Hi, all. I've been trying to work out the bending stresses caused by a BSLD, and I think I've got it but would like confirmation from someone with more experience.
So the lift distribution (right wing shown only, 1/2 span is pi/2) is sin^3, like this:
Then the bending moment each point in the span exerts on the root is the lift at that point times its distance from the root, x*sin^3:
Then the bending stress at any point in the span is the integral of the purple function, from that point to the wingtip, which is the antiderivative of x*sin^3 evaluated at x minus the antiderivative evaluated at the wingtip, which is a constant and can be disregarded by translating the graph. The bending stress is then this:
This looks visually correct to me, but if someone who has done this or something similar before could check if I'm going about it the right way it would be greatly appreciated.
I'm most worried about the logical step I took in saying that the graph of the moment exerted on the root can be applied to every point on the span, but the bending stress graph looks correct. (not exactly a rigorous proof, I know)
I know that I will need to subtract the downward bending moment caused by the weight of the structure to get an accurate answer, that comes next.
So the lift distribution (right wing shown only, 1/2 span is pi/2) is sin^3, like this:
Then the bending moment each point in the span exerts on the root is the lift at that point times its distance from the root, x*sin^3:
Then the bending stress at any point in the span is the integral of the purple function, from that point to the wingtip, which is the antiderivative of x*sin^3 evaluated at x minus the antiderivative evaluated at the wingtip, which is a constant and can be disregarded by translating the graph. The bending stress is then this:
This looks visually correct to me, but if someone who has done this or something similar before could check if I'm going about it the right way it would be greatly appreciated.
I'm most worried about the logical step I took in saying that the graph of the moment exerted on the root can be applied to every point on the span, but the bending stress graph looks correct. (not exactly a rigorous proof, I know)
I know that I will need to subtract the downward bending moment caused by the weight of the structure to get an accurate answer, that comes next.
