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reinforcing a cylindrical beam

reinforcing a cylindrical beam

reinforcing a cylindrical beam

(OP)
hello all,

i'm in the process of designing a payload section for an autonomous underwater vehicle (e.g., http://www.hydroidinc.com/remus600.html).

this section will be rated to 1000psi.  it is Al 7075-T6.

My problem background:

the payload section must fit inline with the vehicle diameter, which is 12.75".  however, the thin-walled pressure vessel that will house our electronics is only 10" OD (0.35" thick) and will not be a structural part of the assembly, i.e. it does not support a bending moment, it will only undergo compression from the hydrostatic pressure at depth.  this means that when we pull the vehicle out of the water, the entire section weight will have to be transferred to a cross-member.  At the moment, i have a 2" OD aluminum tube (0.2" thick) that runs the length of the assembly whose centerline is located roughly 4.5" from the longitudinal payload centerline.

My question:

I am interested in knowing whether the 2"OD tube can support the weight of the payload section.  To determine this, I have used a uniform load that represents the weight of the section (~1000N/m) to calculate the bending of this tube, using the cross-sectional inertia and Young's modulus of the tube.  It appears that the 2"OD tube might deflect too much, so i am interested in suggestions on how to increase the strength of this system.

Ideally, i would like to know how to model the deflection of  two beams that are rigidily mounted to a common endcap in the same vertical plane, but are of different cross-sections and located an arbitrary distance from one another... very similar to a composite I-beam in my mind, but i have trouble modeling the constituitive end-condition.

thank you for any insight.  below is a cross-sectional rendering

Cross section of payload:

| | | | | | | | | |Uniform Load 1000N/m
v v v v v v v v v v
---------------------\ 12.75"OD
---------------------|
10"OD electronics |
---------------------|
..........................|..............Payload Centerline
                          |             }
---------------------|             }offset is ~4.5"
2"OD tube           |.............}
---------------------|
--------------------/

RE: reinforcing a cylindrical beam

1) plane sections remain plane

2) strain is proportional to the distance from the neutral axis

3) work out the neutral axis by using the first moment of area, and the Ixx by using the parallel axis theorem.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: reinforcing a cylindrical beam

You need to check the collapse pressure of that thin- walled pressure vessel, too.  

Mike Halloran
Pembroke Pines, FL, USA

RE: reinforcing a cylindrical beam

I'm not sure I understand the problem, but will note that steel and stainless steel have much higher young's modulus than aluminum, hence lower deflection for an equivalent cross sectional area.  Not sure about titanium.

You might also consider a tapered member if feasible (IE, tapered thickness, constant OD, variable ID).

RE: reinforcing a cylindrical beam

(OP)
thanks Mike and Greg.  by FEA, and looking at Roark's Stress and Strain, we are operating below the collapse pressure of the vessel...

indeed i've calculated the Ixx for the 2"OD member and there is a 2 order of magnitude increase in inertia, which consequently will reduce my deflection at that member.

so, you're saying that i can basically treat this problem like a composite beam, despite the separation of the members?  

makes sense... just wasn't sure.

RE: reinforcing a cylindrical beam

Perhaps I'm missing something:

The payload sits on the 2"OD beam, not the 12.75" vehicle shell, but if it deflects enough, it would rest on the ID of the vehicle body?  The payload section is not the 1000N/m (please note the unit descrepancy -- don't want to miss Mars, do we?) load, it is the weight of the entire section?

It sounds like the 2" beam is supporting the payload and the 12.75" shell is supporting the rest of the section weight.  It seems that you are saying that the only common connection between the 2" beam and the 12.75" vehicle body is at the ends.  If this is the case, then I do not believe you can consider it a composite beam.  I think you react the payload out on the 2" beam and the reaminder out through the vehicle body.

My 2 cents...

