Wing spar stress calculations 2

Karl,

Calculating the stresses in a wing spar is pretty straightforward once you have the loads, but there is no such thing as a single spreadsheet that does that sort of thing.

The more difficult task here is to figure out what kinds of loads you have. Airloads, inertia loads, fuel loads, etc. are pretty much impossible to reverse-engineer just from drawings.

Once you have your loads, you're basically just analyzing a beam, albeit a fairly complex one. Spar caps and webs need to be analyzed, as well as the attachments between them. Cutouts cannot be neglected.

Many aircraft wing spars are intermediate diagonal tension beams, so a full analysis (per NACA TN 2661 or similar) needs to be performed.

Upper cap stability (column, lateral-torsional, etc.) must be verified.

A good aircraft stress analysis textbook (Bruhn's "Analysis and Design of Flight Vehicle Structures" or Niu's "Airframe Stress Analysis and Sizing" ISBN 962-7128-08-2 or similar) can help show you what your certification authorities are looking for.

Good luck.
SuperStress

"a plans design that has already been flying for some time"

Just in case the wing isn't made of metal, there are references on wooden spar design that are also very valuable. Probably ANC-18 would be best - if you need a copy I can help you get one (it's pretty hard to find).


Steven Fahey, CET

Surely if the design has been flying for some time the check stress must have been done already?

Thanks everybody for your help.

Not every country requires the calculations for a homebuilt aircraft. I.E. proof that a design has been flying for many years in another country without mishap is enough evidence for some authorities.
The design in question is flying in France and the USA. The designers say they have never done the calculations relying purely upon prior knowledge and therefore cannot help.
The UK authorities accept that the aircraft has been flying for some time but insist I produce stress calculations for the spars and spar fittings.
I guess I was kind of hoping that there would be a spreadsheet that required wing loading, speeds, weights, max "G" ETC to produce a figure on spar strength required.

Once again, thanks everyone for the help and advice.

karl.

If the designers haven't done any stress calculations, it probably means that they weren't capable of doing the calculations in the first place. I'd wonder what else wasn't analysed (i.e engine mounts,tailplane, ailerons, hinges etc)

DC

karlbamforth,

What kind of wing beam do you have?
You could have a single closed wing box with front and rear spars.
You could also have a wing box made up by most (or part) of the wing with several webs forming a multiple closed cells beam.
In the case you have distinct spars, these could be made up of upper & lower flanges and webs (and vertical struts for stabilizing diagonal tension due to shear buckling), but you could also have a truss-structure instead of webs.
All these different possibilities require their specific approach. It is not so difficult, but you have to deal with several things like for example compression buckling of the flanges, combined compression & bending & shear buckling of the webs and all that goes with it like diagonal tension loads in the flanges and the struts, inter rivet buckling (if you have rivet connections of course) , also maybe you have to check fatigue loads etc... I don’t want to discourage you, as a matter of fact I would be happy to help you, but I have too much other stuff to do and this website is not meant for finding people but to share knowledge. I think it would be worthwhile to find a friend structural engineer and show him your problem.

You also need to define some load cases to load your wing beam with. I think you can get inspiration in subchapter C of the airworthiness regulations on what limit load cases you might consider. Once you have defined your most critical load cases, you should know per case what the translation and rotation accelerations are and the airspeeds. From these you determine the air loads and the inertial loads on your wings. If your wing is slender enough I would determine the inertial loads along the wing sections cg-line and the air loads along the wing section aerodynamic center (quarter chord) line.

A simple example.

A. Air Loads:
For the air loads, the lift forces will be most important.
To know this lift force you can proceed in several ways. For example if you know only the vertical aircraft acceleration and vertical gravitational acceleration component you can estimate the Lift force as follows.
To stay in a simple situation, for example for a vertical up gust case or a pull-up maneuver with wings level and fuselage horizontal,

the Lift on the wings = (Aircraft Mass)*(Aircraft vertical acceleration + g ).
By the way g is the gravitational acceleration (9,81 m/s2).
Now this lift is produced by the wing and has to be distributed according to a realistic wing lift distribution.

Lift = CL 0.5 rho V2 S,

Rho = air density (1,225 kg/m3 at sea level for standard atmosphere)
S = wing projected area (m2)
V is air speed (m/s)
and CL = integrated lift coefficient cl along the wingspan:

CL = 2* Integral from 0 to half span (cl c dy) / S

S = wing projected area, y = span coordinate, c is local wing section chord, cl is local wing section lift coefficient, dy is wing span increment.

