Stability design of steel frames

A unified approach to the Timoshenko 3D beam-column element tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations

Vibration analysis of laminated composite higher order beams under varying axial loads

Formulation for nonlinear dynamic analysis of steel frames considering the plastic zone method

ABSTRACT A numerical formulation was carried out in this paper to produce the tangent stiffness matrix for two-nodal tapered Timoshenko beam-column elements for geometrically nonlinear analysis. The proposed solution is based on the exact shape functions and their derivatives describing the non-uniformity of the element properties. The section properties were presented as exponential functions with tapering indices to illustrate the variations in section properties along the tapered element length. The model is applicable for elements with different solid and hollow cross-sections. The proposed formulation is embedded into a Visual Basic code to carry out the analysis accompanied by many examples for validating its accuracy and efficiency. The model results are compared with those of commercial software and cited references that showed high accurate results with a small number of elements.

Finite element formulation of Timoshenko tapered beam-column element for large displacement analysis based on the exact shape functions

Nonlinear analyses using an updated Lagrangian formulation considering the Euler-Bernoulli beam theory have been developed with consistency in the literature, with different geometric matrices depending on the nonlinear displacement parts considered in the strain tensor. When performing this type of analysis using the Timoshenko beam theory, in general, the stiffness and the geometric matrices present additional degrees of freedom. This work presents a unified approach for the development of a geometric matrix employing the Timoshenko beam theory and considering higher-order terms in the strain tensor. This matrix is obtained using shape functions calculated directly from the solution of the differential equation of the problem. The matrix is implemented in the Ftool software, and its results are compared against several matrices found in the literature, with or without higher-order terms in the strain tensor, as well as the Euler-Bernoulli or Timoshenko beam theories. Examples show that the use of the Timoshenko beam theory has a strong influence, especially when the structure has small slenderness (short members). For high axial load values, the consideration of higher-order terms in the strain tensor results in larger displacements as expected.

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A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

Complete Tangent Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor and Large Rotations for a Euler Bernoulli - Timoshenko Space Beam-Column Element

Marcos Antonio Campos Rodrigues

Papers

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

A unified approach to the Timoshenko 3D beam-column element tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations

Complete Tangent Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor and Large Rotations for a Euler Bernoulli - Timoshenko Space Beam-Column Element

Avaliação de uma Formulação Completa da Matriz de Rigidez para Análise Não-Linear de Estruturas

pproximated Method of Nonlinear Geometric Analysis Applied to Optimum Design of Steel Frames