Deflection of a Beam in Neutral Equilibrium a la Conjugate Beam Method: Use of Support, Not Boundary, Conditions

摘要

Beams with flexural rigidity will deflect under loading. Is it possible to ascertain the deflection of a loaded beam in neutral equilibrium? The answer is yes according to the conjugate beam method, but a resounding no according to all other established methods. The objective of this paper is to share with fellow engineering educators the insights, highlights, and several illustrative examples for teaching the conjugate beam method. In particular, it is pointed out that (a) support conditions (or types), rather than boundary conditions, are what the conjugate beam method needs in finding solutions for deflections of loaded beams, (b) more support conditions than boundary conditions are usually known for beams in neutral equilibrium, and (c) the conjugate beam method often works better than other established methods in determining deflections of beams. It is demonstrated in this paper that the conjugate beam method does find the likely, or unique, deflection of a loaded beam in neutral equilibrium.