Static Timoshenko Beam‐Columns on Elastic Media

1988 ◽  
Vol 114 (5) ◽  
pp. 1152-1172 ◽  
Author(s):  
Franklin Y. Cheng ◽  
Chris P. Pantelides
Keyword(s):  
Timoshenko Beam ◽  
Elastic Media ◽  
Beam Columns

Dynamic Timoshenko Beam‐Columns on Elastic Media

1988 ◽  
Vol 114 (7) ◽  
pp. 1524-1550 ◽  
Author(s):  
Franklin Y. Cheng ◽  
Chris P. Pantelides
Keyword(s):  
Timoshenko Beam ◽  
Elastic Media ◽  
Beam Columns

Closure to “Dynamic Matrix of Timoshenko Beam Columns”

1974 ◽  
Vol 100 (9) ◽  
pp. 1945-1949
Author(s):  
Franklin Y. Cheng ◽  
Wu-Hsiung Tseng
Keyword(s):  
Timoshenko Beam ◽  
Beam Columns ◽  
Dynamic Matrix

A numerical method for static and free-vibration analysis of non-uniform Timoshenko beam–columns

2006 ◽  
Vol 33 (3) ◽  
pp. 278-293 ◽  
Author(s):  
Z Canan Girgin ◽  
Konuralp Girgin
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Beam Columns ◽  
Geometrical Properties ◽  
Stiffness Matrices

A generalized numerical method is proposed to derive the static and dynamic stiffness matrices and to handle the nodal load vector for static analysis of non-uniform Timoshenko beam–columns under several effects. This method presents a unified approach based on effective utilization of the Mohr method and focuses on the following arbitrarily variable characteristics: geometrical properties, bending and shear deformations, transverse and rotatory inertia of mass, distributed and (or) concentrated axial and (or) transverse loads, and Winkler foundation modulus and shear foundation modulus. A successive iterative algorithm is developed to comprise all these characteristics systematically. The algorithm enables a non-uniform Timoshenko beam–column to be regarded as a substructure. This provides an important advantage to incorporate all the variable characteristics based on the substructure. The buckling load and fundamental natural frequency of a substructure subjected to the cited effects are also assessed. Numerical examples confirm the efficiency of the numerical method.Key words: non-uniform, Timoshenko, substructure, elastic foundation, geometrical nonlinearity, stiffness, stability, free vibration.

scholarly journals An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

2021 ◽  
Vol 10 (4) ◽  
pp. 253-268
Author(s):  
Ruhi Aydin
Keyword(s):  
Timoshenko Beam ◽  
Mass Matrix ◽  
Tensile Force ◽  
Three Dimensional ◽  
Beam Axis ◽  
Order Effects ◽  
Shape Functions ◽  
Stability Parameters ◽  
Beam Columns ◽  
Mass Matrices

In the static analysis of beam-column systems using matrix methods, polynomials are using as the shape functions. The transverse deflections along the beam axis, including the axial- flexural effects in the beam-column element, are not adequately described by polynomials. As an alternative method, the element stiffness matrix is modeling using stability parameters. The shape functions which are obtaining using the stability parameters are more compatible with the system’s behavior. A mass matrix used in the dynamic analysis is evaluated using the same shape functions as those used for derivations of the stiffness coefficients and is called a consistent mass matrix. In this study, the stiffness and consistent mass matrices for prismatic three-dimensional Bernoulli-Euler and Timoshenko beam-columns are proposed with consideration for the axial-flexural interactions and shear deformations associated with transverse deflections along the beam axis. The second-order effects, critical buckling loads, and eigenvalues are determined. According to the author’s knowledge, this study is the first report of the derivations of consistent mass matrices of Bernoulli-Euler and Timoshenko beam-columns under the effect of axially compressive or tensile force.

scholarly journals Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

2019 ◽  
Vol 9 (18) ◽  
pp. 3814 ◽  
Author(s):  
Hu ◽  
Pan ◽  
Tong
Keyword(s):  
Structural Analysis ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Bending Moment ◽  
Order Effect ◽  
Second Order ◽  
Equilibrium Analysis ◽  
Beam Columns ◽  
The Stability ◽  
Shear Deformable

Shear deformable beams have been widely used in engineering applications. Based on the matrix structural analysis (MSA), this paper presents a method for the buckling and second-order solutions of shear deformable beams, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, this paper develops the element stability stiffness matrix of axial-loaded Timoshenko beam–columns, which relates the element-end deformations (translation and rotation angle) and corresponding forces (shear force and bending moment). First, an equilibrium analysis of an axial-loaded Timoshenko beam–column is conducted, and the element flexural deformations and forces are solved exactly from the governing differential equation. The element stability stiffness matrix is derived with a focus on the element-end deformations and the corresponding forces. Then, a matrix structural analysis approach for the elastic buckling analysis of Timoshenko beam–columns is established and demonstrated using classical application examples. Discussions on the errors of a previous simplified expression of the stability stiffness matrix is presented by comparing with the derived exact expression. In addition, the asymptotic behavior of the stability stiffness matrix to the first-order stiffness matrix is noted.

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