Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu - - PDF document

bending stress
SMART_READER_LITE
LIVE PREVIEW

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


slide-1
SLIDE 1

Bending Stress

Lecture 3

ME EN 372 Andrew Ning aning@byu.edu

Outline

Axial Stress Bending Stress

slide-2
SLIDE 2

Axial Stress

F A σx = F A

slide-3
SLIDE 3

Bending Stress Pure Bending

Mz Mz

slide-4
SLIDE 4

Mz Mz

Mz Mz y y

slide-5
SLIDE 5

Mz Mz y y Iz = ZZ

A

y2dA

Mz Iz y σx σx(y) = −Mzy Iz

neutral axis

slide-6
SLIDE 6

Flexure formula: σx = −Mzy Iz Simplified (ignore coordinate system subscripts and

  • nly include max value)

σmax = Mc I

slide-7
SLIDE 7

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

slide-8
SLIDE 8

Parallel Axis Theorem

I = Ic + Ad2

Example: moment of inertia

4 in 2.5 in 0.875 in 0.875 in

slide-9
SLIDE 9

Example: wind turbine tower Bidirectional Bending

σx = −Mzy Iz + Myz Iy