Cantilever Beam Deflection

by Gavin Pate

Submitted : Spring 2018

A flagpole with one fixed end is a cantilevered beam. With an ornament hanging off of the end, it is acceptable to label this situation as a cantilevered beam with a concentrated load at the free end. When approaching this problem, a few things must be established first- the length of the rod (L), the cross-sectional area (A), and the shear modulus of elasticity (G). The shear modulus of elasticity, shear meaning that the force is originally perpendicular to the rod, is a measure of stiffness of an elastic material and is used to describe the elastic properties of things like rods and wires.

            Finding the height of the bottom of the ornament is not a tough task. The center of the pole is 11’ high and the rope suspending the ornament from the pole is 2’ long, ending at 9’. The diameter of the ornament is 1’, so the bottom of it is now at 8’. Due to the pole bending, the ornament is now 27.9449” (2.3287’) lower than before, so the bottom of the ornament will be 5.6713’ off the ground. Therefore, the tallest person that could walk under the ornament would be 5’8”.

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