A numerical method for static and free-vibration analysis of non-uniform Timoshenko beam-columns - Girgin, Z. Canan; Girgin, Konuralp (CANADIAN SCIENCE PUBLISHING, 2006)
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. T his 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.
Keywords: non-uniform; Timoshenko; substructure; elastic foundation; geometrical nonlinearity; stiffness; stability; free vibration; DYNAMIC-STIFFNESS MATRIX; FINITE-ELEMENT; TRANSVERSE VIBRATIONS; SHEAR; FORMULATION; FREQUENCIES; RANGE; Engineering