/sci/ - Science & Math » Thread #12465173

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Anonymous Mon 14 Dec 20:08:53 2020 No.12465173 View Reply Original Report

Quoted By: >>12465242 >>12465670 >>12465763

What is the coordinate transformation between pure shear stress and pure tension and compression?

Anonymous

Anonymous Mon 14 Dec 2020 20:11:05 No.12465176 Report

Quoted By: >>12465209

A translation or a rotation

Anonymous

Anonymous Mon 14 Dec 2020 20:24:57 No.12465209 Report

Quoted By:

>>12465176
I'm talking about the same point, so it can't be a translation.

Anonymous

Anonymous Mon 14 Dec 2020 20:35:29 No.12465242 Report

Quoted By: >>12465647

>>12465173
mathematically your question is "how do i diagonalize a symmetric matrix with a diagonal zero"

Anonymous

Anonymous Mon 14 Dec 2020 22:16:03 No.12465647 Report

Quoted By: >>12465679 >>12465763 >>12469094

>>12465242
And why is the tensor symmetric?

Anonymous

Anonymous Mon 14 Dec 2020 22:23:56 No.12465670 Report

Quoted By: >>12465763 >>12466755 >>12466756

>>12465173
shear is not compression/tension
i suppose you could decompose tensor into two tensors, one for shear components and one for compression/tension components.

Anonymous

Anonymous Mon 14 Dec 2020 22:25:24 No.12465679 Report

Quoted By:

>>12465647
all tensors in physical systems are symmetric

Anonymous

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Anonymous Mon 14 Dec 2020 22:42:25 No.12465763 Report

Quoted By: >>12465796 >>12465866

>>12465173
What is Mohr's circle? Now how does one interpret it?

>>12465647
Probably because unbalanced torques would cause rotational acceleration rather than shear.

>>12465670
I think Mohr's circle says you are wrong.

Anonymous

Anonymous Mon 14 Dec 2020 22:49:27 No.12465796 Report

Quoted By:

>>12465763
>you are wrong
wouldn't surprise me haha.

Anonymous

Anonymous Mon 14 Dec 2020 23:09:26 No.12465866 Report

Quoted By: >>12465906

>>12465763
explain how a shear stress becomes a compression stress under coordinate transformation

Anonymous

Anonymous Mon 14 Dec 2020 23:24:02 No.12465906 Report

Quoted By: >>12465927

>>12465866
https://en.wikipedia.org/wiki/Mohr's_circle#Finding_maximum_and_minimum_shear_stresses
$\tau_{min,max}=\pm R$
Since I assume transformations are continuous, there must be a transformation where shear stress is zero, but stresses do not disappear, so there must be either tension or compression. Not sure how I would prove that there is tension and compression simultaneously.

Anonymous

Anonymous Mon 14 Dec 2020 23:28:58 No.12465927 Report

Quoted By: >>12465949

>>12465906
>there must be a transformation where shear stress is zero
why
shear is by definition a force parallel (and compression normal) to the plane. that doesn't change just because of coordinate transform

Anonymous

Anonymous Mon 14 Dec 2020 23:38:34 No.12465949 Report

Quoted By: >>12465955 >>12465959 >>12466059 >>12466083

>>12465927
Symmetric tensors are diagonalizable. Also if there is compressive movement in one axis and tensive in the other, naturally there should be angular momentum. Also, my proof above should be valid if my assumptions hold.

Anonymous

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Anonymous Mon 14 Dec 2020 23:40:26 No.12465955 Report

Quoted By: >>12465959

>>12465949
>Also, my proof above should be valid if my assumptions hold.
Diagram

Anonymous

Anonymous Mon 14 Dec 2020 23:41:55 No.12465959 Report

Quoted By:

>>12465949
>>12465955
Damn, I'm sperging out. Meant to quote this.
>Also if there is compressive movement in one axis and tensive in the other, naturally there should be angular momentum.

Anonymous

Anonymous Tue 15 Dec 2020 00:06:29 No.12466059 Report

Quoted By:

>>12465949
makes sense, thanks.

Anonymous

Anonymous Tue 15 Dec 2020 00:10:04 No.12466083 Report

Quoted By: >>12466256

>>12465949
still hard to picture tension x + compression y = shear, but im willing to take your word for it

Anonymous

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Anonymous Tue 15 Dec 2020 01:02:31 No.12466256 Report

Quoted By: >>12466730

>>12466083
>but im willing to take your word for it
You shouldn't.

Anonymous

Anonymous Tue 15 Dec 2020 03:50:02 No.12466730 Report

Quoted By:

>>12466256
ok. on reconsideration. I no longer do.
tension x + compression y ? shear

Anonymous

Anonymous Tue 15 Dec 2020 03:57:46 No.12466755 Report

Quoted By: >>12468600

>>12465670
and is still don't understand why this is wrong
i dont think there is a coordinate system / rotation where tension + compression forces in the original become shear forces in the new system, and vice versa.

Anonymous

Anonymous Tue 15 Dec 2020 03:59:14 No.12466756 Report

Quoted By: >>12468600

>>12465670
say you start out having only shear forces in 1 plane, you can rotate that coordinate system all you want and the most you'll ever get is shear forces in 2 planes in the new coordinate system.

Anonymous

Anonymous Tue 15 Dec 2020 16:36:51 No.12468600 Report

Quoted By: >>12470322

>>12466755
>>12466756
Wouldn't a compressive force along the x-axis and tension force along the y-axis of equal magnitudes necessarily lead to a net force parallel to some vector at 45° to either axis? If this vector becomes a basis vector in another coordinate system, then you have effectively converted tension and compression to shear stress.

Also, may I ask what project of yours depends on stresses or strains?

Anonymous

Anonymous Tue 15 Dec 2020 19:08:21 No.12469094 Report

Quoted By:

>>12465647
Conservation of mass, linear momentum and angular momentum.

Anonymous

Anonymous Wed 16 Dec 2020 00:04:19 No.12470322 Report

Quoted By:

>>12468600
no i don't think so, because tension/compression forces are parallel to the derivative vector, and shear forces are perpendicular, which makes them fundamentally different kinds of forces.

I'm honestly not sure though. I'm thinking maybe in some weird coordinate system transform like cartesian to polar/spherical or something...

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