Stress Tensor Homework: Finding Traction Vector

[racnna]

Homework Statement

http://img842.imageshack.us/img842/9577/stresstensor.png

Homework Equations

'traction vectors' are just the rows of the stress tensor. that is, the first row of the stress tensor(the i-component of the tensor) is the first traction vector, second row is the second,etc.
traction vector equation is
$$<b>t_n</b>=<b>n</b> dot <b>T</b>$$

The Attempt at a Solution

I was trying to find a surface whose normal vector forms the same angle with the three coordinate axes. and then dot this normal vector with the stress tensor in order to determine the traction vector. but the result i get is not any of the three given traction vectors

 

[racnna]

uh oh...58 views and no replies? i am positive you experts have encountered stuff like this...there are much harder problems on this forum! if it helps, please IGNORE my post about relevant equations and just focus on the problem statement

alright...and let me know if there's any confusion about the problem statement

 

[gabbagabbahey]

I was trying to find a surface whose normal vector forms the same angle with the three coordinate axes. and then dot this normal vector with the stress tensor in order to determine the traction vector. but the result i get is not any of the three given traction vectors

What result do you get? Why do you think there are only 3 traction vectors?

uh oh...58 views and no replies? i am positive you experts have encountered stuff like this...there are much harder problems on this forum! if it helps, please IGNORE my post about relevant equations and just focus on the problem statement

alright...and let me know if there's any confusion about the problem statement

Please exercise some patience. Most students are still on summer break, and homework helpers do not check the forum as frequently. None of us are paid to help you, it is just something we choose to do in our free time.

 

[racnna]

woah easy there. I didnt mean to offend you. I just got worried because there were so many views and no replies so i thought there was a problem with the way the problem is worded.

I think there's an infinite number of traction vectors?...but the rows of the Tensor should give you three traction vectors?

i used the unit vector $$\frac {1}{√3}, \frac {1}{√3}, \frac {1}{√3}$$ and dotted this with the stress tensor to get the traction vector they are asking for. Is that correct?

 

[gabbagabbahey]

I think there's an infinite number of traction vectors?...but the rows of the Tensor should give you three traction vectors?

Yes. The 3 rows of the stress tensor correspond to traction vectors for surfaces normal to one of the 3 basis coordinates. Your surface normal isn't directed along any of the basis vectors (i, j, k) though, so there is no reason to expect the traction vector to be one of those rows.

i used the unit vector $$\frac {1}{√3}, \frac {1}{√3}, \frac {1}{√3}$$ and dotted this with the stress tensor to get the traction vector they are asking for. Is that correct?

Yes.

 

[racnna]

Aha! thanks so much gabba