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# Fuselage Bending

## Fuselage Bending

(OP)
New to aviation and getting my feet wet in the analysis side. Analyzing a fuselage mounted antenna installation and was told to use these calculations (attached) for fuselage bending. However I can't find what reference/text book this came from and the person who gave it to me is unaware also. Don't have anybody else to ask; working for a design firm with no analysts. Do these calculations come from a text book? I have done some reading online and understand how to go about calculating the fuselage bending but it would be nice to read the text book that these equations came from too.

Thanks!

### RE: Fuselage Bending

Moment = Load * level arm

For the first equation, the effective moment arm is x1/2. The load is the weight of the fuselage at the cut, which would be Wf*x1/Lf. The assumption is that the mass is evenly distributed along the length of the fuselage. You can solve the rest of the equations in the same manner.

Brian
www.espcomposites.com

### RE: Fuselage Bending

Book: Roark - Formulas for Stress and Strain
Chapter: Bending of Beams
You can find the 7th edition of the book online if you are not using it commercially.

You will see these equations and its derivatives for different boundary conditions (i.e. constant distributed load, variable distributing load & etc.)

Roark would be a good book to refer to most of these kinds of equations used.
If you want to go more into theory and background, your order should be:

An simple Elasticity book for the background of these equations(preferably one for a university undergrad course wouldn't get you too tired)

Bruhn - Analysis and Design of Flight Vehicle Structures
Niu - Airframe Stress Analysis and Sizing

But you should know that there is a lot going on. So, you would have to put at least 2000-3000 hours before achieving an beginner level (even for hand calculations).
So a total of 4000-6000hours (2-3 years) gets you up to industrial level if you are really into it.

You can cut these hours by 2000-3000 hours if you have a good college structural courses' background.

Spaceship!!
Aerospace Engineer, M.Sc. / Aircraft Stress Engineer

### RE: Fuselage Bending

these are horribly coarse assumption of fuselage loads ... it looks like FAA Chicago Office DT assumptions ?

If you're doing an antenna install on the pressure cabin the main thing to worry about is fuselage pressure.

You may have no-one there to help you, but someone will be signing for compliance. ask them to help.

### RE: Fuselage Bending

(OP)
Thanks for all the replies.

I have lots of examples of fuselage bending and pressurization. Bruhn and Niu have been lots of help too.

I am more annoyed that people have been blindly using these equations without a reference or showing their own derivations. I will not use these without a reference.

### RE: Fuselage Bending

I think they go back to some report that FAA Chicago Office put out to "help" modifiers account for gust and manoeuvre loads. IMHO the assumptions are awfully coarse and penalising. But you will have a DER or maybe someone in the FAA making the findings on your mod, so you'll need to follow their lead.

### RE: Fuselage Bending

Yes, definitely a coarse assumption. These equations are simple so need to reference them. It is just a cantilever beam with a distributed load and a point load in some cases. Its a one line derivation that would allow the checker/others to see what is going on. That is more powerful/simple/useful than having to go dig up a reference and demonstrates you understand the basic principles (which a reference does not do). You can also make some quick modifications to see what the effect might be as opposed to relying on a static reference. If the load distribution was more complex, then a reference would make more sense.

Brian
www.espcomposites.com

### RE: Fuselage Bending

What type of antenna i.e. a VHF blade antenna?

### RE: Fuselage Bending

If you want to use those equations with a reference, I had already written that above in my first post - which was:
Book: Roark - Formulas for Stress and Strain
Chapter: Bending of Beams

You will find tables of equations where bending of beams are investigated - and no doubt, you will find the exact same equation on that chapter. It is an easy equation to find a reference for.

But I think more importantly you have a problem with your work. If no one knows nothing about aircraft structural analysis, at least they should be able to find reference stress reports for these kinds of analysis. If you can't find a reference stress report, I don't think you will be able to cover "every aspect" of this analysis. Antenna analyses are a different package of aerospace stress analysis area and they are repeatedly performed by multiple companies.

