Thermal Expansion Behavior

[CTW]

I'm evaluating a steel "bucket" with four legs attached to the side. The "bucket" is simply what you envision. A cylinder with a bottom. The top is open. There are four legs that are symmetrically placed around the perimeter and welded to the side of the bucket but not attached to the floor. The bucket will be heated to 750 deg F. I started looking at this as the legs restraining the thermal expansion of the bucket at the location of the legs only and the bucket being allowed to expand in the areas between the legs. But I'm second guessing this now and would like some other opinions. It seems to me that the high thermal stresses combined with the retraint from the legs would warp the perimeter of the bucket if not fail it depending on the grade of steel used.

 

[EngineerTex]

Two thoughts:

1) If the legs aren't attached to the floor, how will the legs restrain expansion?

2) If you're concerned about the legs themselves applying hoop stresses for a very short arc around the outside of the bucket, the biggest question would be whether or not the legs become as hot as the bucket. If the legs get as hot as the bucket and it's all steel (regardless of grade), then I would think that every dimension on it would grow by the thermal expansion coefficient and result in a state of zero additional stress.

Or did I not understand the question?

-T

Engineering is not the science behind building. It is the science behind not building.

 

[vpl]

I got the impression that the bucket assembly rests on the floor but the legs are not physically attached (bolted, welded, etc.) to the floor. Kind of like a cauldron, only the legs go up the side?

The way it sounds, I don't see how there could be much of a temperature differential between the legs and the bucket because they're all one component. Are they different materials?



Patricia Lougheed

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[corus]

Depending on how big the legs are then I'd expect the outside of the legs to be cooler than the point of contact with the bucket and hence you may get some localised stresses due to that region of the bucket having a lower temperature, on average. As far as thermal expansion of the legs go, then EngineerTex makes valid points. In the worst case though, you might expect the legs to be pinned to the ground at ambient temperature (with friction). If they're bolted down then in the worst case you could assume that they were fully built in (at ambient temperaure). In either case there'd be a load imposed on the shell dependent on the rotational stiffnesss of the shell and the bending stiffness of the legs. At the very very very worst you could do a simple calculation based upon an attachment imposing a fixed displacement on the shell equivalent to the difference in thermal expansion. If those stresses are ok then there'd be no problem. Otherwise you'd have to use finite elements to assess it.

corus

 

[CTW]

Thanks for the replies. Very good questions and comments!

EngineerTex
1) If the legs aren't attached to the floor, how will the legs restrain expansion?
Certainly a question I've asked myself before but since the friction between the base of the legs and the floor will play a role in the level of restraint, I decided that the bucket and legs will not move as one unit during expansion. I envision the legs leaning outward from the base when the bucket expands. How much? Who knows. It would depend on the level of frictional resistance developed between the base of the leg and the floor.

2) If you're concerned about the legs themselves applying hoop stresses for a very short arc around the outside of the bucket, the biggest question would be whether or not the legs become as hot as the bucket. If the legs get as hot as the bucket and it's all steel (regardless of grade), then I would think that every dimension on it would grow by the thermal expansion coefficient and result in a state of zero additional stress.
You bring up a good point about the temperature of the legs versus the bucket. There is a 6" distance between the bucket and the legs and they are attached by two tees. The legs are 12" pipe. The stem of one of the tees is welded to the bucket and the second tee's stem is welded to the pipe. The two are then bolted together through the flanges. So the question is how much heat will the legs see? The exterior of the bucket is insulated, but this does not affect the tees since they are welded to the bucket. I would think the legs would be somewhat cooler than the bucket although probably fairly warm from heat transfer, but the expansion of the two will not be the same.

vpl

I got the impression that the bucket assembly rests on the floor but the legs are not physically attached (bolted, welded, etc.) to the floor. Kind of like a cauldron, only the legs go up the side?
Correct.

The way it sounds, I don't see how there could be much of a temperature differential between the legs and the bucket because they're all one component. Are they different materials?
They are all steel. The grade may vary depending on availability.

corus

I'm definitely trying to avoid doing an FEA on this as I think it can be simplified to a few minor hand calcs.

