Let the strength of a beam be proportional to the cross sectional area. What is the shape of a horizontal beam anchored at one point, of constant density, which at every point is just thick enough to support the mass of rest of the beam?
A beam supported at both endpoints I think has the boring decomposition of two beams supported at each endpoint, and the thickness vanishes to zero at the center. What happens for a circular plate supported at its edge (the thickness again is zero at the center)? Or non-circular plate?
Or simpler, a beam in two dimensions, with strength proportional to width.
No comments :
Post a Comment