Web repair design 8

[koopas]

Hello all,

It's been a while since I've posted on here. Hope everybody is doing well, and happily employed.

I posted a question on webs a while ago and was essentially told to do some more reading on the subject before coming back. I started thinking about it today when I had to do a repair on a web, near the lower cap. The part was only an aluminum shield that went over the hydraulic reservoir in the wheel well, rather non-structural but it got me thinking about web repairs again.

The SRM calls out two rows around a cut out for a web repair. In fact, if you use Ftu to size the number of fasteners, you'll end up with four, maybe five rows of fasteners. However, if you use Fsu, you'll be back down to two rows. Checking replies to my older post, someone mentioned that you still need to size to Ftu since, in a diagonal tension or even pure diagonal tension web, the web takes most (if not all) the shear load in diagonal tension, respectively. Hopefully, I paraphrased the latter part correctly.

1. How do you identify if the web is a shear resistant web, that doesn't buckle under ultimated shear load, or rather a diagonal tension-type of web? In the first case, I believe that designing to Fsu is prudent, since Fsu is never exceeded by design. In the second case, the web has no compressive stiffness, and takes most of the load in tension. In such a case, it would make sense to design a web repair to Ftu.

2. I was also thinking...Do you guys/gals assume that the web portion of the beam, regardless of its location with respect to the caps (which carry axial load), takes only shear loads? Reason I am asking is that the repair today was in the web area close to the cap. I conjecture that the loading is a mix of shear and axial loads. However, most books assume that caps take purely axial load and webs all the shear load, most likely (and I am speculating) because the web is so thin that it contributes very little first moment of the area "Q" to the shear flow/stress formula VQ/I or VQ/It.

3. This is a continuation of question 2...what allowable (Fsu, Ftu, or something else?) do you use in such combined loading cases? This particular area may experience a combination of shear and axial load which, separately, may result in individually positive margins of safety against Fsu and Ftu, respectively. However, when combining these two loading types, is designing to Fsu, even Ftu, even enough to yield a positive combined-loading margin of safety?? What allowable do you design to in combined-loading cases? Do you bump up Ftu? I guess I am asking for the ultimate stress allowable in shear + bending for say, 7075-T6. Does such a beast exist? Does the question even make sense? Perhaps I am finding myself asking a question in the "design" realm to a "repair and salvage" issue. Reading Niu's red book, pp 469, you can calculate shear stress ratios fs/Fs and bending stress ratio fb/Fb and use the interaction formula Rs^2 + Rb^2 = 1 to determine the combined-loading M.S. How do you relate that to a repair scenario?

Hoping these questions make sense,
Alex

 

[SuperStress]

Alex,

Okay, let's see if I can shed some light on some of your questions...

1. There's no real way to tell from looking if a web is shear resistant or not. Some clues might be the thickness of the web and the spacing of the stiffeners. Very thick webs and/or very small spacing on stiffeners might indicate a shear resistant beam. Most other deep built-up beams are intermediate diagonal tension, since it carries less of a weight penalty. The standard way to analyze these beams is the NACA 2661 method, which is explained pretty well in Niu's stress book starting on p.485. The NACA method sizes webs based on Fsu for shear, not Ftu.

2. It is conservative to assume that the caps take all the axial loads and the webs only take shear. Part of the problem with letting the webs take axial loads is determining (and justifying) an effective area. Without some test data to back up your assumptions, it's usually just easier to assume the web is ineffective in resisting bending. Your VQ/I formula is what tells you that your caps are nearly ineffective in resisting shear, not that the webs don't contribute to bending.

3. Combined loads are dealt with as you described using interaction equations. You can also use a von Mises failure criteria, or octahedral shear stress criteria which are usually compared against Ftu. To be conservative for the web, you may want to assume some effective area (say 15t on either side of the fastener) in bending, and take the average bending stress over that section and combine it with the shear stress when writing your margin. This is reasonable for relatively deep beams. If your beam is shallow, you may want to write your margin according to the maximum bending stress in your effective web area.

When working with repairs, you don't always know the design loads involved. The design load for a repair is usually determined by either the strength of the damaged material, or the strength of an adjacent joint.

In the example of the wheel well shroud you mention, how is it attached to the airplane? How many fasteners of what diameter and what pitch? The load in the part is limited by the ability of this joint to transfer load to/from the airplane structure. Therefore, your design doesn't necessarily have to restore Ftu of the material, you only have to restore the amount of load the joint can transfer back to the airplane. Remember too, that in thin sheet material, the joint is very likely bearing critical.

SuperStress

 

[koopas]

SuperStress,

Thanks for your reply. If I may, I will expound on my last two questions.

2. You wrote "Part of the problem with letting the webs take axial loads is determining (and justifying) an effective area". I am afraid I don't understand. With the MC/I stress distribution, the web is indeed still taking some axial stress from bending. Now, it's true that the caps carry the highest axial stress but the web does carry some axial load in addition to its shear load. Perhaps you could clarify...

