HENCKY BAR-CHAIN MODELS FOR BEAMS AND ARCHES IN BUCKLING AND VIBRATION

Abstract

The Hencky bar-chain model (HBM) for the buckling and vibration analyses of Euler-Bernoulli beams and circular arches is developed in this thesis. The HBM may be regarded as the physical representation of the first order central finite difference method as they possess the same form of governing equations and boundary conditions. This thesis advances the HBM to handle beams with elastic intermediate and end restraints, the allowance for its selfweight, non-uniform cross-section, resting on partial Winkler foundation and circular arches. The establishment of such a physical discrete model allows the analyst to (1) readily obtain solutions by solving a set of algebraic equations (instead of a differential equation), (2) optimize the shape of columns with varying cross-section and (3) calibrate small length scale coefficient e0 in the nonlocal beam and arch theory due to similar phenomenological characteristics of the HBM and the nonlocal models.