Application of Calculus in the Elastic Curve (Deflection)

Abstract

Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any brittle materials that may be connected to or around it such as concrete. In this paper, we investigate how to determine the displacement of due to deflection at one point along an overhanging beam