Mechanic - Solidity (Stress, Deformity)

[HaRdTeChnO]

Hello.. I am new to this forum, just registered, so again hi everyone

May I ask for the help with the following task. I looked at it alone a few times but I am not able to realize where is the mistake.



Task: We put this square in the rigid gutter and give the force on the upper side of the square (look at picture). This force does symetrical divide all over upper side (surface). We also warm this square. Get the result (in the accordance to the datas above) of stress (σ) and deformity (ε). We neglect friction!


I used those three formulas:



My steps:


σ: σxx = need to figure it out in next steps
σyx = 0
σzx = 0
σxy = 0
σyy = need to figure it out in next steps
σzy = 0
σxz = 0
σyz = 0
σzz = 0

ε: ε xx = need to figure it out in next steps
ε yx = 0
ε zx = 0
ε xy = 0
ε yy = need to figure it out in next steps
ε zy = 0
ε xz = 0
ε yz = 0
ε zz = need to figure it out in next steps

(Comment to this first step: I belive those ''parameters'' are true, so the mistake should be in the next steps)

Next steps:

ε xx is the same as ε x

ε yy is the same as ε y

ε zz is the same as ε z

σxx is the same as σx

σyy is the same as σy

σzz is the same as σz

(I mentoined this because in my formulas is like this ε x and not like this ε xx )

σy = F/S = - 4600000 / 429 * 1373 = - 4600000 / 589017 = - 7.81 MPa

σx : ε x = 1/E (σx – v(σy + σz)) + α * △T

0 = 1/210000 (σx – 0.3(-7.81+0)) + 30 * 10^-6 * 37
0 = 0.000004762 (σx – 0.3(-7.81 + 0)) + 0.00111
0 = 0.000004762 σx + 0.0000111574 + 0.00111
0 = 0.000004762 σx + 0.001121157
0.000004762 σx + 0.001121157 = 0
0.000004762 σx = - 0.001121157
σx = - 235.43826 MPa

(I used to set ε x as 0 – at least in the accordance to my book is like that, so i could get σx )


ε y : ε y = 1/E (σy – v(σx + σz)) + α * △T

ε y = 1/210000 (-7.81 – 0.3(-235.43826 + 0)) + 30 * 10^-6 * 37
ε y = 0.000004762 (-7.81 + 70.631478) + 0.00111
ε y = 0.000004762 (62.821478) + 0.00111
ε y = 2.99 * 10^-4 + 0.00111
ε y = 0.001409

ε z : ε z = 1/E (σz – v(σx + σy)) + α * △T
ε z = 1/210000 (0 - 0.3(-235.43826 – 7.81)) + 30 * 10^-6 * 37
ε z = 0.000004762 (0 + 72.974478) + 0.00111
ε z = 3.475 * 10^-4 + 0.00111
ε z = 0.00146


Something is wrong in my steps but I don't know what because for ε y and ε z must come '' something * 10^-4 '' (where ''something'' is the number).
I need to get the results for the following four things: σx , σy , ε y , ε z

I wouldn't be able to help you here, Did you try your search engine?

Try ε xx is the same as ε x and see what you come up with, there are a few there that may open the path that you seek.

[HaRdTeChnO]

ε xx is totally the same as ε x. I just marked with ε x. I used google.com but it was useless in my situation because in the equations is some specific mistake (the thing when i was wrong might be typical for stress and deformity tensors) but i checked like 10 times alone and still can't find what i have done wrong... I think parameters of both tensors are right, formula and result for σy is 100% right

At times, I find it best to get up and walk away from homework in any form. The grey cells get locked into a loop, that can be detrimental to what one is trying to accomplish.

Take a break, get some fresh air, listen to Motzart, try to completely forget the problem your working on.

When you get back look these up:
www.lhup.edu/~dsimanek/errors.htm - 70k
www.thames-side-maywood.com/faultfinding.asp - 18k
composite.about.com/library/weekly/aa990714.htm - 26k

[HaRdTeChnO]

chendoh thank you but I need someone who could take a look at my steps in the task and tell me where is the mistake. I know what should I do in the situation when I am confused . I didn't find anything useful in those three links, I searched on google.com also. Those formulas are in the first system of Hook's law and im sure they are true for my task. Your links wasn't useful but thank you very much anyway to take your time for me.

Your welcome,

Why not try the teacher that gave you the problem?

He/She won't give you the answer, but maybe give you a clue to help you understand.

'Solutions are more important than Answers'

[HaRdTeChnO]

Hmm why no useful replies to my topic yet?