Let's assume that a closed hollow cylinder is filled with a gas that expands tremendously during heating. Assuming that the cylinder does not expand from heat, if it is heated, what kind of strain will be exerted on the wall of the cylinder (not the end) from the pressure? Tensile or compressive? If both, which would be more severe?
Physics question.
- Thread starter Howard
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Zenmervolt
Elite member
- Oct 22, 2000
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My guess is that it would experience tensile pressure, since with the interior volume expanding, the circumference must expand, meaning the outer wall is stretched.
ZV
ZV
Actually, it matter quite a bit. A thick wall cylinder will have a much more complex stress state with stress levels changing through the thickness of the material.
Judging from your complete lack of clue, I'm guessing this is an introductory mechanics course, in which case it's almost certainly a thin wall cylinder.
In that case, draw a free body diagram with the cylinder split lengthwise. Draw in some vectors denoting the pressure force on the cylinder. Now, use some mental calculus to figure out the resultant force vector on each half. It should be fairly obvious. Now, what kind of force @ the cut edges would be required to hold the cylinder together? What kind of stress would this create?
This will get you the hoop stress. That's not the whole answer, but you can get it by a similar construction.
tensile stress is applied to the cylinder. the gas is exerting a force on the interior of the cylinder causing the atoms in the cylinder to be pulled apart. that's a tensile force. severity? severe to what?
Depends on the diameter of the cylinder.
Rough rule of thumb:
R/t > 10 : thin-wall
R/t < 10 : thick wall
R: Radius
t: thickness
thickness doesn't matter. the force is always acting normal to the curved surface, so the strain is tensile.
While its true that the direction of the strain is qualitatively the same for either case, thickness is very significant to the quantitative results.
The original question appears to be asking for a qualitative answer, so you're right, thickness doesn't matter for the qualitative answer.
If it's thick wall though, there will be a radial component of the strain-state that will be compressive.
Howard: stress is a second-order tensor... you can't say that stress is "compressive or tensile" without noting a face and a direction. The "hoop" stress, as others have pointed out" will be tensile. The "radial" stress will be compressive. So, its not really a "bit of both"--it depends on what you're looking at. I assume that your professor/teacher will be MUCH more interested in the hoop stress--as it is the higher of the two.
As far as the thick/thin argument--it really doesn't matter. The "thin" cylinder assumption is just that, an assumption. You ASSUME that the radial stresses are zero--which isn't actually the case, but its pretty close for R/t > 10.
As far as the thick/thin argument--it really doesn't matter. The "thin" cylinder assumption is just that, an assumption. You ASSUME that the radial stresses are zero--which isn't actually the case, but its pretty close for R/t > 10.
CaptnKirk
Lifer
- Jul 25, 2002
- 10,053
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Boyles Gas Laws
V1xP1.... V2xP2
---------- = -----------
...T1 ..........T2
Load is Tensile.
Mechanical properties of a load in tension can reach levels about 10X those of compression before failure.
Compression buckling is most common structural failure.
V1xP1.... V2xP2
---------- = -----------
...T1 ..........T2
Load is Tensile.
Mechanical properties of a load in tension can reach levels about 10X those of compression before failure.
Compression buckling is most common structural failure.
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