My concern is having too much stress or deflection of the bucket between the legs. Let's assume worst case that the legs end up attached to the floor and the legs are rigid enough to restrain the expansion of the bucket. This will cause the area between the legs to deflect some amount (depending on the thickness of the bucket's shell) and possibly crack if the stresses are too high. At least this is the way I'm envisioning the behavior. If anyone sees this behaving differently, please let me know.

On the other hand, what if there was some sort of expansion material placed between the flanges of the tees? This would allow the bucket to expand independant of the legs, offer a thermal break between the bucket and the legs, and greatly simplify the behavior of the bucket.

See the link below for a plan view of the bucket.

http://files.engineering.com/getfil...1-4db3-8535-056f99084e6f&file=Bucket_Plan.pdf

 

[jedward]

could you insert a simple flexure in place of the Tee attach point to essentially eliminate the thermally induced strain?
- split the Tee into two parts with a space
(two Tees head to head with a small gap in the middle)

 

[CTW]

jedward-
I think I understand your logic. Basically an air gap, right? But how can the gap be created with two tees bolted together and still not transfer heat through the bolts?

 

[DesignerGuy16]

You could create a flange that has a thermal resistant gasket material, then line the bolt holes with a similar material, and a washer of similar material on each side of the flange.

So you're surrounding the bolts with insulation. I've done similar on a robot end effector picking up 1500F parts post forging and worked out fine.

You might think of using a compliant foot/leveling pad on the legs so it will stay stable if it expands in any direction?

James Spisich
Design Engineer, CSWP

 

[jedward]

instalal a spacer or sorts and use titanium bolts, the thermal isolation and stress relief will result from geometry

/**/
/ /
--//// ////--- two tees top to top with * for Ti bolts
/ /
/**/

?

 

[zekeman]

Mostly depends on the diameter of the cylinder,weight of the cylinder and coefficient of friction of legs against the floor.
For steel, the expansion from 70 to 750 deg, the expaansion of 1/2 of the cylinder is
u*R*delta T
I got 6.5*10^(-6), so
for example if R =20 inches
the free expansion would be
.1 inches.
You first determine friction at the floor and use that force to push cylinder.Check resultant stress on cylinder (4 point forces on cylinder)( use Rourke or Timoshenko stresses in Shells) to see whether it can take that load. If it can, you are done. If not, you can either use some flexible device between leg and cylinder or redeign the leg to make it laterally flexible but rigid enough to suppoert the load or put a ball roller at the floor end of the legs.
You need to provide:
Diameter
weight
thickness of cylinder
material of cylinder
length and dimensions of leg, the more flexible the better
static coefficient of friction at floor to leg
You don't need any fancy computer methods for this one.

 

[CTW]

Diameter=56 inches
Weight=14,000 lbs
Thickness of cyliner=5/8 inch
Material of cylinder=A514 grade G Steel
Length of leg=87 inches
Leg is 12" diameter sch 80 pipe
coeff of friction=0.3

 

[jedward]

could you put rollers or wheels on two of the legs to effectively eliminate the friction with the supporting surface?

 

[CTW]

Unfortunately, no.

 

[TGS4]

I am going to chime in on this discussion,m particularly when the topic of friction comes up. I will point out that your coefficient of friction (0.3) is probably an unconservative choice, and I will explain why.

Typically, when we look at friction, it is as a penalty factor. In that case, a value like 0.3 is probably appropriate. HOWEVER, in your situation, where you need to take credit for a lack of friction to make your evaluation work, it may be more appropriate to iteratively calculate what the maximum-acceptable value of the coefficient of friction is that makes your evaluation work. Since you've come to the conclusion that if the legs were welded to the floor (friction = infinite), then you would have stresses that are excessive, then a coefficient that is anything less than infinite helps you. In a way, it's a bit of a reverse problem, but I would highly recommend that you not take this lightly.

