- #1

- 2

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

In summary: Hi again, I am not sure if you're referring to experimental data or a theoretical problem, but if you're dealing with experimental data you can basically rotate the reference frame so that the plane in question becomes aligned with one of the axes, and from there it's just a matter of plugging in the values. If it's a theoretical problem, then it'll be a bit more complicated but the same principles apply. Just make sure you're using consistent units throughout and that you're using the correct formulas for the direction cosines. In summary, the shear stress components on an arbitrary plane in a cubic under 3D stress state can be derived by using a generalized 3D stress transformation, which involves using 9 direction cosines obtained from

- #1

- 2

- 0

Physics news on Phys.org

- #2

Science Advisor

Gold Member

- 902

- 1

- #3

- 2

- 0

You are right. Thanks.

PerennialII said:

- #4

Science Advisor

Gold Member

- 902

- 1

[tex]

\left(

\begin{array}{c}

\sigma_{xx}^'\\

\sigma_{yy}^'\\

\sigma_{zz}^'\\

\sigma_{yz}^'\\

\sigma_{xz}^'\\

\sigma_{xy}^'

\end{array}

\right)

=[T_{\sigma}]

\left(

\begin{array}{c}

\sigma_{xx}\\

\sigma_{yy}\\

\sigma_{zz}\\

\sigma_{yz}\\

\sigma_{xz}\\

\sigma_{xy}

\end{array}

\right)

[/tex]

where

[tex]

[T_{\sigma}] =

\left(

\begin{array}{cccccc}

l_{1}^2 & m_{1}^2 & n_{1}^2 & 2m_{1}n_{1} & 2n_{1}l_{1} & 2l_{1}m_{1}\\

l_{2}^2 & m_{2}^2 & n_{2}^2 & 2m_{2}n_{2} & 2n_{2}l_{2} & 2l_{2}m_{2}\\

l_{3}^2 & m_{3}^2 & n_{3}^2 & 2m_{3}n_{3} & 2n_{3}l_{3} & 2l_{3}m_{3}\\

l_{1}l_{3} & m_{1}m_{3} & n_{1}n_{3} & (m_{1}n_{3}+m_{3}n_{1}) & (l_{1}n_{3}+l_{3}n_{1})& (l_{1}m_{3}+l_{3}m_{1})\\

l_{2}l_{3} & m_{2}m_{3} & n_{2}n_{3} & (m_{2}n_{3}+m_{3}n_{2}) & (l_{2}n_{3}+l_{3}n_{2})& (l_{2}m_{3}+l_{3}m_{2})\\

l_{1}l_{2} & m_{1}m_{2} & n_{1}n_{2} & (m_{1}n_{2}+m_{2}n_{1}) & (l_{1}n_{2}+l_{2}n_{1})& (l_{1}m_{2}+l_{2}m_{1})

\end{array}

\right)

[/tex]

where the direction cosines are

[tex]l=cos\alpha[/tex]

[tex]m=cos\beta[/tex]

[tex]n=cos\gamma[/tex]

and [itex]\alpha[/itex] is the angle between [itex]x,x^'[/itex], [itex]\beta[/itex] is the angle between [itex]y,y^'[/itex], [itex]\gamma[/itex] is the angle between [itex]z,z^'[/itex] where you'll get the direction cosine components.

- #5

- 3

- 0

thanks

- #6

Science Advisor

Gold Member

- 902

- 1

http://www.electromagnetics.biz/DirectionCosines.htm

http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node52.html

http://en.wikipedia.org/wiki/Direction_cosines

if you need a general form what's in #4 will do, but if you need something which works for example in 2D it can be clarified a whole lot ... what sort of a problem you're working with?

- #7

- 3

- 0

I am trying to rotate 3 d stresses like the matrix above but I am not sure what L1..L3, n1.. N3 and m1 m2 and m3 are .

thanks

- #8

Science Advisor

Gold Member

- 902

- 1

- #9

- 3

- 0

PerennialII said:

thanks again i think I am nearly there just having a few probelms now with the rotated shear stresses

"3d stress on arbitrary plane" refers to a type of stress analysis technique used in engineering and materials science. It involves calculating the stress distribution on a specific plane within a three-dimensional object or structure.

Understanding 3d stress on arbitrary plane allows engineers and scientists to accurately predict the stress and strain on various components of a structure. This information is crucial in designing and building safe and durable structures.

To calculate 3d stress on arbitrary plane, a combination of mathematical equations and computer simulations are used. This involves determining the forces acting on the structure, as well as the material properties, and using them to calculate the stresses on the specific plane.

The 3d stress on arbitrary plane can be affected by various factors such as the material properties, external forces, and the geometry and shape of the structure. Changes in any of these factors can alter the stress distribution on the plane.

3d stress on arbitrary plane is used in a wide range of real-world applications, including building construction, aerospace engineering, and materials testing. It allows engineers to analyze the structural integrity of various components and make necessary design improvements for safety and efficiency.

Share:

- Replies
- 6

- Views
- 777

- Replies
- 21

- Views
- 1K

- Replies
- 24

- Views
- 1K

- Replies
- 10

- Views
- 893

- Replies
- 9

- Views
- 540

- Replies
- 1

- Views
- 496

- Replies
- 3

- Views
- 488

- Replies
- 19

- Views
- 2K

- Replies
- 4

- Views
- 1K

- Replies
- 5

- Views
- 635