Slope Displacement by Integration

by Thomas Musgrave

Submitted : Spring 2009

The goal of the project is to develop an understanding of the integration techniques used to calculate the slope displacement, or deflection of a given beam. By using successive integrations over various pertinent function intervals of a beam, the Elastic Equation can be derived. The Elastic Equation as a function of x will yield the deflection of the beam at any given value of x coordinate. Solving for successive integration constants, evaluating with a given x, and multiplying by EI (flexural rigidity, a constant), the maximum deflection or displacement of a beam or member is computed using Calculus; not computers. This is useful for design, as well as forensic engineering purposes, and can be counted on when computer systems may not be available. Slope Displacement by Integration is powerful tool for prospective engineers indeed.

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