Trouble with Bruhn, A17 2

[Sparweb]

Trouble with Bruhn, A17:

I'm trying to find stress in skin due to pressurization. I'm using Section A17.7 of Bruhn, because it combines plate and membrane analyses. (I've already tried analyzing the membrane stresses, this section looks more realistic). The coefficient given as

(q/E) * (a/t)⁴

is used in the table, and given for typical values of 12.5 to 250. When I try to calculate the coefficient using the data I have:
pressure = 5 psi
a = 8 inches
E = 10.7 E⁶ psi
t = 0.032 in

The resulting coefficient is an order of magnitude greater than the values in the table.

What could I be doing wrong?

STF

 

[edbgtr]

Hello STF

Fig A17.7 appears to be assymptotic around the value of 16 implying that the stress in your panel is around 2.7 ksi. However, if I use some other curves I have (for a 250=b/t panel)the stress comes out at 15 ksi on a general long thin panel curve, simply supported, but restrained in-plane, like most skin panels are. Or, if I use a short thin panel analysis curve (panel AR=1) then I get 14.8 ksi. These curves are taken from company manuals, but are similar to those in Prof Niu's "pink" book (Analysis and Sizing)and if you extrapolate the hinged edge "f"-curve (Fig. 7.2.9)and you should come close to my results. If you would like the de-sensitized curves from the Manuals, post your e-mail address in your reply on this site, and I'll send them to you.
Regards,
Ed.

 

[KSshopper]

Is your skin a flat plate or is it a cylinder? If it is a cylinder, I'd recommend calculating hoop stress using classical methods: f=pr/t. If you're skin panel is a flat plate, I'd recommend using FEM to determine the plate stresses. Remeber to turn on stress stiffenning to capture the membrane effects.

Also, if this is an ultimate analysis, all skins are experiencing pure membrane stress prior to rupture.

 

[Sparweb]

philcondit, edbgtr,

Thanks for the info so far. Things I didn't state in the original post are that I'm dealing with a FAR 23 aircraft, it's got chem-milled skins (0.050 under the frames, 0.032 between). Everything is 2024-T3 aluminum.

The big picture goes like this: We've been designing antenna installations for a long time for various operators using the same basic approach all along. Recently, an operator had an antenna nearly break off for all the vibration it produced. The antenna they used and the antenna we originally saw are two different animals, but the antenna manufacturer claims that one is a "replacement" for the other. The replacement has an airfoil shape, hence side loads, that we never accounted for on the original round one.

Since dealing with the repair [thread2-60032] I've been suspicious of our entire approach to antenna installations, even though the failure wasn't our fault. I've been taking it on as more of a personal challenge to do this as well as possible, and I'm exploring all possibilities that I can.

Philcondit, my personal belief is that FEM is best used on the original design of a structure, because that is the only place where the effort is worthwhile. When it comes to fiddly little mods midway through an aircraft's life cycle, the expense of a FEM analysis cannot be justified.$$

Analyzing the fuselage like a pressure vessel is easy, but it ignores the effect of the frames and stringers, doesn't it?

[ul]Pressure vessel hoop stress: (5*psi)(25*in)/(0.032*in)= 3.9 ksi
[ul]Since the frames and stringers are ignored, does the stress get higher? What effect does the chem-milling have?[/ul][/ul]
[ul]Membrane stress (Bruhn Table A17.2): n₂=0.356 (square panel) so stress max = 9.1 ksi
[ul]This also leads to the conclusion that the skin bulges out by nearly 1/8". That would be an unacceptable amount, so the designers must have been using another stress theory.[/ul][/ul]
Edbgtr seems to be coming up with 15 ksi; ouch.
I'm interested in your suggestion from Niu's book (I have Airframe Structural Design, which focuses only on wing cut-outs, it seems). I'd be pleased to see these curves:
[sparweb@hotmail.com]

All this goes to simply understanding the basic stress in the fuselage, and I admit, I'm a bit out of my depth.

STF

 

[KSshopper]

SparWeb:

I've delt with antenna modifications as well, so I can appreciate the dilemma. The static analysis for your airplane's fuselage skin was most likely based on hoop stresses due to pressure (pr/t). Additionally, Bending stresses in the longitudinal direction due to pressure (pr/2t) and body bending were analyzed for the stringers and effective skin. The effects of the frames (resisting radial expansion of the fuselage) were conservatively ignored in a static analysis because it tends to reduce the stress in the fuselage skin.

