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

A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ respectively. The limiting values of $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ are :

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