Allowable Loads - Net Area in Tension 2

[StressTheGame]

Hi!

During my 12 yrs @ Boeing (747/767 Stress) we routinely used the following formula to calculate the net area capability of structure having fastener details:

Allowable Load = 0.9 X Ftu X Anet

From Boeing's internal course No. V4011.6 titled "Detail Design and Analysis"- taught by Gus Gustafson ("Mr 747 Strut Stressman") I quote:

--> Section 4.2.4 "NET AREA TENSION ... A stress concentration factor Kt is used to obtain an allowable Ft stress across the plate at the hole location to compensate for the uneven stress distribution. Experience has shown that a Kt of .90 is acceptable for sheet metal joint design

--> Section 4.3.3 "ALLOWABLE NET AREA IN TENSION: Experience has shown that the allowable net area tensile stress for multiple fastener lap joints 1s 90% of the tensile ultimate values shown in the material mechanical properties tables."

Northrop's 1969 Strength Check Notes for the 747 Fuselage outline a set of standardized skin-stringer checks on the 747 Fuselage skins (Northrop substantiated all of the 747 Fuselage except Section 41). Within these standardized guidelines, they clearly state in several checks that Ft-allow = 0.9 Ftu

I have been in Australia for 11 yrs working within the local industry. In the Australian company I recently joined, they have been calculating tensile net area allowables with a uniform Ftu X Anet type approach (regardless of whether fastener holes are present or not). This can be either overly conservative or unconservative (capability vs. restoration).

I am trying to convince other engineers that this .9 factor is an acceptable and accurate practice within the aircraft industry when used appropriately.

Could anyone offer me some additional reference sources or ideas that would help me support this as an acceptable and accurate real world practice?

Thanks!

 

[rb1957]

you presented a good set of references for including the 0.9 factor (tho' i'd dispute calling this a stress concentration factor ... 1/.9 might be).

I'm sure the Ozzies have just as good a set for their approach ... Bruhn uses a "fancy" figure (D1.12) with many factors less than 0.9, and some geometries = 1.0. Bruhn also checks many other sections in the lug, so it's unclear which one is critical.

At the end of the day, neither approach has caused "lost of hull" accidents, the 0.9 factor should provide a level of conservatism (I doubt it is "too" conservative ... adding weight to lugs is IMHO a good idea).

in your post I'm not sure what "regardless of whether fastener holes are present or not" means (in the presence of Anet).

 

[RPstress]

The Hawker Siddeley Design Handbook Volume 2, stress data, Book 1 (dated 1976), Section 1.41 is entitled "Effect of Holes on Nett Ultimate Strength."

The first sentence of the section is "Aluminium alloys when subjected to an ultimate tensile load develop a nett ultimate stress which varies according to the presence of holes."

The section has graphs of sigma_D/W vs. the reduction factor on the UTS. (sigma_D is the sum of all the diameters of the holes across the specimen - some specimens were single holes and some were multiple holes in a row across the specimen). Spot checks showed that the factors could also be applied to filled holes. Mostly the factors were unaffected by grain direction, but for 2024-T3 bar the factors would be 10% higher in the transverse direction.

For naturally aged L89 (clad 2014A-T3) and DTD5100 (clad 2024-T351) the strength reduction factor varies from 0.925 for a reduction in area of just 3% (sigma_D/W = 0.03), drops to 0.885 for a reduction of 15% - 18% then rises linearly to 0.965 when the holes amount to 50% of the nett area.

For aged alloys L73 (clad 2014A-T6), L88 (clad 7075-T6), DTD5070 (clad 2618A-T6) and DTD5020 (unclad 2014A-T651 plate) the factor is 0.955 when the holes amount to 3% - 12% of the width, and it then rises more or less linearly to 0.965 when the holes are 50% of the area.

For aged alloys L65 (unclad 2014A-T6 and -T651 bar), DTD5014 (unclad 2618A-T6 and -T651 bar) and DTD5050 (unclad 7075-T651 plate) it starts out at 0.94 for 4%, drops to 0.92 between 8 and 12% then rises more or less linearly to 1.0 for 70% holes.

There is also a graph for L64 (unclad 2014A-T4 and -T451 bar), which is not so good: it starts out at 0.87 for 4.5% holes, and drops to 0.795 between 10% and 17%, then gradually rises in a curve to 0.94 for 70% holes.

While these results look a little unexpected to me (aged being less notch sensitive and 2014-T4 being so poor), they are based on tests and this item was still current back in 1999 (though it may have been updated).

 

[ieaz123]

You can use the Neuber method to calculate allowable tension load of a ductile member with a hole. There's a section in the BDM's on it.

