The Deflection of Beams

by Jose Paula

Submitted : Fall 2019

When a beam is subjected to a load, the beam bends because it is under the stress due the force applied by the subjected load. The deformation of the beam when it undergoes this bend stress is called deflection. The deflection of a beam must often be limited in order to safely provide integrity and stability of a structure or machine and prevent the cracking of any attached brittle materials such as concrete or glass. Furthermore, code restrictions often require these members not vibrate or deflect severely in order to safely support the intended load. To determine the deflection points on a beam when it is being subjected to a load it is important to sketch the deflected shape that will occur. This will help to visualize the results and thereby check the results. The deflected shape of the longitudinal axis that pass through the centroid of each cross-sectional area of the beam that occurs is called the elastic curve. Sketching the elastic curve is usually easy but can be challenging in some cases. It is also important to take into the account of how the slope or displacement is restricted at various types of supports given a subjected load. This project will dive into how to solve the deflection of a cantilever beam by using the method of integration.

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