Bending

From the enlarged view of the linear variation of normal stress σ, we see that σ varies from zero at the beam’s neutral axis to a maximum value, σ_max at a distance farther from the neutral axis.

Stresses are given by the following formulas

σ = - (y / c)σ_max

σ_max = M c / I

σ = - M y / I

where,

σ_max = the maximum normal stress in the beam.

I = the moment of inertia of cross sectional area computed about the neutral axis

M = the resultant internal moment, determined from the method of section and the equilibrium, and computed about the neutral axis of cross section

c = the perpendicular distance from the neutral axis to a point farthest away from the neutral axis, where σ_max acts.

y = the distance far away from the neutral axis.

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This material is based upon work supported by the National Science Foundation under Grant No. 0633602. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

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