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The out-of-plane displacement w of a beam
is governed by the Euler-Bernoulli Beam
Equation,
![]() where p is the distributed loading (force per unit length) acting in the same direction as y (and w), E is the Young's modulus of the beam, and I is the area moment of inertia of the beam's cross section. If E and I do not vary with x along the length of the beam, then the beam equation simplifies to,
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