 

[StressTheGame]

rb1957

Thanks for your reply! I will try to clarify my previous post by commenting to your reply:

"the 0.9 factor (tho' i'd dispute calling this a stress concentration factor ... 1/.9 might be)" - I agree this is a so-so term. The reason Boeing used the term "stress concentration factor" is to assign a label to the origin of the knockdown factor. The factor is applicable to what they refer to as "multiple fastener lap joints" or as i discovered through everyday use to structure where fastener holes are present. It basically accounts for the fact that the Kt of 3 experienced at the edge of the hole under uniaxial tension will have a small effect on the overall strength of a panel which is mechanically fastened.

This raises a question: when should we apply this factor and should it be a constant .9? In other words, is this phenomena related to the percentage of hole-out within the panel we're analyzing? One might think that it would be overly conservative to apply this .9 factor for a panel with only 1 hole over a few inches - while it may be more appropriate to apply it - say over a lap splice with a multitude of fasteners.

"Bruhn also checks many other sections in the lug, so it's unclear which one is critical" - I failed to mention that Boeing does not endorse this "generic" knockdown on lug analysis. For lugs we used the lug analysis procedure. This generic .9 knockdown only applies where there's "multiple fasteners".

You state: "I'm not sure what "regardless of whether fastener holes are present or not" means (in the presence of Anet)." - what i meant was that sometimes a net area calculation might be the result of a cutout (as in an access hole) - not necessarily the result of fastener holeout.

Thanks again for your help!!

 

[StressTheGame]

RPstress:

Thanks for your very detailed reply. A few comments:

You state: “The section has graphs of sigma_D/W vs. the reduction factor on the UTS. (sigma_D is the sum of all the diameters of the holes across the specimen - some specimens were single holes and some were multiple holes in a row across the specimen).”

This might be along the lines of what I mentioned to in my reply to rb1957: “is this phenomena related to the percentage of hole-out within the panel we're analyzing? One might think that it would be overly conservative to apply this .9 factor for a panel with only 1 hole over a few inches - while it may be more appropriate to apply it - say over a lap splice with a multitude of fasteners.”

Lockheed Stress Memo 56b “Efficiency of Sheet Joints Attached with Shear Fasteners” appears to have a procedure to account for the variability of the phenomena accounting for percentage area losses. I will pursue this avenue and post back my results.

If I understand you correctly, it's interesting the trends you describe. You say the degradation increases in severity as you go – let’s say – “from 0.925 for a reduction in area of just 3% (sigma_D/W = 0.03), drops to 0.885 for a reduction of 15% - 18% then rises linearly to 0.965 when the holes amount to 50% of the net area”. If I understand correctly that implies that the net area loss component/effect becomes dominant (over what I refer to as the “Kt effects”) once you exceed 15 – 18% D/W. Interesting!!!

Could it be possible for you send me a pdf of that section 1.41? I would of course claim it fell off a truck!!

Thanks again for your very detailed feedback!!

 

[StressTheGame]

ieaz123 - thanks for your feedback! Could you please tell me the BDM number so I may try to locate the limitations within the decsribed technique? Thanks again!

 

[RPstress]

Re getting you a copy of the old Hawker manual, no problem in principle...however, we have the perennial Eng-Tips issue of posting contact details, as they hate any sort of e-mail addresses, etc., appearing. You could try posting an e-mail address and see if you get your wrist slapped. Worst case, I guess the thread gets removed. NB: they don't seem to mind a website URL being cited. Most people seem to alter it a little to stop Google picking it up (with an explanation of how it's been altered - spaces every other letter, etc.).

The Boeing method is in BDM 6040 (at least, I assume that's the only place it's covered). It's quite a bit more numerate and theoretical than the simple use of a reduction factor. You need fairly comprehensive stress strain curve data for the material involved. The MS you get is dependent on the material yield characteristics and the elastic stress concentration factor, so there is no simple relationship with hole area vs. nett area.

Thanks for the Lockheed Stress Memo ref. I'll check that out.

Re the effect of hole area vs. total area, I initially thought it odd that there should be an effect. Exactly what the physical mechanism underlying it is, I'm not sure. (It may have to do more with hole proximity, perhaps.) The way the Hawker data shows the factor at first dropping and then increasing is curious. If there was an effect I'd have thought it would only go the one way. Going "two ways", as it were, indicates to me at least two competing processes.

Also, I'd have thought there ought to be a size effect, with smaller holes having a smaller effect. Because the Hawker information doesn't have specifics of the test specimens it's hard to say if they didn't test for it or if it wasn't present. It would be nice to see a copy of the test plan or report. Annoyingly, the Hawker item doesn't reference those.

I'm not sure what method Airbus use. For large cutouts like wing access panels they have test data from A310 or something. This is then modified somewhat by the geometry being analysed. I can't remember the details.However, that was specialised to large cutouts in essentially 2024-T3. I'd have thought they must have a more generally applicable method.

 

[rb1957]

sometiimes i wonder about myself !

i guess i read tension net area and went off on a tangent about lugs ... sigh.

