Convert rosette strain measurement to pricipal stress

[AmJam]

It would be appreciated if anyone could answer my question about measuring stress using Rosette strain gauges.

I have measured the strain of a vibrating beam using a rosette strain gauge and now trying to calculate the principal stress from these measurements, but I'm not sure if the result makes sense.

The attached pictures are as follows:

Picture 1: one of my rosette measurements (gauge a, b and c)
Picture 2: The equation that I use to calculate the maximum principal stress
Picture 3: The principal stress

What would be the cause of the nonsinusoidal stress?
While I understand that this occurs because of the phase shift between measurements a, b, and c, is this the best method for calculating stress when the load fluctuates?

Thank you in advance for taking the time to read this.

AJ

 

[rb1957]

picture what's happening to your strains.

strains go to zero, stress goes to zero.

principal stress looks "odd" because the direction is changing, as the sign of the stress/strain changes.
you're also plotting max and min principal stress. so initially the max principal is large and the min principal small. Magnitudes flip at the other end of the cycle.

I would plot as 3D ... x = max principal, y = min principal, z = time,
or plot as an element so you'd see the directions of the stresses, and see this element rotating CW then CCW in time with the applied strains.

another day in paradise, or is paradise one day closer ?

 

[AmJam]

Thanks, @rb1957.
However, since the load is reversible and the beam undergoes tension and compression stresses, shouldn't the principal stress also be cyclic? Why the direction is changing?

Please help me to understand the results from the 2D and 3D plots of the maximum and minimum principal stresses:

AJ

 

[rb1957]

what does "sensor C" and "sensor D" mean ? two strain gauges ?? where on the section ??

"shouldn't the principal stress also be cyclic?" they are, but you're plotting max principal. You can work through a hand calc to shown that the max principal changes from direction 1 to direction 2
"Why the direction is changing?" 'cause the strain rate (the slope of the strain o/p) is different for the three channels.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

No, principal stress is not cyclic, since it is a magnitude, not a tensor value.

 

[rb1957]

sorry, but of course principal stress has a direction. Review using Mohr's circle to find principal stress.

Along with principal stress there is an angle ... the direction from the x normal stress.

Does von Mises stress have a direction ? Is it a mathematical construct, or the actual stress in the material (therefore acting in some direction) ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

Yes, principal stress has a direction, but VM does not.