Transactions of the Canadian Society for Mechanical Engineering · 1991 · 61 citations · 0 references
EngineeringMechanical EngineeringStructural DynamicsStructural EngineeringVibrationBeam AnalysisBeam TheoryBending Of BeamsDeflection Of BeamsElasticity TheoryStructural MechanicsCantilever Beam DeflectionCantilever LoadingCantilever MechanicsDimensionless QuantitiesElasticity Of BeamsEquilibrium ConfigurationsLoad-deflection RelationshipsStability Of Equilibrium Configurations
In this research a method is presented to study the alternate equilibrium configurations of a cantilever beam subjected to a uniform gravitational distributed load. The prismatic cantilever beam is assumed to be initially straight in addition to its material being homogeneous, elastic, and isotropic. It is shown in this research that the number of equilibrium shapes of a cantilever beam under a prescribed uniform gravitational distributed load is dependent on a dimensionless parameter. The ranges for this parameter and the number of equilibrium shapes of the beam in each of these ranges are provided. The method outlined in this paper can also be utilized to obtain the alternate equilibrium configurations of cantilever beams subjected to the simultaneous action of the uniform gravitational distributed load and an inclined end load, or just an inclined end load. Finally this paper discusses several equilibrium shapes which are experimentally verified for a cantilever beam subjected to its own uniform distributed weight.