theory of beams
On the Large Deflections of a Class of Cantilever Beams
Moses Frank Oduori, Ph.D.,
Department of Mechanical and Manufacturing Engineering,
The University of Nairobi.
Abstract
An equation for the determination of large deflections of beams is derived from first principles. Laboratory tests were carried out in order to validate the theory. The theoretical and experimental results were found to be in good agreement.
Introduction
In much of the study and practice of mechanical and structural engineering, the equations used for the determination of beam deflections are derived with the assumption of small deflections. This is appropriate because, in most mechanical and structural engineering applications, small deflections are a functional requirement. However, there may arise cases in agricultural machinery engineering, for instance, where beam deflections can no longer be assumed to be small. Then, it becomes necessary to develop and use equations other than those commonly found in the mechanical and structural engineering literature. Such an equation is developed and evaluated in this presentation.
An example of an application that would involve large crop stem (beam) deflections, is to be found in the design and operation of the combine harvester reel, as illustrated in Fig. 1.
Model formulation
Assumptions
The assumptions made in formulating a model of the deflected crop stems are the following:
A bunch of crop stems deflected by the reel shall be considered to behave like a single, initially vertical cantilever that is fixed at the base.
At its point of action, the deflecting force shall be considered to be directed normal to the curvature of the cantilever beam.
The stress-strain relationship for the deflected stems shall be assumed to be linearly elastic.
The assumption of small deflections, commonly made in mechanical and structural engineering applications, is not made here.
Formulation of the model
Referring to Fig. 2, according to
Moses Frank Oduori, Ph.D.,
Department of Mechanical and Manufacturing Engineering,
The University of Nairobi.
Abstract
An equation for the determination of large deflections of beams is derived from first principles. Laboratory tests were carried out in order to validate the theory. The theoretical and experimental results were found to be in good agreement.
Introduction
In much of the study and practice of mechanical and structural engineering, the equations used for the determination of beam deflections are derived with the assumption of small deflections. This is appropriate because, in most mechanical and structural engineering applications, small deflections are a functional requirement. However, there may arise cases in agricultural machinery engineering, for instance, where beam deflections can no longer be assumed to be small. Then, it becomes necessary to develop and use equations other than those commonly found in the mechanical and structural engineering literature. Such an equation is developed and evaluated in this presentation.
An example of an application that would involve large crop stem (beam) deflections, is to be found in the design and operation of the combine harvester reel, as illustrated in Fig. 1.
Model formulation
Assumptions
The assumptions made in formulating a model of the deflected crop stems are the following:
A bunch of crop stems deflected by the reel shall be considered to behave like a single, initially vertical cantilever that is fixed at the base.
At its point of action, the deflecting force shall be considered to be directed normal to the curvature of the cantilever beam.
The stress-strain relationship for the deflected stems shall be assumed to be linearly elastic.
The assumption of small deflections, commonly made in mechanical and structural engineering applications, is not made here.
Formulation of the model
Referring to Fig. 2, according to