COE 3001 Lecture 16: 16+Beam+Deflection
23 Nov 2016
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Document Summary
So far we have only talked about the forces, moments, and stresses generated in the beam. We have thus far neglected the deformations of the beam. First we must mathematically describe the deflection of the beam. We already developed the idea of curvature of a beam. For a small segment of a deflected beam ds, we can identify the angle of rotation (a. k. a. the angle of slope or angle of inclination) of the beam at position x as the angle . As we proceed along ds, the angle of rotation increases to + d , where d is related to the curvature as previously defined. We can define the slope of the deflection curve by: If the deflection is small (and therefore the angle of rotation is small), we can make some simplifying assumptions to solve for the curvature as a function of the deflection curve:
