# Mohr circle for 3dimensional stress state

• chandran
In summary, The Mohr Circle is a way of analyzing stress in a plane, and is still used from time to time by engineers. There are many different Finite Element modeling packages out there that are more accurate and user-friendly, so the art of hand stress analysis is practically extinct.
chandran
I am not sure how to draw a mohr cirlcle on a 3d stress state. I haven't seen
any website sofar. Is it being used by engineers these days or some alternate
method is available.

I doubt that many engineers actually use the Mohr Circle analysis anymore. There are so many neat Finite Element modeling packages out there that the art of doing stress analysis by hand is virtually extinct.

I use it occasionally, just to keep my head into the theory and if the problem is simple enough.

A 2 second search yielded the following
http://me.queensu.ca/courses/MECH422/Lecture5a.ppt
http://portal.cs.umass.edu/projects/mohr/
http://www.utm.edu/departments/engin/lemaster/Machine%20Design/Lecture%2003.pdf

There's plenty of information out there on how to do this technique.

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fred,

unfortunately the links doesn't tell me how to draw the three circles from
the scratch. Can you pls.

Are you familiar or have studied the two dimensional Mohr's circle?

fred.
I have studied plane stress state(i.e 2d) and know how to draw a 2d mohr
circle.

Here's a quickie:

http://www.aoe.vt.edu/~jing/java/nsfapplets/MohrCircles2-3D/Theory/theory.htm

This is from the same site that has an appelet to draw them for you:
http://www.aoe.vt.edu/~jing/java/nsfapplets/MohrCircles2-3D/Applets/applet.htm

Last edited by a moderator:
in this link there is reference to the eigen value. example they say "the
two principle stresses are the eigne value of the 2x2 matrix of sigmax and tauxy"

I was looking for a practical application of eigen value. can you now tell this
what is an eigen value?

fred,
I am not getting it. How to draw the 3 circles(centre and diameter of the circles).

eigen value can help with the mohr circle but it's really really long from what i jus reviewed... anyhow i have a book that explains ti and i dont' have a digital camera but this book is pretty good...

Mechanics of Material by Ferdinand P Beer

from the book it gives
sigY = 3.5
Sigx = 6
txy = - 3ksi

The book I'm lookin at develops the mohr circle by tne normal sigAVE(4.75ksi) equation
from that you know the center of circle and the radius (3.25ksi) etc

Now the bigger circle comes from the principla streseses
which is 8ksi and 1.5ksi.
now from 0 to 8 is the new diameter of the third circle
and from 0 to 1.5 is the small circle
and from 1.5 to 8 is the medium circle...

das what the book has and i guess the key is your principle stress...

Hi Guys,

Can someone advise me how you would find the sigma(x), sigma(y), tau(xy) values?

Chris

p.s.
also...is the following equation valid for 3d models...

Smax= 0.5*(Sx-Sy) + 0.5*(sqrt( ((Sx-Sy)^2) + (4*Tauxy^2) )

## 1. What is the Mohr circle for a 3-dimensional stress state?

The Mohr circle is a graphical representation of the stress state at a point in a material under 3-dimensional stress. It shows the principal stresses on the x-y plane and the maximum shear stress on the z plane.

## 2. How is the Mohr circle constructed?

The Mohr circle is constructed by plotting the principal stresses on the x-y plane and drawing a circle with a radius equal to the maximum shear stress on the z plane. The center of the circle represents the average stress at the point.

## 3. What information can be obtained from the Mohr circle?

The Mohr circle provides valuable information about the stress state at a point, such as the principal stresses, maximum shear stress, and stress invariants. It can also be used to determine the orientation of the principal stress axes.

## 4. How is the Mohr circle used to analyze stress states?

The Mohr circle can be used to analyze the stability of a material under different stress states. It can also be used to determine the failure criteria for a given material and to design structures that can withstand certain stress conditions.

## 5. Are there any limitations to using the Mohr circle for 3-dimensional stress states?

Yes, the Mohr circle assumes that the material is in an elastic state and does not account for plastic deformations. It also does not consider the effects of temperature or time on the stress state. Additionally, the Mohr circle is only applicable for isotropic materials.

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