rear spar bending load

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pylon500

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Been a while since I worked on one, but I think it's just four bolts up into the inner steel tube cabin frame?
Just found this; looks like the frame bolts to the lower cap in the spar, as well as a forward stabilising attach (like a cherokee), and a couple of bolts somewhere on the rear spar. Not sure if they double up holding the front and rear sections of the fuselage together? ( I know the skin are riveted as well.)
Mooney_wing.png

Just as a fun Mooney fact, if you get a tape measure and measure from the tip to the side of the fuse on each side, you will find the left wing nearly 3/4 inch shorter!
Turns out the fuse skin is bulged out to allow the electrical looms past the steel tube structure without imposing on the interior space (and there's not a lot of it inside a Mooney...)
 
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raytol

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I'm just doing this part of the design of my aircraft at the moment. Traditionally , I have just used a small tube that is in line with the rear spar that fits in to a larger tube that continues through the fuselage. I then put a vertical bolt in a slightly oversized hole through both the tubes.
My new rear spars are a "Z" section with the shear web at about 45 degrees to the airfoil chordline ( closes out the slotted flap). Tried to think of a fancy solution to make join but have gone back to the tubes as above! Any suggestions?
 

wsimpso1

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Lancair Legacy 3 peace wing attachments - front spar with two bolts and rear spar with one bolt:
Illustration shows what I had said before about overlapped main spar and pinned aft spar on a three-piece wing. Main spar bolts are big.
 

Malish

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Illustration shows what I had said before about overlapped main spar and pinned aft spar on a three-piece wing. Main spar bolts are big.

Yes, they are big to hold that shear load:

Безымянный.jpg
S5000069 (Large).jpg
I liked this design to mount outer wing section, so we did same thing on our aircraft...

P6270101 (Large).jpg PB060299 (Large).jpg
 
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Richard Roller

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Been a while since I worked on one, but I think it's just four bolts up into the inner steel tube cabin frame?
Just found this; looks like the frame bolts to the lower cap in the spar, as well as a forward stabilising attach (like a cherokee), and a couple of bolts somewhere on the rear spar. Not sure if they double up holding the front and rear sections of the fuselage together? ( I know the skin are riveted as well.)
View attachment 126626

Just as a fun Mooney fact, if you get a tape measure and measure from the tip to the side of the fuse on each side, you will find the left wing nearly 3/4 inch shorter!
Turns out the fuse skin is bulged out to allow the electrical looms past the steel tube structure without imposing on the interior space (and there's not a lot of it inside a Mooney...)
On M20's anyway, there is a line of bolts aft of the main spar that bolt into the fuselage structure (both sides). They run fore and aft right up close to the outer skins. Mooney wings are a pain to remove in the field!
 
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ragflyer

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Billski as usual has described the trade offs very well.

1. the wing has to react three forces: Lift (vertical), Drag (horizontal, can be forwards or backwards as it includes the lift component in the horizontal direction), and wing pitching moment that twists the wing about the aero centre and typically nose down.

2. The most common way in a cantilever wing is for the main spar to take all the vertical loads. The horizontal forces are reacted (in chordal bending) by the main spar and the rear spar acting as caps of a beam and the wing skin acting as a shear web. The pitching moments are reacted by box enclosed by the main spar and rear spar and the wing skin taking the torsional loads.

3. In order to keep the forces determinate ( in point 2) for paper or simple analysis the main spar will be designed to carry moments and shear while the rear spar will be pinned which prevents it from carrying moments and limits it to only shear. This type of set up is very easy to analyze reliably.

4. It is possible to have the rear spar carry moments (not pinned) and be a single beam or connected as the main spar. In that case the problem is indeterminate and you would need FEA or some complex paper solutions to estimate the loads. One exception is if the wing skin is assumed to be very flexible (say like KR2 or in a fabric wing). In this case the vertical bending loads will be shared in proportion based on the centre of pressure in a particular flight condition. And the pitching moment torque is taken in differential bending. This is similar to how strutted (or wire braced) wings are analyzed.

So, if I do understand correctly, the rear spar of a KR2 could be changed to a pinned connection (hypothetically speaking) and all would still be good and maybe even better . . . ?

No, not necessarily! If the two spars are designed to share the bending loads, then pinning the rear spar will overload the main spar. If on the other hand the two spars where designed such that the main spar can take all the bending load then the rear spar can be pinned.
 
