Static Deflection of Continuous Beams with Nonlinear Supports

Abstract

A method to calculate the static deflection, the bending moment, the reactions at supports, etc. is proposed for continuous beams which have nonlinear supports. The calculation method is a kind of relaxation method. We linearize the system by replacing nonlinear supports with linear springs, and carry out the calculation of static deflection for the line-arized system. By iterating the linear calculations in which the linear spring constants are determined from the previous calculation result, we can obtain the solution which also satisfies the characteristics of nonlinear supports. The characteristics of the following supports are described as the examples of nonlinear ones: (1) a section of stern tube bearings made of lignumvitae, (2) a rigid support with backlash, and (3) a spring of which the end is separable from the beam when unloaded. As an example of numerical calculation, a calculation result for a propeller shaft of a ship is illustrated.