mohrs cirlce
TRANSCRIPT
![Page 1: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/1.jpg)
MOHR’S CIRCLE
![Page 2: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/2.jpg)
Mohr's circle, named after Christian Otto
Mohr, is a two-dimensional graphical
representation of the transformation law for
the Cauchy stress tensor.
![Page 3: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/3.jpg)
3
![Page 4: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/4.jpg)
4
Stress Transformation
A Mini Quiz
Strain Transformation
Click here
Click here
Click here
![Page 5: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/5.jpg)
PLANE STRESS TRANSFORMATION
![Page 6: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/6.jpg)
~ 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
![Page 7: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/7.jpg)
![Page 8: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/8.jpg)
![Page 9: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/9.jpg)
![Page 10: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/10.jpg)
![Page 11: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/11.jpg)
Solving equilibrium equations for the wedge
2 sin2 cos22
' xy
yxyx
x
2 os2in 2
' cs xy
yx
xy
![Page 12: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/12.jpg)
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
![Page 13: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/13.jpg)
![Page 14: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/14.jpg)
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 ….
![Page 15: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/15.jpg)
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.
2
2
![Page 16: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/16.jpg)
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
![Page 17: Mohrs cirlce](https://reader030.vdocuments.net/reader030/viewer/2022032611/55a682fb1a28ab48498b469a/html5/thumbnails/17.jpg)
THE END