3a. I seem to understand your methodology for stress checking the web, say, using the interaction equations. Let me paraphrase what you wrote, and please let me know if I am wrong:

You want to analyse a point on the web between its neutral axis and the web to cap rivets. There are no immediate fasteners in the area. You calculate the axial stress due to bending. You then calculate the shear stress. Form the stress ratios with Ftu and Fsu, respectively. Stick those ratios in your interaction formula to get your combined-loading M.S. and hope it comes out positive. Does that sound correct?

3b. The above makes sense in a "design" scenario. However, the repair engineer does not have the loads. How do you design your doubler repair so that ultimate loads are transferred? I need this load to size the number of fasteners around the cutout. The SRM and most repair books tell you to use Ftu. Wouldn't this assume that you only have axial load in the web? We've discussed that webs do carry mostly shear. So I am claiming that you often have a combined loading situation of mostly shear and some axial stress. Is it still correct to design your repair based on Ftu?

Another way to say it...if I design my repair to carry Ftu, and the web sees that axial load at some point in the airplane's service life, it's fine...the load can be transferred to the repair doubler from the web via the fasteners, which were sized to carry the Ftu load. The repair doubler, of course, is usually one gage up, so it too can carry the load. Then, that ultimate load is dumped back into the structure from the doubler.

Now, assume that along with this ultimate load, you have some shear load. I don't believe your repair fasteners, which were sized to carry Ftu, can be shown good for static strength. You now have a high axial load (Ftu) plus a shear load. If you combine these two loads, wouldn't you end up with a combined-loading MS that's negative? I know it may sound idiotic that I am implying that designing to Ftu is not enough, but in a combined loading situation, I just don't know what ultimate stress allowable to design to. Does Ftu really suffice?

Thanks,
Alex

 

[hombre]

Alex,

In regards to 2), it may be necessary to include a portion of the web to show the cap good. For instance, a very high compression load.

In this case it is justifiable to include an effective width of web based on the crippling allowable with one end fixed and one end free.

For example, for aluminum, the point at which the material begins to cripple, I believe, is approximately (b/t)=10. Since you know your web thickness, you can solve for the width, b.

This additional area may be used for both compression and tension analysis (it is conservative for tension).

Hope this helps,

Hombre

 

[joekm]

For more on question 2, check out Bruhn chapter C7.11 for a more complete discussion of effective areas.

BTW - the fact that you intuitively recognized the interaction between the cap and skin is a good thing. It looks to me that you did take some time to research this.

For question 3, SuperStress actually has you going in the right direction. Try mentally replacing the web with a single diagonal beam and applying your loads, then ask yourself what becomes different when you replace the beam with the skin. Then, look for the "modified Wagner method" and the "NACA method" for analyzing this type of beam. That might help you visualize the loads.

I'm a bit buried in a project right now and haven't yet had my morning caffiene . However, if I get a break in the action, maybe I'll re-visit this in more detail.

--
Joseph K. Mooney
Director, Airframe Structures - FAA DER
Delta Engineering Corporation

 

[jetmaker]

koopas,

More on question 2. Often times, some effective width of the skin is lumped into the stringer/chord area. This method recognizes that a well attached web will have to strain with the chord at these locations. Beyond a certain distance tho from the chord, the skin has a different stiffeness and strains differently from the rest of the structure, thereby carrying less load. Calculating this effective width is difficult, usually based on a correlation with test data. Therefore, it is conservative just to assume the chords carry all axial load due to bending.

More on question 3. The primary reason to design to Ftu is because of the principal stresses. Even in a pure shear field, the shear stress can be resolved into max and min principal stresses. It is these stresses that you should be designing to and then comparing to Ftu. This is the typical failure mode for a web. Now if you were designing a pin with a small gap between loading lugs, that would be primarily governed by Fsu.

Hope this helps.

jetmaker

 

[SuperStress]

Alex,

Hopefully everyone's comments have helped clarify my earlier post. I was out for a long weekend (seeing the Thunderbirds! Woo Hoo!)

Let me add a couple of things.

First, for the effective areas: What we're talking about is the Ad^2 term in your moment of inertia equation. In deep beams, the second moment "I" of the cap is usually small in comparison to the Ad^2 term, and is often neglected. So, what you're looking at is a lumped mass at a distance "d" from the neutral axis. If you are going to assume some part of the web is effective in that lumped mass, you need to estimate an effective length (times width) to use. Easier to just ignore it, unless you are trying to "sharpen your pencil" and resolve a small negative margin.

For 3a, your understanding of the use of the interaction equations is correct.

For 3b, remember that you can't have your material loaded to ultimate in axial loads and add any shear. At that point you've failed your parent material.

Try looking at it this way, from the standpoint of the interaction equations we discussed earlier. If the web is in pure shear, then your margin is written against Fsu. If you have shear + tension, then you have an interaction based on Fsu and Ftu. If you have only tension, then you write the margin against Ftu.

