How do you calculate reactions for a simply supported beam with a concentrated load?

For a simply supported beam with span L and concentrated load P at distance 'a' from left support: Taking moments about right support gives left reaction Ra = P(L-a)/L. Taking moments about left support gives right reaction Rb = Pa/L. Verify by checking that Ra + Rb = P. When load is at midspan (a = L/2), both reactions equal P/2. This approach uses equilibrium equations (sum of moments and forces equal zero).