Garland

RE: reinforcing a cylindrical beam

Hi rdamus

I think I agree with GBor if you have 2 beams that are only
connected at the ends and there is a space between them with no physical connection you cannot consider it a composite beam. I invisage that if you load the top beam it will deflect independently of the bottom beam.

Regards desertfox

RE: reinforcing a cylindrical beam

(OP)
GBor:

sorry for the unit mismatch; i think in SI, but the Navy, and hence the vehicle manufacturer, uses English units...

the entire weight of the payload is roughly 100kg.  it is about 1.2 m in length, so 1000N/m is close enough...

indeed the only common connection between the 2" beam and the 12.75" vehicle body is at the ends; this is my point about the 10" can not taking a bending moment.  

thus the 2" beam is where the reaction takes place, but the section mass acts through the center of gravity, which is ~4.5" above the 2" beam's centerline.  i'm under the impression that the Ixx i actually need to use would be the Ixx by the parallel axis theorem using d=4.5" as the lever arm.  at least, this is how i interpret GregL's comment, and was how i was solving for my bending deflection...

RE: reinforcing a cylindrical beam

Oh, sorry I misread your problem. I agree with Gbor etc, if the fixity between the two tubes is poor then the 2" tube is the only part that bears the load and you don't need the composite section properties.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: reinforcing a cylindrical beam

rdamus,

I spent 13 years working for a Navy contractor, so I definitely understanding the Navy's thinking and the confusion that it sometimes causes...as long as you keep them straight in your calculations, I'll hang with you.

If I'm understanding correctly, there is no parallel axis theorem here, just a straight forward beam calculation.  It looks like you should have something like:

Ixx = Iyy = PI/64*d^4 = 0.7854

Sounds like the end connection is probably closer to pinned than fixed.  I don't remember the formula off the top of my head, but it seems like maximum deflection is something on the order of 5*W*L^4/384EI for a distributed load?  Works out to about 0.04" (0.1 cm)...seems pretty small...perhaps my equation is off...probably should double check.

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
www.borowskiengineering.com
Lower Alabama SolidWorks Users Group
http://laswug.borowskiengineering.com

RE: reinforcing a cylindrical beam

Surely your FEA answers the fixity question?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: reinforcing a cylindrical beam

FEA is only as good as the input..."garbage in, garbage out".

RE: reinforcing a cylindrical beam

The photos in the brochure shows the entire vehicle being hoisted from the middle, which suggests that the outer wall and whatever internal structures can support the full weight of the vehicle and payload with some specified deflection.  

Do you have the ICD from the manufacturer?  

You seem to be implying that your pressure vessel is sitting on top of your beam.  Why can't your pressure vessel be supported with cross members that rest directly on the bottom of the vehicle housing?

Does the supplier have representative designs that you can use?

TTFN



RE: reinforcing a cylindrical beam

(OP)
thanks for the numerous replies.

GBor: for a distributed load on a beam, i'm using w*L^4/(8*E*I)... and the I for the section is (pi*(a^4-b^4))/64;

where
a=outerDiameter=2"=0.0508m
b=innerDiameter=1.8"=.0457m
I=2.2485e-007m^4

(i forgot to mention, the 2"OD tube is actually a thin-walled cylinder; carries cabling from stern to bow, so it must be hollow for that purpose)

i do not understand why i can't use the PAT for the 2" tube.  technically, the weight of the section acts through the center of gravity of the section, which is located ~4.5" above the centerline of the 2" beam, thus the reaction the beam carries is not taken along the same plane that the weight acts through- wouldn't this be a PAT case?

Greg: the guy who does our FEA modeling is out this week, so i'll have the final answer next week...  in the meantime, he ran the FEA with the section supporting the load and it did deflect - is there a way to post images in these forums?