Since Ftu is greater than Fsu for pretty much every common aerospace material, designing your repair to be good for Ftu will always be conservative for any combination of Ftu and Fsu in an interaction.

Let me also restate something from my earlier post; you don't always have to design every repair to Ftu. You have to develop an equivalent strength repair for the original airplane structure. The gage of the original part may have been sized by other considerations besides Ftu (vibration damping, or environmental close-out, for instance). In that scenario, you may see a relatively heavy-gage part fastened with an insufficient number of fasteners to develop Ftu of the material. In that case, you only have to restore the strength that can be developed by the joint attaching the part to the airplane; that is the "weak link" in the chain.

Hope that adds some clarification.

SuperStress

 

[joekm]

SuperStress:

Regarding effective areas, you're talking about the parallel axis theorem for computing cross-sectional inertia. While what you say is absolutely correct, I think the original post was referring to the portion of the web that is considered to be "part of the spar-cap" for reacting buckling loads. For that, there is the Von-Karman-Sechler method (sometimes modified based upon experiments by Newell).

A discussion of this method with example problems is found in Bruhn chapter C7.12.

--
Joseph K. Mooney
Director, Airframe Structures - FAA DER
Delta Engineering Corporation

 

[koopas]

Thanks everybody for pitching in with your comments.

Superstress:

You write:

"Try looking at it this way, from the standpoint of the interaction equations we discussed earlier. If the web is in pure shear, then your margin is written against Fsu. If you have shear + tension, then you have an interaction based on Fsu and Ftu. If you have only tension, then you write the margin against Ftu."

I completely agree here.

"Since Ftu is greater than Fsu for pretty much every common aerospace material, designing your repair to be good for Ftu will always be conservative for any combination of Ftu and Fsu in an interaction."

That's exactly where I have my doubts. If you design a repair good for Ftu, and the repair only sees AXIAL loads up to ultimate, then it's fine...no problems there. However, if the repair sees AXIAL loads, say close to Ftu, in addition to SHEAR loads (less than Fsu), then your combined margin of safety may come out negative, even though individual M.S. in axial and shear stresses may be positive. In this case, simply designing to Ftu doesn't appear to be enough.


Jetmaker:

I am glad you mentioned principal stresses. I did some reading today on theories of failure for ductile materials in a plane stress condition. The Tresca failure criterion of maximum shearing-stress states that if both principal stresses have the same signs, each principal stress must be less than the yield stress (if yielding is the failure criterion). If the principal stresses have opposite signs, the difference of the principal stresses must be less than the yield stress. So it appears that yield stress Fty is the design allowable used. Indeed, using Ftu follows the same line of logic, except for the added conservatism. It now makes sense to use Ftu as the allowable to restore when designing repairs to parts that undergo both axial and shear loads.

One could also use the Von Mises criterion, which appears to be a bit more accurate for pure shear loadings.

Interaction formulas and these failure theories both predict failure under combined loadings...which one do you use? Is a particular one more appropriate? Or are they different beasts? Any comments?

Have a good week,
Alex

 

[SuperStress]

Alex,

I see where you are coming from on the issue of Ftu and Fsu and interactions. Yes, it is possible to have a failure condition where neither the applied axial or shear loads exceed Ftu or Fsu, respectively. This is the whole intent of using the interaction equations, to determine when this is the case.

Most interaction equations are simplified versions of one of the more comprehensive failure theory models, e.g. Von Mises, etc.

What do I use? Depends on who I'm working for; many companies have their own analysis manuals that dictate such decisions. When not guided by simple interactions, I usually use Von Mises.

Keep in mind, too, that for most beam construction, areas of high axial loads from bending (outer fibers) have virtually no shear stress, and areas of maximum shear stress (neutral axis) have virtually no axial loads from bending. At points in between you have both, but these areas are rarely critical. I can't think of any examples from memory where a point in the middle of a beam sized any of the components because of bending/shear interaction.

If you are looking at more complex geometry than simple I-beam-type construction, those simplifications may not apply.

SuperStress

 

[koopas]

Superstress,

Thanks for taking the time to reply. By the way, what do the stars next to your name mean?

Alex

 

[SuperStress]

It means that people have clicked the "Thank SuperStress for this valuable post!" link at the lower left of the post.

SS

 

[edbgtr]

Superstress

I have a small piece to add to this discussion. From a set of notes I have from Bill McCombs, he has the following to say about flat web tension field beams.

Sometimes it is lighter to allow the thin web to buckle, in which case it becomes a so-called "tension field" or "partial tension field" beam. As a general rule when V^0.5/hc<7 (Square-root V divided by hc) (a "deep beam") the tension field type is lighter, and when V^0.5/hc>11 (a "shallow beam") a shear resistant type is lighter. In between these limits other factors affect the choice.
V is the shear load in pounds and hc is the beam height, in inches, between flange centroids.

This may help you to determine whether a beam web has been designed as shear resistant or in diagonal tension.

Regards,

Ed