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Assuming linear elastic bending with small deformations and planes perpendicular to the neutral axis remain plane after bending, then for a rectangular beam:

Moment = (Yield Stress)*(Second Moment of Area)/(Distance of surface to Neutral Axis)

For Ultimate Bending Moment, assume stress is uniform throughout the beam, and acting through half the distance from surface to neutral axis, then:

Moment = Stress * (Area/2)*(h/4 + h/4)

For a better visualization check out Popov's textbook, Engineering Mechanics of Solids, Chapter 6, Section 6.10

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13y ago
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8y ago

The maximum bending moment is located at the point where shear is zero. This occurs because shear is the mathematical derivative of bending moment, and the maximum bending moment occurs when its derivative (i.e. Shear) is zero.

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Q: How do you find ultimate bending moment of steel beams?
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