A simply supported beam $$AB$$ of span, $$L = 24$$ $$m$$ is subjected to two wheel loads acting at a distance, $$d = 5$$ $$m$$ apart as shown in the figure below. Each wheel transmits a load, $$P = 3$$ $$kN$$ and may occupy any position along the beam. If the beam is an $$I$$-section having section modulus, $$S = 16.2\,c{m^3},$$ the maximum bending stress (in $$GPa$$) due to the wheel loads is __________________

Beam $$PQRS$$ has internal hinges in span $$PQ$$ and $$RS$$ as shown. The beam may be subjected to a moving distributed vertical load of maximum intensity $$4$$ $$kN/m$$ of any length anywhere on the beam. The maximum absolute value of the shear force (in $$kN$$) that can occur due to this loading just to the right of support $$Q$$ shall be:

The span$$(s)$$ to be loaded uniformly for maximum positive (upward) reaction at support $$P,$$ as shown in the figure below, is $$(are)$$

The influence line diagram $$(ILD)$$ shown is for the member