 

[rb1957]

but talking about splices, is the ultimate strength the critical design criteria ?

i'd have thought that fatigue allowables would be critical, so there'd be a +ve static margin for the ultimate case.

 

[StressTheGame]

Rpstress

thanks for the reference to the BDM - I will look into it this morning.

It appears that Boeing, Northrop, and Hawker Sidley's approach show a common thread: there is an additional knockdown from what a strict net area calculation would predict a fastened joint to be able to carry.

The dilema I'm facing is - if we are to apply a knockdown factor, would it be accurate if it were a simple constant factor (such as the "0.9") or would we need to go through a more rigorous approach? At Boeign we routinely used this 0.9 factor and it was no big issue but it's hard to change other engineers' methodologies in the outside world.

Good observation regarding the hole proximity effect. It may be that the Kt's of holes interact due to hole proximity with what i refer to as near-field effects.

I will try to find a good contact within Airbus to see if they have a knockdown factor - and whether is a simple one. I will let you know in here about my findings.

I would really appreciate it if you could please send me a pdf of the Hawker Sidley section 1.41 to pombo at optusnet dot com dot au. I have a good reference set and would be happy to exchange information as needed.

Thanks again for your comments. It's refreshing to exchange ideas with people who also wonder about the why's.

 

[StressTheGame]

rb1957

N/P regarding your dreaming about lugs ;-)

regarging your comment "i'd have thought that fatigue allowables would be critical, so there'd be a +ve static margin for the ultimate case": IMO it would depend as to the what the ultimate design condition is and the specifics of the joint design. For instance, sometimes the design condition might be something strange like a 90 degree tow-condition on a 747 (which is not supposed to occur at all). Sometimes the joints might be designed by ultimate cabin pressure differential (not related to maneuver conditions), or some other might be floor-frame conditions such as classic 747's 9g fwd or decompression loads where the area around the floor-frame intersection becomes critical on a one-off scenario. All of these conditions might present critical net-area type failure along fastened joints.

Let me know if I misinterpreted your coment. I've also been known to go along tangents once in a while.

 

[rb1957]

i was thinking of the 2deltap ultimate case (which i think should be less critical than fatigue requirements). but i agree there can be some way out ultimate cases and fatigue requirements (DT inspection intervals) don't have to be very difficult (tho' everyone wants long intervals).

 

[ieaz123]

For Boeing commercial airplanes, the .9 x net area is specified in the design requirements memo for each airplane program. Using the .9 factor is conservative for static strength analysis of aluminum and eliminates the need for stress people sit around debating what the appropriate method for accounting for nonuniform stress distributions at ultimate load.

If, for some reason you need a more accurate number you can use the Neuber method.

 

[mcclain]

Is BDM 6040 available to the general public?

 

[StressTheGame]

jeaz123

Thanks for your feedback.

I agree that the 0.9 factor is an easy way of developing consistency within Boeing - a way to account not only for real behaviour but also to ensure Northrop's assumptions (when they did the 747 fuselage stresss analysis) are maintained.

The problem I'm facing is that different companies follow their own unique methodologies - giving different results of course.

I am currently working on Lockheed's P3 Orions and Lockheed's method is not as simple as Boeing. It is hard to convince people who havent done a significant amount of work at Boeing that Boeing's one-size-fits-all approach is reasonable and accurate enough for everyday use - regardless of the aircraft your working in.

One of the main arguments I hear is that applying a knockdown factor when establishing capability of the as-delivered configuration is un-conservative. Although that statement is correct, I believe we should not be so conservative in our analysis to attribute behaviour to the structure which in real life is incapable of attaining.

 

[StressTheGame]

mcclain

BDM 6040 is not publicly available as it is propietary data. However, sometimes this type of data sometimes falls of the back of trucks and job-shoppers are quickly to pick them up - solely in the interest of keeping our roads clean of ocurse. ;-)

 

[Kwan]

My take on this is that it's not a bad idea to have a little extra margin. Most static analysts do not (and perhaps can't due to lack of knowledge and/or schedule) determine stress concentration and check against fast fracture.

It can hurt you to design the structure to have zero margin, and possibly create 500 hour recurring inspections. Another note: if you concentrate on using good design principles (loadpath, loadpath, loadpath) the structure will benefit. Let's look at an example.

Take the P3. The wing is fabricated (was might be a better verb) out of machined down 7075-T6 extrusion. These are about 7ish inches wide and run the length of the wing. They are joined together using one row of fasteners. Now statically the one row is fine. However, look into fatigue/damage tolerance and you have some issues. Also, think about stress corrosion cracking. Nowadays we would never design a wing like this (hopefully). But there are many operators out there that have to deal with this problem.

Shall we talk about Boeing's lap splices? Or perhaps this can be a later discussion.

Food for thought.