beam deflection integration method

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Last updated 2:17 AM on 11/13/25
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5 Terms

1
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σ: bending stress, MM: moment, yy: distance from NA, II: moment of inertia

Bending stress relates curvature to moment.

<p><span><span>Bending stress relates curvature to moment.</span></span></p>
2
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ρ: radius of curvature, MM: bending moment, EE: Young’s modulus, II: moment of inertia

Relationship between curvature and bending moment (core of deflection theory).

<p><span><span>Relationship between curvature and bending moment (core of deflection theory).</span></span></p>
3
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v(x): deflection, M(x)M(x): bending moment

Starting point for integration method.

<p><span><span>Starting point for integration method.</span></span></p>
4
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First integration gives slope.

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5
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Second integration gives deflection.

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