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

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 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 superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and 33° banking. Given this information, the coefficient of side friction required in order to allow a vehicle to travel at 320 km/h along the curve is