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9-152-HorizontalBeam-ModelingScenario

Author(s): Tiernan Fogarty1, Gregg Waterman1

Oregon Institute of Technology, Klamath Falls OR USA

Keywords: Polynomial dynamical system beam cantilever

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Abstract

Resource Image This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

Students will investigate the vertical deflection of a thin horizontal beam under various end (boundary) conditions. Vertical deflections at points along the beam are measured and it is verified that the deflection curve is a portion of the graph of a polynomial.

Vertical deflection occurs as a result of the weight of the beam alone, with no compressive force at the ends or distributed loads other than the mass of the beam. Data is collected to measure the vertical deflection from horizontal against the distance from one end for several boundary condition situations, and a mathematical model is arrived at for the vertical deflection. From this model the general form of the governing ODE can be inferred.

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Authors

Author(s): Tiernan Fogarty1, Gregg Waterman1

Oregon Institute of Technology, Klamath Falls OR USA

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