# Help with determining the dimension change in the xyz direction of a component under a load?

I'm stuck on this question. I got the first part right which is to work out the dimension change in the x direction but I got the y and z directions wrong. I had to submit this online and it doesn't show what you did wrong so I'm really frustrated on why I got this wrong I was hoping someone could correct me. Since I put my answers online I left the negatives in both my y and z values which might be why I got it wrong I just wanted someone to help to see if I have actually done something wrong. I forgot to add in my diagram the length of the x which is 200mm sorry. It's in my working though.

## 1 Answer

Did you include the stress applied to the Y direction (your drawing shows Py = 10 kN) this contributes to the strain in the Y direction.

Also If you take the Y direction as "up" (as you have with the load 10 kN) then your Z dimension is out of the page, when you calculate the displacement in those directions it looks like you got the signs mixed up.

Remember the load in the Y direction will cause expansion in Y and contraction in X and Z. You need to add up all these effects in each direction.

• Oh I totally forgot that how would I do that though ? and for the Z direction ? So would I work out the stress in the y direction and then do the same as x ? How would I do this for Z though ? Also I'm still not sure what you mean by how I got the signs mixed up ? Could you explain that ? Thank you so much for the help I really appreciate it. – Cinna Apr 1 at 21:16
• Sorry I also wanted to ask what areas would I use for y and z ? – Cinna Apr 1 at 21:18
• Okay so you have stress in the X, you solved it right. Find the strain in each direction due to that stress. Now do the same with the Y direction, find the stress in Y and the strain in all 3 directions. After this add the strain up in each direction. Then calculate the change in length in each direction. .... As for the signs, you need to multiple the strain in a given direction, by the length of the body IN THAT direction. To me it looks like your length in the y direction (Ly =30 mm) this should be multiplied by the strain ey to find change in length in Y. – ShadowMan Apr 1 at 21:20
• Okay thank you so to work out the stress in y would my area be 200 x 20 though ? – Cinna Apr 1 at 21:36
• Yes that is the projected area in the X-Z plane. So your length in Y is again 30mm. – ShadowMan Apr 1 at 21:37