And I honestly wouldn't want you guys to certify an antenna without "exactly knowing" what you are doing.. I'm sorry but aerospace is no joke. Whoever didn't take it seriously either paid lots of penalty, or had their projects cancelled when they were just months away from getting certified. Some supplier companies even lost their regular main aerospace customers because of this. This is just the financial aspect. People are flying in these structures(!!!) and this is the most important reason to why I worked on all my projects day and night when I needed to go the extra mile to "double check" what we were doing..

I would advise you or your company to hire a 5-10 years (even 15 would be better if you don't have any know-how built in yet) experienced person with this kind of experience "and more" to make sure that everything is safe in this analysis. (that's if you have the future workload for a new contractor) That's why most companies have "principal stress engineers". You have to know what you are doing if you are doing it on a commercial aircraft..

Spaceship!!
Aerospace Engineer, M.Sc. / Aircraft Stress Engineer

### RE: Fuselage Bending

with respect, those are only partial references, about basic bending. you also need the FAA Chicago Office doc, which includes the "logic" of the assumptions.

They won't certify without someone making a finding of compliance, maybe a DER maybe the FAA; so someone knowledgable will get involved, hopefully before they have to redo a bunch of stuff.

### RE: Fuselage Bending

I "humbly" want to add this below to explain my concern in more detail:
• I've worked with DERs who have asked me really critical questions for confirmation (which they should already have known the answers to with their "years of experience")..
• I've also heard in some places people "with signature authority" are getting fired simply because they are not signing the "already accomplished" stress tasks (just because they think the work isn't complete at all)..
With these 2 above, I sincerely want these guys to bring in someone invested in aerospace stress analysis to their team. Otherwise, there are loop holes everywhere. You can't make someone with "no aerospace stress experience" do such a job "without any supervision". It is just not right. Hire a remote stress consultant in the worst case. There are many on Linkedin and other websites.

Spaceship!!
Aerospace Engineer, M.Sc. / Aircraft Stress Engineer

### RE: Fuselage Bending

The particular equation you posted goes back to Dr. Broek's fracture mechanics book and in fact it is also contained in his Manual TN9501. This dates back to 1980's and was in the fracture course I took under him back then. Since then, it has been cited in various FAA documents. So, that being said, it has been around for a long time. But, and this is a big BUT, most people have misused, misinterpreted and misunderstood the main point of this equation, particularly engineers that do not have an aeronautics background.

The equation Dr. Broek cited was specifically to be used to establish a 1g trimmed condition fuselage bending moment for use in developing a fatigue spectrum. It ignores any balancing tail load assuming the trimmed conditions requires little to no tail load. This must be validated for each aircraft being analyzed, it cannot be taken verbatim. So, one must know how to balance an aircraft to use this equation. Additionally, the configuration of the aircraft plays a major role in developing this. If the method is used by an "experienced" engineer, then a conservative but representative fuselage bending spectrum can be developed. Note, I know of very few experienced stress/structures engineers able to do this correctly as it requires both an aeronautics background and lots of experience in loads/stress spectrum development which few people possess.

Second, if your intent is to develop FAA limit and ultimate loads for static analysis, then this equation is not for you. The weight distribution fundamentals of the equation are acceptable but you must do much much more. You need to look at each FAA condition, balance the aircraft, calculate the resulting load factors, and then calculate the necessary tail load. For this, you should go to the book by Ted Lomax, AIAA "Structural Loads Analysis for Commercial Transport Aircraft".

Lastly, as a DER, I have watched for many years numerous people in the industry make erroneous and inaccurate statements regarding fuselage bending loads and spectra. First off, pressure is absolutely NOT the only driving factor. People have continually tried to simplify the spectrum requirements down to pressure only because they simply don't know or do not have the capability technically to do so. Also, many "simplified" approaches have been presented which are either totally devoid of basis or inaccurate, among them is the so called Chicago method. This method not only starts with Ftu as the basis but then generally assumes a 1.3g alternating load for all aircraft. One look at all of the FAA/DOT Load History documents (over 30 for all various types of aircraft) illustrates that this is not a valid assumption nor representative. There are far too many other issues with this approach for me to go into at this time.

