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In a Nut Shell:
Normal Stress in a Bending Member (Beam) (Bending Stress)
Under the assumption
that plane sections before bending remain plane afterwards it can be
shown that the curvature
of the beam (1/ρ) is directly proportional to the couple (bending
moment) and inversely
proportional to the flexural rigidity (EI) of the beam where E is the
modulus of elasticity
and Izz is the moment of inertia of the entire cross-sectional
area about
the centroidal
(neutral) axis.
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Curvature =
1/ρ = M / EIzz
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In addition the strain
at a distance, y, above the centroidal (neutral)
axis is
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εx =
- y/ρ
So εx =
- My/EIzz =
- My/EI
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For linear elastic
response σx =
E εx (Hooke’s Law)
and substituting the
expression for εx
the “bending stress” becomes
σx =
- My/I
If c
is the maximum distance to the “outer” fiber of the beam, then the
maximum
bending stress is
σm
= Mc / I
Common units for stress
are psi, ksi, MPa, N/mm2 (English/Metric)
Click here for a
discussion of strategy in the analysis of bending stresses in beams.
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