The effects of the frames become more of an issue in a fatigue analysis. The skin still behaves like a membrane, however, some of the pressure load is drawn into the frames throught the stringer-to-frame joints. I have seen some handbook approaches to determining the internal loads distribution, but the calculations are cumbersome and the results are difficult to rationalize. That's why I prefer FEM to get the internal loads in such circumstances. Nothing fancy... Just something that models skin thickness, frame, stringer and floor beam stiffness.

It sounds like your antenna had some loads and dynamic issues. Maybe aeroacoustic fatigue. Did the antenna have a solid load path into the frames and stringers? I'm curious on how the antenna failed.

 

[Sparweb]

The pilots reported hearing a vibration during descent (I bet they were a bit beyond Vmo, but if I asked, they probably wouldn't tell). The mechanics pulled the head liner down, tightened the nuts, put it all back together. Same vibration happened, so they tried the same solution, and to no avail. They knew they had a problem, so they inspected the a/c regularly, and caught the cracks about 1/2 inch before all of the skin under the antenna would have peeled away. Two cracks on either side of the antenna had grown to about 4 inches each, both running lengthwise on the fuse. The antenna was obviously vibrating side-to-side, bending the skin maybe several times per second.
The antenna was in the middle of the panel, so no frames or stringers were directly involved.

I've tried running a few examples through the FAA's RAPID. My disbelief of the results was given substance when I ran horrible repair designs, full of as many no-no's as the software would permit, and it still gave the repair a 300,000 cycle life!

I still remain suspicious of a FEM analysis, unless it can be made simple enough to be put through an Excel spreadsheet and/or with MathCAD. Otherwise, as you mentioned, the results are "difficult to rationalize".



STF

 

[KSshopper]

Okay, I think I understand. It sounds like you have a couple of things going on.

The first is the antenna is experiencing aeroacoustic buffeting. air flow across the antenna sheds vortexes as it passes. Simply put, these vortexes are a forcing function with a frequency that varies with airspeed. This is what caused the famous collapse of the Tacoma Narrows Bridge. Apparently the frequency at descent is close to the natural frequency of the antenna installation.

The second problem is the antenna load path isn't stiff enough. By making the load path stiffer, you can tune the natural frequency of the antenna away from the frequency of the buffeting.

Skins are good at carrying tension and shear, but poor at tranfering bending moments and compression loads. Based on your posts, I really recommend "boxing out" your antenna to transfer the bending moments due to antenna air loads into the stringers and frames. For larger antennas this is normally done with intercostals and shear ties.

The analysis should be simple and straight forward: P/A and Mc/I. What to use for loads? Maybe Vmax*sin(max sideslipangle)*Cd*1.5 for side load and 1.5*Vmax*Cd for aft load.

I hope I make sense. It's very difficult to type these things out. Normally when I'm speaking with another engineer, I've got a pencil and a pad of paper.

 

[graemew]

A comment if I may. Many years ago I came across an instance of antenna "buzz".
The aircraft was a Fokker F28 and the antenna had been place too far forward on the fuselage. It was seeing transonic airflows.
Perhaps the placement of the antenna could be worth looking at.
I concur with PhilCondit with regard to transferring the loads into the structure. It is normal to consider a pair of intercostals between adjacent frames and a couple of lateral stiffeners that pick-up on the intercostals at each end and the antenna attach screws in the centre. Depending upon the size of the antenna, radius blocks on the laterals at the screw holes may be a good idea.
If the aircraft is certified for flight into known icing you will also need to consider the drag load if an ice accretion on the front of the antenna. There is an FAA AC on the subject (the number escapes me at the moment ). I have seen OEM reports that have assumed a rough 2" radius semicircular shape along the full LE of the antenna.
You will see that if you follow this approach, you will be able to seperate the antenna installation into 2 parts for design purposes:
1. Reinforcing the feed-thru hole.
2. Carrying/mounting the antenna.
Please consider galvanic effects due to the removal of external paint for antenna grounding. It is a good idea (often overlooked by structures engineers ) to install an external sacrificial plate of the size of the antenna base, tack-riveted and sealed to the structure to provide a good earth, but easy to remove at replace if (or when ) it corrodes (as often happens beneath antennas ), and to enable inspection of the hull periodically to satisfy damage-tolerance requirements.
With chemically milled skins, consider the landings as part of the stringers/frames. Reinforcing the feed-thru hole is best accomplished by a smallish bonded doubler if you have access to the technology for proper surface prep. and adhesives. Cold working the antenna attach holes is likewise a very good idea.

