MOHR’S CIRCLE

Mohr's circle, named after Christian Otto

Mohr, is a two-dimensional graphical

representation of the transformation law for

the Cauchy stress tensor.

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Stress Transformation

A Mini Quiz

Strain Transformation

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PLANE STRESS TRANSFORMATION

~ where all elements of

the body are subjected

to normal and shear

stresses acting along a

plane (x-y); none

perpendicular to the

plane (z-direction)

z = 0; xz = 0; zy = 0

Solving equilibrium equations for the wedge

2 sin2 cos22

' xy

yxyx

x

2 os2in 2

' cs xy

yx

xy

Squaring and adding above two equations

gives us with an equation of a circle whose

center is at

of radius

0,

2

xy

22

2

'2

' Rxy

yx

x

2

2

2xy

xy

A point on the Mohr circle represents the x’

and xy’ values on a specific plane.

is measured counterclockwise from the

original x-axis.

Same sign convention for stresses as before.

i.e., on positive planes, pointing positive directions

positive, and ….

When we rotate the

plane by 180°, we go

a full round (i.e.,

360°) on the Mohr

circle. Therefore….…

. …..when we rotate

the plane by °, we go

2° on the Mohr

circle.

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Mohr circle represents the state of stress at a

point; thus different Mohr circles for

different points in the body

Mohr circle is a simple but powerful

technique

Get the sign convention right

Quit Continue

THE END