Biaxial Shear and Mohr's Circle 1

[nhtr86]

Imagine one of those stress cubes that were so popular in college. I apply a shear stress to the top surface in one direction (V1) and a larger shear stress in the perpendicular direction (V2). No normal stresses are applied.

Now, if I plot the 3d Mohr's circle for this, it should be a circle centered on the origin with a radius of V1 and another circle centered on the origin with a radius of V2. Two circles that don't intersect or touch.

I am sure that this is wrong because the maximum shear stress has to be the root sum of the squares of the individual shear stresses, not the larger of the two.

Why is the method of drawing the Mohr's circle above wrong?

 

[ajose]

hi nhtr86 ,


Yes you are right it is not the right way of analysis.

The 2D Mohr's circle is build with principal stresses S1, S2 (S1>S2). Because they are principal stresses have no shear so you have two points and one rule "there cannot be lower stresses than S2 or bigger stresses than S1". Now go and build it up in a Shear & Normal stresses axis.


The 3D Mohr's circle is build with three principal stresses S1, S2, S3 (S1>S2>S3). Again they are principal stresses and there is no shear. To build the circles (plural) in a Shear & Normal stresse axis have to:

Build an outer circle with stresses S1, S3 (and the rule quoted above)
Build an inner circle with S1, S2.
Build an innner circle with S2, S3.

Now you have the 3D Mohr's cricle.


ajose

 

[flash3780]

Eh... your forces don't balance in the above case.

tau_xy = tau_yx or your stress cube flys away.