- #1
Mike J
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Homework Statement
Refer to image attached.
Lets say I have a deformable solid that is being accelerated by a force that is equally distributed along the back face of the Main Body that is drawn in the picture. Attached to this Main Body is a Wing. At high accelerations, there will be inertial stresses that reach a maximum at the base of the wing where it is attached to the Main Body. How can I calculate those stresses? I need to find these stresses so that I can determine how large d has to be in order to prevent material failure. I am kind of lost at where to start.
Homework Equations
The Attempt at a Solution
My attempt:
I tried making a cut at the base of the wing (viewed from bottom of the picture shown above)
From here I can take sum of the moments to find the bending stress caused by the moment, M.
The equation I get is:
-M = mwingaw/2.
Then I plug into bending stress formula for cantilever beam and compare to the yield stress:
|σmax|=|M|d / (2I) ≤ σyield
where I = 1/12 L d3
If I solve the equations above for d so that σ does not exceed my yield stress, I end up getting unrealistically small values for d. I don't think my approach is correct because I believe it assumes rigid body acceleration when this is not the case. Maybe there's a continuum mechanics approach that involves solving a differential equation to take into account these inertial stresses of a non-rigid accelerating body.
Any help would be appreciated!