• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Archived Plane Stress Transformation

  • Thread starter theBEAST
  • Start date
366
0
1. Homework Statement
Here is the problem with my attempt at the solution:
8Ezm0.jpg


The magnitude of my answers are correct, HOWEVER I am getting the wrong signs. For the force balance in the x direction I get a negative P but for the force balance in the y direction I get a positive P. Does anyone know why?

I was thinking it was because I have the wrong direction for shear stress on my free body diagram... But I thought this wouldn't matter since the math will always work itself out?
 
Last edited:
19,357
3,839
The stress tensor in the members is ##\vec{\sigma}=\frac{P}{(0.05)(0.08)}\vec{i}_x\vec{i}_x=250 P\vec{i}_x\vec{i}_x## Pa. The unit normal to the joint is ##\cos {25}\vec{i}_x+\sin{25}i_y##. From the Cauchy stress relationship, the stress vector acting on the joint is ##250 P\cos {25}\vec{i}_x##. The component of this stress vector normal to the joint is ##250 P\cos^2 {25}##. The unit tangent to the joint is ##\cos{25} \vec{i}y-\sin{25}\vec{i_x}##. The component of the stress vector tangent to the joint is ##250 P\sin{25}\cos {25}##. So, for the joint not to fail,
$$250 P \cos^2 {25}< 800000$$and $$250 P\sin{25}\cos {25}<600000$$So,$$P<3896\ N$$and $$P<6266\ N$$So the critical load is 3896 N.

This result is basically the same as the result obtained by theBEAST, and thus confirms his answer.
 

Want to reply to this thread?

"Plane Stress Transformation" You must log in or register to reply here.

Related Threads for: Plane Stress Transformation

Replies
1
Views
3K
Replies
1
Views
9K
  • Posted
Replies
2
Views
4K
  • Posted
Replies
0
Views
2K
  • Posted
Replies
2
Views
4K
  • Posted
Replies
13
Views
1K
  • Posted
Replies
6
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top