I is the section's second moment of area or moment of inertia. The following techniques can be used to determine the equation for the elastic curve of a beam.
The first and second derivatives of the function that represents the curve in terms of the Cartesian coordinates x and y are dydx and d2ydx2, respectively. Assuming that the longitudinal stresses on the fibers are within the elastic limit, the elastic curve of a beam is the curve formed by the intersection of the neutral surface with the side of the beam. The Bending Moment Equation's double integral is taken in order to perform the fundamental calculation. There are formulas for both cantilever beams and beams that are simply supported.
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