IRStuff: the tricky thing about this section is that there is no outer wall that spans the entire 12.75" diameter along the length of the section.  our 10" pressure vessel is where the primary electronics live, and thus the drawing above is a bit misleading - there is no shell that we can transfer the load from the endcaps to; the purpose of the 2"OD tube running along the bottom of the section is to handle the loading on the section.

and as for supplier designs, a legacy design will typically
look like the images from the mfg website - namely, a payload will fit within a 12.75" thin-walled housing which is mated to either endcap using MK48 band clips; indeed the REMUS relies on this design for its structural integrity.  thus, the problem we are having is different

RE: reinforcing a cylindrical beam

now i'm confused ... i thought i was, but now i know for sure; i guess it's the problem of not posting good pictures.

is the 12.75" dia body water proof ? ... if so, this is where your pressure is applied.  it doesn't need to be continuous, but you have to provide a load path between the various elements.

is the 10" electronics section the water proof compartment (i'd hope so ! electronics and water don't mix).  then the hyrostatic pressure would pass thru the 12.75" dia. cover and apply itself to the 10" dia compartment (and the 2" dia tude).

is the 10" electronics bay "nailled" into the rest of the strcuture, or is it fitted in (so that it's easily removable) ?  then your FE should have gap elements so that it only takes load if/when the strcuture defelects enough.

i guess you're trying some hand calcs to verify your FEA

RE: reinforcing a cylindrical beam

Sorry, I think I gave "I" for a solid bar, not a hollow tube.

I don't think we're fully understanding how this thing is put together.  If the payload is reacting through the entire length of the shell and not just the attachment points at the end, then you may be able to use the composite beam theory, but it sounds like the internals are supported by the 2" tube, which is only connected at the ends.

If the payload is connected to the shell, or the 2" tube is connected along the entire length of the shell, then you can calculate the "I" of the cross-section of the shell/tube using what sounds like something just below the shell centerline as the neutral axis (it would be below the geometric center since some of the structural integrity would come from the tube, which is below the centerline).

Garland

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

RE: reinforcing a cylindrical beam

I (almost) see clearly.  Thanks, rdamus, that helped a great deal.  One final question:  The payload is apparently in the 10" thin-walled portion and is, therefore, supported primarily by that feature, but you are trying to gain some advantage from the 2" thin-walled tube.  Do the rib structures connect to the tube?

If not, you will not gain any significant advantage from it until your 10" shell has deflected significantly to contact the 2" tube with one minor caveat...the beam equations that you are trying to use probably assume no shear deformation.  The 2" tube will provide some stiffening as the shell attempts to shear deform and "pulls" on the tube at the ends.  You may be able to analyze this using some of Timoshenko's theories.

If the ribs DO connect to the tube, you will gain some advantages as described in the previous paragraph, but with the strength of the ribs holding on as well as the end caps.

Garland

RE: reinforcing a cylindrical beam

Well, I'm still a little confused.  

Page 2 of the their brochure shows the entire vehicle suspended from a ring clamped to the vehicle body in two places near the center of the length:
http://www.hydroidinc.com/pdfs/remus600web.pdf

How does the front and back ends keep from bending down if the outer wall isn't strong enough to support all the weight?

TTFN



RE: reinforcing a cylindrical beam

(OP)
Garland:

the ribs do not connect to the tube.  please see:

RE: reinforcing a cylindrical beam

(OP)
IRStuff:

since my section has arrays on either side, we cannot take advantage of the 12.75" hulls that you see in the REMUS brochure.  this is the crux of the problem.  please refer to the image i posted, or view it here: http://www.zhrodague.net/~rdamus/hull/ribbed-mod2-front-no-array.jpg

RE: reinforcing a cylindrical beam

So how does the load feed into the 2 inch tube?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: reinforcing a cylindrical beam

Only through the shear deformation of the 10" shell I would think.

I would be very reluctant to take advantage of any stiffness from the 2" tube.  It would be difficult from a stiffness standpoint.  I don't think you can call this a "composite beam".  The FEA would give you a more realistic, less conservative answer, but, if performed properly, would be the way I would go.

RE: reinforcing a cylindrical beam

I see, but I don't see.  

