# Stress and deformity (mechanic - solidity)

1. Mar 30, 2006

### Andreii

Hi, 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