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Bending of Beams
The Engineer
posted on October 23, 2006 |
The stress in beam due to a bending moment can be derived with three principals: geometry, Hooke's Law, and equilibrium.
Geometry:
Hooke's Law:
Equilibrium:
Assumptions:
Beam is initially straight and unstressed
Beam material is homogeneous and isotropic
Material preperties are the same in tension and compression
Plane cross sections remain plane after bending
Therefore:
Second Moment of Area of Common Shapes
:
Rectangular cross-section
Circular cross-section
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