Anyways, as most everyone else has pointed out, you need some experienced level of support for your efforts.

### RE: Fuselage Bending

Yes,I took Dr.Broek's correspondence course,using his fracture mechanics book as a text,thru the AIAA if I recall correctly,in the early 80's.An excellent text and course overall.Like everything else in engineering or life as far as that goes,one must know of the limltations and boundary conditions before simply plugging in numbers.This is a very serious problem we have in this day and age.Thought must be given to the application,this is where I guess experience comes into play.This experience can be gained only through many years of ,as they used to teach in school,by working problems.the more problems you work and see it's application,the more you expertise level increases.Simply reading the lecture section of a text and not participating in the problems is simply not good enough.Engineering is not a passive science,it's an applied science,and the more you try it out the more you will see the limitations and the little secrets that are usually so well hidden.This is why I have always appreciated Schaums College Outline Series texts in engineering.A very limlted,but to the point lecture and presentation followed by numerous problems and examples.This applies very well to this writer's post.

### RE: Fuselage Bending

@crackman,
it depends on the accuracy desired. I contend that pressure is a dominate component of the fuselage fatigue spectrum. IMHO you can account for gust and manoeuvre cycles by factoring hoop stress. I think it'd be a worthwhile university project to assess many aircraft types to see if an agreed conservative factor can be defined. in the meantime I think a factor of 1.5 is horribly conservative. In my experience, I see this assumption as a second order effect, compared with the definition of da/dN ... a small difference here can have an enormous effect on the results.

### RE: Fuselage Bending

rb1957
As I stated previously, I agree that pressure is an important contributor to fatigue loads and may very well be the most significant for areas of the forward fuselage. However, I don't believe in any shape or form that one can ever just factor or modify pressure to obtain a representation of flight loads. This is the current industry problem and the problem with the Chicago method. In fact, numerous papers and texts have been published and an entire series of FAA/DOT reports with spectra for almost all commercial aircraft have also been published. It is not difficult to do, but requires experience and time. I think industry just needs to roll up their sleeves and do the work.

### RE: Fuselage Bending

i've found only very few aircraft spectra on FAA site ... like S227. if you've got other links, could you share ?

deriving gust loads for a flight isn't hard, I use the ESDU gust curves ... which go back to earlier research, i believe. The difficulty is deriving fuselage bending moment, ie Ht/g, and fuselage stress, ie modelling the entire fuselage cross-section; without using gross assumptions like the method above.

my experience shows me that small changes in da/dN curve produce much larger changes in crack life than different 1/flt stress ... for a fuselage.

### RE: Fuselage Bending

thy seem too have buried them really well on the FAA website, but did find these

I also remember that the SA227 one seemed to have a mistake in the cargo door hinge tab cracking, in that after the first tab cracked off the new end tab didn't see an increase in loading.

### RE: Fuselage Bending

At one time the FAA had a good web page to document all of the reports while they were doing their operational loads survey research. Guess once the funding ended, the page was not supported any longer.

Anyways, here is a list of the reports that I know of:
DOT/FAA/CT-91/20 General Aviation Aircraft Data
DOT/FAA/AR-96/114 Fokker F27 and F28 Loads Data
DOT/FAA/CT-89/36 Vol 3 B-727 VGH Data
DOT/FAA/CT-89/36 Vol 4 B-747 VGH Data
DOT/FAA/AR-02/129 Ground Side Loads for Boeing 737, 747, 767
DOT/FAA/CT-89/36 Vol 5 Douglas DC-10 VGH Data
DOT/FAA/CT-89/36 Vol 2 Lockheed L1011 VGH Data
DOT/FAA/AR-00/50 Empennage flight loads for GA aircraft

If one goes back further, there are numerous other reports with loads data. However, for any of the new aircraft there is no reason why the spectrum loading for the aircraft cannot be developed.

### RE: Fuselage Bending

they seem to be there ... google "dot/faa/ar-xx/yy"

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