Choice of support points Airy points
a uniform beam deflects based on supported. (vertical sag exaggerated.)
a kinematic support one-dimensional beam requires 2 support points. 3 or more support points not share load evenly (unless hinged in non-rigid whiffle tree or similar). position of points can chosen minimize various forms of gravity deflection.
a beam supported @ ends sag in middle, resulting in ends moving closer , tilting upward. beam supported in middle sag @ ends, making similar shape upside down.
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