A beams $$PQRS$$ is $$18$$ $$m$$ long and is simply supported at points $$Q$$ and $$R$$ $$10$$ $$m$$ apart. overhangs $$PQ$$ and $$RS$$ are $$3$$ $$m$$ and $$5$$ $$m$$ respectively. A train of two point loads of $$150$$ $$kN$$ and $$100$$ $$kN$$, $$5$$ $$m$$ apart, crosses this beam from left to right with $$100$$ $$kN$$ load leading.

During the passage of the loads, the maximum and the minimum reactions at supports $$'R'$$ in $$kN,$$ are respectively

Muller Breslau Principle in structural analysis is used for