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Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu Outline Axial Stress Bending Stress Axial Stress F x = F A A Bending Stress Pure Bending M z M z M z M z M z y M z y y M z M z y ZZ y 2 dA I z = A M z I z x y
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Bending Stress Pure Bending
Mz Mz
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Mz Mz
Mz Mz y y
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Mz Mz y y Iz = ZZ
A
y2dA
Mz Iz y σx σx(y) = −Mzy Iz
neutral axis
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Flexure formula: σx = −Mzy Iz Simplified (ignore coordinate system subscripts and
- nly include max value)
σmax = Mc I
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Neutral Axis
Neutral axis is at y-centroid. ¯ y =
- A
ydA
- dA
A few common moments of inertia
Rectangle: I = bh3 12 Circle: I = πr4 4 Thin Shell: I = πr3t
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Parallel Axis Theorem
I = Ic + Ad2
Example: moment of inertia
4 in 2.5 in 0.875 in 0.875 in
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