# Homework Help: Biaxial forces

1. Aug 8, 2017

### Confusedbiomedeng

1. The problem statement, all variables and given/known data
Consider the cube with sides a=b=c=10cm . This block is tested under biaxial forces that are applied in the X and y directions. Assume that the forces applied have equal magnitudes of Fx=Fy=2x10^6 and that the modulus and poissons ratio of the block material is E=2x10^11 Pa and poissons ratio is = 0.3
I) find the new dimensions of sides if both are tensile and I) if Fx is tensile and fy is compressive

2. Relevant equations
σ=F/A
εX=1/E(σx-νσy)

3. The attempt at a solution
σX=2x10^6/0.1=2x10^7
Same for σy as same variables

εX= 1/2x10^11(2x10^7-0.3(2x10^7))

εX = 7x10^-5

εY= same as same variables

=> a=0.100007m
b=0.100007m
C=0.09993m

I know that this is wrong but I can't seem to figure out why and I can't seem to do when one is tensile and one is compressive could really use help

2. Aug 8, 2017

### haruspex

Check the area term in there.

Your work would be much easier to follow if you were to use parentheses as appropriate.

3. Aug 8, 2017

### Confusedbiomedeng

Sorry yes your right it should be 0.01
I mistyped as I only have my phone it's quite hard to reread probably

4. Aug 8, 2017

### haruspex

It's not just that you mistyped that line, though. You carried the error through the rest of the calculation, no?

5. Aug 8, 2017

### Staff: Mentor

Also, C is wrong. What is the equation for epsilonC?

6. Aug 9, 2017

### Staff: Mentor

$$\epsilon_C=-\frac{\nu(\sigma_x+\sigma_y)}{E}$$

7. Aug 9, 2017

### Confusedbiomedeng

And what is the difference then between tensile and compressive ? Also the equations εx=1/E(σx-μ(σy+σz))
εy=1/E(σy-μ(σx+σz))
εz=1/E(σz-μ(σy+σx))

Sorry I got thrown all these equations but no explanation on which or why use them

8. Aug 9, 2017

### Staff: Mentor

No. That is just the result of substituting $\sigma_z=0$ into the equation below.
Yes. These equations are correct. You can choose whichever directions you please for the three stresses. In your problem, two of them are non-zero (and equal), and the third is zero.

9. Aug 9, 2017

### haruspex

Then let me break this down: εz=1/E(σz-μ(σy+σx))
With only a force in the x direction, the consequence for the z direction would be εz=(1/E)(-μσx). Similarly for a force in the y direction only.
For a force in the z direction only, the consequence for that direction is (1/E)(σz)
With forces in all three directions, to a first approximation, you can just add them together.

10. Aug 9, 2017

### Confusedbiomedeng

i did it out again , does this look more correct??

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11. Aug 9, 2017

### Staff: Mentor

Both calculations of C are incorrect. In part (a), you made an algebra error and in part (b) you calculated $\epsilon_z$ incorrectly.

12. Aug 9, 2017

### Confusedbiomedeng

On the final page is it ? A and B dimensions are correct thou?

13. Aug 9, 2017

### Staff: Mentor

Yes, A and B are correct. But, there is no calculation on either page for $\epsilon_z$ in case (b)