Resumo

ARISTIZABAL-OCHOA, J. DARIO. FIRST AND SECOND ORDER STIFFNESS AND LOAD MATRICES OF AN ORTHOTROPIC BEAM COLUMN WITH SEMIRIGID CONNECTIONS: I) THEORY. Dyna rev.fac.nac.minas [online]. 2010, vol.77, n.164, pp.130-140. ISSN 0012-7353.

The first- and second-order stiffness and load matrices of an orthotropic Timoshenko beam-column of symmetric cross section with semirigid connections including the effects of end axial loads (tension or compression) and shear deformations along the member are derived in a classical manner. Both matrices can be used in the stability, first- and the second-order elastic analyses of framed structures made of Timoshenko beam-columns with rigid, semirigid and simple connections of symmetric cross sections. The “modified” stability approach based on Haringx´s model described by Timoshenko and Gere (1961) is utilized in all matrices. The proposed stiffness matrices can also be used in the inelastic analysis of frames whose members suffer from flexural degradation or, on the contrary, stiffening at their end connections. The closed-form second-order stiffness matrix and load vector derived and presented in this paper find great applications in the stability and second-order analyses of framed structures made of beam-columns with relatively low shear stiffness such as orthotropic composite polymers (FRP or composites) and multilayer elastomeric bearings commonly used in seismic isolation of buildings. The effects of torsional warping along the members are not included. Analytical studies indicate that the buckling load and the stiffness of framed structures are reduced by the shear deformations along the members. In addition, the phenomenon of buckling under axial tension forces in members with relatively low shear stiffness is captured by the proposed equations. Tension buckling must not be ignored in the stability analysis of beam-columns with shear stiffness GA_s of the same order of magnitude as EI/h². The validity of both matrices is verified against available solutions of stability analysis and nonlinear geometric elastic behavior of beam-column structures. Five examples are included that demonstrate the effectiveness of the proposed method and corresponding matrices.

Palavras-chave : Buckling; Columns; Construction Types; Computer applications; Frames; Loads; P-D Effects; Shear deformations; Second-order analysis; Semirigid Connections; Stability; Tension Buckling.

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