$,$ Find the most economic column section for BE $($Note: you are asked to design only column BE$)$ in the following loading condition. The ends $"$ A $"$ of simply supported beam $AB$ and cantilever $AC$ rest on the end $"A"$ of $AD,$ which means $AD$ will have to support the load applied on it directly plus the portions of load at A due to beams $AC$ and $AB.$ Assume the loads transferred by the beams $AC$ and $AB$ are vertical.