Department

Earth ScienceCourse Code

EARTH 135Professor

TanimotoStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**2 pages of the document.**Earth 135 Lecture 6

Summary : Plate Bending

1. The basic equation

Dd4w

dx4=q(x) (1)

where Dis the ﬂexural ridigity given by

D=Eh3

12(1 −ν2)(2)

with hbeing the thickness of a plate and (E, ν) are the Young’s modulus and

the Poisson’s ratio of a plate. Vertical displacement wis controlled by this

parameter.

2. Moment is given by

M(x) = −Dd2w

dx2(3)

Its deﬁnition is

M(x) = Zh/2

−h/2

zσxxdz (4)

3. Shear force is given by

V(x) = −Dd3w

dx3(5)

Shear stress in this 2D problem is given by σxz =V/h.

4. Bending stress: σxx is called the bending stress or ﬁber stress. Since strain ǫxx

is given by

ǫxx =−zd2w

dx2(6)

where yis the distance from the neutral plane, bending stress is given by

σxx =−E

1−ν2zd2w

dx2(7)

1

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