The weight of your assembly appears to be resting on the vehicle body at the ends of your structure, so the vehicle walls are supporting your entire weight.  Your 10-inch tube is apparently strong enough to support the weight transfer to tbe ends, which means that extending your other fins to the same diameter as the end plates would allow you support the entire weight on 7(?) cross members, rather than just two, and get rid of the 2-inch pipe.

TTFN



RE: reinforcing a cylindrical beam

sorry, i'm dumbing this down to my level ...

it sounds like you have a sensor outside of the 10" dia tube "since my section has arrays on either side, we cannot take advantage of the 12.75" hulls", so you're expecting to see water on the inside of the 12.75" outer shell ... seems a bit wierd to me, but i don't know the project as well as you do.  but this means that you're going to have water pressure on all faces of the latter picture.

i assume the latter picture is structure that is well built into the structure of the sub, and that you've got loads ahappening all over the place ... ahead of this section, behind it, inertia loads, pressure loads ...  i also assume that the 10" tube pretty much slides into the big hole on the latter picture (for easy removal).  If this is the case, the the 10" tube is pretty much just reacting pressure and the structure of the sub is doing it's thing all around the this tube.  if this is the case, then i suspect you need structure (ribs) to support (and structurally join) the fwd and rear bulkheads.

but maybe the 10" tube is built in, attached with lots of screws.  in which case it can react the sub loads.  i see the two tubes (10" and 2") working together, but not as a composite beam, as they don't have a shear path between them.  the two beams could react external moments by having different endloads and by individually assuming a bending stress field, but i think this is alittle tricky to calc on the back of an envelope as it looks redundant.  Plane sections remaining plane sounds like a sensible assumption.

but what's happening with the outside shell whilst all this is happening to the "inards" ?  is the shell attached so that the interior structure is going to take all the load, and deflect without transferring load to the shell ? seems abit odd.
 

RE: reinforcing a cylindrical beam

Dude - I hope you're not using my tax dollars to get your job done by committee for free!! winky smile

Maybe hire an unemployed torpedo designer??

RE: reinforcing a cylindrical beam

(OP)
rb1957:

you have hit the nail on the head.  this is the key point: the the 10" tube is pretty much just reacting pressure and the structure of the sub is doing it's thing all around the this tube.  the 10" housing will float in space, and all the reaction will take place along the 2" tube.  this is a requirement for the design, as the radial contraction of the 10" tube must soleley be influenced by the hydrostatic pressure; this ensures that the struts (ribs) contract uniformly and the deformation at the center of the tube is roughly equivalent at either end.

i started this thread making this claim, and was interested in understanding if
1)i could do something to strengthen the system without influencing the 10" section
2) how to properly model the bending of the 2" beam - i.e., is the system a composite beam, and if not, what assumptions will guide my calcs to generate reasonable FEA analysis, for as Garland notes, "garbage in, garbage out"


arto:

dude, first off, i've never used a forum like this.  i'm just curious what people have to say.  the design is more ore less done.  i appreciate all the commentary and activity.  it definitely feels like people are interested.  i hope to respond in kind in other forums on this site.

Garland and Greg and IRStuff:

thanks mucho for the insights and keeping me diligent in addressing this problem.

-rob

RE: reinforcing a cylindrical beam

radmus,

why do you think the outside shell is doing nothing (to react loads) ?  certainly it's best placed to stiffen the structure.  it sounds like you can remove the 10" tube from the model without affecting the results (since the tube is only reacting pressure) ... tho' you should check the displacements of teh surronding structure to make sure the surrounds aren't butting up against the 10" tube.  

i'd start by making sure the bulkheads at both ends of the 2" tube are stiff enough to redistribute their loads into the 2" tube, you probably want some sort of stiffeners to reinforce the bulkheads.  then the loading of the 2" tube is simple enough ... loads from the bulkheads and hydrostatic pressure

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