you forgot the extreme fiber distance (c) from the moment axis:Sorry, but a 10% reduction in thckness of a rectangular part in bending results in a 27% reduction in stiffness or force to yield, not a 35% reduction. THIRD power.
Stress = Mc/I
I = bh^3/12, b = base width, h equals height and strong axis dimension
c = h/2
substitute and solve:
sigma = M *(h/2) / (bh^3/12) = M*12/(2*b*h^2) = 6M/bh^2
Bending stress (sigma) is proportional to the square of height for a rectangular section in bending.