Deflection Of A Beam In Neutral Equilibrium À La Conjugate Beam Method: Use Of Support, Not Boundary, Conditions

Abstract

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.

Enriching Students’ Study Of Beam Reactions And Deflections: From Singularity Functions To Method Of Model Formulas

“…The method of model formulas is best taught to students as an alternative method, after they have learned one or more of the traditional methods. [2][3][4][5][6][7][8][9][10][11][12] This method enriches students' study and set of skills in their determining reactions and deflections of beams, and it provides engineers with a means to quickly check their solutions obtained using traditional methods.…”

“…Then they learn the determination of deflection of beams under a variety of loads. Traditional methods that are used in determining statically indeterminate reactions and deflections of elastic beams include: [2][3][4][5][6][7][8][9][10][11][12] method of integration (with or without the use of singularity functions), method of superposition, method using moment-area theorems, method using Castigliano's theorem, method of conjugate beam, and method of segments.…”