A steel strip of length, $$L = 200$$ $$mm$$ is fixed at end $$A$$ and rests at $$B$$ on a vertical spring of stiffness, $$k = 2$$ $$N/mm.$$ The steel strip is $$5$$ $$mm$$ wide and $$10$$ $$mm$$ thick. $$A$$ vertical load, $$P = 50$$ $$N$$ is applied at $$B,$$ as shown in the figure. Considering $$E = 200$$ $$GPa,$$ the force (in $$N$$) developed in the spring is _______________

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 __________________

A horizontal beam $$ABC$$ is loaded as shown in the figure below. The distance of the point of contraflexure from end $$A$$ (in $$m$$) is

A fixed end beam is subjected to a load, W at $$1/3rd$$ span from the left support as shown in the figure. The collapse load of the beam is