How to calculate wing deflection? 5

[oriolbetriu]

Hi!

Albeit I studied aero engineering, I never finished my studies. I have been lately reading Timoshenko, to learn some beam theory basics. I can calculate deflection for a single beam, but I do not know how to calculate deflection for the whole wing? In fact, I can not even tell how to calculate deflection for the two spars, at once?

I am guessing that, I can calculate deflection of each spar independently, and then make both have the same deflection, to avoid internal stresses inside the wing structure. Another option would be, to calculate Moments around both spars, and thus obtain a single Moment equation for both spars, that can be integrated to obtain deflection. This can be achieved, since both spars have the same Young Modulus.

This all makes me wonder about, how to calculate deflection of a cantilever composite spar? That is, what happens if the materials that make up the wing section, have different E and G values? Like a full wing section, D-tube plus spars plus shear webs etc.

Any comments will be greatly appreciated!

Oriol

 

[rb1957]

I've analyze similar. You design the ribs to be stiff enough that the front spar and the rear spar work together (rather than independently) ... bend the same. You design the ribs so they distribute load from teh centroid of the section to the two spars. You also need to include the Cm load, which will load the spars differentially, yes?

Deflection of anything other than a constant chord, constant I wing is a PITA. I (as in M(x)/EI) is no longer a constant (in a tapered wing) but a function in x (like the moment), so you're integrating M(x)/EI(x). But why calc deflections ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Hi rb1957!

The current example is intended to cover a full analysis, but a very simplified one; the model can be improved by changing every parameter with later iterations/additioms. Regarding moments/Cm, I did something a bit against the rules. Instead of working with Cm, I have followed Frati's example. I have placed the center of pressure at 1/3C for CL max, and at 1/2C for CL cruise, I have not yet considered this last case, because I was wondering about deflection etc. Later models can incorporate CM, the thing is that right now, I am not too worried about aerodynamics, I am focused on the structure part; to obtain a realistic value for the empty weight of the wings.


Yes, working with a non constant section involves more effort, both for analysis and construction, but can result in a weight reduction that can justify the trouble!


Frati in his design book The Glider, considers a constant section spar, and does not calculate wing deflection, only Torsional strength [Tau = M/(2*t*a)], and Torsional stiffness [Phi = T*L/(G*J)].

In order to use some basic guidelines for calculating loads etc, I have looked at the regs 14 CFR Part 25, section 25.305;

"The structure must be able to support limit loads without detrimental permanent deformation. At any load
up to limit loads, the deformation may not interfere with safe operation."

"(1) The effects of deformation are not significant;
(2) The deformations involved are fully accounted for in the analysis; or
(3) The methods and assumptions used are sufficient to cover the effects of these deformations."

The regulations does not specify how much deflection is considered to be not significant, but it implies that deflections have to be accounted for, or at least the structure has to be oversized to neglect deflection, like Frati's example, in were the author uses worst than actual load conditions, to have sufficient margin.


In any case, do you omit calculating deflection for a taper ratio wing? Or is it possible to analize the wing in segments, like I suggested in my previous post; by considering the average section between two stations, and calculating deflection for that section, and then adding the resulting deflection of all the small sections to obtain total deflection?

Thanks for your help!!!

Oriol

 

[rb1957]

Following Frati's example is not "going against the rules" ... it is following some other "expert" opinion/guidance. Applicability of such opinion/guidance is a whole different story !

Please don't look at 25.305 (or any other Part 25) for your work, you'll massively over do it. A good source would be a historical version (not the current one) of Part 23. That includes guidance on how to calculate loads. Also the ACs. That and some local home builder.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.