My experience in this respect is the design of pressure vessel support skirts. When the pressure vessel is very hot and the support skirt is very short, you have essentially the same situation as you describe. If you want to understand how we handled that problem, check out the paper

http://www.asmedl.org/vsearch/servl...=JPVTAS&key=DISPLAY&docID=1&page=1&chapter=0.

 

[zekeman]

I fail to see why temperature in the legs is ANY problem at all. The simple problem is that the cylinder is expanding radially about 0.15 inches and it matters little what the legs are doiing. Either you allow the thermal growth to be absorbhed by the cylindrical wall or flexure in the legs or both is the first line of cnsideration.
Now if you take 0.3 as an assumption for static friction you get about 1K of lateral force at the 4 points, but as TGS4 points out, this is problematical and crucial to this thinking.
I now believe that the safest approach is the interface flexibility, that almost everyone favors including the OP.
My own opinion is that you can still use the 2 TEEs but use a greased stainless steel bushing and sleeve instead of a tight bolting to allow the growth of 0.15 inches with an effective friction considerably less than the 0.3 we spoke of.

 

[CTW]

I like the idea of using a greased stainless bushing and sleeve but this requires periodic maintenance and people normally neglect these things. Any other thoughts on how to achieve a low friction? Even if the support configuration has to change? So far, I have not been able to come up with anything that works.

 

[EngineerTex]

1) Weld the legs together at the bottom with a 0.25" plate.

2) Remove the tees

3) Weld a shear web vertically on the leg that reaches all of the way to the cauldron, but make the web only half as tall as the existing tees.

4) Weld a shear web vertically on the cauldron that reaches all of the way to the leg and make that web only half as tall as the existing tees.

6) In steps 3 & 4, stagger the two shear plates such that the one on the leg is above the one on the cauldron.

7) Tie them together with a linkage of two pieces of plate on each side and connect the leg to the cauldron with these links bolted to each.

Now, your legs are fixed and your cauldron is suspended by the links. Just make sure that the plate at the base can handle the induced moment from the legs. Add gussets if it can't.

-T

Engineering is not the science behind building. It is the science behind not building.

 

[Albigger]

I like Tex's suggestion. (Basically, in your plan view, turn your bolts 90deg from where they are now, and allow slop in the joint for growth).

But, even considering the worst case as you have it now, I would think you could treat the legs as cantileverd beams, firmly attached to the floor. I get that the diameter will expand almost 1/4", so figure the legs would each have to bend 1/8" at the bucket. Figure out the force needed to bend the leg by that much, and if the leg will take it. Then apply that force in 4 locations to the bucket, and see if the bucket will hold up.

 

[prex]

CTW, can't really see where your problem is.
TGS4 showed as an example the analysis of a skirt to vessel junction. However this situation is only representative of yours as far as stress classifications are concerned, but is far worse in stress levels, as the skirt represents a circumferential restraint and generates a circumferential membrane stress in the shell that is by far the one of most concern.
Anyway in both cases all the stresses generated by the temperature differential are secondary in nature, so they can't 'crack' your vessel, unless you are in a high thermal cycle fatigue condition.
Also I don't understand those that above suggest methods to thermally separate the legs from the bucket, as this would of course be useful to limit the heat loss from the container, but would be detrimental for the stresses in argument.
From the proportions you quote my feeling is that you can't have any problem, be the legs fixed to floor or not.
But if you want a calculation proving this you should go this way IMHO:
-by a conservative assumption of a friction coeff (depends much on floor condition, may be reduced and controlled with PTFE pads) determine from equipment weight the transverse force acting at leg base, and from that the bending moment and the radial load acting on bucket wall
-the stresses in bucket wall may be evaluated by the methods of WRC107 or WRC297 (a calculation sheet for the latter is in the first site below), though your loads are applied more along a line than on a circular area like for a nozzle
-you'll get however an idea of the level of stress (that I expect quite low), and if you still have doubts, you could add a generous repad under the tee leg
-the stresses determined as above will have to be combined with those coming from mechanical loads and be compared with the limits for secondary stresses


prex

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