$14-8.$ An old$-$time stone quarry often used horses and a derrick system, as shown below, to lift stones onto wagons. Suppose the stone weighs $14\mathrm{.}7kN$ and is being lifted slowly by the horse. There are pulleys with two wheels at joints $E$ and $B.$ Member $AE$ is a cylindrical post made of Red Oak and having a diameter of $15\mathrm{.}0cm.$ Member $GE$ is a rope under tension. Determine the design factor for this situation regarding the propensity of post $AE$ to buckle.