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Deflections due to Bending - MIT OpenCourseWare

------10 Deflections due to Bending The Moment/Curvature Relation Just as we took the pure Bending construction to be accurate enough to produce useful estimates of the normal stress due to Bending for loadings that included shear, so too we will use the same moment/curvature relationship to produce a dif-ferential equation for the transverse displacement, v(x) of the beam at every point along the neutral axis when the Bending moment varies along the beam. Mb EI -sd d = The moment/curvature relation-ship itself is this differential equa-tion.

discontinuity in the shear force at B allows the discontinuity in slope of M -P b at that point. Our linear, ordinary, second Mb(x) order differential equation for the deflection of the neutral axis becomes, for x < L/4 x 2 -P(L-a) x > a dv Mb() x 3P x < a dx 2

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