reinforcing a cylindrical beam

[rdamus]

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 |.............}
---------------------|
--------------------/

 

[GregLocock]

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.

 

[MikeHalloran]

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



Mike Halloran
Pembroke Pines, FL, USA

 

[JStephen]

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).

 

[rdamus]

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.

 

[GBor]

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

 

[desertfox]

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

 

[rdamus]

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...

 

[GregLocock]

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.

 

[GBor]

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.

http://www.borowskiengineering.com

Lower Alabama SolidWorks Users Group

http://laswug.borowskiengineering.com

 

[GregLocock]

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.

 

[GBor]

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

 

[IRstuff]

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

 

[rdamus]

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

 

[rb1957]

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

 

[GBor]

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

 

[CorBlimeyLimey]

"A picture is worth ....."

faq559-1100 or faq559-1177


Helpful SW websites FAQ559-520
How to get answers to your SW questions FAQ559-1091

 

[rdamus]

sorry for confusing some, but this should clear things up:

http://www.zhrodague.net/~rdamus/hull/

click on ribbed-mod2.htm

 

[GBor]

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

 

[IRstuff]

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