Deformation Performance Analysis of a Truss Structure Based on the Deformation Decomposition Method

This article examines the application of the theory of critical strain energy levels to the determination of the limiting states of rod systems. A redundant truss is chosen to illustrate the peculiarities of changes in the self-stressing states of the structure at critical strain energy levels. The removal of ties when they reach their stress or strain limits leads to a change in the state of self-stress in the structure, which is illustrated by the removal of the rods in the trusses. The matrix notation of the governing equations for the structure allows us to visualize both the formulation of the problem and the course of its solution. We present the formulation and algorithm for solving the problem of a weak link in the structure by the example of a five-core redundant truss. The basic equations of matrix structural mechanics are given, allowing us to implement the algorithm and to determine the unknown parameters of the problem in the form of the method of displacements and the method of forces. The mathematical model of the problem is presented in the form of an eigenvalues problem, which allows us to investigate the extreme properties of the structure’s strain energy in the whole area of admissible parameter values, including the boundaries. The eigenvalues and eigenvectors make it possible to determine the extreme values of the nodal reactive forces of the structure or displacements, depending on the chosen formulation of the problem. The internal forces and deformations in the rods depend on the nodal vectors of external influences. The applied design load is balanced by the internal forces of the system and remains unchanged. This follows from the equality of the work of external forces to a part of the potential energy of the structure. The remaining part of the strain energy allows us to find the limit values of the reactive response of the structure to external actions. Additional actions on the structure can lead to the bearing capacity lost if they exceed the limits of the structure’s response. Examples show an algorithm for finding the weak link in a structure and identifying the rods that will be the first to fail under external loads. The matrices of stiffness and flexibility are formed, and the eigenvalues and vectors are found, which allow for the construction of the limit surface of allowable influences on the structure.

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“…There are optimizations and other methods for evaluating trusses' internal forces presented in [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Implementation of the Weak Link Problem for Trusses

Stupishin

Mondrus

2023

Buildings

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“…(Chen et al 2023;Li and Deng 2023;Pejatović et al 2023). The deformation decomposition method is a structural analysis method that can decompose the comprehensive deformation into basic macroscopic deformation (Shi and Goodman 1989;Jin et al 2011;Zhang and Hoa 2014;Wang et al 2022). However, the existing deformation decomposition method is only applicable to isotropic materials and cannot be used to analyze orthotropic wood structures.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of mechanical properties for wood frame and reinforced concrete frame based on deformation energy decomposition method

Sun,

Liang,

Wang

2023

BioRes

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As a typical orthotropic material, the mechanical properties of wood in the parallel and perpendicular-to-grain directions are very different. Based on mathematical orthogonality, mechanical force balance condition, and energy comparability, the deformation energy decomposition method of planar wood element is proposed, and then the quantitative and visual analysis of the basic deformation performance of wood structure is realized. The basic deformation performance of wood structure and isotropic structure is analyzed using the deformation energy decomposition method, and the seismic performance of wood frame structure and concrete frame structure is compared. The results show that the lateral resistance and beam ductility of wood frame are greater than those of concrete frame under seismic load. However, the reduction of deformation energy proportion of wood frame beam leads to greater deformation energy of the frame column, so it is suggested to take targeted strengthening measures to the bottom of the wood frame column and the joint area.

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