Maximum bending moment in simply supported beam under equally spaced in the middle uniform load.
Bending moment
$$ M_{B_{d_{max}}} = {\left({ {W_d \over 4} }\right) \cdot \left({ 2 \cdot a + b - {b \over 2} }\right)} $$
Calculate minimum diameter of shaft subject to bending by distributed load using AS1403 formula 1 (no tension & no torsion).
This is based on AS 1403, Table 2, Formula 1 for manually or power applied condition.
Original formula has been shortened due to Pq = 0 and Tq = 0.
Minimum shaft diameter
$$ D_{shaft_{min_d}} = {\left({ {F_S \over F_Y} \cdot M_{B_{d_{max}}} \cdot 10 ^ 4 }\right) ^ \left({ {1 \over 3} }\right)} $$