The shape of cl distribution is determined by your wing plan form = wing taper, wing twist and wing sweep. You can either look it up in a book like ‘Theory of wing sections’ By IRA H. ABBOOTT & E. VON DOENHOFF or calculate it with a panel program or just use common sense and take a approximate approach. For example suppose you have an elliptical lift distribution, then cl = cl is constant. In that case CL = cl.

So cl = cl = Lift / (0.5 rho V2 S),

thus the local lift load increment at span position y is dl = cl * c * dy * 0.5 rho V2

Besides the Lift distribution, you also have to find the Torque distribution on the wing, this is simply cm = cmac at the wing section aerodynamic center (quarter chord) line .

thus the local torque load increment at span position y is dm = cmac * c*c * dy * 0.5 rho V2

Concluding you have dl forces upwards and dm pitch down moments acting on the wing at span wise positions y and at the quarter chord line section locations.


B. Inertial load:

In this simple situation of just a vertical acceleration, your distributed inertial loads along the wing span y are simply

(Section mass per span length at position y)*(Aircraft vertical acceleration + g )*dy.

This inertial load increment (inertail relief) is pointing downwards and acts at the mass cg’s of your wing section at wing span position y.

If you want to be conservative and your wing does not contain any important masses, you can neglect this force. That is to say, if you can prove that your wing is strong enough when taking just the air loads without inertial relief, then the authorities will be even happier!

Good Luck,

OneMoreChance

PS soon I may also need help in the future in a question

Thanks for that OneMoreChance, that was just the kind of information I was looking for.
A friend has loaned me his books on the subject so I am doing a bit of self study and any calculations I make will be checked by the certifying authorities.

Karl

Hi Karl,

Do you mind me asking which plane you are building?

Jan
RV6

Hi Jan,

I havn't started the build yet. I wanted to make sure everything was OK first. If you are still interested the aircraft is called the Ibis and can be seen at the link below.

Karl,
I do design clearance checks, certification work and stress analysis on a lot of PFA aircraft. I advise you that a perfect stress analysis of the spar is useless if the bending moment and shear forces loads you are using are wrong. This is especially so of a canard arrangement with the swept wing. Good luck with getting the IBIS thru Francis!!!

Ref also JW

Karlbamforth,

Don’t loose courage.
You will never have a perfect loads (lift and torque) distribution over your wing and canard, that is true, but you can take a conservative approach. The wing sweep will increase the cl distribution towards the tips and lower it towards the middle, same thing for wing taper, while the wing twist (decreasing angle of attack towards tips) will lower cl towards the tips and increase it towards the middle. (A book like IRA H. ABBOOTT & E. VON DOENHOFF I mentioned before may help). Besides that, the deformation of the wing itself under this loads distribution will influence your loads distribution.
So, get a sensible idea of how these influences are and make a distribution shape that gives you a conservative bending moment (highest root moment).
Then you do also have some induced influences of wing lift distribution on canard lift distribution and otherwise, but I would not consider them.
What is also important besides the shape of the loads distributions on canard and wing is the positions of the aerodynamic center of the wing, the aerodynamic center of the canard and the position of the aircraft CG. Because this will (because of force and moment equilibrium about CG) determine the distribution of total lift on wing and on canard.

When using common sense and some conservatism I think you can achieve a lot with the authorities.

OneMoreChance

loads are going to be one headache, but i think strength is going to be another.

an approach for loads is to be conservative as a previous poster mentioned. if you include a specific fudge factor in your calculations you can quickly revise them if you've been too conservative, and you can quickly show the authorities how conservative you are. i think you may need a book on stability and control (etkin) or a general design book (torenbeek, raymer) to appreciate the overal loads on the wing and the canard. tehn you have to understand the details of the wing cross-section (the local airload distribution). once you've done this you can quickly calculate the wing bending moments ... it looks like a simple lay-out (no large masses stuck to the wing).

but then, how strong is the wood being used to build the structure ? maybe if you've got some off-cuts you could do some structural tests. how strong is the manufacturing method ? particularly the glueing of the gussets, etc ?

I'd also suggest you take a look at "Aircraft Loading and Structural Layout" by Denis Howe. It's quite a detailed book on basic prelimirary sizing and aircraft loading. It's got details of the analysis performed for the Cranfield A1.

This is going to be a hell of a lot of work in any case! But good luck!

Cheers,
SkyD

Thanks to everybody for all your help.

After a little research I have managed to contact 3 other potential IBIS builders in the UK and we have decided to have the calculations done proffesionally and share the costs. This would seem the most efficient way of getting the calculations done and with 3 others a little more reasonable on cost.

Once more, thanks to everybody for your input.

Karl