiled to determine the natural period and seismic response of the structure. The results show that the results based on the MS-TMM are similar to those obtained by ANSYS, but the calculation time of the MS-TMM method is only 1/20 of that of the ANSYS method. Additionally, it is shown that the MS-TMM method greatly increases the calculation efficiency while maintaining accuracy.

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Pounding between Adjacent Frame Structures under Earthquake Excitation Based on Transfer Matrix Method of Multibody Systems

Advances in Civil Engineering ◽

10.1155/2019/5706015 ◽

2019 ◽

Vol 2019 ◽

pp. 1-31 ◽

Cited By ~ 1

Author(s):

Yin Zhang ◽

Jianguo Ding ◽

Hui Zhuang ◽

Yu Chang ◽

Peng Chen ◽

...

Keyword(s):

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Maximum Error ◽

Frame Structure ◽

Frame Structures ◽

Earthquake Excitation ◽

Computation Efficiency ◽

Adjacent Frame ◽

The Moment

In this paper, the case of two adjacent frame structures is studied by establishing a mechanical model based on the transfer matrix method of multibody system (MS-TMM). The transfer matrices of the related elements and total transfer equation are deduced, combining with the Hertz-damp mode. The pounding process of two adjacent frame structures is calculated by compiling the relevant MATLAB program during severe ground motions. The results of the study indicate that the maximum error of the peak pounding forces and the peak displacements at the top of the frame structure obtained by the MS-TMM and ANSYS are 6.22% and 9.86%, respectively. Comparing the calculation time by ANSYS and MS-TMM, it shows that the computation efficiency increases obviously by using the MS-TMM. The pounding mainly occurs at the top of the short structure; meanwhile, multiple pounding at the same time may occur when the separation gap is small. The parametric investigation has led to the conclusion that the pounding force, the number of poundings, the moment of pounding, and the structural displacement are sensitive to the change of the seismic peak acceleration and the separation gap size.

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Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

Advances in Structural Engineering ◽

10.1177/1369433220986632 ◽

2021 ◽

pp. 136943322098663

Author(s):

Yi-Qun Tang ◽

Wen-Feng Chen ◽

Yao-Peng Liu ◽

Siu-Lai Chan

Keyword(s):

Coordinate System ◽

Stiffness Matrix ◽

Traditional Method ◽

Local Coordinate System ◽

Frame Structures ◽

Global Coordinate System ◽

Single Element ◽

Geometrically Nonlinear ◽

Geometrically Nonlinear Analysis ◽

Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

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