Mechanics of Materials basic exercise

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The discussion revolves around a mechanics problem involving a graded steel cylinder (AISI 1030) subjected to axial forces, requiring analysis of internal forces, strength checks, and total distortion calculations. Participants clarify that the problem should be treated as a 3D scenario, emphasizing the importance of calculating tensile stress separately for each cylinder based on their respective cross-sectional areas and forces. There is confusion regarding the application of forces, with suggestions to ensure proper unit conversions and the correct use of formulas for stress and distortion. Ultimately, the goal is to determine whether either cylinder exceeds its yield strength limit under the applied loads. Accurate calculations and free body diagrams are essential for solving the problem effectively.
  • #31
I drew them that way. ;)

The reason is that the one is the reaction to the other.
Since we're talking about a static problem (no movement), they have to cancel out.

Of course, and if there's a 3rd vector, they can still cancel each other out, it all depends on their value...

Doesn't matter.
If the result is negative, it only means that the force apparently went the other way.
It won't matter for the calculations.
However, in your case you know which way is the largest force, so you can draw and calculate it right.

Ok, so I know A1 and A2.

Sigma1 = 2.5F-F/A1
Sigma1= 1.5F/A1

Is that correct?
 
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  • #32
Femme_physics said:
Of course, and if there's a 3rd vector, they can still cancel each other out, it all depends on their value...

Yes.

Note that the force by the wall will go to the other direction with your 3rd vector.


Femme_physics said:
Ok, so I know A1 and A2.

Sigma1 = 2.5F-F/A1
Sigma1= 1.5F/A1

Is that correct?

Yep! :smile:
 
  • #33
Note that the force by the wall will go to the other direction with your 3rd vector.

Sorry, I'm stupid, I should've started with basic mechanics and not have overcomplicated things!

Anyway, I'll have a scan ready for you this evening with my sigma results.. :smile: then again, my teacher might solve it today and class starts in 20 minutes.

I'll tell you why I was confused though. I'm used to the fact that in isolated free body diagrams, all forces = 0, yet, here,

http://img832.imageshack.us/img832/7379/seethis.jpg

Uploaded with ImageShack.us

If I look at each of them INDIVIDUALLY, they don't = 0. But, I guess I shouldn't expect it in materials strength (unless it's dynamics).

But tell me one thing, shouldn't it be the second pic instead of the first pic?

http://img856.imageshack.us/img856/4535/insteads.jpg

Makes more sense to me...

Will reply in 5-6 hours maybe going to college. THANKS A LOT. :)
 
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  • #34
Femme_physics said:
I'll tell you why I was confused though. I'm used to the fact that in isolated free body diagrams, all forces = 0, yet, here,

http://img832.imageshack.us/img832/7379/seethis.jpg

If I look at each of them INDIVIDUALLY, they don't = 0. But, I guess I shouldn't expect it in materials strength (unless it's dynamics).

I don't understand. :confused:
In the picture you have 2 free bodies.
And each free body has all forces = 0 (since this is statics).



Femme_physics said:
But tell me one thing, shouldn't it be the second pic instead of the first pic?

http://img856.imageshack.us/img856/4535/insteads.jpg

Makes more sense to me...

Will reply in 5-6 hours maybe going to college. THANKS A LOT. :)

The force F is a force that pulls the entire object to the right (on the right side of the object).
Effectively, it pulls cylinder 2 to the right, and indirectly it also pulls cylinder 1 to the right.
 
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  • #35
Well?
How did it end?
 
  • #36
We had a lab session where we tested hook's law until the breaking point of a brass specimen, so no exercising. We'll probably solve it tomorrow. The teacher actually said I'm jumping ahead of myself since we haven't learned the basics of solvng that (which makes me feel less stupid :smile: ) but regardless he told me my answer is wrong. Too bad I forgot too scan it last night. But, it appears to be wrong at any rate.

I don't understand.
In the picture you have 2 free bodies.
And each free body has all forces = 0 (since this is statics).

OK let's see if I got the basics mechanics right now.

http://img526.imageshack.us/img526/8374/nafix.jpg
 
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  • #37
Femme_physics said:
We had a lab session where we tested hook's law until the breaking point of a brass specimen, so no exercising. We'll probably solve it tomorrow. The teacher actually said I'm jumping ahead of myself since we haven't learned the basics of solvng that (which makes me feel less stupid :smile: ) but regardless he told me my answer is wrong. Too bad I forgot too scan it last night. But, it appears to be wrong at any rate.

Cool! So you got to break stuff? :cool:
Femme_physics said:
OK let's see if I got the basics mechanics right now.

http://img526.imageshack.us/img526/8374/nafix.jpg

You got the complete picture right with the proper normal force from the wall. :)

Your picture (b) is right too.

But in your picture (a) you have attached N to the wrong side of cylinder 2.
The cylinder is fixed on the left side, so it's only there that N can push.
 
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  • #38
Actually, when tensional forces are calculated, usually a diagram like the following is made.

That is, first all external forces are charted and calculated.

Then a cylinder is sawn into half, and the force H is figured out to keep the system in balance.
This is the force used to calculate the tensional stress.

Then the other cylinder is sawn into half, and the process is repeated.

attachment.php?attachmentid=40829&stc=1&d=1320914233.gif
 

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  • #39
Cool! So you got to break stuff?

Yes, made a big "BANG" sound and scared the shizzle out of me!

Anyway, thanks!

I'll print your last reply now and look at it in class (starts in 1 hr). Can see what I did wrong, We'll probably solve it today. Will reply later. Thanks :smile:
 
  • #40
Did you solve it today?
 
  • #42
Nice!
Complete with a graph for the expansion and a neat table!

Did you do all that by yourself?
 
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  • #43
I like Serena said:
Nice!
Complete with a graph for the expansion and a neat table!

Did you all that by yourself?
:smile:

No actually the teacher did. But hey, at least I know how to do them now and am ready for new challenges!

Thanks a lot, Klaas! I love the fact it's based on mechanics...bringing back those good ol' days... *grins*
 
  • #44
Femme_physics said:
:smile:

No actually the teacher did. But hey, at least I know how to do them now and am ready for new challenges!

Thanks a lot, Klaas! I love the fact it's based on mechanics...bringing back those good ol' days... *grins*

Oh, you'll get your challenges...
Wait till you get to load, shear, and moment diagrams!

(Poor little cartoon men! :eek:)
 
  • #45
LOL. Yea, for now, I keep practicing basic exercises. I'll scan my latest one this afternoon if you'll be here.
 
  • #46
I'll take a look at it when you get to it...