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PiperCruisin

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Yes, they are big to hold that shear load:

I liked this design to mount outer wing section, so we did same thing on our aircraft...

Nice photos of the joints.

I just want to point out, being Captain Obvious here, that the "large bolts for the shear loads" is because the shear loads are large to counter wing bending moments. (Wing bending moment)/(reacting bolt distance) = shear force.

In a wing, like a Mooney, Jodel, Glasair, etc. where the spars are continuous, the joint at the fuselage only takes shear loads because the spar takes the bending. The bolt requirements from the shear loads only are generally much smaller. I'm simplifying here, but that is the general idea.

Also, on overlapping spar connections, single shear will require a bigger bolt than double shear such as the glider overlapping joint below (Marske's books has some great illustrations of this and I think the Caro motorglider is similar). Single shear plane and bending moments due to local bolt loading.
1655306387123.png 1655306726273.png
 

Malish

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I just want to point out, being Captain Obvious here, that the "large bolts for the shear loads" is because the shear loads are large to counter wing bending moments. (Wing bending moment)/(reacting bolt distance) = shear force.
On M20's anyway, there is a line of bolts aft of the main spar that bolt into the fuselage structure (both sides). They run fore and aft right up close to the outer skins. Mooney wings are a pain to remove in the field!

Glasair(I, II and III) single peace wing don't need large bolts to hold those bending(shear) loading and it's mounted to fuselage with small bolts and brackets. But doing that, it's makes wing almost NOT removable from fuselage:

5833-1.jpg 6976-2.jpg 7740-1.jpg
 

BJC

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But doing that, it's makes wing almost NOT removable from fuselage:
I have modified the leading edge of the wing fairing, shown in the second photo, to allow the wing to be removed by dropping it straight down. Otherwise, it needs to be rotated to clear the fairing, which necessitates removal of the aft mounting angle inside the fuselage.


BJC
 

WonderousMountain

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My new rear spars are a "Z" section with the shear web at about 45 degrees to the airfoil chordline ( closes out the slotted flap). Tried to think of a fancy solution to make join but have gone back to the tubes as above! Any suggestions?
45 degree bolt, off aft shear web.
 

Rob de Bie

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3. In order to keep the forces determinate ( in point 2) for paper or simple analysis the main spar will be designed to carry moments and shear while the rear spar will be pinned which prevents it from carrying moments and limits it to only shear. This type of set up is very easy to analyze reliably.

I *have* to ask now: does anyone know of an accepted analysis method for a pinned rear spar? I looked high and low for many years, through maybe two or three dozen aircraft structural analysis books, and never found one. Any hint is welcome!

Rob
 

ragflyer

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I *have* to ask now: does anyone know of an accepted analysis method for a pinned rear spar? I looked high and low for many years, through maybe two or three dozen aircraft structural analysis books, and never found one. Any hint is welcome!

Rob

It is in Bruhn for sure. The example though is a metal covered single braced main spar and the rear spar is unbraced and reacts the wing pitching moments. In the section after they describe the case where the main spar is unbraced as well though they do not go through a worked example as in the previous case.
 

wsimpso1

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Does anyone know of an accepted analysis method for a pinned rear spar? I looked high and low for many years, through maybe two or three dozen aircraft structural analysis books, and never found one. Any hint is welcome!

Answering your question, Yes. It has probably already crossed your path a few times and you just did not recognize it.

The preparation for calculating these loads and survival or failure of the joint is covered in prerequisites to the coursework of airplane design. They are usually taught as ME courses prior to ME/CE/AE getting to their respective design classes.
  • Beam theory is applied. I like Timoshenko. The distributed lift of the foil is collected as bending and shear at the main spar connection;
  • Pitching moment of the outer panel is computed;
  • Added to it is the effect of lift being applied chordwise at about 0.25c versus its being reacted by the main spar set perhaps forward or aft of 0.25c. That produces another pitching moment of the shear load times the distance between main spar and 0.25c;
  • Then add in any swept wing effects, and you have the total pitching moment;
  • Divide that moment by the longitudenal distance from main spar to drag spar connection to get the reaction at the pinned connection;
  • After that I go to Shigley's chapter on bolted fasteners and check all of the failure modes he mentions applied to webs, bushings, and bolt.
Billski
 
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Rob de Bie

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Yes. These subject of designing this stuff is covered in prerequisites to the coursework of airplane design. They are usually taught as ME courses prior to ME/CE/AE getting to their respective design classes. but I feel I must point out it has probably already crossed your path a few times and you just did not recognize it.
Thanks for taking the time to answer my question so extensively. I completely follow your explanation, with two question marks:

Step 1 is where I keep hearing alarm bells. And I have problems finding the words to describe it, please bear with me. Maybe the analogy with a false spar would work. A false spar is not clamped at its root, it's probably not even pin jointed. Yet in a beam analysis, running from the tip to the root, that false spar is assumed to be continuous, and that makes it in effect a clamped beam. You cannot simply leave it out of the analysis, it's there, and it adds to E*I, and it carries a small part of the lift load. I just checked the index of my 10+ books on aircraft structural analysis, and none mentions 'false spar', so that did not help me to understand or explain it better.

Step 5 assumes a main spar weak in torsion, correct? For a box spar, it would be a statically indeterminate problem. That still can be solved, but it's a a lot more work.

Rob
 

wsimpso1

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Now for the load due to drag and anti-drag that produces loads in the fore-aft direction and in left-right direction:
  • Beam theory is applied. The distributed drag of the foil outboard is collected as bending and shear in the fore-aft direction at the main spar connection;
  • The shear load from the above step is sometimes assumed to be taken by the main spar and is thus zero at the drag spar. But if the drag spar joint is made solid to fore-aft loads, a more conservative result is obtained by distributing fore-aft shear per the proportion of areas of the outer spars, and is rigorous if the spars are all one material and orientation. If the drag and main spars are wood or composite, having material with different orientation and thus different shear shear modulus, a rigorous result is obtained by distributing shear per GA or A66 fraction of the total spar set. This is load fore-aft on the drag spar joint;
  • Divide the bending moment by the longitudenal distance from main spar to drag spar connection to get the left-right direction reaction at the pinned connection;
  • Repeat the above steps for forward component of lift accumulated by the panel outboard of the joint and understand that it is opposite sense from the drag sourced loads;
  • After all this, combine loads from Post 35 with these loads to have a more complete three dimensional picture of the loads, then go to Shigley's chapter on bolted fasteners and check all of the failure modes he mentions applied to webs, bushings, and bolt.
I feel a need to point out that each load calculated has direction - that is one needs to keep track of not only each magnitude but the direction of each load on the joint. This means establishing a frame of reference and a convention for which way is positive and negative for forces.

I feel a need to point out also that while one can compute the total load state for a flight condition, to design this joint correctly for an airplane would require a survey of the envelope including deflected flaps and ailerons to make sure that the worst flight and landing load case has been found, and ensure that all elements of the joint is adequate.

Billski
 
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wsimpso1

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Thanks for taking the time to answer my question so extensively. I completely follow your explanation, with two question marks:

Step 1 is where I keep hearing alarm bells. And I have problems finding the words to describe it, please bear with me. Maybe the analogy with a false spar would work. A false spar is not clamped at its root, it's probably not even pin jointed. Yet in a beam analysis, running from the tip to the root, that false spar is assumed to be continuous, and that makes it in effect a clamped beam. You cannot simply leave it out of the analysis, it's there, and it adds to E*I, and it carries a small part of the lift load. I just checked the index of my 10+ books on aircraft structural analysis, and none mentions 'false spar', so that did not help me to understand or explain it better.

Step 5 assumes a main spar weak in torsion, correct? For a box spar, it would be a statically indeterminate problem. That still can be solved, but it's a a lot more work.

Rob

OK, let's remember that structurally, the outer panel can be isolated for purposes of structural analysis. Once we know the loads into the outer panel and how it is constrained you can get to your answers.

Starting with how airloads are distributed, we can work the lift, shear, bending moment, and torsional moment. The outer panel is a big beam with several important pieces: Skin, Main spar, Aux spars. At any spanwise section, you can work up the stiffnesses in shear, bending, and torsion. In sheet metal, you might recognize them as G*webi, E*Ixx & E*Iyy, and G*J. In wood and composites or with mixed metals and using plate theory, they are A66, D11, D22, and D66. If you know the configuration and loads at each spanwise cross section, you can work up the local deflections and work to the total deformations in shear, bending, and twist.

Sure, all of the wing skins and spar pieces count in doing this math. For my airplane I have run all of these numbers. In wing tip bent up bending, the main spar is 72% of my bending stiffness, the skin is 27%, and the drag spar is 1%. OK, how about bending the tips aft or forward? Main spar 4%, skin 71%, and drag spar 24%. And anti-drag is what, a quarter of lift loads? Then we have torsional stiffness, 11% main spar, 22% drag spar, and 67% wing skins.

