Elliptical Distributed Force Brain Waves
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- Опубликовано: 6 окт 2024
- Here's a short example showing how to use integrals to find moment on a cantilever beam with a distributed load. I used an elliptical load distribution, but the method will work with any continuous load distribution.
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Lift/Shear is 157.08, if moment is 66-2/3rds.
Else moment is 33.333 if semi-span lift is 78.54.
4/3rds divided by Pi = 0.42441318. The span-wise location of the elliptical lift centroid, as measured from the fuselage side.
1/2 total aircraft lift multiplied by [(4/3)/Pi] is moment for a spemi-span of unity.
Multiply by semi-span length outboard the fuselage for bending-moment.
And multiply again by spar height...And again by ratio of distance of the area centroid of the spar caps from the outer most fiber of the top spar cap surface.
Then divide by maximum allowable material compressive (yield) stress.
Again multiplied by load-factor...
This is minimum Ix for a spar at this span-wise station. Not accounting for additional spar(s) wing skin, or stiffeners contribution to bending resistance. Or accounting for moment reliving affect of wing weight and weight of fuel or landing gear located outboard of the 4/3rd over Pi span-wise station.
Also doesn't account for mass position forward of the aerodynamic center, moment coefficient of wing at Vd, tail down-load, etc...
integral of f(t) from 0 to x is a constant, i.e. there is only 1 answer... I'm assuming x is a constant because because "t" would be your variable in this example.
integral of f(t) from 0 to t depends on the value of t... there can be an infinite number of answers.
excuse me, I don't understand how did you get the answer with respect to the moment? 66.67? because mi answer is 157.34N.m
I found: 157.079633
I mean what's the difference between integral of f(t) from o to x and integral of f(t) from 0 to t in the long run?
He really dropped the C-bomb on us 😭💔
Because the answer is then variable.
Why do mathematicians get so testy when you have the function's variable in the integral limits?