- Oct 18, 2003
- Saline Michigan
Using the simple approach of dividing moment by spar dept only is approximate at best, and should probably be left behind once you get past initial sizing. Issues with this: Asymmetric caps move the neutral axis of the spar section, changing y's to extreme fibers for stress calcs; Ignores effect of the web and of the wing skins.Some quick back of the envelope calcs for the KR2.
Wing loading: 14 lbs/ft^2
Wing span: 24 feet
wing area: 93 ft^2
Make the gross assumption that the wing is a rectangle. Ignore that the wing starts outside the cabin. Chord = 93 ft^2/ 24 feet = 3.875 feet
Spar load per foot = 3.875 x 14 = 54.25 lbs/ft
Moment at center fo spar = 1/2 12^2 x 54.25 = 3906 foot pounds = 48,872 in lbs.
Spar height at center = 7 inches
Cap forces = 6,981 pounds, roughly
Each main spar cap has 6 rods in it. The Secondary spar caps (front and back) have 10 rods in the top and 7 rods in the bottom. So the top has 16 rods in total and the bottom has 13 rods. The force in each top rod is 6981 pounds/16 = 436 pounds. The force in each top rod is 6981/13 = 537 pounds.
All loads at max weight, 1g, no safety factor.
The rods are 0.070 x .437 Graphite, solid rectangle. Area = 0.0306 in^2.
The static 1g stress in the top rods is 436 pounds / 0.0306 in^2 = 14,250 PSI.
The static 1g stress in the bottom rods is 537 pounds / 0.0306 in^2 = 17,500 PSI
Does this look correct ?
A more accurate look is to compute neutral axis position, then y's (distance to extreme fibers from neutral axis and I for the caps, then stress is My/I. This still skips contribution of the web and the skin, but is closer;
A more accurate look is obtained by computing EA and raw y's for the caps, the webs, and all of the wraps taken around the spar putting it together, compute the neutral axis position and corrected y's, compute the EI's for the set of lamina, sum them up, then divide by E for the cap material to get a better I, then compute My/I for extreme fibers in both caps;
Then the best is to do the full up composite mechanics run.
Now let's check your numbers to see if the spar mentioned looks OK.
First we recognize that the bending moment is overstated. For elliptical lift distribution, centroid of lift is around 42% of semi-span, not 50%.
Next, I do not know if the spar height of 7" is extreme fiber to extreme fiber or from center of cap to center of cap. It matters. Bending resistance is from neutral axis to centroid of the cap, stress is neutral axis to extreme fibers in both directions.
Minimum FOS for composites is 2.0. For the KR2, I suspect that its design n1 is 4 g because that is pretty common. Many later composite airplanes use 5 or 6 g because some folks just can not resist rolling or looping the things. So, at minimum, multiply your stresses by 8 or 10 or 12. You get to pick. Using 12 gives stress in the tensile side of 210,000 psi. I suspect that with corrected numbers, you will have higher stresses in both caps. Get out the mechanics of materials text, go through the beam chapters and the section on composite beams (talking steel reinforced concrete).
As to shear web stress, on flanged beams and hollow rectangular beams, the shear stress is mostly carried on the free web, that is the part not supported by the flanges. Shear stress is slightly higher at the neutral axis than by the flanges, but it is slightly conservative to assume constant in the free section of the web and also slightly conservative to assume only the free portion of the web carries all of the shear. So tau = V/A where V is shear load, A is area of the free portion of the glass/resin part of the web. In metal, shear yield is 0.577 times tensile yield. In composites we do not have such stuff so well nailed down.
Then to finish the whole thing, the webs at the flanges are distorting with the caps, so they have not only shear stress close to that calculated in the para above, they have some tension or compression. So we end up beefing the caps and web. Full up analysis, automated by putting it into Excel makes all of this fairly easy, but you have to get through all of the undergraduate stuff mentioned above plus matrix algebra and plate theory, then the equivalent of a gradate course in composites materials mechanics to do the full up analysis. UGH! Composites are sort of like getting old, it is not for sissies!