Now let's contrast that with assumptions. Size the main spar for all bending, size the skins for torsion, and size the drag spar to react torsion and drag/anti-drag to the next structure... Hmm. Use the simple rule and the main spar gets over spec'ed, everything else is no problemo on stress. We do have to bump cap thickness and shear web until it survives, and we can seek out a min weight combo of web and caps. Look at local strains in each direction and sum them up to get deflection starting at constraints, and we see how much our wing bends and twists.

Then we can constrain our outer panel as we think the real world does and see what happens. The assumption we have mostly been working under in this thread is main spar constrained against bending and drag spar pinned to center section drag spar.

While all this fancy stuff is neat, it can let you make sure your outer wing panel stays together, let's you forecast changes to wash-out, what does it do for the drag spar discussion? Whether you do this using composite plate theory and a lot of Excel or by making up FEA models, if you constrain your wing with the main spar connections against movement in all three axes and constrain the drag spar against up-down and left-right movement, one of the things that comes out is loads in all three directions at each of those bolts. The subject of this thread...

The main spar is torsionally soft. In my bird, as cited above, the outer panel at connection to the center section has only 11% of its torsional stiffness from the main spar... The skin is 2/3 of the outer panel torsional stiffness, and the very conservative airplane design professors tell us to just assume the wing skins carry all of our torsion. We may over spec the skins this way, or just keep twisting of the main spar to small levels. Do the full up composite plate analysis and/or FEA, and get all of the loads and deflection considered. Go a little further and look at constraints again, and torque from pitching moment is tough to get into the center section unless you stick in a connection at the drag spar. Yes, you can make a big torsion box main spar for both center section and outer panels, bolt them together. Look at Long EZ and derivatives.

But when you use an aux spar or two to anchor the outer panel against torsion, it can become a straightforward exercise of calculating loads as I summarized in earlier posts. Or do the full up anaylsis that puts in all of the stiffnesses, distributes loads accordingly, and outputs loads at the constraints. Then throw a FOS of 4 on the pin, check stresses in the fasteners, bushings, webs for adequate FOS, and move on to your build...

Billski
 

Rob de Bie

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Sorry for the delayed reply - I had to find time to study and think about your extensive explanation carefully.

Again, I follow you completely. I've done most of the calculations you describe for fairly large UAV wings, with a 3000 N / 6000 lb limit load. My calculated deflections agreed well with the load tests. No strain gauges though. They had a continuous rear spars by the way.

I think you imply that the assumption of a clamped rear spar is conservative in respect to a pinned rear spar, and I think that's largely correct. But I would like to see that in my calculations.

I've been thinking more about my question, and my discomfort is mainly with not having learned how to deal with discontinities in structures. So that's what I need to search for now.

Thanks for your time and interest!

Rob
 

wsimpso1

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I think you imply that the assumption of a clamped rear spar is conservative in respect to a pinned rear spar, and I think that's largely correct.
"Clamped rear spar" - I do not know what you are talking about here. Please define that term.

As to being conservative, I have pointed out that several simplifying assumptions are conservative in that some of the stiffness in each direction is in structures other than the primary path:
  • Shear and bending from lift air loads does mostly go into the main spar, but some is carried elsewhere;
  • Pitching moments from air loads does mostly go into the skin, but some is carried elsewhere;
  • Pitching moment and moments from drag/anti-drag are mostly reacted by the drag spar, but some is reacted by the main spar.
The common assumptions result in some overbuild. As to the pinned drag spar, reacting only linear loads but no moments, instead of reacting some bending loads... if you are going to react bending at both main and drag spars, you had better design the structure to do that.

Back to the OP, with a pinned joint at the drag spar, there will be loads in all three axes at the pinned joint in the center section drag spar, and we can get pretty good estimates of what those loads are. Going inboard on the center section drag spar, the pin load will contribute shear in both axes, bending will accumulate as you go inboard. If the center section drag spar carries some wing skin and its airload, the center section will accumulate some shear, bending, and torsion that will go to the fuselage. These loads will accumulate in the center section, be distributed per their stiffnesses in each type of load, and find their way to the fuselage too, just as Timoshenko and others taught us back in Mechanics of Materials...

Now if I knew what a clamped rear spar was, we could accomplish more here.

Billski
 
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