forgot... The parabola comes from the thickness squared dependence of the bending moment of a cantilever as the distance from the support increases. The beam will remain flat if the thickness decreases parabolically as the distance from the support increases.
I’m still having trouble with this.
A member in tension tends to elongate. Easy to see in the bottom chord of a flat truss. The bottom chord elongates as the truss deflects.
I don’t see how an arched bottom chord can be in tension. If it elongates, the truss sags UPWARD.
I’m not arguing with you, I’m trying to clarify, because if this is true, it is decidely counter-intuitive.