 

[Sparweb]

The aircraft isn't as fast as a F28, but the antenna was mounted very far forward. In fact, Beechcraft mounts 12" fin antennas a bay forward of where this antenna was. We never suspected that the forward placement would be a problem, but I've have the same feedback from an engineer at the company that manufactures the antennas. His point of view is that ice forms more readily near the front, since the farther back you go, the more heat has radiated out from the hull into the air. This is definitely going to be considered in the future.

The structure supporting the antenna is simple enough - I've gone a step further than your suggestion because Roark has cases of torsion in channels with end restraints that very nicely take care of the loads on the antenna itself.

The stress this induces in the skin is still a mystery...
I think I'll model it as a "pressure" by applying the antenna reaction load to half the base of the antenna and see what I get. It will probably be too high from a fatigue point of view, though maybe okay from a static strength view, so I'll have to fudge an assumption somewhere in the fatigue analysis...

BTW, you make perfect sense, philcondit. You're speaking my language.

Graeme, most of the techniques you listed we already practice, although the cold-working of the mounting holes is a surprise. We usually just polish things smooth to take out the drilling cracks. Are you referring specifically to a cold-expansion of the holes where a mandrel is drawn thru a sleeve in the hole, leaving a residual compressive stress in the hole? I don't know of anybody who has that kind of tooling, apart from the OEM's. Have you tried it?


STF

 

[graemew]

I certainly have, and its use is much more widespread than you may realize (although not necessarily for antenna applications ). Most airlines with an engineering organisation will have FTI tooling.
I think that if you contact Len Reid, Mark Weiss or Scott Gulick at FTI in Seattle; ph (206)246-2010 they will be able to give you a list of nearby organisations with the tools, or will be able to hire them to you, along with necessary training.
Mention Graeme.Willaton.
Thanks

 

[Sparweb]

I'm back everyone; my project was put on hold for a while. In the meantime, I've learned a few disturbing things. I'm not sure how "nice" it is to do so, but I posted a warning about these antennas in a separate thread; [thread2-67807].

The antenna was never tested above 210 knots at Sea Level. Vibration at the tip of the antenna was observed at this speed in the wind tunnel. The company claims that the antenna can be used at speeds up to 350 KTAS. This ridiculous exaggeration of the facts is irresponsible on their part. It makes no sense to try to develop a structure to support this antenna when the manufacturer is inventing numbers.

Thanks for all the tips, everyone, they're all getting filed away in my "standard practices" notes, but I feel vindicated that there was nothing inherently wrong with my original support structure.

One last thing I want to suggest to philcondit: I use an old standard for designing antenna installations called "AL 970" which has been superseded by Def-Stan-970. There's a chapter on antenna installations that you might find handy. edbgtr linked me to a website with the Def-Stan documents but I'm damned if I can find the link as I type this. If you're interested, I'll look harder.


STF

 

[JSF]

Sparweb,
What type of Antenna? I agreed with Philcondit. Any antenna may have vibration and side loads. The antenna installation is not correct. Either it tied to frame or have stiffeners to take the side load moment out. Skin can not take the large side load and due to the vibration the skin will crack.

JSF

 

[Sparweb]

Well, this is a finer point in the history, but in the beginning of the design, we had one antenna to work with. A year later the antenna manufacturer came out with a replacement product touted as a "drop-in replacement", so aircraft operators did just that. We weren't told about the change of antenna configuration. It used to be a thin, cylindrical whip, 16" long. Now it's a high-aspect ratio wing.

The first time I ever saw this killer antenna was the day the aircraft operator phoned saying it had almost come off.

From many people's point of view, the antennas look so similar that they don't see the problem with the new antenna, so of course the failure is "our fault". The antenna manufacturer said the antennas were equivalent, after all!

JSF, many antennas can be mounted in the middle of skin panels, provided that the side loads are taken through a structure. This could be via an intercostal, or simple stiffening flanges at the edges of the doubler. The latter is what was done on the original antenna installation, given that the maximum side loads that it could produce were very small.

The new antenna has such a significant flutter that the only way to "correctly" mount it is with a 1" thick plate bolted to both frames ahead and behind the antenna.

If you still want me to clarify what I mean, I could post names and p/n's of the two antennas so you can see for yourself how different they are.

STF

 

[edbgtr]

Hi STF

The Def-Stan website is

http://www.dstan.mod.uk/

Their regulations contain lots of good stuff, and a set of the "old" AvP 970 is even better. Someone should make them available in electronic format.

Ed