Bending: Encyclopedia II - Bending - Stress in a beam

Bending - Stress in a beam

Beam bending is analyzed with the Euler-Bernoulli beam equation. The classic formula for determining the bending stress in a member is:

• σ is the bending stress
• M - the moment at the neutral axis
• y - the perpendicular distance to the neutral axis
• I_x - the second moment of inertia about the neutral axis x

This equation is valid only when the stress at the extreme fiber (i.e. the portion of the beam furthest from the neutral axis) is below the yield stress of the material it is constructed from. At higher loadings the stress distribution becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere in the beam, with a discontinuity at the neutral axis where the stress changes from tensile to compressive. This plastic hinge state is typically used as a limit state in the design of steel structures.

Adapted from the Wikipedia article "Stress in a beam", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki